Computational Methods and Experiments in
Materials Characterisation III
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THIRD INTERNATIONAL CONFERENCE ON COMPUTATIONAL METHODS AND EXPERIMENTS IN MATERIALS CHARACTERISATION MATERIALS CHARACTERISATION 2007 CONFERENCE CHAIRMEN A.A. Mammoli University of New Mexico, USA C.A. Brebbia Wessex Institute of Technology, UK
INTERNATIONAL SCIENTIFIC ADVISORY COMMITTEE A. Benavent-Climent D. Bernard S. Bordere M. Bush
S. Hernandez J. W. Leggoe P. Prochazka P. Viot
Organised by Wessex Institute of Technology, UK and University of New Mexico, USA
Sponsored by WIT Transactions on Engineering Sciences
WIT Transactions on Engineering Sciences Transactions Editor Carlos Brebbia Wessex Institute of Technology Ashurst Lodge, Ashurst Southampton SO40 7AA, UK Email:
[email protected]
Editorial Board B. Abersek University of Maribor Slovenia K S Al Jabri Sultan Qaboos University Oman J A C Ambrosio IDMEC Portugal H Azegami Toyohashi University of Technology Japan G Belingardi Politecnico di Torino Italy S K Bhattacharyya Indian Institute of Technology India A R Bretones University of Granada Spain J Byrne University of Portsmouth UK D J Cartwright Bucknell University USA A Chakrabarti Indian Institute of Science India J J Connor Massachusetts Institute of Technology USA L Debnath University of Texas-Pan American USA S del Giudice University of Udine Italy
B Alzahabi Kettering University USA A G Atkins University of Reading UK A F M Azevedo University of Porto Portugal R Belmans Katholieke Universiteit Leuven Belgium E Blums Latvian Academy of Sciences Latvia F-G Buchholz Universitat Gesanthochschule Paderborn Germany W Cantwell Liverpool University UK S K Chakrabarti Offshore Structure Analysis USA H Choi Kangnung National University Korea L De Biase University of Milan Italy R de Borst Delft University of Technology Netherlands G De Mey Ghent State University Belgium M Domaszewski Universite de Technologie de Belfort-Montbeliard France
I Doltsinis University of Stuttgart Germany J Dominguez University of Seville Spain J P du Plessis University of Stellenbosch South Africa M E M El-Sayed Kettering University USA M Faghri University of Rhode Island USA C J Gantes National Technical University of Athens Greece R Gomez Martin University of Granada Spain R H J Grimshaw Loughborough University UK R Grundmann Technische Universitat Dresden Germany J M Hale University of Newcastle UK L Haydock Newage International Limited UK C Herman John Hopkins University USA M Y Hussaini Florida State University USA D B Ingham The University of Leeds UK Y Jaluria Rutgers University USA D R H Jones University of Cambridge UK S Kim University of Wisconsin-Madison USA A S Kobayashi University of Washington USA S Kotake University of Tokyo Japan
W Dover University College London UK K M Elawadly Alexandria University Egypt F Erdogan Lehigh University USA H J S Fernando Arizona State University USA E E Gdoutos Democritus University of Thrace Greece D Goulias University of Maryland USA D Gross Technische Hochschule Darmstadt Germany R C Gupta National University of Singapore, Singapore K Hameyer Katholieke Universiteit Leuven Belgium P J Heggs UMIST UK D A Hills University of Oxford UK T H Hyde University of Nottingham UK N Ishikawa National Defence Academy Japan N Jones The University of Liverpool UK T Katayama Doshisha University Japan E Kita Nagoya University Japan A Konrad University of Toronto Canada T Krauthammer Penn State University USA F Lattarulo Politecnico di Bari Italy
Y-W Mai M Langseth University of Sydney Norwegian University of Science and Technology Australia Norway B N Mandal S Lomov Indian Statistical Institute Katholieke Universiteit Leuven India Belgium T Matsui G Manara Nagoya University University of Pisa Japan Italy R A W Mines H A Mang The University of Liverpool Technische Universitat Wien UK Austria T Miyoshi A C Mendes Kobe University Univ. de Beira Interior Japan Portugal T B Moodie A Miyamoto University of Alberta Yamaguchi University Canada Japan D Necsulescu G Molinari University of Ottawa University of Genoa Canada Italy H Nisitani D B Murray Kyushu Sangyo University Trinity College Dublin Japan Ireland P O’Donoghue S-I Nishida University College Dublin Saga University Ireland Japan K Onishi B Notaros Ibaraki University University of Massachusetts Japan USA E Outa M Ohkusu Waseda University Kyushu University Japan Japan W Perrie P H Oosthuizen Bedford Institute of Oceanography Queens University Canada Canada D Poljak G Pelosi University of Split University of Florence Croatia Italy H Power H Pina University of Nottingham Instituto Superior Tecnico UK Portugal I S Putra L P Pook Institute of Technology Bandung University College London UK Indonesia D Prandle M Rahman Proudman Oceanographic Laboratory Dalhousie University UK Canada F Rachidi T Rang EMC Group Tallinn Technical University Switzerland Estonia K R Rajagopal B Ribas Texas A & M University Spanish National Centre for Environmental Health USA Spain D N Riahi W Roetzel University of Illinios-Urbana Universitaet der Bundeswehr Hamburg USA Germany
K Richter Graz University of Technology Austria V Roje University of Split Croatia H Ryssel Fraunhofer Institut Integrierte Schaltungen Germany A Savini Universita de Pavia Italy B Scholtes Universitaet of Kassel Germany G C Sih Lehigh University USA P Skerget University of Maribor Slovenia A C M Sousa University of New Brunswick Canada C-L Tan Carleton University Canada A Terranova Politecnico di Milano Italy S Tkachenko Otto-von-Guericke-University Germany E Van den Bulck Katholieke Universiteit Leuven Belgium R Verhoeven Ghent University Belgium B Weiss University of Vienna Austria T X Yu Hong Kong University of Science & Technology Hong Kong M Zamir The University of Western Ontario Canada
S Russenchuck Magnet Group Switzerland B Sarler Nova Gorica Polytechnic Slovenia R Schmidt RWTH Aachen Germany A P S Selvadurai McGill University Canada L C Simoes University of Coimbra Portugal J Sladek Slovak Academy of Sciences Slovakia D B Spalding CHAM UK G E Swaters University of Alberta Canada J Szmyd University of Mining and Metallurgy Poland S Tanimura Aichi University of Technology Japan A G Tijhuis Technische Universiteit Eindhoven Netherlands I Tsukrov University of New Hampshire USA P Vas University of Aberdeen UK S Walker Imperial College UK S Yanniotis Agricultural University of Athens Greece K Zakrzewski Politechnika Lodzka Poland
Computational Methods and Experiments in
Materials Characterisation III Editors A.A. Mammoli University of New Mexico, USA C.A. Brebbia Wessex Institute of Technology, UK
Editors: A.A. Mammoli University of New Mexico, USA C.A. Brebbia Wessex Institute of Technology, UK Published by WIT Press Ashurst Lodge, Ashurst, Southampton, SO40 7AA, UK Tel: 44 (0) 238 029 3223; Fax: 44 (0) 238 029 2853 E-Mail:
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[email protected] http://www.witpress.com British Library Cataloguing-in-Publication Data A Catalogue record for this book is available from the British Library
ISBN: 978-1-84564-080-4 ISSN: 1746-4471 (print) ISSN: 1743-3533 (on-line) The texts of the papers in this volume were set individually by the authors or under their supervision. Only minor corrections to the text may have been carried out by the publisher. No responsibility is assumed by the Publisher, the Editors and Authors for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. © WIT Press 2007 Printed in Great Britain by Athenaeum Press Ltd. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the Publisher.
Preface
In an age of dwindling resources, knowledge of the behavior of materials takes on an even more important role than was traditionally the case. Not only must a material perform its basic function, but it must do so while satisfying constraints given by ecology, economy, safety and durability. Alongside the science of traditional materials, new areas are emerging. At the very small scale, materials are being engineered down to their very microstructure, sometimes even their molecular structure. These microengineered materials promise exceptional performance, however it becomes increasingly difficult to characterize their structure and behavior with traditional methods. In many cases, characterization occurs by indirect means, requiring a computer model to interpret the measurement data to finally recover the material properties sought, for example in the case of nanoindentation of heterogeneous materials. In some cases, it is even difficult to define a property, or at what scale it applies. The second recent trend in materials science is the re-emergence of traditional and natural materials, sometimes in combination with more ‘conventional’ ones, as in the case of natural fibre reinforced composites. These pose particular challenges, as their microstructure and properties can be even more complex than in synthetic materials. The characterization of materials is an extremely broad topic, which could mean different things to different people. We have, nevertheless, endeavoured to structure the book in a logical manner. It comprises three broad areas: papers focusing on the materials and their microstructures, papers focusing on experimental characterization techniques, and papers focusing on computational methods. As in the previous two conferences, we are confident that cross-pollination of ideas and methodologies will occur, leading to new collaboration and new research paths. As always, the editors wish to thank the authors for contributing their work, and the scientific advisory committee in particular, for their help with obtaining and selecting many quality articles. The Editors Bologna, Italy 2007
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Contents Section 1: Microstructures – novel composite materials Study on static and creep properties of CFRP using rubber modified matrix K. Takemura & Y. Yasuda.....................................................................................3 Determination of the fatigue behavior of coatings by means of an improved impact testing evaluation procedure C. David, K. G. Anthymidis, P. Agrianidis & D. N. Tsipas ................................13 Effect of fly ash reinforcement on the corrosion behaviour of cast Al-Mg alloy A535 in 3.5wt% NaCl solution E. R. Obi, I. N. A. Oguocha & R. W. Evitts.........................................................21 Testing of palm fibre as reinforcement material in polyester composites V. V. S. Prasad, D. N. Rao, K. N. S. Suman & N. R. M. R. Bhargava ................31 Section 2: Microstructures – ceramics and advanced materials Experimental study on fracture behaviour of polycrystalline ceramics under shock loading J. T. Zhou & G. W. Yao .......................................................................................43 Blocking and self-locking of superdislocations in intermetallics B. A. Greenberg & M. A. Ivanov.........................................................................51 The properties and performance of polymer fibre reinforced bituminous mixtures I. Kamaruddin & M. Napiah ...............................................................................61 Hardness determination of EBiD-layers containing tungsten and cobalt T. Wich, T. Luttermann & I. Mircea ...................................................................73
Section 3: Microstructures – alloys Thermodynamic modelling of a 6w/o Al P/M processed Ni base superalloy D. A. Akinlade, W. F. Caley, N. L. Richards & M. C. Chaturvedi......................85 An investigation into martensitic transformation in hot stamping process M. Naderi & W. Bleck .........................................................................................95 Quantitative assessment of strain and heat treatment on twin formation in commercially pure nickel Q. Li, J. R. Cahoon & N. L. Richards ...............................................................105 Three-dimensional crystallographic characterization and mechanical modeling of a commercial stainless steel A. C. Lewis, D. J. Rowenhorst, G. Spanos & A. B. Geltmacher .......................115 Section 4: Microstructures – cements and cement based materials Reactive powder concrete: material for the 21st century D. Mestrovic, D. Cizmar & V. Stanilovic..........................................................127 Impedance spectroscopy as a tool to study modifications in the microstructure of concrete in ionic migration experiments G. de Vera, M. A. Climent & I. Sánchez ...........................................................135 Section 5: Experimental methods – imaging and analysis Laser speckle measurements and numerical simulations of the deformation of masonry loaded in compression A. T. Vermeltfoort..............................................................................................147 Quantitative analysis of polyurethane nanocomposites with boehmite structures modified using lactic acid J. Ryszkowska....................................................................................................159 The spatial controlling of Lamb waves excited by a point source on the cylindrical wall V. Sukackas .......................................................................................................169 3D strain mapping inside materials by microstructural tracking in tomographic volumes H. Toda, M. Kobayashi, K. Uesugi, D. S. Wilkinson & T. Kobayashi..............177
Fractal and spectral analysis of fracture surfaces of elastomeric materials D. Ait Aouit & A. Ouahabi ................................................................................187 Multi-scale foam behaviour characterisation P. Viot & D. Bernard ........................................................................................197 Section 6: Experimental methods – thermal analysis Thermo-analytical evaluation of wear debris for thermoplastic and sintered polyimide P. Samyn, I. Van Driessche, G. Schoukens & P. De Baets ...............................209 Analysis of adiabatic heating in high strain rate torsion tests by an iterative method: application to an ultrahigh carbon steel J. Castellanos, I. Rieiro, M. Carsí, J. Muñoz & O. A. Ruano ...........................219 Section 7: Experimental methods – mechanical characterisation and testing Collapse of FRP/syntactic foam sandwich panels M. Perfumo, C. M. Rizzo & M. P. Salio............................................................231 Modelling of viscoelastic properties of a curing adhesive J. de Vreugd, K. M. B. Jansen, L. J. Ernst & J. A. C. M. Pijnenburg...............241 Flexural bond strength of clay brick masonry C. G. Yuen & S. L. Lissel ..................................................................................253 Structural, economic and material comparison of various steel grades under dynamic/fatigue loading I. U. Amobi & H. C. Uzoegbo ...........................................................................263 Mechanical compression tests to model timber structures behaviour V. De Luca & D. Sabia......................................................................................273 Section 8: Experimental methods – new methods Millimeter wave spectroscopy and materials characterization of refractive liquid crystal polymer/titania composites B. R. Dantal, A. Saigal, M. A. Zimmerman, K. A. Korolev, M. N. Afsar & U. A. Khan .................................................................................281
Assessment of surface roughness for the analysis of the water vapour condensation process A. J. Klemm, P. Klemm & I. Ibrahim ................................................................291 Use of impedance spectroscopy to determine the displacement of water in cement paste under small loads I. Sánchez, G. Castro, M. A. Climent & X. R. Nóvoa........................................301 Assimilation of porosity in modern bricks by computational means M. A. Stefanidou................................................................................................313 Dynamic tensile test and specimen design of auto-body steel sheet at the intermediate strain rate S. B. Kim, J. H. Song, H. Huh & J. H. Lim .......................................................319 Utilization of ground coloured glass cullet in construction materials A. Karamberi & A. Moutsatsou ........................................................................329 In situ dynamic characterization of soils by means of measurement uncertainties and random variability G. Vessia & C. Cherubini .................................................................................339 A natural and biodegradable scaffold of electrospun eggshell membrane W. D. Kim, T. Min, S. A. Park, J. H. Park & G. H. Kim ...................................349
Section 9: Computational methods – discrete computational methods Characterization of cementitious materials by advanced concurrent algorithm-based computer simulation systems Z. Q. Guo, M. Stroeven, W. Yang, H. He & P. Stroeven...................................361 A simulation of the behaviour of propane bulks on a grid platform A. Laganà & A. Costantini................................................................................373 Section 10: Computational methods – damage mechanics Failure characterisation of Ti6Al4V gas turbine compressor blades A. Kermanpur, H. Sepehri Amin, S. Ziaei Rad, N. Nourbakhshnia & M. Mosaddeghfar............................................................383 Seismic damage assessment of steel components A. Benavent-Climent .........................................................................................393
A visco-plastic damage model for high temperature creep of single-crystal superalloys A. Staroselsky & B. Cassenti.............................................................................403 Failure mechanics of slope slip with predestinate slip plane J. Vacek & S. Sedláþková..................................................................................413 Section 11: Computational methods – innovative techniques Back analysis of reinforced soil slopes P. Procházka & J. Trckova ...............................................................................423 Towards 3D simulation of sintering processes S. Bordère, D. Bernard, S. Vincent & J.-P. Caltagirone ..................................433 Author Index ...................................................................................................443
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Section 1 Microstructures – novel composite materials
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Computational Methods and Experiments in Materials Characterisation III
3
Study on static and creep properties of CFRP using rubber modified matrix K. Takemura1 & Y. Yasuda2 1 2
Department of Mechanical Engineering, Kanagawa University, Japan Graduate Student of Kanagawa University, Japan
Abstract In this study, the static and creep properties of Carbon Fiber Reinforced Plastics (CFRP) are examined. Plain woven carbon fabric is used as reinforcement. As the matrix, epoxy resin is modified by using cross-linked rubber particles. Four weight contents (0%, 5%, 10%, and 15%) of rubber modification are used. Three point bending loading is applied to the specimen. Static and creep tests are conducted. The results can be summarized as follows. For epoxy resin bulk and CFRP specimens, the strength and maximum strain decrease by rubber modification at static bending test, but the reduction rates of the strength and maximum strain for CFRP are smaller than those of resin bulk specimens. For example, when the weight content of rubber particles for epoxy resin is 5%, the strength reduces to about 50% and the maximum strain reduces to about 60% in the resin bulk specimen, but the strength and maximum strain reduce to about 35% and 25% respectively in CFRP. For the creep test, the creep strain rate in the secondary state is improved for CFRP with rubber modification. When the weight content of rubber particles is big, the improvement of the creep strain rate in the secondary state is great. For example, for CFRP whose weight content of rubber particles is 15%, the creep strain rate decreases by 25%. When an environmental temperature is beyond 120 degrees centigrade, the creep strain rate at the secondary state increases rapidly for unmodified CFRP, but the creep strain rate for modified CFRP is not so increased. So, an effect of rubber modification is great in the high temperature environment. In the case when the environmental temperature is 190 degrees centigrade, a 5% modification is most effective. Consequently, the rubber modification method for CFRP is effective for creep strain in an elevated temperature environment. Keywords: CFRP, epoxy, rubber modification, creep, bending loading. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/MC070011
4 Computational Methods and Experiments in Materials Characterisation III
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Introduction
CFRP has high specific strength and modulus compared to conventional metal materials. So, CFRP is widely used in automobile and airplane parts. When CFRP is used as the structural materials of airplane wings, constant load is supplied for several hours. So, the creep property for CFRP is important. Static and creep properties are dependent on environmental temperature because the polymer matrix is used. Therefore, the mechanical properties at elevated temperature are important too. In the case that epoxy matrix of CFRP is modified with cross-linked rubber particles, the static tensile strength and fatigue lives of CFRP have increased [1, 2]. But, as far as the authors know, few papers have been published about the effect of rubber particle to creep properties for CFRP. The objective of this present work is to demonstrate the static and creep properties for CFRP with a rubber modified matrix. The effect of environmental temperature on the properties is also examined.
2
Specimens
Plain woven carbon fabric (Toray Co.) is used as reinforcement. The number of laminates is eight. Epoxy resin is used as the matrix. The matrix is modified by using cross-linked rubber particles. Four weight contents (0%, 5%, 10%, and 15%) of rubber particle are used. Specimens are laminated by the hand lay up method, and they are cured by a hot press facility. The pressure at moulding is about 10MPa. The length, breadth and thickness of the specimens are 100mm, 15mm and 2mm respectively.
3
Experiment
3.1 Static bending test Three point bending tests are conducted with Shimadzu universal testing instruments (AG-IS). Crosshead speeds are 2.0 mm/min for resin bulk and 5.0 mm/min for CFRP specimens. An extensometer (MTS Co.) is used to measure a strain. The number of specimens is five at one test condition based on JIS (Japanese Industrial Standard) 7171 and 7074. 3.2 Creep test Constant temperature oven facility (Advantec Co.) is used for the creep test. Three point bending loading (20N) is applied. The deflection is measured and recorded with a remote scanner (NEC Co.). The creep test continues until failure or near 150 hours. Environmental temperatures are 110, 120, 130 and 190 degrees centigrade.
WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
Computational Methods and Experiments in Materials Characterisation III
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3.3 Observation of flat wise surface In the case of creep test, flat wise surfaces are observed with a scanning electron microscope (SEM-EDX: Hitachi Co.) 㪈㪉㪇
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Stress–strain curves for epoxy resin bulk.
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Stress–strain curves for CFRP.
Results and discussion
4.1 Static bending test Figure 1 shows stress-strain curves for a resin bulk specimen which has no reinforcement. Figure 2 shows stress-strain curves for CFRP. Table 1 and table 2 show the mechanical properties for resin bulk and CFRP respectively. From these results, it is understood that the strength (maximum stress) and maximum strain decrease by rubber modification for resin bulk and CFRP. It is because of WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
6 Computational Methods and Experiments in Materials Characterisation III Young’s modulus that the decrease is due to the rubber modification to the matrix. The reduction rates for CFRP are smaller than that of resin bulk specimen. When the weight content of rubber particles for the epoxy resin bulk is 5%, the strength reduces by about 50% and the maximum strain reduces by about 60%. But the strength reduces by about 35% and the maximum strain reduces by about 25% for CFRP. So, the reduction of mechanical properties for CFRP is smaller than that of resin bulk. Table 1:
Mechanical property for epoxy resin bulk at static bending test.
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Table 2:
Mechanical property for CFRP at static bending test.
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4.2 Creep test Figures 2–5 show the relationships between creep strain and time in 110, 120, 130 and 190 degrees centigrade respectively. Creep curve can be divided into three stages. The first stage is the transient creep region which includes the elastic strain region. The second one is constant creep region which is called secondary creep, and the last one is the tertiary creep region. So, creep strain H at first and second stages can be written as follows.
H
H 0 Et n kt
H 0 : elasticity strain t : time Et n : strain of transient creep region kt : strain of secondary creep region WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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Figure 7 shows coefficients k of creep curves at each temperature environment. The coefficient k decreases as the rubber contents increase. From fig.3 and 7, when the temperature is 110 degrees centigrade, the strain of the secondary creep region is small. From the viewpoint of static property, Young’s modulus decreases with the increase of rubber content. Therefore, it is thought that the creep strain at 110 degree centigrade is dependent on the static property especially Young’s modulus. 㪇㪅㪋
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Relationship between strain and time (110°C).
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Relationship between strain and time (120°C).
In the case that the environment temperature is beyond 120 degrees centigrade, secondary creep strain rate becomes big which are seen in figs 4 and 5. From Fig.7, the effect of rubber modification to the creep strain is great in the WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
8 Computational Methods and Experiments in Materials Characterisation III high temperature environment. Epoxy resin has glassy property under some temperature which is thought 125 degrees centigrade [3]. But, this temperature is affected by a quantity and a kind of hardening agent. Therefore, it is thought that the temperature decrease to 115 degrees centigrade. In addition, it is known that the creep property is improved by crumb rubber modified to bitumen. Therefore, it is thought that the creep property of CFRP is improved with rubber modification. 㪇㪅㪋
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Figure 5:
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Relationship between strain and time (130°C).
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Figure 6:
Relationship between strain and time (190°C).
In the case that the environmental temperature is 190 degrees centigrade (Fig.6), unmodified and 15% modified specimen fails rapidly. But, 5% and 10% modified specimens do not fail until 150 hours. So, excess modification is not effective for an extreme high temperature environment. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
Computational Methods and Experiments in Materials Characterisation III
9
㪎 㪈㪈㪇㷄
㪚㫆㪽㪽㫀㪺㫀㪼㫅㫋㩷㫆㪽㩷㪸㩷㪺㫉㪼㪼㫇 㩷㪺㫌㫉㫍㪼㩷㫂㩿㪈㪇 㪄㪋 㪀
㪍
㪈㪉㪇㷄
㪈㪊㪇㷄
㪌 㪋 㪊 㪉 㪈 㪇 㪇㩼
㪌㩼
㪈㪇㩼
㪈㪌㩼
㪮㪼㫀㪾㪿㫋㩷㪺㫆㫅㫋㪼㫅㫋㩷㫆㪽㩷㫉㫌㪹㪹㪼㫉㩷㫇㪸㫉㫋㫀㪺㫃㪼㫊㩷㩿䋦㪀
Figure 7:
Coefficient of creep curve k .
After the creep test, flat wise surfaces of CFRP are observed with SEM. Figure 8 shows SEM micrograph. The images can be compared with that at 25 degrees centigrade. In the case of 110 degrees centigrade, it looks like the same as that of 25 degrees centigrade. In the case of 120 degrees centigrade, fibers can be seen on the surface. In the case of 190 degrees centigrade, fibers can be seen on the surface clearly. In addition, the weight of specimen in 190 degrees centigrade decreases 1.3 percent. Therefore, it is thought that epoxy resin is removed from the surface when the environmental temperature is 190 degrees centigrade. In the case that the temperature is above 120 degrees centigrade, it is thought the resin may be removed. So, the secondary creep strain rate of CFRP increases rapidly over 120 degrees centigrade.
5
Conclusions
The effect of rubber modification to static and creep properties for CFRP is examined. In the result, following conclusions are obtained. For static test, the mechanical properties decrease due to rubber modification. The reduction rate of CFRP is smaller than that of resin bulk. For creep test at elevated temperature, in the case that the weight content of rubber particles is big, there is an improvement of creep strain rate in the secondary state. Therefore, the rubber modification method has an effect to creep strain rate in secondary region. When the environmental temperature is above 120 degrees centigrade, epoxy resin is removed due to the heat. Therefore, this phenomena affects the acceleration of creep strain rate.
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10 Computational Methods and Experiments in Materials Characterisation III
30Ǵm (a)
30Ǵm (b)
30Ǵm (c)
30Ǵm (d)
Figure 8:
(a) 25°C, (b) 110°C, (c) 120°C, (d) 190°C SEM image of CFRP.
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References [1] [2]
[3] [4]
K. Takemura and T. Fujii, Improvement in Static, Impact and Fatigue Properties of CFRP due to CNBR Modification of Epoxy Matrix, JSME International Journal Series A, Vol.43, No.2, pp.186-195, 2000. M. Higashino, K. Takemura and T. Fujii, Strength and damage accumulation of carbon fabric composites with a cross-linked NBR modified epoxy under static and cyclic loadings, Composite Structures, Vol.32, No.1-4, pp.357-366, 1995 Engineering Materials Handbook, Vol.1 Compoiste, ASM International, pp.66-77, 1987. Sharma, V., Goyal, S., Comparative study of performance of natural fibres crumb rubber modified stone matrix asphalt mixtures. Canadian Journal of Civil Engineering, 33(4), pp134-139, 2006.
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Determination of the fatigue behavior of coatings by means of an improved impact testing evaluation procedure C. David1, K. G. Anthymidis2, P. Agrianidis1 & D. N. Tsipas3 1
Mechanical Engineering Department, Technical University of Serres, Greece 2 Materials Department in Applied Research Center of Serres, Greece 3 Mechanical Engineering Department, Aristotle University of Thessaloniki, Greece
Abstract Impact testing is an efficient experimental procedure that enables the determination of the fatigue resistance of mono- and multilayer coatings deposited on various substrates, which is not possible with the common testing methods previously available. In this paper an advanced impact tester, capable of assessing the fatigue failure resistance of coatings working under cyclic loading conditions, is presented. The fatigue failure of the tested coating was determined by means of scanning electron and optical microscopy. The test results were recorded in diagrams containing the impact load versus the number of successive impacts that the tested coating can withstand. Keywords: thin films and coatings, materials characterization, fatigue.
1
Introduction
The impact test method has been introduced as a convenient experimental technique to evaluate the fatigue strength of coatings being exposed in alternate impact loads [1–4]. According to this method a coated specimen is cyclically loaded by a hard ball that repetitively impacts on the specimen surface. The superficially developed Hertzian pressure induces a complex stress filled within the coating, as well as, in the interfacial zone. Both these stress states are responsible for distinct failure modes, such as a cohesive or adhesive one. The WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/MC070021
14 Computational Methods and Experiments in Materials Characterisation III exposure of the layered compounds against impulsive stresses creates the real conditions for the appearance of coating fatigue phenomena based upon structural transformation, cracking generation and cracking growth, which are responsible for the gradual microchipping and the degradation of the coating.
2
Experimental procedure:
In this research coatings were characterized using an advanced impact tester system, which is shown in Fig.1. The system consists of three main parts: x The main test device (centre) x The power supply unit (left) x The evaluation and controlling unit (right)
Figure 1:
Impact tester system.
In the present paper characterization of coatings were carried out in such a system. This experimental set up is simple and user friendly and allows the determination of the fatigue behavior of a wide range of single and multielement coatings. The working principle of the impact tester is presented in figure 2 and is based on the alternate Laplace magnetic forces produced by the electromagnetic field, which is induced within the mechanical unit. In order to make the impact tester system more efficient we redesigned the mechanical unit using finite elements to achieve the optimum magnetic flux density, which gives the higher magnetic force of the electromagnetic field and correspondingly an increased impact load (figure 3). Further more the control and the monitoring of the impact tester was improved. All four most important test parameters, the induced impact force, number of successive impacts, the impact frequency and the level of the coil temperature are monitored throughout WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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each experiment. The whole mechanical apparatus is flexible and allows the operator to modify the desirable total number of impacts and impact force during the test procedure easily via the front panel of the evaluation and controlling unit (figure 4).
Figure 2:
Figure 3:
Impact tester working principles.
Increased impact load due to design optimisation.
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16 Computational Methods and Experiments in Materials Characterisation III
Figure 4:
Front panel of the evaluation and controlling unit.
Figure 5:
Impact crater with the developed coating failure.
The stress strain problem related to the impact test is the Herzian contact, which develops between the spherical indentor (carbide ball) and the examined layered space. Gradual intrinsic coherence release and coating microchipping or abrupt coating fracture and consequent exposure of the substrate material designate the coating failure. In all impact craters resulted from the experiments three different zones inside the impact cavity were identified (figure 5). A central zone in the mid of the impact cavity, where the coating is strained with WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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compressive stresses and a gradual cohesive degradation takes place. The intermediate zone inside the piled up rim formed around the impact cavity, where tensile and shear stresses are building up and both cohesive and adhesive delamination arises. Finally, the peripheral zone of the impact cavity, where macrocracks might propagate and coating failure occurs. The coating failure mode and its extent were assessed by SEM observations and EDX analysis. The contact load leading to coating fatigue fracture was recorded in diagrams (endurance strength curves) versus the number of impacts (figure 6). The impact load for which the coating after 106 impacts do not fail is called limit of continues endurance of the coating.
Figure 6:
3
Typical endurance strength curve.
Results and discussion
In figure 7 the high cycle fatigue diagram of a Al, Fe pack coating on P92 steel (9% w.t. Cr, 1.8% w.t. W) substrate is shown. This coating consists of an outer Fe14Al84 layer and an inner FeAl13 layer. From impact testing procedure it was concluded that its limit of continues endurance was 100 N (Fig.8, 9). The main failure of the examined coating-substrate compound occurred in the central zone of the impact crater with coating degradation.
4
Conclusions
The work presented here shows a step forward in understanding the failure mechanisms of pack coatings. More specifically the paper reports the results of a novel experimental approach adapted to investigate the endurance performance of coating systems with refer to their mechanical properties and to deliver a semi-empirical design approach. Current impact testing investigations revealed the fatigue strength of Al, Fe pack coating on P92 steel substrate.
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18 Computational Methods and Experiments in Materials Characterisation III 700
Impact Force (N)
600 500 400 300 200 100 0 0
500000
1000000
1500000
Number of impacts
Figure 7:
Endurance strength curve of Al, Fe pack coating on P92 steel substrate.
Figure 8:
SEM photo of the Al, Fe coating deposited on P92 steel substrate after 1.000.000 impacts with an impact force of 100 N, failure initiation.
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Computational Methods and Experiments in Materials Characterisation III
Figure 9:
19
EDX diagram of the Al, Fe coating deposited on P92 steel substrate after 1.000.000 impacts with an impact force of 100 N. Traces of W and Cr indicates failure initiation.
Acknowledgements We express our gratitude to the E.U. for financing this work through the project SUPERCOAT, Contract No: ENK5-CT-2002-00608 and to Technical University of Serres also.
References [1] [2] [3] [4]
Voevodin A.A., Bantle R., Matthews A., Dynamic impact wear of TiCXNY and Ti-DLC composite coatings, Wear, 185 (1995), pp. 151157. Bantle R., Matthews A., Investigation into the impact wear behaviour of ceramic coatings, Surface and Coatings Technology, 74 -75 (1995), pp. 857-868. Heinke W., Leyland A., Matthews A., Berg G., Friedrich C., Broszeit E., Evaluation of PVD nitride coatings, using impact, scratch and Rockwell-C adhesion tests, Thin Solid Films, 270 (1995), pp. 431-438. Ziegele H., Rebholz C., Voevodin A.A., Leyland A., Rohde S. L., Matthews A., Studies of the tribological and mechanical properties of laminated CrC-SiC coatings produced by r.f. and d.c. sputtering, Tribology International, Vol. 30, No. 12 (1997), pp.845-856. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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Effect of fly ash reinforcement on the corrosion behaviour of cast Al-Mg alloy A535 in 3.5 wt% NaCl solution E. R. Obi1, I. N. A. Oguocha1 & R. W. Evitts2 1
Department of Mechanical Engineering, University of Saskatchewan, Canada 2 Department of Chemical Engineering, University of Saskatchewan, Canada
Abstract The effect of fly ash reinforcement on the room temperature corrosion behaviour of cast Al-Mg alloy A535 in 3.5 wt% pH 7 NaCl solution was investigated using an immersion corrosion test, electrochemical tests and optical microscopy. The materials studied were A535 and its metal matrix composites (MMCs) containing 10wt% fly ash, 15wt% fly ash, and a hybrid reinforcement (5wt% fly ash+5wt% SiC). The immersion corrosion test results showed that the corrosion rate of the MMCs increased with increasing fly ash content while the electrochemical test results indicated that their corrosion potential (Ecorr) and critical pitting (breakdown) potential (Ep) decreased with increasing fly ash content. The repassivation potentials of the MMCs were found to be more positive than that of the matrix alloy. The corrosion of the MMCs, which was accompanied by loosening of fly ash particles, was also affected by porosity and the presence of several reaction products. Keywords: Al-Mg alloy, A535, fly ash, MMCs, corrosion rate, corrosion potential, pitting potential, repassivation potential, intermallic compounds, Mg2Si.
1
Introduction
Particle-reinforced aluminum metal matrix composites (MMCs) containing SiC and Al2O3 have received great attention in the past few decades because of their improved wear resistance, reduced coefficient of thermal expansion (CTE), high WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/MC070031
22 Computational Methods and Experiments in Materials Characterisation III elastic modulus, and improved strength compared to unreinforced aluminum alloys [1, 2]. Although they have found potential applications in weight-critical components in automobile, aerospace, and defence systems [2–5], the application base of these particulate MMCs is limited by their high production cost. Recently, inexpensive aluminum alloy MMCs reinforced with fly ash, a waste by-product of coal combustion, has been engineered [6–11] to serve as a substitute for conventional particulate MMCs in several applications in order to widen the application bases of this class of MMCs. The addition of fly ash into aluminum MMCs is a value-added initiative that lowers the disposal cost of fly ash, increases energy savings by reducing the quantity of aluminum produced, and creates a healthier environment. Many potential applications of particulate Al MMCs in naval structures such as ship and boat hulls, offshore structures and desalination plants involve exposure to saline environments with high chloride ion concentrations. Also, particulate Al MMCs used in automobile engine parts usually encounter hostile environments containing chloride, sulphate and nitrate ions as well as exhaust gases like CO2, CO and NOx [12]. Since corrosion resistance is a key design parameter which must be factored in when considering the application potentials of particulate MMCs in structural applications, it is important to understand the corrosion behaviour of these materials in different corrosive environments. The corrosion behaviour of Al-based MMCs reinforced with particles such as Al2O3, garnet, TiC, AlN and SiC particles have been studied by several workers [12–21]. A close look at the results obtained from these studies shows that three types of corrosion can occur in particulate Al MMCs at room temperature. These are galvanic corrosion between the reinforcement and the matrix alloy, crevice corrosion around the reinforcement and in surface pores, and pitting corrosion of the matrix alloy as well as the interface between the matrix and the reinforcement. De Salazar et al [13] investigated the effect of heat treatment and reinforcement volume fraction on the corrosion behaviour of AA6061 and AA7005 reinforced with Al2O3 particles. They found that the pitting corrosion mechanisms of AA6061 MMCs were affected by post-fabrication heat treatment and that the number of corrosion pits increased with increasing Al2O3 volume fraction. Gnecco and Beccaria [14] investigated the corrosion behaviour in sea water of a SiCp/Al-Mg MMC and found that SiC particles acted as cathodic sites with respect to the matrix alloy, which experienced selective aluminium dissolution. They also observed that the MMC suffered localized corrosion of the matrix where Al-Cu intermetallic compounds were present. Also, Gavgali et al [15] studied the effect of reinforcement content on the corrosion behavior of SiCp/Al-Si-Mg MMCs in both aerated and deaerated 3.5wt.% NaCl aqueous solutions. The results showed that the corrosion resistance of the MMCs decreased with increasing SiC particle content. However, Kiourtsidis et al [16] who studied SiCp/AA2024 MMCs reported that the overall performance of the matrix alloy was independent of the volume fraction of SiC particles as they observed no detrimental galvanic attack between the matrix and the particles.
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Similarly, Aylor and Moran [17] observed that SiC did not alter the corrosion potential of AA6061 in aerated seawater. Although there is a significant amount of research on the corrosion behavior of Al alloys and conventional particulate Al MMCs, there is a dearth of information on the corrosion behaviour of Al alloys reinforced with fly ash particles [9,11]. The present investigation was therefore initiated to contribute to better understanding of the effect of fly ash additions on the corrosion behavior of cast Al-Mg alloy A535 in 3.5wt% NaCl solution. A535 is a non-heat treatable Al-Mg alloy with good combination of strength, machinability, corrosion resistance, weldability and good surface finish. It is used for manufacturing naval vessels, aircraft landing gears, rocket launchers, lightweight armoured vehicles and components of instruments and computing devices.
2 Experimental materials and procedure 2.1 Materials The fly ash reinforced A535 MMCs used in this study were fabricated by the stir casting technique. The MMCs contained 10wt% fly ash (10FA/A535), 15wt% fly ash (15FA/A535) and a hybrid mixture consisting of 5wt% fly ash and 5wt% SiC (5FA5SiC/A535). The composition of the A535 alloy used was 6.17wt% Mg, 0.01wt% Cu, 0.01wt% Si, 0.02wt% Fe, and 0.04wt% Ti, bal. Al while the composition of the raw fly ash used is shown in Table 1. Table 1: Compound Weight %
SiO2 44.8
Weight percent of various oxides in fly ash. Al2O3 22.2
Fe2O3 24.0
MgO 0.9
CaO 1.8
TiO2 0.8
K2O 2.4
Na2O 0.9
SO3 1.4
Balance = oxides of other trace elements. 2.2 Corrosion testing The corrosion behavior of the test materials was evaluated using static immersion test, potentiodynamic and cyclic polarization tests, visual inspection and optical microscopy. The immersion test was conducted at room temperature using conventional weight loss method (ASTM G31) to an accuracy of 0.0001g. Rectangular specimens measuring 10 mm x 10 mm x 5 mm were cut from the A535 and its MMCs, metallurgically polished with emery cloth to high smoothness, cleaned ultrasonically in acetone and methanol, and dried. They were subsequently weighed and immersed in a solution of 3.5wt% NaCl (pH = 7) exposed to the ambient air. The specimens were suspended in the electrolyte using a plastic string and a plastic crocodile clip to avoid crevice and galvanic corrosion. The specimens were removed from the solution at regular intervals and cleaned in accordance with ASTM G1-90 standard, dried and re-weighed. The exposure times used in this study were 1, 3, 5, 7, 10, and 14 days. The surface of each specimen was examined visually and by optical microscopy before and after each exposure test. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
24 Computational Methods and Experiments in Materials Characterisation III Electrochemical polarization measurements were conducted on all specimens of the matrix alloy and composites using a Gamry ECM 8 electrochemical multiplexer with PCI4 potentiostat controlled by a computer. A saturated calomel electrode (SCE) and a graphite electrode were used as reference and auxiliary electrodes, respectively. As in the immersion test, all specimens were metallurgically polished to high smoothness using emery cloth, rinsed in acetone, dried, and immersed in a 3.5wt% pH 7 NaCl electrolyte at room temperature exposed to the atmospheric air. Before starting the measurements, all specimens were allowed to equilibrate for approximately 30 minutes to their corrosion potential (Ecorr). A scan rate of 1 mV/s was used to determine the corrosion potential (Ecorr), pitting potential (Ep) and repassivation potential (Erp). 0.018 A535 5FA5SiC/A535 10FA/A535 15FA/A535
0.016
Corroion Rate (mm/year)
0.014 0.012 0.010 0.008 0.006 0.004 0.002 0.000 0
2
4
6
8
10
12
14
16
Immersion Time (days)
Figure 1:
3
Variation of corrosion rate of A535 and its fly ash reinforced MMCs with time in 3.5wt% NaCl solution (pH = 7).
Results and discussion
Fig. 1 shows the variation of corrosion rate with exposure time for specimens immersed in 3.5wt% NaCL (pH = 7) solution at room temperature. It can be seen that the matrix alloy (A535) and its composites showed similar corrosion behaviour. The corrosion rate of all the tested materials decreased rapidly during the first three days of exposure to the electrolyte but, with further exposure time, the decrease was very gradual. Passivation of the matrix alloy is believed to be responsible for the phenomenon of monotonically decreasing corrosion rate with increasing exposure time observed in these materials [12]. It is also seen that 15FA/A535 composite showed the highest rate of corrosion, followed in decreasing order by 10FA/A535, 5FA5SiC/A535, and A535. It was also observed that the corrosion of the composites was accompanied by loosening of fly ash particles, with the amount of loosened fly ash being greatest in 15FA/A535 composite, followed by 10FA/A535 composite. It was believed that the corrosion of the fly ash-matrix interface caused the loosening of fly ash particles which were finally dislodged from the specimens during postimmersion cleaning process. Ramachandra and Radhakrishna [11] have reported that fly ash particles acted as pit initiation sites in Fly ash/Al-Si alloy composites WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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and that there was a buildup of corroded fly ash particle debris in corrosion pits. The loss of such particles during contributed to the high weight loss recorded for the MMCs in the present study. The effect of fly ash addition on the corrosion potential of A535 alloy is shown in Fig. 2 where curves of potential versus current density obtained via potentiodynamic polarization measurements are plotted for the tested materials. It can be seen that all the curves are similar indicating that polarization behaviour of unreinforced A535 alloy and its composites is similar. The corrosion potential (Ecorr) of the unreinforced alloy is more positive than that of the composites which tends to increase with increasing fly ash content. The corrosion potential of A535 alloy is -415 mV (SCE) while those of 10FA/A535 and 15FA/A535 composites are -443mV (SCE) and -507mV (SCE), respectively. Hence, the unreinforced A535 alloy is more noble than its MMCs. Similar results have been reported by Bienias et al [9] for fly ash/AL-Si alloy composites. Fig. 3 shows the cyclic potentiodynamic polarization curves obtained for A535 alloy and its fly ash-reinforced MMCs immersed in 3.5wt% NaCl (pH = 7) while Figs 4 and 5 show respectively the variation of critical pitting potential (Ep) and repassivation potential (Erp) with increasing fly ash content. Fig. 4 shows that the Ep of the tested materials became more negative with the addition of fly ash. It decreased from about 166 mV in A535 to -237.8mV in 15FA/A535 composites, indicating that A535 alloy has better pitting corrosion resistance in 3.5wt% NaCl solution than its composites. On the other hand, Fig. 5 shows that Erp increases (in the active direction) with increasing fly ash content. It increased from -822.5mV (SCE) in A535 alloy to -799.3mV (SCE) in 15FA/A535 composite. Since Erp measures the ability of a material to repassivate, the present results show that pit propagation in the composites is retarded more than in the matrix alloy. A measure of the tendency for pits to nucleate in a material is given by the difference between Ep and Ecorr. Thus, the ability of a material to resist pit initiation during localized corrosion increases as the value of Ep – Ecorr becomes larger [20]. Fig. 6 shows a plot of Ep – Ecorr for the materials studied. It can be seen that A535 alloy has superior pitting corrosion resistance to the composites. -0.35
Potential (V)
-0.40
-0.45
-0.50
A535 5FA5SiC/A535 10FA/A535 15FA/A535
-0.55
-0.60 1e-8
1e-7
1e-6
1e-5
1e-4
Current density (Acm-2)
Figure 2:
Potentiodynamic polarization curves for A535 alloy and its fly ash reinforced MMCs in 3.5wt% NaCl solution (pH =7).
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26 Computational Methods and Experiments in Materials Characterisation III 0.4
A535 5FA5SiC/A535 10FA/A535 15FA/A535
0.2 0.0
Potential (V)
-0.2 -0.4 -0.6 -0.8 -1.0 -1.2 -1.4 1e-8
1e-7
1e-6
1e-5
1e-4
1e-3
1e-2
1e-1
2
Current density (A/cm )
Figure 3:
Cyclic potentiodynamic polarization curves for A535 and its MMCs in 3.5wt% NaCl solution (pH = 7). 200
Potential (mV)
100
0
-100
-200
-300 A535
5FA5SiC/A535
10FA/A535
15FA/A535
Materials
Figure 4:
Effect of fly ash content on the pitting potential of A535 and its MMCs.
The corrosion behaviour of particulate Al MMCs is influenced by several factors such as porosity, high dislocation densities at the matrix-reinforcement interfaces, the presence of intermetallic compounds (IMCs) and reaction products, and the electrical conductivity of the reinforcing phases [19]. Gikunoo and Oguocha [24] have reported that the amount of dimagnesium silicide, Mg2Si, and spinel, Al2MgO4, in fly ash/A535 composites increased with increasing fly ash content. Mg2Si is produced in the matrix alloy through a solid-state reaction between Si and Mg 2Mg Si l Mg 2Si (1) In the MMCs, the SiO2 phase present in fly ash particles or covering the surface of SiC particles in 5FA5SiC/A535 composite is reduced by molten magnesium through a two-step reaction leading to the formation of the Mg2Si phase: 2Mg + SiO2 l 2MgO + Si (2) (3) 2Mg + Si l Mg2Si
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The spinel phase is formed in the MMCs via a reaction between elemental magnesium of the matrix alloy and fly ash constituents, particularly the alumina (Al2O3) and quartz phases, following either of the chemical reactions: (4) 3Mg + 4Al2O3 l 2Al + 3MgAl2O4 2SiO2 + 2Al +Mg l MgAl2O4 + 2Si (5) -795 -800
Erp (mV)
-805 -810 -815 -820 -825 A535
5FA5SiC/A535 10FA/A535
15FA/A535
Materials
Figure 5:
Effect of fly ash content on the repassivation potential of A535 and its MMCs. 700 600
Ep - Ecorr (mV)
500 400 300 200 100 0 A535
5FA5SiC/A535
10FA/A535
15FA/A535
Materials
Figure 6:
Plot of Ep–Ecorr for A535 alloy and its MMCs in 3.5wt% NaCl solution (pH = 7).
The presence of the intermetallic phases and porosities in the MMCs serve as preferential sites for localized corrosion. In the present study, optical microscopy observation of the corroded surfaces of specimens immersed in NaCl solution for several days showed that pits occurred where the Mg2Si phase existed prior to immersion. This was well pronounced in the matrix alloy thus indicating that Mg2Si has a less noble potential than the alloy in 3.5wt% NaCl solution at room temperature. It was reported by Birbilis [22] that Mg2Si does not show any breakdown potential and is capable of corroding freely above its Ecorr, which was WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
28 Computational Methods and Experiments in Materials Characterisation III measured to be -1536 mV (SCE) in 0.6M NaCl [22] and -1530 to -680 mV (SCE) in 3wt% NaCl [23] as compared to -849 mV SCE for pure aluminum in 0.6M NaCl [22] and -760 to -810 mV (SCE) for Al-Mg binary alloy in 53g/l NaCl+3g/l H2O2 solution [23]. Since aluminum is noble to Mg2Si, the microgalvanic couple formed between them in A535 alloy and its MMCs would selectively corrode Mg2Si away. Therefore, the deep pits observed in the A535 alloy are attributed to the dissolution of the Mg2Si
4 1 2 3 4
Conclusions The corrosion rate of fly ash/A535 MMCs immersed in 3.5wt% NaCl solution at room temperature was higher than that of the matrix alloy and increased with increasing fly ash content. Fly ash/A535 MMCs showed increased susceptibility to pitting corrosion compared to the unreinforced A535 alloy in NaCl solution. The pitting potential (Ep) of the composites decreased with increasing fly ash content. The sites for pit initiation in A535 alloy were the intermetallic compounds, especially the Mg2Si phase which dissolved away with increasing immersion time. The predominant pit initiation sites in the MMCs were the interfaces between the matrix alloy and fly ash and intermetallic compounds such as Mg2Si and Al2MgO4.
Acknowledgement This work was supported by the Natural Sciences and Engineering Research Council of Canada via a discovery grant to I. N. A. Oguocha.
References [1] [2] [3] [4] [5] [6]
Chawla, N. & Shen Y., Mechanical Behavior of Particle Reinforced Metal Matrix Composites. Advanced Engineering Materials, 3(6), pp. 357-370, 2001. Lloyd, D.J., Particle-Reinforced Aluminum and Magnesium Matrix Composites. International Materials Reviews, 39(1), pp. 1-23, 1994. Fujine, M, Kaneko, T, & Okijima, J, Adv. Mater. Process, 143(6), pp. 2021, 1993. Akbulut, H, Durman, M & Yilmaz, F, Scripta Materialia, 36, pp. 835-840, 1997. Goni, J, Mitxelena, I, & Coleto, J, Mater. Sci. Technol., 16, pp.743-746, 2000 Rohatgi, P.K, Kim, J.K, Guo, R.Q, Robertson, D.P & GajdardziskaJosifovska, M, Age-hardening characteristics of aluminum alloy-hollow fly ash composites, Metall. Mater. Trans., 33A, pp. 1541-1547, 2002.
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[7] [8] [9] [10] [11] [12] [13]
[14] [15] [16] [17] [18] [19]
[20]
[21]
29
Golden, D, Ashalloys: aluminum-fly ash composites. EPRI Journal, 19(1), pp. 46(4), 1994. Guo, R.Q & P K Rohatgi, P.K, Chemical reactions between aluminum and fly ash during synthesis and reheating, Metall. Mater. Trans., 29B, pp. 519-525, 1998. Bienias, J, Walczak, M,. Surowska, B & Sobczak, J., Microstructure and Corrosion Behaviour of Aluminum Fly Ash Composites. Journal of Optoelectronics and Advanced Materials, 5(2), pp. 493-502, 2003. Gikunoo, E., Omotoso, O. & Oguocha, I.N.A., Effects of Fly Ash Particles on the Mechanical Properties of Aluminum Casting Alloy 535. Material Science and Technology, 21(2), pp. 143-152, 2005. Ramachandra, M & Radhakrishna, K., Microstructure, Mechanical Properties, Wear and Corrosion Behaviour of Al-Si/flyash Composite, Materials Science and Technology, 21(11), pp. 1337-43, 2005. Seah, K.H. W, Krishna, M., Vijayalakshmi, V.T. & Uchil, J., Corrosion Behaviour of Garnet Particulate Reinforced LM13 Al Alloy MMCs, Corrosion Science, 44, pp. 917-925, 2002. De Salazar, J.M.G., Urena, U., Manzanedo, S. & Barrena, M.I., Corrosion behaviour of AA6061 and AA7005 reinforced with Al2O3 Particulates in Aerated 3.5% Chloride Solutions: Potentiodynamic Measurements and Microstructure Evaluation, Corrosion Science, 41, pp. 529-545, 1999. Gnecco, F.F, Corrosion Behaviour of Al-Si/SiC Composite in Sea Water. British Corrosion Journal, 34(1), pp. 57-62, 1999. Gavgali, M., Dikici, B. & Tekmen, C., The effect of SiCp Reinforcement on the Corrosion Behaviour of Al Based Metal Matrix Composites, Corrosion Reviews, 24(1-2), pp. 27-37, 2006. Kiourtsidis, G & Skolianos, M., Corrosion Behavior of Squeeze-cast Silicon carbide-2024 composites in aerated 3.5 wt.% sodium chloride. Materials Science and Engineering, A248, pp. 165-172, 1998. Aylor, D.M & Moran, P.J, Effect of Reinforcement on the Pitting Behavior of Aluminum-Base Metal Matrix Composites. Journal of The Electrochemical Society, 321(6), pp. 1277-1281, 1985. Candan, S. & Bilgic, E., Corrosion Behavior of Al-60 Vol.%SiCp Composites in NaCl Solution. Materials Letters, 58, pp. 2787-2790, 2004. Albiter, A., Contreras, A., Salazar, M. & Gonzalez-Rodriguez, J.G, Corrosion Behaviour of Aluminium Metal Matrix Composites Reinforced with TiC Processed by Pressureless Melt Infiltration, Journal of Applied Electrochemistry, 36 (3), pp. 303-308, 2006. Pardo, A., Merino, M.C., Merino, S., Viejo, F., Carboneras, M. & Arrabal, R., Influence of Reinforcement Proportion and Matrix Composition on Pitting Corrosion Behaviour of Cast Aluminium Matrix Composites (A3xxx.x/SiCp). Corrosion Science, Vol. 47, Issue 7, 2005, pp. 17501764. . A. Pardo, M. C. Merino, F. Viejo, S. Feliu, Jr., M. Carboneras and R. Arrabal, Corrosion Behavior of Cast Aluminium Matrix Composites
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30 Computational Methods and Experiments in Materials Characterisation III
[22] [23] [24]
(A3xxx.x/SiCp) in Chloride Media. Journal of Electrochemical Society, 152(6), pp. B198-B204, 2005. Birbilis, N.N., Electrochemical Characteristics of Intermetallic Phases in Aluminum Alloys: An Experimental Survey and Discussion. Journal of The Electrochemical Society, 152(4), pp. B140-B151, 2005. Buchheit, R. G, Compilation of Corrosion Potentials Reported For Intermetallic Phases in Aluminium Alloys. Journal of The Electrochemical Society, 142(11), pp. 3994-3996, 1995. Gikunoo, E. & Oguocha, I.N.A. Proc. Of the 6th Joint Canada-Japan Workshop on Composites, ed. J. Lo, T. Nishino, S.V. Hoa, H. Hamada, A. Nakai, C. Poon, DEStech Publications, Inc., Toronto, Canada, pp. 387396, 2006.
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31
Testing of palm fibre as reinforcement material in polyester composites V. V. S. Prasad1, D. N. Rao2, K. N. S. Suman2 & N. R. M. R. Bhargava3 1
Department of Marine Engineering, Andhra University, Visakhapatnam-53003, India 2 Department of Mechanical Engineering, Andhra University, Visakhapatnam-53003, India 3 Department of Metallurgical Engineering, Andhra University, Visakhapatnam-53003, India
Abstract In this present work, palm fibre is incorporated in a polyester resin matrix to form unidirectional reinforced composites and bi-directional composites. Samples of different fibre volume fractions are fabricated and specimens with 0°, 45° and 90° fibre orientations are prepared. The specimens are tested on a universal testing machine applying tensile force. The tensile strength is measured as a function of fibre volume fraction. These properties follow “Rule of mixtures” relationship, with the volume fraction of palm. Because of the low density of natural fibers and high electrical resistance, these composites are more suitable for electrical and mechanical applications. Keywords: palm fibre, hand lay up technique, mechanical and electrical properties.
1
Introduction
There is a great interest in the development of new materials which enhance optimal utilization of natural resources, and particularly of renewable resources. Natural fibres such as palm, jute, coir, banana, sisal etc., belong to this category. These fibres are abundantly available in developing countries, particularly in
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32 Computational Methods and Experiments in Materials Characterisation III India and some places of South Africa [1]. The cotton polymer composite made contributions during the II world war [2,3]. As fibre reinforced plastics, it was first used by the military for radar domes on aircraft. During that period, bearings for ships were made of cotton-phenolic systems; also, brake linings of plywood-phenolic trainer wings and fuselages of British Mosquito bombers, and more than a thousand other items were made. During 1942, the Goodyear Aerospace Corporation for use in aircraft fuel cell produced backing sheet materials made of cotton fabric-polyester. It is recently reported [4] that cotton fabric reinforced phenolic resin composites have been used as bearings in place of phosphor bronze in the roll necks of steel and non-ferrous rolling mills. This resulted in energy savings up to 25%. Reddy, et al [6, 7] studied on fabrication, testing, damage characterization and feasibility of jute-polyester composites. Unprocessed jute yarn and fabric are used as fibers. Twisted jute yarn and fabric, which are semi finished raw materials and commercially produced widely in India, are selected for the work. General-purpose polyester is used as the matrix. Jute reinforced polyester laminates are prepared using 'Hand lay-up' technique to simulate practical production methods. Results indicate that there exists definite correlation between the tensile strength or elastic modulus and fiber volume fraction of the composite and with variation in fiber orientation in the composite. One of the earliest natural fibre-polymer composites are investigated by Paramasivan and Abdulkalam [5] by incorporating sisal fibres and epoxy matrix. The fabrication process attempted by them includes winding and lamination. It is found that the fabrication of these composites is fairly easy and cost of production is quite low. Winding of cylinders with longitudinal or helical and hoop reinforcements is successfully carried out. Tensile strength of the sisalepoxy composites is found to be 250-300 Mpa, which is nearly half the strength of fibre glass–epoxy composites of the same composition. Because of the low density of sisal fibre, however, the specific strength of sisal composites is comparable with that of glass composites. The unidirectional modulus of sisalepoxy composites is found to be about 8.5Gpa. This study indicates the feasibility of developing composites incorporating one of the abundantly available natural fibres, to be used in the field of consumer goods, low-cost housing and civil structures. Lakkad and Patel [8] compared the values of ultimate tensile and compressive strength and young’s modulus of elasticity of bamboo specimens with those of mild steel and glass reinforced plastics. But they have not specified the speciename of the bamboo specimens tested. There are more than 500 species of bamboo available in India and each has different mechanical properties. Extensive literature is available on the production and mechanical behavior of composites obtained by reinforcing epoxy with fibre of glass, boron, carbon silicon carbide etc. Many researchers in the past have developed composites with natural fibres such as sisal henequen, jute, banana, cotton, etc., but the work on the palm reinforced plastic composites and palm reinforced oriented plastic composites are not available in the literature.
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2
33
Fabrication of palm reinforced plastic composites
Palm fibre is extracted from the leaf stem of the palm tree, which is not optimally used. Initially the cut stem from the plant is collected in a heap, and the stem is kept wet by spraying water for 48 hours for free release of the husk. Later by tapping lightly with wooden hammer, on the stem the fibre is separated in two forms as coarse fibre (i.e. 150Pm-1500Pm), length up to 500mm and fine fibre (i.e.75Pm-150Pm) length up to 70mm The fibres are flexible compared to the coarser fibres and segregated in the form of bundles. A rectangular thick tapered plastic plate of size (200 X 50) cm2 is used as a mould for making the composite by using “Hand- lay-up technique”. Acetylene is used as a cleaning agent for cleaning the casting surface of the mould, a releasing agent polyvinyl alcohol is used for easy removal of the casting. After thoroughly mixing the resin with hardener, it is applied over the entire sheet using a soft brush and a coat of wax is applied on this resin layer. The finer fibres are inserted in the wax placing them parallel to the longer edges of the mould plate, and brushing is done smoothly so that resin spreads through the yarn. Care is also been taken to see that the yarns are not being displaced from respective positions after brushing. This process is repeated till all the palm fibres are wet properly. The laminates are cured at room temperature for 24 hours. Laminates with approximately 10%, 20%, 30% and 40% of the fibre volume fraction are prepared as shown Fig 2. For the laminates with volume fraction 50% above it is
Figure 1:
Figure 2:
Palm fibre (finer type) bundle.
Palm reinforced plastic laminate.
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34 Computational Methods and Experiments in Materials Characterisation III observed that wetting of the fibre is not proper and there is no much improvement in strength. To fabricate the bi-directional composite, the second layer of palm is placed perpendicular to the first layer and the above process is repeated till the resin spreads over the entire surface. Fig.3 shows the bi-directional composites. Oriented fibre composites are prepared by placing second layer of palm at different angles of 15o, 30o and 45o for each composite. Figs.4–6, depict the various orientations respectively.
Figure 3:
Palm bi-directional composites.
Figure 4:
Laminates with 15° fibre orientation with a fibre volume of 20%.
Figure 5:
Laminates with 30° fibre orientation with a fibre volume of 20%.
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Computational Methods and Experiments in Materials Characterisation III
Figure 6:
3
35
Laminates with 45° fibre orientation with a fibre volume of 20%.
Experimental procedure
3.1 Tensile test As per ASTM standards the specimen are prepared to the required size of 250mmx25.5mmx4mm with 0o, 45o 90o of fibre orientation. The standard specimens are marked with marking scriber and samples are cut to size using power band saw. PFRP samples are tested on tensile testing machine; UNITEK95100 under a load of 25KN and with a cross head speed of 20mm/min. The specimens are held by flat graved grips. To avoid slipping of grippers during load application, the ends of specimens are made rough by filing. The breaking loads and displacements at various loads are measured. The observing results are presented in figs. 7, 9 and 10 for different percentages of volume fraction and orientations of fibre. 3.2 Electrical test The present test is designed to measure the leakage current between two points. Leakage test is conducted on Cascade transformer, 100 kVA, 500 kV, 200 µA and an ammeter is connected to measure the leakage current. Resistance is calculated using the Kirchoff’s law (V=I R) at constant voltage. Specimens in the normal and soaked in sea water for 12hrs, are tested for breakdown voltage, at the High Voltage Laboratory, Department of Electrical Engineering, Jawaharlal Nehru Technical University, Kakinada, Andhra Pradesh, India.
4
Results
From Fig. 7, it is observed that the tensile strength of the composites increases with increase in the fibre volume fraction. Fibres are the main load carrying agents in composites and as the number of load carrying elements increases in a material, its strength increases. The composite tensile strength decreases with increasing the orientation of the fibre from 0° to 90°. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
Breaking load ,kN
36 Computational Methods and Experiments in Materials Characterisation III 0 Degree orientation
5 4.5 4
45 Degree orientation 90 Degree orientation
3.5 3 2.5 2 1.5 1 0.5 0 0
10
20
30
40
50
% Volume of fibre
Figure 7:
Effect of % volume and orientation of palm fibre on breaking load for uni-directional composite.
Figure 8:
Fractured surface of 10 vol % palm fibre reinforced polymer composite 10X.
Figure 8 shows the fractured surface of the 10 vol % palm fibre reinforced composite. Matrix is found to be deformed to a lesser extent while fibres are protruding from the surface. It shows that fibres have been pulled away from matrix indicating poor bonding at the fibre- matrix interface. This effect is much more pronounced at higher percentages of the fibre and has resulted in lower breaking load values compared to the theoretical calculations of rule of mixtures. Figure 9 shows the effect of fibre volumes and the fibre orientation on the breaking load of bi-directional composites. Since the composite is made bidirectional, breaking load values for the fibre orientations of 0o and 900 have shown similar values at all the fibre contents. These values are found to increase with increasing fibre contents. Composites with fibre orientations of 450 have shown a similar trend but have shown lesser strength values. These results are self explanatory as the strength of the fibre in the warp direction is more than that of in the weft direction.
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37
Breaking load vs Volume of fibre
Breaking load,kN
0 Dgree orientation
4 3.5 3 2.5 2 1.5 1 0.5 0
45 Degree orientation
0
10
20
30
40
50
% volume of fibre
Effect of palm fibre volume and orientation on breaking load of bidirectional composite.
B reakin g lo ad ,kN
Figure 9:
2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0
10
20
30
40
50
Fibre orientation angle
Figure 10:
Effect of palm fibre volume and orientation on breaking load of palm oriented composites.
Figure 10 shows the effect of fibre orientation angle on the tensile strength of the composites. As the orientation angle increases the tensile strength drops to a minimum at the maximum weft of 450. Figure 11 shows the effect of palm fibres volume on the leakage current. Leakage current found to be increasing with increased fibre volumes initially and almost stabilizes at higher contents. From the literature it is found that presence of voids and air pockets enhance the leakage currents. Since palm is natural one and is also in the thoroughly dried condition, sufficient voids are readily present in it. This might have lead to the increased leakage currents in the reinforced composite. As the fibre volume increases, the presence of these discontinuities also increases which might have lead to the increased leakage currents. During processing increased fiber volumes enhance the chances of void presence due to practical problems. This might have further accentuated the leakage voltage at higher volumes of the fibre. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
38 Computational Methods and Experiments in Materials Characterisation III L.C. vs Applied voltage
Leakage current , M icro am pears
60 50 40 30 20 10 0 22
23
25
28
Applied Voltage,kV
Figure 11:
Effect of palm fibre volume on leakage current. Normal
90
Saline
Break down voltage,kV
100 80 70 60 50 40 30 20 10 0
10
20
30
40
50
% Volume of fibre
Figure 12:
Effect of fibre volume on break down voltage.
Figure 12 shows the effect of fibre volume on breakdown voltage. Specimens soaked in the saline water have shown drastic drop in the breakdown voltages compared to the normal samples. A similar trend of drop in breakdown voltage with increasing fibre volumes has been observed with both the conditions of normal and seawater soaked ones. Since the presence of voids, impurities and the moisture decreases the breakdown voltage, the above discussion holds good for this behaviour as well. Presence of moisture has dropped the values further.
5
Conclusions
1.
Palm fibre can be used as reinforcement and filler in the polymer based composites. It shows a conventional behaviour in mechanical properties depicting higher breakdown strength values with increasing fibre volumes. Composites with fibre orientation in the warp direction exhibit better mechanical properties than the weft direction ones.
2. 3.
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Computational Methods and Experiments in Materials Characterisation III
4. 5. 6.
39
Leakage current increases with increasing fibre volumes. Breakdown voltage decreases with increasing fibre volumes. Saline water soaked samples exhibit poor breakdown voltage compared to the normal ones.
References [1]
[2] [3] [4] [5] [6]
[7] [8]
Satyanarayana, K.G., Kulkarni, G.Sukumaran, K., Pillai, S.G.K. Cheriyan, K.A. and Rohatgi, P.K., “on the possibility of using natural fiber polymer composites”. Proc. First International Conference on Composite Structures, 16-18(Sept., 1981), ed. 1.H.Marshall. Applied Science publishers, London, pp.618-623. Piggot, M.R., “Load Bearing Fiber Composites”. Pergamon press, Oxford, 1980. Lubin, G. (ed), “Hand Book of Composites”. Van Nostrand Reinhold, New York 1982. “Save energy – Save money – composite news. Composites”, 10 (April 1979) pp.61. Parmasivam, T and Abdulkalam, A.P.J., “On the study of natural fiber composites” Fiber Science and Technology I (1974) pp. 85-88. Govardhan Reddy, B., Rao, D.N., Bhargava, N.R.M.R. Prasad, V.V.S,. “Damage Mechanism under tensile loading of continuous jute reinforced polyester composites” Proc. Third International conference on ‘Advances in composites’ ADCOMP-2000, August 2000, Bangalore, India. pp.24-26. Govardhan Reddy, B., Rao, D.N., and Rao, R.N.S. “Jute-reinforced polyester composites – A study of properties”, Proc. Of 11th AGM, Materials Research Society of India, India, July 2000. Lakkad, S. C. and Patel, J. M., "Mechanical Properties of Bamboo, a Natural Composite," Fibre Science and Technology, Vol. 14, (1980-81) pp. 319-322.
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Section 2 Microstructures – ceramics and advanced materials
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Computational Methods and Experiments in Materials Characterisation III
43
Experimental study on fracture behaviour of polycrystalline ceramics under shock loading J. T. Zhou & G. W. Yao School of Civil Engineering and Architecture, Chongqing Jiaotong University, People’s Republic of China
Abstract Plate impact experiments and impact recovery experiments were performed on 92.93wt% alumina ceramics using a 100-mm-diameter compressed-gas gun. Free surface velocity histories were traced by a VISAR velocity interferometer. There is a recompression signal in free surface velocity, which shows evidence of a failure wave in impacted alumina. The failure wave velocities are 1.27km/s and 1.46km/s at stresses of 7.54GPa and 8.56GPa respectively. It drops to 0.21km/s after the material released. SEM analysis of recovered samples showed the transit of intergranular microcracks to transgranular microcracks with increasing shock loading. The failure wave in impacted ceramics is a continuous fracture zone which may be associated with the damage accumulation process during the propagation of shock waves. Keywords: plate impact experiment, alumina ceramics, failure wave, dynamic fracture, SEM.
1
Introduction
Since failure waves were first observed propagating in glass rods under dynamic compression by Bless et al [1] and in glass plates under high-pressure impulsive loading by Rasorenov et al [2], a series of plate impact experiments, bar impact experiments and impact recovery experiments have been performed on a range of glasses under various impact stresses [3–6]. These experiments show the failure fronts are generated in silicate and filled glasses at a stress near or below their Hugoniot Elastic Limits and propagate from impact surface to interior at velocities in the range of 1.5–2.5km/s. The failed glass has lower acoustic impedance and sound speed than the intact material. The failed layer nearly loses WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/MC070051
44 Computational Methods and Experiments in Materials Characterisation III complete tensile strength, and its shear strength is significantly degraded. The longitudinal stress and transverse strain remain constant cross the failure front, but the transverse stress and longitudinal strain are increasing with time in the region behind the failure front. All these variations of material properties across this front provide experimental evidences for the existence of a failure wave phenomenon for glass under plate normal impact loading. In recent years, there also have been some wide researches made into other brittle materials. Bourne et al [7] and Zhang et al [8] have extended these studies to the polycrystalline ceramics alumina, silicon carbide and titanium diboride, gabbro and 3D-C/SiC composite materials and have postulated similar impact induced fracture front in these brittle materials. There also been recent discussion of the phenomenon of gradual failure behind the elastic wave in mortar by Grote [9]. In the work presented, we have conducted a matrix of plate impact experiments on alumina monitored by VISAR focused on the rear surface of the sample in seeking to pursue the failure wave in brittle materials other than glass.
2
Plate impact experiments
Plate impact experiments on alumina specimens were carried out on the 100mm light gas gun. Impact velocities were measured to an accuracy of 1.5% using three pairs of electric signal pins at different distances away from the impact surface. The copper flyers and targets were circular with different diameters of 94mm and 100mm, with their two cut faces polished in order to ensure smoothness of the impact and measurement area. Free surface velocity histories were traced using VISAR with a fringe constant 101m/s/fringe and a measured response time 1.5ns. The free surface of target was polished and aluminized with a layer 5000 angstroms in thickness to strengthen the reflection of incident laser (see fig. 1, which shows a schematic of the experimental setup). The impact recovery experiments were also performed to study micro-structures of impacted samples. Cushion rubber was filled in target room to absorb the dynamic energy of flyer and target. The flyer and target will be embedded in rubber.
Figure 1:
Plate impact experimental schematic with VISAR.
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The alumina samples consist of 92.93wt% alumina by weight and a small amount of silicon dioxide, calcium oxide and lanthana analyzed by energy spectrum. The relevant parameters of the specimens are density 3896kg/m3, longitudinal sound speed 9.259km/s, and a shear wave velocity 5.557km/s respectively. The longitudinal sound speed in copper flyer is 4.60km/s and the thickness of flyers and targets range from 4.0mm to 6.1mm. The acoustic impedance ratio of flyer and target is 1.14, then long enough duration pulse generates at the impact surface to avoid the unloading wave propagating into targets from flyers. A summary of experimental conditions and results are presented in table 1. Table 1:
Parameters of plate impact experiments.
Parameters
Impact velocity (m/s)
Impact stress (GPa)
Impactor Thickness (mm)
Target Thickness (mm)
Shot 405
397.8
7.54
4.14
6.08
Shot 425
448.8
8.56
6.10
6.04
Figure 2:
Free surface velocity profiles of shots 405 and 425.
Fig. 2 shows reduced VISAR data by software from the experiments of shots 405 and 425 under shock stresses 7.54GPa and 8.56GPa. These profiles indicate that the alumina specimens did not spall. The distinct feature of note on the traces is the slight recompression signal pointed on top of the stress wave. This velocity jump behaves beyond the elastic behaviours because there is not reflected tensile pulse recorded in the profiles and the time interval between the start of free surface motion and the moment of this reloading signal is less than the elastic wave reverberation time in the sample. And alumina does not behave plasticity in macroscope as typical brittle material, so this inelastic behaviour does not characterized plasticity though the free surface velocity profile has twowave structure. The additional weak compression wave is associated with a WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
46 Computational Methods and Experiments in Materials Characterisation III reflection from a layer of material which has dynamic impedance lower than that of the intact alumina, and this material layer bordering the interface does not pass tensile stresses. So we conclude that the shock-compressed alumina is comminuted behind this interface. This phenomenon is akin to the failure wave which has been observed to occur in glasses under shock compression. On the assumption that the moving speed of failed layer boundary is the failure wave velocity CF, a simple evaluating equation for CF has been derived as the following (see fig. 3, which shows diagram of elastic wave and failure wave propagating). The thickness of the failed layer hf is determined from the measured time interval of ts through the equation
Figure 3:
Propagation of Compression, Rarefaction and Failure waves.
1 (1) h CP ts 2 where h is the sample thickness and CP is the longitudinal wave speed in alumina specimen. Then the failure wave velocity CF can be estimated by hf (2) CF h CP t s 2 It implies that the failure wave has propagated at a velocity of 1.27km/s in shot 405 and 1.46km/s in shot 425 on average before the moment tf. The free surface velocity history from VISAR measurements has shown that the failure front propagates at a speed much lower than longitudinal stress wave velocity, depending on the peak shock stress. The free surface velocity profile from shot 425 is analyzed further in expanded region and there is another smaller recompression signal observed following the first (see fig. 4, which shows second smaller recompression indicated by a narrow). This can be explained if the reflected rarefaction wave from rear surface is reflected again on the failure layer and then reflected on rear surface where a weak jump of velocity is produced at the same time. During the hf
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time interval ts1 of two recompression signals, the distance of failure layer expanded can be determined through 1 (3) 'h f h f 1 h f h CP ts1 h f 2 Then the average velocity CF1 of failure wave propagating from the moment tf to tf1 can be estimated from the measured time interval of ts1 by 'h f (4) CF 1 (ts ts1 ) 2 This implies that the failure wave has propagated at an average velocity of 210m/s in shot 425 following unloading by the reflected rarefaction wave. This unloading slows down and even eventually arrests the failure procedure in material and results in great lowness in the failure wave propagating.
Figure 4:
3
Expanded region of free surface velocity profile of shot 425.
SEM for samples
To explain the failure process of shock-compressed polycrystalline ceramics in mesoscope, initial and soft-recovered samples were scanned by S530 scanning electron microscope. Each fragment was cut in the centre along a plane parallel to impact surface with 0.2mm distance to impact surface. Fig. 5(A) shows the micro-structures of initial 92.93wt% alumina. Grains and intergranular pores distribute randomly with diameters 1-15µm. Intergranular glassy phase is distinct in compact area. And initial porosity is 5.68% determined by metallurgical analysis software. Pores and glasses weaken mechanical capabilities and these heterogeneous meso-structures result in high singularity in stress distribution. Fig. 5(B) shows intergranular microcracks in recovered sample after 5.76GPa loading and Fig. 5(C) shows transgranular microcracks in recovered sample after 8.65GPa loading. Microcracking transmits from intergranular to transgranular with increasing impact compression. Alumina grains begin to fragment with transgranular microcracks and original pores begin to collapse. And discontinuous microcracks induce dilation after unloading. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
48 Computational Methods and Experiments in Materials Characterisation III
Figure 5:
SEM micrographs of (A) initial and recovered alumina samples under (B) 5.76 GPa and (C) 8.65 GPa shock loading.
The polycrystalline ceramics are heterogeneous in mesoscope. There are many pores, microcracks and other defaults inducing high singularity in stress distribution. Once the local stress exceeds the threshold, the original microcracks will grow up along the pores and crystal boundaries and new microcracks will nucleate in ceramics under shock loading. The original and nucleated microcracks grow up and expand, then excite the neighbour microcracks nucleation and expansion. So the failure wave appears and propagates from impact surface to interior of specimen, and it propagates at higher velocity under stronger shock loading. In essence, the failure wave is characterized by moving damage or fracture zone of material which presented by microcracking system in mesoscope, and it is also called after fracture wave by Resnyansky et al [12].
4
Summary
Ceramics are extensively applied to national defence engineering and military science as effective armour defence with their excellent physical and mechanical capabilities, especially higher dynamic elastic threshold and acoustic velocity than metals. We performed plate impact experiments of 92.93 wt% aluminas with 100-mm-diameter compressed-gas gun and the free surface velocities were traced by VISAR. There is a reloading signal observed in free surface velocity which indicates the failure wave propagation behind the elastic precursor. The failure wave propagates at a speed much lower than longitudinal stress wave velocity, depending on the peak shock stress. And the failed layer has much lower dynamic impedance than that of the intact material. The unloading by the reflected rarefaction wave slows down and even eventually arrests the failure front propagating in alumina. SEM analysis of intact samples shows heterogeneous meso-structures, and SEM analysis of soft-recovered samples shows transit of intergranular microcracks to transgranular microcracks with increasing shock loading. The failure wave is a continuous fracture or damage front which may be associated with nucleation and expansion of microcracks from impact surface to interior during the propagation of shock waves. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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References [1] [2] [3] [4] [5]
[6]
[7] [8] [9] [10] [11] [12]
Bless, S.J., Brar, N.S. & Rosenberg Z., Failure of Ceramic and Glass Rods under Dynamic Compression. Shock Compression of Condensed Matter1989, eds. S.C. Schmidt, APS: New Mexico, USA, pp. 939-942, 1990. Rasorenov, S.V., Kanel, G.I., Fortov, V.E., & Abasehov, M.M., The Fracture of Glass under High-pressure Impulsive Loading. High Pressure Research, 6, pp. 225-232, 1991. Rosenberg, Z., Bourne, N.K., & Millett, J., Direct Measurements of Strain in Shock-loaded Glass Specimens. Journal of Applied Physics, 79, pp. 3971-3974, 1996. Bourne, N.K., Millett, J., & Rosenberg, Z., On the Origin of Failure Waves in Glass. Journal of Applied Physics, 81, pp. 6670-6674, 1997. Millett, J., Bourne, N.K., & Rosenberg, Z., Measurements of Strain in a Shock Loaded, High-density Glass. Shock Compression of Condensed Matter-1999, eds. M.D. Furnish, AIP: Utah, USA, 505, pp. 607-610, 2000. Cazamias, J.U., Fiske, P.S., & Bless, S.J., Sound Speeds of Post-failure Wave Glass. Fundamental Issues and Applications of Shock-Wave and High-Strain-Rate Phenomena, EXPLOMET 2000, eds. K.P. Staudhammer, New Mexico, USA, pp. 173-179, 2000. Bourne, N.K., Millett, J., Pickup, I., Delayed failure in shocked silicon carbide. Journal of Applied Physics, 81(9), pp. 6019-6023, 1997. Zhang, Q.M., Huang, F.L., & Han, L.M., Failure Wave Motion of 3DC/SiC Composites Subjected to Shock Compression. Chinese Science Bulletin, 45, pp. 408-411, 2000. Grote, D.L., Park, S.W., & Zhou, M., Experimental Characterization of the Dynamic Failure Behavior of Mortar under Impact Loading. Journal of Applied Physics, 89, pp.2115-2123, 2001. Kanel G.I., Bogatch A.A., Razorenov S.V., & Zhen Chen, Transformation of shock compression pulses in glass due to the failure wave phenomena. Journal of Applied Physics, 92(9), pp. 5045-5052, 2002. Zhao J.H., Sun C.W., Zhao F., Duan Z.P., et al, Velocity overshoot of rear free-surfaces of glass under impact. Explosion and Shock Waves, 22(1), pp. 72-78, 2002. (in Chinese) Resnyansky, A.D., Romensky, E.I., & Bourne, N.K., Constitutive Modeling of Fracture Waves. Journal of Applied Physics, 93, pp. 15371545, 2003.
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Blocking and self-locking of superdislocations in intermetallics B. A. Greenberg1 & M. A. Ivanov 2 1
Institute of Metal Physics, Ural Division, Russian Academy of Sciences, Ekaterinburg, Russia 2 Institute of Metal Physics, National Academy of Sciences, Kiev, Ukraine
Abstract Superdislocations are carriers of plastic deformation in intermetallics. A large translation vector, different types of stacking faults and antiphase boundaries determine the diversity of dislocation configurations, both glissile and blocked ones. A significant point is that blocked superdislocations, which are formed due to re-splitting of glissile superdislocations or rearrangement of the superpartial dislocation core, have the lowest energy. A new concept about the possibility of thermally activated blocking of superdislocations in the absence of external stresses (self-locking) was proposed. A sufficiently general thermally activated process, which causes the extension of a dislocation in a preferred direction and constitutes a necessary step in dislocation transformations leading to blocking, was revealed. By its nature, this process represents the flip of a dislocation from a shallow valley to a deep valley of the potential relief. Reasons for the multivalley relief and the presence of preferred directions vary for dislocations of different types in different materials. Consecutive stages of the rearrangement of an initial dislocation include the formation of a double kink and its subsequent reorientation along a preferred direction. The driving force of the process was calculated and conditions for its realization in the cases of perfect, superpartial and partial dislocations were formulated. An experimental proof of the proposed concept was obtained: self-locking of dislocations, which were induced by preliminary deformation, was detected in Ni3(Al, Nb) and TiAl during no-load heating. Keywords: dislocations, plastic deformation, potential relief, shallow valley, deep valley, dislocation blocking, self-locking, no-load heating.
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52 Computational Methods and Experiments in Materials Characterisation III
1
Introduction
Although dislocation blocking mechanisms, which determine the deformation behavior of materials, are diverse, they can be divided into two groups. In the first group point blocking is due to pinning centers. In the second group linear blocking is explained by different factors, such as dislocation reactions, collisions of dislocations with domain boundaries and, finally, dislocation inherent transformations [1]. Such transformations, which are inherent in dislocations as linear defects, just represent the subject of this study. They are accomplished without participation of other dislocations and result from the rearrangement of the core of a perfect dislocation (BCC metals, TiAl – a single dislocation) or a partial dislocation (semiconductors). In some high-temperature intermetallics such transformations also result from re-splitting of a perfect or a superpartial dislocation [2]. Regardless of transformation details, a common feature is that the dislocation energy is gained at the expense of the dislocation mobility: a glissile dislocation turns to a dislocation barrier, which either remains indestructible or, under certain conditions, can re-transform to a glissile configuration. The barrier axis is the preferential direction along which the transformation to a low-energy configuration is realized. As a result, the potential relief is a multi-valley one for a dislocation: deep valleys extend in the preferential direction and shallow valleys go in other directions (fig. 1). Valleys of different depth along different directions can be distinguished (unlike fig. 1) in a three-dimensional display of the potential relief.
Figure 1:
2
Schematic image of the potential relief; shallow valleys and deep valleys of one type (a) or two types (b).
Flip-process
The flip of a dislocation from a shallow to a deep valley of the potential relief, which causes the extension of the dislocation in the preferential direction, is a sufficiently general thermally activated process and constitutes a necessary step in dislocation transformations leading to blocking. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
Computational Methods and Experiments in Materials Characterisation III
Figure 2:
53
Consecutive stages of the rearrangement of the initial dislocation whose direction is close to the preferential direction: a – double kink; b – reorientation in the preferential direction.
The flip process includes the formation of a double kink (fig. 2a) and its subsequent reorientation in the preferential direction resulting in the formation of an asymmetric kink (fig. 2b). The internal structure of the dislocation changes in the preferential direction and, hence, the dislocation energy decreases. Because this process takes place at different points along the dislocation line, the initial dislocation is broken down into long blocked segments. The flip process and the subsequent transfer from a deep to another deep valley ultimately determine the temperature dependence of the yield stress, Vy(T). If the release from deep valleys is possible, Vy(T) will exhibit a normal behavior. If such release is hampered (indestructible barriers), an anomalous trend of Vy(T) will be observed in certain conditions. According to Indenbom et al. [3], a double kink may be viewed as the nucleus of a "new phase" corresponding to the transition to a neighboring valley. We think that a chain [4] of asymmetric kinks rather than a single kink can be formed near the preferential direction (fig. 3a). This chain may be considered as a nucleus capable of transforming to a segment extended along the preferential direction and a multiple kink (fig. 3b). In any case, the extension of a dislocation in the preferential direction is a thermally activated process since it includes formation and propagation of kinks.
3
Nucleation and propagation of kinks
3.1 Perfect dislocations Let us consider a potential relief of the following form: shallow valleys and a deep valley in some preferential direction, with the deep valley separated from the nearest shallow valley by a potential barrier. We shall assume for simplicity that the initial direction and the preferential direction are almost parallel. The double kink consists of initial dislocation segments located in a shallow valley, a segment of the length d flipped to the deep valley, and single kinks connecting WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
54 Computational Methods and Experiments in Materials Characterisation III these segments. According to [5], the energy of the double kink can be written as the sum of the following contributions (with the corresponding signs): the double energy of a single kink; the work of the external stress V consumed for the formation of the double kink; and the interaction energy of the kinks. Furthermore, it is necessary to consider the change of the linear energy as the dislocation is transferred from a shallow valley to the deep valley. This contribution, which is connected with different depth of the valleys, was disregarded earlier and distinguishes the present study from other investigations. The critical configuration of the double kink, which is determined from conditions of the total energy extremum, has the length dc equal to
dc
Ka 2 , (ıba ǻE ) ǻE E0 Ev ,
(1) (2)
Here E0 is the energy of the dislocation in a shallow valley, Ev is the energy of the dislocation in the deep valley (both energies per unit length of the 2
dislocation), K kµb , P is the shear modulus, and k is a coefficient depending on the dislocation orientation. If the external stress is not applied, the unstable configuration, which causes dispersion of the kinks, appears, as can be seen from (1), due to an additional driving force proportional to ǻE . If ı = 0, the condition for the flip process, which causes autoblocking of the dislocation, is the inequality ǻE ! 0.
Figure 3:
Chain of asymmetric kinks (a) and its transformation (b).
Obviously, this driving force simultaneously counteracts the reverse transition from a deep valley to a shallow valley. Therefore, thermally activated formation of indestructible barriers can be expected during no-load heating. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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Self-locking is still possible if directions, along which shallow and deep valleys are extended, are not parallel, but the angles between them are not too large. However, the critical configuration is not formed at large angles, because the energy loss during the kink spreading is not compensated by the energy gain during the dislocation flip to a deep trap. Let us estimate, rather roughly, the possibility that the configuration, which appears after the double kink reorientation (fig. 2b), develops or, oppositely, collapses. We shall assume for simplicity that a single kink is perpendicular to the preferential direction. Then the condition of the self-locking is that the energy of the dislocation, which is a broken line and consists of a segment of the length d extended in the preferential direction and a single kink of the length h, is smaller than the energy of the initial rectilinear dislocation of the length l. This condition can be written as Ev d E0 h E0l . (3) Introduce the angle M between the preferential direction and the direction of the initial dislocation (fig. 2b). Using (2) and writing Ev as Ev
E0 'E
where 'E ! 0 is assumed, we obtain from (3):
E0 (1 tgM 1/ cosM) 'E .
(4)
Thus, the condition of self-locking has the form
'E / E0 !
cos M sin M 1 . cos M
(5)
, where It can be easily shown that the condition (5) is fulfilled at angles M M M is determined from the equation 'E / E0
cos M sin M 1 . cos M
(6)
is the limiting angle for auto-locking. If M ! M , this process is Actually, M impossible, naturally in terms of the given model and the adopted approximations. 3.2 Partial and superpartial dislocations It is possible that not perfect, but partial dislocations sink into a deep valley and just partial dislocations have the preferential direction. In this case, the development of the partial dislocation in the deep valley requires an additional energy proportional to the area of the stacking fault. Then, instead of (3), the condition of self-locking takes the form ( Ev E0 tgM 1/ 2JdtgM)d ( E0 / cosM)d , (7) where J is the stacking fault energy (per unit area). The condition (5) changes correspondingly:
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56 Computational Methods and Experiments in Materials Characterisation III
· 1 § Jd (8) ) 1¸ . ¨ cos M sin M(1 cos M © 2 E0 ¹ by the relationship (6), then at M ! M and any d If we introduce the angle M 'E / E0 !
the inequality
'E / E0
· 1 § Jd ) 1¸ , M ! M ¨ cos M sin M(1 cos M © 2 E0 ¹
(9)
is fulfilled. This means that the condition (8) does not hold in this case and the flip of the similarly to the partial dislocation to the deep valley is impossible at M ! M perfect dislocation considered above. , the condition (8) holds at small values of the segment length d. If M M However, unlike for perfect dislocations, this condition no longer holds for partial dislocations as the length d increases. The segment length d J , at which the condition becomes invalid, is defined by the relationship
'E / E0
· 1 § 1 J d J ) 1¸ , M M . (10) ¨ cos M sin M(1 cos M © 2 E0 ¹
The existence of the physically reasonable solution of the equation (10) for d J at a preset value of the angle M depends on the relationship between 'E and Ja . To demonstrate this, we shall introduce the critical kink length
hJ
d J tgM . Obviously, the condition hJ / a ! 1 should be fulfilled for the
kink to exist in reality. Using hJ , the equation (10) can be rearranged to the form
hJ a
'E / E0 (cosM sin M 1) / cosM , M M Ja / 2 E0
(11)
Let us consider the case when
'E Ja .
(12)
hJ / a 1, M M .
(13)
Then from (11) we have Hence, if the relationship (12) is fulfilled, a physically reasonable solution of the equation (11) is unavailable, i.e. self-locking does not take place. Self-locking is possible only if the condition 'E ! Ja (14) is fulfilled. Moreover, it can be easily shown that the additional condition M min{'E / E0 , M } (15)
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should be met. Therefore, if the inequality (14) is fulfilled, the extension of segments, whose orientation satisfies (15), becomes possible. The above expressions also hold when a preferential direction exists for superpartial dislocations connected by the APB band. It is assumed as before that kinks are formed independently (inconsistently) in each of the superpartial dislocations making up the superdislocation. Therefore, the nucleation and the propagation of kinks are determined by the relationship between ǻE and the APB energy in the corresponding plane.
4
Examples
4.1 Blocking of a superpartial dislocation located initially in the cube plane (Ni3Al) The initial superpartial dislocation is not splitted and, therefore, recombination is not required. The superpartial dislocation is blocked due to octahedral splitting. Since octahedral splitting is athermal, we have the only process that requires thermal fluctuations, namely the extension of the superpartial dislocation in the preferential direction. The preferential direction is a direction of the <101> type parallel to the line of intersection between the cube and the octahedral plane. The energy gain from octahedral splitting determines ǻE and in the relationship (2) E0 is the constricted dislocation energy and Ev is the splitted dislocation energy. It is easily shown that ǻE can roughly be written as
ǻE # ȥ(ȕ1 , ȕ 2 ) ln ȥ(ȕ1 , ȕ 2 )
d csf Ȗ csf d csf r0
ȥ(ȕ1 , ȕ 2 ) (ln
µ e1e2 (1 Q )s1s 2 2ʌ(1 Q )
d csf 1) r0
(16)
Here Ȗ csf is the energy of a complex stacking fault, d csf is the equilibrium splitting width of the superpartial dislocation, e and s denote respectively the edge and the screw component of the Burgers vector ȕ of the partial dislocation,
r0 is the dislocation core radius, and v is the Poisson ratio. for self-locking is determined, as before, from the The limiting angle M relationship (6). In this case, the energy J should be replaced by the APB energy Ȣc in the cube plane in the inequality (7) and the subsequent expressions containing J . If the relationship
'E ! Ȣca ,
(17)
which is analogous to (14), is fulfilled, the self-locking process becomes possible.
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58 Computational Methods and Experiments in Materials Characterisation III Indeed, experiments on no-load heating of Ni3(Al, Nb) single crystals predeformed at a high temperature demonstrated that superdislocations, which initially glided in the cube plane, turned to dislocation barriers [6, 7].
4.2 Blocking of a superpartial dislocation located initially in the octahedral plane (Ni3Al) A superpartial dislocation is blocked due to a series of consecutive transformations, including the cross slip of the superpartial dislocation from the octahedron to the cube plane, and its octahedral splitting. At each stage the superpartial dislocation extends in the preferential direction of the <101> type, which is parallel to the line of intersection between the octahedron and the cube plane of the cross slip. The effective force
K (effb,nc)
providing the cross slip of the superpartial
dislocation has the form [8]:
K (effb ,nc)
bıf (ĮȢ Ȣc) ,
(18)
where Į 1/ 3 and f is the coefficient dependent on the Schmid factors. It readily follows from (18) that the cross slip of a superpartial dislocation is possible at V 0 too. Therefore, self-locking of a superpartial dislocation, which is initially located in the octahedral plane, is possible if two conditions ĮȢ - Ȣc > 0 , (19)
'E ! Ȣca (20) are fulfilled simultaneously. The condition (19) ensures the transfer of a superpartial dislocation to the cube plane. If (19) is fulfilled, the component ĮȢ of the elastic repulsion force in the cube plane due to another superpartial dislocation is larger than the surface tension Ȣc . The condition (20) is responsible for the subsequent extension of the superpartial dislocation along the line of intersection between the cube and the octahedral plane. Indeed, experiments on no-load heating of Ni3(Al, Nb) single crystals predeformed at a low temperature showed that superdislocations, which initially glided in the octahedron plane, transformed to dislocation barriers [6, 7]. 4.3 Blocking of a single dislocation (TiAl) A single dislocation in TiAl is not connected with either the APB band or the stacking fault band, or another dislocation capable of initiating its blocking. The transfer of a single dislocation from a shallow to a deep valley corresponds to the dislocation core rearrangement [9]. Considering the covalent-like character of TiTi bonds, one may think that a screw dislocation with a narrow core has the lowest energy, because such bonds can be restored thanks to a constricted core. The preferential direction is the <110] direction parallel to the Burgers vector of the single dislocation. Deep valleys are located along the said <110] direction. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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In actuality, the situation is more complicated because several types, rather than one type, of deep valleys are available. The potential relief (fig. 1b) was reconstructed [2, 10] using data on the nonmonotonic temperature dependence of the yield stress Vy(T) in TiAl. Of course, the reconstruction of the potential relief is rough, but it reflects the variety of the core structure. Different forms of the core of a single dislocation in TiAl were obtained from computer simulation, specifically ab-initio simulation [11]. Several types of blocked core structures were revealed in each case. Experiments on no-load heating of pre-deformed TiAl were performed. Only curvilinear dislocations were observed after deformation at room temperature. Blocked single dislocations were observed after subsequent no-load heating.
4.4 Extension of a dislocation in the preferential direction in elementary semiconductors Preferential directions are those of the <101> type with deep valleys of the Peierls potential relief for 30-deg and 90-deg partial dislocations. The difference ǻE is determined by the decrease in the energy of the partial dislocation core, resulting from its reconstruction. The possibility of a partial dislocation extending in crystallographic directions depends on which of the relations (12) or (14) between ǻE and Ja is fulfilled. All known experiments (see, for example, [12, 13]), which revealed segmentation of dislocations in preferential directions, were performed under a load. The extension in crystallographic directions was not detected after no-load heating of Si crystals [14]. One may think therefore that the relationship (12) holds in elementary semiconductors.
5 Summary and conclusion Some thermally activated process, which is a necessary step of dislocation transformations, was revealed. This process represents the flip of a dislocation from a shallow valley of the potential relief to a deep valley located along the preferential direction. The flip process involves the formation of a double kink and its subsequent reorientation. Conditions for realization of the flip process at a zero external stress, which ensure self-locking of dislocations, were determined. Theoretically predicted self-locking of dislocations was confirmed in experiments on no-load heating of intermetallics after their preliminary deformation. An explanation was proposed why blocking of partial dislocations in elementary semiconductors is impossible without an external stress.
Acknowledgements This study was performed under the State contract No. 02.467.11.2007 and supported by a grant from RFBR (project No. 04-03-96008) and the program of the Presidium RAS (project No. 10).
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60 Computational Methods and Experiments in Materials Characterisation III
References [1] [2] [3]
[4] [5] [6]
[7]
[8] [9]
[10] [11] [12] [13] [14]
Escaig, B., Dislocation splitting and the plastic glide process in crystals. J. de Physique Suppl., 35(7), pp. 151-166, 1974. Greenberg, B. A. & Ivanov, M. A., Microstructure and Deformation Behavior of Ni3Al and TiAl Intermetallic Compounds, Ural Div. Rus. Akad. Sci: Ekaterinburg, pp. 88-102, 2002 (in Russian). Indenbom, V. L., Petukhov, B. V. & Lothe, J., Dislocation motion over the Peierls barrier (Chapter 8). Elastic Strain Fields and Dislocation Mobility,. eds. V.L. Indenbom & J. Lothe, Elsevier Science Publishers B.V. pp. 491-516, 1992. Seeger, A. & Schiller P., Bildung und diffusion von kinken als grundprozess der versetzungsbewegung bei der messung der inneren reibung. Acta Met., 10(4), pp. 348-357, 1962. Duesbery, M. S., The influence of core structure on dislocation mobility. Phil. Mag., 19(159). pp. 501-526, 1969. Greenberg, B. A., Antonova, O. V., Ivanov, M. A., Patselov, A. M. & Plotnikov, A. V., Some features of formation and destruction of dislocation barriers in intermetallics. II. Observation of blocking superdislocations after no-load heating. The Physics of Metals and Metallography, 102 (1) pp. 69-76, 2006. Greenberg, B. A., Ivanov, M. A., Antonova, O. V., Patselov, A. M. & Plotnikov, A. V., Deformation behavior of intermetallics: models and experiments. Proc. of the 4th Int. Conf. On Mathematical Modelling and Computer Simulation of Material Technologies. Ariel, Israel, 1, pp. 122131, 2006. Greenberg, B. A. & Ivanov, M. A., Some features of formation and destruction of dislocation barriers in intermetallics. I. Theory. The Physics of Metals and Metallography, 102 (1), pp. 61-68, 2006. Greenberg, B. A., Anisimov, V. I., Gornostirev Yu. N., Taluts G. G. Possible Factors Affecting the Brittleness of the Intermetallic Compound TiAl. II. Peierls Manyvalley Relief. Scripta Metall., 22 (6), pp. 859-864, 1988. Greenberg, B. A., Antonova, O. V., Volkov, A. Yu. & Ivanov, M. A., The non-monotonic temperature dependence of the yield stress in TiAl and CuAu alloys. Intermetallics, 8, pp. 845-853, 2000. Woodward, C. & Rao, S. I., Ab-initio of (a/2<110] screw dislocations in J -TiAl. Phil. Mag., 84 (3-5), pp. 401-413, 2004. Alexander, H., Dislocations in covalent crystals (Chapter 35). Dislocations in Solids, ed. F.R.N. Nabarro, Elsevier Sci. Publ. B.V. pp. 113-234, 1986. Rabier, J., George, A. Dislocations and plasticity in semiconductors. Revue Phys. Appl., 22(11), pp. 1327-1351, 1987. Patel, J. R. & Kimerling, L. C., Dislocation defect states in Si. J de Physique. Suppl., 40(6), pp. 67-70, 1979.
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The properties and performance of polymer fibre reinforced bituminous mixtures I. Kamaruddin & M. Napiah Department of Civil Engineering, Universiti Teknologi PETRONAS, Malaysia
Abstract The low tensile strength of bituminous mixtures has been recognized as a source of its poor performance, particularly that which relates to cracking. Laboratory investigations into improving their tensile properties have been performed utilizing polypropylene and polyester fibres which were added to Hot Rolled Asphalt (HRA) bituminous mixtures as partial replacement of Ordinary Portland Cement (OPC) used as the filler material. The incorporation of the polymer fibres into the bituminous mixtures altered the rheological properties and behaviour of the resulting binder whilst resulting in a higher optimum bitumen content for the mixture. Laboratory tests showed that the fibres reduced the density, stability and stiffness of the resulting mixture while increasing its porosity and permeability. Bituminous mixtures containing the fibres displayed lower susceptibility to moisture induced damage. Even though these mixtures have a higher void content than the base mixture, the additional bitumen in the fibre mixtures increased the film thickness on the aggregate particles thus affording greater protection from moisture. The addition of the fibres into the bituminous mixtures caused a slight decrease in the tensile strength and a slight increase in the tensile strain (elongation) at failure, indicating that the additional bitumen added flexibility or extensibility to the mixtures. This was manifested in the higher toughness and energy that was obtained in the mixtures, thus improving its resistance to cracking. This was supported by the fatigue tests which showed improved fatigue performance of the mixtures. The fatigue properties of the fibre mixtures were not enhanced at low strain levels; but at high strain levels, the fibre mixtures provided a far superior performance than the base mixture, making it appealing for use as a base-course in highway construction. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/MC070071
62 Computational Methods and Experiments in Materials Characterisation III
1
Introduction
Excessive permanent deformation and cracking are generally accepted as the main forms of distress in bituminous road pavements. While permanent deformation occurs predominantly at elevated temperatures, thermal cracking is normally a low temperature phenomenon. In addition to temperature, cracking can also be brought about by traffic loading. Load associated fatigue cracking is the phenomenon of fracture as a result of repeated or fluctuating stresses brought about by the traffic loads. Traffic loads can cause a pavement structure to flex and the maximum tensile strain will occur at the base of the bituminous layer. Cracking occurs when the thermally induced tensile stresses together with stresses caused by traffic, exceeds the tensile strength of the material. If the structure is inadequate for the imposed loading conditions, the tensile strength of the material will be exceeded and cracks are likely to initiate, which will be manifested on the surface of the pavement. As a result, it is generally assumed that there is a significant reduction in the load distribution capacity within the pavement. This paper describes and presents the results of a laboratory investigation to assess the influence of polymer fibres on the properties and performance of Hot Rolled Asphalt (HRA) bituminous mixtures.
2
Materials used in the investigation
2.1 Mineral aggregates, filler and bitumen Limestone aggregates and Ordinary Portland Cement (OPC) filler and a binder of nominal penetration 50 were used in this study. Some relevant properties of these materials are shown in Table 1. Table 1:
MATERIAL
Properties of the mineral aggregates, filler and bitumen used in the study. PERCENTAGE BY WEIGHT (%)
RELATIVE DENSITY
35
2.75
0.47
55
2.65
1.37
10
3.15 Softening Point (˚C) 48.5
Penetration Index (PI) -0.37
Coarse Aggregate Fine Aggregate (Sand) Filler OPC Bitumen
Penetration (dmm) 52
ABSORPTION (%)
BS SPECIFICATION BS 594:Part 1:1992 Table 3, Type F Wearing Coarse Designation 30/14 BS 4699:1985
2.2 Synthetic fibres Two types of synthetic polypropylene and polyester fibres were used in this study. The fibres were used as a partial replacement of the filler, on an equal volume basis, at two different concentrations of 0.5% and 1% filler/bitumen ratio WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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by weight of mix. The fibres; in chopped form; were the by-products of the textile industry and thus their potential use was desirable on environmental grounds. Some characteristics of the fibres used are shown in Table 2. In order to maintain thermal stability when using the polypropylene fibres, it was decided that the mixing temperature during the preparation of the HRA mixtures should not exceed 140˚C and compaction be done at 130˚C. Table 2: FIBRE TYPE
SPECIFIC GRAVITY
Characteristics of fibres used. DENIER
LENGTH (mm)
AVERAGE DIAMETER (µm)
Polypropylene 0.91 6 6 22* (PP) Polyester (POL) 1.41 3 6 17* * Values obtained from 20 readings including a light microscope at 400x magnification.
3
DEGRADATION TEMPERATURE § 160 – 170 § 250 – 260
Engineering properties of bituminous mixtures
The engineering properties of the bituminous mixtures in this study are summarized in Table 3. Polyester and polypropylene fibres do not prove to be strength enhancing elements when incorporated in bituminous mixes. In fact, the tests conducted have shown that the addition of fibres reduces the strength properties of the bituminous mixes. The results obtained showed that the addition of fibres reduces the density, stability, compacted aggregate density and workability of the mixes. In addition, fibre reinforced bituminous mixes increase the porosity, voids in mineral aggregates, flow, and permeability characteristics of the resulting mixes. The degree of increase is greater with higher fibre concentrations. Table 3: Properties
Properties of bituminous mixtures at optimum bitumen content. Control
0.25% PP
Optimum Bitumen 7.35 7.48 Content (%) Density (gm/cc) 2.320 2.298 Compacted Aggregate 2.15 2.13 Density (gm/cc) Voids in Mineral 21.4 21.6 Aggregate (%) Porosity (%) 4.75 4.90 Permeability (E-3 cm/s) 10.0 11.5 Creep Stiffness (MPa) 12.2 11.4 Workability Index 8.5 8.2 Stability (kN) 12.1 11.2 Flow (mm) 3.90 4.17 Marshall Quotient 2.97 2.7 (kN/mm) *Note: PP – Polypropylene, POL – Polyester.
0.5% PP
1% PP
0.25% POL
0.5% POL
1% POL
7.76
8.44
7.54
7.90
8.68
2.260
2.236
2.292
2.252
2.226
2.09
2.05
2.12
2.08
2.04
22.4
22.6
22.0
23.3
24.3
5.60 8.0 9.8 7.7 9.8 4.62
5.80 6.0 9.0 7.4 8.4 5.7
5.35 14.0 11.8 7.8 11.4 4.2
6.30 12.0 10.9 7.2 10.6 5.0
6.00 6.0 9.2 7.0 9.4 6.18
2.05
1.45
2.78
2.10
1.50
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64 Computational Methods and Experiments in Materials Characterisation III The introduction of fibres into a HRA mix therefore does not act as a reinforcement for the mix nor do they enhance the strength of the mix but act to change the strain allowable in the mix. Incorporation of fibres into a HRA mix would also increase the optimum bitumen content. This increase being higher for increasing fibre concentration. In this study, the polyester fibre incorporated mix displayed higher demand for bitumen than the polypropylene fibre incorporated mix. The additional bitumen is necessary to coat the fibres which is similar to the addition of very fine aggregate. The proper quantity of bitumen for consistent coating of all the particles is different not only for different concentrations but also for different types of fibre which is likely due to the variation in the surface area of the different types of fibres.
4
Indirect tensile test on bituminous mixtures
The indirect tensile mode of testing can be used to establish the tensile and structural properties of bituminous mixtures. This test has been used widely by Kennedy and Hudson [6], Kandhal [4] and Wallace and Monismith [10] amongst others. The method has been standardized by both the BSI [2] and the ASTM [1]. The tensile characteristics of bituminous mixtures are evaluated by loading the vertical diameter of a Marshall specimen with a single or repeated compressive load acting parallel to and along the vertical diametrical plane of the specimen. This loading configuration develops a relatively uniform stress perpendicular to the direction of the applied load and along the vertical diametrical plane, ultimately causing the specimen tested to fail by splitting along the vertical diameter. Table 4:
Tensile properties at optimum bitumen content.
Indirect Tensile Strength (MPa) Strain (mm/mm) Static Tensile Modulus (MPa) Indirect Tensile Stiffness Modulus (MPa) Toughness (Joules/cc) Energy (Joules/cc)
5
Control 0.925 0.013 152.2
0.5 PP 0.87 0.0148 136.7
1 PP 0.83 0.0168 116.4
0.5 POL 0.78 0.0155 106.3
1 POL 0.73 0.0175 96.7
2100
2180
1970
2200
1950
0.0265 0.053
0.0295 0.0563
0.0328 0.06
0.0318 0.058
0.033 0.062
Indirect tensile properties
From the load deformation characteristics of the indirect tensile test, a number of parameters relating to the properties of the material tested were determined. These include the indirect tensile strength (ITS), strain at failure, tensile modulus of elasticity, toughness and tensile energy. These properties are summarised in Table 4. In making an overall comparison between the mixes, the control mix can be seen to exhibit greater tensile strength over the fibre-reinforced mixes. The WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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addition of fibres caused a reduction in tensile strength in the bituminous mixtures. The mixes were progressively weaker as the percentage of fibres increases. Mixtures incorporating the polypropylene fibres appear to exhibit higher strength than that of the polyester. The general trend that was observed suggests that the more difficult the fibres were to disperse within the mixtures, the weaker the mixtures were in tensile strength. The fibre-induced weakness in the mixtures may be due to the fibre strands having a tendency to remain together as bundles even with thorough mixing. Consequently, their inclusions in the mix could introduce ‘weak spots’ that resulted in a lower tensile strength. This behaviour also helps explain the superior performance of the polypropylene mixtures that undergo a more homogeneous mixing as compared to the polyester fibre mixes. In addition, due to the higher viscosity in the polyester-bitumen system, samples of the polyester incorporated mixtures may not have been compacted as well as those of the polypropylene-bitumen system. This resulted in a higher porosity in the polyester mixes which may be responsible for the lower strength obtained. The tensile strain (elongation) at failure provided a different scenario. The 1% fibre mixes showed higher strain capacity than those mixes that have 0.5% fibres as well as the control mix. The highest strains were recorded in the polyester fibre mixture. If the tensile strain at failure can be increased while not appreciably reducing the tensile strength, the mix will be made more flexible. This combination of properties may mean that more energy is required to produce cracking in the material. Increase in fibre concentration has also resulted in an increase in both the toughness and energy. The fiber incorporated mixtures exhibited greater toughness than the control mix. The polyester fibre mixtures showed greater increase in toughness than that of the polypropylene fibre mix. This behaviour is also true with regards to energy/volume in the mixtures studied. The higher toughness and energy that characterized the fibre mixes are indicative that these mixes are more resistant to cracking than the control mix. It can be deduced that the addition of fibres in bituminous mixtures reduces the strength properties of the mix but enhances their tensile properties. With this finding in mind, the use of fibre-reinforced mixes is deemed less suitable for use in the wearing course of pavements where the problem of rutting is most expected. They may however be more suited for use as a base-course where the problem of cracking is most likely to occur from the tensile stresses that build up at the base of the bound layer.
6
Effect of moisture
The damaging effects of moisture on the physical properties and mechanical behaviour of bituminous mixtures have been the focus of study for many years. Many laboratory tests have been developed in order to evaluate and quantify the amount of damage that is caused by water on bituminous mixtures. The most widely used laboratory method in conducting these tests appear to be the
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66 Computational Methods and Experiments in Materials Characterisation III immersion-mechanical tests which measures the changes in mechanical properties of the bituminous specimens after exposure to moisture. Typically the results are reported in terms of percentage retained strength of the specimens.
7
Wet-dry indirect tensile test
The wet-dry indirect tensile test was adopted as a principal measure of the bituminous mixture response to moisture damage. Most evaluations on moisture damage have been assessed quantitatively by mechanical tests in which such properties as loss of tensile strength or decrease of resilient and stiffness moduli have been measured. These are then given in the form of tensile-strength ratio and a moduli ratio, for which the tensile strength modulus of the dry specimens served as references. The tensile strength ratio (TSR) and modulus of elasticity ratio (MER) are dimensionless numbers used to represent the portion of tensile strength and modulus retained following moisture conditioning. Low values indicate high moisture damage. These ratios are given as: Tensile Strength Ratio, TSR
ITS wet ITS dry
Modulus of Elasticity Ratio, MER
MERwet MERdry
Lottman [7] used the static indirect tensile strength test to study the effect of moisture on bituminous mixtures and recommended a minimum tensile strength ratio of 0.7 to differentiate between stripping a non-stripping bituminous mixtures while Maupin [8] reported values of between 0.7 – 0.75. Ishai and Nesichi [3] cited values of 60-75 % retained stability values for roads and highway pavements and 75 % for airfield pavements as the quality criteria used in Israel. Kennedy and Anagnos [5] were also of the opinion that mixtures with less than 70 % retained strength are moisture susceptible and would require treatment.
Figure 1:
Indirect tensile strength ratios vs. bitumen content.
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Variations of the indirect tensile strength in wet and dry conditions with bitumen content allowed the determination of the indirect tensile strength ratio (TSR). This is shown in Figure 1. It can be seen from the figure that the TSR generally increases with an increase in bitumen content. The control mix showed that they are more vulnerable to moisture damage and reveal a higher level of moisture sensitivity as indicated by the lower tensile strength ratio as compared to the fibre-incorporated mixtures. A lower value of tensile strength ratio is indicative of more damage in the control sample. The control mix had the lowest TSR ranging from 69.5-80.4%. The TSR for the 1% PP mix ranges from 80.588.2% while that for the 1% POL mix ranges from 83.8-91.6%. The highest TSR were obtained in the 0.5% fibre mixtures. The 0.5% PP mix had a TSR ranging from 73.2-92.2% while the TSR for the 0.5% POL mix ranges from 88.2-98.2%. Fibres thus showed that they are good tensile reinforcement elements in bituminous mixtures while at the same time indicating that at certain concentrations, they can protect the mixtures from the weakening effect of water. More evidence of the decrease in susceptibility to moisture damage can be seen in the tensile modulus of elasticity ratio (MER) obtained for the various mixtures as shown in Figure 2. It is clear from the figure that the untreated control mixture experiences greater damage as a result of exposure to water. The MER values for the control ranged from 68.4-74.5% while the fibre modified mixes exhibited higher MER values: 73.6-84.2% (0.5PP), 80.3-89.3% (0.5POL), 71.9-76% (1PP) and 78.1-83.3% (1POL). As was the case with the TSR, the MER generally also showed higher resistivity of the polyester fibre mixtures over the polypropylene fibre mixtures to moisture damage.
Figure 2:
8
Modulus of elasticity ratio vs. bitumen content.
Fatigue relationship
Fatigue tests can be carried out in two principal methods, namely the constant stress tests where the stress level is kept constant throughout the test and the constant strain tests where the magnitude of the peak cyclic strain is kept WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
68 Computational Methods and Experiments in Materials Characterisation III constant throughout the test. Before the fatigue performance of a bituminous material can be assessed, the failure of the specimen tested must be consistently defined. Defining the failure criterion in the constant stress mode is relatively easy as the specimens undergo a relatively short crack propagation period. Hence, the failure point is taken as when the specimen has completely failed. However, in the constant strain mode of loading, the failure point is not very well defined, due to the large amount of crack propagation included in the test. An arbitrary point of failure must thus be assumed which is normally defined as the point when the specimen has reached a reduction in its initial stiffness of 50% or in a practical term is the point when the stress applied has been halved to achieve a constant strain. A linear relationship exists between the log of stress V, or strain H, and the log of the number of load repetitions, N f to failure. The failure criteria can therefore be expressed as Log. stress against log. load applications and log. strain against log. load applications. This can be written in the form: Log ( V or H ) = a + b log N f (1) For the strain controlled tests, the results are normally presented in the form:
Nf
§1· A¨ ¸ ©H ¹
b
(2)
while in the stress controlled tests, the results are presented in the form
Nf
§1· C¨ ¸ ©V ¹
d
(3)
where N f = Number of load applications to failure
V ,H
= Tensile strain or stress repeatedly applied load
A, b, C , d = Materials coefficients 9
Flexural beam fatigue test
The flexural beam fatigue test was used to study the fatigue behaviour of the mixtures. This involved a bituminous beam subjected to cyclic loading and resting on a rubber support which simulates the elastic foundation in a road structure. A crack was induced in the beam and the time and number of cycles taken for the cracks to propagate in the control and fibre-reinforced beams were compared. The test used is essentially a simple arrangement and does not simulate the more complicated stress regime at the crack tip that occurs during a load pulse caused by traffic loading. Despite this limitation, the test produces useful data in showing the benefit, or otherwise, of reinforcing bituminous mixtures with the synthetic fibres. The bituminous mixtures for the fabrication of the beams were prepared in the laboratory. The amount of materials required to produce a 500x100x100 mm WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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beam that have density close to that of the mix compacted with the Gyratory Testing Machine (GTM) were calculated and prepared.
10 Flexural beam fatigue test results The beam flexural fatigue test was conducted at ambient temperature and at three different stress levels to determine the relationships between initial strain and the number of load applications of failure. The results of the fatigue tests are summarized in Table 5. Figure 3 is a comparison of the fatigue behavior of the mixes at their optimum bitumen content. The results indicated that the beams that were reinforced with fibres showed superior fatigue properties when compared to the control beams. The effect of higher bitumen content in the fibre mixes must have contributed to the superior fatigue behaviour. Mixes with 1% fibre concentration displayed better fatigue behaviour than mixes with 0.5% fibre concentration. The polyester mixes exhibited better fatigue performance than the polypropylene mixes. This is in agreement with the findings where the polyester showed higher toughness and energy per unit volume than those of the polypropylene mixes in the indirect tensile tests. Table 5: Test Series and Binder Content (%) Control (OBC) 7.35% BC 0.5 PP (OBC) 7.76% BC 0.5 POL (OBC) 7.9% BC 1 PP (OBC) 8.4% BC 1 POL (OBC) 8.68% BC
Stress (MPa) 0.683 1.076 1.267 0.341 0.724 1.076 0.532 0.679 1.021 0.330 1.297 1.825 0.33 0.968 1.514
Summary of fatigue test results. Initial Strain (x 10-6) 172 233 306 165 351 882 202 381 475 215 750 1400 192 582 1072
Stiffness (GPa)
Porosity (%)
Fatigue Life (Nf)
3.971 4.618 4.141 2.067 2.063 2.131 2.634 1.782 2.149 1.535 1.729 1.304 1.719 1.663 1.412
4.92 4.88 4.68 5.49 5.57 5.74 5.29 5.33 5.04 4.29 4.08 3.38 4.16 3.95 4.08
169000 46520 13600 244610 18970 795 201780 25330 15160 170000 8000 800 576240 17340 3710
Figure 3 also indicated that at a high strain levels or low number of cycles to failure N, the fibre mixes exhibit superior performance. The fatigue lines for the fibre mixes are always higher than the control but these lines converge at high number of cycles to failure N and low strain. This means that the fibre reinforced HRA mixes will provide about the same fatigue performance as the control mixes at low strain levels, but at high strain levels, the fibre reinforced mixtures will provide superior fatigue performance. This may have a practical application in that for major highways with stiff bases and subgrades, reinforcement of bituminous mixes with fibres may not provide enhanced benefits of fatigue performance as compared to conventional HRA mixes. However, for secondary WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
70 Computational Methods and Experiments in Materials Characterisation III roads with weak bases and subgrades and thin pavement surfacings, the use of fibre-reinforced bituminous mixes as the surface course may be a viable alternative for increasing the pavement service life. All the fatigue beams were prepared using the same compactive effort. It should be pointed out that the air void contents (porosity) of the fibre-reinforced specimens were greater than those of the control specimens. The significance of this lies in the fact that the fatigue performance of bituminous mixes will usually suffer when the air voids contents is increased. It appears that fibres have the potential to increase fatigue performance of HRA mixes provided adequate compaction is achieved.
Figure 3:
Fatigue lines for control and fibre reinforced mixes at optimum bitumen content.
11 Conclusion Based on the work done, the following conclusions can be drawn: 1 Addition of synthetic fibres to the HRA bituminous mix decreases the density and increases the resulting air void content when the compactive effort remains the same. As the quantity of the fibre increases, the amount of air voids also increases. This is important from the stand point of achieving a desired density since mixtures with fibres would require greater compactive effort to achieve similar porosity than the conventional HRA mixtures 2 Based on a limited number of constant stress flexural fatigue test, it appears that the incorporation of synthetic fibres in Hot-Rolled Asphalt (HRA) mixtures have the potential of improving the fatigue performance of the mix. 3 Fatigue testing confirm the high strain capacity of the fibre-modified mixes owing to their higher bitumen content and the thicker bitumen film coating the aggregates. 4 The air void content of the fiber-modified specimens was higher than that of the control. This is significant in that the fatigue performance would usually suffer when the void content is increased. The test results indicate that the fibre WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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mixtures provide about the same fatigue performance as the control at low strain levels. At high strain levels however, the fibre-modified mixes provided superior fatigue performance, making it appealing for use as a base-course material in highway construction.
References [1] [2] [3] [4] [5]
[6] [7]
[8] [9] [10]
America Society for Testing of Materials, ASTM D 4123 – 82 (Reapproved 1987), Standard Test Method for Indirect Tension Test for Resilient Modulus of Bituminous Mixtures, ASTM, 1982 British Standard Institution, Draft for Standard Development for Determination of the Indirect Tensile Stiffness Modulus if Bituminous Mixture DD213, 1993 Ishai, I. and Nesichi, S., “Laboratory Evaluation of Moisture Damage to Bituminous Paving Mixtures by Long-term Hot Immersion”, Transportation Research Record No. 1171, 1988, pp. 12-17 Kandhal, P.J., “Evaluation of Six AC-20 Asphalt Cement by Use of the Indirect Tensile Test”, Transportation Research Record 712, 1979 Kennedy, T.W. and Anagnos, J.N., “Wet-Dry Indirect Tensile Test for Evaluating Moisture Susceptibility of Asphalt Mixtures”, Centre for Transportation Research, University of Texas at Austin, Research Report 253-8, Nov. 1984 Kennedy, T.W. and Hudson, W.R., “Application of the Indirect Tensile Test to Stabilised Materials”, Highway Research Record No. 235, Highway Research Board, 1968, pp. 36-48 Lottman, R.P., “Laboratory Test Method for Predicting Moisture-Induced Damage to Asphalt Concrete”. Transportation Research Record 843, Transportation Research Board, National Research Council, Washington D.C., 1982 Maupin Jr. G.W., “The Use of Anti-stripping Additives in Virginia”, Proceedings of the Association of Asphalt Paving Technologists, Vol. 51, 1982 Read, J.M. and Collop, A.C., “Practical Fatigue Characterization of Bituminous Paving Mixture”, Proceedings of the Association of Asphalt Paving Technologists, Vol. 66, 1997, pp. 74-108 Wallace, K. and Monismith, C.L., “Diametrical Modulus Testing on NonLinear Pavement Materials”, Proceedings of the Association of Asphalt paving Technologists, Vol. 49, 1980, pp. 633-652
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Hardness determination of EBiD-layers containing tungsten and cobalt T. Wich, T. Luttermann & I. Mircea Division Microrobotics and Control Engineering, University of Oldenburg, Germany
Abstract Electron Beam induced Deposition (EBiD) is a promising process technology for nano-structuring and -prototyping inside a scanning electron microscope (SEM). Firstly, the EBiD-process used for layer deposition is described. We have performed nanoindentation experiments on EBiD-layers with the purpose of determining their hardness. A special setup for nanoindentation inside the SEM is described. Before performing tests on EBiD-layers, calibration measurements on fused silica and sapphire were necessary. Hardness of the silicon wafer substrate and of the EBiD-layers has been also determined. The layers were small quadrates, with dimensions in the range of 20 x 20 µm2, with a thickness varying between 93 and 2256 nm. Nanoindentation tests on the deposited layers revealed values between 7.1 and 10.0 GPa for tungsten containing deposits and between 3.4 and 3.5 for cobalt containing deposits depending on the metal-content. Keywords: Electron Beam induced Deposition, hardness, nanoindentation.
1
Introduction
The effect of Electron Beam induced Deposition (EBiD) was first observed in 1933, by R.L. Stewart. At that time he noted that on surfaces under electron bombardment thin insulating films have been observed [14]. These insulating films have been regarded as an inevitable effect in evacuated electron tubes. Ennos et al. have conducted tests with different seals, grease materials, and oil for vacuum pumps, for determining their influence on the contamination thickness [6]. Based on the results of these tests, Christy developed in 1960 a theoretical model which can explain the deposition of polymer films under electron bombardment [2]. Later, these deposits have always been seen as a WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/MC070081
74 Computational Methods and Experiments in Materials Characterisation III possible deposition technology for manufacturing nanometer scale resists [1] or conducting lines on the nanometer scale [7]. However, about the mechanical properties of such deposits, only few data are available. They are of great interest, because, in the last years, many mechanical devices on the nanometer scale are developed using this technology e.g. bonding of nanowires [5, 18] or formation of AFM-super-tips [11]. Only few material data have been reported i.e. the elasticity modulus of deposits [9, 15] or their tensile or bending strength [9, 15]. The elasticity modulus has been determined by means of the bending test method. However, hardness of layer deposits manufactured by the EBiD process has only been determined for a paraffin precursor, resulting in hydrogenated amorphous carbon deposits [5], by means of the nanoindentation test method. After this introduction, in section 2 the EBiD-process is shortly explained. In section 3 the testing procedure is described, containing the description of the nanoindentation set-up, the necessary calibration of this set-up, the nanoindentation tests on EBiD-layers, the AFM measurements of the thickness of the layers, and the EDX analysis of their chemical content. In section 4, the results from these experiments on layer containing tungsten-hexacarbonyl (W(CO)6) and di-cobalt-octacarbonyl (Co2(CO)8) precursors are shown and discussed, as well as the observed futures of the imprints after nanoindentation tests are described and discussed. Finally, in section 5, conclusions have been drawn.
2 Processing of specimens by EBiD The indentation experiments in this work have been conducted on very thin layers, deposited from metallo-organic precursors by EBiD inside a scanning electron microscope (SEM). The substrate was a silicon wafer with a shape of a square and dimensions of 5 x 5mm². While scanning the substrate in the simple viewing mode of the SEM in a range of approx. 20 x 20µm², the evaporated precursor flux is directed to the deposition area using a capillary. A side view of the substrate surface with precursor flow area, scan area of the electron beam and the resulting deposition is shown in figure 1. The precursor molecules adsorb on the substrate surface and are decomposed into volatile and non-volatile fragments. The volatile fragments are pumped by the SEM’s vacuum system whereas the non-volatile parts form a solid layer in the scanned area on the substrate. In the literature [13] it has been shown that the secondary electrons generated by the primary electron beam when hitting the substrate activate the dissociation process. The influence of the heat is not clear and is still discussed in literature [3, 8]. The tested layers in this work were deposited from the metallo-organic precursors W(CO)6 (tungsten hexacarbonyl, CAS-Nr. 14040-11-0) and Co2(CO)8 (dicobalt octacarbonyl, CAS-Nr. 10210-68-1). In both cases, the exposure to the electrons leads to separation of volatile fragments (e.g. CO and CO2); the resulting solid deposition consists of tungsten or cobalt, respectively and remaining carbon and oxygen [4, 17].
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Figure 1:
Side view of the substrate surface with precursor flow area, scan area of the electron beam and resulting deposition.
Table 1:
Deposition parameters and precursors for the prepared layers. Testing procedure.
Specimen
Precursor
Co #1 Co #2 Co #3 W #1 W #2 W #3
Co2(CO)8 Co2(CO)8 Co2(CO)8 W(CO)6 W(CO)6 W(CO)6
Layer Deposition Beam dimensions, time, current, [nA] [µm x µm] [hours] 25x25 6 3 25x25 6 5 25x25 0.5 7 30x30 6 5.5 20x20 6 5.5 25x25 6 17
The principal parameters of the deposition process of the layers have been the following: an acceleration voltage of the electron beam of 20kV and a beam current of 6nA, excepting the third Co-deposition (see table 1).
3
Hardness determination by nanoindentation
3.1 Indentation set-up Because of the small dimension of the EBiD layers, for determining their hardness, it was necessary to build up a specialized set-up for nanoindentation inside the SEM. The main reason was the small dimension of the layer deposits i.e. width and length were in the range of approx. 20 µm. The setup inside the SEM simplified the positioning of the indentation tip on the deposited layer. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
76 Computational Methods and Experiments in Materials Characterisation III Figure 2 shows the nanoindentation setup inside the SEM. The main advantage of this setup is its compactness. The whole setup has been fixed on the 5-axis stage of the SEM. The indentation setup consists of the part holding the specimen and the indentation tip with sensors for force (load cell) and displacement measurements (piezo stack with strain gages). g
f
a e
c d
b
Figure 2:
Nanoindentation setup inside the SEM: (a) SEM’s vacuum chamber; (b) 5-axis stage; (c) specimen holder; (d) three Cartesian drives; (f) load cell; (g) piezo stack actuator.
The specimen holder is mounted on one of the three Cartesian linear drives (SmarAct GmbH, Germany), which utilize the slip-stick driving principle; the minimum slip-stick step size is approximately 20 nm. These drives are used for the coarse positioning of the specimen beneath the indenter. A distance below 1 µm is required. The used indenter was a diamond Berkovich tip. For penetrating the EBiD layers, a piezo stack actuator has been used. It is equipped with integrated strain gages which allow the measurement of the deflection of the indenter. The differential voltage of the Wheatstone bridge built up by the strain gages of the piezo actuator has been evaluated by using a bridge amplifier. The deflection of the piezo stack and the corresponding signal of the bridge amplifier have been calibrated using a laser interferometer, resulting in a linear behaviour. For measuring the force applied on the specimen during indentation, a highly sensitive load cell (Honeywell) has been mounted between the piezo stack actuator and the indentation tip. The load cell has been calibrated by using small WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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precision weights. It has also a linear behaviour. The control and the data acquisition have been managed with the help of a LabVIEW-program. This program allows performing a cycle with a defined indentation depth (displacement controlled nanoindentation) and holding time. 3.2 Calibration tests of the nanoindentation set-up After the work of Oliver and Pharr [12], for a precise determination of mechanical properties of a bulk material or of a coating system (Young’s modulus and hardness), two calibrations are necessary: the calibration of the area function of the indenter and the calibration of the stiffness of the nanoindentation device. For this purpose, nanoindentation tests with minimum 10 different maximum loads on two different reference specimens e.g. fused silica and sapphire with a relative high Young modulus must be performed. Fused silica has a Young’s modulus of 72 GPa, sapphire has a Young’s modulus of 420 GPa. Moreover, to assure a good statistic, 5 tests with the same maximum indentation load have been conducted. The maximum measured indentation depth was 1 µm. A small quadrate of fused silica (8 x 8 mm2, thickness 3 mm) and a small disc of sapphire (diameter 8 mm, thickness 3 mm) have been the reference specimens. They are very well polished on both sides, so that the roughness of their surfaces is very low (RMS<1÷2 nm). The calibration tests have been performed with the set-up described above. The reference specimens have been glued on a small holding plate; then this plate was screwed on the positioning table. A Berkovich indenter (Producer Synton MDP, Switzerland) was used for performing all calibrations. The data of the tests have been processed with a special software (Indent Analyser, ASMEC Germany). The software can calculate the area function of the indenter and the stiffness of the nanoindentation set-up, by processing the recorded data. Unfortunately, because of the precision limits of our used force and displacement sensors in the range of small depths, we have no sufficiently good calibration data on fused silica specimen. Having only the area function of the indenter, we have only determined the hardness of the tested materials. We have verified the obtained area function by performing tests on Si substrate. The calculated values of the Si hardness are in accordance with results in literature. 3.3 Indentation tests The specimens were investigated just after the processing of the coating. The maximum measured indentation depth was 1 µm. Knowing the thickness of the layers (see section 3.4), we have tried to keep an approximately ratio of 1/10 between the indention depth and the coating thickness [19], which was not always possible. It is especially critical for very thin layers (e.g. <100nm). The used load-time sequence was the same as Oliver and Pharr [12] have used in their work: loading, then a loading time of 100s and finally unloading, see fig.3. For calculating hardness, the data have been processed with the same software as that used for the calibration tests.
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78 Computational Methods and Experiments in Materials Characterisation III 120000
Load, [µN]
100000 80000 60000 40000 20000 0 0
Figure 3:
20
40
60
80 100 Time, [s]
120
140
160
Load-time diagram of a test on Si substrate.
3.4 Measurement of the thickness and determination of the chemical composition of the layers For measuring the thickness of the EBiD-layers, the specimens have been examined with an Atomic Force Microscope (AFM) in contact mode. The results of these measurements can be seen in table 2. However, it was not possible to measure the thickness of all deposits. The samples Co #1 and Co #2 were samples which delaminated during indentation. Thus AFM measurements have damaged the samples. As these samples were very thick compared to the others, it was possible to measure the thickness by tilted imaging in the SEM. Thus, the error should be bigger than indicated through the standard deviation of the data shown in table 2. Sample Co #4 could not be measured with the AFM, because a relative large area of the deposited layer spalled up and the chips were spread over the deposition area. This has led to not exact AFM measurements because of the fouling of the tip. Each deposited layer was examined for determining its material composition, by using X-ray analysis after the nanoindentation tests. The specimen Co #3 has been deposited with a lower beam current, resulting in a lower Co content. Because the power irradiated on the deposition spot was higher for high beam currents, it leads to heating effects resulting in deposits with a higher metal content. This effect has been also reported in literature [16]. Table 2: Specimen Co #1 Co #2 Co #3 W #1 W #2 W #3
Thickness measurements and chemical composition of the deposited layers with the standard deviation of the measurements. Thickness [nm] ~1436 ± 34 ~2256 ± 90 93 ± 45 353 ± 76 116 ± 114 469 ± 59
Meas. with SEM SEM AFM AFM AFM AFM
atm% C 42 ± 7 47 ± 3 52 ± 3 42 ± 5 39 ± 3 29 ± 4
atm% O 10 ± 1 9±0 13 ± 1 11 ± 1 10 ± 1 8±1
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atm% Co 48 ± 11 44 ± 2 35 ± 2 -
atm% W 47 ± 8 50 ± 4 62 ± 4
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79
Results and discussion
4.1 Hardness of EBiD-layers The results of the hardness measurements for the different EBiD deposits, for Si substrate and for carbon deposits from literature [5], are shown in table 3. The hardness of Si substrate of 12.81 GPa agrees well with a value from literature e.g. 12.1 GPa [10]. The hardness of W(CO)6 coatings is bigger than the hardness of the Co2(CO)8 coatings. There are also small differences between the hardness of coatings deposited in the same composition. The fact that the hardness of the W(CO)6 is bigger than the hardness of the Co2(CO)8 coatings is also confirmed by the difference in the slope of the loading stage of the nanoindentation tests, see figure 4. Table 3:
Measured hardness of each deposit and values from literature for Si and carbon. Specimen
Calculated hardness, [GPa]
Si (substrate) Co #1 Co#2 Co#3 W #1 W#2 W#3 Carbon
12.81 3.51±0.13 3.56±1.75 3.40±1.81 10.00±0.55 7.16±0.29 7.2±0.20
Hardness values found in Literature [GPa] 12.1 [10]
3.6 – 4.4 [5]
140000 120000
Discontinuities
Load, [µN]
100000 80000 60000 40000 20000
Si1
0 0
Figure 4:
200
400 600 Depth, [nm]
800
W12
1000
Different slopes of the loading stage of nanoindentation curves for materials with different hardness.
For the material with a bigger hardness, namely Si, its load-depth diagram has a steeper slope for the loading stage of the test than the corresponding slope of WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
80 Computational Methods and Experiments in Materials Characterisation III diagram of the test on W(CO)6 coating. It can be concluded that, for reaching the same indentation depth as in the case of the W(CO)6 coating (smaller hardness), a higher indentation force was necessary for the case of Si. 4.2 Evaluation of the imprints after nanoindentation tests on the different EBiD layers If the SEM photos of the imprints on the layers deposited from W(CO)6 and of the imprints on the layers from Co2(CO)8 (see figure below) are compared, there are some differences between their fracture behaviours under indentation load to notice. plastic deformation
spallation
10µm
10µm a Figure 5:
b
Overview of imprints in the coating after nanoindentation tests (a) on a Co2(CO)8; (b) on a W(CO)6 deposit (right picture).
The harder layers (W) shows an accentuate spallation; many chips around the imprint area can be seen. This fracture behaviour is characteristically for a brittle material. This effect has also been observed during bending tests on pin-like deposits made from tungsten-hexacarbonyl; elastic deformation until brittle breaking of the pins has been observed [15]. In contrast, the imprints areas on the layers containing Co show accentuate plastic deformation which is characteristically for a ductile material. The brittle fracture of the layers containing W can be also associated with discontinuities observed during the loading stage of the nanoindentation tests (see figure 4). Brittle fracture implies crack propagation during loading; in this way, a part of the total energy dissipated in the material system is consumed for the crack propagation; therefore such discontinuities can occur. 4.3 Discussion Bigger hardness of W(CO)6 layers can be explained by taking into consideration good mechanical properties of W. The small differences between the hardness of the W(CO)6 layers can be partially explained by the small difference in W atm.% WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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and additionally by the influence of the hardness of the Si substrate for the case of thinner layers. For the Co2(CO)8 layers, the specimens Co #1 and Co #2 have almost the same hardness i.e. 3.51GPa for specimen Co #1 in comparison with 3.56 GPa for specimen Co#2. It can by probably explained by an almost equal Co atm.% (48% respectively 44%). The specimen C0 #3 has a smaller Co atm.% (35%) and consequently its hardness is slightly smaller, of 3.4 GPa. For this difference in Co atm.%, a bigger difference in hardness could be probably expected. We have to keep in mind that the thickness of specimen Co #3 was with 93 nm by far the thinnest for this chemical composition. Therefore, in this case the influence of the hardness of the Si substrate was bigger.
5
Conclusion
In this work, hardness of EBiD deposited layers with thicknesses ranging from 90 nm to 2200nm has been determined by means of the nanoindentation test method. For this purpose, a self built nanoindentation set-up has been used. The big advantage of this set-up is that, because of its compactness, it can be used inside of a SEM. In this way, the indenter can be easily positioned on the desired area for testing. For the EBiD deposits, precursors tungsten-hexacarbonyl (W(CO)6) and di-cobalt-octacarbonyl (Co2(CO)8) have been used. The hardness of tungsten containing EBiD layer has been found to be in the range of 7.2 to 10.0 GPa and for cobalt containing layers of 3.4 to 3.6 GPa. The measured hardness of the silicon substrate was 12.8 GPa, which agrees well with a value reported in literature (12.1 GPa, [10]). Moreover, different fracture behaviours for these EBiD deposits have been observed. By examining the shape and the features of the imprints in the coatings after nanoindentation tests, it has been found that the tungsten containing layers have a brittle cracking behaviour, while the cobalt containing layers have a ductile fracture behaviour.
References [1] [2] [3] [4] [5]
A. N. Broers, W. W. Molzen, J. J. Cuomo, and N. D. Wittels. Electronbeam fabrication of 80ǖ metal structures. Applied Physics Letters, 29(9):596–598, 1976. Robert W. Christy. Formation of thin polymer films by electron bombardment. Journal of Applied Physics, 31(9):1680–1683, 1960. F. Cicoira and P. Hoffmann. Focused electron-beam deposition of three dimensional free standing nanometer structures. Technical report, Institute of Applied Optics, DMT-IOA, EPFL, CH-1015 Lausanne, June 1999. Natalia Silvis Cividjian. Electron Beam Induced Nanometer Scale Deposition. PhD thesis, Technische Universiteit Delft, 2002. W. Ding, D. A. Dikin, X. Chen, R. D. Piner, R. S. Ruoff, E. Zussman, X. Wang, and X. Li. Mechanics of hydrogenated amorphous carbon deposits from electron-beam-induced deposition of a paraffin precursor. Journal of Applied Physics, 98(1):014905, 2005. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
82 Computational Methods and Experiments in Materials Characterisation III [6] [7] [8] [9] [10] [11]
[12]
[13] [14] [15] [16]
[17] [18] [19]
A E Ennos. The sources of electron-induced contamination in kinetic vacuum systems. British Journal of Applied Physics, 5(1):27–31, 1954. M. Rudolph H. W. P. Koops, J. Kretz. Characterization and Application of Materials Grown by Electron-Beam-Induced Deposition. Jpn. J. Appl. Phys., 33(Part 1, 12B):7099–7107, 30 1994. P. Hoffmann, I. Utke, F.Cicoira et al. Focused electron beam induced deposition of gold and rhodium. Mat. Res. Soc. Symp. Proc., 624:171–177, 2000. Stephan Fahlbusch Ivo Utke, Vinzenz Friedli. Tensile Strengths of MetalContaining Joints Fabricated by Focused Electron Beam Induced Deposition. Advanced Engineering Materials, 8(3):137–140, 2006. Follstaedt D.M. Myers S.M. Petersen G.A. Knapp, J.A. Finite element modelling of nanoindentation measurements of crystallline and amorphous si. In Mat. Res. Soc. Symp. Proc., volume 649, 2001. H. W. P. Koops, C. Schossler, A. Kaya, and M. Weber. Conductive dots, wires, and supertips for field electron emitters produced by electron-beam induced deposition on samples having increased temperature. Volume 14, pages 4105–4109. AVS, 1996. W.C. Oliver and G.M. Pharr. An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. Journal of Materials Research, 7(6):1554–1583, June 1992. N. Silvis-Cividjian, C.W. Hagen, L.H.A. Leunissen, and P. Kruit. The role of secondary electrons in electron-beam-induced-deposition spatial resolution. Microelectronic Engineering, 61-62:693–699, 2002. R. Lariviere Stewart. Insulating films formed under electron and ion bombardment. Phys. Rev., 45(7):488–490, Apr 1934. S. Fatikow T. Wich, S. Kray. Microrobot based testing of nanostructures inside an SEM. In Proceedings on the 10th International Conference on New Actuators, 2006. I. Utke, T. Bret, D. Laub, Ph. Buffat, L. Scandella and P. Hoffmann. Thermal effects during focused electron beam induced deposition of nanocomposite magnetic-cobalt-containing tips. Microelectron. Eng., 7374(1):553–558, 2004. I. Utke, F. Cicoira, G. Jaenchen, P. Hoffmann, and et al. Focused electron beam induced deposition of high resolution magnetic scanning probe tips. Mat. Res. Soc. Symp. Proc., 706:Z9.24.1–Z9.24.6, 2002. Sievers Wich, T. Assembly inside a Scanning Electron Microscope using Electron Beam induced Deposition. In Proceedings of 2006 IEEE/RSJ International Conference on Robots and Intelligent Systems, 9 2006. Chen X. Yan J. Karlsson A M. Zhao, M. Determination of uniaxial residual stress and mechanical properties by instrumented indentation. Acta Materialia, 54:2823–2832, 2006.
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Section 3 Microstructures – alloys
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85
Thermodynamic modelling of a 6w/o Al P/M processed Ni base superalloy D. A. Akinlade1, W. F. Caley2, N. L. Richards1 & M. C. Chaturvedi1 1
Department of Mechanical and Manufacturing Engineering, University of Manitoba, Canada 2 Department of Process Engineering and Applied Science, Dalhousie University, Canada
Abstract A thermodynamic java based software package (JMatPro) was used to predict the powder metallurgy (P/M) processing of a superalloy based on the composition of IN600. The effects of adding 6w/o Al to the alloy on sintering time and temperature were estimated and compared with results obtained experimentally from a combination of X-ray diffraction and metallography. Phases predicted by the modelling compared favourably with microstructural observations and phase identification of the P/M processed alloy in terms of prediction/microstructural observation of austenite, gamma prime and chromium rich carbides. Furthermore, both microstructural predictions for the alloy after solution treatment and hardness values generated were in agreement with metallographic observations and hardness measurements respectively. These results suggest that the software and predictions used in this study offer a reasonable way to simulate the characterisation of P/M processed nickel-based superalloys. Keywords: superalloy, powder metallurgy, thermodynamic modelling, morphology.
1
Introduction
Superalloys are high temperature and high strength alloys. Among the large number of superalloys available is Inconel 600 which is a NiCrFe alloy. Some advantages of this alloy include: good mechanical properties at elevated temperatures, good workability and reasonable weldability. Because of these WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/MC070091
86 Computational Methods and Experiments in Materials Characterisation III advantages, this alloy has found usage in both cryogenic and elevated temperature environments, examples of which include: furnace components, chemical and food processing materials and nuclear applications [1]. The ternary NiCrFe alloy is strengthened via a solid solution mechanism and on addition of an element such as Al can also benefit from precipitation hardening [2]. This strengthening can be achieved through various fabrication techniques including processing through powder metallurgy (P/M). Whereas it is important to determine the phase(s) present in an alloy, a prediction of alloy microstructure using modelling tools has to date been quite difficult [3], perhaps because of the chemically dynamic nature of superalloys and the inherent complexity of a P/M process. However a new Java-based material processing software, JMatPro, has recently been developed by Sente Software TM to address some of these modelling shortcomings [3, 4]. In the present study this thermodynamic modelling tool has been used to characterise the microstructure of the ternary alloy, with and without addition of 6w/o Al. Also, the results from the simulation are compared to similar alloys produced experimentally using P/M techniques previously developed by the authors.
2
Experimental
The powder used was a prealloyed NiCrFe alloy (particle size 45µm), fabricated by inert gas atomisation [5]. The optimum P/M processing parameters have been reported previously [6]. Briefly, the process involves compacting prealloyed NiCrFe alloy powders and adding 0.75w/o lubricant (microwax). Sintering regime included delubrication at 4000C for 0.5h, heating to 13000C (10K/min.), holding for 2h at 13000C followed by furnace cooling, all under a vacuum of 6 millitorr. To enhance precipitation hardening via formation of intermetallics such as gamma prime, up to 12w/o Al (average particle size ~ 10µm) was added to the prealloyed alloy and subsequently sintered at the optimised conditions. Samples were prepared for characterisation following standard metallographic techniques (samples ground through 1200Pm SiC and polished through 0.1Pm diamond). Etching was carried out electrolytically using 5V for 10s in a solution of 12ml H3PO4 + 40ml HNO3 + 48mlH2SO4. Microstructure was observed using a JEOL (JSM5900LV) scanning electron microscope (SEM) with EDS capability whereas the phase(s) present were identified using a Rikagu XRD with Cu, KD radiation, a wavelength of O = 1.54056nm, current of 40mA and voltage of 44kV. Vickers hardness and image analysis were used to measure the mechanical response (10kgf, 5s, average of 9 indentations) and to estimate the amount of pertinent phases present, respectively.
3
Results and discussion
Representative micrographs for the ternary alloy and the alloy with up to 12w/o Al addition are given in Figure 1(a)–(d). Because the 6w/o Al modified ternary alloy gave a reasonably high quantity of a second phase (determined to be Ni3AlȖ’) in the as-sintered compact and because 5 to 6w/o Al is traditionally added for oxidation resistance, this composition was selected for subsequent study. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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A Ternary NiCrFe alloy solid solution
Porosity
(a) B
Ternary NiCrFe alloy solid solution Porosity
(b) Figure 1:
(a): SEM-BE image of the ternary NiCrFe alloy showing porosity and the ternary solid solution. (b): SEM-BE image of the 3w/o Al modified ternary NiCrFe alloy showing porosity and the solid solution. (c): SEM-SE image of the 6w/o Al modified ternary NiCrFe alloy showing porosity, primary and secondary gamma prime. (d): SEM-BE image of the 12w/o Al modified ternary NiCrFe alloy showing the presence of gamma prime and the ternary NiCrFe alloy rich in Al. A
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88 Computational Methods and Experiments in Materials Characterisation III C
Primary gamma prime region located at the grain boundary Secondary gamma prime intermetallic region located in
the grains
(c) D Ternary Ni-CrFe alloy region
Wetting/reaction front Gamma prime intermetallic region
(d) Figure 1:
Continued.
An equilibrium phase step calculation for the alloy (Ni - Cr: 11.3, Fe: 8.5: C: 0.045 [wax residual], Al: 6, all in w/o) is shown in Figure 2. Briefly, the phase identification was based on determination of the minimum free energy of the calculation based on CALPHAD analysis [3, 4] and simplified into eqn (1):
'G
ideal xs 'G 0 'Gmix 'Gmix
(1)
o
where 'G = Gibbs free energy, 'G is the Gibbs free energy due to ideal
contributions from pure components, 'G mix is the ideal mixing term, and xs 'Gmix is the excess free energy of mixing (J.mol-1). WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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From Figure 2, five main phases were predicted to be present. These are gamma, gamma prime, M7C3, M23C6 and liquid. Because their presence was based on equilibrium conditions without regarding kinetic considerations, not all phases may be present in the experimental samples. For example, gamma and gamma prime should predominate as temperature is increased from room temperature to the melting point (approximately 14250C) whereas the carbides may be difficult to detect on the SEM if they are finely distributed. However, it should be noted that the presence of carbides in superalloys acts to reduce grain boundary sliding and therefore should enhance the creep resistance of the alloy. Ni-6.0Al-11.28Cr-8.46Fe-0.045C w/o 120
W/o of phase(s)
100 80 Gamma phase
60
Liquid
M7C3 Carbide
Gamma prime phase
40
M23C6 Carbide
20 0 0
Figure 2:
500
1000 Temperature (0C)
1500
2000
JMatPro step calculation for the 6w/o Al modified ternary NiCrFe alloy.
The continuous cooling transformation (CCT) curves were derived from the Johnson Mehl Avrami Kolmogorov model for various temperatures and times based on nucleation and growth principles. For nuclei that reach the critical nucleus, the model gives the following relationship [7].
f t 1 exp ª¬ S 3 NG 3t 4 º¼
(2)
where t is the time for the fraction of phase(s)/or materials transformed (in seconds), f(t) is the fraction transformed in the time t, N is the nucleation rate (number of nuclei/cm3/seconds), G is the growth rate (cm/seconds). This was the basis for Figure 3. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
90 Computational Methods and Experiments in Materials Characterisation III
1400 cooling curve
Gamma phase region
1300
Temperature (oC)
1200
Cooling (100C/min)
1100
20% gamma prime transformation 25% gamma prime transformation 30% gamma prime transformation
1000 900 800 700 600 1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04 1.00E+05 1.00E+06
Time (min)
Figure 3:
JMatPro CCT simulation for the 6w/o Al modified NiCrFe ternary alloy.
Figure 3 shows the cooling regime superimposed onto the sintering profile. Whereas Figure 2 represents all the phases that are thermodynamically feasible, Figure 3 shows the JMatPro CCT simulation indicating the presence of the matrix gamma phase, and also the 20, 25 and 30% transformation curves for the gamma prime. From the curves it may be seen that the cooling profile after sintering at 13000C for 2h cuts across the gamma prime transformation after 25% transformation but before 30% transformation. This suggests that if the alloy is fabricated in the as-sintered condition, the amount of gamma prime present in the compact should be in the range 25-30%. To verify the simulation, compacts were fabricated with the optimum 6w/o Al and sintered at 1300°C. EDS analysis confirmed the presence of gamma prime in the compact. From the SEM micrograph, Figure 4, two main types of gamma prime precipitates were noticed. The first type is fine, well-distributed gamma prime phase (A), whereas the other is the gamma prime phase formed along the grain boundary, being larger and identified as (B). When cooling from 13000C, gamma prime precipitates are initiated with preferential formation at the grain boundaries; as cooling continues, the grain boundary gamma prime grows as in (B) of Figure 4. The finer gamma prime precipitates are formed as a result of nucleation and growth at relatively lower temperatures being similar to the morphology previously reported by Johnson, and Donachie Jr. [8]. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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B A
5µm
Figure 4:
SEI-SEM image of the as sintered 6w/o Al modified NiCrFe ternary alloy, showing fine (A) and coarse (B) gamma prime precipitates.
Image analysis showed that the amount of gamma prime in Figure 4 is estimated to be 62±5%. It is suggested that the difference is related to the numerous micrograin boundaries present as a result of the powder fabrication route used. These tend to encourage nucleation of precipitates and therefore may lead to higher levels of gamma prime than might be expected for a similar alloy produced through ingot metallurgy. X-ray diffraction (XRD) analysis was carried out on the as-sintered compact to identify all phases present, to estimate their lattice parameters and to also determine any lattice mismatch present between the gamma prime and gamma phase. Figure 5 shows an XRD spectrum for an as-sintered compact. Referring to the figure it is evident that the two main phases predicted by JMatPro, namely gamma and gamma prime, are present. In particular, (100) and (110) are specific to gamma prime whereas the remaining peaks are as a result of superimposition of both gamma prime and gamma phase. Using the Bravais lattice 2
2
2
( h k l ) sequential method [9] for FCC and Bragg’s law, the lattice parameter of gamma prime was calculated to be 3.5634 0A ±0.0005, whereas that of the gamma phase was estimate to be 3.5565 0A ±0.0005. Using eqn (3) [10] the lattice parameter mismatch, į, may be written as:
G
2(aJ ' aJ ) ( aJ ' aJ )
WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
(3)
92 Computational Methods and Experiments in Materials Characterisation III where aJ ' is the lattice parameter for the gamma prime phase and aJ is the lattice parameter for the gamma phase, the lattice parameter mismatch, į, which can be used as an indication of strength (resistance to dislocation movement), was estimated to be 0.0019. According to Decker [11], a lattice mismatch as much as 0.8% could double the peak-aged hardness of some materials. Although this amount of lattice mismatch was not achieved in this study, it should still be noted that the effect of coherency strains introduced into the crystal structure due to the formation of gamma prime would enhance the strength of the sintered compact.
(111)
(200)
(220) (100)
Figure 5:
(110)
(311) (222)
XRD spectrum for the 6w/o Al modified NiCrFe ternary alloy.
Vickers hardness values for the 6w/o Al modified NiCrFe alloy were 183±5 as measured and 192 as predicted from JMatPro. Although the predicted value was slightly higher than experimental it is within experimental error; also, a slightly lower value would be expected for the experimental samples due to the presence of minor residual porosity.
4
Conclusions
From the results, the following conclusions may be drawn: (1)
Despite various problems reported in P/M processing for a typical superalloy, some of which include porosity and prior particle boundaries, WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
Computational Methods and Experiments in Materials Characterisation III
(2) (3) (4)
93
the experimental methodology used provides a sample compact with a microstructure that should be comparable to a wrought product. The main phases expected from thermodynamic calculations using JMatPro, Ȗ and Ȗ’, were successfully predicted and their presence confirmed experimentally. Predicted hardness values were in reasonable agreement with experiment. The software may be used as a guide to design and model this alloy system.
Acknowledgements The authors would like to thank the Natural Sciences and Engineering Research Council of Canada for financial support as well as I. MacAskill and K. Plucknett, Dalhousie University for technical assistance. Also, D.A. Akinlade wishes to acknowledge University of Manitoba for the award of a Graduate fellowship.
References [1] [2] [3] [4] [5] [6] [7] [8] [9]
Mankins, W.L. & Lamb, S., Nickel and Nickel Alloys, ASM Metals Handbook, ed. S. R. Lampman, & Zorc, T.B., 2, 10th edition, The Materials Information Society, USA. p. 438, 1992. Sullivan, C.P. & Donachie Jr., M.J., Some effect of microstructure on the mechanical properties of Nickel-base superalloy. Metal Engineering Quarterly, 8, pp 250-259, 1967. Saunders, N., Guo, Z., Li, X., Miodownik, A.P. & Schille, J.Ph., Using JMatPro to Model Materials Properties and Behaviour, JOM, pp 60-65, 2003. Saunders, N. Li, X. Miodownik, P. & Schillé, J.Ph., in Proc. Symp. Materials Design Approaches and Experiences, eds J.-C. Shao et al., pp185-197, Warrendale, PA, TMS. 2001 German, R.M., Powder Metallurgy Science, Metal Powder Industries Federation: Princeton, NJ, pp 99-116, 2001. Akinlade, D.A., Caley, W.F., Richards, N.L. & Chaturvedi, M. C., Development of a nickel base superalloy using powder metallurgy, International Journal of Powder Metallurgy, MPIF, in press, 2006. Reed-Hill, R.E. & Abbaschian, R., The Iron-Carbon Alloy system (Chapter 18). Physical Metallurgy Principles, 3rd edition, PWS Publishing Company, Boston, USA, p 610, 1994. Johnson, J. & Donachie, Jr., M.J., Microstructure of precipitation strengthened nickel-base superalloy, Presentation at the 1966 National Metal Congress, Chicago, Illinois, US, pp 1-26, 1966. Suryanarayana, C. & Grant Norton, M., Crystal Structure Determination, (Module 1). X-ray diffraction, A practical approach, Plenum Press, New York, USA. pp 97-104, 1998.
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94 Computational Methods and Experiments in Materials Characterisation III [10] [11]
Muller, L., Glatzel, U. & Feller-Kniepmeier, M., Modelling thermal misfit stresses in nickel-base superalloys containing high volume fraction of Ȗƍ phase, Acta Metallurgical et Materialia, 40, p1321, 1992. Decker R.F., Strengthening mechanisms in nickel-base superalloys, Presentation at the Steel Strengthening Mechanisms Symposium, Zurich, Switzerland, p 1-23, 1969.
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An investigation into martensitic transformation in hot stamping process M. Naderi & W. Bleck Institute of Ferrous Metallurgy, RWTH Aachen University, Germany
Abstract The main target of the hot stamping process is to get fully martensitic microstructure in the end product. In the current study, the hot stamping process is simulated by the simultaneous forming and quenching experiments. This is done through uniaxial compression tests at high temperatures by a dilatometry machine. The effects of process parameters like strain, strain rate, initial deformation temperature and austenization soaking time and mainly the applied force, on martensitic transformation of the ultra high strength boron steel are investigated. Besides, the presence of other phases like bainite and ferrite and their effects on martensitic transformation is considered. It is concluded that by increasing strain rate and initial deformation temperature, martensite content, hardness and martensite start temperature (Ms) are increased. On the contrary, by applying higher deformations, the above mentioned properties are decreased. It is also concluded that, regardless of the process parameters, higher applied forces deteriorate the successful martensitic transformation during the hot stamping process. Keywords: hot stamping, boron steel, martensitic transformation.
1
Introduction
In hot stamping process, the material is subjected to a high temperature austenization and subsequently formed. Then, it is cooled in the die rapidly enough to ensure the formation of martensite. In this process the material is subjected to the thermo-mechanical treatment in the austenite region. This thermo-mechanical treatment will influence the final microstructure and properties of the material.
WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/MC070101
96 Computational Methods and Experiments in Materials Characterisation III The martensitic transformation depends on several factors such as chemical composition, heat treatment schedules and plastic deformation. The influence of chemical composition [1], primary austenite grain size [2] and prior plastic deformation [3] on the martensitic transformation has been reported for low alloy steels. In the current study, the influence of process parameters on martensitic transformation through simultaneous forming and cooling is studied.
2
Experimental set up
The studied material is hot rolled boron steel from the 27MnCrB5 grade in the form of plates. Table 1 exhibits chemical composition of the investigated steel. Table 1:
Chemical composition of the investigated steel, mass%.
C
Si
Mn
P
S
Cr
Ti
B
0.25
0.21
1.24
0.010
0.001
0.34
0.042
0.002
The Continuous Cooling Transformation (CCT) diagram, fig. 1, has been produced by dilatometry tests, metallographic investigations and hardness measurements. The circled numbers indicate the values of final hardness in the HV10 scale. For a heating speed of 5qC/s, the eutectoid reaction temperature (Ac1) is 730qC and the start temperature of austenite to primary ferrite transformation point (Ac3) reaches 820qC. After austenitization at 950qC for eight minutes followed by quenching, microstructure becomes fully martensitic. The martensite start and finish temperatures, Ms and Mf lie at 400qC and 200qC, respectively. It can be seen that a cooling rate greater than 37qC/s results in fully martensitic microstructure.
Figure 1:
CCT Diagram of the 27MnCrB5 Boron steel.
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A Baehr DIL 805 deformation dilatometer was employed to create the thermo-mechanical schedules. Such conditions were produced by several simultaneous forming and quenching tests at temperatures between 600°C – 850°C. Different strain rates between 0.1s-1 – 1.0s-1 were applied. Unless otherwise, in all of the tests, samples were austenitized at 950°C for five minutes and quenched to compression temperature by 50°C/s. To fix the initial deformation temperature TiD, the samples were kept for 1s at the favourite TiD and then the deformation was carried out. The above mentioned processes as well as an example Force-Time-Temperature diagram which shows the accuracy and reproducibility of tests are illustrated in fig. 2.
16
850°C
800
14
600
600°C
400
0
50°C/s
Simultaneous forming and quenching _1
-1
dH/dt = 0.1s -1.0s Hmax = 0.5
200
0
100
200
Temperature
,,
750
300
400
10
700
8 650
6 4
-1
2
(a) 500
600
700
800
0
dH/dt = 0.1s Hmax = 0.5 dT/dt = 50°C/s
Force
(b)
-2 587
588
589
590
Time (s)
Figure 2:
800
,
Fix TiD for 1s
12
200°C/min Force (KN)
Temperature (°C)
950°C; 5'
591 592 Time (s)
600
Temperature (°C)
18
1000
550 593
594
595
Simultaneous forming and quenching plan: a) the consequence of the experiment and b) an example of temperature and force evolution.
The experimental set up was as follows: inserting the cylindrical Specimen (10×5mm) in a vacuum chamber, resistance heating to austenization temperature and performing subsequent compression between SiN2 anvils followed by controlled cooling. Molybdenum foils were used to prevent the specimens sticking to the anvils and the glass powder was utilized for lubrication. The Pt/Pt-Rh10% thermocouple was welded to the specimen in order to measure the temperature. The atmosphere was initially protected by vacuum and then argon and helium shower were employed for a controlled cooling.
3 Results and discussions The martensites start (Ms) and finish (Mf) (or M%) temperatures, martensite content, hardness and also microstructure were considered. Besides, influence of strain values, rate of deformation, austenization soaking time, magnitude of applied force and initial deformation temperature on the transformation were studied. The effect of process parameters on critical temperatures in martensitic transformations as well as hardness and fraction of martensite in final parts are represented in fig. 3. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
98 Computational Methods and Experiments in Materials Characterisation III
600
600 -1
400 300
97
Mf(%)
95
96
Numbers on the Mf(%) trend indicates
(a)
the amount of Martensite.
5
10 15 Austenisation soaking time (s)
20
200
HV10
300
300 79
92
200
100 0,0
Figure 3:
Mf(%)
200
Numbers on the Mf(%) trend indicates
(c)
the amount of Martensite.
0,2
0,4 0,6 0,8 -1 Strain rate dH/dt (s )
30 200
Mf(%)
Numbers on the Mf(%) trend indicates
(b)
the amount of Martensite.
0,1
0,2 0,3 True Strain H (-)
0,4
0,5
100
1,0
500
dH/dt = 0,1s , Hmax = 0,2
500
HV10
Ms
67
400
300 61
94
99
200
500
400
400
61
363
300
100 0,0
100
375 Ms
400
-1
TiD = 800°C , Hmax = 0,4
500
500
400
400 Ms
300
300 77
Mf(%)
200
100 650
94
100
200 Numbers on the Mf(%) trend indicates
(d)
100 1,2
80
Hardness - HV10
95
200
TiD = 800°C, dH/dt = 0,1 s
Hardness - HV10
300
100
Temperature (°C)
363
Temperature (°C)
379 Ms
Temperture (°C)
400
-1
HV10
500
500 Hardness - HV10
HV10
Hardness - HV10
Temperature (°C)
TiD = 800°C, dH/dt = 0.1 s , Hmax = 0.2 500
the amount of Martensite.
700
750
800
850
100 900
Initial deformation temperature TiD(°C)
The effect of process parameters on the martensitic transformation; a) austenization soaking time, b) strain level, c) strain rate and d) initial deformation temperature.
It is seen that: By increasing austenization soaking time from five to twenty minutes, the Ms temperature decreased about 15°C while changes in martensite contents were negligible. Similarly, due to martensite contents, the Mf(%) temperatures are varied. It is in agreement with Unemoto [4] and Ankara’s [5] observations. They described that the lath shaped martensite transformation is often associated with grain boundaries. Therefore, a nucleation argument would suggest that the finer grain sizes result in higher Ms temperatures, i.e. easier nucleation since grain boundary area increases. However, the difference between the martensite contents was negligible but, due to larger martensite lath packets, hardness values decreased. It is evident that the larger austenite grain sizes resulted in coarser martensite lath packets with lower hardness levels. During hot stamping process, the blanks are austenitized at austenite regions for a definite period of time. Concerning to the above mentioned results, the optimum austenization soaking time and temperatures must be selected to get homogenized austenite solid solution without any remaining carbides. The finer martensite lathes gives better combination of strength and formability, therefore, it is necessary to avoid coarse martensite needles formation. In the simultaneous compression and cooling tests at constant initial deformation temperature and strain rate, larger strains will be obtained for a long time at lower temperature. It means that the possibility to have more secondary phases like ferrite and bainite owing to crossing the ferrite and bainite zones in CCT diagram is enhanced. Accordingly, martensite fractions were lowered at WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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larger strains and consequently hardness values were decreased. The decrease in Ms was about 15°C but owing to martensite contents reduction, the Mf(%) temperature increased about 50°C. These results are in qualitative agreement with the earlier observations that compressive stresses decrease the Ms and dilatation values [3]. In contrast, it has also been reported that both the compressive and the tensile stresses raise the Ms, but the effect is small [6]. The reason for the reduction of the Ms might be that, as a consequence of ferrite formation, carbon becomes enriched in the remaining austenite, which therefore transforms into martensite at somewhat lower temperature. Fig. 3.b displays that at larger strains, martensite fraction is decreased and accordingly, amount of ferrite and bainite increased. Acceleration of ferrite formation and particularly the nucleation rate by plastic deformation in the non-recrystallization regime of austenite has been reported for micro-alloyed steels [7]. Lee and Choo [8] found that pancaking of the austenite by rolling at 871-843°C resulted in appearance of ferrite in subsequent quenching. Without rolling, the microstructures were martensitic. With the same interpretation as above, at the same initial deformation temperature and the same strain level, the process with higher strain rate is finished in shorter time and at higher temperature. In this regard, the possibility of the formation of secondary phases is decreased. Hence, the higher strain rates yielded to higher martensite contents and evidently higher hardness levels. The Ms increased about 10°C and due to increase of the martensite contents the Mf decreased about 50°C, fig. 3.c. The rise of the Ms might be due to finer austenite grain sizes which lower required activation energy for martensitic transformation and/or decrease of ferrite fraction which enrich remaining austenite. At lower rates the presence of bainite is dominant. For instance, at 0.1s-1 microstructure comprises of bainite and martensite while at higher rates, ferrite is also formed as separated islands. Ferrite is a very soft phase and deteriorates the strength. The deformation speed during hot stamping process must be optimized to avoid ferrite formation and also to diminish the presence of bainite. The higher TiD resulted in the higher Ms temperature. As is seen in fig. 3.d, the Ms temperature decreased from 385°C at the TiD of 850°C to 365°C at the TiD of 700°C. It might be due to the fact that austenite phase is strengthened during deformation at lower temperatures than at higher temperatures. Recrystallization possibility at higher deformation temperatures will impede more dislocation generation. Consequently, the higher dislocation density, the strengthen austenite matrix before transformation. So, the Ms temperature was lowered by decreasing TiD. It is also evident from the diagram that the higher TiD results in higher fraction of martensite and consequently higher hardness values which are aimed in hot stamping process. It means that forming must take place at a sufficiently high temperature i.e. >800°C where the driving force for austenite decomposition is low. Another realistic alternative to get martensitic microstructure might be forming at low temperatures, such as < 600°C, i.e. below the ferrite regime. In that case, ferrite formation is not happened, although some enhancement of bainite formation may take place. This may not WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
100 Computational Methods and Experiments in Materials Characterisation III be so detrimental, however, due to the notably smaller strength difference between bainite and martensite. Accordingly, the proper temperature range is quite narrow. Concerning to the before mentioned results and discussions, it can be concluded that the deformation in austenitic region will accelerate thermally activated phase transformations and shifts the CCT diagram to the left. Despite the CCT diagram exhibits that at cooling rates higher than 37°C/s, the final microstructure would be fully martensite, but at faster cooling rates, 50°C/s, due to deformation effects, it will be hard to get full martensite microstructure. Although, it is not so easy to distinguish between bainite and martensite in optical microscopy, but hardness measurements can be suitable method to interpret the microstructures. Ferrite is a much softer phase than martensite. It is given a value of 160 HV for ferrite while the martensite has a hardness of >470 HV10. Hardness measurements in fig. 3.a-d confirmed that the microstructure formed after a high temperature plastic deformation has hardness levels between 330-530 HV10. If the hardness of bainite is about 400 HV10, practically some of the secondary phases in addition to the ferrite might be bainite. The other interesting phenomena to be studied are variation of the dilatation values at different forming conditions. Fig. 4 shows the effect of process parameters on the dilatation curves.
0,1
-1
0,0
TiD = 800°C, dH/dt = 0.1s
-1
950°C-15 min
950°C-5 min -0,2
Dilatation
0.12
0.16
0.13
-0,3
950°C-20 min
Hmax = 0.5
950°C-10 min
(a) 100
200
0.02 0.01
-0,2
Hmax = 0.2
-0,3 0.16
-0,4
Hmax = 0.1
0.24
-0,5
0.13
-0,4
300
(b)
-0,6
400
500
600
700
0
100
200
Temperature (°C)
300
400
500
0,1
TiD = 800°C, Hmax = 0.4
0,0
600
700
Temperature (°C)
0,1 -1
0.1 s
-1
0.2 s
750°C 800°C
-1
-1
0.4 s
dH/dt = 0.1s , Hmax = 0.2
0,0
700°C
-0,1
-0,1
-1
1.0 s
-0,2
0.02
-0,3
0.04 0.09 0.15
-0,2 Dilatation
Dilatation
Hmax = 0.4
-0,1
-0,1 Dilatation
TiD = 800°C, dH/dt = 0.1s
0,0
0.07 0.07 0.16 0.24
-0,3 -0,4
850°C
-0,5
-0,4
-0,6
(c)
-0,5 0
100
200
300
400
500
600
700
800
-0,7
(d) 0
100
200
Temperature (°C)
Figure 4:
300
400
500
600
700
Temperature (°C)
The effect of process parameters on the dilatation values during martensitic transformation, a) austenization soaking time, b) max. strain values, c) strain rate and d) initial deformation temperature TiD.
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It must be pointed that the dilatation term is mainly the magnitude of the plastic deformation which is occurred by the martensitic transformation during cooling. This dilatation is an invariant plane strain which is the combined effect of a uniaxial dilatation and a simple shear. The higher volume fractions of martensite result in higher dilatation magnitudes. The variations of martensite contents and the Ms and Mf(%) temperatures as well as the magnitude of dilatation as numbers at different conditions can be discussed by using the diagrams in fig. 4(a)-(d). 3.1 The role of applied force The main process parameter in stamping process which can be controlled and monitored is applied force. The applied force in stamping process is determined by load cell on punch and therefore it can be assumed as an independent parameter. 600
400 363
300 200
240 200
Ms 300 Mf(%)
Martensite (%)
100 0
400
2
4
6
8
10
12
14
200 100
(a) 0
0,0
16
18
0 20
0.01
-0,2 Dilatation
400
0,2
500 Hardness (HV10)
Temperature (°C)
500
600 HV10
-0,4
0.24
-0,6
Force (KN)
-0,8
without Force
-1,0 0.29 -1,2
(b)
-1,4 0
100
200
Force (KN)
Figure 5:
300
400
500
600
700
800
900
Temperature (°C)
The effect of applied force in austenite region on martensitic transformation parameters, a) hardness, Ms and Mf(%) and martensite content, b) dilatation values.
Hence, the attempts were focused on finding the relationship between applied force and martensitic transformation during simultaneous forming and quenching process. The achievements are represented in figs. 5 and 6. It is seen that regardless of other process parameters like rate and magnitude of deformation and even TiD, applied force during compression and cooling in austenite region results in: The Ms temperature decreased about 40°C through different applied forces between 0-16 KN while, the Mf(%) temperature were raised about 40°C. By applying higher force levels the dislocation density of austenite matrix increases and as a consequence, more activation energy is needed to make martensitic transformation. Hence, the Ms temperature is lowered. The martensite contents and in the same manner the dilatation magnitudes-as is seen in figs. 5.a and b were lowered by increasing the max. applied forces. The microstructure in absence of applied force was fully martensitic whereas in the case of 16 KN applied force, there was only about 30% martensite in microstructure. There is a minimum force limit which yielded fully martensitic microstructure and higher hardness level. As is seen in fig. 5.a, the minimum WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
102 Computational Methods and Experiments in Materials Characterisation III applied force which gave fully martensitic microstructure and higher hardness in comparison with the forceless samples was 6 KN. The hardness in the sample which tolerated 6 KN was 523 HV10 while in the forceless sample was 500 HV10. It might be due to finer martensite lathes in deformed samples. It can be concluded that lower applied forces during hot stamping process result in more successful martensitic transformation and better material properties.
Figure 6:
Microstructure evolution by applying different force levels in austenite region; a) 0 KN, b) 6.1 KN, c) 12 KN and d) 16 KN.
As can be seen in fig. 6.a-d, the higher applied forces yielded on more bainite networks and some ferrite islands as the secondary phase. It can be concluded that by increasing the applied stress level in the austenite region, the nose of bainite in the CCT diagram not only shifts to the left but also to the lower temperatures (due to decreasing of the Ms temperature). It can be interpreted that by applying higher force levels on constant shape or volume of samples, more dislocations will be formed. Accordingly, these forests of dislocations will accelerate the thermally activated phase transformations and therefore, the nose of ferrite and bainite phases shift more and more to the left. It was also seen that the applied force in the austenite region altered the bainite nose more than ferrite zone. That is, to get fully martensitic microstructure in the final sample in hot stamping, cooling rate must be sufficiently higher than the minimum cooling rate which is mentioned in the CCT diagram, i.e. higher than 37°C/s. It can be simply concluded that to get full martensite in the end product, WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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cooling rates are strongly dependent on the maximum applied force level. Instead, the higher force levels need higher cooling rates to get fully martensitic microstructure. The above mentioned facts gives the best key points to control martensitic transformation during hot stamping process, because the applied force is the best parameter which can be in hand and in control during the process.
4
Conclusions
The martensitic transformation which occurs during hot stamping process was investigated by means of simultaneous hot compression and cooling in dilatometry machine, resulting in the following conclusions. 1- The Ms temperature is decreased by increasing austenization soaking time. The variation of martensite content is negligible. Due to coarser martensite lathes at longer soaking time, hardness is decreased. Hence, to have a successful hot stamping process, the optimum soaking time is required to get fully fine lath martensitic microstructure. 2- At constant initial deformation temperatures TiD and constant rates, higher deformation levels are ended at lower temperatures and therefore, the possibilities to cross ferrite and bainite noses are raised. Accordingly, the martensite fractions are lowered and as a result lower hardness values are achieved. The decrease in Ms is about 15°C but owing to martensite content reduction, the Mf(%) temperature is increased about 50°C. 3- The higher rates of stamping, the higher temperatures to finish the deformation. At constant deformation magnitudes and constant initial deformation temperatures, higher strain rates results in more martensite fractions and higher hardness. The possibility of the presence of ferrite islands is increased by increasing the rates of deformation. 4- The higher initial deformation temperatures results in higher volume fraction of martensite which is favorite in hot stamping process. It means the time to transfer material from furnace to press must be as short as possible. The 850°C800°C ranges is recommended as the best start temperature to deform the studied steel through hot stamping process. 5- Regardless of rate, magnitude and start temperature of deformation, maximum applied force as an outstanding parameter in hot stamping process can give the best interpretations. The higher forces are applied in austenite region, the martensite volume fractions and the hardness levels are decreased. The Ms temperature is decreased about 40°C by applying 16 KN force to compression samples. In hot stamping process, the lowest possible level of force must be applied to achieve the favorite microstructure. 6- It can be concluded that by applying deformation in austenite region the CCT diagram shifts not only to the left but also to the lower temperatures. Accordingly, the criteria to get full martensitic microstructure in final product through hot stamping process do not follow the CCT boundary conditions and must be cared. Instead, the higher applied force, the faster cooling rate to get fully fine lath martensitic microstructure. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
104 Computational Methods and Experiments in Materials Characterisation III
References [1] [2] [3]
[4] [5] [6] [7] [8]
C. Capdevila, F.G. Caballero and C. Garcia de Andres, Analysis of the effect of alloying elements on the martensite-start temperature of the steels, Materials science and Technology, 2003, Vol.15, no.5, 581-586. P.J. Brofman, G.S. Ansell, The Effect of Fine Grain Size on the Ms Temperature in Fe-27Ni-0.025C Alloys, Metal. Trans. A, 1983, 14A, 1929-1931. M.C. Somani, L.P. Karjalainen and M. Eriksson, Dimensional changes and microstructural evolution in a B-bearing steel in the simulated forming and quenching process, ISIJ International, Vol. 41, No.4, 2001, 361-367. M. Unemoto, W.S. Owen, Effects of austenitizing temperature and austenite grain size on the formation of athermal martensite in an ironnickel and an iron-nickel-carbon alloy, Metal. Trans., 1975, 5, 2041-2053. O.A. Ankara, A.S. Sastri, D.R.F. West, Some effects of austenitizing conditions on martensite formation in an iron-20% nickel alloy, J. Iron and steel institute, 1966, 509-511. S. Denis, E. Gautier, A. Simon, and G. Beck, Stress-phase-transformation interactions-basic principles, modelling and calculation of internal stresses, Mater.Sci.Technol. 1, 1985, 805-814. I. Tamura, C. Ouchi, and T. Tanaka, Thermo-mechanical processing of high strength low alloy steels, Butterworth, London, 1988, 99. C.S. Lee, and W.Y. Choo, Effects of austenite conditioning and hardenability on mechanical properties of B-containing high strength steel, ISIJ Int. 40, 2000, S189-S193.
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Quantitative assessment of strain and heat treatment on twin formation in commercially pure nickel Q. Li, J. R. Cahoon & N. L. Richards Department of Mechanical and Manufacturing Engineering, University of Manitoba, Winnipeg, Manitoba, Canada
Abstract Thermomechanical treatment comprising cold working to 6% strain followed by annealing at temperatures in the range 700 oC to 1000 oC greatly increases the fraction of special boundaries, primarily 63 type. The accompanying generation of annealing twins is analysed using the accident growth model due to Gleiter and the phenomenological model of Pande et al. It is shown that Gleiter’s model, which contains no scaling factors, when used correctly, predicts the twin density in Cu alloys and pure nickel. The model due to Pande et al also predicts the twin density in Ni but this model incorporates two scaling factors that detract from its generality. Keywords: special grain boundaries, annealing twins, copper alloys, nickel.
1
Introduction
It has been long accepted that thermomechanical treatments can alter the size, shape and crystallographic orientation of grains. In 1984, Watanabe [1] proposed that the type of grain boundaries present could also be controlled sand thus the concept of “grain boundary engineering” was initiated. Grain boundary engineering has been used to increase the fraction of “special grain boundaries”, usually defined in terms of coincidence lattice site (CSL) boundaries. A high fraction of low 6 CSL boundaries {6 ( 29)} has been shown to improve resistance to intergranular crack propagation in Inconel 600 [2, 3] and to substantially improve the elevated temperature crack growth resistance of a nickel-based superalloy [4]. For type 304 stainless steel and alloy 600, high WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/MC070111
106 Computational Methods and Experiments in Materials Characterisation III 6 CSL boundary fractions resulted in reduced crack growth rates. High special grain boundary fractions also resulted in a significant reduction of intergranular stress corrosion cracking in irradiated type 304 stainless steel [5]. It has been clearly demonstrated that high fractions for 6 CSL special boundaries can substantially improve the resistance to creep, fatigue, and environmental degradation of engineering alloys. The purpose of the present investigation was to increase the fraction of 6CSL special boundaries in commercially pure nickel by employing an appropriate thermomechanical treatment. Following treatment, the fraction of special boundaries was determined using orientation imaging microscopy and the annealing twin density was also determined. The experimental values for annealing twin density are compared to the theoretical models of Gleiter [6] and Pande et al [7].
2
Experimental
The material used for this investigation was commercial purity nickel sheet, 3mm thick, mill annealed at 750qC. Work completed by Guyot et al [8] indicated that cold rolling 6% reduction in area would be a good starting point for the investigation. Therefore, strips of the as-received sheet were cold rolled 6% reduction in area and annealed for various times at temperatures from 500qC to 1000qC to obtain a range of grain sizes. Following the anneals, the fraction of special grain boundaries was determined using orientation imaging software EDAX/TSL, version 3.5, on a JEOL 5900 SEM equipped with an ultra thin, Oxford EDS window. Grain sizes and annealing twin densities were determined using the linear intercept method on a Zeiss microscope equipped with a Clemex Vision Image Analysis System. The results from at least 600 intercepts were averaged to obtain the values.
3
Results and discussion
The fraction of special boundaries after ten minutes at the annealing temperature is shown in fig 1. Over 80% of the special boundaries were of the 63 type with small fractions of 69, 627 and other types. The effect of annealing time at 700qC on the fraction of special boundaries is given in fig 2 which shows that the optimum annealing time at 700qC is 2.2 X 105 s or about 61 hours (220,000 s). The maximum 75% of special boundaries obtained by annealing at 700qC for 61 hours is the same as the maximum percentage of 75% obtained after annealing at 900qC for 10 minutes (600s). If the formation of special boundaries is diffusion controlled, then the product of Dt, where D is the diffusion coefficient and t is the annealing time, should be similar for the optimum times at the various annealing temperatures. However, the formation of special boundaries could be controlled by either grain boundary diffusion or lattice diffusion so both cases must be considered. For the grain boundary diffusion coefficients, we use the results of ýermák [9] who obtained Dgb = 5.1 X 10-15 exp (-120,000/RT) m2/s where R = 8.3145 J·K-1· mole-1 and T is the absolute WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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107
Percentage of Special Boundaries
temperature. (Actually, ýermák’s results were primarily for the grain boundary diffusion of Co in Ni, but he obtained a few results for the grain boundary diffusion of Ni in Ni that were essentially identical to the values for the diffusion of Co in Ni. Since Co and Ni atoms are very similar, ýermák concluded that the grain boundary diffusion of Ni in Ni was similar to that for the grain boundary diffusion of Co in Ni. Further, ýermák’s results agree well with the earlier results of Wazzan [10].)
80 70 60 50 40 30 20 10 0 500
700
800
900
1000
Annealing Temperature (oC) Figure 1:
Percentage of special boundaries after cold rolling 6% reduction in area and annealing for 10 minutes.
Percentage of Special Boundaries
100 80 60 40 20 0 0.E+00
2.E+05
4.E+05
6.E+05
8.E+05
Annealing Time (sec) Figure 2:
Percentage of special boundaries after cold rolling 6% reduction in area and annealing at 700qC.
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108 Computational Methods and Experiments in Materials Characterisation III For 700qC, the grain boundary diffusion coefficient is 1.84 X 10-21 m2/s and for an annealing time of 220,000 s, the product Dt = 4.1 X 10-16 m2. For 900qC, the grain boundary diffusion coefficient is 2.31 X 10-20 m2/s and for an annealing time of 600s, the product Dt = 1.4 X 10-17 m2. For grain boundary diffusion, the Dt values for the two temperatures differ by a factor of about 40. The lattice diffusion coefficient for the diffusion of Ni in Ni is given by Dlatt = 1.82 X 10-4 exp(-285,000/RT) m2/s [11]. For 700qC, the lattice diffusion coefficient is 9.13 X 10-20 m2/s and for an annealing time of 220,000 s, the product Dt = 2.0 X 10-14 m2. For 900qC, the lattice diffusion coefficient is 3.71 X 10-17 m2/s and for an annealing time of 600s, the product Dt = 2.2 X 10-14 m2. For lattice diffusion, the Dt values for the two temperatures are almost identical. Therefore, it appears that the formation of special grain boundaries in commercially pure Ni is controlled by lattice diffusion. The annealing twin densities for annealing temperatures of 700qC, 800qC, and 1000qC are plotted versus grain size in figs 3-5 respectively. Two models were used to calculate the theoretical values for the twin density. The first is due to Gleiter [6] who proposed an atomistic model for the formation of annealing twins. Gleiter proposed that the probability, p, of a {111} plane being a coherent twin plane is given by:
p
° § 'G 0 exp®V z ¨¨ Q kT ln kT °¯ ©
· ª SkTH 2 h 2 ¸¸ / «kTV z 0 Q kT ln 'kTG ¹ ¬«
º ½° »¾ . ¼» °¿
(1)
In eqn (1), Vz is the surface energy of a coherent twin boundary, Q is the activation energy for grain boundary migration, 'G0 is the difference in the Gibbs’ free energy between the growing and the shrinking grain, h is the step height formed by the twin nucleus (taken as the distance between {111} planes), H is the surface energy of a step of height h, and k and T have their usual meanings. The twin density is simply calculated from the product of the number of {111} planes per unit length and the probability that any {111} is a coherent twin plane. Gleiter, noting that kT << Q, deleted the entire term kTln ('G0/kT) from the denominator of eqn (1) (but not the numerator) and obtained a simplified equation. The use of Gleiter’s simplified equation usually results in a temperature dependence as well as a grain size dependence for the twin density. Several investigators [7, 12–15] have obtained experimental results (or have proposed) that the twin density is essentially independent of temperature and have therefore considered Gleiter’s theory as incorrect. However, Li et al [15] showed that the entire term {kTln ('G0/kT)} is in fact not negligible and should not be removed from the denominator of eqn (1). Li et al also showed that when Gleiter’s complete equation is used, the twinning probability in Cu-3 wt% Al alloy with a grain size of 300 Pm is essentially independent of temperature as shown in fig 6. This is in agreement with the observations of Meyers and McCowan [13] as well as Pande et al [14] who suggested that the twinning probability for 300 Pm grain size Cu-3 wt% Al alloy is independent of the annealing temperature with a constant value of p | 2.75 X 10-5 (fig 6). WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
Computational Methods and Experiments in Materials Characterisation III
Experimental Calculated - Gleiter [6]
-1
Twin Density ( Pm )
1.E-01
109
Calculated Pande et al [7] 1.E-02
1.E-03 20
40
60
80
Grain Size (Pm) Figure 3:
Twinning density for nickel annealed at 700qC. (G = 1.04 J/m2, Vz = 0.0367 J/m2).
Experimental Calculated-Gleiter [6] Calculated Pande et al [7]
-1
Twin Density ( Pm )
1.E-01
1.E-02
1.E-03 45
50
55
60
65
70
75
Grain Size (Pm) Figure 4:
Twinning density for nickel annealed at 800qC. (G = 0.994 J/m2, Vz = 0.0333 J/m2).
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110 Computational Methods and Experiments in Materials Characterisation III
Twin Density ( m-1)
1.E-01
Experimental Calculated-Gleiter [6] Calculated-Pande et al [7]
1.E-02
1.E-03 10
20
30
40
50
60
70
80
90 100 110 120
Grain Size (Pm) Figure 5:
Twinning density for nickel annealed at 1000qC. (G = 0.899 J/m2, Vz = 0.026 J/m2).
1.E-04 Twinning Probability
Experimental [12] Calculated - Eq (1)
1.E-05 400
500
600
700
800
Annealing Temperature (oC) Figure 6:
Comparison of experimental values of twinning probability with values calculated from Gleiter’s theory, eqn (1), for a grain size d = 300 Pm. (Vz=0.01037 J/m2, Q=1.9 X 10-19 J/atom, G=0.6 J/m2, h=2.097 X 10-10 m, H = G/2 = 0.3 J/m2, 'G0 = 4G/d = 8 X 103 J/m3 = 9.58 X 10-26 J/atom).
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Assuming that the annealing twin density is independent of annealing temperature, Pande et al [7, 14] developed a phenomenological equation giving the probability of a {111} plane being a twinning plane as:
p
kG § d A n¨ d ¨© d 0
· ¸¸ ¹
(2)
where G is the grain boundary energy, d is the grain diameter, d0 is a material constant representing the smallest grain size for which twinning can occur, and k is a scaling factor also dependent upon the material.
–1 -1 (µm Annealing Twin Density ( ٛٛ m ))
1.E-01
1.E-02
Experimental-700 C
Experimental-800 C
Experimental-900 C Experimental-1000 C
Gleiter-700 C
Gleiter-800 C Gleiter-1000 C
1.E-03 0
10 20 30 40 50 60 70 80 90 100 110 Grain Size (µm) Grain Size (ٛ m)
Figure 7:
Experimental results for the twin density compared to values calculated from eqn (1) for different grain sizes and annealing temperatures.
The experimental values for the annealing twin densities in commercially pure Ni are compared with the values calculated from both eqn (1) and eqn (2) in figs 3 to 5. The values used for the variables in eqn (1) were Q = 120,000 J/mole = 2.0 X 10-19 J/atom and h = 2.0344 X 10-10 m. The value of the step energy, H, is taken as H = G/2 [6] where G is the grain boundary energy which varies with temperature and is taken from data given by Murr [16]. The value of 'G0 is WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
112 Computational Methods and Experiments in Materials Characterisation III taken as 'G0 = 4G/d [6] and converted to the appropriate units using the atomic weight and density of pure Ni. Following Gleiter [6], the surface energy of a coherent twin boundary, Vz , was used as an adjustable parameter to obtain a good fit with the experimental data. The values of twin density calculated from the Gleiter model, eqn (1), are given by the solid lines in figs 3-5. Pande et al [14] suggested that the constant d0 in eqn (2) should be about 1 Pm for Ni. Choosing values of d0 = 1.5 Pm and k = 1.9 X 10-11 m3/J results in reasonable agreement with the experimental values as shown by the dashed lines in figs 3-5. However, the formulation due to Gleiter is more general in that it uses only one adjustable parameter, Vz , and this is approximately 0.03 J/m for the temperature range 700qC - 1000qC. The value of Vz = 0.03 seems reasonable in comparison to the values of Vz = 0.01 for Cu - 3 wt% Al and Vz = 0.02 J/m2 for pure Cu [15]. Further, use of the Gleiter formulation, eqn (1), results in calculated values for the twin density that are essentially independent of temperature even though the formulation explicitly contains the temperature. This is illustrated in fig 7 where the calculated twin density is essentially independent of temperature and agrees well with experimental values.
4
Conclusions
1.
The percentage of special grain boundaries in commercially pure Ni can be increased from about 30% in the as received material to about 75% in material cold rolled 6% reduction in area and annealed at temperatures from 700qC to 1000qC.
2.
The special boundaries are primarily 63 type.
3.
The formation of special grain boundaries in commercially pure Ni appears to be controlled by lattice diffusion.
4,
The annealing twin density in commercially pure Ni is essentially independent of temperature for annealing temperatures from 700qC to 1000qC.
5.
Values for the annealing twin density calculated from the Gleiter model and including all terms in the equation, agree well with experimental values.
6.
The phenomenological equation due to Pande et al [7, 14], eqn (2), results in calculated values for annealing twin densities that agree well with experimental values using values of d0 = 1.5 Pm and k = 1.9 X 10-11 m3/J.
Acknowledgements The authors are grateful for the technical support of John Van Dorp, Mike Boskwick, and Don Mardis. The financial support of NSERC in the form of Discovery grants to two of us (J.R. Cahoon and N.L. Richards) is greatly appreciated. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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References [1] [2]
[3]
[4]
[5] [6] [7] [8] [9] [10] [11]
[12] [13]
[14]
Watanabe, T., An approach to grain boundary to grain boundary design for strong and ductile polycrystals. Res. Mech. 11, pp. 47-84, 1984. Palumbo, G., Lehockey, P. Lin, Erb, U. & Aust, K.T., Grain boundary engineering for intergranular fracture and creep resistance. Microscopy and Microanalysis, Eds Bailey, G.W., Corbett, J.M., Dimlich, R.V.W., Michael, R. & Zaluzec, N.J., San Francisco Press: San Francisco, pp. 362363, 1996. Palumbo, G., Lehockey, P. Lin, Erb, U. & Aust, K.T., A grain boundary engineering approach to materials reliability, MRS Proceedings of the Symposium on Interfacial Engineering for Optimized Properties, 458, pp. 273-383, 1997. Gao, Y., Kumar, M., Nalla, R.K. & Ritchie, R.O., High cycle fatigue of nickel-based superalloy ME3 at ambient and elevated temperatures: Role of grain-boundary engineering, Metall. Mater. Trans. A, 36A, pp. 33253333, 2005. Was, G.S., Alexandreanu B., Andresen, P. & Kumar, M., Role of coincident site lattice boundaries in creep, corrosion and stress corrosion cracking, Mat. Res. Soc. Symp. Proc., 819, pp. N2.1.1-N2.1.14, 2004. Gleiter, H., The formation of annealing twins, Acta Metallurgica, 17, pp.1421-1428, 1969. Pande, C.S., Imam, M.A. & Rath, B.B., Study of annealing twins in FCC metals and alloys, Metall. Trans. A, 21A, pp. 2891-2896, 1990. Guyot, B., Lee, S-L., and Richards N.L., Effect of Small Strain Levels on Special Boundary Distribution in Commercially Pure Nickel, J. of Mat. Eng. & Performance, 14 (1), pp. 85-90, 2005. ýermák, J., Grain boundary diffusion of Co-60 in nickel, phys. stat. sol., (a), 117, pp. 387-393, 1990. Wazzan, A.R., Lattice and grain boundary diffusion in nickel, J. Appl. Phys., 36 (11), pp. 3596-3599, 1965. Burachynsky, V., & Cahoon, J.R., A theory for solute impurity diffusion, which considers Engel-Brewer valences , balancing the Fermi energy levels, and differences in zero point energy, Metall. Mater. Trans. A, 28A, pp. 563-582, 1997. Bäro, G. & Gleiter, H., The formation of annealing twins, Z. Metallkde, 63, pp. 661-663, 1972. Meyers, M.A. & McCowan, C., The formation of annealing twins: overview and new thoughts, Interface migration and control of microstructure, Proc. of an Int. Conf. Symp. held in conjunction with ASM’s Metals Congress and TMS/AIME fall meeting, Detroit, MI, USA, Sept. 17-21, 1984, eds. C.S. Pande, D.A. Smith, A.H. King & J. Walter, ASM, Metals Park, OH,1984, pp. 99-123, 1984. Pande, C.S., Iman, M.A. & Rath, B.B., Annealing twins in f.c.c. metals and alloys, ibid, pp. 125-129.
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114 Computational Methods and Experiments in Materials Characterisation III [15] [16]
Li, Q., Cahoon, J.R. & Richards, N.L., On the calculation of annealing twin density, Scripta Metall., 55, pp. 1155-1158, 2006. Murr, L.E., Interfacial Phenomena in Metals and Alloys, Addison Wesley Publishing Company, Reading, MA, p.133, 1975.
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Three-dimensional crystallographic characterization and mechanical modeling of a commercial stainless steel A. C. Lewis, D. J. Rowenhorst, G. Spanos & A. B. Geltmacher Multifunctional Materials Branch, U. S. Naval Research Laboratory, Washington, DC, USA
Abstract The microstructure, crystallography, and mechanical response of a commercial super-austenitic stainless steel, AL-6XN, has been investigated. Three-dimensional (3D) reconstructions, generated by combining serial sectioning techniques with Electron Backscatter Diffraction (EBSD), are used for characterization of the microstructure and crystallography of the material, and as input for 3D Image-Based Finite Element Models (IB-FEM). Using these techniques, the distributions of crystallographic 3D grain boundary normals have been quantified, and are shown to provide critical new information not previously attainable from the commonly used morphological descriptors. Image-based finite element simulations, with the 3D microstructure and crystallography as input, were performed to determine the critical microstructural features at which failure is likely to initiate. Keywords: 3D microstructures, 3D analysis, austenitic stainless steel, crystallography, finite element modeling.
1
Introduction
Three-dimensional experimental materials characterization and analyses are becoming increasingly prevalent, as recent advances have made both the acquisition of 3D datasets and the analysis of these data faster and more readily available (i.e. [1-4]). As material data evolves from classic two-dimensional micrographs and cross-sectional images to complete three-dimensional datasets, the modeling and simulation techniques used to analyze the properties and predict the performance of these materials must also adapt to accommodate these WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/MC070121
116 Computational Methods and Experiments in Materials Characterisation III 3D microstructures. Particularly in the case of mechanical performance, the true 3D microstructural characteristics of a material must be understood in order to model its behavior accurately [5–11]. In addition, crystallographic orientation, which plays a critical role in the elastic and plastic behavior of many materials, must be considered in the simulation of mechanical behavior at the mesoscale. With complete 3D spatial and crystallographic information of a given microstructure, Image-Based Finite Element Modeling (IB-FEM) can be used to determine critical microstructural features where failure or fracture is likely to initiate in the material. To understand fully the crystallography of a material, it is essential to use three-dimensional information about the grain morphology and orientation, particularly when studying grain boundaries. While a great deal of information on grain orientation, boundary structure, and misorientation can be obtained from conventional electron backscatter diffraction (EBSD) techniques, the complete (5-parameter) description of a grain boundary cannot be sufficiently determined from extrapolations of 2D data [12]. Combining experimentallydetermined spatial and crystallographic microstructural data and using these data as input for finite element modelling of mechanical response thus provides a wealth of information not previously available for real 3D microstructures, and through the quantitative analysis of these data, a complete characterization of material microstructures can be established.
2
Materials and methods
The material examined in this study is AL-6XN, a commercially available superaustenitic stainless steel. The as-received material was in the form of a continuously cast and milled annealed (>11000C) 6.35 mm-thick (1/4”) plate. The mechanical properties of AL-6XN have been reported in detail [13], including high observed ductility (strain >40%) over a broad range of temperatures, and little sensitivity to strain rate. A second phase (V) has been observed at the centerline of AL-6XN plates, which can result in reduction in mechanical performance and initiation of fracture and failure [14]. This work focuses on the austenite matrix, and specimens were collected far from the centerline to avoid any interaction of the austenite with the second phase precipitates. Serial sectioning in conjunction with optical microscopy and automated EBSD were used to create a three-dimensional reconstruction of the austenite matrix, incorporating crystallographic orientation of austenite grains. Optical micrographs were recorded for each section, followed by the removal of approximately 3.3 Pm of material by mechanical polishing. This process was repeated over 100 times, with EBSD scans recorded every tenth section (every 33 Pm). Image processing was performed using Matlab and Photoshop software packages, and 3D reconstruction and data analyses were performed using Matlab and the Interactive Data Language (IDL). Further details of the data collection and 3D reconstruction procedures are provided in prior works [15], in which the same techniques were applied to a preliminary dataset. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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A complete set of 3D microstructural analyses was applied to the reconstructed volume. The dataset consists of a 3D array of integers, each representing a grain identification number, and corresponding to each grain ID there is an associated crystallographic orientation, averaged over all measured values for that grain. Formatting the data in this way make microstructural characterization relatively straightforward – grain volumes, for example, are calculated by recording the number of voxels in each grain, and multiplying by the appropriate microns-per-voxel conversion. Grain aspect ratios are measured by fitting a 3D ellipsoid to each individual grain and twin, and calculating the major axis and the shortest minor axis. This measure, along with the number of facets each grain has, gives a quantitative measure of the grain morphology, without the need for categorizing the varied and complex shapes found within such a highly twinned microstructure. A single crystallographic orientation was assigned to each grain and twin within the 3D microstructure, based on the averaged values measured using EBSD. Attaining the true 3D shape of each grain and twin along with its crystallography allows for the measurement of the complete 5-parameter grain boundary definition [12, 16]. Although this dataset contains just 120 complete reconstructed grains, the number of interfaces between grains number over 2000, and it is not necessary to reconstruct the entire surface between two grains to determine the misorientation between them, or, in most cases, the complete grain boundary definition. The convention used here to describe the grain boundary plane is to define the two crystallographic normals of the intersecting plane (with respect to the two grains on either side of the plane), and the angle of twist between them. In addition to microstructural and crystallographic characterization, the simulated mechanical response of this material was studied using image-based finite element modeling, with the 3D spatial and crystallographic reconstruction as input. The finite element mesh is a regular rectangular grid generated using the 3D microstructural data array, and defining one element per voxel. Due to constraints on file size and computation time, the mesh for these simulations was created by sampling every fourth voxel in each sectioning (x-y) plane. Each element is therefore 3.6 x 3.6 x 3.3 µm in size and comprises the ABAQUS® C3D8 element type. Each of the 346 grains is represented by an individual element set, and each element set is assigned the average calculated crystallographic orientation for that grain. All simulations were run using anisotropic elasticity. Further details of the meshing and simulation techniques were reported previously for work on a smaller, preliminary data set [10].
3
3D microstructural analysis
A 3D reconstruction of the AL-6XN microstructure is shown in Figure 1. The reconstructed volume measures 450 x 450 x 260 Pm, and contains 346 grains and twins. (For the purposes of this analysis, a “grain” is defined by a single orientation, and twins are therefore considered as separate from their parent grains.) Of these 346 reconstructed grains, 120 are completely contained within the dataset, that is, they do not intersect the edges of the reconstructed volume. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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Figure 1:
3D reconstruction of the austenite phase of AL-6XN. The color of each individual grain and twin corresponds to the crystallographic orientation parallel to the sample z-axis, according to the legend.
Two- and three-dimensional analyses of the AL-6XN microstructure were performed on a preliminary dataset, reported previously [15]. The preliminary dataset, however, contained only a handful of “interior” grains not intersecting the edges of the reconstructed volume. The current dataset shown in Figure 1 contains 120 such grains, and although this does not represent a statistically significant number of grains, analysis of the size and shape of these grains does provide useful information with respect to the microstructural characterization of this material. Figure 2 shows the grain size distribution for the 120 interior grains in the above microstructure. The values reported are the spherical equivalent radius, calculated based on the volume of each individual grain, which is equal to the number of voxels each grain comprises, multiplied by the appropriate cubic micron-per-voxel conversion (in this dataset, one voxel equals approximately 2.7 Pm3). The average (mean) measured grain volume is 156,000 Pm3, or approximately (54 Pm)3. Figure 3 shows the distribution of 3D grain aspect ratios for the interior grains in the microstructure. The grain aspect ratio is measured by fitting an ellipsoid to each grain, and measuring the major axis, divided by the shortest minor axis. Note that the majority of the grains in this microstructure have an aspect ratio much greater than 1, suggesting that there are very few equiaxed grains, and that the distribution of shapes in this microstructure is quite complex. Previous 2D measurements of the crystallography of this material have shown that the microstructure contains a significant number of recrystallization twins with the 6=3 coincident site lattice (CSL) misorientation relationship [15]. Visualization of the reconstructed 3D microstructure confirms that a large number of these twins have plate-like morphologies, and therefore fall into the larger end of the aspect ratio distribution. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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Figure 2:
Grain size distribution for the “interior” grains in the reconstructed 3D microstructure shown in Figure 1.
Figure 3:
3D aspect ratio distribution for the “interior” grains in the reconstructed 3D microstructure shown in Figure 1.
Figure 4 shows 3D reconstructions of the grain boundary networks in this AL-6XN volume. In this figure, grain boundaries and junctions are color-coded based on the junction type. Only two types of boundary surfaces were considered here: 63 CSL boundaries (light color in the figure), and general high-angle (>150) grain boundaries (dark color in the figure). The triple junction networks were also reconstructed, but are not shown in the figure. The 3D reconstruction of the boundary and junction networks in this microstructure, particularly the network of 63 twin boundaries, are used for additional analysis of crystallography, corrosion properties, and, using image-based FEM, the critical microstructural features where plasticity is likely to initiate.
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Figure 4:
4
3D reconstruction of grain boundaries in the AL-6XN microstructure shown in Figure 1. General high-angle grain boundaries are shown in blue (dark color), 63 CSL boundaries are shown in yellow (light color).
Crystallographic analysis
Because this microstructure is so highly twinned, a wide range of grain sizes and shapes are present, and conventional morphological descriptors are not sufficient to characterize it completely; the crystallography must therefore also be quantified. Using the information obtained from serial sectioning and EBSD, the crystallographic normals of each grain boundary plane can be determined, and boundaries between two grains can be defined completely by the two crystallographic normals of the intersecting plane (with respect to the two grains on either side of the plane), and the angle of twist between them [15]. To quantify the crystallography in the AL-6XN microstructure, the crystallographic normals were calculated for all boundary surfaces. Rather than fit a plane to each grain boundary and determine a single set of normal vectors, the microstructure was converted to a 3D surface mesh, and the crystallographic normal for each patch or “sub-surface” on the mesh was calculated and plotted. (Details of this procedure are reported elsewhere [2].) Figure 5 is a Crystallographic Interface Normal Distribution (CIND) plot for all surfaces within the AL-6XN microstructure shown in Figure 1. In the figure, the largest peaks are observed near the <101> and <113> directions. The largest concentration of normal directions is within 50 of the <101> directions. This peak corresponds to <101> 63 twist boundaries, which dominate the twin structure. Note that, although it is the lowest energy family of boundary planes, the strongest peak is not found near the <111> normal direction. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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Figure 5:
5
121
Crystallographic Interface Normal Distribution (CIND) plot for each interface in the AL-6XN microstructure shown in Figure 1.
Image-based finite element modeling
The 3D spatial and crystallographic information obtained from serial sectioning and EBSD was used as input into an image-based finite element model, to simulate the response of the microstructure to a variety of loads under a number of different constraints. The model was tested under uniaxial stretch, plane strain tension and uniaxial tension conditions by applying the appropriate displacement boundary conditions to the faces of the model. A detailed quantitative analysis of the simulated mechanical response was performed, and is to be reported a future manuscript [17]; a few examples of the type of analysis and visualization techniques are presented here. Figure 6 is a contour plot of the von Mises stress as a result of 0.2% applied elastic strain in the x-direction, as indicated by the axes in the figure. In this simulation, the strain was applied uniformly to the positive x-face, and all other faces were constrained to be fixed. Variations in von Mises stress resulting from this strain due to local anisotropy are visible in the figure. In these datasets, quantitative data mining and advanced scientific visualization techniques are used to determine correlations between microstructure and mechanical properties. In previous studies [1, 10], high stresses have been observed at grain boundaries and junctions. In particular, the behavior of 63 boundaries under different loading conditions is of interest, as it has been observed that the preferential response of these boundaries depends on the loading conditions applied [17]. To determine the effect of crystallography and grain structure on mechanical behavior, the mechanical response of the material around grain boundaries and triple junctions was studied under a variety of loading conditions. Finite element simulation outputs such as von Mises stress and maximum principal strain for the reconstructed volume were analyzed at specific crystallographic and microstructural features, including general and special grain boundaries and WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
122 Computational Methods and Experiments in Materials Characterisation III triple junctions. It was found that, under constrained uniaxial tensile loading, values of von Mises stress are highest near the junctions between two 63 grain boundaries. This is not the case, however, for simple shear loading, which results in highly variable stresses at these junctions, which in some cases are lower than at any other junction type.
Figure 6:
6
Contour plot of von Mises stress resulting from 0.2% applied elastic strain in the x-direction.
Conclusions
The microstructure, crystallography, and mechanical response of a commercial super-austenitic stainless steel, AL-6XN, was investigated. Three-dimensional reconstructions, generated by combining serial sectioning techniques with (EBSD), are used for characterization of the microstructure and crystallography of the material, and as input for 3D Image-Based Finite Element Models. Using these techniques, the distributions of crystallographic 3D grain boundary normals have been quantified, and are shown to provide critical new information not previously attainable. The microstructure, which is dominated by 63 recrystallization twins, contains a majority of <101> twist boundaries. Imagebased finite element simulations, with the 3D microstructure and crystallography as input, were performed to determine the critical microstructural features at which failure is likely to initiate. This combination of 3D crystallography, morphology, and mechanical modeling provides new insight into the characterization and analysis of this material not possible with 2D imaging and simulations.
Acknowledgements This work was jointly sponsored by the Office of Naval Research (ONR) and DARPA as part of the Dynamic 3-D (“D3D”) Digital Structures program. Additional funding was from ONR under the “Design of Naval Steels” program. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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The authors wish to express their gratitude to Mr. Leroy Levenberry, Ms. Jessica Woods and Mr. Jehud Flores for their significant efforts in the serial sectioning and image processing of the data. The material used in this study was provided by Mr. E. Czyryca at the Naval Surface Warfare Center – Carderock Division.
References [1] [2] [3] [4] [5] [6] [7]
[8] [9]
[10] [11] [12] [13]
Lewis, A.C., et al., Quantitative analysis and feature recognition in 3D microstructural data sets. JOM, 58(12), p 52-56, 2006. Rowenhorst, D.J., et al., 3D crystallographic and morphological analysis of coarse martensite: Combining EBSD and serial sectioning. Scripta Materialia, 55(1): p. 11-16, 2006. Spowart, J.E., Automated serial sectioning for 3-D analysis of microstructures. Scripta Materialia, 55(1): p. 5-10, 2006. Uchic, M.D., et al., 3D microstructural characterization of nickel superalloys via serial-sectioning using a dual beam FIB-SEM. Scripta Materialia, 55(1): p. 23-28, 2006. Cailletaud, G., et al., Some elements of microstructural mechanics. Computational Materials Science, 27(3): p. 351-374, 2003. Chawla, N. and Deng, X., Microstructure and mechanical behavior of porous sintered steels. Materials Science and Engineering A, 390(1-2): p. 98-112, 2005. Chawla, N., Ganesh, V.V., and Wunsch, B., Three-dimensional (3D) microstructure visualization and finite element modeling of the mechanical behavior of SiC particle reinforced aluminum composites. Scripta Materialia, 51(2): p. 161-165, 2004. Ghosh, S. and Moorthy, S., Three dimensional Voronoi cell finite element model for microstructures with ellipsoidal heterogeneties. Computational Mechanics, 34(6): p. 510-531, 2004. Kenesei, P., Borbely, A., and Biermann, H., Microstructure based threedimensional finite element modeling of particulate reinforced metalmatrix composites. Materials Science and Engineering A, 387-89: p. 852856, 2004. Lewis, A.C. and Geltmacher, A.B., Image-based modeling of the response of experimental 3D microstructures to mechanical loading. Scripta Materialia, 55(1): p. 81-85, 2006. Youssef, S., Maire, E., and Gaertner, R., Finite element modelling of the actual structure of cellular materials determined by X-ray tomography. Acta Materialia, 53: p. 719-730, 2005. Wolf, D. and Yip, S., eds. Materials Interfaces: Atomic-level structure and properties. 1992, Chapman and Hall: London. Nemat-Nasser, S., Guo, W.G., and Kihl, D.P., Thermomechanical response of AL-6XN stainless steel over a wide range of strain rates and temperatures. Journal of the Mechanics and Physics of Solids, 49(8): p. 1823-1846, 2001.
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124 Computational Methods and Experiments in Materials Characterisation III [14] [15] [16] [17]
Stauffer, A.C., Koss, D.A., and McKirgan, J.B., Microstructural banding and failure of a stainless steel. Metallurgical and Materials Transactions A, 35A(4): p. 1317-1324, 2004. Lewis, A.C., et al., Two- and three-dimensional microstructural characterization of a super-austenitic stainless steel. Materials Science and Engineering A, 418(1-2): p. 11-18, 2006. Randle, V. and Engler, O., Introduction to Texture Analysis: Macrotexture, Microtexture and Orientation Mapping, CRC Press, Boca Raton, FL, 2000. Lewis, A.C., Geltmacher, A.B., and Jordan, K.A.: p. (unpublished research). 2007.
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Section 4 Microstructures – cements and cement based materials
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Reactive powder concrete: material for the 21st century D. Mestrovic, D. Cizmar & V. Stanilovic Faculty of Civil Engineering, Zagreb, Croatia
Abstract The most popular engineering material is concrete. It is used for buildings, industrial structures, bridges and dams. Every day the quality of concrete is improving, to achieve better characteristics, lower prices and to be environmentally acceptable. First the historical overview of concrete is given – from ancient civilizations to the 21st century. Then the making of reactive powder concrete (RPC), a composite material with compression strength up to 170 N/mm2 is presented. The components for the RPC mixture are cement, fine aggregate, steel fibers, silica fume and super-plasticizer. They are carefully selected to achieve the optimal mixture. Detailed concrete mix proportions are given in the article. Preparation and testing of materials are made in the laboratory of the Faculty of Civil Engineering in Zagreb. As well as mechanical properties the durability parameters were also tested (gas permeability test, capillary water test). It is concluded that due to very high compression strength RPC can be used for big spans. RPC also has superb durability parameters such as abrasion resistance and reduced chloride permeability. These durability enhancements decrease maintenance costs and lengthen the service life of a structure. RPC is a material whose potential is yet to be identified. Keywords: reactive powder concrete, durability.
1
Introduction
The first specimens of cement are around 12 millions years old. Reactions between limestone and oil shale during spontaneous combustion occurred in Israel to form a natural deposit of cement compounds. These deposits were characterized by geologists between 1960 and 1970. In 3000 years BC the Egyptians used mud mixed with straw to bind dried bricks. They also used WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/MC070131
128 Computational Methods and Experiments in Materials Characterisation III gypsum mortars and mortars of lime in the pyramids. The Chinese used cementitious materials to hold bamboo together in their boats and in the Great wall. The Romans used pozzolana cement from Pozzuoli, Italy near Mt. Vesuvius to build the Apian Way, Roman baths, the Coliseum & the Pantheon in Rome and the Pont du Gard aqueduct in south France. They used lime as a cementitious material. Pliny reported a mortar mixture of 1 part lime to 4 parts sand. Vitruvius reported a 2 parts pozzolana to 1 part lime. Animal fat, milk, and blood were used as admixtures (substances added to cement to increase the properties.) Figure 1 shows Maxentius basilica built in the 4th century. During the middle ages these materials were not used until the beginning of the 19th century. In 1824 Joseph Aspdin of England invented Portland cement by burning finely ground chalk with finely divided clay in a limekiln until carbon dioxide was driven off. The sintered product was then ground and he called it Portland cement named after the high quality building stones quarried at Portland, England. The beginning of the Portland cement era incorporating modern composition was in 1828 when I. K. Brunel made the first significant engineering application of Portland cement, which was used to fill a breach in the Thames Tunnel.
Figure 1:
Maxentius basilica.
In 1867 Joseph Monier of France reinforced William Wand's (USA) flowerpots with wire ushering in the idea of iron reinforcing bars (re-bar). In 1889 the first concrete reinforced bridge was built. Around 1950 concrete with a compression strength of 40 N/mm2 was made. In 60 years of the 20th century the High Performance Concrete (HPC) was made. High performance concrete (HPC) is the name given to a class of materials that exhibits properties superior to those of conventional concrete. The superiority may lie in one or more of several attributes, such as strength, stiffness, freeze-thaw durability, or resistance to chemical attack. The properties are selected on the basis of the requirements of WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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the particular application. Its compression strength ranges from the 50 N/mm2 to 100 N/mm2. In the 1970's fiber reinforcement in concrete was introduced. During the 1980's super-plasticizers were introduced as admixtures. Around 1990 the Reactive Powder Concrete (RPC) first appeared. The strength of RPC goes up to 800 N/mm2. While HPC is being used for bridges more and more, RPC is still very rarely used.
2
Components of RPC mixture
2.1 Introduction This article presents the possibility of making RPC concrete with a compression strength of up to almost 200 N/mm2. Four different mixtures are analyzed. First is the mixture of hybrid micro-fiber concrete, the others are composed of only one type of fiber. 2.2 Cement As the class of cement increases the compression strength increases. For this mixture is selected the Portland cement (PC 55) with no mineral ingredients. 2.3 Fine aggregate The aggregate that is used for the making of this mixture is quartz aggregate. Two fractions of this material are used, one with soil size of 0.125 – 0.25 mm, the other with 0.25 – 0.5 mm, effectively meaning that the maximal size is 0.5 mm. 2.4 Steel fibers Two different types of steel fibers are used (shorter and longer fibers). Shorter fibers are 13 ± 2 mm long, with diameter 0.2 ± 0.02 mm. Minimal tensile strength is 2600 MPa. Longer fibers have curvature ends, their length is 40 ± 3 mm, diameter 0.5 ± 0.02 mm. Minimal tensile strength is 2600 Mpa. In both cases the high tensile fibers are used to achieve necessary ductility. 2.5 Silica fume Silica fume is a pozzolanic additive, with specific area of 20 m2/g. Other parameters are: - density 2.23 g/cm3 - sieve residue 45 µm 5.6% - pH value 8.44
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130 Computational Methods and Experiments in Materials Characterisation III 2.6 Super-plasticizer Superplasticizer is primarily used to decrease the participation ratio of water in the concrete mixture. The chosen superplasticizer is based on policarbon-silate. It is brown fluid, dissolves in water and doesn’t contain chlorides. Other parameters are: - density 1.064 kg/dm3 - pH value 7 - alkalinity 0.31% - viscosity on 20˚C 134 mPas 2.7 Compatibility of cement and super-plasticizer Compatibility of PC 55 cement and super-plasticizer Glenium ACE 30 is one of the very important demands for achieving a good RPC mixture. Compatibility is measured by the change of consistency of concrete. To achieve proper treatment of concrete it must detain its characteristics for approximately 1.5 h for site application and 0.5 h for prefabrication. Table 1:
Ingredients per m3 of RPC.
Mixture number
M1
M2
M3
M4
Steel fibers (kg/m3) SF1 (40/0.5) SF2 (13/0.2)
76 190
228
228
234
720
955
720
980
230
239
230
303
123 1112
105 945
123 1111
105 965
Superplasticizer (kg/m3)
30
35
31
40
Water (l/m3)
190
215
190
209
24˚C 5% 2,41 kg/m3 140 mm
25˚C 5% 2,35 kg/m3 250 mm
24,5˚C 5% 2,36 kg/m3 190 mm
26˚C 5% 2,306kg/m3 220 mm
Cement (kg/m3) Fine aggregate (kg/m3) Quartz sand 0,125-0,25 0,25-0,5 (kg/m3)
Concrete properties temperature pores density consistency
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131
Experimental results
Compression and tensile strength measurement were conducted on 4 specimens with prismatic shape (40 x 40 x 160 mm). The specimens were 28 days old. First the tensile strength was measured, than the compression. Table 2 presents the experimental results for each mixture. Figures 2 and 3 show specimens after the tests. Table 2:
Flexure strength (mean) (MPa)
Compression strength (mean) (MPa)
M1 M2
46.9 42.8
132.0 155.6
M3 M4
42.8 48.8
153.3 174.8
Figure 2:
4
Experimental results.
Specimens after testing.
Gas permability test
Gas permeability is tested according to Croatian regulations EN 993-4. Specimens were cylindrical, with diameter and length 50 mm. They were taken from a prism 10 x 10 x 50 cm (first mixture). The specimens were put in a dry chamber until constant mass was achieved. The specimens were than cooled to room temperature, polished and coated with epoxy. A pressure difference of 3 bars wasn't detected which means that gas permeability is very low (none was detected).
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132 Computational Methods and Experiments in Materials Characterisation III
Figure 3:
Specimens after testing.
0,0008
Water permeability (kg/m2/s)
0,0007 0,0006 0,0005 Sample "A" 0,0004
Sample "B" Sample "C"
0,0003 0,0002 0,0001
360
1440
300
240
180
60
120
30
15
5
10
3
1
0
0
Time (minutes)
Figure 4:
5
Capillary water test.
Capillary water test
Capillary water testing was conducted according to Croatian regulations HRN.U.M8.300:1985 in the laboratory of Civil engineering faculty in Zagreb on specimens 28 days old. The diameter of the specimen was 15cm and the height was 10cm. Before testing, the specimens are dried on 105˚C and then left for 2 days in the laboratory. Sealing putty was applied on one side. Specimens were than weighed. Capillary water testing was made in intervals of 1, 3, 5, 10, 15, and 30 minutes after immersing in water, and then after 1, 2, 3, 4, 5, 6, 24 hours. Results WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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show the linear proportion between the capillarity water and square root of time. Height of capillarity water could not be determined because it didn't cross the area sealed with sealing putty. Starting absorption capacity is for ordinary concrete after 10 min 0.25, after 30 min 0.17, and after 1 hour 0.10 ml/m2/s. These results show (figure 4) that RPC has very little water permeability. Its absorption after 10 minutes is much less than that of ordinary concrete after an hour.
6
Conclusion
This article presents the possibility of making RPC concrete with a compression strength up to 180 Mpa. Due to the very high compression strength RPC can be used for big spans. RPC also has excellent durability parameters like abrasion resistance and reduced chloride permeability. This makes RPC an ideal material for bridges in the Adriatic coast because durability problems are primary related to the fact that the protective layer to reinforcement is rapidly being destroyed. High speed winds drift large amount of chlorides that destroy the bridge structure, primary arch and the columns. These durability enhancements provide RPC with decreased maintenance costs and lengthen the service life of a structure, which is vital for bridges in the Adriatic region.
References [1] [2] [3] [4]
Candrlic, V., Concrete arch bridge over Bakar straits. Proceedings for Conference of Croatian builders, eds. V. Simovic, Cavtat, pp. 358-364, 2001. Jagar, A., High performance concrete, Faculty of civil engineering: Zagreb, 2003. Edward Nawy, G., Fundamentals of high-performance concrete, John Wiley & Sons: New York, 2001. Cizmar, D., Mestrovic D., Radic, J., “Arch bridge made of reactive powder concrete”, HPSM 2006, Ostend, 2006.
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Impedance spectroscopy as a tool to study modifications in the microstructure of concrete in ionic migration experiments G. de Vera, M. A. Climent & I. Sánchez Departament d’Enginyeria de la Construcció, Obres Publiques i Infraestructura Urbana, Universitat d’Alacant, Spain
Abstract The study of the penetration of chloride ions in concrete structures is of great interest, because of the pernicious effects that these ions have on the corrosion of steel reinforcements. Accelerated methods have been developed to obtain the diffusion coefficient of chlorides through cement-based materials. One of these methods allows the calculation of both steady and non-steady state diffusion coefficients using a very simple conductivity measurement [1]. The presence of an electric field causes modifications in the microstructure of cement-based materials, and also an acid attack can be produced on the material if the porosity is high enough [2]. As has already been proved, impedance spectroscopy is a powerful technique to study the microstructure of cement-based materials [3]. This technique is used to characterize during the experiment the modifications that are produced in the microstructure of concrete samples during the forced migration tests. The results obtained using impedance spectroscopy have been compared with the results obtained with the mercury intrusion porosimetry, and a very good agreement has been observed. Keywords: impedance spectroscopy, ionic migration, diffusion, chloride, microstructure.
1
Introduction
Chloride ions are responsible of many of the corrosion problems of steel embedded in reinforced or prestressed concrete. These corrosion phenomena lead frequently to early deterioration and eventually to risky situations for the stability of structures. In any case, the economical costs inherent to reparation works are WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/MC070141
136 Computational Methods and Experiments in Materials Characterisation III considerable. The most frequent cause of the presence of Cl- in concrete is its ingress from environment and through the pore paths of concrete. Big efforts have been made to design test methods of chloride ingress into concrete [4-8]. Most methods intend to determine Cl- transport parameters, mainly the diffusion coefficient. These parameters can be used, in conjunction with transport models, for service life estimations of new or existing structures [8]. Pure diffusion tests are time consuming and involve big experimental effort for chemical analysis of Cl- content of many samples. This lead early to the proposal of forced migration tests, based on the application of electrical fields, to speed up the transport of ions through concrete specimens [6]. Both steady-state and non steady-state ionic diffusion coefficients can be derived from migration experiments. Several researches have shown that ionic migration through concrete causes microstructural variations [9]. These modifications have been studied mainly by mercury intrusion porosimetry (MIP) and by scanning electron microscopy (SEM) analysis, which are destructive techniques. The technique used in the present work to determine modifications in concrete microstructure has been impedance spectroscopy (IS), which is a non-destructive one. A recently published work [10] shows the influence of migration on the impedance spectra. However, this study does not intend to study microstructural changes, but proposes a new theoretical study on the influence of the AC electric field on the ionic transfer. The simplicity of impedance measurements, and the possibility of measuring in situ, whenever it is considered necessary, suggests that IS technique is really useful to study the modifications that can be introduced in concrete microstructure by means of forced migration. The main interest of the present paper is to establish the possibility of using impedance spectroscopy to measure the modifications in microstructure in real time and without perturbing the migration experimental conditions.
2
Experimental setup
Concrete samples were prepared using CEM II A-L 42.5R. The water/cement ratio used was 0.5. The dosage used for concrete preparation is shown in Table 1. The mixture was cast in cylindrical moulds 10 cm in diameter, and 10 cm high. Samples were kept at 100% RH during the hardening time, until starting the experiment. The samples were cut into slices of 1 cm thick. These slices were placed in the cells designed for the forced migration tests. Table 1:
Composition of concrete.
Component Cement II A-L 42.5R Coarse aggregate 6-12mm Coarse aggregate 4-6mm Sand Water Plasticizer
Dosage (kg/m3) 350 714 489.5 662.75 175 1.40
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2.1 Forced migration tests The forced migration experiments have been performed following essentially an experimental procedure described in [6], which is based on monitoring the conductivity of the anolyte. This procedure allows one to obtain both the steadystate and the non steady-state diffusion coefficients. The concrete samples were preconditioned previously to the migration tests, following a standardized water saturation procedure [11]. The cell consists of two electrolyte compartments separated by the sample. Two stainless steel rods are used as electrodes in order to apply the driving electrical field. Catholyte and anolyte chambers are filled with a 1 M NaCl solution and with distilled water, respectively. A voltage of 12V is applied, and the effective potential drop between both sides of the concrete disc is measured periodically by means of two saturated calomel reference electrodes (SCE). Conductivity measurements were performed with a Crison GLP31 conductimeter (Barcelona, Spain), with automatic compensation of the readings to 25ºC standard temperature. Temperature data of the electrolytes were also recorded, and in some cases pH in both chambers was also measured. C1 R0
R1
C2
Figure 1:
R2
Equivalent circuit used for the interpretation of the impedance spectroscopy measurements in the high frequency region.
2.2 Impedance spectroscopy measurements The impedance spectra of the system solutions-concrete disk were obtained using an AGILENT 4292A impedance analyser. This equipment permits the measurement in the frequency range from 40 Hz to 110 MHz. The impedance analyzer allows measurements in a capacitance range from 10-14 F to 0.1 F with a precision of 10-15 F. A two-electrode configuration (flexible graphite circular electrodes with 6.5 cm Ø) was employed to perform the measurements. Impedance spectra were measured in the frequency range from 100 MHz to 100 Hz, because this is the range were dielectrical properties appear [12]. The obtained impedance spectra were validated using the Kramers-Kronig (K-K) relations, to ensure causality, linearity and stability of the measurements made, with satisfactory results. Measured data were fitted to an equivalent circuit to obtain the parameters of interest in the system. The circuit used in this work, shown in Figure 1, has already been proposed [13, 14]. The circuit was originally proposed for cement paste but it has been shown to be effective to fit the impedance spectra obtained for cement mortar, just including the aggregates into the solid phase [13]. The fitting of the measured data to the model proposed is made using a simplex optimization method which is described elsewhere [15]. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
138 Computational Methods and Experiments in Materials Characterisation III 2.3 Mercury intrusion porosimetry In order to validate the microstructural modifications detected with the impedance spectroscopy measurements, a classical and well-known technique, such as mercury intrusion porosimetry was used. The pore structure of different samples, at different times of exposure to chloride migration was determined using this technique. Samples were vacuum dried for 48 hours and then kept in oven at 50ºC. This procedure assures that no structural water is evaporated. With this preparation, the chosen value for the contact angle was of 130º. To ensure that samples used for this measurements were representative they were cut off with irregular and random shapes. The porosimeter employed was an AUTOPORE IV 9500 from Micromeritics. This porosimeter allows pore diameter determination in the range from 5 nm to 0.9 mm. It has to be considered, that as reported by Diamond [16], only the dimensions of the pore superficial structure can be detected by MIP, and the irregularities in pore shape cannot be determined. Nevertheless, information on the possible tortuosity of pore network can be obtained from the mercury retained in the sample after the end of the experiment. The analysis of the curve plotting the logarithmic differential intrusion volume vs. pore size, or applied pressure, shows the size ranges where pores appear. It is possible to determine the number of pore families that exist in the sample, and the contribution of each one to the total porosity of the sample.
3
Results and discussion
3.1 Forced migration results After the beginning of the experiment the values of conductivity and temperature on both cathodic and anodic sides, and the potential drop between both sides of the sample were measured. As it has been shown in [6] the conductivity in the anodic side is proportional to the chloride content in this solution. Results are depicted in Figure 2. It can be seen for anolyte that conductivity does not show a significant growth during the first 42 hours (time lag), and then it increases linearly. During the initial hours chlorides penetrate concrete, until the sample is chloride saturated. After this saturation time chloride concentration increases in the anolyte. This situation allows the calculation of diffusion coefficients both in stationary and non stationary states. Conductivity increases in both sides of concrete as migration proceeds. The increase in the conductivity of the cathodic side is due to the migration of cations from concrete, and also due to the products of cathodic electrode reactions, where OH- is produced. These ions have a much greater mobility than the Cl-, and make the catholyte more conductive. This last effect can be seen in figure 2(D), where pH in both catholyte and anolyte chambers has been recorded during the migration test. The main electrodic reaction on the cathode is water reduction and hence OH- formation, which explains pH and conductivity increase of catholyte.
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10
(B)
100
14
98
12
Vanolito, mS/cm
Potencial, V
9
8
Vanolito V catolito
10
96 94
8 6
92
4
90
2
V catolito, mS/cm
16
(A)
88
0 86 7
-2 0
100
300 G
0
Tiempo, h
25.0 24.5
200
100
12
300
Tiempo, h
14
(C)
200
(D)
24.0 10
23.0
8
22.5
pH
Temperatura, ºC
23.5
22.0 21.5
pH anolito pH catolito
6
4
21.0 2 20.5 20.0
0 0
100
200
300
0
100
Tiempo, h
Figure 2:
200
300
Tiempo, h
Evolution of the following experimental data during migration test: (A) Effective potential drop, (B) conductivity in anolyte (circle) and catholyte (square) chambers, (C) temperature, and (D) pH in anolyte (circle) and catholyte (square) chambers.
The values for the non stationary and stationary diffusion coefficients are obtained using equations (1) [6]:
DNS
2 x2 ª Q º Q coth 2» ; DS 2 « WQ ¬ 2 ¼
Jx Q C1J
; Q
zF 'I RT
(1)
x is the sample thickness, IJ is the time lag (time elapsed until the conductivity starts to increase in the anolyte). ǻĭ is the mean value of the potential difference between both sides of the sample. J is the flux of ions in stationary state and is calculated from the slope of the conductivity versus time in the linear region. C1 is the Cl- initial concentration in the catholyte (1 M). Ȗ is the activity coefficient of the catholyte solution (0.656), and T is the average temperature recorded during the experiment. The mean values obtained were DNS=8.36·10-12 m2/s and DS= 2.19·10-12 m2/s. 3.2 Mercury intrusion porosimetry results MIP measurements have been done on five different samples. One on a specimen not submitted to migration test (reference concrete). The other four samples were obtained after 167 hours (linear zone) and 287 hours (end) of test. For each migration time one sample was taken from the face in contact with the catholyte, and another from the face in contact with the anolyte. It seemed interesting to see WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
140 Computational Methods and Experiments in Materials Characterisation III if there was any variation in microstructure at both sides as previous works showed differences between both sides [17]. The values for the total porosity measured and mercury retained after MIP test are shown in Table 2. As it can be observed the porosity decreases slightly as the experiment advances, except for the data of the anodic side after 287 hours. The result of a small increase in porosity near the anode has already been reported [17], and associated to the disturbance in the chemical equilibria or a change in the pH, because of the generation of H+ at the anode, as can be seen in figure 2(D). Table 2:
Total porosity (%) of different concrete samples, determined using mercury intrusion porosimetry.
Time, h 0 167 287
Total porosity, % Anodic side Cathodic side 7.99 7.68 7.57 8.58 7.03
(A)
Hg retained, % Anodic side Cathodic side 55.05 62.39 54.73 69.63 60.93 Fam. 1 Fam. 2 Fam. 3 Fam. 4
0,035
0,035
0,030
60
(B)
0,025
0,030
0,015
log (vol dif intr)
0,010 0,005
0,020
0,000 10
0,015
100
0 hours 167 hours 287 hours
0,010
Contribution to total porosity, %
0,020
0,025
50 40
30 20
10
0,005 0
0,000
0
410-A
410-C
820-A
820-C
Sample 10
100
1000
10000
100000
1000000
Pore diameter, nm
Figure 3:
(A) Pore size distributions for: Reference concrete (solid square), 167 hours test / anodic side (solid triangle), and 287 hours test / anodic side (open circle). (B) Contribution to the total porosity of the different pore families determined by MIP.
The most important result is depicted in Figure 3(A), which shows the logarithmic differential of the intrusion volume vs pore size for the reference concrete, and for the samples of the anodic side after 167 and 287 hours. Values of the contributions to total porosity are shown in Figure 3(B). It can be seen in this figure that for the reference concrete five pore families are present in the following diameter ranges: family 1 (2000-3000 nm), family 2 (700-800 nm), family 3 (80-90 nm), family 4 (30-40 nm) and family 5 (5-10 nm). It is important to notice that the 5th pore family that appears in the case of concrete not exposed to the experiment and the anodic side after 167 hours becomes so small in the rest of the samples that it is not possible to be detected with the porosimeter used. For families 2 and 3 the central size decreases as the experiment advances. This result also coincides with the prediction of increase of the amount of pores WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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Computational Methods and Experiments in Materials Characterisation III
of small size [17], possibly due to the reaction and the precipitation of chlorine containing compounds. Family 4 increases its contribution to the total porosity after 287 hours. That means that even when the total porosity does not decrease significantly, most of the pores present become smaller than they were before the experiment. The retention of mercury is also increased, as shown in table 2. This means that the tortuosity of the pore network increases, especially at the anodic side. This fact coincides with the diminution of pore sizes at almost constant porosity. 3.3 Impedance spectroscopy results Impedance spectra of the concrete specimens subjected to migration were measured every 12 or 24 hours, and the results were successfully fitted to the circuit depicted in Figure 1 using the procedure explained in section 2.2. The analysis of the evolution of the impedance spectra may allow one to understand the modifications of the concrete microstructure caused by migration. Figure 4 shows 3 impedance spectra for 3 different testing times: 10.5, 34.25, and 57.25 hours. It is evident that important changes occur, and that these changes are not only a consequence of the variation in the resistance of the electrolytes. It is interesting to note that the low frequency resistance decreases in the zone when the conductivity increases (as should be expected).
- Imaginary Part
40 10,5 hours 34.25 hours 57,25 hours
20
10 MHz 1 MHz 100 kHz
0
0
20
40
60
2
Real Part, k:·cm
Figure 4:
Impedance spectra of the sample after 10.5 (circle), 34.25 (triangle), and 57.25 hours (square) of ionic migration experiment.
The equation used for the fitting of measured spectra is the following: Z Z
R0
Z1Z 2 Z1 Z 2
§ ¨ where Z1 ¨ ©
R1 D1
1 jZ R1C1
and Z 2
R2 1 jZ R2C2
D 2
·
¸¸ (2) ¹
The parameters obtained from the fitting are R0, R1, C1, R2, C2, Į1 and Į2. The physical meaning of parameters has already been widely discussed [13, 14]. R0 corresponds to the electrolytes at both sides of the concrete sample, between the reference electrodes and the sample. Due to the high concentration of NaCl in the cathodic side, and the fact that conductivity does not decrease on this side during WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
142 Computational Methods and Experiments in Materials Characterisation III the experiment, the variations on R0 will correspond mostly to variations in the conductivity of the anolyte. R1 has been associated to the pores that connect both faces of the concrete sample (percolating pores), while R2 is related to the other pores, the ones that do not connect the two sides of the sample (occluded pores). C1 is a dielectrical capacitance, and is directly related to the solid fraction in the sample, including cement paste and aggregates. C2 is the capacitance associated to the double layer capacitance at the pore walls. Į1 and Į2 correspond to ColeCole type time constant dispersion factors. These two factors have values between 0 and 1. Value 1 corresponds to the absence of dispersion (all the phenomena present have exactly the same time constant), if Įi < 1 it indicates dispersion (phenomena measured time constants distributed around a central value). 50
100
150
200
250
300
(A)
80
16
0
50
100
150
200
250
300
16
(B) 14
14
12
12
60
40
6
2
10
V, mS/cm
8
R1, k:·cm
R1, k:·cm
2
10
8 40
6 4
4 20 2
W
V, mS/cm
0
2 20
W
0
0 -2
0
50
100
150
200
250
300
0
50
100
Time, h
Figure 5:
150
200
250
300
Time, h
Relation between R1 and time-lag for two different samples. See text for details. (A) Sample 1 with DNS = 8.36·10-12m2/s, DS = 2.19·10-12m2/s, and W = 42.10h. (B) Sample 2 with DNS = 4.84·10-12m2/s, DS = 2.42·10-12m2/s, and W = 73.87h.
Figure 5(A) shows the evolution of R1 parameter among with anolyte conductivity. During the first 50 hours approximately, figure 5(A) shows no variation for the conductivity of the anolyte and simultaneous steep decreases of R1 resistance. The decreasing tendency in resistance R1 may be explained as due to the saturation of the concrete sample with Cl- ions. This part of the experiment has been defined before [18] as a transient period during which porosity is filled with diffusing species, and the concentrations in the solid and the liquid come into equilibrium (by absorption). The experimental observations of Figure 5(A) may be considered thus as a further experimental confirmation of the validity of the above mentioned definition. The duration of this transient period, known as time-lag, is used for determining the non-steady state diffusion coefficients [16]. The explained relation between R1 and time-lag appears evident comparing figures 5(A) and 5(B). In figure 5(B), R1 and anolyte conductivity are plotted together for another sample with higher time-lag. In both cases (figs. 5(A) and 5(B)) R1 value stabilizes when anolyte conductivity starts to increase, i.e. when time-lag is reached. After that initial diminution of the R1 value there is a continuous increase until the experiment finishes which is an indication of continuous blocking of percolating paths. The increase observed in R1 after approx. 100 hours can be associated to the decreases in total porosity and in the WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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mean pore sizes, and to an increase in tortuosity (in accordance with data given in Table 2, and Figure 3). Even though the model used for the fitting of the data is different, some coincidences are observed with the results obtained by Loche et al [10]. The total resistance R1 in this work decreases at the initial stage of the experiment, and remains in a value much lower than the initial one, as observed also by Loche et al.
4
Conclusions
All the previous results can be summarized in the following conclusions: 1. Modifications are induced in the microstructure of concrete when an electric field is applied to accelerate the movement of ions. 2. Impedance spectroscopy is a useful technique to follow these modifications. 3. The definition of the time-lag period of a chloride migration experiment as the time to sample saturation with chlorides is in good agreement with the IS results obtained in this work. 4. The variations of the dielectric parameters determined trough IS measurements can be interpreted in the following terms: the proportion of pores of small size in concrete increases with the time of exposition to the electric field, the tortuosity of pore network increases, and the porosity decreases slightly. These predictions are confirmed experimentally by MIP results.
Acknowledgements This work has been financially supported by the Generalitat Valenciana through project GV05/196, and by the Ministerio de Educación y Ciencia of Spain and Fondo Europeo de Desarrollo Regional (FEDER) through project BIA200605961. Dr I. Sánchez is indebted to the abovementioned Spanish Ministry for a fellowship of the “Juan de la Cierva” programme.
References [1]
[2] [3] [4]
Castellote M., Andrade C., and Alonso C. Measurements of the steady and non-steady-state chloride diffusion coefficients in a migration test by means of monitoring the conductivity in the anolyte chamber. Comparison with natural diffusion tests. Cem. Concr. Res. 31(10), pp. 1411-1420, 2001. Díaz B., Nóvoa X. R., and Pérez, M. C. Study of the chloride diffusion in mortar: A new method of determining diffusion coefficients based on impedance measurements. Cem. Concr. Comp. 28(3), pp. 237-245, 2006. Cabeza M., Merino P., Miranda A., Nóvoa X. R., Sánchez I. Impedance spectroscopy study of hardened Portland cement paste. Cem Concr. Res., pp. 881-891, 2002. D. Whiting, Rapid measurements of the chloride permeability of concrete. Public Roads, 45 (1981) 101-112 WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
144 Computational Methods and Experiments in Materials Characterisation III [5] [6]
[7]
[8] [9] [10] [11] [12] [13]
[14] [15] [16] [17] [18] [19]
L. Tang, L.O. Nilsson, Rapid determination of the chloride diffusivity in concrete by applying an electric field. ACI Mater. J., 89 (1) (1992) 49-53 M. Castellote, C. Andrade, and C. Alonso, Measurements of the steady and non-steady-state chloride diffusion coefficients in a migration test by means of monitoring the conductivity in the anolyte chamber. Comparison with natural diffusion tests. Cem. Concr. Res. 31, (10), (2001) 1411-1420 M.A. Climent, G. De Vera, J. F. Lopez, E. Viqueira, C. Andrade, A test method for measuring chloride diffusion coefficients through nonsaturated concrete. Part I. the instantaneous plane source diffusion case. Cem. Concr. Res., 32 (2002) 1113-1123 Chlortest Project, www.chlortest.org M. Siegwart, J.F. Lyness, B.J. McFarland, Change of pore size in concrete due to electrochemical chloride extraction and possible implications for the migration of ions. Cem. Concr. Res. 33 (2003) 1211-1221 J.M. Loche, A. Ammar, P. Dumargue, Influence of the migration of chloride ions on the electrochemical impedance spectroscopy of mortar paste. Cem. Concr. Res., 35, (2005) 1797-1803 ASTM Standard C 1202-97: Standard test method for electrical indication of concrete’s ability to resist chloride ion penetration. Annual book of ASTM Standard Section 4 Vol 04.02 (2000) C. Andrade, L. Soler, X. R Nóvoa, Advances in electrochemical impedance measurements in reinforced concrete. Mater. Sci. Forum, 19214 (1995) 843-856 I. Sanchez, Aplicación de la espectroscopía de impedancia a la determinación de la microestructura y propiedades mecánicas de la pasta y mortero de cemento Pórtland. PhD thesis. Universidade de Vigo (Spain) (2002) M. Cabeza, P. Merino, A. Miranda, X.R. Nóvoa, I. Sanchez, Impedance spectroscopy study of hardened Portland cement paste. Cem Conr. Res., 32, (2002) 881-891 C. Alonso, C. Andrade, X.R. Nóvoa, M. Keddam, H. Takenouti, Study of the dielectric characteristics of cement paste. Mater. Sci. Forum 289-292 (1998) 15-28 S. Diamond, Mercury porosimetry. An inappropriate method for the measurement of pore size distributions in cement-based materials. Cement and Concrete Research. 30 pp 1517-1525 (2000) M. Castellote, C. Andrade, C. Alonso, Changes in concrete pore size distribution due to electrochemical chloride migration trials. ACI Mater. J., 96 (3) (1999) 314-319 A. Atkinson, A.K. Nickerson, The diffusion of ions through watersaturated cement, J. Mater. Sci., 19 (1984) 3068-3078 M. Cabeza, M. Keddam, X.R. Nóvoa, I. Sanchez, H, Takenouti, Impedance spectroscopy to characterize the pore structure during the hardening process of Portland cement paste. Electrochim. Acta, 51(2006) 1831-1841
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Section 5 Experimental methods – imaging and analysis
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Laser speckle measurements and numerical simulations of the deformation of masonry loaded in compression A. T. Vermeltfoort Technische Universiteit Eindhoven, the Netherlands
Abstract This study focuses on the comparison of the results of a laser speckle technique, ESPI, and numerical simulations with DIANA when used for research into the role of brick–mortar interaction on the deformation of masonry loaded in compression. When a masonry structure is loaded, the interaction of brick and mortar is considered of paramount importance with respect to the mechanical behaviour of masonry. As a consequence of the brick laying process and positioning of the unit, masonry has weak spots at the mortar-unit interface. The clay–brick–mortar interaction was measured in detail with ESPI, a specially designed laser speckle test equipment. It was shown that most of the deformation occurred in the brick–mortar interface. DIANA was used for some numerical simulations of the brick–mortar interaction. Simulated specimen dimensions were as in the experiments. An interface layer of 1 mm thickness was modelled between mortar and top unit to simulate the contact layer. Fissures were modelled as 15 mm deep openings. Similarities between ESPI and DIANA are seen in the way the results i.e. node displacements are presented. Both DIANA and ESPI produce a similar tabular output with node coordinates and their displacements. This output can be used in spread sheet programs for further analyses. As DIANA and ESPI give comparable results, the advantage of DIANA – i.e. the calculation of stresses – can be utilized. Results of the study can be used for more detailed modelling of masonry. Keywords: experimental methods, composites, optical method, numerical simulation, brick mortar interface, compressive loading.
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148 Computational Methods and Experiments in Materials Characterisation III
1
Introduction
Masonry structures are made in layers of bricks and mortar. The ways these components affect masonry deformational behaviour and strength have been studied over the years (e.g. Hendry [1]). One of the key factors concerns the brick–mortar interaction under compression and the resulting deformation of bricks and mortar separately [2]. For reliable estimation of the capacity of a structure, analytical and numerical simulations can be performed, for which input data obtained from detailed experiments are required. Data, like the modulus of elasticity and Poisson’s ratio, are obtained by measuring the change in length of a part of the specimen by means of an LVDT, a Demec gauge or a strain gauge, Figure 1. All these instruments measure the change in distance between two points. To observe the deformation in more detail of a mortar joint, measuring at a (large) number of points and preferably over a shorter distance is required. In addition, reliable values for lateral expansions are difficult to obtain from ordinary walls with LVDTs or Demec gauges. Therefore, a refined measurement methodology, based on the laser speckle technique (ESPI) was used. The major advantage of using a laser-speckle system like ESPI over systems like LVDTs or Demec is that the displacement of a (theoretically infinite) number of points of a certain area can be observed. In addition, DIANA was used for the numerical simulations. Both methods were used to observe the brick–mortar interaction under concentric compression, using 25 mm thick specimens.
Figure 1:
Demec, LVDT, clip-on gauge and strain gauges.
This paper discusses refined ESPI measurements and numerical simulation of the deformation of masonry specimens in the area of the mortar joint. The effects of fissures on deformational behaviour both in the loading direction as in the lateral direction are emphasized. The use of DIANA as a numerical simulation tool is compared with the use of ESPI as an experimental tool.
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(a)
Figure 2:
2
149
(b)
(c) (d) (e) Steps in the brick-laying process: (a) putting mortar on the wall; (b) the brick is pushed into the mortar; (c) mortar moved from the centre bulges at the edges; (d) surplus of mortar scraped off; (e) unsupported mortar at the edge of a joint.
Brick–mortar joint
Brick-laying is the piling of bricks on top of each other. Mortar serves as a tolerance aid, allowing for size variation of the bricks. In The Netherlands, the mason puts the quantity of mortar needed for one brick on the wall (Figure 2). The brick is first pushed into the fresh mortar and then the surplus of mortar is scraped off (Figure 2(c)). The fresh mortar in the centre of the joint is compressed to the appropriate joint thickness, and the mortar is squeezed from the centre to the edges. At the edges, the mortar is hardly compressed vertically. After scraping off, the fresh mortar at the edges is not supported. Due to gravity, the top surface will drop a little. Depending on the moisture content and the sand used, the edge material runs off under a certain slope (approximately 30 - 45q).
Figure 3:
Fracture surfaces between brick and mortar showing bonded central area.
Traces of the brick-laying process can be observed in fracture surfaces after bond wrench bending tests, Figure 3. The central part of the mortar joint that first WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
150 Computational Methods and Experiments in Materials Characterisation III came in contact with the brick shows residues of the brick surface. This indicates better bonding in the centre than at the edges. The “settlement” of the mortar at the edges (Figure 2(e)) also negatively affects bonding. 2.1
Specimen dimensions and appearance
Brick–mortar interaction was studied by testing representative pieces of masonry representing a sample of a joint, in combination with the adjoining bricks. The specimens, cut from couplets as 25 mm thick slices, were loaded vertically, i.e. perpendicular to the bed joint. The specimens were approximately 100 mm wide, the original width of the brick, and 115 mm high, two bricks and one joint. The deformation of the front surface was observed with ESPI. With these specimen sizes a representative sample is obtained in which a stress distribution develops, similar to that in the real wall.
Figure 4:
RW couplet and a 25 mm thick specimen after testing.
Esteel
= 210000 N/mm2
Ebrick
= 4000 N/mm2 = 5000 N/mm2
Emortar
Einterface = 1000 N/mm2 Xsteel = 0.30 Xbrick = 0.18 Xmortar = 0.15 X = Poisson’s ratio
Figure 5:
3
Scheme of element pattern and mechanical values used.
Numerical simulations
The finite element program DIANA [3] was used for some explorative numerical simulations. Figure 5 shows a scheme of the model used. Specimen dimensions were as in the experiments except for the thickness for which one layer of elements of 10 mm thickness was used. An interface layer of 1 mm thickness WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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was modelled between mortar and top unit to simulate the contact layer. The fissures were modelled as 15 mm deep openings. The specimen was loaded by assigning a 1 mm displacement to two points on top of the steel block. Figure 6 shows contour plots of the displacements and stresses of a concentrically loaded specimen with a fissure on either side. The parts of the specimen above and below the fissure remained without stress. Peak stresses occurred at the load introduction point in the steel load block and at the crack tips.
a Figure 6:
3.1
b
(a) Deformation and (b) stress contours of a concentrically loaded specimen, DIANA results.
Vertical deformation
The DIANA software provides a table with X- and Y-coordinates for each point (node of an element) and “measured values”. This table was used to draw graphs of vertical displacements against the horizontal position (X-value) of the corresponding node (Figure 7). Specimen behaviour is symmetric about the joint. The effect of the fissure is clear. The node displacements are smaller near these openings. Nodes of the bottom brick displace more and those of the top brick less than expected for a closed joint. The close contour lines represent the softer interface layer. The node displacement lines of this softer layer with smaller elements fan out at the end, near the fissure. Symmetry around the joint can be observed. It should be noted that strains and stresses in this section are obtained for a vertical displacement of 1 mm at the top edge, resulting in an averaged reaction stress of 29.8 N/mm2 and an E-value of the specimen of Espec = 3400 N/mm2. This E-value was smaller than the Ebrick of 4000 N/mm2, due to the softer interface layer and the fissures in the model. The largest tensile stress, which occurred 15 mm from the edge was 0.8 N/mm2. The applied load, in the simulation, was approximately three times the strength of this type of masonry. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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-0.4 -0.6 -0.8
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Figure 7:
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Vertical node displacements of a concentrically loaded specimen DIANA results.
100
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Figure 8:
-0.05 0.00 0.05 lateral deformation [mm]
0.10
Horizontal node displacements of a concentrically loaded specimen DIANA results. The bricks deform in a barrel ( ) shape.
Horizontal deformation
In Figure 8 the horizontal displacement of each node was plotted versus the vertical position of the node. The image is almost symmetric around a vertical and a horizontal axis. Deviations are caused by the boundary conditions. The bottom nodes were confined both in vertical and horizontal direction. The top edge was loaded via a steel block, which results are omitted. The bricks expand laterally, the mortar is in compression. The barrel bulging shape of deformation contours in the bricks is the result of the boundary conditions and of the fissures modelled at brick mortar transition (Y = 65 mm). Lateral stresses, plotted in Figure 9, show that the specimen is in compression in the centre, and that tensile stresses occur, in an area at 15 mm from the vertical edges of the specimen. The stress distribution is ‘rounded’, in contrast with the usually assumed ‘blocked’ stress distribution in the analytical model from Haller [4]. The highest lateral stress (37.5 N/mm2) occurred in the soft interface layer. 120
height [mm]
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Figure 9:
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Horizontal stresses of a concentrically loaded specimen, in the centre and at 15 mm from the edge, DIANA results.
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The ESPI equipment
ESPI is an abbreviation for Electronic Speckle Pattern Interferometry [5]. It is a non-contact, 3-D, displacement measurement system based on optical interference techniques that allows for the observation of deformation of surfaces. The ESPI instrument is presented in Figure 10. This section gives a short description of the employment of the ESPI system. More details are given in [2].
Figure 10:
Figure 11:
Figure 12:
Front and side view of the ESPI apparatus.
Specimen seen through the digital camera lens.
Speckle pattern image.
Figure 13: Fringe pattern, made by subtracting two speckle patterns. Masked circles due to the attachment of an LVDT.
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-
5
The ESPI system is employed in the following steps. Take a photograph of the specimen. Establish a relationship between the real dimensions of the specimen and the number of pixels in the photograph. Illuminate the specimen from two sides with a split laser beam. Capture the reflected light with a charge-coupled device (CCD camera). Store the speckle pattern, Figure 12, in a computer. Speckle patterns include the reflection information of points of the measured object. During a test, speckle patterns are taken at various load levels. Speckle patterns were taken at a stress of approximately one third of the estimated strength of the specimen (load L1) and at a stress approximately 1 N/mm2 higher (load L2). Subtract speckle pattern images taken at e.g. load L2 and load L1 to form interference fringes, Figure 13. The number of fringes is a measure of the displacements of points on the illuminated area. Determine displacements and plot them, Figure 14. By changing the polarity of the laser, displacements in X (horizontal) and Y (vertical) direction were obtained. A resolution of 10 nm was possible. If desired, calculate ‘strains’ from the measured displacements taking into account the load increment at which deformations were obtained.
ESPI-results
As an example, the vertical ESPI-displacements of a JW specimen are plotted versus their X position in Figure 14. In this case the deformation differences between brick and mortar are relatively small. The effect of fissures at the edges is visible, indicated by the lines with a larger spacing. At mid height of Figure 14 the lines represent the displacements of points in the joint. Their distance is largest at the edges, from X between 0 and 20 mm and from X between 80 and 100 mm. The lines at the bottom and the top of the figure indicate the brick deformation, which is contrary to the joint.
Vertical displacements [ Xm ]
F
F'
40
20
D'
C
C'
0 A
A'
-20 0
Figure 14:
20
40 60 horizontal position [mm]
80
X
100
Vertical displacements of points, plotted versus their horizontal position (X). Displacements of brick contours are indicated.
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The lines AA’ in Figure 14 are almost straight, lines CC’ and DD’ have a kink. The letters refer to the position of the observed points on the specimen (Figure 11). The distance between the displacement lines is a measure of the strain that occurred. In the centre, the strain is roughly the same for mortar and brick. The prominence of the ‘joint’ varied, depending on the brick mortar combination used. 5.1
Lateral displacements
ESPI was used to measure the horizontal deformation of the specimens in the same way as already discussed regarding vertical deformations. Figure 15 shows an example of the horizontal displacements. The data were handled in the same manner as the vertical deformations. Now, the horizontal displacements of the grid points were plotted versus the Y-values of these points and the results of points with the same X values were connected with straight lines.
Figure 15:
Lateral displacements show a barrel ( ) shape in the bricks.
The displacement lines in Figure 15 indicate that this specimen rotated during the test and kinked at joint height. Still, the similarity with DIANA results in Figure 8 is clear.
6
Discussion
By using the ESPI-technique more information was obtained from the brick– mortar interaction than with traditional LVDT-measurements. In addition, the ESPI-measurements were obtained in a similar format as the FE simulation results, allowing for easy comparison. Both methods result in displacements of a number of points at the surface. Variation of material properties may blur the experimental result while in numerical simulations the properties are uniform. The advantage of a finite element program like DIANA is that besides strains, stresses can be calculated and the good correlation between strains both from simulation and experiments allowed the use of DIANA to establish stresses. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
156 Computational Methods and Experiments in Materials Characterisation III Both the numerical simulation and the ESPI measurements confirmed that stresses concentrate in the middle of the joint as a result of the fissures at the edges. The B-shaped deformation over height (Figure 16) observed in the experiments is almost identical to the numerical one. Strain distribution is affected by friction between the specimen and the load platens. Equilibrium over a vertical section, with stresses given in Figure 17, is only possible by means of friction forces at the specimen’s edges. 120
120
90
80
hoogte [mm] height [mm]
Hoogte [ mm ]
100
60 40 20 0 -0.06
Figure 16:
30
DIANA ESPI -0.03 0 0.03 0.06 Horizontale rek [ mm/m]
60
druk compression positive positief
0.09
Horizontal strain versus height ESPI and DIANA result.
0 -0.1
Figure 17:
0
0.1
0.2
0.3 0.4 [-]
Vaxial/Vlateral
Stresses versus (DIANA).
0.5
height
Less friction will reduce the lateral stresses, indicated by the dotted line in Figure 17. If the lateral stress distribution does not change, mortar is in compression, bricks are in tension. The strain distribution showed the effect of fissures in the brick mortar interface. The load was transferred via the central 60 to 70 mm in the 100 mm wide specimen.
7
Conclusion
x x
Brick and mortar expand laterally to axial compressive loading. Deformations from measurements and simulations correspond and therefore the stress distribution found with numerical simulation was considered reliable. Fissures at the edges of the joint affected lateral deformation. Results of DIANA and ESPI can be treated in a similar manner: a table with X- and Y-coordinates and “measured” values is available. The advantage of DIANA is that stresses can be calculated. A disadvantage is that (for practical reasons) properties are uniform over the volume considered, in ESPI the real material is tested. ESPI and DIANA proved to be a complementary couple.
x x x x x
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References [1] Hendry, A.W., Structural masonry, MacMillan Education Ltd, ISBN 0-33349748-1, 1990. [2] Vermeltfoort, A.T., Brick–mortar interaction in masonry under compression, PhD Dissertation, TU Eindhoven, 2005. [3] Witte, F.C. de (editor), DIANA – Finite Element Analysis, TNO Building and Construction research, Delft, 1996. [4] Haller P., Die technische Eigenschaften von Backstein, Schweizerische Bauzeitung, 1958. [5] Jones R. and and Wykes, C., Holographic and Speckle interferrometry, 2nd edition, Cambridge University Press, Cambridge, ISBN 0521232686, 1983.
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Quantitative analysis of polyurethane nanocomposites with boehmite structures modified using lactic acid J. Ryszkowska Warsaw University of Technology, Faculty of Materials Science and Engineering, Woloska, Warsaw, Poland
Abstract In this paper the results of a quantitative description of polyurethane nanocomposites with boehmite microstructure are reported. These nanocomposites have higher abrasive wear and thermal resistance. Quantitative image analysis of SEM images has been performed in order to describe the microstructure of the polyurethane and its nanocomposites. The dependence between the sizes of the spherulities obtained on brittle fractures of materials and their resistance properties were analysed. Keywords: nanocomposites, polyurethane, boehmite, lactic acid, image analysis.
1
Introduction
Machine components made from polyurethane are mainly used in mining [1–4]. Often, they can also have high resistance for abrasive wear and thermal stability [2, 3]. Components like nano-clays or plate-shaped, for example kaolin, mica and aluminium hydroxides, have been added to the polymeric matrix to obtain required heat resistance, high modulus and some other physical and mechanical properties [5–8]. However, the macroscopic properties of such composites heavily depend on the dispersion of the added particles in the polymer matrix [7, 8]. In order to improve this dispersion, modified nanofillers are used and special processing routes are employed [8]. This paper presents the application of quantitative image analysis to the description of morphological properties of boehmite modified using lactic acid and its nanocomposites. Fracture surface images of nanocomposites were WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/MC070161
160 Computational Methods and Experiments in Materials Characterisation III obtained using a high-resolution electron microscopy technique. Quantitative analysis of the images, obtained with that technique, allowed us to explain the mechanism of changes of mechanical and thermal properties of polyurethane nanocomposites, as well as allowed us to determine the relationships between the structure characteristics and the properties of examined materials. Hardness, abrasive wear, glass transition temperature and thermal stability of polyurethane nanocomposites were investigated.
2
Materials and methods
Boehmite (Al2O3 content 76 wt%, specific surface: 220 m2/g, particle size 10–100µm) was purchased from CONDEA-Vista, Catapal D Alumina. Lactic acid was supplied from Aldrich. Boehmite was modified by reaction with lactic acid for 15 hours [9]. Unmodified and lactic acid modified boehmites were used. Components used for PUR synthesis were: poly(ethylene adipate) (PEA) – 2000 Da Alfaster T-620 (Alfa Systems), 4,4’diphenylmethane diisocyanate (MDI) Isonate M 125 (Dow Chemical), glycol (G1) and glycerin (G2) (POCH). Polyurethanes with PEA:MDI:G1:G2 molar ratio 6:9:2:1 were synthesized. The modified and unmodified boehmite were added to PUR matrix in 0.5 and 3.5 wt%. All the samples were synthesized by a one-step method of in situ polymerization. Samples were formed by casting. The curing reaction was performed at a temperature of 120ºC for 16 hours. Analysis of nanofillers was performed with Scanning Electron Microscopy SEM LEO 1530 and Transmission Electron Microscopy Jeol Jem 3010. The morphology of polyurethanes and nanocomposites was characterized by high resolution scanning electron microscopy (HRSEM) LEO 1530. Brittle fracture samples for SEM study were obtained by cryogenically fracturing ca. 2mm thick polymers samples (previously frozen in liquid nitrogen). The fracture surfaces were coated with carbon films of a total thickness of 20nm by sputtering. A differential scanning calorimeter (DSC), TA Instruments Model Q 1000 was used for thermal analysis. The weight of the samples was about 10 mg. Samples were heated from –100 to 200ºC at the rate of 10ºC min-1 in nitrogen atmosphere. Thermogravimetric analysis (TGA) was carried out with a TA Instrument TGA Q 500 thermogravimetric analyser. The samples weight was 10–12 mg. The work was performed at temperatures beginning from room temperature to 600ºC at a heating rate of 10ºC min-1 in nitrogen atmosphere. Tensile tests were performed using an Instron 1115. The samples were elongated at the rate of 500mm/min according to ISO 527. Hardness was measured using an indentation hardness tester according to ASTM D2240-75, abrasive wear according to ISO 4649.
3
Results and discussion
Boehmite modified with lactic acid was introduced into the polyurethane matrix. Images of boehmite before and after the modification are shown in Fig.1. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
Computational Methods and Experiments in Materials Characterisation III
a)
161
b) Figure 1:
Figure 2:
Images of boehmite modified by lactic acid: a) TEM, b) SEM.
SEM images of cryogenically fractured surfaces of polyurethane.
Modification boehmite creates aggregates in cubic form built from tiles 5nm thick, its specific surface is 13.6m2/g and helium density 1.46g/cm3. Images of fracture surface of the polyurethane matrix are presented in Fig 2. In Fig 2 spherulite structures can be seen, obtained on the images of brittle fractures of polyurethanes [10]. Such structures were also observed in polyurethanes researched by Li et al [11] and Briber and Thomas [12]. One type of spherulite structure observed by Briber did not show optical nonbirefringence. Observations of nanocomposite with boehmite brittle fractures were also performed and are shown in Fig. 3(a) and (b). Filler gain is evenly distributed in the matrix. The fracture images of nanocomposites resembling spherulite are visible. Their boundaries are not, however, as clearly visible as spherulite boundaries in a polyurethane matrix. Image analysis allows us to conclude that the sizes of the areas resembling spherulite decreases with an introduction of higher amounts of nanofiller. In order to confirm this, quantitative image analysis was performed and sizes of spherulities were calculated. The scheme [13] of the method is presented in 4 WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
162 Computational Methods and Experiments in Materials Characterisation III images of polyurethane structure shown in Fig. 4. Measurements were performed for a minimum 100 domains. The results of equivalent diameter analysis of nanocomposite soft domains is shown in Fig. 5 and enumerated in Table 1. Increasing nanofiller causes decreasing spherulite size.
a)
b)
Figure 3:
SEM images of cryogenically fractured surfaces of nanocomposites with boehmite: a) 0.5 wt%, b) 3.5 wt%.
Table 1:
Equivalent diameter (d2) of soft domain the polyurethane and its nanocomposites.
Samples PUR PUR05 PUR35
Average d2, [Pm] 72.9r37.5 24.4r12.6 13.1 r 6.9
Max d2 162.7 108.7 43.9
Min d2 18.4 1.6 1.3
Thermal analysis using DSC and TGA was performed; the results are gathered in Fig. 6. On the basis of these results, the glass transition temperature of soft domains (Tg) was specified (tab. 2). We determined that the introduction of the nanofiller does not change the character of the thermogram. Glass point transition temperatures of soft domains of nanocomposite increases slightly. Thermodegradation using TGA was performed; the results are presented in Fig 7 and in table 2. On the basis of the weight variation curves the temperature by 2 and 5% weight loss (T2%, T5%) was specified. Temperature at the maximum for first and second step of weight loss rate read from the peak values of the derivative weigh loss curves (DTG) (Tmax1 and Tmax2), see Table 2. Introduction of nanofiller does not influence the change of glass temperature of soft domains. Judging by the gathered results it can be said that the thermal resistance of nanocomposites (Tmax1) increases by about 45-50qC. Changes were observed in the size of spherulities occurring on the brittle fractures of nanocomposites. The effect of structure on mechanical properties was evaluated for such properties as: hardness (H), tensile at 100 and 300% elongation (V100, V300), tensile strength (Rm), elongation at break (Hr) and abrasive wear ('V). The results of evaluations are presented in Fig.8. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
Computational Methods and Experiments in Materials Characterisation III
a)
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b) 25
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Figure 4:
Procedure for soft domain measurement: a) polyurethane microstructure, b) manual object selection, c) image after analysis with use of micrometer program, d) graph showing the distribution of the measurement of equivalent diameter (d2) results.
A decrease of spherulities size is connected with a drop in tensile strength and an increase of elongation at break in researched materials. Likewise, decreasing spherulities size is connected with changes in abrasive wear and hardness. Positive changes of abrasive wear after introduction of 0.5 wt% of modified boehmite are a result of strengthening in the material. Introduction of larger amounts of nanofiller does not influence the change in abrasive wear, which might be connected with pull out whole nanofiller grains.
4 Conclusion Modification using lactic acid causes a change in boehmite structure, which enhances its dispersion in the polyurethane matrix. Introduction of 0.5 wt% modified boehmite improved the abrasive wear of nanocomposite. Introduction of the nanofiller causes a decrease of resistance properties of researched polyurethanes according to measurements in static tensile tests. Images of brittle fracture surfaces of researched materials were analysed and prove that an increase in the amount of nanofiller decreases the size of pseudosferolitów occurring on the fracture. A connection has been observed between the decrease of spherulities size and resistance properties specified WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
164 Computational Methods and Experiments in Materials Characterisation III during stretching. Our previous research reported that the introduction of nanofillers into an elastic matrix causes an increase of elasticity modulus and hardness of such composites but a decrease of stretching resistance. Observations obtained during this research help explain the reasons for this phenomenon. 40
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20
30
40
50
b) Figure 5:
Graph showing the distribution of the measurement of equivalent diameter (d2) results. Table 2:
Type PUR PUR05 PUR35
The thermal properties of obtained materials.
Tg1 (qC)
T2% (qC)
T5% (qC)
Tmax1(qC)
Tmax2 (qC)
-28.0 -27.8 -27.8
270.4 278.0 278.2
295.8 298.9 297.8
308.0 353.6 362.2
401.1 377.9 -
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Computational Methods and Experiments in Materials Characterisation III
Figure 6:
Figure 7:
DSC analysis of polyurethane and nanocomposites.
TGA thermograms of polyurethane and nanocomposites.
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166 Computational Methods and Experiments in Materials Characterisation III A
7
B
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C
5 4 3 2 1 0 0
20
40
60
80
d2, um
D
80
E
F
Properties
60 40 20 0 0
20
40
60
80
d2, um
Figure 8:
Selected mechanical properties of the polyurethane and nanocomposites as a function of d2; A, B - tensile at 100 and 300% elongation (V100, V300), C - elongation at break (Hr), D- hardness (H), E - tensile strength (Rm), F - abrasive wear ('V).
Acknowledgements The author thanks Professor Zbigniew Florjanczyk from Warsaw University of Technology, Faculty of Chemistry for the modified boehmite. This scientific work was funded from the finances for education in the years 2005-2008 as research project no. 3T08A/07428
References [1]
Hepburn A. Polyurethane Elastomers, Elsev. Sci. Publ., London, 1992.
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[2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
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Gruin I, Ryszkowska J, Boczkowska A, Markiewicz B, ZaleĪnoĞci wáaĞciwoĞci makroskopowych od budowy lanych elastomerów nitrylomocznikowych, Polimery 1994; 39: 226-233. Gruin et al. Polish patent 148671, 1990. Gruin et al. Polish patent 150154, 1991. M.J. Schulz, A. D. Kelkar, M. J. Sundaresan, Nanoengineering of Structural Functional, and Smart Materials, CRC Taylor &Francis, New York, 2006. Gogotsi Y., Nanomaterials Handbook, CRC Taylor &Francis, New York, 2006. Mai Y. –W., Yu Z.-Z, Polymer nanocomposites, CRC Press, Boca Raton, 2006. Zheng J., Ozisik R., Siegel R W, Phase separation and mechanical responses of polyurethane nanocomposites, Polymer, 2006, 47, 77867794. FlorjaĔczyk Z, Rogalska-JoĔska E, Nawrocka K, Molenda A, Affek M.: Organoaluminium polymers, Polimery, 2002,47,9, 611- 618. Foks J, Janik H. Microscopic studies of segmented urethanes with different hard segment content, Polymer Eng. Sci 1989; 29,113-119. Li Y., Liu J., Yang H, Ma D, Chu B, Multiphase Structure of segmented polyurethanes: Its relation with spherulite structure, J. Polym. Science: Part B Polym. Physics, 1993, 31, 853-867. Briber R. M., Thomas E.L., Investigation of two crystal forms in MDI/BDO-based polyurethanes, J. Macromol. Sci. – Phys., 1983, B22, 509-528. Ryszkowska J: Materials Science Forum III, Vols 514-516, (May 2006), p. 1658-1662.
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The spatial controlling of Lamb waves excited by a point source on the cylindrical wall V. Sukackas Physics Department, Kaunas University of Technology, Lithuania
Abstract A Lamb wave excited on one point of a hollow cylindrical point reaches every other point in different ways, such as: by the shortest way and turning around 1, 2, 3… times. This factor can be used to control the wave field in the space, as it is impossible in the other ways when the source is a point. The waves can be focused if the emitter is excited by a series of short pulses calculated so that at the same time the pulse that has spun the cylinder n times is received, the second pulse with n-1 rotation around the cylinder and so on, and finally the last pulse that came by the shortest way. The focus point can be changed, i.e. scanned when the pulse’s position in the series is changed. The only one transducer becomes equivalent to the array that has the period equal to the perimeter of the cylinder. In the same way the signal in the receiving point can be processed by delaying and summing it so that constructive superposition occurred only when the signal comes from the desirable point. In this way the dynamic focusing and scanning can be performed irradiating the object or receiving the waves propagated by some point. In the latter case this can be the point of the passive reflecting defect in pulse-echo NDT mode or the source of the acoustic emission. The scanner is very simple – it consists of one point-form transducer. In the same way the more complicated and typical only to cylinder modes can be excited. Keywords: Lamb waves, cylinder, scanner, dynamic focusing, virtual array.
1
Introduction
Lamb waves with the propagating medium restricted by two surfaces perfectly suit for the testing of hollow cylinder type objects, such as pipes (Alleyne et al [1] and Alleyne and Cawley [2]) and their inner surface (Volkovas and Sukackas [3]). Three exciting modes can be distinguished there: WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/MC070171
170 Computational Methods and Experiments in Materials Characterisation III -
The excited signal is close to the continuous waves, i.e. wave burst length is much more longer than the time of passing by the perimeter, - the burst length is close to the time of passing the perimeter, - the excited signal is much more shorter. In the first case the wave components with the wave vector perpendicular to the axis of the cylinder makes standing waves. The cylinder becomes a ring resonator with the parameters carrying information (e.g. about the sediments on cylinder pipe of the inner surface). Resonance signal as a rule is distorted. This reason stimulated the use of untypical solutions for the resonance measurement technique, such as correlation analysis (Sukackas et al [4, 5]). Sukatskas and Volkovas [6] found that the transmitter and receiver must not necessary be fixed on the same cut (one against the other) and this broadens the possibility of the application. The formation of the received signal was observed in the second case by Sukackas and Ramanauskas [7]. In this case the use of two - dimensional Fourier transform method (2D FFT) is promising (Alleyne and Cawley [8]). The 2D FFT of the received signal as a function of two variables – carrier frequency and time – allows solving about the attenuation of the waves and about the thickness of the sediment layer inside. The measurement process is much faster as in resonance mode (Sukatskas and Volkovas [9]). In both cases the integral value of the researched parameter is obtained in all the cut of cylinder. The case with the considerably short excited signal is not enough researched. It has advantages when the local non-homogeneity is researched and allows scanning them with the wave beam.
2 The principle of controlling The layout of transducers on the surface of the pipe is shown in Fig. 1(a), evolvent of waves’ path in Fig. 1(b). Using waves that have spun several times, the transmitter becomes equivalent to the virtual phased array with the period 2ʌR, where R is the radius of the cylinder. 2.1 The research of beam focusing Both h1 and h2 in this case are so big that wave reflection from the end of the cylinder is not felt. The transmitter 1 is excited by the pulse burst, the transducer 2 is used for the wave receiving. The time of transmitting of the pulses is chosen so that at the some time the receiver 2 is reached by the latest pulse direct, and by the earlier transmitted - with 1, 2,…i rotations. In such way we can get the constructive interference. The passed way of every wave li is calculated accordingly and delay time IJi
li2 = h2+(a2+2ʌR(i-1))2, IJi = li/c,
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(1) (2)
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where h and a – coordinates of the receiving point, c – the velocity of waves, R – radius of the cylinder, i – pulse number (1 – the latest). The example of the excited and received signals is shown in fig. 2. The steel pipe with 2R = 150 mm and wall thickness of 8 mm was analyzed. It was excited with the rectangular pulses of 5 µs length, that corresponds a half of the period of transducers resonance frequency, i = 1...4.
R h2 h1
2 h 1 a
(a)
(a)
li h
2ʌR
a 0 (b)
Figure 1:
-2ʌR
-4ʌR
(b)
Layout of the transducers (a), evolvent of waves’ path (b).
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172 Computational Methods and Experiments in Materials Characterisation III The coordinates of the receivers are: h = 400 mm, a = 240 mm = ʌR; so the images for the waves propagating clockwise and anticlockwise coincide. The sharp increase of the amplitude in the receiving point is observed. The traditional way for the analysis of directional diagram – to change the position of the receiver – was not used as the acoustic contact stability could not be ensured. It was evaluated by scanning, i.e. changing the focus point calculated according the eqns (1), (2), when the position of the receiver is fixed. The step of scanning on both coordinates is 10 mm. The example to the case with the coordinates of the receiver h = 400 mm, a = 240 mm is shown in fig.3). Fig. 3 and the corresponding theoretical research show that directional diagram is oriented to the “center of gravity” of the virtual array. Its position depends also on the damping of the waves. 2.2 Focusing in the receiving mode In this case the transmitter radiates waves once. The receiver registers the direct signal, stores it, then stores the signal that spin once around the cylinder, etc. The appearance time of the signals that must be stored is determined by eqns (1) and (2). After that they are summarized. The source of the signal can be chosen in the experiment – the transmitter (imitating acoustic emission) or very well reflected defect. The medium version was the imaginary source – reflection of the transmitter 1 from the end of the pipe.
Figure 2:
Exciting burst (on the top) and received signal (at the bottom).
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U, mV 800
600
400 200
Figure 3:
h, mm
200 400
450
250
a, mm
300 0
The received signal “peak-peak” obtained by scanning in the rectangular (190,360) – (190,460) – (300,460) – (300,360). The coordinates of the receiver (240,400); the first number is a.
0.1 Urel 0.05 0 -0.05 -0.1 10 Figure 4:
100 501
200 1001
300 1501
400 t, µs 2001
The received signal, when a = 0, h1= 150 mm, h2 = 130 mm. The calculated appearance time of the signals from the imaginary source is marked by vertical lines.
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Urel 700 600 500 400 300 200 100
Figure 5:
9
7 5 3
0
S1 1
S3
h,c m3 0
S5
35
S7
S9
0 5 a,cm
The received signal “peak-peak” obtained by scanning in the rectangular (-40,290) – (-40,380) – (50,380) – (50,360). The first number is a.
In this case a = 0, h1= 150 mm, h2 = 130 mm were chosen. The receiver 2 was focused to the point that is at the distance h1 above the pipe end, i.e. the distance h in the eqn (1) is chosen to be equal to h1 + h2. The example of the received signal is shown in Fig. 4. The bigger signals came from the transmitter directly and with 1-3 turns around the cylinder. The time moments that are expected to have pulses from imaginary source (also directly and with 1-3 turns) are marked by vertical lines. At those moments enough intensive signals are really received. The last two pulses as from the transmitter as from the imaginary source almost coincide. So only two first pulses were used for focusing. The received signal was sampled and stored. The intervals from its appropriate places were selected a bit longer that the transducer own oscillation period (10 µs) and the signals were summarized. Such operations are accomplished for the coordinates a = -40...+50 mm and h = 290...380 mm. The results of this scanning (voltage “peak-peak”) are shown in fig. 5. The imaginary source (the point with coordinates a = 10, h=330 mm) is clearly seen. The distance a must be 0 and h=280 mm when the cut at the end of the pipe is flat and perpendicular to the axis; in our case the cut was not such. 2.3 The effectiveness of focusing The intensity of the waves radiated by every array element decreases by their propagating because of two reasons: - wave scattering, - damping. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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Those factors influence all the elements almost equally in traditional array constructions, as array period is less that the distance to the focus point. In our case the period 2ʌR is of the same order or longer that the distance li (fig. 1b) and the influence of those factors is different to every wave. Overall, the amplitude U of the wave in the focus point is equal to the sum of separate wave amplitudes and for the plane wave perpendicular to the cylinder axis, we will have such expression: U = U1(1+r+r2...+ri-1+...),
(3)
where U1 is the amplitude of the first wave, r =exp(-2ʌRĮ), Į is the coefficient of the attenuation, i – is the number of the wave. The limit of the eqn (3) when i is infinite: U = U1/(1-r). (4) Because of the scattering every member of the series eqn (3) must be multiplied from the accordingly the member of that series
1
1 2
1 3
...
1 i 1
...
(5)
It can be seen that according to the case of classical array U/U1 is close to the used wave number n. U/U1
3
Conclusions
The researched case of the wave control in the space is distinct by the construction that cannot be simplified, as the array consists of the only one alldirectional transducer. But the combinations of a and h must be avoided when not all the waves can coincide. Those cases generate the disturbing noise. Two means can be proposed: - to use the wave pulses as short as possible, - not to use the method for the part of the cylinder where it is impossible the coincidence of all waves.
References [1] Alleyne, D.N., Lank, A.M., Mudge, P.J. & Cawley. P., The Lamb wave inspection of chemical plant pipework. Trend in NDE Science & Technology, Vol. 4, Ashgate publishing company: New Delhi, pp. 2303 2306, 1996. [2] Alleyne, D.N., .& Cawley. P., The Interaction of Lamb waves with Defects. IEEE Trans. on Ultr., Ferroel. and Freq. Contr. 39(3), pp. 381- 397, 1992.
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176 Computational Methods and Experiments in Materials Characterisation III [3] Volkovas, V. & Sukackas. V., Technical diagnostics of pipe-lines by the approach of wave interference. Proc. of IMEKO XIV World Congress, ed. J. Halttunen, Finnish Soc. of Automation, Tampere, VII, pp. 67-70, 1997. [4] Sukackas, V., Giedraitienơ, V.& Ramanauskas, R., The non-destructive method of estimation of sediment layer thickness in pipes: problems, algorithms, PC-simulation. Proc. of the 2nd Int. conf. on emerging technologies in NDT, eds. D. Van Hemelrijck, A. Anastassopoulos & Th. Phillipidis, A. A. Balkema: Rotterdam, pp. 351-356, 2000. [5] Sukackas, V., Giedraitienơ, V.& Ramanauskas, R., Nondestructive testing of the pipe inner cavity. Proc. of IMEKO XVI World Congress, eds. M.N. Durakbasa, P.H. Osanna & A. Afjehi-Sadat, Austrian Soc. for Measur. and Autom.: Vienna,VI, pp. 273-277, 2000. [6] Sukackas, V. & Volkovas, V., Investigation of Lamb Wave Interference in a Pipeline with Sediments on the Inner Surface. Russ. Journ. of NDT., 39(6), pp. 445 453, 2003. [7] Sukackas, V.& Ramanauskas, R., A PC Simulation of the Propagation of the Lamb Waves in Pipes. Proc. of the 3nd Int. conf. “Acoustics III”, eds. D. Almorza, C. A. Brebbia, R. Hernandez, WIT Press: Southampton, Boston, pp. 390-398, 2003. [8] Alleyne, D.N. & Cawley, P., A two - dimensional Fourier transform method for the measurement of propagating multimode signals. Journ. Acoust. Soc. Am., 89(3), pp. 1159 - 1168, 1991. [9] Sukatskas, V. & Volkovas, V., A Technique of Signal Processing for Interferometric Estimation of the Amount of Deposit in Pipes. Russ. Journ. of NDT., 41(7), pp. 430 435, 2005.
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3D strain mapping inside materials by microstructural tracking in tomographic volumes H. Toda1, M. Kobayashi1, K. Uesugi2, D. S. Wilkinson3 & T. Kobayashi1 1
Department of Production Systems Engineering, Toyohashi University of Technology, Japan 2 Japan Synchrotron Radiation Research Institute, Japan 3 Department of Materials Science and Engineering, McMaster University, Canada
Abstract X-ray absorption microtomography has been employed to trace the physical displacement of internal microstructural features in order to obtain local strain distribution inside materials. The number of microstructural features visible by means of state-of-the-art synchrotron radiation microtomography sometimes reaches into the tens of thousands or more in ordinary structural materials. It implies that high-density strain mapping is enabled if such large-scale tracking is accurately performed. The present paper describes a method to accurately track microstructural features by utilising the information on the size, shape and gravity centre of microstructural features together with the spring model particle tracking algorithm and exploratory registration using macroscopic deformation pattern. A model material which contains artificially introduced micro-pores has been prepared and used for the investigation. It has been clarified that almost perfect tracking is realised if the procedure is adequately applied to 3D image data sets. 3D internal strain mapping is also demonstrated and correlated to the localised ductile fracture of the model material. Keywords: microtomography, tracking, three dimension, strain mapping, microstructure, spring model, ductile fracture, image analysis.
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178 Computational Methods and Experiments in Materials Characterisation III
1
Introduction
As the resolution level of the synchrotron radiation microtomography is improved [1, 2], it has gradually come into use in various materials science and engineering fields in this decade. Especially, an in-situ observation utilising a specially designed rig has been proved to be a highly effective way of directly assessing various physical phenomena via the quantification of internal physical quantities three-dimensionally. For example, Maire et al [3] investigated 2-D strain distribution in a SiCf/Ti composite combining the X-ray synchrotron radiography and X-ray diffraction. 3D internal strain measurement was demonstrated by Bay [4] for a trabecular bone. Random surface speckle is automatically recognized in the technique as a basis for correlation. Other approaches have been reported recently for plastic displacement field visualisation by Nielsen et al [5], local crack opening displacement measurement by Toda et al [6] and fatigue crack driving force determination by Toda et al [7]. In these examples, microstructural features, such as particles or micro-pores were extracted by applying a fixed threshold value for each tomographic data thereby gravity centre of each feature is determined. Matching identical microstructural features in different datasets is performed semi-automatically by applying simple matching criterion such as physical displacement and/or the shape and the size of each microstructural feature. Some matching errors were inevitably included in the results due to the irregular trajectory caused by local deformation or resemblance in the shape and size of features, by which laborious manual corrections were subsequently obliged to delete them almost manually [5, 7]. Another approach to derive internal strain distribution is the digital image correlation technique. Concerning the high resolution microtomography images in which a secondary phase has a sharp interface and different X-ray absorption with a matrix, the former seems to be clearly advantageous. Particles and micro-pores embedded in a metal would be such examples. On the other hand, the latter would be potentially effective in biological objects. This paper reports how the accuracy of tracking numbers of microstructural features is ensured by applying several different procedures. Experimental verification of accuracy is performed by producing a model material in which micro-pores of known size and spatial distribution is artificially introduced.
2
Experimental and image analysis procedures
2.1 Image analysis 2.1.1 Preliminary image processing The tomographic volumes are first processed to extract microstructural features. The features are segmented using a fixed threshold value and then converted into a binary image with either gray values of 0 (background) or 1 (object). A labelling algorithm is subsequently applied in order to distinguish features. Geometrical information of each microstructural feature, i.e. surface area, WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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volume and gravity centre are calculated utilizing the Marching Cube algorithm that gives pentagonal faceted isointensity surface [8]. Before tracking each marker in a set of tomographic volumes, registration among volumes is performed as a first step to compensate translational and rotational shifts relative to each other. The registration is executed as follows; first, eight sets of tracking marker pairs, which can be readily distinguished from surrounding markers, are selected manually in each tomographic volume. A home-made software that can output marker locations is used for it. Second, a transformation matrix is calculated so that the sum of differences in distance between corresponding pairs is minimised. It is applied to all the makers to superpose a chronologically late volume onto a chronologically-advanced volume. 2.1.2 Base tracking procedure using matching probability parameter As is easily supposed, deformation or deterioration of a real material does not allow correct correlation if only the above simple registration is applied. A matching probability parameter (MPP), Mp, is introduced to extract tracking errors as well as correctly matched pairs. This is fundamentally two-frame particle tracking procedure [9]. Index numbers, i and j, denote feature number which is assigned in the labelling process. MP = D Li,j + E Si,j + J Vi,j
(1)
Here Li,j, Si,j and Vi,j are location, surface area and volume parameters, respectively. D, E and J are weights, where D + E + J = 1. Firstly one microstructural feature is picked up from a quantified dataset, and then Mp values for all markers in another corresponding dataset are calculated using eqn (1). If the maximum Mp value is larger than a pre-determined first threshold value, Mpth1, and a difference between the maximum and the second largest values is larger than a pre-determined second threshold value, Mpth2, then the marker pair with the largest Mp value is labeled to be tracked (Hereafter it is called “tracked marker”.). If the difference is less than Mpth2, then the marker pair is held in a waiting list (Hereafter it is called “pended marker”.). If no marker satisfies the first criterion on Mpth1, the marker is not used for the tracking purpose (Hereafter it is called “rejected marker”.). By repeating the above operation for all the markers in the first dataset, the initial tracking procedure is terminated. In this study, the Mpth1 and Mpth2 values are set to be 0.8 and 0.1, respectively after preliminary investigation. The definition of Li,j is as follows: Li , j
(rs l i , j ) / rs ® 0 ¯
, l i , j d rs , l i , j ! rs
(2)
where li,j is a distance between the marker with index i in the first dataset and the marker with index j in the second dataset, rs is the radius of a search space in which corresponding marker is searched. Therefore Li,j increases when a marker suspected to be identical is located close to the relevant marker, and becomes 0 outside the search space. Si,j and Vi,j are also defined in a similar way.
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180 Computational Methods and Experiments in Materials Characterisation III 2.1.3 Macroscopic trajectory prediction Two kinds of additional tracking procedures are used together with the abovementioned procedure. One is a macroscopic trajectory prediction (MTP) on the basis of known macroscopic deformation pattern. The method adopted here is quite simple. Provided that applied strain distributes homogeneously throughout a material, centre of gravity coordinate of each marker in the image dataset of a deformed sample is linearly interpolated before the two-frame tracking algorithm described in the section 2.1.2 is applied. In this study, the model sample was monotonously tensioned, so the image dataset has been just extended in the longitudinal direction and contracted in the vertical directions assuming Poisson's ratio of 0.5. 2.1.4 Spring model tracking algorithm Another tracking algorithm, which is called the modified spring model algorithm (SMA) [10] is applied for markers classified as “Pended”. The spring model tracking algorithm is one of the particle image velocity methods to measure the velocity of flows which has been utilised in the field of fluid mechanics. The schematic illustration of this method is shown in Fig. 1. This method identifies particle pairs by searching the smallest total spring force among particle clusters, in which particles are connected by imaginary springs each other. The method would be effective for locally inhomogeneous deformation, because the model can cope with apparently random deviation of relative position among the markers. 2.1.5 Post processing and final assessment Finally the assessment of tracking results is performed by calculating the ratio of success tracking, Kwhich is the number of correctly tracked markers normalised by that of all the markers. The correctness is checked using a database in which the trajectory of each marker has been examined in advance and recorded.
Figure 1:
Schematic illustration of the spring model for matching pended markers. Provided that four pended markers are observed in the second image. One of which is suspected to be identical to a single marker observed before deformation.
Tetrahedrons, whose vertex is occupied by markers, are generated by the Delaunay tessellation technique [12]. Normal and shear strains are calculated WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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from the deformation of the tetrahedron assuming a linear displacement field inside it. Local strain distribution is demonstrated as a form of cross-sectional or 3D colour contour maps. 2.2 Model material A model sample used to examine the performance of the series of the procedures is a dispersion-strengthened copper in which micro-pores of uniform size have been introduced artificially. The material consists of four sheets containing holes of 15 Pm in diameter all the way through each sheet and five hole-free sheets, which were sandwiched alternately and then diffusion-bonded. The thickness values of the sheets are 15, 30 and 50 Pm for the drilled sheets and the inner and outer hole-free sheets, respectively. In total 188 pores were introduced in the model sample. Tensile test specimens with a cross-section of 250×300 µm were cut out from the joined plate. 2.3 Tomographic observation of deformation and fracture High-resolution tomographic experiments were performed using a monochromatic X-ray beam having a photon energy of 35keV at beamline BL20XU in the synchrotron radiation facility SPring-8. The tensile load was applied by successively increasing displacement using a test rig specially designed for this purpose [11]. Four CT scans were performed for a specimen; one prior to loading and the other three at different loading states. An isotropic voxel with a cutting edge of 0.474 Pm was achieved using the present set up. Each voxel has a 16-bit gray-scale depth, which corresponds to linear absorption coefficient (LAC) value. To reduce the size of image sets, 16-bit LAC values ranging 0 to 80 was linearly mapped to a range between 0 and 255 in an 8-bit gray-scale. The other details of the imaging procedure are available elsewhere [11].
3
Evaluation of results
Figure 2 shows a 3D reconstructed image captured at the final loading step which is just before the final rupture. All the micro-pores has been cylindrical and of uniform size before loading. Randomly distributed micro-pores lying on the four layers appear to overlap in the figure. The micro-pores have been gradually elongated and then necking region is observed as is shown in fig. 2. Damage evolution is observed in the figure where some of the micro-pores located in the necked region are linked up with each other to be a coarse cracklike damage. Macroscopic applied strain was measured using a couple of markers located at almost the both ends of the field of view shown in the figure. The applied strain ranged between 3.5 and 22.1%. Closer inspection revealed that interlayer delamination and its interaction with micro-pores. Changes in the ratio of tracked, pended, rejected and correctly tracked markers for all the markers, m with the radius of a search space, rs, are shown in fig. 3 where only the basic MPP method is applied. Two examples for different WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
182 Computational Methods and Experiments in Materials Characterisation III applied strain difference, ', between the two consecutive images (3.5 and 16.3%) are included in the figure. Apparently 16.3% strain difference is too large for an ordinary in-situ experiment since the common fracture strain of engineering materials: several ten% divided by 10 observation stages falls to several% strain difference. Therefore it is an unrealistic extreme case to test the potential of the procedure. It can be seen that the number of tracked markers has a maxima at rs=71.1 and 106.7 Pm for ' of 3.5 and 16.3%, respectively. Although the available marker points vary with rs, perfect matching was obtained for ' of 3.5%, while it is fairly low (29.0% at maximum) for ' of 16.3%.
Figure 2:
A reconstructed 3D image acquired at the fourth loading step, representing inner pore (in green) and damage evolution in the necked region.
Figure 3:
Changes in the ratio of tracked, pended, rejected and correctly matched markers with increasing the size in search space, rs, for the strain differences of (a) 3.5% and (b) 16.3%.
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Figure 4:
183
Changes in the ratio of success tracking with applied strain. The matching probability parameter (MPP) is used for all, while the macroscopic trajectory prediction (MTP) and/or the spring model algorithm (SMA) are added in the remaining two trials.
The feasibility of the additional two tracking algorithm (MTP and SMA) can be seen in fig. 4. As shown in fig. 3, the ratio of success tracking decreases with macroscopic applied strain if only the basic MPP method is applied. The application of all three algorithm provides satisfactorily high success ratio below the applied strain of 16.3%, while the application of SMA causes the deterioration in the ratio for a very large '. This deterioration has little influence on practical measurement because ' higher than 10% is practically unrealistic as described above. Figure 5 also shows the effects of search space. If only the MPP method is applied as shown in fig. 5(a), the ratio of success tracking is critical to the search space. This implies that considerable preliminary trial is needed to find out the optimum parameter, which seems to be quite impractical. When the MTP method is, however, added as shown in fig. 5(b), the ratio of success tracking ranges between 94.2 and 100% for rs above 23.7 Pm. Therefore unless otherwise parameters are irrelevantly small, the accuracy of the method is quite insensitive to the parameter setting, which seems to be beneficial from a practical point of view.
Figure 5:
Ratio of success tracking against the size of search space, rs. The matching probability parameter (MPP) is used in (a) and the macroscopic trajectory prediction (MTP) is added in (b).
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184 Computational Methods and Experiments in Materials Characterisation III
Figure 6:
Ratio of success tracking for the tracking in consideration of volume parameter, Mv, and surface area parameter, Ms. Volume and surface area of each marker are intentionally varied with predetermined variation ranges. The other conditions are similar to fig. 4.
Figure 6 also demonstrates the effects of a likely supposition that the volume and surface area of each particle are different between two consecutive images. This is most likely when micro-pores grow under an applied loading. Partial dissolution or growth of a secondary phase during a secondary process such as a heat treatment also brings about the similar situation. The application of the MTP procedure provides almost perfect tracking even if such geometrical disturbance occurs.
Figure 7:
Comparison of cross-sectional representation of axial strain, Hz, with a corresponding tomographic slice. Strain concentration along obliquely aligned pores and final fracture through them are clearly demonstrated.
It is concluded that the combination of the three tracking algorithms may lead to reliable and robust microstructural tracking, relatively independent of the WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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parameter setting conditions: such stability may be seen to enable automatic accurate strain mapping when a suitable population of particles is identified, especially in the case of aluminium alloys which inherently contain small but closely interspersed intermetallic particles and micro-pores.
4
Comparison with in-situ visualisation
3D strain distribution and its change with applied loading have been successfully visualised utilising the present procedure. Fig. 7 is one of such examples. Although 3D display is possible using the method described in the section 2.1.5, strain distribution is shown in the figure on a 2-D virtual cross-section to show positional relationship between the aligned micro-pores and calculated localised strain directly. Fig. 7(a) clearly demonstrates that the upper four micro-pores lying along a downward-sloping line and the lower three micro-pores lying along a somewhat upward line cause strain localisation within the area surrounded by the micro-pores. A virtual slice on the identical cross-section shown in fig. 7(b) exhibits a final crack path on fracture passing through the upper pores. Overall, the high resolution in-situ synchrotron X-ray microtomography offers a highly effective way of visualising internal strain distribution in 3D which might give us a direct solution for the interpretation of realistic physical phenomenon.
5
Summary
A tracking procedure for microstructural features contained in the high resolution in-situ synchrotron X-ray microtomography image has been developed in order to measure 3D local strain distribution within a deforming material in highdensity. Especially it is crucial to raise its accuracy. The developed tracking method consists of the matching probability parameter, macroscopic trajectory prediction and spring model tracking algorithms. By combining these three algorithms, the robust procedure for internal strain visualisation is realised, being appropriate for automatic high-density mapping in the case of practical materials which inherently contain small and closely interspersed intermetallic particles or micro-pores. The tracking results were relatively independent of the parameter setting conditions and such stability may be crucial from practical point of view.
Acknowledgements NEDO has been supported this work as Collaborative Research of Production and Fabrication Technology Development of Aluminum useful for Automobile Light-weighting. The supports of the Grant-in-aid for Scientific Research from JSPS through subject No. 17360340, JASRI through proposal number 2005A0066-NM-np, the Tatematsu Foundation and the Light Metal Educational Foundation are also gratefully acknowledged.
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186 Computational Methods and Experiments in Materials Characterisation III
References [1]
[2]
[3] [4] [5]
[6]
[7]
[8] [9] [10] [11]
[12]
Cloetens, P., Pateyron-Salome´, M., Buffie`re, J.-Y., Peix, G., Baruchel, J., Peyrin, F., Schlenker, M., Observation of microstructure and damage in materials by phase sensitive radiography and tomography. J. Appl. Phys., 81(9), pp. 5878-5886, 1997. Toda, H., Uesugi, K., Takeuchi, A., Minami, K., Kobayashi, M. & Kobayashi, T., Three-dimensional observation of nanoscopic precipitates in an aluminium alloy by microtomography with Fresnel zone plate optics. Applied Physics Letter, 89(14), pp. 143112, 2006. Maire, E., Owen, A., Buffiere, J.-Y., Withers, P.J., A synchrotron X-ray study of a Ti/SiCf composite during in situ straining. Acta Materialia. 49, pp. 153-163, 2001. Bay, B.K., Texture correlation: A method for the measurement of detailed strain distributions within trabecular bone. Journal of Orthopaedic Research, 13(2), pp. 258-267, 1999. Nielsen, S.F., Poulsen, H.F., Beckmann, F., Thorning, C., Wert, J.A., Measurements of plastic displacement gradient components in three dimensions using marker particles and synchrotron X-ray absorption microtomography. Acta Materialia, 51(9), pp. 2407-2415, 2003. Toda, H., Sinclair, I., Buffière, J.-Y., Maire, E., Connolley, T., Joyce, M., Khor, K.H., Gregson, P.J., Assessment of fatigue crack closure phenomenon in damage tolerant aluminium alloy by in-situ highresolution synchrotron X-ray microtomography. Philosophical Magazine, A83, pp. 2429-2448, 2003. Toda, H. Sinclair, I., Buffière, J.-Y., Maire, E., Khor, K.H., Gregson, P. and Kobayashi, T., A 3D measurement procedure for internal local crack driving forces via synchrotron X-ray microtomography. Acta Materialia. 52(5), pp. 1305-1317, 2004. Lohmann, G., Volumetric Image Analysis, John Wiley & Sons Ltd: Chichester, pp. 183-186, 1998. Kim, H.-B., Lee, S.-J., Performance improvement of two-frame particle tracking velocimetry using a hybrid adaptive scheme, Measurement Science & Technology, 13(4), pp. 573-582, 2002. Okamoto, K., Hassan, Y.A., Schmidt, W.D, New tracking algorithm for particle image velocimetry, Experimental Fluids, 19(5), pp. 324-347, 1995. Toda, H., Ohgaki, T., Uesugi, K., Kobayashi, M., Kuroda, N., Kobayashi, T., Niinomi, M., Akahori, T., Makii, K. and Aruga, Y., Quantitative assessment of microstructure and its effects on compression behaviour of aluminium foams via high-resolution synchrotron X-ray tomography, Metallurgical and Materials Transactions. A, 37A(4), pp. 1211-1220, 2006. Barber, C.B., Dobkin, D.P. and Huhdanpaa, H.T., The Quickhull Algorithm for Convex Hulls, ACM Transaction on Mathematical Software, 22(4), pp.469-483, 1996. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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Fractal and spectral analysis of fracture surfaces of elastomeric materials D. Ait Aouit & A. Ouahabi Ecole polytechnique de Tours, Université Francois Rabelais, France
Abstract Crack path identification was based on a multifractal spectrum calculated upon the fracture surfaces of an elastomeric material. This identification was carried out under various mechanical loading (stress level, frequency and loading ratio) and thermal damage. The self-affinity nature of the surface roughness anisotropy is roughly identified through the power spectrum analysis. Then, the clustering singularity structure and its multiscaling characteristics are further examined with the box-counting technique and multifractal analysis. According to the features extracted from the multifractal spectrum obtained, it is apparent that the fracture surface morphology exhibits fewer irregularities with the crack initiation, and more irregularities appear with the crack propagation, until the phase of the final rupture of the material which presents fewer irregularities. This identification is very useful to determine the fracture causes of manufactured parts from the studied material. Keywords: surface roughness, multifractal, fracture, irregularities.
1
Introduction
The fracture surfaces contain the history of micro crack signatures, which are the indices of the fatigue of the studied materials. In the past few years, most commonly applied methods in a numerical description of fracture surfaces are quantitative fractography and image analysis [1, 2]. The concept of fractal geometry has been proved to be very useful in describing fracture morphology of materials. The Stach’s works [3–6] have shown the effectiveness of multifractal analysis in the fractographic study.
WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/MC070191
188 Computational Methods and Experiments in Materials Characterisation III A lot of works have shown that a broad range of metal and ceramic materials exhibit a multifractal property on their fracture surface [7–9], but there are very few contributions to the fractographic study of elastomeric materials [10, 11]. However, in the present work an investigation of the multifractal analysis for elastomeric material is presented. This paper is organized as follows. In Section 2, we describe the mathematical foundation of multifractal analysis and the characteristics of the data used. In Section 3, we present the results obtained with the multifractal spectrum in the context of scanning electron microscope of fracture images, and then we discuss these results. We conclude our work in Section 4.
2
Tools and research material
2.1 Data In this study, crack propagation tests using a Dynamic Mechanical Analyser (a TA instrument DMA 2980) have been carried out under various mechanical conditions (stress level, frequency and loading ratio) and thermal damage. For the crack propagation study, we used an edge cracked simple tension specimen, the elastomeric sample sizes are: 14 mm of length × 8 mm of width × 1.70 mm of thickness. In order to make a global study of the surface roughness, we have digitized the fracture surface with a white light optical profiling using vertical scanning interferometer. An example of 3D and 1D fracture profiles is given by figure (1). The extraction process of the 1D profiles is carried out in the direction of the crack propagation. The morphology developments of the fracture surface were examined by a JOEL JSM-6480 LV scanning electron microscope instrument. The acquisition is done with a secondary electron and high vacuum mode. Some examples of fracture development images of the elastomeric studied material are presented in figure (2). 2.2 Theory and methods Multifractal structure was first introduced by Mandelbrot [12], it is characterized by an infinite set of critical exponents describing the scaling of the moments of the distribution of some quantity. Since then, this feature has been observed in various objects, such as the energy dissipation set in turbulence [13], strang attractors in chaotic dynamical systems [14] and others. In our work, the multifractal analysis has been carried out using Legendre transform. This method is based on the approach proposed by Stanczyk and Sharpe [15] for natural texture classification, in our application this method is applied to fracture texture identification. It uses a box-counting approach for determining fractal dimension, which estimates the probability pi (H ) of every single box that contain irregular mass (fracture patterns).
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1 2
-a0
0.3
1
2
0.25
-0.05
0.2 0.15
-0.1 z (m m )
z (m m )
0.1
-0.15
0.05 0 -0.05
-0.2
-0.1 -0.15
-0.25
0
0.2
0.4
0.6
0.8 1 y(mm)
1.2
1.4
1.6
-0.2
1.8
0
0.2
0.4
0.6
0.8 1 y(mm)
1.2
1.4
1.6
1.8
-bFigure 1:
a
Example of digitized fracture surface. (a) 3D roughness profile, (b) two transverse sections.
b
Figure 2:
c
Fracture development SEM images: (a) crack initiation, (b) crack propagation and (c) final rupture.
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190 Computational Methods and Experiments in Materials Characterisation III Doing so for SEM images of size 840×840 pixels, the images can be divided into many boxes of size l × l, and let İ = l/L (H o0) (L = 840). We briefly recall some basic facts about the multifractal theory. See also [16]. P is defined as a Borel probability measure on [0,1]×[0,1]. Let Q n a linear size of “box” around (i,j) upon which we evaluate
P . We also define the sub-
region I i , j , n as follow: I i , j ,n
ª i i 1º ª j j 1º «v , v »u «v , v » n ¼ ¬ n n ¼ ¬ n
(1)
If we consider the quantity W n defined by the formula (2)
W n ( q) and if lim W n (q ) nof
log( ¦ P ( I i , j ,n ) q ) i, j
logQ n
(2)
W (q) , we can say that P exhibits a multifractal behaviour.
With q the moments order in a non-empty interval of R. So, W (q) characterizes the global behaviour of the measure. For the local structures, the Hölder exponent D at point (i, j) is defined according to the formula (3) dW (q) (3) DIi , j (q) dq
To obtain the Legendre multifractal spectrum f (D ) associated with P , the Legendre transform is applied as follow: f (D ) inf(qD W (q)) (4) qR
During the data acquisition process, the images can be corrupted with noise, thus to remove this noise from the images we have used wavelets DWT-2D. Hence, the spectrum is calculated from the de-noised images.
3
Analysis and results
3.1 Spectral analysis of fracture surface roughness anisotropy
Spectral analysis provides an essential tool for understanding the frequency components of a surface roughness. It has been used to study different topics such as the upper and lower limits of fractal dimensions of a fracture surface and the selection of a proper sampling bandwidth for 3D surface topography measurement [17]. The method of power spectrum can simply be realized by means of the fast Fourier transformation and it leads to useful results [18]. As demonstrated in figure 3(a) the fracture surface under 20%-5Hz displays a
f 8 / 3 power-law shape over a range of frequencies (f = spatial frequency (mm-1)). This decrease of power-law corresponds to a scale-invariance by WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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anisotropic transformation. This phenomenon is observed for all the fracture surfaces obtained from the four fracture conditions (figure 3(b)). 3.2 Multifractal analysis
The shape and the extension of the f (D ) -curve contains significant information about the distribution characteristics of the examined data set. In general, the spectrum has a concave downward curvature, with a range of D values increasing correspondingly to the increase in the heterogeneity of the distribution. In our work, we analyse the fracture surface in order to identify the fracture morphology that we can find in the direction of the crack propagation. This identification is shown by three separate multifractal spectrums, the first one is estimated upon the crack initiation SEM images, the second one from the crack propagation SEM images, and the last one from the final rupture zone (see figure 4(a)). This phenomena, is repeated for the four applied fracture conditions (see figures 4(a), 4(b), 4(c) and 4(d)). The width of each multifractal spectrum of all fracture conditions is reported in table 1. For the majority of the fracture conditions, we notice that the spectrum of the crack initiation zone is less wide than that calculated on the crack propagation zone, and wider than the spectrum of the final rupture zone. Therefore, we can say that, at the crack propagation zones the surface texture contains more irregularities. The fracture surfaces of the studied material under different fracture conditions display distinct multifractal behaviours. This difference of behaviours was estimated by the correlation coefficient between the various obtained multifractal spectrums. The correlation coefficient R2 was calculated by comparing the various f (D ) curves with a curve of the three zones (crack initiation, crack propagation and final rupture) obtained at the fracture condition of 20%-5Hz. The correlation results are shown in table 2. We note that we note that the fracture surface at the condition of 20%-5Hz-120° presents a best correlation with a correlation coefficient equal to 0,9924 (~1). Therefore, the fracture patterns presented at the two zones are almost similar.
4
Conclusion
A new method of crack path identification has been developed by combining scanning electron microscopy, secondary electron signal and multifractal image analysis. An advantage of the multifractal analysis methods is the possibility of taking into account the complicated fracture morphology development (crack initiation, crack propagation and final rupture). According to the multifractal spectrum results calculated upon the three zones at each fracture conditions, we conclude that the fracture structure at the crack propagation step displays more irregularities then other zones. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
192 Computational Methods and Experiments in Materials Characterisation III
24 20%-5Hz
22
20%-10Hz 40%-5Hz
20
20%-5Hz-120°
24
slope=-8/3
22
18 log(spectral density)
log(spectral density)
20 18 16 14
16 14 12
12
10
10
8
8
6
6 -3
-2
-1
0
1
2
3
4
5
6
4 -3
7
-2
-1
0
log(spatial frequency(mm-1))
1
(a)
Figure 3:
2
3
4
5
6
7
log(spatial frequency(mm-1))
(b)
Log-log plot of the power spectral density of the fracture profiles resulting from: (a) 20%-5Hz fracture condition only, (b) 20%-5Hz, 20%-10Hz, 40%-5Hz and 20%-5Hz -120° fracture conditions. 2
2
1.8
1.8 1.6
1.6
1.4
f f(q) (Į)
1.4
f (Į)f(q)
1.2 1
1.2
0.8
1
0.6
crack initiation crack propgation final rupture
0.4 0.2 1.5
1.6
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crack initiation crack propagation final rupture
0.8
1.9
2
2.1
2.2
2.3
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1.6
2.5
1.7
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2
(a)
2
2.1
2.2
2.3
2.4
2.5
D (q)
(b)
D (q) 2 1.8
1.8
1.6
1.6
f (Į)
ff(q) (Į)
1.4 1.4
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1.2
1 1
crack initiation crack propagation final rupture
0.8
1.5
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2
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crack initiation crack propagation final rupture
0.8 0.6
2.2
2.3
2.4
2.5
0.4 1.6
1.7
1.8
D (q)
(c)
Figure 4:
1.9
2
2.1
D (q)
2.2
2.3
2.4
2.5
(d) Multifractal spectrum of fracture surface for four different fracture conditions: a) 20%-5Hz, b) 20%-10Hz, c) 20%-5Hz-120°, d) 40%5Hz.
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20 15 10 5
W (q)
0 -5 -10 -15 -20 -25 -30 -10
-8
Figure 5: Table 1: Fracture conditions 20%-5Hz 20%-10Hz 20%-5Hz120° 40%-5Hz
Table 2:
-6
-4
-2
0 q
2
4
6
8
10
The relationships of slope W q with q.
Fracture conditions and the width of the f (D ) spectrum upon the crack path. Crack initiation Įmin Įmax
¨Į
Crack propagation Įmax Įmin ¨Į
Final rupture Įmax Įmin
¨Į
2.4834 2.4005 2.4137
1.6891 1.6789 1.6194
0.7943 0.7216 0.7943
2.3600 2.4643 2.3884
1.5351 1.6693 1.5479
0.8249 0.7950 0.8405
2.4074 2.4158 2.4055
1.6404 1.7127 1.6409
0.7670 0.7031 0.7646
2.4073
1.6261
0.7812
2.4371
1.6168
0.8203
2.4833
1.7281
0.7552
Correlation coefficient between fracture conditions. Fracture conditions 20%-5Hz 20%-10Hz 20%-5Hz-120° 40%-5Hz
R2ci 1 0.9596 0.8828 0.9878
f (D ) curves of two different R2cp 1 0.8647 0.9924 0.9491
R2fr 1 0.9802 0.9905 0.9907
R2ci: correlation coefficient between the crack initiation f (D) curves for two different fracture conditions. R2cp: correlation coefficient between the crack propagation f(D) curves for two different fracture conditions. R2fr: correlation coefficient between the final rupture f (D) curves for two different conditions. Anisotropic and heterogeneous fractal properties of fracture surfaces of the elastomeric studied material are highlighted.
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194 Computational Methods and Experiments in Materials Characterisation III The multifractal behaviour of fracture surface indicates that multifractal spectra carry much additional information on the fracture conditions and structural properties of fracture surfaces, which seems to be helpful in understanding structural phenomena of fracture surfaces.
References [1] [2] [3] [4] [5] [6] [7]
[8] [9] [10]
[11] [12] [13] [14]
Wojnar, L., Quantitative fractography: basis and computer aid of investigations. Krakow: Cracow University of Technology; 1990. Wojnar, L., Image analysis: applications in materials engineering. CRC Press, 1999. Stach, S. & Cybo, J., Multifractal description of fracture morphology: theoretical basis. Mater Charact’03; 51(1):79-86, 2003. Stach, S. and al, Multifractal description of fracture morphology: investigation of the fractures of sintered carbides. Mater Charact’03, 51(1):87-93, 2003. Stach, S. and al, Multifractal or fractographic fracture line description. Inz Mater’04; 140(3):440-3, 2004. Stach, S. & Cybo, J., Multifractal detection of overlaps based on a stereometric analysis of fracture surface: assumptions. Materials Characterization’06; 56:449-53, 2006. Sim, B. L., Agterberg, P. and Beaudry, C., Determining the cutoff between background and relative base metal smelter contamination levels using multifractal methods. Computers & Geosciences, Volume 25, Issue 9, pp. 1023-1041, 15 November 1999 Jing, L.I. and al, Fractal analysis of crack paths in Al2O3-TiC-4%Co composites. Transactions of Nonferrous Metals Society of China, Volume 16, Issue 4, pp. 795-799, August 2006. James, L. and al, Fracture surface examination of dental ceramics using fractal analysis. Dental Materials, Volume 21, Issue 6, pp. 586-589, June 2005. Jelcic, Z., Holjevac-Grguric, T. and Rek, V., Mechanical properties and fractal morphology of high-impact polystyrene/poly(styrene-b-butadieneb-styrene) blends. Polymer Degradation and Stability, Volume 90, Issue 2, pp. 295-302, November 2005. Ouahabi, A., AIT AOUIT, D., Fractales et ondelettes pour le signal et l’image (Chapter 3). Optimisation en traitement du signal et de l’ image, ed. Hermes Lavoisier, Paris, pp. 73-104, 2006. Mandelbrot, B. B., Intermittent turbulence in self-similar cascades: Divergence of high moments and dimension of the carrier. J. Fluid Mech. 62 (1974), pp. 331-358, 1974. Frisch, U., and al, Turbulence and predictability in geophysical fluid dynamics and climate dynamics. International School of Physics Enrico Fermi, North Holland Amsterdam, 1985. Grassberger, P., Procacia, I., Measuring the strangeness of strange attractors. Physica. D, vol. 9, no1-2, pp. 189-208, 1983. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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[15] [16] [17] [18]
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Stanczyk, P. & Sharpe, P., Classification of natural images from shape analysis of the Legendre multifractal spectrum. Fractals: Theory and applications in Engineering, Springer-Verlag, pp. 67-79 London, 1999. Jaffard, S., Construction de fonctions multifractales ayant un spectre de singularités prescrit. C.R. Acad. Sci. Paris, pages 19-24, T. 315, Series I, 1992. Lin, T.Y., Blunt, L. and Stout, K. J., Determination of proper frequency bandwidth for 3D topography measurement using spectral analysis. Wear. 166, 221-232, 1993. Russ, J.C., Fractal surfaces. Plenum Press, New York, 1994.
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Multi-scale foam behaviour characterisation P. Viot1 & D. Bernard2 1 2
LAMEFIP, ENSAM de Bordeaux, Talence Cedex, France ICMCB, CNRS, Université Bordeaux1, PESSAC, France
Abstract The mechanical behaviour of polymeric foams depends on several parameters such as temperature, material density and strain rate. The identification of the parameters characterizing this behaviour under dynamic loading requires the design of special apparatus like a fly wheel, drop tower or Hopkinson bars, allowing high compression speeds. The foams studied here are multi-scale materials; the agglomerated beads (mesoscopic scale, millimetric diameters) are composed of microscopic closed cells (a few tens of microns). Constitutive materials of these foams are polypropylene, polystyrene and cork. The response of the material to a dynamic loading consists of three regions: an elastic phase, a plastic phase and densification. The first part of this work deals with the identification of the behaviour of these multi-scale foams as a function of density and strain rate. In the second part, original observations of the physical phenomena initiated during the yield plateau are presented and analysed. Buckling of bead and cell wall and strong localisation of damage were studied using several devices and techniques such as high speed cameras, SEM, and micro tomography. Keywords: multi-scale foam, cellular material, dynamic loading.
1
Introduction
Polymer foams are used in many applications of passive safety for consumer goods (packaging for electronic equipment…) or for consumers themselves (helmets, knee pads…). It is usual to classify cellular materials in closed or opened cell foams [1], but it is also important to distinguish between foams which are constituted only of micro cells (commonly used in large plates for thermal or sound isolation applications in civil engineering) and those composed of fused beads (their size is millimetric and constitute the mesostructure) which are themselves made of micro cells (figures 1 and 2). WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/MC070201
198 Computational Methods and Experiments in Materials Characterisation III
Figure 1: Pictures of multi-scale foams (a) polypropylene foam (knauf), (b) polypropylene foam (JSP), (c) polystyrene foam (knauf), (d) cork.
Figure 2:
SEM of multi-scale foams (a) polypropylene foam (knauf), (b) polypropylene foam (JSP), (c) polystyrene foam (knauf), (d) cork.
These last foams are multi-scale materials. The mesoscopic morphology of these foams is determined during the manufacturing process: expanded plastic foam beads are injected into a mould where individual beads are fused together under steam heat and pressure. The constitutive material of these foams can be a polymer such as polypropylene (figures 1a and 1b) and polystyrene (figure 1c) or natural cellular material as agglomerated cork (figure 1d). The structure is always multi-scale: beads are millimetric (from 2 to 8 mm) whereas the size of the cells is a few tens of microns (figure 2). For the cellular materials studied in this paper, the size of the cells is relatively homogeneous for the polypropylene and polystyrene foams supplied by Knauf industries (the diameter is about 60 microns, figure 2a and 2c). On the contrary, the structure of the PP foam given by JSP industries is heterogeneous (the diameter can reach 100 microns figure 2b). Concerning the cork, the cells are not spherical and can be instead considered as tubes of diameter 25 microns (figure 2d). The mechanical behaviour of cellular material is well known. Under static or dynamic compressions, foam response shows three regimes: an elastic behaviour followed by a stress plateau corresponding to plastic yielding. Finally, for high strains, a rising hardening phase occurs due to foam densification. Many works treat of the effect of parameters such as foam density, strain rate or temperature [2, 3] but scarce are the studies which investigate the global response of the porous material taking into account the multi-scale structure of the foam, and the phenomena observed during a loading (local heterogeneity of the strain, buckling of bead and cell walls) [4]. Usually, elastic-plastic-rigid foam models are built from the homogenization of simplified cell (a cube, a polyhedron constituted of beams and walls) response [5]. The behaviour of this volume is identified from the beam and wall deformation and elastic-plastic-densification phases can be there modelled: the elastic phase corresponds to the compression of beams and WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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walls, the plastic plateau is due to the buckling of beams and the stretching of walls and the densification appears when the cell volume tends towards zero. From this approach, the model can be finally identified measuring the average cell dimensions (diameter, wall thickness) and taking into account the mechanical properties of the constitutive material of the foam. The homogenisation of this microscopic model is the final step to obtain the macroscopic response of the cellular material. This numerical method is particularly appropriate if the foam is not multi-scale and if no deformation localisation is observed during a compression. For multi-scale foams, it is necessary to develop another approach in order to take into account the mesoscopic scale (beads) and the microscopic one (cells). This article presents the first results of a project aiming to describe the behaviour of multi-scale foams under dynamic loading: firstly, dynamic compression tests were done to identify the macroscopic behaviour of these foams. Secondly, foam structure was analysed before, during and after impacts to observe physical phenomena caused by the loading at high strain rates. The experimental data obtained and the microscopic 3D observations acquired are necessary to develop a model for the material macroscopic behaviour taking into account bead and cell scales.
2
Foam behaviour under dynamic loading
2.1 Macroscopic response of cellular material Four cellular materials have been studied: two polypropylene (PP), one polystyrene (PS) foam and agglomerate cork. For PP and PS foams provided by Knauf industry, four densities U were tested: 70, 80, 90 and 100 kg/m3. Densities of JSP polypropylene foams were 35, 75 and 85 kg/m3. Only one density of cork was tested: U = 270 kg/m3. Several machines were used to qualify the behaviour of these cellular materials. A universal testing machine Zwick was used to identify the response of foams under quasi-static compression. For intermediate strain rates ( H about 100 s-1), compression loadings were done on a drop tower. These tests permit to estimate the macroscopic response of foams even if the velocity of the projectile decreases during the impact. To complete the behaviour identification and to carry out dynamic compressions at constant strain rates, a new compression device was developed on a fly wheel [6] ( H [100, 500] s-1). Lastly, Hopkinson bars were used to measure the foam response for higher strain rates ( H = 1500 s-1). To qualify the foam macroscopic response on these devices, the stress V is calculated as the ratio of the measured force by the initial section S0 (Poisson’s ratio is very low and the S section of the sample can be considered as constant). The true strain H can be calculated as an average deformation obtained by the Napierian logarithm of the ratio between the height h(t) of the sample (function of time t) and its initial value.
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200 Computational Methods and Experiments in Materials Characterisation III
Cork PP
fig. 5
Figure 3:
fig. 5 PS
Stress vs. time response of polypropylene and polystyrene foams (density 95 kg/m3) and cork for dynamic compressions H 100 s-1 .
Results showed figure 3 concern compressions at strain rates of 100 s-1 carried out on samples of PP, PS (from Knauf, same densities U = 95 kg/m3) and agglomerate cork (U = 270 kg/m3). The evolutions of the stress as a function of time are similar for the three cellular materials. For these 3 tests, the compression duration is close to 10 ms and these stress evolutions correspond to the classical behaviour of foam: an elastic phase followed by a plastic plateau and lastly the densification. On dynamic apparatus, although it is really difficult to measure with accuracy the elastic modulus, these results allow to compare the elastic behaviour of these foams. The elastic responses of PS and PP foams (provided by the same manufacturers, same densities) seem similar. The Young modulus of PP and PS as dense materials being close, it’s logical that the elastic responses of these foams are close too. In the same way, since the yield stress of dense PS is twice smaller than PP, the plastic plateau appears for lower stress for PS foam. The fact that the yield stress Vpl is higher for polypropylene foams than for polystyrene foams have been verified for all the different densities. Similarly, the slope Epl of the stress plateau (also designed as the tangent modulus) is larger for PP foams than for PS foams. Dynamic compressions using a fly wheel apparatus were also performed on these foams for different densities. For example, figure 4 presents the stress vs. strain responses of PP foams (Knauf) for 5 different densities (from 61 to 108 kg/m3). Only the elastic phase and plastic plateau were plotted. The yield stress Vpl is increasing with density. Indeed, a higher density involves a higher quantity of polypropylene, corresponding either to smaller cells in higher number or to WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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thicker cell walls. In both cases the foam is more resistant. Finally, the density appears also to have an influence on Epl, the slope of the stress plateau (also known as the tangent modulus). This modulus Epl is greater for higher densities. In conclusion, these compression tests performed at different strain rates (from quasi static to high strain rates) on several multi-scale foams of different densities, and different morphologies allow to constitute a useful experimental database. For each cellular material, the classical stress – strain curve was acquired and the corresponding parameters identified.
Figure 4:
Stress vs. strain of polypropylene foams under dynamic compressions H 100 s -1 .
2.2 Mesoscopic phenomena Dynamic compressions carried out in the fly wheel were recorded with a speed camera phantom V7 at 6688 frames per second (the time between two pictures is 150 Ps and the exposure time is 30 Ps) with a resolution of 800 x 600 pixels. For each multi-scale foam studied, these short movies reveal the strong localisation of the deformation during plastic plateau. Figure 5 presents pictures extracted from these movies before loading (t = 0 ms) and during dynamic compression at t = 3 ms for PP and PS foams (Knauf). On the first pictures (at t = 0) the bead structure of these foams is visible on the sample surface. The second pictures (t = 3 ms) show the sample deformed during the plastic plateau (the curves presented figure 3 have shown that the stress plateau begins about 1.1 ms). By comparison between the images at these two times, it is obvious that the deformation is strongly localised during the plastic plateau of these samples. One can see (particularly on PS, figure 5b) some foam beads which have been clearly damaged (darkened areas). This damage is diffused and located in the centre of the sample. The damaged layer is perpendicular to the compression axis and the beads located above and below this layer do not seem to be damaged. The same WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
202 Computational Methods and Experiments in Materials Characterisation III remarks can be done for PP foams (figure 5a); the foam damage appears also in the centre of the sample. The initial position of the damage layer seems however to be stochastic. To complete this study, a micrographic analysis of compressed samples was carried out in order to confirm the heterogeneity of the foams damage. The SEM picture (figure 6) shows the residual deformation of PP foam after impact. At the mesoscopic scale, one can observe many bands of plastically deformed cells, with their fine walls buckled under loading. Other bands, yet intact, have kept their initial shapes. This damage mechanism, by local buckling of cell walls, explains the stress-strain curves; the plastic plateau corresponds to the propagation of foam cells buckling. At mesoscopic scale, bead walls have been also deformed by buckling. The damage mechanism can be thus considered multi-scale.
Figure 5:
Pictures of foam samples (a – polypropylene, b- polystyrene) before and during dynamic compression (after t = 3 ms).
Figure 6:
SEM view of PP foam sample after dynamic compression.
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The analysis of these pictures revealed the phenomena of strain localisation of these cellular materials during dynamic compression. The main ruin mechanism observed on these foams is the buckling of bead and cell walls. Lastly, if the damage appears systematically in layers perpendicular to the compression, its initial position cannot be predicted. As a first hypothesis, one can suppose that the variability of the bead density has an influence on the damage location. A complementary investigation of the deformation mechanism has been initiated to validate (or reject) this assumption. 2.3 Bead density effect on local deformation To complete this study, micro tomography technique was considered to observe the deformation inside the foam structure at different scales. The experimental method consists in carrying out several interrupted impact tests on a sample using a drop tower, and acquiring a micro tomograph in between each impact [7, 8]. An image of the foam structure is taken before the first impact and after each dynamic compression; a device of dynamic compression was developed to control the maximum sample deformation during each impact and maintain the sample in compression during the micro tomographic measurement. The data presented in this paper have been obtained on the BM05 beam line at the European Synchrotron Radiation Facility (ESRF) in Grenoble (France). With this approach, first results of micro tomographic reconstructions reveal in 3D the state of the foam structure. The behaviour described in this section is based on observations made in a vertical plane inside the 3D micro tomograph (sample of diameter 10 mm and height 10 mm). Figure 7 shows a vertical cross-section of the sample prior to impact. The pixels of high intensity correspond to points of dense material (within a bead wall for example). The reconstructed image is of good quality since one can observe the large air bubbles and closed cells are also distinguishable. At a larger scale, the geometry of the compacted beads can be identified as a classical polyhedral structure. This geometry can be followed for the successive impacts. In order to confirm the phenomena of strain localisation, one chooses to highlight the behaviour of 5 beads after each impact. A numerical filter was applied on this zone of the image (figure 7) to better distinguish bead structure. The same filter was applied on images reconstructed after each impact (figures 8a, b and c). From these pictures, the state of deformation of each bead can be estimated and the analysis of the deformation of bead wall reveals that the loading can not be considered as an uni axial compression at the mesoscopic scale, the local loading seems more complex because the local deformation of bead walls corresponds certainly to a deformation resulting from a combination of compression and shear. The shape of bead 4 (figure 9) after each impact clearly confirms this hypothesis. From this micro tomographic measurement, vertical strain H is also calculated (in the compression axis) and variation of density between beads can be estimated from the average of the grey level of each bead [8]. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
204 Computational Methods and Experiments in Materials Characterisation III
Figure 7:
Vertical section (obtained by micro tomography) of polypropylene foam sample before impact.
(b) 2nd impact (a) 1er impact Figure 8:
(c) 3e impact
Vertical sections (obtained by micro tomography) of the same polypropylene foam sample after impacts.
After the first impact, these 5 beads are slightly deformed. The strain value calculated is beyond 4 % whereas the strain imposed on the sample is 10 % (table 1). In fact, the strain analysis on the complete sample shows that deformation is principally localized on the upper and lower part of the sample, near the punches. For the second impact on the same sample, the macroscopic strain imposed is 30 %. Strong heterogeneous deformation of the 5 beads can be observed on Figure 8b. This can be verified on the strain value of each bead (table 1): The strain of bead 4 is four times bigger than the strain of bead 2 whereas the density (estimated from the average of grey level) of this last one is significantly higher.
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If we compare density of beads (or grey level) and their strain, a correlation between these two parameters cannot be established; higher density of a bead does not involve lower strain. On the contrary, in some case, beads of high density are more deformed. These observations can also be done for the third impact (strain imposed of 50 %). One can note a strong heterogeneity of bead strain and there is no direct relation between bead density and strain. Lastly, for the fourth impact (sample strain is 70 %), bead strain values are more homogeneous since the densification of the complete sample is reached. To conclude, this last study performed using the micro tomographic technique has confirmed the strong localisation of bead deformation during dynamic compression within the material and not only on the sample external surface. The analysis of these last results has also revealed that a simple relation between bead density and deformation cannot be established. Phenomena observed are more complex and the localisation of the damage in cellular material depends certainly on a combination of several factors such as local density, obviously, but also defaults in the foam structure and morphology at both, meso and micro, scales.
Figure 9:
Sections of the same polypropylene bead (N° 4) after several impacts.
Table 1:
Strain values of beads marked on figure 7 and of the complete sample for the different interrupted impacts. Strain (%)
Bead 1 Bead 2 Bead 3 Bead 4 Bead 5 Sample
Surface (pixel) 250522 153920 245959 274272 225409 460.104
Grey level 77,7 81,3 77,6 78,2 81,2 82,2
Impact 1
Impact 2
Impact 3
Impact 4
-3,7 -1,7 0,0 -4,0 -4,0 -10,0
-20,0 -8,6 -24,0 -41,4 -35,2 -30,0
-34,0 -24,2 -41,2 -59,2 -50,6 -50,0
-61,6 -54,5 -64,3 -72,9 -67,3 -70,0
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3
Conclusion
Dynamic compressions carried out on several multi-scale foams allowed to identify the global response of these cellular materials. The elastic step, the plastic plateau, during which the material is progressively damaged, and the final step, densification, have been characterized. The influence of density and strain rate on the foam behaviour was highlighted. These macroscopic measurements were complemented by microscopic analysis performed using use of High-Tech apparatus (high speed camera, SEM, micro tomography). At this scale the foam damage appears severe on layers perpendicular to the loading direction and develop from this localization band. The heterogeneity of the strain in the sample is then significant. The deformation mechanism of fine wall cells and larger expensed grain walls is mainly buckling. This damage mechanism, by local buckling of cell and bead walls, explains the stress-strain curves; the plastic plateau corresponds to the buckling propagation on foam structure. This damage mechanism is multi-scale. The initiation and propagation of buckling are complex and the localization of the damage in a cellular material structure depends certainly on a combination of local beads density and foam morphology at the meso and micro scales. One can suppose that it is the combined effect of the multi-scale structure and of the heterogeneous density field which creates a specific deformation field for a dynamic compression.
References [1] [2] [3] [4] [5] [6] [7] [8]
Gibson L. and Ashby F.: “Cellular solids. Structures and properties”, Edition: Cambridge Solid State Science Series. Chen W., Lu F., Winfree N.: “High-strain-rate compressive behavior of a rigid polyurethane foam with various densities”, Experimental Mechanics, March 2002 vol. 42, no.1. Mills N.J., “Micromechanics of polymeric foams”, Proceedings of the 3rd Nordic meeting on Materials and Mechanics, May 2000, Aalborg, Denmark, 45-76. Viot P. and Vacher P., “Identification of foam behavior under dynamic loading by the use of particle imaging techniques”, Revue Matériaux et Techniques, hors série:39-43, December 2004. ISSN 0032-6895. Patel M.R and Finnie I., “Structural Features and Mechanical Properties of Rigid Cellular plastics”, J. of Materials, Vol. 5, No. 4 pp 909 – 932 Viot P., Beani F. and J-L. Lataillade, “Polymeric foam behavior under dynamic compressive loading”, J. Mater Sci, 2005, vol. 40, p. 5829-5837. Viot P. and Bernard D., “Impact test deformations of polypropylene foam samples followed by micro tomography”, J. Mater Sci, vol 41 (2006) 1277. Viot P., Bernard D. and Plougonven E., “Phenomenological study of polymeric foam deformation under dynamic loading by the use of micro tomographic technique”, Journal of Materials Science, (in press) WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
Section 6 Experimental methods – thermal analysis
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Thermo-analytical evaluation of wear debris for thermoplastic and sintered polyimide P. Samyn1, I. Van Driessche2, G. Schoukens3 & P. De Baets1 1
Department of Mechanical Construction and Production, Ghent University, Belgium 2 Department of Inorganic and Physical Chemistry, Ghent University, Belgium 3 Department of Textiles, Ghent University, Belgium
Abstract Transitions in friction and wear properties for polyimides are related to thermogravimetric analysis (TGA), differential thermal analysis (DTA) and mass spectroscopy (MS) of wear debris particles. Debris interactions in the sliding interface are important for the formation of a transfer film on the counterface. For sintered polyimide, fine wear debris particles are observed after sliding at 100 to 180°C, corresponding to high friction and lack of transfer. Conglomerated particles at 180 to 260°C coincide with a drop in friction and stabilisation in wear rates. Chemical reactions in the sliding interface such as hydrolysis and imidisation are illustrated. For thermoplastic polyimide, dark-coloured particles after 100 to 120°C sliding indicate hydrolysis, flake-like particles after 120 to 180°C sliding indicate imidisation and roll-like debris at 220 to 260°C show melting. It is confirmed by DTA that the glass transition and recrystallisation temperatures shift or disappear depending on the sliding temperature, representing the formation of cross-links and better ordered crystalline phase under sliding. Debris becomes brittle and consequently acts more abrasive during sliding. Keywords: polyimide, tribology, wear debris, differential thermal analysis, thermogravimetric analysis, mass spectroscopy, hydrolysis, imidisation.
1
Introduction
Polyimides are used in sliding contacts with steel counterfaces because of their self-lubricating effect. This means that no external lubricants such as oil or WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/MC070211
210 Computational Methods and Experiments in Materials Characterisation III grease are necessary. The lubricating mechanisms of polymers are attributed to the formation of a polymer transfer film adhering to the steel counterface and reversing the polymer/steel contact into polymer/polymer contact. In literature, the role of wear debris in establishing a transfer film is mainly described mechanically (e.g. Jacko et al. [1]). The roughness asperities of the steel counterface act as mechanical anchor points for accumulation of wear debris. However, homogenisation of the transfer film depends on interaction of the separate wear debris particles by thermal or chemical processes. Most reported polymer sliding mechanisms focus on melting of the polymer surface. To get better insight in the sliding mechanisms, however, a close evaluation of wear debris particles can provide additional information. Due to the joint action of repeated shear and high temperature, the wear debris particles undergo physical and chemical reactions since its generation. As a result, the properties of those small particles would not be identical to those of the bulk material and are characteristic for the wear process. The transitions between glass and rubbery phase occur at specific temperatures and crystallisation during sliding affects the melting behaviour. Also degradation mechanisms as melting, oxidation and pyrolysis take place and further control the sliding stability, possibly leading to severe wear. Thermo-analytical analysis methods common to polymer science attracted the attention of only few researchers for better understanding of the changes in polymer structure under sliding (e.g. Sharf and Singer [2]). Presently, debris of thermoplastic polyimide (melting temperature Tm = 385°C) and sintered polyimide (no melting temperature) after sliding at 60 to 260°C is evaluated for demonstrating that transitions in sliding are explained by chemical reactions below the melting temperature.
2 Friction and wear testing Sintered polyimide (SP) and thermoplastic polyimide (TP) cylinders were slid in a line contact against high-alloy steel counterfaces (DIN 1.2738) under 50 N normal load and 0.3 m/s sliding velocity on a universal reciprocating Plint TE 77 tribotester. The temperature of the steel counterface was controlled at 60 to 260°C. An average coefficient of friction (µ = Ff/Fn with Ff the horizontal friction force and Fn the normal load) after different sliding distances and the wear rates at the end of test (determined from weight loss) are shown in Figure 1 and Figure 2. For sintered polyimides, there are two sliding regimes with high friction at 60 to 180°C and low friction at 180 to 260°C. The wear rates are minimum at 140°C and stabilise at higher temperature. For thermoplastic polyimides, there is a regime with increasing friction at 100 to 120°C, a regime with decreasing friction at 120 to 180°C and a regime with overload at higher temperature due to melting. The transitions in friction coincide with transitions in wear behaviour. Besides the mentioned bulk temperature, also the maximum polymer surface temperature T* is calculated from the frictional heat input.
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(a)
211
0.7
T* = 198°C Coefficient of friction
0.6 0.5 0.4 0.3 0.2 0.1
partial imidisation
hydrolysis
0 0
50
100
150
200
250
300
Bulktem perature (°C) Bulk temperature (°C)
0.9
(b) Coefficient of friction
0.8
hydrolysis
0.7
T* = 180°C
0.6
melting
0.5 0.4 0.3
T* = 200°C partial imidisation
0.2 0.1 0 0
50
100
150
200
250
300
Bulk (°C) Bulktemperature tem perature (°C)
Figure 1: Overview of friction as a function of bulk temperature for (a) SP, and (b) TP, after 30 m (x), 100 m (Ƒ) and 15000 m or end-of-test (Ŷ). 200
160 140 120
Wear rate (10
-4
mm 3/m)
180
100 80 60 40 20 0 0
50
100
150
200
250
300
Bulk tem temperature Bulk perature (°C)
Figure 2: Overview of wear rates as a function of bulk temperature for SP (Ɣ) and TP (ż). WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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3
Thermo-analytical analysis of sintered wear debris
From literature (e.g. Tewari and Bijwe [3]), the colour of thermoplastic polyimide wear debris varied with increasing temperature and became very dark near wear peaks, suggesting that thermal decomposition was the main degradation mechanism. Comparing the maximum polymer surface temperatures T* and degradation region of 500 to 700°C for sintered polyimide reveals, however, that transitions are not caused by thermal degradation but rather by chemical and/or physical changes. The morphology of sintered SP debris (Figure 3) shows small particles after sliding at 100°C (adhesive wear), conglomerated smooth particles above 180°C (chemical reaction in the interface) and some debris with original sintered structure at 260°C (mechanical overload by brittleness).
100°C
180°C
220°C
260°C
1 mm
Figure 3:
Optical microscopy of sintered polyimide SP wear debris after sliding at high temperature, 50 N, 0.3 m/s.
Thermo-analytical DTA/TGA analysis of wear debris particles (3 mg) is made on a Stanton Redcroft 1500 Thermobalance to identify changes in thermal stability, weight loss and position of the endotherm peak (Figure 4, Table 1). Measurements indicate that debris particles imidised in the interface during the frictional process at T* > 180°C. Two subsequent heating cycles from 23 to WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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450°C and 23 to 590°C at 20°C/min are applied in nitrogen atmosphere, showing less variation compared to original polyimide through homogenisation under heating. 0
unworn -1
Heat flow (µV)
-2 -3
-4 -5
60°C 80°C 100°C
-6
-7
180°C 260°C
-8 0
100
200
300
400
500
600
Temperature (°C)
Figure 4:
Differential thermal analysis (DTA) of SP wear debris after sliding at 60 to 260°C.
No significant thermal degradation of the SP-1 wear debris is noted: the debris weight loss for each sliding temperature is restricted to 2% during the first heating cycle. The weight loss during the second heating cycle is higher and solely concentrated at 450 to 590°C. The endotherm peak temperature or dehydration temperature Thydrat (maximum dehydration intensity) is determined from fitting curves in Figure 4 and it shifts towards higher temperatures for wear debris relatively to the unworn SP. The dehydration reaction of wear products depends on sliding temperature and normal loads: there is a general trend that the dehydration temperature increases for high sliding temperatures while this trend is stronger for high normal loads; at low loads, however, a critical bulk temperature of 180°C must be exceeded to increase the dehydration temperature. The upward shift in dehydration temperature of wear debris indicates chemical changes after sliding, such as imidisation, that cause a delay in dehydration. After formation of polyimide networks modified by sliding, higher temperatures or activation energy is needed for dehydration. Nevertheless, this process remains reversible during subsequent heating-cooling-heating cycles. According to Nagai [4] it is known that polyimides are sensitive to water absorption, but its relation to polyimide structures that are modified by wear was not yet illustrated.
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214 Computational Methods and Experiments in Materials Characterisation III Table 1:
TGA weight loss and DTA endotherm peak position of SP wear debris after sliding at 50 and 200 N, 0.3 m/s at high temperature. 50 N normal load sliding test
Bulk temperature (°C)
Weight loss (%) st
1 heating*
nd
2 heating*
Thydrat (°C)
200 N normal load sliding test Weight loss (%) 1st heating*
2nd heating*
Thydrat (°C)
original
0.72
13
182
0.72
13
182
60°C
0.64
16
204
1.45
32
200
100°C
1.51
18
199
1.82
32
220
180°C
1.59
18
192
0.94
31
222
220°C
1.15
18
197
0.23
30
228
260°C
1.20
18
200
0.20
30
230
* First heating between 23 to 430°C, second heating between 23 to 590°C
4
Thermo-analytical analysis of thermoplastic wear debris
The variations in the structure of thermoplastic polyimide wear debris are more important than for sintered polyimides and can be well-correlated to different transitions in friction and wear. It mainly indicates thermal changes in the amorphous phase through crystallisation and/or cross-linking. The shift in dehydration temperature at 180°C as noted for sintered polyimides is less clear for thermoplastics through interference with complex phase changes. Thermo-analytical DTA measurements of TP debris under similar conditions to SP are presented in Figure 5, during a first heating step (23 to 450°C) and a second heating step (23 to 590°C) at 20°C/min. The corresponding TGA curves are given in Figure 6. The original TP has clear transition temperatures, but they smoothen for wear debris. Chemical reactions progressively change the thermoplastic polyimide structure into the properties of sintered polyimides that lack transitions and/or melting. Both sintering and/or sliding are thus considered as a ‘thermal treatment’ altering the polymer structure. The first heating step in DTA (Figure 5(a)) shows that the glass transition temperature Tg increases or finally disappears when it becomes smoothened over a broad interval from 230 to 280°C. The glass transition temperature Tg is representative for linear molecular structures in an amorphous ordering and shifting or disappearance indicates that the amorphous zone is affected by crosslinking into the formation of a more stable and ordered structure after sliding at high temperature. This evolution is also reflected in the disappearance of a crystallisation peak Tc. The melting exotherm Tm decreases in intensity and its maximum value increases from 387°C (unworn) to 391°C (after sliding at 140 to 180°C) in parallel to the formation of crystalline and strongly cross-linked structures. The recrystallisation peak during cooling disappears because crystal WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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0
(a)
Tc
unworn
Heat flow (µV)
-2 -4
Trex
-6
Tg Tm
-8 -10
< 100°C 120°C
140°C 180°C 220°C 260°C
-12 -14 -16 0
100
200
300
400
500
Temperature (°C) 0
(b)
unworn Tc
-2
Heat flow (µV)
-4
Tg
-6
Tm
-8 -10
< 100°C 180°C 120°C 140°C 220°C 260°C
-12 -14 -16 0
100
200
300
400
500
600
Temperature (°C)
Figure 5:
Differential thermal analysis of TP wear debris after sliding at 60 to 260°C, (a) first DTA heating cycle, (b) second DTA heating cycle.
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216 Computational Methods and Experiments in Materials Characterisation III nucleation lacks in the modified amorphous phase. The conclusion that the amorphous phase modifies under sliding agrees to visual observations that debris particles change from transparent to opaque yellow colour. Debris becomes brittle (and consequently acting more abrasive) after sliding in parallel to the behaviour of sintered polyimides. The second heating step in DTA (Figure 5(b)) shows that the structural modifications of the amorphous phase are partially reversible after a first heating step. The transition zones in tribological properties of TP (Figure 1(b)) are compared to wear debris evaluation and parallel transitions in thermo-analytical analysis are found: x
After sliding at 100 to 120°C (increasing friction), dark coloured particles indicate chemical degradation by hydrolysis. This is confirmed by TGA analysis showing lowest thermal stability for 120°C wear debris.
x
After sliding at 120 to 180°C (decreasing friction), flake-like particles indicate an increase in polyimide strength by imidisation. This is confirmed by TGA analysis showing high thermal stability of those particles. The DTA analysis also indicates crystallisation or cross-linking of debris particles after 120 to 180°C sliding tests, although at lower temperature relatively to unworn TP.
x
After sliding at 220 to 260°C (increasing friction), rolled debris particles indicate melting. As those particles are rapidly removed out of the sliding interface, TGA analysis shows high thermal stability.
5
Thermo-analytical mass spectroscopy (MS) of sintered wear debris
The emission of gaseous species during thermal decomposition of SP wear debris is analysed with a mass spectrometer coupled to DTA/TGA measurements. One single heating step from 23 to 600°C at 20°C/min is applied, using argon carrier stream. It will demonstrate that the instrumentation is sensitive to detect water volatilisation (only 1% weight loss) and confirms that the endothermic reaction at 180°C is surely related to dehydration. Other degradation products are characterised and have lower intensity, which further decreases when the sliding temperature was higher. Some spectra for SP wear debris after sliding at 50 N, 0.3 m/s and 100, 180, 260°C, are given in Figure 7. Spectra represent the volatilisation intensity for a specific emission product as a function of the heating temperature. Each decomposition product is characterised by its atomic mass unit (a.m.u.) and intensities are related to the ion current (A) in the mass detector (scaled to sample weight), which is proportional to the concentration of decomposition product in the carrier stream.
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105
220 to 260°C
1 Residual weight weight (%) Residual (%)
100
2
3
95
140 to < 100°C 180°C 120°C
90 85 80 75 70 0
100
200
300
400
500
600
Temperature (°C) Temperature (°C)
Thermogravimetric (TGA) analysis of TP wear debris after sliding at 60 to 260°C over a heating cycle 1, cooling cycle 2, heating cycle 3.
(a)
-9
6.0 10
-10
-9
5.0 10
-9
4.0 10
-9
3.0 10
-9
2.0 10
-9
1.0 10
Intensity a.m.u. = 18 (water)
5.8 10
-10
5.7 10
-10
5.6 10
-10
5.5 10
-10
5.4 10
-10
5.3 10
Wear debris 100°C
-9
0
5.2 10
0
0.0 10 100
200
300
400
500
600
Temperature Temperature(°C) (°C)
(b)
5.0 10
-11
4.0 10
-11
3.0 10
-11
2.0 10
-11
1.0 10
-11
0.0 10
0
Intensity a.m.u. = 30 (nitrogen
Wear debris 180°C
Wear debris 260°C Wear debris 100°C
0
100
200
300
400
500
600
Tem perature (°C) (°C) Temperature
Figure 7:
Mass spectroscopy for sintered polyimide wear debris.
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Intensity a.m.u. = 16 (oxygen)
Figure 6:
218 Computational Methods and Experiments in Materials Characterisation III Most important decomposition fraction for tribological performance is the production of water (a.m.u. = 18, Figure 7(a)). Water volatilisation occurs at 180 to 200°C heating temperatures as a peak intensity for the debris samples after 100°C sliding or a maximum intensity for debris samples after 180 and 260°C sliding (not shown). Water volatilisation at 200 to 600°C heating temperatures depends on the sliding temperatures, showing: (i) a constant or increasing tendency of water volatilisation for 100°C debris indicating progressive imidisation during heating, and (ii) a decreasing trend for 180 to 260°C wear debris indicating that debris is more inert by imidisation during sliding. The peak in water emission for high temperature wear debris broadens through variations in structure (and molecular weight) after wear. Water volatilisation agrees to the previously noted shift of dehydration temperature Thydrat in DTA thermographs, rising for debris after 180 to 260°C sliding. A second small peak in a.m.u. = 18 intensities for debris after 100°C sliding occurs at 380°C and corresponds to small weight loss. The oxygen intensity (a.m.u. = 16) is plotted over the intensities of water volatilisation in Figure 7(a) and confirms that dehydration or water condensation is responsible for the noted endothermic reaction at 180°C. The nitrogen-monoxide NO fraction (a.m.u. = 30, Figure 7(b)) has similar features to nitrogen N fraction (a.m.u. = 14). It is firstly stressed that the concentration of released nitrogen is a factor 10-2 to 10-3 smaller than water concentrations. The decomposition of polyimide wear debris into nitrogen monoxide is postponed and finally disappears with increasing sliding temperatures through formation of a strong imide structure after sliding.
6
Conclusions
For sintered polyimides, hydrolysis and imidisation reveals from thermoanalytical analysis of wear debris and explains transitions in friction and wear. For thermoplastic polyimides, crystallisation and melting effects are most important.
References [1] Jacko M.G., Tsang P.H.S., Rhee S.K., Wear debris compaction and friction film formation of polymer composites, Wear, 133, pp. 23-38, 1989. [2] Sharf T.W., Singer I.L., Monitoring transfer films and friction instabilities with in situ Raman tribometry, Tribology Letters, 14, pp. 3-8, 2003. [3] Tewari U.S., Bijwe J., Tribological behaviour of polyimides. Polyimides, ed. M. Dekker, Marcel Dekker: New York, pp. 533-583, 1996. [4] Nagai N., Hironaka T., Study of interaction between polyimide and Cu under high humidity condition, Applied Surface Science, 171, pp. 101-105, 2001.
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Computational Methods and Experiments in Materials Characterisation III
219
Analysis of adiabatic heating in high strain rate torsion tests by an iterative method: application to an ultrahigh carbon steel J. Castellanos1, I. Rieiro1, M. Carsí2, J. Muñoz1 & O. A. Ruano2 1
Department of Mathematics, University of Castilla - La Mancha, Spain Department of Physical Metallurgy, National Center for Metallurgical Research (C.E.N.I.M.), Spain
2
Abstract An iterative algorithm has been developed to establish the adiabatic heating correction of flow curves for torsion tests of an ultrahigh carbon steel containing 1.3% C. High temperatures (1223 to 1473 K) and high strain rates (2, 5, 10 and 26 s-1) were used. The curves are corrected in a finite and discrete set of strain data by means of parametric derivatives and integration on the initial curve without correction. The process is repeated until the termination tolerance for the stress is less than 10-2 MPa. Usually, four iterations are needed to reach this tolerance. The corrections are bounded by the maximum of mechanical energy available to be converted into heat. The corrections are carried out until a true strain H 4 in order to avoid the effects of flow localization in the material. Keywords: adiabatic heating, torsion test, modelling, simulation, Garofalo equation, hot working.
1
Introduction
Torsion tests at high temperatures and strain rates of materials usually show a strong increment of temperature during the test above the programmed temperature that is attributed to adiabatic heating [1]. The temperature correction due to adiabatic heating has been discussed in various works [1–6]. The following expression is usually considered: 'Ti (H )
K. A U C
H
V H dH ³ H max
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(1)
220 Computational Methods and Experiments in Materials Characterisation III where T is the test temperature, C is the specific heat capacity, U is the density, K and A are efficiency coefficients of the energetic conversions and V (H ) is the stress-strain relation. Some authors assume a variable energy performance in eqn (1) [2] or a constant one [6]. Other authors use the relation V (H ) without considering the intrinsic error due to the adiabatic heating itself [3]. In general, it is not considered that determination of the term V (H ) implies derivatives at constant temperature, which is not true under the effect of adiabatic heating. These derivatives appear in the calculation of the strain rate sensitivity and the strain hardening coefficients. In addition, constant values for U and C are used in the entire working range. In this work, we consider the following expression for determining the true value of the corrected relation V c , in contrast to the experimental value V wc :
V ic (H ) V iwc H
. wV iwc (H , H , T ) 'Ti (H ) '[ wT H ,H
(2)
where '[ is the error associated to the experimental value of the stress that should be bounded to avoid wrong answers. The goal of this work is to design a modular and iterative algorithmic method that guarantees the convergence of the experimental function V iwc (H ) to the nominal function V ic (H ) . This method is based in eqns (1) and (2). The validity ranges of the algorithms are adjusted taken into account physical fundaments on flow localization [3,5] and bounds of the performance for the conversion on mechanical energy into heat.
2
Material and experimental procedure
The UHC-1.3%C steel studied in this investigation has the following composition: 1.3% C, 0.5% Mn, 0.6% Si, 0.18% Cr and balance Fe [1]. The manganese was added to neutralize the deleterious effects of sulphur and phosphorus. The steel was obtained at Sidenor Industry as a cast of 8 litres by means of an induction furnace. The as-cast ingot was initially soaked at 1050ºC and forged into a bar of 60 mm x 55 mm cross section. Simulation of the forming process of forged parts was carried out by means of torsion tests. An induction furnace heats the test sample and the temperature is continuously measured by means of a two-color pyrometer. A silica tube with argon atmosphere ensures protection against oxidation. A helium atmosphere is used to obtain, after testing, a cooling rate of 325 K/s. The torsion samples have an effective gage length of 17 mm and a radius of 3 mm. The density and specific heat are 7800 kg·m-3 and 670 J·kg-1·K-1, respectively. Strain rates in the range 2 to 26 s–1 were used. The temperature WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
Computational Methods and Experiments in Materials Characterisation III
221
range was 900 to 1200 ºC. The samples were deformed in a SETARAM torsion machine at CENIM (National Center for Metallurgical Research) in Madrid, Spain.
3 Theoretical approach Two main processes limit the conversion of mechanical energy into heat in an adiabatic framework: changes in the internal energy of the material and flow localization. Both processes are related to the start of catastrophic failure [2–4]. A differential expression for the first law of thermodynamics V dH U c dT du mst where du mst is the variation of the microstructural internal energy can be considered. The plastic work carried out by the material is transformed into heat that is used to increase the internal energy of the material. Some authors assume du mst 0 [3]. Other authors consider du mst z 0 leading to the general expression [2]: dT
V dH § 1 du mst · ¨1 ¸ U c © V dH ¹
V dH K H , H, T U c
(3)
where K H , H, T 1 (1 V ) >du mst dH @ is the performance of the conversion and it is variable. A constant value for K of 0,90 or 0,95 may be taken but an iterative procedure would be necessary to eliminate the effect of this approximation. The approach of Prasad et al. [4] is convenient to estimate the upper limit bound of the increase of temperatures due to adiabatic heating. A simple constitutive equation for the energy dissipation is the following: H
V H
³
V
V dH H dV
0
³
GJ
(4)
0
where G is the dissipator content and J is the dissipator co-content. Part of the power dissipated by the plastic flow, G, can be converted into heat. The quantity J is related to the processes of form change. The limit for G is Gmax (V max Hmax ) 2 . The following expression can be deduced from eqn (4): K G max (5) 'Tmax U C V that represents the limit for the adiabatic 'T in a volume V. The increment in temperature can be expressed as [3]: Hp'
'T
K V dH U c
³
H0
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222 Computational Methods and Experiments in Materials Characterisation III where K is constant and H p ' is the deformation limit where the plastic instability starts [3]. Therefore, a critical deformation can be considered above which it is not possible to apply this kind of corrections [5]. Values of dT dH 165 K from eqn (6) are obtained for the UHC-1.3%C steel. Assuming the analysis of Armstrong et al. [3] and considering the stressstrain relation V K1 .H T , together with the definition of the stress exponent, n, in the Garofalo equation and the definition of constant strain rate tests, H p H p t , the condition for plastic instability gives the following equation: ª dT º « » «¬ d H p »¼H p '
1· § ¨ T ¸ (H p ' E ) n¹ ©
(7)
Under stability conditions, dV ! 0 . The instability starts at dV be expressed as [7, 8]: dV
0 , that can
§ wV · § wV · § wV · dH ¨ dH ¨ dT ¨ ¸ ¸ ¸ w w H H © ¹ H , H © ¹ H , H © wT ¹ H , H
0
(8)
Under adiabatic heating conditions, and assuming H constant, by means of Q § · ¨ ¸ R the Garofalo equation ¨ H A.e T sinh(D V ) n ¸ it is obtained [7] that ¨ ¸ © ¹
wV
wH H,T
T V H
and
wV
wT H ,H
V Q R T 2 .
Taken
these
expressions into the plastic instability condition, an expression for the flow stress at which the instability starts, V in , can be obtained:
V in
T R T 2 U c K Q H
(9)
This expression will be applied later to the UHC-1.3%C steel.
4
Basic methodology
The following assumptions are used in the algorithm developed in this work: 1) adiabatic conditions in the deformation process, 2) U and C do not vary with T, 3) K and A are constant with strain, and 4) adiabatic heating has an important effect from the peak stress of the curve V (H ) , to a value H f . For a given test at constant H j and Ts , the initial temperature, and for a given value of H , the uncorrected stress, V 0 wc (experimental stress), can be expressed as a function of the corrected stress, V 0c , as: WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
Computational Methods and Experiments in Materials Characterisation III
V 0 wc (T ) V 0c (T 'T )
223 (10)
Applying Taylor expansion of the function V 0c in eqn (10) about the point T:
V 0 c (T ) V 0 wc (T )
wV 0 wc (T ) 'T wT
(11)
where it is assumed that wV 0wc wT | wV 0c wT . On the other hand, the temperature increment for each measured strain H i , for a given test at constant H j , can be expressed as: 'T0 H i
KA U C H
Hi
0
³H
V 0wc H , H j , T d H
(12)
max
Substituting eqn (12) in eqn (11):
V H i , H j , T V 0wc H i , H j , T c 0
wV 0wc H i , H j , T K A H i ³ V 0wc H i , H j , T d H (13) wT U c H 0 H max
A single time application of these equations would result in a value of V H , H, T that is not accurate. This is due, as mentioned in the introduction, to c 0
the associated error in the determination of V 0 wc and consequently in the integral part of eqn (13). Furthermore, calculation of wV 0wc H , H, T wT in eqn (13) is also not accurate since the function V 0 wc H is a warped curve in the space
^H , V , T ` . To minimize the inaccuracies of the calculation carried out in eqn (13), an iterative algorithm based in eqns (11) and (12) has been developed using as initial value the stress V 0c H , H, T . It is a modular algorithm in three steps. In the first step, the value of 'Tk H i in the iteration k (from k=1 to the number of iterations) is calculated according to the following expression: Hi
'Tk (H i )
KA V wc V kc1 d H U C H ³ k 1
(14)
max
where V kwc1 , is the uncorrected stress in the iteration k-1, and V kc1 is the corrected stress in k-1. The integration interval is divided in sufficiently enough small parts. In this work, we have worked step by step with all the output data WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
224 Computational Methods and Experiments in Materials Characterisation III given by the machine. Therefore, a trapezoidal rule is used in order to compute the numerical integration in eqn (14). In the second step, the partial derivative with respect to T of the uncorrected stress, wV kwc H i , H j , T wT in the iteration k, is calculated by means of the H ,H
expression: wV kwc Ts , H i wT
#
V kwc Ts 1 , H i h V kwc Ts , H i h Ts 1 Ts
(15)
where s 1 refers to the test conducted at the same strain rate but at a temperature Tk+1, belonging to the temperature set ^Ts `s 1, N , that is next in the ascendent sequence. This approximation is good enough since the discretization intervals are small. Finally, the value of the corrected stress in the iteration k is given as:
V kc H i , H j , T V kwc H i , H j , T
wV kwc H i , H j , T K A 'Tk (H i ) d H wT Uc
(16)
The criterion adopted for stopping the algorithm, i.e. the termination tolerance, is 'V d 10 2 MPa for a given control strain. By means of this procedure, the final measured temperature is reached at a given iteration for a value H but the correction is used only up to H f , a value at which the flow localization is not considered important to distort our correction.
5
Results and conclusions
5.1 Analytical basis The results obtained in section 3 for the bound limits are applied in our model to establish the adiabatic correction of the UHC-1.3%C steel. For this steel, at H 10 s 1 and T=1323 K, the peak stress is V max 100 MPa and, according to eqn (5), 'Tmax 172 K . For H 2 s 1 and T=1323 K, 'Tmax 24 K . This gives an idea of the upper bounds of the uncorrected values. Using the data of Castellanos et al. for this steel [9], the relation V (T ) K 2 e 0,0037T is obtained. The values of the Garofalo equation are: Q=274,3 kJ/mol and n=4,66. A value T | 0.2 is obtained for an integration on all deformation paths. For comparison, it was obtained for H 1,5 , T | 0.11
and dT (H 'p ) d H p dT (H 'p ) dH p
28 H p ' K
and for H
next to the peak, T | 0 and
58 H p ' K .
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Computational Methods and Experiments in Materials Characterisation III
225
Table 1 shows the limit strains, H 'p , for the start of plastic instability or flow localization for the UHC-1.3%C steel. The values were calculated by means of eqn (9) using T
0,90 . The values H 'p are determined in the
0.2 and K
point where the experimental curve V (H ) cross the curve V in H . The table shows that the plastic instability is delayed at high temperatures and low strain rates. It is worth noting that the local instability develops progressively with plastic strain. At H =5 a clear change of behavior of the flow curves is observed characterized by oscillations of the derivates of the stress with respect to the strain. A value of H f 4 was chosen because up to this value the corrections were meaningful. Table 1:
Limit strains, H 'p , for the start of plastic instability for the UHC1.3%C steel as a function of strain rate and temperature.
T(K) 1223 1273 1323 1373 1423 1473
from eqn (9)
V in V in V in V in V in V in
H
2 s 1
H
5 s 1
H 10 s 1
H
26 s 1
52.7 / H
0.45
---
0.3
0.3
57.1 / H
0.6
0.5
0.45
0.4
61.7 / H
0.8
0.65
0.55
0.45
66.4 / H
1.05
0.8
0.7
0.5
71.3 / H
1.5
1.2
0.9
0.7
76.4 / H
1.9
1.5
1.1
0.9
5.2 Correction of flow curves for the UHC-1.3%C steel The flow curves of the UHC-1.3%C steel have been modified to consider the adiabatic heating. The curves were conducted at H 2, 5, 10, and 26 s-1 and T from 1223 to 1473 K, with a variation of 50 K. A maximum of four iterations were conducted for the attainment of the final measured temperatures for H >6,8@ although the corrections were carried out up to H f 4. Figure 1 shows true stress vs. true strain curves at various strain rates and temperatures for the UHC-1.3%C steel. The solid lines represent the correction for adiabatic heating according to eqn (12). The corrections agree with those carried out by other authors [10, 11]. However, somewhat different results were obtained when compared with other investigations where unreliable approximations were conducted [12, 13]. Figure 2 shows the evolution of 'T , according to eqn (11), with strain for H 26 s 1 at various temperatures. All the temperature increments are inside the bounds established for the maximum increments. The convergence of the iterative algorithm was reached at a maximum of four iterations. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
226 Computational Methods and Experiments in Materials Characterisation III
Figure 1:
Figure 2:
Flow curves for the UHC-1.3%C steel. Solid lines are corrected curves for adiabatic heating and dotted lines are uncorrected curves.
Evolution of 'T with strain for several T0 ' s at a H =26 s-1.
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Computational Methods and Experiments in Materials Characterisation III
Table 2:
H
Values of 'V at H (a) 2 s 1
H 5 s 1
1 (a) and H
3 (b) for the corrected tests.
1223 K 5.38
1273 K 2.06
1323 K 1.91
1373 K 1.85
1423 K 0.9
1473 K 0.9
---
3.68
2.69
1.39
1.15
1.02
1
5.44
2.17
2.62
2.34
0.86
0.99
1
(b) H 2 s 1
6.54 1223 K 12.16
2.76 1273 K 6.21
2.49 1323 K 5.90
2.37 1373 K 5.70
1.41 1423 K 3.32
1.28 1473 K 2.79
H 5 s 1
H 10 s H
26 s
H 10 s H
---
8.92
9.25
6.08
3.08
2.67
1
14.11
8.46
6.32
7.57
3.48
3.29
1
16.81
9.4
7.73
7.78
7.32
6.23
26 s
227
Table 2 shows a summary of all the results obtained in this work. The accumulated values of 'V are given for each pair ^H, T ` at H 1 and 3. Values at H 5,6 are higher but were not considered due to flow localization. It can be concluded that the method, and the implemented algorithm, that we have developed in this work is reliable and convergent. The corrected stressstrain curves are efficient and reliable and take all the experimental data set without the need of average approximations. In addition, the method provides the detailed corrections at the discretization level given by the machine. The main conclusions of this work are: 1. A new iterative approach for the adiabatic heating correction for torsion tests has been established. It is a natural generalization of a previous approach where the correction was carried out in a single run. 2. The new approach brings an improvement in the precision of the corrected flow curves. The relative errors associated to determination of the experimental stresses are minimized. 3. The temperature increments obtained for the UHC-1.3%C steel are inside the bounds established for the maximum increments due to adiabatic heating.
Acknowledgement The work was carried out through the Project PBC-05-010-1 from JCCM (Castilla-La Mancha, Spain).
References [1]
Fernández-Vicente, A., Carsí, M., Peñalba, F., Carreño, F. & Ruano, O.A., Deformation behavior during hot torsion of and ultrahigh carbon steel containing 1.3 wt.% C. Zeitschrift für Metallkunde, 94(8), pp. 922929, 2003. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
228 Computational Methods and Experiments in Materials Characterisation III [2] [3] [4]
[5] [6] [7] [8] [9]
[10] [11] [12] [13]
Pantleon, W., Francke, D. & Klimanek, P., Modelling adiabatic heating during high-speed deformation. Computational Materials Science, 7, pp. 75-81, 1996. Armstrong, R.W., Coffey, C.S. & Elban, W.L., Adiabatic heating at a dislocation pile-up avalanche. Acta Metallurgica, 30, pp. 2111-2116, 1982. Prasad, Y.V.R.K., Gegel, H.L., Doraivelu, S.M., Malas, J.C., Morgan, J.T., Lark, K.A. & Baker, D. R., Modelling of dynamic materials behavior in hot deformation: Forging of Ti-6242. Metallurgical Transactions A, 15A, pp. 1883-1892, 1984. Lindholm, U.S., Mechanical Properties at High Rates of Strain. Conference Series nº 21, ed. J. Harding, Institute of Physics: London and Bristol, pp. 3-21, 1974. Bhattacharyya, A., Rittel, D. & Ravichandran, G., Strain rate effect on the evolution of deformation texture for D -Fe, Metallurgical and Materials Transactions A, 37(A), pp. 1137-1145, 2006 Semiatin, S.L., Staker, M.R., & Jonas, J.J., Plastic instability and flow localization in shear at high rates of deformation. Acta Metallurgica, 32 (9), pp. 1347-1354, 1984. Staker, M.R., The relation between adiabatic shear instability strain and material properties. Acta Metallurgica, 29, pp. 683-689, 1981 Castellanos, J., Rieiro, I., Carsí, M, Muñoz, J., Ruano, O.A., Analysis of several methods for the data conversion and fitting of the Garofalo equation applied to an ultrahigh carbon steel. Journal of Achievements in Materials and Manufacturing Engineering, 18(1-2), pp. 447-454, 2006. Wei-Guo, G., Nemat-Nasser, S., Flow stress of Nitronic-50 stainless steel over a wide range of strain rates and temperatures. Mechanics of Materials, 38, pp. 1090-1103, 2006. Zhou, M., Clode, M.P., Thermal analysis of the torsion test under hotworking conditions. Computational Materials Science, 9, pp. 411-419, 1998. Holzer, A.J. & Wright, P.K., Dynamic plasticity: a comparison between results from mechanical testing and machining. Materials Science and Engineering, 51, pp. 81- 92, 1981. Venugopal, P., Venugopal, S. & Seetharaman, V., Some aspects of the dependence of the flow curve of commercially pure titanium on the forming temperature and the strain-rate. Journal of Materials Processing Technology, 21, pp. 201-217, 1990.
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Section 7 Experimental methods – mechanical characterisation and testing
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231
Collapse of FRP/syntactic foam sandwich panels M. Perfumo1, C. M. Rizzo2 & M. P. Salio2 1
Cantieri SANLORENZO S.p.a., La Spezia, Italy Department of Naval Architecture and Marine Technologies (DINAV), Genoa University, Italy
2
Abstract In the framework of a wider research project, large scale testing of composite sandwich panels has been carried out at the DINAV shipbuilding laboratory. The skins of the sandwich are made of fibre glass epoxy prepreg and the core consists of a syntactic epoxy foam. Strain gages have been bonded on the outer skins and also located in between the core and the skins. The captioned material is currently used for small components of naval ships (e.g. shields, stanchions, etc.) either in single skin laminates or sandwiches: the final goal of the project is to study its applicability in building pleasure craft hulls, taking advantage of its high strength. The large scale tests have been completed by usual testing on small scale specimens, according to well-known international standards and analytical and finite elements (FE) numerical models have been calibrated with the experimental data. Different options of FE codes have been investigated in order to catch their capabilities and approximations in modelling the composite material and their damage up to collapse. Some advice on the behaviour of quite large sandwich panels is reported, highlighting the effects of the size of the structure on the material mechanical properties. Keywords: FRP, prepreg, syntactic epoxy foam, composite sandwich, laminates, mechanical tests, large scale tests, numerical simulation (FEM).
1
Introduction
Composite sandwiches are commonly adopted in marine and aeronautical engineering for structures or structural elements requiring high stiffness and strength, mainly to flexural loads, together with low specific weight. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/MC070231
232 Computational Methods and Experiments in Materials Characterisation III This paper presents the main results of an experimental and numerical study on the mechanical behaviour of a type of sandwich currently used for small components of naval ships (e.g. shields, stanchions, etc.). The external facings of the sandwich (skins) are prepreg glass-fibre/epoxymatrix composites whereas the central part of the sandwich (core) is a syntactic foam consisting of hollow glass microspheres embedded in an epoxy resin matrix. The final goal of the project is to study the applicability of such material in building entire hulls of pleasure craft, taking advantage of its high strength. It is remarked that prepregs have very high mechanical properties, also against fatigue and shock and syntactic foam is a core fabric with superior physical properties, (Greene [1]). Another significant advantage concerns prepreg low environmental impact, with no styrene emission. In fact, more and more reducing VOC (Volatile Organic Content) requirements force builders to look for alternative construction methods; it is therefore expected that demand will drive more prepreg manufacturers towards the development of products specifically suited for the marine industry. Other distinct advantages are ease of handling and excellent resistance against water, seawater, oil and hydrocarbons, (Greene [1]). Main advantages of the syntactic foam adopted are lightweight, high resistance against stability loss due to compression, quite high strength against impact loads. An attractive option for structural optimization seemed to limit the stiffening of the shell plates using sandwich panels and gradually varying the lamination sequences of the skins and of the core thickness in the different hull areas, according to loads demands. Design of such structures needs a reliable and quite precise numerical model of the whole hull shell. Therefore, analytical and numerical finite elements (FE) models have been studied as well. The mechanical characterization of this highly heterogeneous material (or rather, structural element) has been carried out at the Department of Naval Architecture and Marine Technologies (DINAV), Genoa University, with the collaboration of Centro Tecnologico Sperimentale S.r.l., La Spezia for small scale testing and Nuova Connavi S.r.l. for experimental data about the syntactic foam, through the following sequence of steps: (a) experimental testing on small specimens of the material adopted for the skins; (b) collecting data about the syntactic foam material adopted for the core; (c) experimental testing of the sandwich panels, both on large and small scale; (d) development of analytical and numerical FE models calibrated with the experimental data, firstly simulating the small scale tests, then the large scale ones. The paper is organised as follows. In Section 2, the sandwich under study is fully described. Section 3 is devoted to the construction of the numerical model with reference to the theoretical formulations used and the judgement of their applicability. The numerical simulations of tests carried out on small scale specimens and the description of large scale tests together with relevant results are presented respectively in Section 4 and Section 5. Lessons learned are briefly resumed in Section 6. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
Computational Methods and Experiments in Materials Characterisation III
2
233
The sandwich under study
The FRP/syntactic-foam sandwich under study was manufactured by Nuova Connavi s.r.l. (Italy). The sandwich structure is represented in Figure 1. The materials adopted for the skins are called EPREG UD 52TM and EPREG DIAG 43TM and are prepregs obtained by impregnation with an epoxy resin system of an E-glass tissue. EPREG UD 52TM is a unidirectional composite with 97% of fibres oriented longitudinally and 3% transversally whereas EPREG DIAG 43TM is bidirectional and has ±45° fibres.
Skins: prepreg composite
Figure 1:
Core: syntactic foam
The sandwich under study.
The syntactic foam core, whose trademark is EFOAMTM, is assembled with the same epoxy matrix as EPREGTM which embeds hollow air-filled glass microspheres, mixing resin and hardener under vacuum and by adding microspheres repeatedly until full homogenization. Bubbles have an average diameter of 70 mm and an average wall thickness of 0.58 mm. The density of the resulting syntactic foam averages 0.53 g/cm3 (see [2] for all details).
3
Material modelling
To analyze a sandwich structure, many challenging issues need to be addressed such as the complexity of the mechanical interactions between material constituents, particularly when applied loads produce local damage and sequential failure. The mechanisms of failure in FRP sandwich structures are entirely different from that of conventional steel structures. Static/dynamic failure involves matrix cracking, fibre buckling and rupture, and layer delamination in an interrelated manner. The complexity of the mechanical response of FRP sandwich structures presents great difficulties in predicting reliably composite’s performance, nevertheless, finite element method (FEM) is becoming a very popular and powerful tool for simulating an engineering system. After a preliminary study of a few commercial finite element codes, the software ANSYS® has been adopted for all the numerical simulations performed. This code allows to model composite materials with specialized elements called layered elements. Several formulations are available: linear and nonlinear, shell and solid, with different capabilities. SHELL91 and SHELL99 in particular have been used because fitting better the material under study. SHELL 91 is an WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
234 Computational Methods and Experiments in Materials Characterisation III 8-node, nonlinear, layered element with 6 degrees of freedom at each node that supports plasticity and large-strain whereas SHELL 99 is an 8-node, linear, layered element, without the nonlinear capabilities of SHELL91. Each of these shell elements is shear deformable and allows failure criterion calculations, [3]. The first input required within the software is the definition of the layered configuration, obtained by specifying, layer-by-layer, ply thickness, ply orientation and material properties. To this aim, being the sandwich skins assumed made of an orthotropic material, the widely known micromechanics formulations have been applied, by superimposition of elementary layers. These equivalent layers have unidirectional fibres and are characterized by the same content of reinforcement as a given layer, whatever the type of reinforcement used. In order to determine the elastic characteristics of that equivalent layer, classical rule-of-mixtures equations for longitudinal moduli and modified equations for transverse and shear moduli have been then used, (Tsai and Hahn [4]). It is remarked that similar formulations are adopted within the HSC Code, [5], whereas semiempiric formulations are adopted by Class Society, estimating average properties but not accounting for fiber orientation, lay-up method (e.g. manual, prepreg or infusion), stacking sequence, etc. The material used for the sandwich core has been considered as homogeneous and isotropic. Failure analysis has been carried out as well, using the capabilities of the software adopted. Within ANSYS®, possible failure of the material can be evaluated by up to six different criteria, of which three are predefined (max strain, max stress and Tsai-Wu). In this study, two failure criteria were examined, max stress and Tsai-Wu, but, since a complete analysis of the sequential collapse is quite difficult to be implemented in the ANSYS® environment, this tool has been used to determine only the first ply failure, leaving to further developments of the research the automatization of the procedure for the progressive failure. Concerning the sandwich core, Drucker Prager criterion has been considered, supported by the code as well. The elastic properties for the materials under study are presented in Table 1: as regards the sandwich skins they are calculated as previously mentioned whereas the core characteristics have been provided by the manufacturer. Table 1:
EPREG UD 52TM EPREG DIAG 43TM EFOAMTM
Elastic properties for the materials under study. Ex (MPa) 29966
Ey (MPa) 12584
Ez (MPa) 10833
Gxy=Gyz=Gxz (MPa) 4282
Qxy
Qyz
Qxz
0.207
0.208
0.127
27125
10613
8783
3413
0.212
0.204
0.121
1512
582
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Small scale testing
The mechanical behaviour of the sandwich and its components (skins and core) has been investigated through the following series of tests on specimens directly prepared by the manufacturer: tension, compression, three point bending tests and short beam tests as regards the skins, [6], three point and four point bending tests, uniaxial compression, uniaxial tension, constrained compressive tests on the core, (Cecchinelli [2]), and, concerning the specimens taken from the sandwich panels, three and four point bending tests, [6]. For each group of tests, specimen shapes and sizes have been chosen according to the relevant standards. FE models of all tests have been developed as mentioned before and nominal dimensions have been considered. A few significant results are presented as an example in Table 2, Figure 2 and Figure 3, comparing the averaged experimental data for the three point bending tests and short beam tests on EPREG UD 52TM. Satisfactory agreement between tests and calculations was found for skins laminates while larger difference exists for the sandwich specimens. Such discrepancies may be explained taking into account that small single skin specimens were specifically made for tests while large sandwich panels, from which small specimens were taken, were built according to the usual shipyard practice. Table 2:
Weft Warp
Weft Warp
Figure 2:
Comparison between averaged experimental data and FEM results for the three point bending tests (TPB) and short beam tests (SBT). fmax exp (mm) 8.54 2.12
Vmax exp (MPa) 638 54
Wmax exp (MPa) 47.77 8.15
TPB - EPREG UD 52TM fmax FEM Vmax FEM (mm) (MPa) 8.85 656 2.82 54 SBT - EPREG UD 52TM Wmax FEM (MPa) 59.00 11.00
Error fmax exp/FEM 4% 25%
Error Vmax exp/FEM 3% 0%
Error Wmax exp/FEM 19% 26%
Example of a FE model with the corresponding experimental test.
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236 Computational Methods and Experiments in Materials Characterisation III Tau XZ
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Examples of distributions of stresses in the layers from FE analyses (interlaminar shear and shear of short beam test, tension and interlaminar shear of three points bending).
Large scale tests
Large scale tests have been carried out at DINAV ship structures laboratory on two 2000x1000 mm sandwich panels supplied by Nuova Connavi S.r.l. The three point bending test has been deemed the most significant for the mechanical characterization and for comparisons with small scale tests. 5.1 Panel 1 Panel 1 has a lower skin (in tension) with a 5-ply [0/90/±452/0] staking sequence and a 4-ply [0/90/±452] staking sequence upper skin (in compression); each layer has a nominal thickness of 0.4 mm, whereas the core is 50 mm thick. Strain gages have been bonded on outer skins following the map of Figure 4: the three mid-span channels are rosettes, placed to evaluate the on-plane shear stress as well as the longitudinal stress induced by bending moment. This layout has been repeated also in between the lower skin and the core to evaluate interlaminar shear stresses. Signals of gages have been recorded using a routine developed on purpose in Labview® and analysed by means of some Matlab® routines: some examples are shown in the following Figure 6 to Figure 8. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
Computational Methods and Experiments in Materials Characterisation III
Figure 4:
237
Strain gages layout bonded on Panel 1.
FPF
Figure 5:
Comparison of Load-Displacement experimental data of panel 1 with FEM calculation of First Ply Failure (FPF).
Panel collapsed at 52 kN with 130 mm displacement and FPF (First Ply Failure) has been reached at 25 kN with 45 mm displacement. Figure 6 shows the behaviour of some significant gages and FPF may be noted. Such curves highlight that some areas of panel collapsed at 25 kN and others maintained residual strength up to the final collapse. Shear stresses have been evaluated using the rosettes signals (Figure 7). Moreover, three constantan wires (Ch.0, Ch.1, Ch.2) have been inserted between the lower skin and the core to obtain the bending average deformation. It is worth to point out that all wires, other than Ch.2 whose signals went lost due to wiring connection problems, behave in the same way: they all failed to provide electrical signals only when the panel collapsed, reaching a strain of nearly 5000 PHFPF may be noted when the slope of plots in Figure 8 suddenly changes.
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238 Computational Methods and Experiments in Materials Characterisation III
Figure 6:
Figure 7:
Examples of plots representing gages signals vs. load.
Load vs. shear stress calculated by internal east and west strain gages (IntW & IntE) and by external center strain gage (ExtC).
Figure 8:
Constantan wires signals of panel 1.
Figure 9:
Large scale test and panel collapse.
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5.2 Panel 2 Panel 2 has both skins with 8-ply [0/90/±452]2 staking sequence; each layer has a nominal thickness of 0.4 mm, whereas the core is 30 mm thick. Strain gages have been bonded according to the map of Figure 4. Constantan wires have been also placed and recorded data are shown in Figure 11. The final collapse occurred just after the FPF, probably because of the symmetry of the skins and of the lower thickness of core with respect to panel 1. Strain gages provided signals similar to the ones of panel 1, not reported here for sake of shortness. FEM calculation estimates exactly the collapse load of panel 2 (60 kN) but overvalued the displacement (191 mm instead of 180 mm).
FPF
Figure 10:
Comparison of Load-Displacement experimental data of panel 2 with FEM calculation of First Ply Failure (FPF).
Figure 11:
Constantan wires signals of panel 2.
6 Lessons learned The study presented in this paper highlights that material characterization needs to be carried out looking towards the overall size and behaviour of the structure. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
240 Computational Methods and Experiments in Materials Characterisation III While failure modes of small scale tests are clearly identifiable, the failure of the large scale specimens follows a progressive collapse where different areas of the sandwich are affected by different failure modes. The interaction of different failure modes might not be simply superimposed. FE models are in substantial agreement with the small scale tests while larger differences have been found with the large scale ones. Further to the manufacturing defects, whose density may be higher in larger structures, interaction of failure modes may lead to lower material strength. A larger number and size of defects have been noted in the 50 mm thick core with respect to the 30 mm one because of the different manufacturing procedures. This impacted onto the strength of the panels. The gages and the constantan wires inserted between the lower skin and the core allows estimating the interlaminar shear stresses and shows that bonding of skins and core is better than in traditional sandwich used for pleasure craft, probably because of the same origin of the constituent materials. Finally, it is believed that constantan wires can be used to realize a cheap and very light system for structural monitoring of very large areas of FRP hulls. Constantan wires would be weaved in glass reinforcement fabric as weft or warp. Of course, prototypes cited in this paper need to be further developed and tested.
Acknowledgements The present paper originated from the research project no. 23 founded by the European Union, in the framework of PRAI-Liguria (Programma Regionale di Azioni Innovative). At that time, the author M.P. was an employee of DINAV. The authors wish to acknowledge the invaluable support of Professor Giovanni Carrera.
References [1] [2] [3] [4] [5] [6]
Greene, E., Marine Composites, Eric Greene Associates, Inc: Annapolis, p. 73, pp. 272-273, 1999. Cecchinelli, A., Mechanical characterization of an epoxy syntactic foam, MSc thesis, Pisa University, 2005. ANSYS® Release 8.0 Documentation, ANSYS Inc: Canonsburg, 2003. Tsai, S.W., Hahn H.T., Introduction to composite materials, Technomic Publishing Company: Lancaster, pp. 392-399, 1980. Rules for the Construction and Classification of High Speed Craft, HSC Code, EEIG UNITAS, 2002. Della Biancia, C., Reports of small scale tests CTS job no. 416/06, Centro Tecnologico Sperimentale S.r.l.: La Spezia, 2006.
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Modelling of viscoelastic properties of a curing adhesive J. de Vreugd1, K. M. B. Jansen1, L. J. Ernst1 & J. A. C. M. Pijnenburg2 1 2
Delft University of Technology, Delft, The Netherlands TNO Science and Industry, Delft, The Netherlands
Abstract Thermoset adhesives are widely used in high tech applications to join two bodies together. The main advantages of using adhesives are the low weight of the construction and the easy way to apply the adhesive to the surfaces which have to be fixed together. The disadvantage of thermoset adhesives however is that cure shrinkage occurs. Shrinkage and evolution of mechanical properties during cure leads to development of internal stresses. In this paper, the mechanical behaviour of a curing adhesive is investigated. In the case of using a thermoset adhesive in high precision applications like optical instruments, care should be taken. Small displacements and distortions of important components caused by cure shrinkage may already lead to malfunctioning. For this reason a material model suitable for implementation in a finite element program is developed to predict stresses and strains in glued objects. The temperature and cure dependent viscoelastic shear modulus of the adhesive are obtained by using Dynamic Mechanical Analyzing methods. The bulk modulus is obtained at fully cured state with a high pressure dilatometer. Curing-time–time superposition is applied to model the shear modulus at any state of cure. It is assumed that the bulk modulus remains constant during cure. The kinetics of the adhesive is investigated by using Dynamic Scanning Colorimetric techniques. The relation between time and degree of cure is modelled by making use of the KamalSourour equation. Also diffusion limitation is added to this equation. The cure shrinkage of the adhesive is experimentally determined by making use of the principle of Archimedes. Finally a validation experiment is performed. The validation experiment is simulated in the finite element program ABAQUS and compared with the experiment. It turned out that the developed material model is accurate enough to predict reaction forces, stresses and strains caused by cure shrinkage. Keywords: adhesive, cure shrinkage, DMA, DSC, viscoelastic properties. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/MC070241
242 Computational Methods and Experiments in Materials Characterisation III
1
Introduction
Thermoset adhesives are used in many high-tech applications to fix two bodies together instead of other bonding techniques. Thermoset adhesives are often used when a low construction weight is required. Another advantage is the easy way of applying the glue to the surfaces. Next to above mentioned advantages of using an adhesive, also some negative properties are present. An important disadvantage of using an adhesive for bonding is the shrinkage of the adhesive during the transformation from a fluid to a solid material. The shrinkage results in distortions and internal stresses. In instruments where a high precision is required like optical instruments, cure shrinkage might cause problems. Displacements and rotations of important parts in high precision instruments are undesirable because of the necessary accurate position. It is even possible that cure shrinkage leads to cracks in a glued object. An example is shown in figure 1 where a glass plate is glued to a metal surrounding. In this example shrinkage forces were that high that the glass plate is cracked.
Figure 1:
Cracks caused by cure shrinkage.
In order to avoid the mentioned problems, cure shrinkage should be taken into account at the design state of instruments where a high precision is required. To be able to produce a fail-proof design, a reliable model of both cure shrinkage and viscoelastic material properties is needed to predict stresses and strains during cure. The Araldite AV 138 M adhesive is a frequently used adhesive in aerospace. The cure shrinkage of this adhesive caused many problems in the past. For this reason is chosen to investigate the viscoelastic behaviour of this adhesive during the transformation from a fluid to a solid material. The mechanical behaviour of the adhesive is completely characterized and modelled such that all viscoelastic properties are available at a large range in time, temperature and at a certain degree of conversion. The obtained model is used to solve the linear viscoelastic stress-strain relation: t
V ij t 2 G t [ Hij d[
³
f
t
2
³ «¬K t [ 3 G t [ »¼ H ª
º
eff 11
eff eff H 22 H33 G ij
(1)
f
In equation (1) the variables G and K refer to shear and bulk modulus respectively, which are a function of time (t), temperature (T) and degree of WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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conversion (Į). The variable H iieff is the effective volumetric strain which includes cure shrinkage and thermal contributions. A model of both shear G(t,T,Į) and bulk K(T) modulus as well as cure shrinkage İcure is proposed in this paper. The mechanical properties are experimentally found by using DMA (Dynamic Mechanical Analyzing) techniques and by using a high pressure dilatometer. The chemical reaction model is found by using DSC (Dynamic Scanning Calorimetric) measurements. Finally the decrease in density of the adhesive is measured during cure by using the method of Archimedes. All experimentally found properties are modelled so that they can be implemented in a finite element program. In order to validate the material model of the adhesive during cure, a validation experiment was done. This experiment showed that the determined material model is accurate enough to do reliable predictions of stresses and strains.
2
Cure kinetics
Chemical reaction is started by applying a thermal loading to an uncured or not fully cured material. During this reaction, the individual epoxy monomers transform to a three dimensional network. This network prevents the molecules to slide past each other; this is the reason that a fluid like material transforms into a solid. The rate of reaction is dependent on the applied temperature. At the instant that the curing reaction is finished, one speaks about a fully cured material. The states between un- and fully cured situation are expressed by the expression: degree of cure or degree of conversion which is represented by the symbol Į. The value of Į varies between 0 and 1. To be able to model the cure reaction it is necessary to describe the progress of the reaction, such that it is possible to calculate the degree of conversion at any moment of time and temperature. The reaction progress is measured in this research project by a DSC 2920 of TA instruments. 2.1 Degree of cure determination During cure, heat comes free because of the chemical process (cross-linking). The degree of cure Į is related to the maximum heat which comes free after a complete reaction (Hmax) and the heat which comes free after a certain state of reaction (H). The degree of cure (Į) is defined as 1-H/Hmax. In order to measure the degree of conversion of a partly cured sample, it is necessary to calculate the total heat generated by a complete cure reaction. A temperature ramp is applied to an uncured sample and the rate of heat generation dH/dt is measured. Several heating rates (ȕ) are applied: 1, 2, 5, 10ºC/min. (dynamic scanning). The heat of reaction H is the amount of heat generated during dynamic scanning. The total generated heat, caused by the reaction is calculated for every measurement by the following equation:
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244 Computational Methods and Experiments in Materials Characterisation III t
Hu
§ dH ·
³ ¨© dt ¸¹dt
(2)
0
The thus obtained total heat of reaction varied between 130.27 and 135.42 J/g. A value of 135.42 J/g is used in further calculations. 2.2 Cure dependent Tg determination Viscoelastic materials have the property that at low temperatures the material behaves glassy and at high temperatures more rubbery. The temperature at which this behaviour changes from a glassy to a rubbery behaviour is the glass transition temperature (Tg). The glass transition temperature is a cure dependent property and is therefore measured as a function of degree of conversion. This property is measured as a sudden change in heat capacity Cp (Seifi et al [1]). The heat capacity is measured by applying DSC scans to samples of different conversion levels. The results of these tests are shown in figure 2.
Figure 2:
Glass transition temperature as a function of degree of conversion.
The above measured data points are fitted to the Di-Benedetto equation: T gf T g 0 O D (3) T g D T g 0 1 1 O D Tgf and Tg0 represent Tg at fully and uncured state respectively. The measurements showed that, Tgf = 77.5°C and Tg0 = -32.1°C. The value Ȝ is a material dependent parameter. For the adhesive studied in this paper, Ȝ = 0.474.
2.3 Kinetic model The chemical reaction is described by the model of Kamal and Sourour. This model is given in equation (4).
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§ Ea ·
¨¨ ¸¸ dD k 0 e © RT ¹ D m 1 D (4) dt In this equation Ea denotes an activation energy (Starink [2]), R denotes the universal gas constant § 8.314 J/(mol·K) and T represents the absolute temperature as a function of time. The parameters k0, m and n are fit variables. The following values are found: k0 = 3.2982·105, m = 0.185, n = 1.5154 During isothermal curing, a thermosetting resin vitrifies if the reaction temperature is lower than the maximum glass transition temperature of the fully cured material. Due to the vitrification process, the kinetics becomes diffusion controlled. This phenomenon is also observed in the studied adhesive. It turned out that a sample cured at a room temperature could not reach maximum conversion. The maximum conversion level turned out to be 81%. Therefore, the kinetics model is modified to:
dD ª dD º fd (5) dt «¬ dt »¼ chem [da/dt] describes the chemically controlled kinetics. Kamal-Sourour’s equation is used here. fd denotes the diffusion control function (Schawe [3]). If the reaction is chemical controlled fd is equal to unity. In case of diffusion controlled reaction fd will have a value between 0 and 1. The diffusion control function has to show an inflection point if the glass transition temperature is equal to the reaction temperature. A model for this function has to describe the inflection point properly. The following equation is fulfilling the mentioned requirements: 1
3· § ¨ 1 §¨ Treact 'T T g D ·¸ ¸ (6) f d D 1 ¨1 ¨ ¸ ¸¸ 'T ¨ 2© ¹ © ¹ Treact is the temperature where the reaction place. ǻT is a fitting parameter; for this adhesive is found by trial and error that ǻT is 21.5 °C.
3
Mechanical properties
To be able to predict the stresses in a glued object, it is necessary to know the mechanical properties of the adhesive. The properties have to be known at a fully cured state, as well as during the curing trajectory. For the viscoelastic elongation- and shear-modulus a Dynamic Mechanical Analyzer (DMA) is used. The used test device for these measurements is a DMA Q800 of TA-instruments. This instrument has a displacement resolution of 1nm and a force resolution of 1mN. The bulk modulus is measured by a high pressure dilatometer. A GNOMIX dilatometer with a pressure range of 200MPa is used. 3.1 Tensile modulus of fully cured adhesive In order to measure the viscoelastic properties of the fully cured material, a test bar was required. The used dimensions are [22.89 x 3.1 x 0.82 mm]. The test bar WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
246 Computational Methods and Experiments in Materials Characterisation III is produced by curing the adhesive in a suitable mold. Before curing the material submitted to vacuum to subtract the gas bubbles in the uncured resin. A cure temperature of 75 ºC is applied for 5 hours. The test bar is exposed to a sinusoidal strain with different frequencies: 0.3, 0.65, 1.4, 3, 6.5, 13.8, 30, 64.6, 130 Hz. During the frequency sweeps a temperature ramp is applied from -50ºC to 220ºC with a heating rate of 1ºC/min. The result of this experiment is shown in figure 3.
Figure 3:
Result of DMA experiment to a fully cured bar of adhesive.
From this figure it is concluded that the glass-plateau of this material is: E glass 5517 10 6 30.452 10 6 T [MPa]
(7)
By applying the time-temperature superposition principle (Nielsen and Landel [4]) to the rough data, a mastercurve is obtained. The shiftfactors (at) are fitted to the Williams-Landel-Ferry equation: C1 T T R log a t (8) C 2 T TR The constants are treated as fit variables; Tg is taken as the reference temperature TR. By applying a non-linear fit, it is found that C1 = 1.51, C2 = 28.6. Tg is the value where tan(į) at 1 Hz reaches a maximum. Tg turned out to be 84ºC. 3.2 Bulk modulus measurement A GNOMIX high pressure dilatometer is used to measure the bulk modulus. A sample with a typical mass of 1.5 gram is contained in a rigid cell, closed by flexible bellows. This cell contains mercury to fill the cell completely. The cell is placed into a vessel which can be heated. A hydrostatic pressure applied to the cell, will result in a deflection of the bellows. This deflection can be related to deformations inside the cell. The pressure range that can be applied to the sample varies between 10 and 200MPa, the highest applicable temperature is 400ºC. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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In order to measure the bulk modulus of the material, a stepwise temperature scan is applied to the material. At every temperature step, steps of 10MPa are applied. Equation (9) (Fung [5]) is used to calculate the bulk modulus: v K 'p (9) 'v The result of this measurement is presented in figure 4.
Figure 4:
Bulk modulus as a function of temperature.
In figure 4 is shown that the maximum modulus value is about 2900 MPa, the lowest about 1800 MPa. For temperatures above 50ºC the material is time dependent so for these temperatures the measured values cannot be used for finite element simulations but it gives an estimate of the modulus at those particular temperatures. 3.3 Shear modulus during cure To be able to predict stresses and strains in a glued object during cure, it is necessary to know the viscoelastic properties during cure. The cure dependent shear modulus is determined by measuring the change in stiffness of a droplet of adhesive which is clamped between 2 plates. To one of the plates a sinusoidal strain of 5 µm is applied. By recording the forces and amplitudes of the plate during the experiment, the stiffness K of the sample is calculated. With the known dimensions of the droplet of adhesive the shear modulus is calculated: § 2h · (10) G Z K Z ¨ ¸ © A¹ In equation (10), h and A represents the gap between the plates and the crosssectional surface of the adhesive sample respectively. Different isothermal loadings are applied to sample such that the adhesive cures during the experiment. Three experiments are done with isothermal loadings of 40ºC, 45ºC and 50ºC. The results of these experiments are plotted in figure 5. In figure 5 the viscoelastic shear modulus is plotted as a function of degree of conversion. At conversion levels lower than 0.55, the material is still a fluid. The shear modulus in this region is 0. In order to obtain a mastercurve of the shearWIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
248 Computational Methods and Experiments in Materials Characterisation III modulus, the cure-time–time superposition principle (Yongsung [6]) is used. The shiftfactors which are used for determining the mastercurves are fitted to the following equation: Shift D , T 10 C1 C2 T C3 e
C 4 D
(11)
The following values for the fit factors are found: C1 = -2.361, C2 = -0.150, C3 = 16.17, C4 = -3.66.
Figure 5:
4
Result of shear tests during cure.
Cure shrinkage
The cure shrinkage is experimentally found by making use of Archimedes' principle. An apparatus is designed which makes use of buoyancy forces caused by immersing a body in a fluid. By knowing the mass of the sample, the weight of the mass immersed in the fluid, and the density of the fluid, the density of the sample can be calculated. The mass of the sample and the density of the fluid should be known before doing the measurement. As an immersing fluid, silicone oil is used with a density of 0.9670 g/cm2 and a CTE of 8.20·10-4/K. Different isothermal loadings are applied to samples: 20ºC for 70 hrs, 40ºC for 18 hrs and 50ºC for 16 hrs. The result of the measurement at 20ºC is shown in figure 6. From figure 6 is concluded that there is linear relation between degree of cure and density. The total volumetric cure shrinkage Ȗv is calculated with the following equation: 'v 'U 0.0704 Jv 0.0133 (12) v fully 3 U ful 3 1.7674
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ȡ = 1.697 + 0.0704·Į
Figure 6:
Results of density measurement.
5 Validation experiment In order to check the accuracy of the obtained material model, a validation experiment is done, see Figure 7. In this experiment a droplet of adhesive is applied in the middle of a glass-plate which is fixed at both ends. Dimensions of the glass-plate were: [40 x 10 x 2 mm]. Glass-plate
Adhesive bump Figure 7:
Schematic drawing of validation experiment.
Due to the shrinkage of the adhesive, the glass-plate will deflect. A temperature load is applied to the adhesive, firstly a temperature of 40ºC is applied for 35 hours, after that the temperature is changed to 80ºC for 20 hours. In the validation experiment, the reaction force at the bottom of the adhesive bump is measured. Simultaneously the force is calculated by using the finite element program ABAQUS. User-subroutines were used to implement the obtained material model. A picture of the used mesh is given in figure 8. Shell-elements are used for the glass-plate, and solid elements are used for the adhesive bump. Measured and calculated forces are presented in figure 15. In figure 9, the calculated forces are compared to the measured forces. The calculated forces are about 30% too high. This is probably due to the bulk modulus which was implemented in the simulation model as a non-time and noncure dependent value. Another reason is most probably due to friction at the boundary conditions. This is not modelled due to a lack of time. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
250 Computational Methods and Experiments in Materials Characterisation III
Mesh of the validation experiment. 100
10 8 6 4 2 0 -2 -4 -6
80 60 40 20
0
1000
2000
3000
Temperature °C
Force [N]
Figure 8:
Measured force Calculated force
Temperature
0 4000
Time [min.]
Figure 9:
Result of validation experiment.
6 Conclusions and recommendations In this research, a first start is made in characterising the mechanical properties of the adhesive Araldite AV 138M. The mechanical properties which are a function of time, temperature and degree of conversion are studied and fitted in a material model. The kinetics of this material is well described in a relation in which also diffusion limitation is implemented. The cure shrinkage is found and modelled. The material model is implemented in ABAQUS. The following properties of the investigated adhesive were established during this work: Tg varies between -32°C and 77.5°C during cure. The relation between Tg and degree of conversion is well described by Di-Benedetto’s equation. The kinetics is modelled by making use of Kamal-Sourours’ equation. Diffusion limitation is added to this model. The fully cured elongation modulus varies between 6500 MPa at -50°C and 65 MPa at 200°C. The bulk modulus varies between 2700 MPa at 30°C to 1800 MPa at 90°C. A simple cure and temperature dependent shiftfactor is obtained, with which mastercurves at other conversion levels can be found. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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The decrease in density is about 4%. It turned out that there is a linear relationship between degree of conversion and density. From the validation experiment is concluded that the obtained material model is accurate enough for predicting stresses and strains in glued objects. For future work some recommendations are listed below: More validation experiments should be done. Some parameters of the validation experiment can be changed. For instance the thickness of the adhesive layer. It might be that the reaction forces caused by cure shrinkage are very sensitive to the applied layer thickness. It turned out that there is an error of about 30% between the measured and simulated reaction forces. This is probably caused by an inaccurate bulk modulus. So, bulk modulus has to be found as a function of time, temperature and degree of conversion.
References [1] Seifi, R., Hojjati, M., Heat of reaction, cure kinetics and viscosity of araldite LY-556 resin, Journal of composite materials, 39(11), pp. 10271039, 2005. [2] Starink, M.J., The determination of activation energy from linear heating rate experiments: a comparison of the accuracy of isoconversion methods, Thermochimica acta, 404(1-2), pp. 163-176, 2003. [3] Schawe, J.E.K., A description of chemical and diffusion control in isothermal kinetics of cure kinetics, Thermochimca Acta 388(1-2) pp. 299312, 2002. [4] Nielsen, L.E., Landel, R.F., Mechanical properties of polymers and composites, pp.110, 1988. [5] Fung, Y.C., Foundations of solid mechanics, pp. 113, 1984. [6] Yongsung E.O.M., Louis Boogh et al., Time-cure-temperature superposition for the prediction of instantaneous viscoelastic properties during cure, Polymer engineering and science, 60(6), pp. 521-528, 2002.
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Flexural bond strength of clay brick masonry C. G. Yuen & S. L. Lissel Civil Engineering Department. University of Calgary, Canada
Abstract The intent of a new parametric study at the University of Calgary is to investigate the influence of several factors on the flexural bond strength of clay brick masonry. These factors include the absorption characteristics of the brick units, and varying construction and curing methods. A preliminary study was performed with a series of clay brick prisms built from different types of brick with various absorption characteristics, and cured at different conditions. The bond wrench test was used to determine the flexural bond strength between the mortar and brick. The results showed high variation, but did provide some indication of which factors may be contributing to the highly variable findings. The objectives of this continuing study are to eliminate the possible parameters that were causing the highly variable results, and to determine correlations between brick properties and bond strength. The results are presented in this paper. Further research will be ongoing to establish a more definite relationship between the various parameters and bond strength and to investigate effects of mortar, and curing conditions. Keywords: masonry, clay brick, flexural bond strength, bond wrench, initial rate of absorption, sorptivity, absorption, construction method.
1
Introduction
Masonry is a composite material of clay or concrete units held together by mortar. An ineffective bond between the unit and mortar will cause cracking when subjected to lateral loading. Cracks increase susceptibility to moisture ingress, which leads to freeze-thaw damage, and corrosion of metal connectors. Therefore, the bond strength between the brick and mortar acts as an indicator of the overall quality of the masonry structure [1]. For many years, researchers have been interested in determining the factors that affect the bond at the interface of the two materials. These parameters WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/MC070251
254 Computational Methods and Experiments in Materials Characterisation III include the absorption characteristics of the units (initial rate of absorption or IRA, sorptivity, and cold and hot water absorption), mortar properties (type, flow, and retentivity), curing conditions, and workmanship. It is difficult to determine the significance of one factor and its effect on the bond strength because no factor alone is responsible for good bond, making it difficult to devise an experiment to produce consistent results [2]. Numerous studies [3–7] have shown large differences in strengths and highly variable results, and no conclusive findings were obtained from replicating experimental procedures [1]. A preliminary study was performed at the University of Calgary in the summer of 2005 investigating the effects of various absorption properties of clay bricks (particularly the IRA property) and curing conditions on the flexural bond strength of clay brick masonry. Although the variability of the results was high, it did provide some indication of which factors may be contributing to these highly variable findings. The continuing study involves the investigation of two possible causes of variability with the objective to eliminate these factors, and also aims to determine correlations between brick properties and bond strength. This paper identifies the possible causes of variability, and presents the results when new methods were applied to eliminate these factors. Apparent correlations between different brick properties are also presented.
2 Stage 1: eliminate construction factors 2.1 Identifying the factors The first factor identified from the preliminary study is that the mortar was mixed by an experienced mason. It was observed that the color and texture of the mortar joints varied. An explanation for this is that the amount of water added into the mortar was based on the experience of the mason, and each new batch of mortar may have differed slightly. Another possible factor that contributed to the highly variable results is the height of the prism. For the preliminary study, 5-brick high prisms were used. It was hypothesized that the varying weight on each mortar joint along the height of the prism may have caused stress variation at the joints. Lastly, CSA A371-04 [8] requires mortar joints to be 10 mm thick with a tolerance of ±3 mm. Although the joints were fairly consistent with all the prisms, this is also considered as a contributing factor to the high variations. With these identified factors, the first stage of the current study was to attempt to reduce the variability by eliminating these factors using nonconventional construction methods. 2.2 Materials 2.2.1 Bricks Three types of brick were used with various IRA values: tan (IRA = 10 g/min/200cm2); red (IRA = 23 g/min/200cm2), and cream (IRA = 42 g/min/200cm2). These same brick types were also used in the preliminary study. All units are metric modular with dimensions 90 x 190 x 57 mm (W x L x H). WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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2.2.2 Mortar A general purpose Type S 1:0.5:4.5 (Portland cement:lime:sand by volume) mortar was used. The contents were proportioned and mixed in accordance with CSA 179-04 [9]. The amount of water added was measured (by weight) and recorded for future mixes. This entire procedure was performed by the researcher. 2.3 Specimen preparation To eliminate the varying weight on the mortar joints along the height of the prism, it was decided to build 2-brick high prisms. To have all the prisms built the same, a simple jig was designed for proper alignment of the units and to ensure a 10 mm mortar joint in between. The jig consists of four wooden right angled pieces, with an M6 hex screw embedded in the middle. The screw head has a diameter of 9.8 mm and sits on the bed face of the brick, and all the corner pieces are held together by a heavy-duty elastic. A full bed of mortar is then placed, and the top brick is added (Figure 1). Afterwards, the elastic is removed and the corner pieces are pulled out. A total of 110 prisms were made, and all were air-cured at ambient laboratory conditions (temperature of 20ºC and relative humidity 21%).
Figure 1:
Prism construction with jig.
2.4 Test method The bond wrench method described in CSA S304.1 Annex E [10] was used to determine the bond strength of the masonry prisms. The test apparatus and method have been used in other studies as well [11]. 2.5 Results and discussion Specimens were tested at 7 and 28 days. The average bond strengths and standard deviations are plotted, and shown in Figure 2. It can be seen that the variability for the 7-day cure is much greater than the 28-day cure. It is also surprising to see that bond strengths tend to be greater at 7 days then at 28 days. But due to the highly variable results, it is difficult to make any conclusions. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
256 Computational Methods and Experiments in Materials Characterisation III Bond Strength vs IRA at 7 and 28 Days 2.50
Bond Strength (MPa)
2.00 1.50
7 Days 28 Days
1.00
2
R = 0.0114
0.50 2
R = 0.832 0.00 0
10
20
30
40
50
IRA (g/min/200cm2)
Figure 2:
3
Bond strengths of three brick types at 7 and 28 days.
Stage 2: eliminate brick-to-brick variability
3.1 A new factor to consider It is obvious from Stage 1 that despite controlling most workmanship variables, large variability still exists. Therefore, in this stage the variability in brick absorption properties for each individual brick were taken into consideration. This variability has been reported in the literature as well. With a sample of 20 of the same brick type, Lauersdorf and Robinson [12] observed that individual brick IRA ranged from 14.9 to 39.4 g/min/194 cm2. Bailey et al. [13] reported that an individual brick unit may even exhibit significantly different IRA values from one bed face to another. Therefore, for the second stage, brick couplets were paired up according to their individual IRA and sorptivity values. Care was taken to ensure that the tested bed face was the one on which mortar was placed. 3.2 Materials 3.2.1 Bricks Two types of bricks were used: tan and red (both these brick types were used in the previous tests). Prior to construction, each individual brick was tested for its IRA and sorptivity properties in accordance with CSA A82-06 [14], and ASTM C1585 [15]. More than 600 brick units were tested for IRA. For the red brick, individual IRA values ranged from 25.6 to 59.2 g/min/200cm2 (difference of 33.6 g/min/200cm2), whereas for the tan brick IRA ranged from 6.6 to 20.1 g/min/200cm2 (difference of 13.5 g/min/200cm2). Therefore, it was decided to pair up the red bricks according to IRA and the tan bricks according to sorptivity. Approximately 200 of the tan bricks were further tested for sorptivity which WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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ranged from 0.0226 to 0.099 mm/s0.5. Bricks with matching values were paired up (tolerance of ±0.2 g/min/200cm2 for IRA, and 0.0001 mm/s0.5 for sorptivity) for prism construction. 3.2.2 Mortar The same mortar preparation used in Stage 1 was used in Stage 2. 3.2.3 Specimen preparation The same method from Stage 1 was used in Stage 2 to construct the prisms. A total of 50 matched IRA prisms were constructed, and were cured for 14 days: 7 days air-cured at ambient laboratory conditions, and 7 days covered with a sheet of plastic. Only 25 matched sorptivity prisms were built, and all were cured for 14 days, and covered with a plastic sheet for the whole curing duration. 3.3 Test method As in all the previous tests, the same bond wrench method was used to determine the bond strength of the masonry prisms. 3.4 Results and discussion The results from the matched IRA prisms are shown in Figure 3. Bond Strength vs Matched IRA 0.45 Minimum 0.2 MPa bond strength requirement per CSA S304.1
0.40 Bond Strength (MPa)
0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 25
30
35
40
45
50
55
IRA (g/min/200cm2)
Figure 3:
Bond strengths of the matched IRA prisms.
CSA A371-04 [8] uses IRA as a guideline to ensure proper bond strength in masonry construction. It suggests that a brick unit with IRA of 30 g/min/194 cm2 is considered a high IRA brick. Without prewetting, the brick will absorb excessive amount of water and improper curing of the mortar will occur leading to poor bond strength. Despite controlling a number of identified factors, no correlation can be seen in Figure 3 between bond strength and IRA. Although more than half the prisms failed at bond strength below 0.2 MPa (the minimum bond strength required by WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
258 Computational Methods and Experiments in Materials Characterisation III CSA S304.1 [10]), it is possible to have good bond strength without prewetting high IRA bricks. It is also noted that the curing length and conditions did not conform exactly to the procedure outlined in CSA S304.1 [10]. Although the tan prisms were matched according to sorptivity, it was of interest to examine the relationship between bond strength and IRA of these prisms. Interestingly, the IRA values were also quite closely matched. The largest IRA difference was 5.4 g/min/200cm2. The IRAs for each prism were averaged, and then plotted with the corresponding bond strength (Figure 4). Similar to the matched IRA prisms, no correlation is observed between IRA and bond strength. Figure 5 presents the results of the matched sorptivity prisms. It can be seen that no correlation is apparent between sorptivity and bond strength either. Bond Strength vs Average IRA 1.20
Bond Strength (MPa)
1.00 0.80 0.60
Minimum 0.2 MPa bond strength requirement per CSA S304.1
0.40 0.20 0.00 8
9
10
11
12
13
14
15
16
17
18
19
2
IRA (g/min/200cm )
Figure 4:
Bond Strength vs. average IRA from the matched sorptivity prisms. Bond Strength vs Matched Sorptivity 1.20
Bond Strength (MPa)
1.00 0.80 0.60
Minimum 0.2 MPa bond strength requirement per CSA S304.1
0.40 0.20 0.00 0.02
0.04
0.06
0.08
0.1
Sorptivity (mm/s 0.5)
Figure 5:
Bond strengths of matched sorptivity prisms.
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259
Relationship between various brick properties
As a supplement to this current study, it was of interest to determine whether typical brick unit properties (IRA, sorptivity, 24 hour cold water absorption, and compressive strength) correlate to each other. 4.1 Bricks Two types of bricks were chosen: tan, a relatively low absorption brick (same type that was previously used) and light tweed, a relatively high absorption brick that had not been used before. Ten bricks of each type were randomly chosen from the pallet for various property comparisons. 4.2 Properties Four brick properties were determined: IRA, 24 hour cold water absorption, and compressive strength were determined in accordance with CSA A82-06 [14]; and sorptivity was determined in accordance with ASTM C1585 [15]. 4.3 Results and discussions Sorptivity and 24 hour cold water absorption were plotted against IRA for each individual brick, and is shown in Figure 6. It can be seen that the sorptivity correlates well with IRA, but 24 hour cold water absorption does not appear to correlate to IRA. Compressive strength of the unit was plotted against each absorption property for each individual brick (Figures 7–9). It can be seen that compressive strength correlates well with the IRA and sorptivity properties, but not the 24 hour cold water absorption property.
Sorptivity (mm/s0.5)
0.3000 R2 = 0.1576
0.2500 0.2000
R2 = 0.9313
0.1500 0.1000 0.0500 0.0000 0.0
10.0
20.0
30.0
40.0
50.0
60.0
8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0 70.0
Absorption (%)
Sorptivity and 24 h Absorption vs IRA
IRA (g/min/200cm2) Sorptivity
Figure 6:
24h Absorption
Relationship between various absorption properties with IRA.
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260 Computational Methods and Experiments in Materials Characterisation III Compressive Strength vs IRA
Comp. Strength (MPa)
100.0 80.0 60.0 40.0 R2 = 0.8342
20.0 0.0 0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
IRA (g/min/200cm2)
Figure 7:
Relationship between compressive strength and IRA. Compressive Strength vs Sorptivity
Comp. Strength (MPa)
100.0 80.0 60.0 40.0 R2 = 0.7732
20.0 0.0 0.0000
0.0500
0.1000
0.1500
0.2000
Sorptivity (mm/s
Figure 8:
0.5
0.2500
0.3000
)
Relationship between compressive strength and sorptivity. Compressive Strength vs 24h Absorption
Comp. Strength (MPa)
100.0 80.0 60.0
R2 = 0.0601
40.0 20.0 0.0 4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
Absorption (%)
Figure 9:
Relationship between compressive strength and absorption.
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261
Conclusion
This study has shown that despite controlling various factors that affect the bond strength of masonry, such as construction methods, and brick-to-brick variability, there is still a lack of correlation between the flexural bond strength and IRA. Therefore, the question is raised whether Canadian standards should use IRA as a guideline to ensure good bond strength. In addition, no correlation was found between the bond strength and the sorptivity property of brick units, however, relationships between typical brick unit properties were found. More research is needed to determine how these relationships can be applied to the flexural bond strength, and how other factors such as mortar, and curing may also affect bond strength.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
Lawrence, S.J. and Page, A.W., Bond Studies in Masonry. Proc. of the 10th IB2MaC, eds. N.G. Shrive and A. Huizer, University of Calgary: Calgary, pp. 909-917, 1994. Goodwin, J.F. and West, H.W.H., A Review of the Literature on Brick/Mortar Bond. Proc. Of British Ceramic Society, 30(23), pp. 23-37, 1982. Baker, L.R., Some Factors Affecting the Bond Strength of Brickwork. Proc. Of 5th International Brick Masonry Conference, Washington, DC, pp. 62-72, 1979. Sise, A., Flexural Bond Strength of Masonry, MSc Thesis, University of Calgary, Canada, 139 pages, 1984. Venu Madhava Rao, K., Venkatarama Reddy, B.V., & Jagadish, K.S., Flexural Bond Strength of Masonry Using Various Blocks and Mortars. J. of Materials and Structures, 29(2), pp. 119-124, 1996 McGinley, W.M., IRA and the Flexural Bond Strength of Clay Brick Masonry. Masonry. Components to Assemblages: ASTM STP 1063, ed. J.H. Matthys, ASTM: Philadelphia, pp 217-229, 1990. Meslin, M. & Brzev, S., Effect of Mortar Type on Flexural Bond Strength of Brick Masonry. Civil Engineering Research Project from BCIT, Report No. CERP – 2006/01, 40 pages, 2006. Canadian Standards Association, CSA A371-04, Masonry Construction for Buildings. Mississauga, Canada: Canadian Standards Association, 2004 Canadian Standards Association, CSA A179-04, Mortar and Grout for Unit Masonry. Mississauga, Canada: Canadian Standards Association, 2004 Canadian Standards Association, CSA304.1-04 Design of Masonry Structures, 2004. Shrive, N.G. & Tilleman, D., A Simple Apparatus and Method for Measuring On-Site Flexural Bond Strength. Proc. of the 6th Canadian Masonry Symposium, University of Saskatchewan: Saskatoon, pp 283294, 1992. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
262 Computational Methods and Experiments in Materials Characterisation III [12]
[13]
[14] [15]
Lauersdorf, L.R. & Robinson, G.C., Discussion of Paper, “Initial Rate of Absorption of Clay Brick Considering Both Bed Surfaces in the As Received Condition and After Outside Exposure. Masonry: Components to Assemblages: ASTM STP 1063 eds. J.H. Matthys, ASTM: Philadelphia, pp. 22-26, 1990. Bailey, W.G., Matthys, J.H., & Edwards, J.E., Initial Rate of Absorption of Clay Brick Considering Both Bed Surfaces in the As Received Condition and After Outside Exposure. Masonry: Components to Assemblages: ASTM STP 1063, ed. J.H. Matthys, Philadelphia, ASTM, pp. 5-21. 1990. Canadian Standards Association, CSA A82-06 Fired Masonry Brick Made from Clay or Shale, Public Review Draft 2005. American Society for Testing and Materials. ASTM C 1585, Standard Test Method for Measurement of Rate of Absorption of Water by HydraulicCement Concretes, ASTM: Pennsylvania, USA, 2004.
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Structural, economic and material comparison of various steel grades under dynamic/fatigue loading I. U. Amobi & H. C. Uzoegbo School of Civil and Environmental Engineering, University of the Witwatersrand, Johannesburg, South Africa
Abstract As industries are upgrading rapidly from a lower steel grade to higher ones it has become necessary to study the effect of changing from lower steel grades to higher grades. This paper reports on fatigue life and behaviour, economic implications and material composition of these higher strength steels (HSS) as compared to the conventional grades. Three grades are commercially available in South Africa: 300W, 350W and 460W. These different steel grades (conventional and HSS) with the same moment capacities were subjected to constant dynamic stresses and the fatigue crack growth of the overloading and unloading were monitored and compared with each other. The influences of the overloading and unloading made standard grades perform better under repeated loading than the HSS, since HSS have been proved to have poor ductility, resulting in a lower number of cycles to failure. An 85% increase in material cost was generated as HSS replaces the conventional lower steel grades. A reduction in the number of cycles to failure in HSS was over 500%. Keywords: steel grade, HSS, fatigue, low-cycle fatigue, high-cycle fatigue, load capacity, cycles to failure.
1
Introduction
There is a trend towards increasing the strength grade of the general purpose steel for construction in most countries. This trend was prompted by increased loading on structures, larger spans and architectural designs that require smaller sections. Australia and other countries around the world have in recent years changed from lower steel grades to higher ones. In 2005, South Africa changed WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/MC070261
264 Computational Methods and Experiments in Materials Characterisation III from grade 300W steel to grade 350W steel. The current investigation is mainly concerned with the study of the dynamic behaviour of the three main grades in South Africa.
2
Specimen section determination and Loading
Since various steel grades (300W, 350W and 460W) were tested under the same conditions, the load capacities of these steel grades were designed to be equal. To achieve this, an initial I-section of the 300W grade was assumed and its load capacity determined. The load capacity was then imposed on the other sections, 350W and 460W, and their different sections determined. 100 mm
16 mm
250 mm
218 mm
16 mm
16 mm
Figure 1:
Initial 300W section.
In order to maintain consistency, only the overall depth d, of the initial section grade was changed to suit the equivalent load capacity of grades 350W and 460W. As a result, the equation for the section modulus, Zpl became:
Z pl
ª100 xd 2 º ª 42 x d 32 2 º » « » 2« 4 ¬ 4 ¼ ¬« ¼»
(1)
As d = 250 mm for the initial section grade, the moment capacity was easily determined from the following equation:
Mp
0.9 xZ pl xf y
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(2)
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The moment capacity was then imposed on 350W and 460W accordingly and their respective overall depths were determined. A summary of the section dimensions is shown in the following table below: The samples are assumed to be laterally supported. Plates with 16 mm thickness were ordered in all three grades. The samples were factory fabricated to specification and delivered to the laboratory for testing. Table 1:
Specimen Breadth of top flange, btf Breadth of bottom flange, bbf Depth of top flange, ttf Depth of bottom flange, tbf Length of top flange, ltf Length of bottom flange, lbf Breadth of web, bw Depth of web, tw Length of web, lw Overall Depth, d
Section dimensions of the various grades.
300W
350W
460W
100 mm
100 mm
100 mm
100 mm
100 mm
100 mm
16 mm
16 mm
16 mm
16 mm
16 mm
16 mm
2500 mm
2500 mm
2500 mm
2500 mm
2500 mm
2500 mm
16 mm
16 mm
16 mm
218 mm
193 mm
155 mm
2500 mm
2500 mm
2500 mm
250 mm
225 mm
187 mm
2.1 Instrumentation The setup was done in such a way that a constant force was maintained throughout each experiment and the strain measurements were periodically taken. A 100 mm LVDT which was firmly fixed to the specimen was connected serially to both the DC voltage power supply and the memory card of an ‘Agilent’ Data Logger in order that voltage output can be measured during testing. The data logger was then connected to a computer which has the Agilent programme installed in order that the measurements can be adjusted and stored appropriately. Although the setup was not based on maximum deflection method but rather on force method, the LVDT was firmly fixed at mid-span directly under the WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
266 Computational Methods and Experiments in Materials Characterisation III point of load application. This enables us to ascertain the behaviour of the various specimens under specific loadings. Strain gauges were precisely glued at various sensitive places on the specimen and connected to a strain gauge reader. Since the MTS actuator measures its capacity in percentages, a load calibrator was used to convert the load percentage to actual readable loading quantities. 2.2 Loading There were two specimens for each grade of steel and two loading capacities for these various grades of steel. The specimens were tested under the same constant load as tabulated below. The load was applied at mid-span for all cases and supported at the supports. Proper bracings were provided in order to avoid lateral displacement. The applied loads were expressed as a percentage of the static load capacity of the sections. Table 2:
Steel Grade 300W 350W 460W
Load capacities.
Cyclic Load 1
Cyclic Load 2
0.50P = 122 kN 0.50P = 122 kN 0.50P = 122 kN
0.75P = 184 kN 0.75P = 184 kN 0.75P = 184 kN
Figure 2:
Test setup.
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267
Results
Due to varying section compositions, the stresses generated at particular points were peculiar to each specimen. The strain values at support and zone of loading were measured after every 100,000 cycles at a frequency of 1 Hz using strain gauges. The stresses generated at the mid-span until failure is shown in the table below: Table 3:
Mid-span stresses during failure.
Stress generated (N/mm2) 165 192 251 249 290 378
Specimen loading 300W @ 122 kN 350W @ 122 kN 460W @ 122 kN 300W @ 184 kN 350W @ 184 kN 460W @ 184 kN
Top Flange of 300W @ 122KN 17500
17400
0 17380
17300
micro strain
17200
17100
17000
200000 16980
16900
100000 16865
300000 16875
400000 16855
500000 16860
600000 16860
700000 16840
800000 16865
900000 16870
1000000 1100000 16860 16850
16800 1200000 16750 16700 0
200000
400000
600000
800000
1000000
1200000
cycles to failure
Figure 3:
Microstrain result for top flange.
The stresses were constant until failure occurred. Since there were no changes in stresses, i.e. a constant stress was applied to the structure throughout the testing until failure; the stress-strain curve yielded a straight line. The changes in strain were monitored periodically during the life of the experiment. Microstrains were read off at every 100,000 cycles of loading. The behaviour of strain with respect to the number of cycles occurred in the same pattern for all cases. For the microstrain at the top flange, there was a sharp WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
268 Computational Methods and Experiments in Materials Characterisation III contraction after the first 100,000 cycles and afterwards stabilization, showing that the top flange was under compression. For the microstrain in the web, there was a sharp increment of the specimen at the web as measured using the strain gauges. This shows that the web was under tension. Its behaviour was constant for all specimens, although the values were varying due to different loading for each specimen. Figures 1 and 2 show a consistent pattern of the microstrain results with respect to cycles to failure. Figures 3 and 4 are results for 300W at 122 kN. For the other experiments, the graph curve remains constant but with varying results at all points. Web - D of 300W @ 122KN cyclic loading 18550 1200000 18500
18500 18450 18400 100000 18365
micro strain
18350
200000 18390
300000 18370
400000 18390
500000 18395
600000 18380
700000 18410
800000 18410
900000 18390
1000000 1100000 18395 18395
18300 18250 18200 18150 0 18105
18100 18050 0
200000
400000
600000
800000
1000000
cycles to failure
Figure 4:
Microstrain result for web.
Figure 5:
Failed beam.
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There were several initiations of micro-cracks which eventually grew and formed one macro-crack that caused instant fracture of the beams. Failure occurred instantaneously without warning because the beams where tested within their elastic region. When the beams were unloaded, they returned to their original form without any visual deformation. 3.1 Discussions It is observed that as the steel grades increase in yield stress with lower web depth, their cycle to failure reduces. As a wrap up, the tables below show in summary the points of failure for the various steel grades tested under the same load factor. Table 4:
Under 0.5P = 122 kN.
Steel Grades
Failure Cycle
Testing Time
300W
1,200,000
333 hours
350W
786,000
218 hours
460W
182,400
51 hours
Table 5:
Under 0.75P = 184 kN.
Steel Grades
Failure Cycle
Testing Time
300W
322,023
89 hours
350W
60
1 minute
460W
50
50 seconds
Figure 6:
Failed beam.
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270 Computational Methods and Experiments in Materials Characterisation III Grades 350W and 460W failed by deformation under 75% of their capacity indicating poor ductility in material composition. All the specimens failed, whether fracture or deformation, within the zone of loading. The stresses induced at the point of failure where close to the maximum stresses induced at the midspan of the specimens. Even for specimen 1 (300W @ 122 kN) which failed by global buckling, the maximum deformation occurred at the zone of loading.
y, Load capacity (KN)
3.1.1 Structural consideration From tables 4 and 5 above, we can conclude that an increase in the steel grade reduces the capacity for the steel to withstand fatigue loading. The experiment shows clearly a reduction in cycles to failure as the steel grades increase. This statement can be shown graphically in the following graph. Failure behaviour of the specimens under cyclic Load 200
50 184KN
180
322023 184KN
60 184KN
160
y = -7E-05x + 206.74
y = -0.0003x + 184.02
140
y = -8E-05x + 184 182400 122KN
120
786000 122KN
1200000 122KN
100 80 60 40 20 0 0
200000
400000
600000
800000
1000000
1200000
1400000
x, Cycles to failure 300W
Figure 7:
350W
460W
Linear (300W)
Linear (350W)
Linear (460W)
Failure behaviour of specimens under cyclic loading.
Graphic equations were derived from the results in order that predictions for various load capacities of the steel grades can be fairly determined. The graph showed a linear relationship because only two load capacities for each steel grade were tested. As a result, estimations for cycles to failure of various load capacities can only be done within the limits of the experiment. For 300W, y = -7x10-05x + 206.64 For 350W, y = -8x10-05x + 184 For 460W, y = -0.0003x + 184.02 Where x = Cycles to failure and y = Load capacity in kN Range: 122 kN
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3.1.2 Economic consideration The costs per kilogram of various steel grades in South Africa are listed in the table below: Table 6:
Specimen Cost per kg (Rands)
Cost of the various steel grades.
300W 5.50
350W 6.50
460W 12.00
For the specimens tested, the cost of 300W which is 130.4 kg is equivalent to R717.20, the cost of 350W which gave a mass of 122.62 kg is equivalent to R797.03 and 460W (110.7 kg) gave a cost of R1329.12. As a result of the price comparison, the will be an 11% increase in the cost of steel material when converting from 300W to 350W and an 85% increase when converting from 350W to 460W steel grade for the erection of any structure. Considering a structure that involves hundreds of metres of steel, an 11% or 85% increment in material cost will definitely become uneconomical. 3.2 Conclusion Although HSS is 30% thinner, 30% lighter and with a doubled strength, a well refined grain size and easily maintained, it is still poor in withstanding fatigue loading and highly uneconomical when compared with conventional grades.
References [1] [2] [3] [4]
M.A. Gizejowski, H.C. Uzoegbo and A. Kozlowski, Selection Criteria for a general purpose construction steel strength grade, Conf. Proc. 2nd International conference on the African Materials Society (MRS), 2003. A. Koursaris and F.O. Nghoudzweni, Fatigue determination of full-scale Aluminium I-beams. 2002. M. Skaloud and M. Zornorova, The Fatigue life of steel plate girders subjected to repeated loading. Proc. Of the Slovenke Konference, pp. 403408, 2003. R. Maquoi and M. Skaloud, Some remarks in regard to the fatigue analysis of steel plate girders with breathing webs. Proc. Of the Slovenke Konference, pp. 397-402, 2003.
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Mechanical compression tests to model timber structures behaviour V. De Luca & D. Sabia Department DITEC, Università degli Studi della Basilicata, Italy
Abstract The present work aims to improve the definition of the constitutive laws for the wood structure at different grain orientations, by carrying out mechanical compression tests on spruce wood samples. The preliminary tests deal with a compressive uniaxial load. The material tested was clear spruce wood. The samples were 30 mm height, with a cross-section (S1) of 20 mm x 20 mm, for the longitudinal grain orientation (P) and 20 mm height with a cross-section (S2) of 30 mm x 20 mm (according to the UNI-ISO standards) for the orthogonal grain orientation (O). With respect to the 45° (45) angle grain orientation, both S1 and S2 cross-sections were considered, instead. Samples were loaded, for the P orientation, at a cross-head speed of 0.8 mm/min, for the O and 45 orientations at 0.5 mm/min. The load acted radially to the annual rings. For P and O orientations, fifty samples were tried, while for the 45 orientation fifty samples were used for both S1 and S2 cross-sections. The preliminary results for the stress-strain pattern were fitted by a 4th degree polynomial interpolation. In the P orientation the statistical determination coefficient was R2=0.939. The O orientation featured a better statistical significance, R2=0.963. The 45 orientation, however, showed, both for the S1 and S2 cross-sections, R2=0.874 and R2=0.851, respectively, determination coefficients, which are lower than the latter values. In the available scientific literature, the statistical significance of the experimental tests has not proved adequate results, but in this work a good statistical significance has been reached, instead. Keywords: mechanical compression tests, wood models, timber structures.
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274 Computational Methods and Experiments in Materials Characterisation III
1
Introduction
An increasing interest in the timber use, especially structural composite lumber (SCL) in building industry production has induced researchers to develop more efficient models for the mechanical properties of the wood material [1, 2]. The efforts carried out by the researchers have, mainly, focused a better characterization of the stress-strength pattern up the elasticity region [3, 7]. These studies have contributed to a better definition of the mechanical behaviour of the structural wood, with the aim to implement analytical laws in the FEM techniques, covering, so, the lack of definition, respect to other structural buildings materials (steel, reinforced concrete). The most important aspect of this research topic is related to the particular constitutive properties exhibited by wood due to its complex microscopic structure, consisting of the annual rings running and of the diffuse inhomogeneities. So, that behaviour, generally, schematised into orthotropic linear or non-linear [6] models, has been difficult to predict because of a pronounced statistical scattering of the mechanical experimental properties. Also, concerning the mechanical properties at different loading orientations to the grain [4, 5], there is a great lack of studies, particularly at orientations different from three principal directions. The present work aims to contribute to a better definition of the constitutive laws for the wood at different grain orientations, carrying out mechanical compression tests on samples. A main, further objective of this work is to develop a general model with a 3D constitutive equations basis where an incremental-loading technique will be used to describe the non-linear pattern in stress-strength region. The preliminary tests described in this study regarded a compressive loading case. Tensile and bending aspects of this work need further development.
2
Material and methods
The material tested was clear spruce wood. The tests were carried out according to geometrical UNI-ISO standards. The material tested was clear spruce wood. The samples were 30 mm height, with a cross-section (S1) of 20 mm x 20 mm for the longitudinal grain orientation (P) and 20 mm height with a cross-section (S2) of 30 mm x 20 mm (according to the UNI-ISO standards) for the orthogonal grain orientation (O). With respect to the 45° (45) angle grain orientation, both S1 and S2 cross-sections were considered, instead. Samples were loaded, for the P orientation, at a cross-head speed of 0.8 mm/min, for the O and 45 orientations at 0.5 mm/min. The load acted radially to the annual rings. For P and O orientations, fifty samples were tried, while for the 45° orientation fifty samples were used for both S1 and S2 cross-sections The preliminary results, to predict the stress-strain patterns of the wood, were studied by a draft, simple curve-fitting model. A polynomial interpolation (4th power), supported by a statistical validation, has been used in this work. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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However in a further work, it is required to study deeply modelling aspect using an optimal sample’s shape. The aim is to implement other curve-model, according to the scientific literature trend.
3
Results and discussion
First of all, the tests have pointed out, according with other authors [5], that the samples geometry (UNI-ISO) is more favourable to elastic behaviour than to the large strains, where occurred buckling of the sample, notwithstanding, we were interested both in the elastic behaviour and plastic one. For this reason, for a complete definition of the mechanical wood properties another fitted geometry is more suitable, preferable, with a unique cross-section both for tensile and bending case. The results are the following. The fig. 1 shows the stress-strain pattern in the longitudinal compression loading case, where the curve-fitting polynomial interpolation of 4th power exhibits a very high statistical determination coefficient R2=0.939:
V
6 10 9 H 4 2 10 8 H 3 4 10 6 H 2 21078H
60
Stress, N/mm^2
50 40 30 20 10 0 0
0.002
0.004
0.006
0.008
0.01
Strain, mm/mm Experimental Figure 1:
Polynomial 4th
Stress-strain relationship of clear spruce wood in longitudinal compression tests.
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276 Computational Methods and Experiments in Materials Characterisation III The orthogonal loading case, in fig. 2, it is characterized by a more high statistical significance, with a R2=0.963 determination coefficient, of the curvefitting: 9 10 7 H 4 2 10 7 H 3 308818H 2 2031.9H .
Stress, N/mm^2
V
5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 0
0.002
0.004
0.006
0.008
0.01
Strain, mm/mm Experimental Figure 2:
Polynomial 4th
Stress-strain relationship of clear spruce wood in orthogonal compression tests.
The 45-orientation loading case, however, shows, both for the S1 crosssection, in fig. 3
V
7 10 8 H 4 3 10 7 H 3 473922H 2 2999.8H ,
and the S2 one, in fig. 4
V
4 10 9 H 4 1 10 8 H 3 2 10 6 H 2 9206.3H ,
and R2=0.874 and R2=0.851, respectively, determination coefficients, which are below the previous values. This last result is due to the intermediate situation acting between the two opposite behaviours, the P and O orientations, probably, complicated by the annual rings influence. However, the stress-strain pattern follows a typical perfectly elastic-plastic behaviour.
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Stress, N/mm^2
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10 9 8 7 6 5 4 3 2 1 0 0
0.002
0.004
0.006
0.008
0.01
Strain, mm/mm Experimental Figure 3:
Polynomial 4th
Stress-strain relationship of clear spruce wood in 45° orientation compression tests, with specimens cross 20 mm x 20 mm.
25
Stress, N/mm^2
20 15 10 5 0 0
0.002
0.004
0.006
0.008
0.01
Strain, mm/mm Experimental Figure 4:
Polynomial 4th
Stress-strain relationship of clear spruce wood in 45° orientation compression tests, with specimens cross 30 mm x 20 mm.
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278 Computational Methods and Experiments in Materials Characterisation III
4
Conclusions
These first experimental results, contribute to study the modelling of the constitutive laws of the wood, in a structural timber. In fact, these results in compression loading, point out: x Generally in the scientific literature, the statistical significance of the experimental tests it has not reached a sufficient level. For this reason, is difficult to implement a valid mechanical modelling of the wood structure. But, in this work a good statistical significance has been reached. x Different behaviour, different results obtained for the three grain orientations: parallel, orthogonal and 45°confirm, that the wood material is very weak along the orthogonal grain. x These first results need further study, considering, other loading case, tensile and bending cases using the same settings and sample’s shape.
Acknowledgements The authors wish to thank dr. M. Brunetti of the CNR IVALSA, S. Fiorentino (FI) Italy, for supporting the experimental tests.
References [1] [2] [3] [4] [5] [6] [7]
Bodig, J. & Jayne, A.J., Mechanics of wood and wood composites. Van Nostrand Reinhold: New York, pp. 283-293, 1982. Clouston, P.L. & Lam, F., Computational modelling of strand-based wood composites. Journal of Engineering Mechanics, 127(8), pp. 844-851, 2001. Holmberg, S., Persson, K. & Petersson, H., Nonlinear mechanical behaviour and analysis of wood and fibre materials. Computers and Structures, 72, pp. 459-480, 1999. Liu, J.Y. & Ross, R.J., Wood mechanical property variation with grain slope. Proceedings of the 12th Engineering Mechanics Conference, La Lolla, CA, pp. 1351-1354, 1998. Reiterer, A. & Stanzl-Tschegg, S.E., Compressive behaviour of softwood under uniaxial loading at different orientations to the grain. Mechanics of Materials, 33, pp. 705-715, 2001. Tabei, A. & Wu, J., Three-dimensional nonlinear orthotropic finite element material model for wood, Composite Structures, 50, pp. 143-149, 2000. Tsai, S.W. & Kuraishi, A., Comparison of various failure criteria of orthotropic materials, Proceedings of the International Conference on Wood and Wood Fibre Composites, ed. S. Aicher, University of Stuttgart: Stuttgart, pp. 573-584, 2000.
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Section 8 Experimental methods – new methods
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Millimeter wave spectroscopy and materials characterization of refractive liquid crystal polymer/titania composites B. R. Dantal1, A. Saigal1, M. A. Zimmerman1, K. A. Korolev2, 3, M. N. Afsar2 & U. A. Khan2 1
Department of Mechanical Engineering, Tufts University, Medford, USA Department of Electrical and Computer Engineering, High Frequency Materials Measurement and Information Center, Tufts University, Medford, USA 3 Extremely High Frequency Medical and Technical Association, Moscow, Russian Federation 2
Abstract Titanium dioxide (TiO2 or Titania) is one of the most widely used white pigments. Titania is very white and has a very high refractive index. The high refractive index and bright white color of titanium dioxide makes it an effective opacifier for pigments. Light scattering is accomplished by refraction of light as it passes through or near pigment particles (E. McNeil and R. H. French, Multiple Scattering from Rutile TiO2 particles, Acta Materialia, 48(18-19), pp. 4571–4576, 2000). This study deals with the analysis of dielectric properties of a liquid crystal polymer/Titania composite material, in order to better understand the microstructure and the effect of dispersed titanium dioxide particles on the optical properties of the composite material. Complex permittivity, refractive index, absorption coefficient and loss tangent of the composite material have been investigated in the millimeter wave frequency range. The measurements have been performed by using two different techniques: first, free space quasi optical spectrometer equipped with high power sources of millimetre wave radiation tuneable in the 44–90 GHz frequency range and second, Dispersive Fourier Transform Spectrometer (DFTS) in the range of 100–600 GHz. Very low level of losses of millimetre wave radiation has been observed for all samples. Frequency dependences of complex dielectric permittivity have been determined in the broad band millimetre wave range. Strong correlation between dielectric properties and dispersed Titania volume percent has been observed by using the two different techniques. Keywords: polymer composites, reflectivity, refractive index, quasi-optics. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/MC070281
282 Computational Methods and Experiments in Materials Characterisation III
1
Introduction
During the past decade, inorganic/polymer hybrid materials have been the focus of research for their excellent electrical, optical, magnetic, optoelectronic, and enhanced mechanical properties. These hybrid materials combine the advantages of the organic polymers (lightweight, flexibility, relatively high impact resistance, and reasonable processability) and inorganic materials (strong chemical resistance, high thermal stability, and high brittleness). Optical, mechanical, and thermal properties of the hybrid materials are a function of the relative volume percent of each constituent in the composite material. Recently, the development of inorganic/polymer hybrid materials with high refractive index have attracted significant interest for electronic applications.
2
Experimental details
2.1 Free space quasi optical spectrometer Free space quasi optical spectrometer millimeter wave technique has been successfully employed for accurate transmittance spectra measurements. Extended V – band high vacuum backward wave oscillator (BWO) is applied as a source of coherent radiation continuously tunable in millimeter wave range from 44 to 90 GHz. A couple of horn antennas and a set of polyethylene lenses are used to form a Gaussian beam as well as to focus the beam into the sample. A block diagram of BWO-based free space quasi-optical millimeter wave spectrometer is shown in Figure 1.
Modulator
BWO
Isolator
Set of lenses
Horn Sample
Figure 1:
Detector
Block diagram of free-space quasi-optical millimeter wave spectrometer.
Details of the BWO-based free space millimeter wave spectroscopy technique, including measurements’ accuracy and sources of possible errors have been discussed elsewhere [2–4]. Five slab-shaped and parallel Liquid Crystal Polymer/Titania Composite samples with different titanium dioxide concentration have been investigated. The millimeter wave measurements have been performed in a frequency sweep WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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mode. Two consecutive frequency sweeps with and without the sample in the quasi-optical path are made and the transmittance spectra recorded. Transmittance spectral of the samples indicates very low level of losses in the millimeter waves. Additionally, real and imaginary parts of dielectric permittivity are calculated from the transmittance spectra. After obtaining the transmittance spectra of the Liquid Crystal Polymer/Titania composite materials, optimization procedures were applied to extract the best-fit dielectric parameters of the measured samples. 2.2 Dispersive Fourier Transform Spectroscopy (DFTS) A two-beam polarizing interferometer at the Tufts High Frequency Materials Measurement and Information Center has been utilized to perform Dispersive Fourier Transform Spectroscopy (DFTS), a popular electro-optical technique used to obtain the broadband dielectric properties of liquid, solid, powder, and gaseous samples. The interferometer’s radiation source is a mercury-vapor lamp. Radiation beams from the lamp are collimated and polarized before being split in two by a wire-grid beam splitter [6, 7]. As shown in Figure 2, part of the radiation is sent to the sample chamber and the other half to a micrometer-backed moving mirror. A fixed mirror lies on the other side of the sample. After reflecting from mirrors in both chambers, the beams recombine forming an interference pattern and are consequently collected by the Indium Antimonide detector. The sample interference pattern, VS(x), varies from an empty cell reference interference pattern, V0(x), since the signal peak shifts and has smaller voltage amplitude. The difference in the interference patterns provides the two quantities, shift and thickness, required to calculate the specimens’ dielectric properties [5, 6]. Extreme care has been taken to optically align the mirrors, polarizer, and beam splitter to ensure a maximum signal-tonoise ratio. Once the two interference patterns, shift, and sample thickness are known, any multiple reflection signatures can be edited out, and a double-sided Fourier transform of the interferograms is performed to yield information in the frequency domain.
Figure 2:
Diagram of the two-beam polarizing interferometer setup.
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284 Computational Methods and Experiments in Materials Characterisation III One can then proceed to calculate the five dielectric properties as follows. The refractive index is calculated by using equation (1): 2
ˆ ˆ ˆ x p h{ST (v)} p h{SO (v)} p h{ Sc(v) } n(v) 1 S 4S vd dS
(1)
where
x ds ph{}
v~ SˆT (v~ ) Sˆ (v~ ) O
S c(v~ )
Shift Sample thickness Phase of the content within the parentheses Frequency Fourier transform of edited sample Fourier transform of reference sample Ratio of Sˆ (v~ ) and Sˆ (v~ ) T
O
Similarly, the absorption coefficient can be found by D ( v )
1 dS
2º ª SˆO ( v ) ln Sˆ c( v ) » « ln ˆ ¼ ¬ ST ( v )
(2)
From Maxwell’s equations and dielectric definitions one can calculate the loss tangent [5–7]. Complex permittivity can be calculated by using equation (3):
Hˆ( v )
2
^nˆ (v )`
H c(v ) iH cc( v )
(3)
where
H': H" :
real part of complex permittivity imaginary part of complex permittivity
Refractive index can be calculated by taking the square root of the real part of permittivity and is given by equation (4). nˆ( v )
H '( v )
Finally, loss tangent can be obtained from equation (5). H cc( v ) tan G H c( v )
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(4)
(5)
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3 Results and discussions Refractive index of the composite materials measured with quasi optical techniques shows that as the volume percent of the TiO2 particles increases above 21%, the refractive index decreases at both the low and high frequencies as shown in Figure 3. Absorption coefficient measured for all the samples, as shown in Figure 4, illustrate that at the 47 GHz frequency there is not much change in absorption coefficient (~ 0.090 nep/cm) above 22 volume percent of Titania. 2.140
Refractive Index 68 GHz
Refractive Index
2.120
Refractive Index 47 GHz
2.100 2.080 2.060 2.040 2.020 2.000 1.980 1.960 20.0
Figure 3:
25.0 30.0 35.0 Titania volume percent
40.0
Refractive Index as a function of Titania volume percent at 47 and 68 GHz frequency.
Absorption Coefficient (nep/cm)
0.100 0.090 0.080 0.070 0.060 0.050 20.0
25.0
30.0
35.0
40.0
45
Titania volume percent
Figure 4:
Absorption coefficient as a function of Titania volume percent at 47 GHz frequency.
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286 Computational Methods and Experiments in Materials Characterisation III
Absorption Coefficient (nep/cm)
6 21%
5
22% 22%
4
40%
3 2 1 0 100
200
300
400
500
600
700
Frequency (GHz)
Figure 5:
Absorption coefficient for different volume percent of Titania particles. 2.20 20.5%
Refractive Index
2.15 21% 2.10 22% 2.05
22%
2.00
40%
1.95 100
200
300
400
500
600
700
800
Frequency (GHz)
Figure 6:
Refractive index for different volume percent of TiO2.
Results obtained by using DFTS technique are shown in Figures 5, 6 and 7. Figure 5 shows the absorption coefficient for different volume percents of Titania particles obtained by using the DFTS technique. The absorption coefficient of the sample with 40 volume percent of Titania particle is observed to be higher as compared to samples with 21 and 22 Titania volume percent.
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Figure 6 shows the refractive index for different volume percent of Titania particles. Sample with 40 volume percent Titania shows the lowest refractive index. As the volume percent increases, the tendency for agglomeration of particles increases. If the agglomerated particle size is larger than half the wavelength of the incident light, then it will not scatter the light effectively which leads to poor refraction. The agglomeration of TiO2 particles in the scattering media is one example of a general phenomenon known called “dependent scattering”: the light scattered by a unit concentration of scattering particles depends on the concentration of the scattering particles, scatter light which passes both inside and outside of their physical boundaries. In a concentrated suspension, these scattering volumes overlap, so that each particle “receives” less light than it is capable of scattering [8]. At low particle concentrations, the relationship between concentration and opacity is linear: doubling the concentration doubles the opacity. At higher TiO2 concentrations, this is no longer the case. Crowding lowers the scattering power so that a significant increase in the TiO2 concentration may result in very little increase in opacity. Indeed in some cases increasing concentration above certain point decreases the opacity. Clearly, the scattering efficiency of unit volume of TiO2 is dependent upon the concentration of TiO2 [9].
0.04 21% 22%
Loss Tangent - tanį
0.03
22% 40%
0.02
0.01
0 100
Figure 7:
200
300 400 500 Frequency (GHz)
600
700
Loss tangent for different volume percent of TiO2 particles.
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288 Computational Methods and Experiments in Materials Characterisation III Values of refractive index (~2.05 and 2.15) and absorption coefficient is significantly different for the samples with same the volume percent (i.e. 22%) of Titania particles, which can be attributed to the processing conditions of the sample and particle size distribution. Figure 7 shows the loss tangent data measured for all the samples over the range of 100 - 600 GHz using the DFTS technique. Dielectric loss tangent is the ratio of imaginary permittivity to real permittivity, and determines how much energy is lost by the electromagnetic wave while passing through the medium. Small loss tangent indicates high-energy loss while large loss tangent indicates low energy loss. As expected, loss tangent for the sample with 40 volume percent is high (~0.02) as compared to all other samples because the large volume percent of the TiO2 particles creates a barrier for the energy passing through the medium.
4
Conclusions
Dielectric properties, including complex permittivity, refractive index and loss tangent of the composite material have been studied in the millimeter wave frequency range. The measurements have been performed by using a high power free space quasi-optical spectrometer in the 44–90 GHz frequency range and a Dispersive Fourier Transform Spectrometer in the range of 100–600 GHz. Very low level of losses of millimetre wave radiation has been observed for composite samples. In addition, it is observed that the absorption coefficient and the loss tangent increases while the refractive index decreases as the volume percent of Titania particles increases in the composite materials from 20–40%.
References [1] E. McNeil and R. H. French, Multiple Scattering from Rutile TiO2 particles, Acta Materialia, 48(18-19), pp. 4571–4576, 2000. [2] K. N. Kocharyan, M. N. Afsar, and I. I. Tkachov, Millimeter-Wave Magnetooptics: New Method for Characterization of Ferrites in the Millimeter-Wave Range, IEEE Transactions, Microwave Theory and Techniques, 47, pp. 2636-2643, 1999. [3] K. N. Kocharyan, M. N. Afsar, and I. I. Tkachov, New Method for Measurements of Complex Magnetic Permeability in the Millimeter-Wave Range, Part II: Hexaferrites, IEEE Transactions on Magnetics, 35(4), pp. 2104-2110, 1999. [4] M. N. Afsar, I. I. Tkachov, and K. N. Kocharyan, A novel W-band spectrometer for dielectric measurements, IEEE Transactions, Microwave Theory and Techniques, 48, pp. 2637-2643, 2000. [5] M. N. Afsar, J. B. Chamberlain, and G. W Chantry, High precision dielectric measurements on liquids and solids at millimeter and submillimeter wavelengths, IEEE Transactions on Instrumentation and Measurement, IM25 (4), pp. 290-294, 1976.
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[6] J. Chamberlain, M. N. Afsar, D. K. Murray, G. D. Price, and M. S. Zafar, Submillimeter-Wave Dielectric Measurements of Absorbing Materials, IEEE Transactions on Instrumentation and Measurement, IM-23(4), pp. 483-488, 1974. [7] M. N. Afsar and G. W. Chantry, Precise dielectric measurements of low-loss materials at millimeter and submillimeter wavelengths, IEEE Transactions on Microwave Theory and Techniques, MTT-25(6), pp. 509-511, 1977. [8] S. Fitzwater and J. W. Hook, Dependent Scattering Theory: A New Approach to Determine Scattering in Paints, Journal of Coating Technology, 57(721), pp. 39-47, 1985 [9] E. Allen, Prediction of Optical Properties of Paints from Theory (with special reference to Microvoid Paints), Journal of Paint Technology, 45(584), pp. 65-72, 1973.
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Assessment of surface roughness for the analysis of the water vapour condensation process A. J. Klemm1, P. Klemm2 & I. Ibrahim2 1 2
Glasgow Caledonian University, UK Technical University of Lodz, Poland
Abstract This paper presents part of a larger study on water vapour condensation processes on solid surfaces. The strong relationship between the rapid growth of water vapour condensate and the roughness of the surface was the inspiration to undertake this study. A clear need was perceived to address the problem of assessment of the surface properties, selection of parameters for the analysis and the most appropriate experimental methods. An attempt was made here to review the existing methods of analysis of the geometrical microstructure of surfaces. The paper presents experimental results obtained for glass surfaces. Keywords: cementitious materials, measurements of surface roughness, condensation process.
1
Introduction
Moisture performance within buildings and their components is a research area of growing international importance due to the devastating effects which moisture can inflict on building envelopes. Interstitial condensation, high moisture contents and the consequent accumulation of water within a structure can cause a dramatic deterioration in the performance and integrity of building materials [1]. The external surfaces of engineering structures often have lower temperatures than the surrounding environment and in the case of occurrence of high relative humidity of air they are often subjected to water vapour condensation and consequently wetting. Both processes – water vapour condensation and water sorption – are very complex and depend on a number of WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/MC070291
292 Computational Methods and Experiments in Materials Characterisation III factors, primarily surface properties and environmental conditions [2]. Due to its nature it requires therefore non-standard testing and methods of analysis. The investigations previously undertaken by the authors give clear evidence of a strong relationship between the rapid growth of water vapour condensate and the roughness of the surface and lead to the conclusion that the condensation process can be modified by design of the geometrical microstructure of surfaces [3, 4]. A clear need is perceived to address the problem of assessment of the surface properties, selection of parameters for the analysis and the most appropriate experimental methods.
2
Water vapour condensation on solid surfaces
Assuming lack of chemical interactions between water molecules and solid surfaces, it is possible to simplify the problem to physical absorption. During the condensation process two clearly distinguished phases can be observed – spontaneous nucleus creation and growth of a new phase. Nucleus creation is associated with the change of Gibbs energy 'G, which in turn consists of two elements: volumetric energy 'Gv and superficial energy 'Gs. The second parameter is critical radius of a nucleus. During the phase transition the unstable phase with higher thermodynamic potential disappears and the new phase with lower potential is created. It is evident that the nuclei are stable when 'G is decreasing e.g. after reaching their critical size Rcr. If the thermodynamic potential of vapour is lower, then liquid is not usually formed. The initiation of a spontaneous phase transition may occur when the nuclei of new phase reach their critical size. The difference between the potential 'Gv of the original phase and volumetric potential of new created phase does not change in a case of homogeneous nucleation, where: 2J Rcr 'GQ (1) 'G cr
16SJ 3 3 'G Q
2
(2) where Ȗ is surface tension. The increment of the thermodynamic potential that is necessary for the creation of critical nucleus on the plane surface for the contact angle 4 is given by equation: 16SJ3 1 2 'G cr 2 cos 4 1 cos 4 2 4 3 'G Q (3) In a case of spherical surface maximum value of free energy are given by the following equation: 'G cr
16SJ 3 3 'G Q
2
S 4, <
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(4)
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where S is a coefficient dependent on wetting angle Ĭ and surface refraction angle Ȍ.
3 Experimental methods 3.1 Contact method Contact method is based on determination of numerical values of parameters of roughness profile as well as its presentation in a form of profilogram of known vertical and horizontal magnification. In the experiment a needle of a known geometry, moving along the surface with a constant speed is used. Its vertical displacements are converted into electrical signals. These amplified signals are then recorded in a form of profilogram. Measuring needle is made in form of a cone ended with a spherical cap of a radius r. Application of measuring needle of certain value of radius determine the level of accuracy of the profile representation. In the presented investigation a needle of radius ri = 5µm has been used, though precise measurement of very smooth surfaces require smaller radius of ri = 1µm. The vertical angle of a needle was 90° ± 5°. Shape of the needle affects the applied pressure during the measurement. Contact deformations between needle and peaks of the rough surface, due to small forces applied, have an elastic character and have values of order of hundredth or tenth of µm. For the purpose of this investigation profile-meter Rank Taylor Hobson Leicester T85001 has been used to determine the following parameters: Ra, Rq, Rtm, Rpm. Accuracy of the equipment was in a rage of ± 2%, its resolution 0.01µm, range of vertical displacements – 8mm and the range of lateral displacements -120mm. 3.2 Optical method (laser method) As widely published before, light emitted by laser can be successfully used in the studies and metrology of surface roughness [5–7]. The theory of the diffraction of electromagnetic radiation by the rough surface can be used to establish the relationships between the surface parameters and the field parameters of the reflected electromagnetic wave (intensity of reflected and dissipated light, indicatrix). The most general model of surface from the practical point of view is the one with roughness parameters treated as random process. The solution of such a problem simplifies to determination of random characteristics of the dissipated field of electromagnetic wave. The theory of dissipation of electromagnetic field by the rough surface was comprehensively presented by Beckmann and Spizzichino [8]. The most commonly adopted roughness parameters are: the mean arithmetic deviation of profile Ra, the mean square deviation of profile V and the length of correlation T. The choice of the method for the determination of parameters of the reflected (dissipated) electromagnetic wave depends on the boundary conditions associated with geometry of the surface micro-roughness and the length of electromagnetic wave. For the need of this study the principles of the Kirchoff WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
294 Computational Methods and Experiments in Materials Characterisation III method have been adopted. The intensity of reflected light in a mirror direction can be therefore determined from the equation: I
Z
§ 16S 2V 2 · r (T ) I o exp¨ cos 2 4 ¸ 1¸ 1 ¨ O2 © ¹
(5)
where: r(41) is the coefficient of reflection from ideally smooth surface Io is the intensity of light incidencing at the angle 41. If the component of the diffusive reflection (in mirror direction) is small compared to mirror component then the following equation can be obtained from:
V
O 4S cos 4
(6)
Therefore the estimation of such an angle 4 for which the mirror component is not seen on the background of diffusive component, enable determination of the mean deviation of profile ı. 3.3 SEM method (modulation Y) It is well known fact that media heated up to a temperature above absolute zero emit radiation. The laws describing these phenomena do apply only to black body, which is capable of maximum emittance regardless direction and length of wave. This ability is called emissivity and for black body is equal one in any direction and any wavelength. For the real bodies emissivity is always smaller than one and may be different in different directions and wavelengths. Mostly measured and published is total emissivity in the normal direction ET,n. Technical black body (model of black body) is usually built of metals, heat resisting alloys and ceramics. Any body in natural environment has total emissivity to semi space ET smaller than one. In order to obtain effective emisssivity ET,E from the emitting surface of the technical black body very close to unity, the effect of cavity has been applied. The open area of cavity (emitting opening) Ao has much grater effective emissivity ET,EF than total emissivity ET of real area of cavity Ar. Effective emissivity rising up with the increase of ratio ȖȦ = Ar/Ao.
Figure 1:
Cavity - cross-section of a surface.
Emissivity of any body, due to the physical and chemical processes resulting from temperature and humidity changes as well as time, constantly changes. A characteristic feature, which is independent upon type of material, is changing WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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emissivity and roughness. Generally speaking emissivity increases with the increase of surface roughness. If it is assumed that the roughness consist of set of micro cavities and the measure of unevenness is represented by parameter ȖȦ,, then ET,n is changing according to the equations given below: 2
ET .n
§ Ry · ET ,n ,0 1 4¨¨ ¸¸ © Sm ¹ 2 § · § Ry · ¨ ¸ 1 ¨ 1 4¨¨ ¸¸ 1¸ ET ,n , 0 ¨ ¸ © Sm ¹ © ¹
(7)
or
ET .n
ET ,n ,0 1 J Z 1 ET ,n, 0
(8)
where: Ry – average height of unevenness, Sm – average spacing of unevenness, ET,n,o – total emissivity in normal direction. The above equation are true regardless the type of material. Parameter ȖȦ can be a measure of surface roughness since it is a function of parameters characterising geometrical microstructure of surface Ry and Sm. For the purpose of microstructural analysis of surfaces SEM BS300 has been used. The magnified profile of micro-roughness of surfaces has been obtained by “modulation Y”. In principle it is based on application of proportionality between vertical deviation of lines and brightness of scanned images. Brightness depends on chemical composition of analysed layer and geometrical microstructure. Therefore, for the constant chemical composition of surface layer, any deviation of line depends only on geometrical microstructure. Value of magnification in direction Y requires therefore calibration. Cavity can be also determined in simplified way by using the ratio below: ȖȦ = Lr/Lo
(9)
where: Lr – real length of the profile, Lo – geometrical length of the profile. The method, therefore, is based on the measurement of real length of profile on the specified section of geometrical length.
4
Material tested
The experiment has been performed on surfaces of glass samples (BK7). Samples have been prepared in form of discs with diameter 50mm and thickness of 4mm. Surfaces have been sanded with sand of different size particles resulting in different roughness – 100 (sample no 1), 150 (sample no 2), 360 (sample no 3), 500 (sample no 4) and 700 (sample no 5). Roughness of the samples have WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
296 Computational Methods and Experiments in Materials Characterisation III been assessed by contact method, optical method and after covering with thin layer of gold also by modulation Y method, with application of SEM. Physical properties of glass BK7: Ɣ density: 2510 kg/m3 Ɣ average coefficient of linear expansion in temperature rage 293-393K: 7.1·10-6 K-1 Ɣ specific heat under the constant pressure (0.10135MPa) and temperature 299K: 858 J/kgK Ɣ coefficient of thermal conductivity in temperature 293K: 1.10 W/mK Ɣ optical transmittance in range 0.37-1.5 µm: 0.1 cm-1 Ɣ coefficient of light refraction for wave 0.6328 µm : 1.51509 Ɣ temperature coefficient of light refraction for wave 0.6439 µm in the temperature range 213-293K : 0.5·10-6 K-1
5
Experimental results
Analysis of geometrical microstructure of samples surfaces showed clear differences between roughness parameters determined by three methods. Different methods characterised with different level of accuracy. Results roughness parameters obtained by contact method for five different glass surfaces varied significantly. The length of elementary section Lc was 0.70mm. The main parameters of measured profile are shown in Table 1. In optical method experiment was based on determination of such an angle 4 for which the mirror component is not seen on the background of diffusive component. This enabled determination of the mean square deviation of profile and mean arithmetic deviation of profile. The results of surface roughness obtained form optical method are presented in Table 2. Application of the Scanning Electron Microscope allowed to analyse not only the images of different surfaces, but also randomly selected three profiles in a central part of sample, obtained by modulation Y method. The values of cavities ȖȦ have been determined for different profiles Y and presented in Table 3. Table 1:
Main parameters measured by contact method.
Surface No.
Ra [µm]
Rq [µm]
Ry [µm]
Rtm [µm]
Rpm [µm]
Sm [µm]
Ĭw [deg]
mw [1/mm]
1
3.90
4.80
26.00
22.00
10.00
10.7
36
36
2
3.12
3.88
20.40
17.60
9.40
3.90
58
45
3
1.32
1.71
10.10
8.80
3.90
1.23
65
57
4
0.91
1.15
6.88
6.26
2.42
0.55
73
93
5
0.55
0.68
4.08
3.58
1.58
0.10
85
84
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Table 2: Surface No
6
Main parameters measured by optical method.
1 2
Ĭo [deg] 88.50 88.00
ı [µm] 5.81 4.52
Ra [µm] 4.64 3.61
3
86.50
2.11
1.68
4
84.00
1.82
1.45
5
78.00
1.12
0.89
Table 3:
297
Cavities measured by SEM method.
Surface No
ȖȦ1
ȖȦ2
ȖȦ3
1 2 3 4 5
4.20 4.33 4.56 4.02 4.38
3.42 3.81 4.44 4.64 5.08
3.46 4.12 5.27 4.08 4.90
Discussion and final remarks
Based on the experimental results it is possible to identify set of parameters of particular importance. It has been assumed that the following parameters can be used to describe geometrical microstructure of surfaces: mean arithmetic deviation of profile Ra; mean square deviation of profile from the mean line Rq; height of the profile peaks measured by ten points Ry; maximum height of profile peaks Rmax; mean spacing between profile peaks Sm; average angle of peaks inclination Ĭw; number of peaks in the profile mw. From the above group it is possible to select certain parameters particularly useful from practical point of view. Comparison of the results obtained from contact method: Ra, Ry, Rq, Rtm and Rpm (see Fig. 2) give clear evidence of variation in values for different samples. Vertical parameters of profile are usually characterised by mean arithmetic deviation of profile Ra and mean square deviation of profile from mean line Rq. In the case of the roughness assessment by optical method, firstly the average value of unevenness h is experimentally determined, and then it is possible to estimate Ra and ı, which is effectively equal to Rq. The results have been presented in Figure 3.
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298 Computational Methods and Experiments in Materials Characterisation III
Roughness Parameters [um]
30 25 Ra
20
Rq Ry
15
Rtm
10
Rpm
5 0 1
2
3
4
5
Surface Number
Figure 2:
Values of the main roughness parameters – contact method.
Roughness Parameters [um]
7 6 5 4
Rq
3
Ra
2 1 0 1
2
3
4
5
Surface Number
Figure 3:
Values of the main roughness parameters – optical method.
Gam ma Value [um]
6 5 4 3 2 1 0 1
2
3
4
5
Surface Number
Figure 4:
Roughness parameter “gamma” – modulation Y method.
Results obtained from microscopic method very clearly confirm the variations in roughness characteristics of tested surfaces and can be successfully used in comparative studies (Fig. 4).
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The measurements in the Modulation Y method are restricted to determination of parameter ȖȦ, which is the ratio of the real profile length to the geometrical length of profile, and is not a sufficient on its own to describe the geometrical microstructure. The following average results for samples 1 to 5 have been recorded: 3.69; 4.09; 4.72; 4.49 and 4.79. With the exemption of surface no.4 the cavity values showing a tendency to progressive increase, giving the same an evidence of more and more developed surfaces. The main disadvantage of the method for considered application is the fact that the method does not allow direct measurement of parameters such as Ra, Rq, Sm, Ĭw and therefore it is not recommended on its own for analysis of the condensation process kinetics. Parameter Ra determined by both contact and optical methods seems to be of the similar order. Figure 5 presents the relationship between values of Ra obtained for these methods. Figure 6 presents the average results of mean distance between unevenness Sm, average angle of peaks inclination Ĭw, and number of peaks in the profile mw obtained from contact method. 4.5 Ra - Contact Method
4 3.5 3 2.5 2 1.5 1 0.5 0 0
1
2
3
4
5
Ra - Optical method
Comparison of parameter Ra measured by contact and optical methods.
Roughness parameters
Figure 5:
100 90 80 70 60 50 40 30 20 10 0
Number of peaks Distance between peaks Angle of peaks inclination
1
2
3
4
5
Surface Number
Figure 6:
Roughness parameters from contact method.
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300 Computational Methods and Experiments in Materials Characterisation III Number of peaks in a profile mw plays an important role in the overall assessment of surfaces from the point of view of likelihood of water vapour condensation. However in the analysis of the kinetics of individual nucleus creation, mw is only of the secondary importance.
References [1] CIBSE guide. “Moisture transfer and condensation” CIBSE 1986 [2] Klemm P., Gawin D., “Approximated Mathematical Model of Coupled Transport of Mass and Heat in Building Partitions” CPBP 02.21.1.27, Lodz, (1987) (in Polish) [3] Klemm AJ, Klemm P, Rozniakowski K, Galbraith G H “Non-contact methods of measuring moisture concentrations in external layers of building partitions. I – The influence of geometrical microstructure on the kinetics of moisture condensation on glass surfaces” Building and Environment, Vol.37, No12, pp. 1215-1220, 2002 [4] Klemm AJ, Klemm P, Rozniakowski K, Wojtatowicz T “Non-contact methods of measuring moisture concentrations in external layers of building partitions. II – Monitoring of the water vapour condensation on porous surfaces” Building and Environment, Vol.37, No12, pp.1221-1232, 2002 [5] Drobnik A., Rozniakowski K., Wojtatowicz T.W., “Contactless investigations of the porous materials with the aid of a He-Ne laser light” Kv.Elektr., Vol.22, no.7, (1995), p.741 [6] Rozniakowski K, Klemm P, Klemm A J “Some experimental results of laser beam interaction with surface layer of brick” – Building and Environment, Vol. 36, No.4, pp. 485 – 491, 2001 [7] Rozniakowski K., “Laser investigations of electrotechnical steel surface roughness”, Optica Applicata, vol.22 (1992), pp.137-142 [8] Beckmann P., Spizzichino A., “The scattering of electromagnetic waves from rough surfaces”, Pergamon Press, New York, 1963
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Use of impedance spectroscopy to determine the displacement of water in cement paste under small loads I. Sánchez1, G. Castro2, M. A. Climent1 & X. R. Nóvoa3 1
Departament d’Enginyeria de la Construcció, Obres Publiques i Infraestructura Urbana, Universitat d’Alacant, Spain 2 Departamento de Materiales y Procesos de Fabricación, Centro Tecnológico AIMEN, Spain 3 Departament Enxeñería Química, Universidade de Vigo, Spain
Abstract The effect of mechanical loading in concrete structures may cause deformation by creeping. The physical origin of this phenomenon is not well known, but water seems to play an essential role in it. Impedance spectroscopy in the high frequency region can detect water movements towards empty pores, even when the applied load is small. In this paper a system for application of mechanical loading compatible with simultaneous impedance spectroscopy measurements is presented. The effect of several parameters (ageing, water to cement ratio, water content) on cement paste samples’ performance under mechanical loading is analysed through the corresponding impedance spectra. Keywords: impedance spectroscopy, cement paste, microstructure, dielectric properties, mechanical loading.
1
Introduction
Real concrete structures are designed to be mechanically loaded. The effect of the deformation of a structure under a constant load is called creeping and is a classical phenomenon well described in the literature [1, 2]. This effect has a great dependency on some factors such as temperature and relative humidity [1, 3]. The microstructural mechanism that leads to the effect of creeping is still not well known, although water plays an essential role in almost every theory on WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/MC070301
302 Computational Methods and Experiments in Materials Characterisation III the subject [4]. This phenomenon is related to microstructure of cementicious materials. In recent years impedance spectroscopy has been adopted as a technique to study the microstructure of cementicious materials, due to the possibility of correlating dielectrical and mechanical properties [5, 6]. Even though the first works on this field considered de presence of only one time constant in the high frequency loop of the impedance spectra [7, 8] it has been shown that two time constants are present [9]. This has been done using a numerical technique, differential impedance analysis, which does not require previous knowledge about the material studied [10, 11]. The two time constants have been associated to the two phases present in the material. The high frequency time constant was associated to the solid phase, while the low frequency one was associated to the electrolyte filling the pores. This association has been proved using different experiments [12]. If water has something to do with creeping, then the time constant associated to the electrolyte will vary during loading and unloading of samples. A work published in 2003 showed the effect of mechanical loading on the dielectric properties of cement pastes [13]. This effect consisted in an increase of the capacitance and a decrease of the resistance associated to the electrolyte in pores, and was interpreted in terms of water displacements to empty spaces in the microstructure of the material. In this work, some parameters of the samples are varied and the effect of loading is studied. The load was applied using a new system designed for this application.
2
Experimental
2.1 Sample preparation Samples were prepared using CEM I 52.5R cement according to the Spanish standard UNE 80303:96. Two different water to cement ratios, 0.5 and 0.7, were employed. The mixtures were cast in cylindrical moulds of 5.9 cm diameter and 20 cm height. Samples were kept in 100% RH chamber and demoulded after one day setting. Several discs, thickness form 3 to 10 mm, were cut from those cylinders for the impedance spectroscopy measurements. The remaining material was used for mercury intrusion porosimetry determinations. 2.2 Mercury intrusion porosimetry Mercury intrusion porosimetry (M.I.P.) was used to determine the time evolution of the microstructure of cement paste samples, in order to validate the microstructural modifications detected with the impedance spectroscopy measurements. Even though there are many facts suggesting that this technique is not optimal for pore size measurement [14, 15], it is widely used to determine pore sizes and distributions. The pore structure of different samples, at different time of exposure to chloride migration was determined using this technique, which is based on the
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Washburn law, where a relation between applied pressure, P, and pore diameter, D, is given, under the hypothesis of cylindrical pores, by Equation (1).
D
4J cos T P
(1)
where Ȗ is the surface tension of the mercury (0.485 N·m-1, at room temperature) and ș is the contact angle. There has been recently some discussion on the effect that different types of drying have on the MIP measurements [16, 17]. In this work samples were vacuum dried for 48 hours and then kept in oven at 50ºC. This procedure assures that no structural water is evaporated. With this preparation, the chosen value for the contact angle was 130º. To ensure that samples used for this measurements were representative they were cut off core cylinders with irregular and random shapes. The porosimeter employed was an AUTOPORE IV 9500 from Micromeritics. This porosimeter allows pore diameter determination in the range from 5 nm to 0.9 mm. It has to be considered, as reported by Diamond [14, 15], that only the dimensions of the pore superficial structure can be detected by MIP, and the irregularities in pore shape cannot be determined. Nevertheless, information on the possible tortuosity of pore network can be obtained from the mercury retained in the sample after the end of the porosimetry measurement. The experiment is quite simple, after getting high vacuum in the recipient containing the sample, the reservoir is filled with mercury, and the intrusion step starts. The pressure applied on the mercury is fixed by the user, and that value of pressure is hold for 10 seconds to permit the mercury filling the pores having the corresponding diameter. The measurement of the volume that penetrates for each pressure gives the amount of pores with the corresponding size [18]. The analysis of the curve in which the logarithmic differential intrusion volume is plotted vs. pore size (or applied pressure), shows the size ranges where pores appear. It is possible to determine the number of pore families that exist in the sample, and the contribution of each one to the total porosity of the sample. A first step consists in fitting the experimental curve to a function including a number of Gaussians equal to the number of peaks present in the curve. The result of this fitting is the central pore diameter for each pore family. The area under each Gaussian curve is related to the contribution of the corresponding pore family to the total porosity. The intrusion curve allows one to determine the volume of mercury intruded in the sample in a particular pressure range. The division of this volume by the overall intrusion volume gives the contribution of the corresponding pore family to the total porosity of the sample. 2.3 Impedance spectroscopy Impedance spectra of samples were obtained using the method that avoids contact between sample and electrodes, as described in [13]. The electrodes used were of flexible graphite, attached on copper plates of 4 cm diameter, and a foil of polymer was interposed between the graphite sheet and the sample. The thickness of this foil was 100 Pm. The impedance analyzer used was an HP4194-A. It permits the measurement in a frequency range from WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
304 Computational Methods and Experiments in Materials Characterisation III 100 Hz to 40 MHz. The impedance analyzer allows measurements in a capacitance range from 10-14 F to 0.1 F with a precision of 10-15 F. The impedance spectra measured are almost purely capacitive, as can be seen in fig. 1(A). A more clear representation corresponds to the Cole-Cole transformation given in fig. 1(B). The equation for this transformation is eq (2).
C Z
1 j·Z·Z Z
(2)
The impedance spectra in their Cole-Cole representations were fitted to the equivalent circuit already proposed [13]. The fitting to the model was done using a simplex method already described [19]. 300
18
A)
-Imaginary part
-Imaginary part
14
100 kHz
200 150 100 50 0
1 MHz 50
100
150
200
250
300
350
2
Real part, k:·cm
Figure 1:
12 10 8
1 MHz
10 MHz
6 4 2
10 MHz 0
B)
16
250
400
0
0
2
4
6
8
10 12 14 16 18 20 22 24
Real part, pF/cm
2
(A) Impedance spectrum obtained for a cement paste sample with w:c ratio of 0.5 and 0.4 cm thickness. (B) Cole-Cole diagram corresponding to (A).
2.4 Mechanical loading system The objective of this work makes necessary the design of a system to apply mechanical load in a controlled way during the impedance spectroscopy measurements. The main problem that appears when the impedance spectra are measured at such high frequencies comes from the wire’s inductance. This fact makes necessary to use connecting cables as short as possible. Thus, it is necessary to design a mechanical loading system to be placed close enough to the impedance analyzer, and that permits the application of known loads. The system designed for that purpose is shown in Figure 2(a). A steel spring is mounted on a mobile screw. A first step consisted in the determination of the elastic constant of the spring. For that purpose, the spring was compressed using a universal testing machine. The values of force and the reduction of length were registered and are shown in Figure 2(b). As it can be seen, the data show linear behaviour, and the slope corresponds to the elastic constant of the spring. So, just measuring the distance that the spring has moved, with a calibre of 10 Pm precision, the applied force can be easily obtained using Hook’s law. The stress is applied to the sample moving a certain distance the screw and the force is applied through the electrodes used for the impedance spectroscopy measurements. The stress applied can be calculated using equation (3) WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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k ·'x (3) S where x is the compression of the spring, in mm, S the electrode surface (12.56 cm2 in this case) The application of load during the impedance spectra measurements is done in the growing sense. The first impedance measurement is obtained at 0 MPa load, calculated as explained before. Then pressure is applied at regular steps until the end of the experiment. V
a)
b) 1000
Force, N
800
Measured data Linear fit: F= 374.59·'x-1.55 r=0.99
600 400 200 0 0,0
0,5
1,0
1,5
2,0
2,5
3,0
Length diminuition, mm
Figure 2:
3
Loading system used and calibration employed for the calculation of the elastic constant.
Results and discussion
Three variables have been taken into account to validate the hypothesis of water moving to empty pores. These parameters are water to cement ratio, sample thickness and age of the sample. The effect of each of these parameters has been analysed. The evolution of the microstructure during setting and hardening was followed using mercury intrusion porosimetry. 3.1 Mercury intrusion porosimetry results Mercury intrusion porosimetry measurements were done on cement paste samples of water to cement (w:c) ratios of 0.5 and 0.7. The results for the total porosity are shown in Figure 3. As it is easily seen, the value of the porosity is always higher for the w:c ratio of 0.7 and has a clear decreasing tendency with time for both ratios. The analysis of the logarithmic differential intrusion volume as a function of the pore diameter shows the presence of four different pore families for the w:c=0.5, and 3 families for samples with w:c=0.7. The evolution of the central diameters for each family, and the contribution to the total porosity are shown in Figure 4. The central pore sizes have in general a slightly deceasing tendency, but the most important fact that can help us in the understanding of the dielectrical behaviour of samples is the observed change in the contribution to the total porosity of the families for w:c=0.7. The family with the biggest size and the one with the smallest one change their relative contribution at about the WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
306 Computational Methods and Experiments in Materials Characterisation III 10th day. This result will be used during the discussion of the effect of age on the influence of the mechanical loading on the impedance spectra of cement paste samples. 44
w:c =0.5 w:c=0.7
Total porosity, %
42 40 38 36 34 0
5
10
15
20
25
30
35
40
45
Hardening days
Figure 3:
Evolution of the total porosity with the age of cement paste samples. w:c=0.5
w:c=0.7
Fam. 1 Fam. 2 Fam. 3 Fam. 4 (/10)
500 400 300 200 100 0 65 60 55 50 45 40 35 30 25 20 15 10 5 0
0
5
10
15
20
25
30
0
5
10
15
20
25
30
Hardening days
Figure 4:
35
40
45 Contribution to total porosity, %
Contribution to total porosity, %
Central pore diameter, nm
600
Central pore diameter, nm
800
700
35
40
45
700 600 500
Fam. 1 Fam. 2 Fam. 3
400 300 200 100 0 55
0
5
10
0
5
10
15
20
25
30
35
40
45
15
20
25
30
35
40
45
50 45 40 35 30 25 20 15 10 5
Hardening days
Evolution with time of pore diameters and contribution of each family to the total porosity.
For the w:c ratio 0.5, 4 pore families can be found. An important result is that family four has pore sizes greater than any pore present for w:c ratio 0.7, but the contribution to the overall porosity is not important. These results will be used for the interpretation of the impedance spectra of cement paste samples under mechanical loading.
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3.2 Impedance spectroscopy results The influence of each one of the factors has been studied separately. The main results are presented in the following subsections. The variations of all the parameters present in the equivalent circuit have been studied. As expected, the high frequency capacitance C1, associated to the solid phase, do not vary with applied load, as it has already been reported [13]. A common point for all samples is that the capacitance C2 increases and R2 decreases as the mechanical load applied to the sample increases. This fact has been explained in terms of water movement to the empty pores [13]. The influence of sample thickness and w:c ratio was studied with daily impedance measurements. For the sake of simplicity only the evolution of C2 will be discussed. 3.2.1 Influence of hardening time. The evolution of the variations of the dielectric parameters was followed during the first 40 days hardening. The effect can be seen in figure 5 for both w:c ratios tested. The effect of loading decreases as hardening progresses, except for day 2 with the w:c ratio of 0.5. This result matches with M.I.P. The decrease in the value of total porosity means that the space occupied by empty pores decreases, and the influence of loading is not so important. 80
2 days 4 days 18 days
70 60
70 60
40
50
2
C2, pF/cm
C2, pF/cm
2
50
30 20
2 days 4 days 18 days
30 20
10 0 -2000
40
10
0
2000
4000
6000
8000
10000
0
2000
Applied load, MPa
Figure 5:
4000
6000
8000
10000
Applied load, MPa
Effect of hardening age on the influence of mechanical loading on the dielectrical properties of cement paste samples. w:c ratio of 0.5 was used for the sample on the left, while 0.7 was the w:c for the sample on the right.
Another factor that can be taken into account is that during the hardening processes structures with higher resistance to load are developed, and in consequence the transmission of loading is less effective. The effect observed for the w:c=0.5 at the second day can be justified in terms of the fraction of empty pores that can contribute to the increase in C2. The value obtained for the capacitance is really high, much higher than for the 4th and the 18th days. This means, as the results are depicted for the same sample, that at day 2 the sample is almost water-saturated, as proved by the high value obtained for the capacitance C2 without applied load. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
308 Computational Methods and Experiments in Materials Characterisation III 3.2.2 Influence of water:cement ratio The first factor that has a clear influence on the dielectric response of the samples, is the w:c ratio, and in consequence the sample porosity. Figure 6 shows the influence of w:c ratio on the effect of mechanical loading for two different ages. The first one corresponds to 2 days maturing age, while the second one corresponds to 40 days age. As it can be observed in both figures, the value of C2 is greater for 0.7 w:c ratio than for w:c=0.5. This result can be easily explained in terms of porosity. The volume of pores is greater at any age for w:c=0.7, and the capacitance C2 has been associated to the interface solid-electrolyte. The greater the porosity is, the more surface of pores exists in the sample. It also coincides with the theory of water movement. The more electrolyte is in the sample, the higher the possibility of water movement. 200
80
180 w:c=0.5 w:c=0.7
160
2
60
120
C2, pF/cm
C2, pF/cm
2
140
w:c=0.5 w:c=0.7
100 80 60
40 20
40 20
0
0
1000
2000
3000
4000
5000
0
Applied load, MPa
Figure 6:
2000
4000
6000
8000
Applied load, MPa
Effect of water:cement ratio on the changes observed in the low frequency capacitance, C2 , at two different ages, 2 days (left) and 40 days hardening (right).
At 45 days age the slopes of the capacitance vs. load for both w:c ratios are more similar. This result coincides with the classical theory for creeping in concrete, which predicts a smaller influence of load on hardened concrete, and also coincides, with the decrease in the total porosity. The slope found for w:c=0.7 is smaller than for w:c=0.5, in agreement with mercury intrusion porosimetry results, that showed a change in the relative contribution of the different pore families. After the 10th day the smallest pore family increases its contribution to the overall porosity. So, most of the porosity is distributed on small pores, that have a smaller contribution to the variations of this capacity, because the space reachable by water in movement is not very big. 3.2.3 Influence of the sample thickness Samples of different thickness were studied, for the same w:c ratio, and at the same age. It has already been shown [9] that the value of the capacitance C2 increases as the thickness of the sample does. This means that this capacitance is not of dielectric nature. The influence of sample thickness when the sample is subjected to mechanical loading can be seen in Figure 7. As it could be expected, an increase in sample thickness leads to smaller influence of mechanical loading on the low frequency capacitance. It is easily WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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explainable in terms of the water movement towards empty pores. The mechanical stresses have more difficulty to transfer when the sample is thicker. This fact has been proved for both w:c ratios. 140
240
3 mm
120 100
2
C2, pF/cm
C2, pF/cm
2
5mm
80 60 40
8 mm
160 120
8 mm
10000
15000
80
0 0
2000
4000
6000
8000
0
Applied load, MPa
Figure 7:
4
5mm
40
20 0
3 mm
200
5000
Applied load, MPa
Effect of sample thickness on the changes observed in the low frequency capacitance, C2, at two different ages, 2 days (left) and 40 days hardening (right).
Conclusions
The main conclusions that can be obtained from the results previously discussed can be summarized as follows x A system for applying a known load allowing simultaneous high frequency impedance measurements has been designed and proved. x The role of water is important in the creeping of cementitious materials. Several factors have been modified to study their influence on material’s dielectric properties under mechanical loading. x The effect of the possible water movements decreases with the hardening time. x The effects of loading on dielectric properties are more important for more porous samples (higher w:c ratio). x Sample’s thickness is also of importance as it concerns the effect of mechanical loading. The effect decreases in thicker samples.
Acknowledgements This work has been financially supported by the Generalitat Valenciana through project GV05/196, and by the Ministerio de Educación y Ciencia of Spain and Fondo Europeo de Desarrollo Regional (FEDER) through project BIA200605961. Dr I. Sánchez is indebted to the abovementioned Spanish Ministry for a fellowship of the “Juan de la Cierva” programme.
References [1]
I. Soroka. Portland Cement Paste and Concrete. MacMillan, London. (1979) 46-72 WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
310 Computational Methods and Experiments in Materials Characterisation III [2] [3] [4] [5] [6] [7]
[8]
[9] [10] [11] [12] [13] [14] [15] [16]
M.S.J. Gani. Cement and Concrete. Chapman & Hall, London. (1997) 112-116. A.M. Neville, W. H. Dilger, J.J. Brooks. Creep of plain and structural concrete. Construction Press, Londres (1983) 361 B. T. Tamtsia, J. J. Beaudoin. Basic creep of hardened cement paste. A reexamination of the role of water. Cem. Concr. Res 30, pp 1465-1475 (2000) W.J. McCarter, R. Brousseau, The a.c. response of hardened cement paste, Cem. Concr. Res. 20 (1990) 891–900. P. Gu, P. Xie, Y. Fu, J.J. Beaudoin, A.C. impedance phenomena in hydrating cement systems: Frequency dispersion angle and pore size distribution, Cem. Concr. Res. 24 (1994) 86– 88. R.T. Coverdale, B.J. Christensen, T.O. Mason, H.M. Jennings, E.J. Garboczi, Interpretation of the impedance spectroscopy of cement paste via computer modelling: Part II. Dielectric response, J. Mater. Sci. 29 (1994) 4984–4992. R.A. Olson, B.J. Christensen, R.T. Coverdale, S.J. Ford, G.M. Moss, H.M. Jennings, T.O. Mason, E.J. Garboczi, Interpretation of the impedance spectroscopy of cement paste via computer modelling: Part III. Microstructural analysis of frozen cement paste, J. Mater. Sci. 30 (1995) 5078– 5086. M. Cabeza, P. Merino, A. Miranda, X.R. Novoa, I. Sanchez. Impedance spectroscopy study of hardened Portland cement paste. Cem Concr Res 32 (2002) 881–891. D. Vladikova, Z. Stoynov, L. Ilkov, Differential impedance analysis on single crystal and polycrystalline Yttrium iron garnets, Pol. J. Chem. 71 (1997) 1196– 1203. Z. Stoynov, Differential impedance analysis. An insight into the experimental data, Pol. J. Chem. 71 (1997) 1204– 1210. I. Sanchez. Aplicación de la espectroscopía de impedancia a la determinación de la microestructura y propiedades mecánicas de la pasta y mortero de cemento Pórtland. Universidad de Vigo (2002) M. Cabeza, P. Merino, X. R. Nóvoa, I. Sánchez. Electrical Effects generated by mechanical loading of hardened Portland cement paste. Cem. Concr. Comp. 25 (2003) 351-356 S. Diamond, Aspects of concrete porosity revisited Cem. Concr. Res., 29, (1999) 1181-1188 S. Diamond, Mercury porosimetry. An inappropriate method for the measurement of pore size distributions in cement-based materials. Cement and Concrete Research. 30 (2000) 1517-1525 C. Galle, Effect of drying on cement-based materials pore structure as identified by mercury intrusion porosimetry. A comparative study between oven-, vacuum-, and freeze drying. Cem. Concr. Res., 31, (2001) 1467-1477
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[17] [18] [19]
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R. Kumar, B. Bhattacharjee, Study on some factors affecting the results in the use of MIP method in concrete research. Cem. Concr. Res., 33, (2003) 417–424 P.A. Webb, C. Orr, Analytical methods in fine particle technologie. Michromeritics instrument corporation. Norcross GA, USA 1st edition (1997) 155-198 M. Keddam, H. Takenouti, X. R. Nóvoa, C. Andrade, C. Alonso. Impedance measurements on cement paste. Cem. Concr. Res. 27 (1997) 1191-1201
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Assimilation of porosity in modern bricks by computational means M. A. Stefanidou Department of Civil Engineering, Aristotle University, Thessaloniki, Greece
Abstract The study of porosity in building materials is important as porosity is connected to macroscopic mechanical and physical properties which influence the structure behaviour. A world-wide, simple, quick and low-cost method of recording porosity is through water absorption (RILEM CPC11.3). However, in the case of bricks there is a main disadvantage to using the above mentioned method. The clay material absorbs water and the results are altered. In that case another liquid (maybe an organic solvent) is usually used. This method though, is loosing its creditability and no comparisons can be made with other building materials which are in co-operation with bricks. Alternatively, in the present work, microscopic analysis through computational means using image analysis is used in order to record porosity in bricks of modern technology. These porosity values are statistically elaborated in order to estimate open porosity which is usually measured using a liquid adsorption. At the same time the geometry of pores and the pore size distribution are recorded. Keywords: bricks, porosity, water absorption, microscopy, image analysis.
1
Introduction
Bricks are one of the most ancient construction materials as they were used in the Mediterranean countries for 5 thousand years (Papayianni, Stefanidou [1]). They were used in combination with stone and mortar in the construction of masterpieces such as churches (for example Hagia Sophia 4-6th century A.D.), protective city walls and also in humble constructions as houses. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/MC070311
314 Computational Methods and Experiments in Materials Characterisation III The technology of brick production totally changed after the 19th century when industrial methods were introduced (Gerogiannis [2]). From that point, the brick properties have changed as strength has been increased and consequently the porosity has been decreased (Papayianni and Stefanidou [3]). In order to record the porosity of bricks different indirect methods are used such as water absorption, mercury porosimeter and nitrogen absorption [4]. All those methods are recording the open porosity that is interconnecting pores which arrive to the surface of the material (Meng [5]). Porosity has different forms according to the technology used for the bricks construction as is seen in figure 1.
Figure 1:
Pores of different size and proportion in the brick structure.
The present paper is a pilot effort to connect the porosity measured by direct ways (through microscopy and image analysis) with the porosity measured by indirect ways such as those mentioned above in modern technology bricks. It is an attempt to correlate total porosity measured microscopically with the open porosity which is recorded through liquid absorption.
2 Experimental methods Thirty brick samples of ten different brick qualities were tested in order to record their mean porosity both by direct and indirect ways. A modified method of the RILEM CPC11.3 was followed in order to estimate open porosity. The original method suggests water as the solvent. In the case of bricks though, water introduces significant error (table 1) as the clay absorbs an adequate quantity of water. Water is substituted by an organic solvent such as heptane. Heptane has a specific gravity 0.68 at the temperature of 20oC at which all the experiments were performed. At the same time, the samples were tested microscopically using a Leica M10 stereoscope at x8 magnification and a LIDA image analysis system. From each sample 6 measurements were performed and the mean total porosity was measured as recorded in table 1.
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Table 1:
1 2 3 4 5 6 7 8 9 10
315
Porosity measurements using different methods.
% porosity (water absorption) 11.59 7.1 12.19 7.09 16.13 11.82 6.95 12.84 6.57 15.68
% porosity (heptane) 5.86 3.97 6.21 3.34 7.84 7.76 5.44 7.61 4.64 10.04
Difference (waterheptane) % 49.45 44.13 49.03 53.01 51.39 34.33 21.77 40.77 29.50 36.01
% porosity (microscopy) 4.53 1.74 4.10 0.56 5.80 6.65 4.66 6.85 1.93 8.90
An attempt to elaborate statistically the results of the two methods (we consider as Y the open porosity recorded by liquid absorption and X the porosity measured by the microscopic method) shows that there is a linear relationship expressed as shown in Figure 2. Correlation of porosity based on two methods y = 0.7688x + 2.756
12.00
R2 = 0.9473
%porosity(absorpti
10.00 8.00 6.00 4.00 2.00 0.00 0.00
2.00
4.00
6.00
8.00
10.00
% porosity (micoscopy)
Figure 2:
Linear relationship between porosity values of two different methods.
In that case the equation (1) is suggested: Y= 0.7688X+2.756 R2= 0.947
(1)
In order to test the creditability of equation (1), a theoretical porosity was estimated using as X the microscopic values. Comparison between the theoretically estimated porosity and the open porosity measured experimentally shows good relationship (table 2). WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
316 Computational Methods and Experiments in Materials Characterisation III Table 2:
1 2 3 4 5 6 7 8 9 10 average *a= 0.7688 b= 2.756 Table 3:
Theoretical calculation of porosity using the equation 1. % porosity (heptane) 5.86 3.97 6.21 3.34 7.84 7.76 5.44 7.61 4.64 10.04 6.27
Theoretical Porosity (eqn (1)) 6.24 4.09 5.91 3.19 7.22 7.87 6.34 8.02 4.24 9.60 6.27
Porosity (Heptaniotheoretical) -0.38 -0.12 0.31 0.15 0.63 -0.11 -0.90 -0.41 0.40 0.44 0.00
Ȝ (Hept./theoret) 0.94 0.97 1.05 1.05 1.09 0.99 0.86 0.95 1.09 1.05 1.00
Geometrical characteristics of pores of modern bricks.
1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 average
L (length, µm) 58.13 30.18 39.63 37.65 61.54 35.42 41.98 39.81 44.80 36.00 42.51
B (breadth, µm) 29.57 18.23 20.16 18.58 29.31 18.60 21.50 19.30 23.60 19.00 21.79
L/B 1.97 1.66 1.97 2.03 2.10 1.90 1.95 2.06 1.90 1.89 1.94
During microscopic observation additional information concerning the length and the width of the pores are recorded in table 3. The information is important considering that pore sizes are related to the materials properties and the behaviour under deterioration (Larbi [6], Fitzner [7]). Measuring the distribution of pores shows that the maximum volume of pores is gathered to the area of 0-55µm (figure 3).
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Pore size distribution in industrial bricks 80.00 70.00 60.00 50.00 % 40.00 30.00 20.00 10.00 0.00 0-55
55- 110- 165- 220- 275- 330- 385- 440- 495110 165 220 275 330 385 440 495 550 length (µm )
Figure 3:
3
Pore size distribution by image analysis in modern bricks.
Conclusions
The simple and easy to understand method of liquid absorption in order to measure the open porosity very often introduces errors especially when water is used as solvent. Other organic solvents are costly especially when there are a large number of samples to be tested. An alternative way to measure porosity microscopically seems that it can give satisfactory results concerning the correlation of the values of porosity measured microscopically, which may be characterized “not practical”, to an understandable and easy to use porosity values. Equation (1) is suggested in order to substitute liquid absorption methods. Taking into account that the size of the samples tested microscopically is small and the time needed to execute the experiments is short, microscopy can be proved to be a quick, easy and affective method for porosity measurements.
Acknowledgements The author would like to express her thanks to Vassilis Papanikolaou, civil engineer and Panos Fikos, mathematician for their assistance during the elaboration of the results.
References [1]
Papayianni I., M. Stefanidou, 1995, “Characteristics of bricks of old masonries” Workshop on Materials for Consolidation and Restoration of WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
318 Computational Methods and Experiments in Materials Characterisation III
[2]
[3]
[4] [5] [6] [7]
Monuments and Historical Buildings: Reading, Interpreting and Recovering the Knowledge of Traditional Materials September, Thessaloniki, pp.35-48 Gerogiannis G. “Record and study of bricks of the 19th-20th century from the area of Thessaloniki” Post-graduates study on Protection, Conservation and Restoration of Cultural Monuments Theesaloniki, November 2006 Papayianni I, Stefanidou M. “Technology and characteristics of fired bricks of 18th-19th century” 1st National Congress on Appropriate interventions for the safeguarding of monuments and historical buildings. Hellenic Ministry of Culture/ 4th Ephorate for Modern Monuments, Technical Chamber of Greece 23-25 Nov. 2000 Thessaloniki, pp. 281-292 ISO 15901:2002 Pore size distribution and porosity of solid materials by mercury porosimetry and gas adsorption Meng B. “Resolution -dependent characterization of interconnected pore systems: development and suitability of a new method” Materials and Structures Vol.27 1994 p.p.63-70 Larbi J.A “Microscopy applied to the diagnosis of the deterioration of brick masonry: Construction and Building Materials, 18, 2004. pp. 299307 Fitzner B. “Porosity analysis -A method for characterization of building stones in different weathering stages” The Engineering Geology of Ancient Works, Monuments and Historical Sites Proceedings of an international symposium organized by the Greek national group of IAEG/ Athens/ 19-23 September 1988 editors P.G. Marinos, G.C. Koukis
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Dynamic tensile test and specimen design of auto-body steel sheet at the intermediate strain rate S. B. Kim1, J. H. Song1, H. Huh1 & J. H. Lim2 1
School of Mechanical, Aerospace and System Engineering, Korea Advanced Institute of Science and Technology, Daejeon, Korea 2 POSCO Technical Research Laboratories 699, Gumho-dong, Gwangyang-si, Jeollanam-do, Korea
Abstract In this paper, the tensile testing method at the intermediate strain rate is established and tensile tests of steel sheets for an auto-body have been performed to evaluate dynamic material properties. A high speed tensile testing machine has been developed for tensile tests at the intermediate strain rate. A simple jig fixture for gripping a specimen has been designed to diminish the load ringing phenomenon induced by unstable stress propagation at the high strain rate. Design of the specimen has to be performed for the dynamic tensile test considering the inertia and wave propagation effect. Finite element simulations are carried out to investigate the geometric effect of a specimen such as the parallel region, the width and the fillet radius. Optimum dimensions of a specimen are determined from the analysis and experiment. The optimum specimen together with the dynamic tensile test machine with the special jig fixture provides an accurate stressstrain curve with negligible load ringing phenomenon. Keywords: intermediate strain rate, dynamic material properties, dynamic tensile test, load ringing phenomenon, tensile specimen.
1
Introduction
The dynamic tensile properties of auto-body steel sheets in an auto-body are important since the range of the strain rate is several tens to hundreds per second under 500/s in a real auto-body crash and at which the dynamic response of steel WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/MC070321
320 Computational Methods and Experiments in Materials Characterisation III sheets is different from static the one [1, 2]. The flow stress, the tensile strength, the work hardening rate and the elongation of steel sheets highly depend on the strain rate in most cases. Therefore, the dynamic behavior of steel sheets must be examined accurately in order to ensure the crash characteristics of an auto-body member with the numerical analysis [3]. In spite of the importance of the dynamic behavior of steel sheets, an appropriate experimental method has not been standardized yet at the intermediate strain rate due to experimental difficulties. At the range of intermediate strain rates from 1/s to 500/s, there has been relatively little study on the dynamic tensile characteristics for steels sheets.
Figure 1:
High speed material testing machine developed in KAIST.
In this paper, a high speed tensile testing machine was developed to investigate the dynamic tensile behavior of steel sheets at the intermediate strain rate. A jig fixture for gripping a specimen has been designed to diminish the load ringing phenomenon induced at the high strain rate. Moreover, the appropriate dimensions of a specimen were selected from the results of both finite element analyses and experiments in order to induce uniform elongation in the gauge section at intermediate strain rates. Using the dynamic tensile testing machine together with the selected specimen, dynamic tensile tests were performed for steel sheets at various strain rates ranged from 0.003 to 200/s.
2
Dynamic tensile test at the intermediate strain rate
2.1 High speed material testing machine The dynamic response at the corresponding level of the strain rate should be obtained with adequate experimental techniques and apparatus due to the inertia effect and the stress wave propagation. Several loading methods such as mechanical, pneumatic and servo-hydraulic types have been utilized to measure the mechanical properties at intermediate strain rates [4]. Dudder [5] studied to obtain the material properties using a drop weight method and other researchers used a camplastometer and a rotary wheel machine. Servo-hydraulic testing machines are employed in most recent research work [6].
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In the present experiment, a high speed material testing machine of the servohydraulic type as shown in fig. 1 was utilized in order to obtain the dynamic material properties at the intermediate strain rate. The machine has the maximum stroke velocity of 7800 mm/s, the maximum load of 30 kN and the maximum displacement of 300 mm. Two electric motors are used to compress the operating hydraulic oil up to the pressure of 300 bars and two accumulators with the capacity of 5 liters are used to make the response time faster. The maximum flow rate of the servo-hydraulic unit is 4 liter/sec. For the high speed tensile test, the instrument for measuring the load and the displacement must have good response in the dynamic motion since material testing at the intermediate strain rate lasts only for several milli-seconds. The machine equipment is set up with the Kistler 9051A piezo-electric type load cell in a specially designed loading fixture to reduce the noise level and to increase the noise frequency from the load-ringing phenomenon. The displacement is acquired by a LDT (linear displacement transducer) from Sentech company. While the moving gripper needs to maintain the constant velocity during tensile tests, the moving gripper cannot operate at the desired velocity in an instant even if a servo valve with the fastest response time is used. In order to achieve the constant velocity during tests, a special jig is used to move to some distance under no loading and then seize a specimen instantly. Several tests were conducted at the same condition to verify repeatability and the results were very satisfactory for repeatability with robust calibration and indicate that the machine response, testing procedure and material response were consistent. 2.2 Load ringing phenomenon As the strain rate increases, the transmitted load does not become uniformly distributed at a specimen, a jig and a load cell with oscillation since the inertia and stress wave affect parts of the equipment. This phenomenon is called the load ringing. The load ringing distorts experimental results and brings about the inaccurate or false conclusion. The load ringing can be reduced by increasing the natural frequency of an upper jig or by acquiring the load from a specimen directly. In the latter case, however, testing procedure is complicate because strain gauges must be attached to specimens for every test. The natural frequency, f increases as the stiffness, k increases and as the mass, m decreases as shown in eqn (1).
f
1 2S
k m
(1)
Assuming that the cross section area of the jig, A is constant, the force applied to the jig, F and stiffness, k can be obtained by eqn (2) and eqn (3), respectively.
F
k
AE ('l / l )
AE / l , m
UAl
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(2) (3)
322 Computational Methods and Experiments in Materials Characterisation III 16
Load Loadcell cell Upper Upper plate plate Specimen Specimen
Reaction Force (kN)
14 12 10 8 6 4 2
1 m/s
0 0.0
Upper UpperJig Jig
0.5
1.0
1.5
2.0
2.5
3.0
Time (ms)
Figure 2:
Finite element model of a jig.
Figure 3:
Load curves from the tensile analysis of a jig.
Finally, eqn (1) can be converted to the eqn (4) with respect to the Young’s modulus, E, the density, U and the length of the jig, l. f
1 1 E 2S l U
(4)
Eqn (4) shows that the natural frequency increases as the length of the jig decreases and is related to the material properties. The steel, Aluminum, Mgalloy (8.5% Al) and Ti-alloy (6% Al, 4% V) show high E/U of 25.4, 25.8, 25.0 and 25.6 MPam3/kg, respectively. In this paper, the jig is made with the steel because the steel is most effective material for the jig considering the machining process, cost and durability. The jig is designed with ‘L’ shape considering the gripping of the specimen with bolts and the length of the jig is shortened to increase the natural frequency as shown in fig. 2. The tensile analysis is carried out to evaluate the structural safety and natural frequency which is directly effects on the load ringing phenomenon. Fig. 2 shows the finite element model of the jig. The load cell is attached to the jig and the constant velocity of 1.0 m/s is imposed at the end of a specimen. The analysis result indicates that the jig is safe without plastic deformation because the maximum stress is under 200 MPa in the edge of the ‘L’ shape. The result also indicates that the natural frequency of the jig is 15,000 Hz from the loadtime curve as shown in fig. 3. The acceptable experimental result can be expected when the ‘L’ shaped upper jig is utilized on the dynamic tensile test. Experimental evaluation of the upper jig is also performed. Different types of jig fixture as shown in fig. 4 were produced and conducted in the dynamic tensile test. Fig. 5 depicts the load curves from tensile tests of SPRC35R at 100/sec. As natural frequency increases, the amplitude of load ringing decreases and the accuracy of load curve is enhanced. The load ringing phenomenon of the jig of type C is remarkably diminished at the strain rate of 100/sec and the frequency of type C is five times higher than that of type A. The jig of type A shown in fig. 4a is convenient to grip the specimen. However, its frequency of 2,700 Hz is too low to conduct the dynamic tensile test. This low natural frequency comes from WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
323
Computational Methods and Experiments in Materials Characterisation III
(a) Figure 4:
SPRC35R, 100/sec Raw Data Fitted Curve Load [kN] (kN) Load
4 3 2
3 2 1
0
0 1
2
3
4
Time [msec] (msec) Time
(a) Figure 5:
5
6
SPRC35R, 100/sec 5
4
1
0
6
SPRC35R, 100/sec Raw Data Fitted Curve
5
Load [kN] (kN) Load
5
(c)
Upper gripping jigs: (a) type A; (b) type B; (c) type C. 6
6
Load (kN) Load [kN]
(b)
4 3 2 1 0
0
1
2
3
4
5
6
0
Time[msec] (msec) Time
(b)
1
2
3
4
5
6
Time[msec] (msec) Time
(c)
Load curves from tensile tests of SPRC35R at 100 /sec with the jig of (a) type A; (b) type B; (c) type C.
the complex structure and weighty mass. The jig of type B which designed ‘L’ shape and connected with force-link type load cell shows the frequency of 4,800 Hz. Although the natural frequency of the ‘L’ shaped jig is higher than that of type A, the load ringing still occurs because the force-link type load cell decreases the natural frequency. The jig of type C is also designed ‘L’ shape and the load cell is attached to the jig directly. The natural frequency of the jig of type C increases to 13,000 Hz because the length of the upper jig is shortened and the massive upper plate prevents the jig from oscillating due to external loading. Based on the numerical and experimental results, the upper jig of type C is equipped on the high speed material testing machine.
3
Dynamic tensile specimen for an auto-body steel sheet
3.1 Design of specimen using the finite element analysis Tensile specimens for the standard test are specified with the regulation of ASTM as well as the testing method. These regulations, however, does not include the high speed tensile testing method and the corresponding specimens. Appropriate dimensions of a specimen need to be determined for accurate tensile tests with the machine developed at the intermediate strain rate. Major shape factors of a specimen are the length (L), the width (W) of the parallel region and WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
324 Computational Methods and Experiments in Materials Characterisation III 1/
1 R6 A B C
Figure 6:
L W/2 2
3
4
5
0
5
/
4
/
/
/
3 2
Finite element model of a specimen for tensile tests at intermediate strain rates.
the radius (R) of the fillet. The length of the parallel region is the most important factor in dynamic tensile tests because not only the strain distribution but also the level of the strain rate and the inertia effect is directly dependent on this factor. In dynamic tensile tests, it is difficult to utilize a strain gauge or an extensometer for measuring the displacement of a specimen at the gauge section. Instead of using those instruments, the displacement of the crosshead is measured with LDT in a high speed material testing machine and the strain of specimen is calculated from this acquired displacement. Since the calculated strain is different from the exact strain at the gauge section, it is important to determine the dimensions of a specimen to reduce and to compensate the strain discrepancy in the dynamic tensile test. The finite element analyses and experiments were performed to determine dimensions of a specimen for dynamic tensile tests with a high speed material testing machine. The finite element analysis has been carried out with the variation of the length of the parallel region from 10 mm to 50 mm while the width of the parallel region and the radius of fillet were fixed to 6 mm. A commercial explicit finite element code, LS-DYNA3D, is employed in simulation. The material selected was SPRC35R whose thickness is 0.85 mm. The finite element model is shown in fig. 6. The constant velocity of 3.0 m/s is imposed at the one end of a specimen. In order to investigate the strain discrepancy between the calculated one from the displacement of the crosshead and the actual strain at the specimen, the engineering strain is calculated with the displacement measured at designated nodes as shown in fig. 6. The displacement between node 1 and node 1' denotes the displacement of the crosshead measured from LDT during the experiment. Fig. 7a shows the distribution of the calculated engineering strain when the length of the parallel region is 30 mm. The figure indicates that the engineering strain calculated from the displacement of the crosshead which is represented with a solid line is different from the strains calculated from the displacement between designated nodes in the parallel region. This strain discrepancy comes from the deformation near the filleting region. In order to obtain the appropriate gauge length of the specimen, the ratios of the engineering strain obtained from the local displacement between designated nodes in a specimen to the one obtained from the overall displacement of the cross head are calculated and depicted in fig. 7b. The figure represents that when the length of the parallel region is 30 mm, the gauge length of the specimen can be assigned as 22 mm since uniform deformation is observed within the gauge section of 22 mm. The strain ratio in the gauge section is 0.935. The strain ratio at the gauge section of the specimen with the length of the parallel region of 10, 20, 40 and 50 mm WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
Computational Methods and Experiments in Materials Characterisation III 0.30
325
0.94
d11 /L(30mm) /
d22 /L22 (30mm) /
/
d33 /L33 (26mm) /
0.20
Engineering strain ratio
Engineering strain
0.25
/
d44 /L44 (22mm) /
/
d55 /L55 (18mm) /
/
0.15 0.10 0.05 0.00 0.0
0.93 0.92 0.91 0.90 0.89 0.88 0.00
0.5
1.0
1.5
2.0
2.5
3.0
Parallel region=30mm 16
18
20
(a) Figure 7:
24
26
28
30
(b)
Engineering strains measured in a specimen: (a) engineering strain; (b) ratio of the engineering strain with respect to the gauge length.
BCD
A
Figure 8:
22
Gauge section [mm]
Time [ms]
D/ C/ B/
v /
A
Specimen with the length of the parallel region of 30 mm in the experiment: designated points to measure the displacement.
becomes 0.768, 0.875, 0.946 and 0.951, respectively. The calculation results inform us that the strain discrepancy becomes decrease and the uniformly deformed section increases as the length of the parallel region increases. 3.2 Verification of specimen design using the experiment In order to confirm the analysis result, specimens with various lengths of the parallel region were tested while the width of the parallel region and the radius of the fillet were fixed to 6 mm. The material is same as the one used in the analysis. Experiments were conducted using a high speed material testing machine with the tensile velocity of 3.0 m/s. In order to measure the displacement of the specimen during the test, square grids are marked in each specimen. During the test, deforming shapes of the specimen are captured with a high speed camera, Phantom V5.0, with 12,000 frames per second and the displacements between designated points as shown in fig. 8 are acquired using the visual software. The engineering strains of each specimen are calculated with the displacements measured from experiments. Fig. 9 shows the distribution of the engineering strain calculated from the displacement of specimens. Experimental results represent that the engineering strain calculated from the displacement of the crosshead is different from the exact strain at the gauge section and the strain ratios at the gauge section of specimens are 0.770, 0.884, 0.941, 0.950 and 0.952 when the lengths of the parallel region are 10, 20, 30, 40 and 50 mm, respectively. The strain ratios obtained from the experiment are compared with the ones predicted from the analysis as shown in Table 1. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
326 Computational Methods and Experiments in Materials Characterisation III
Engineering strain
G
0.30
0.30
dAA /L(30mm)
dAA /L(50mm)
/
/
dBB /LBB (27.12mm)
0.25
/
dBB /LBB (46.84mm)
0.25
/
/
dCC /LCC (22.19mm) /
0.20
/
0.20
dDD /LDD (17.26mm) /
/
0.15
Strain ratio / AA : 1.000 / BB : 0.913 / CC : 0.934 / DD : 0.941
0.10 0.05 0.00 0.0
0.5
1.0
1.5
2.0
2.5
Table 1:
/
dDD /LDD (17.26mm) /
/
0.15
Strain ratio / AA : 1.000 / BB : 0.938 / CC : 0.946 / DD : 0.952
0.10 0.05 3.0
0.00
0
1
Time [ms]
Figure 9:
/
dCC /LCC (32.05mm)
/
2
3
4
5
Time [ms]
Engineering strain acquired from the experiment with the length of the parallel region: (a) 30 mm; (b) 50 mm. Comparison of scale factors with various parallel regions.
Length of parallel FE analysis region Measured section Strain ratio [mm] [mm] 8.0 0.719 10 2.0 0.768 18.0 0.842 20 12.0 0.875 8.0 0.875 28.0 0.917 24.0 0.932 30 18.0 0.935 38.0 0.934 40 28.0 0.946 18.0 0.946 48.0 0.942 32.0 0.951 50 18.0 0.951
Experiment Measured section Strain ratio [mm] 7.40 0.724 2.47 0.770 17.26 0.856 12.33 0.872 7.40 0.884 27.12 0.913 22.19 0.934 17.26 0.941 36.98 0.932 27.12 0.941 17.26 0.950 46.84 0.938 32.05 0.946 17.26 0.952
The strain ratios obtained from the experiment are closely coincident with those obtained from the analysis. The specimens with the length of the parallel region of 10 and 20 mm are less accurate than the others. Table 1 also represents that the difference of the strain ratio at the gauge section between 30 and 50 mm of the length of the parallel region is less than 2% and the strain discrepancy decreases as the length of the parallel region increases. There is a deficit with the long parallel region in a specimen though. As the length of the parallel region becomes increase, the deformation of the specimen tends to be localized near the loading region due to the longitudinal inertia effect as shown in fig. 10. Consequently, based on the results from both finite element analyses and experiments, it is concluded that a specimen is acceptable when the length of the parallel region is around 30 mm and the strain ratio of the selected specimen should be used as the scale factor of the specimen for compensating the strain discrepancy during the test. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
Computational Methods and Experiments in Materials Characterisation III
L=10mm
Figure 10: 600
L=20mm
L=30mm
L=40mm
327
L=50mm
Specimens after tensile tests with the different parallel region. 800
HS45R-RD
TRIP60-RD
400
200/s 100/s 50/s 20/s 10/s 5/s 2/s 1/s 0.5/s 0.1/s 0.003/s
300 200 100
SPRC45R 0 0.0
Engineering stress(MPa)
Engineering stress(MPa)
500
0.1
0.2
600
400
200
TRIP600 0.3
0 0.0
0.4
0.1
800
1000
HS45R-RD
SPRC45R 0.01
0.1
1
10
100
Flow stress(MPa)
H=0.2 H=0.15 H=0.1 H=0.05 H=yield
200
0 1E-3
TRIP60-RD
600 400 H=0.2 H=0.15 H=0.1 H=0.05 H=yield
200
TRIP600 0 1E-3
0.01
0.1
Strain rate(/sec)
4
0.4
800
400
Figure 12:
0.3
Stressstrain curves of steel sheets with the variation of strain rate.
600 Flow stress(MPa)
0.2
Engineering strain
Engineering strain
Figure 11:
200/s 100/s 50/s 20/s 10/s 5/s 2/s 1/s 0.5/s 0.1/s 0.003/s
1
10
100
Strain rate(/sec)
Strain rate sensitivity of steel sheets with the variation of the strain.
Dynamic tensile characteristics of an auto-body steel sheets
The steel sheets, SPRC45R (1.23t) and TRIP600 (1.46t) were prepared along the rolling direction. Experiments were carried out at the room temperature of 21°C at the intermediate strain rate. Quasi-static tensile tests were carried out at the strain rate of 0.003/s using the static tensile machine, Instron 5583. Dynamic tensile tests were carried out at the range of strain rate from 0.1 to 200/s using a WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
328 Computational Methods and Experiments in Materials Characterisation III high speed material testing machine developed. Stressstrain curves of SPRC45R and TRIP600 are shown in fig. 11 at various strain rates. From the stressstrain curves, the dynamic material properties such as the flow stress and the elongation were investigated quantitatively with the variation of the strain rate. As the strain rate increases, the tensile strength gradually increases and the change of the tensile strength varies with materials. In case of advanced high strength steels (AHSS) such as TRIP600, the flow stress is insensitive to the strain rate compared to the SPRC45R as shown in fig. 12.
5
Conclusion
The tensile testing method at the intermediate strain rate was established and tensile tests of steel sheets for an auto-body were performed to evaluate dynamic material properties. The testing method including an experimental apparatus and the dimensions of the specimen has been established for dynamic tensile tests at the intermediate strain rate ranged from 1 to 200/s. The upper jig with the natural frequency of 13,000 Hz was designed to diminish the load ringing phenomenon. The specimen with the length of the parallel region of 30 mm was selected as a reference specimen when the width of the parallel region and the radius of the filleting section were all 6mm. Uniform deformation was observed at the gauge section of the selected specimen without localized deformation as results of both finite element analyses and experiment. Static and dynamic tensile characteristics of SPRC45R and TRIP600 were investigated at the range of the strain rate from 0.003 to 200/s. The special jig fixture provides an accurate stressstrain curve of steel sheets with negligible load ringing phenomenon.
References [1] [2] [3]
[4] [5] [6]
Khan, A.S. & Huang, S., Experimental and theoretical study of mechanical behavior of 1100 Al in the strain rate range 10-5-104s-1. International Journal of Plasticity, 8, pp. 397-424, 1992. Ishikawa, K. & Tanimura, S., Strain rate sensitivity of flow stress at low temperatures in 304N stainless steel. International Journal of Plasticity, 8, pp. 947-958, 1992. Huh, H, Lim, J.H., Song, J.H., Lee, K.S., Lee, Y.W. & Han, S.S., Crashworthiness assessment of side impact of an auto-body with 60TRIP steel for side members. International Journal of Automotive Technology, 4(3), pp. 149-156, 2003. Zukas, J.A., Nicholas, T., Swift, H.F., Greszczuk, L.B. & Curran, D.R., Impact dynamics. New York: John Wiley & Sons, 1982. Dudder, G.B., Drop tower compression test-metals handbook. Ohio: American Society for Metals, 1985. Kim, J.S., Huh, H., Lee, K.W., Ha, D.Y., Yeo, T.J. & Park, S.J., Evaluation of dynamic tensile characteristics of polypropylene with temperature variation. International Journal of Automotive Technology, 7, pp. 571–577, 2006. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
Computational Methods and Experiments in Materials Characterisation III
329
Utilization of ground coloured glass cullet in construction materials A. Karamberi & A. Moutsatsou Chemical Engineering Department, National Technical University of Athens, Greece
Abstract Due to the imperative need for recycling, the present study was focused on the exploitation of domestic and industrial waste and particularly of finely ground glass cullet in three applications of structural materials. Firstly, the possible use of glass cullet in cementitious materials either as a binder, aggregate or filler was studied. A second study sector was the utilization of glass cullet for the production of foam glass. The particle size effect of glass cullet and the influence of the type and content of foaming agent at the final product were examined. And finally, the vitrification by thermal treatment of industrial waste (fly ashes and slag) with or without the presence of glass cullet and the further crystallization of the glassy products for the production of glass-ceramics was studied. Keywords: glass cullet, fly ash, slag, vitrification, foam glass.
1
Introduction
The utilization of waste glass in industrial applications in which no strict requirements of purity are requested is well-known. Recent works pointed out the feasibility of glass as filler in road paving or cementitious products or as a batch addition in the melting of hazardous wastes. The development of foam glass is also particularly attractive, since large amounts of waste could be employed as raw materials for a very marketable product. Moreover, the utilization of glass cullet as well as industrial by-products for the production of glass and glass-ceramics is possible [1,2].
WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/MC070331
330 Computational Methods and Experiments in Materials Characterisation III A typical pozzolanic material features three characteristics, is rich in silica, is an amorphous material and has a large surface area. Glass is an amorphous material and has high silica content. Therefore glass might satisfy the basic requirements for a pozzolan if it is ground to a size fine enough so as to pacify the alkali-silica reaction and to activate the pozzolanic behaviour. Glass-ceramics prepared by controlled devitrification of glasses were developed in the 1950s and find a wide variety of applications such as microelectronic substrates and packaging, optically transparent components as well as for the matrix of composite materials [3]. The glass-ceramics were produced by conventional glass route and subsequently crystallized, usually by heat treatment in two stages to give nucleation followed crystal growth. For glass-ceramic production via glass processing, nuclei must readily form throughout the bulk of the parent glass, surface nucleation is to be avoided as it is usually detrimental to mechanical performance [4]. Additionally, the possible use of waste glass for the production of lightweight granules has been studied. As foaming agent, MnO2 and SiC were chosen. Granules have been prepared by mixing together finely ground waste glass with the foaming agent and fired at different temperatures above the softening point of glass. Within the temperature range the foaming agent degas and the resulting gasses remain trapped in the glass structure. The granules structure is evaluated using Scanning Electron Microscopy. Foam glass is produced by adding foaming agents to finely ground glass and fired at a temperature above the glass softening point. This temperature is then maintained so that the gas released by the foaming agent is captured in the glass structure, forming a lot of small pores. In the case of agents containing carbon i.e. SiC the agent reacts with the glass or atmosphere, forming gases which also remain captured in glass structure. In the present study there was an effort in utilizing glass cullet in various applications. The first series of experiments is dealing with the use of glass cullet in construction materials and especially in cementitious materials either as aggregate, filler or as pozzolanic material. Moreover, glass cullet is used as a secondary raw material in the production of glass and glass-ceramics from four industrial by-products two lignite fly ashes and two slags. In the final application glass cullet is used as the primary raw material for the production of foam glass. The results are very encouraging and open the way for the sustainable utilization of industrial and domestic wastes.
2
Experimental part
2.1 Materials The used glass cullet derived from the internal recycling of a glass industry and especially from glass bottle containers. The three most common cullet colours, green, amber and flint, were used in order to evaluate the influence of the colour of the glass in the cement mixtures. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
Computational Methods and Experiments in Materials Characterisation III
331
Four industrial wastes were selected: i) two fly ashes, of different chemical and mineralogical composition, derived from the combustion of lignite and originated from Megalopoli and Ptolemais area in Greece. Greek fly ashes are classified as Calcareous Fly Ashes (C according to ASTM), as having a large content of CaO, exceeding 10%, ii) an electric furnace slag derives from a smelting plant for the pyrometallurgical treatment of laterite ore for the production of sponge Ferro-nickel containing 18-25% Ni, iii) an electric arc furnace slag from the production of steel. The specific steel making plant uses scrap as a raw material. The chemical composition of glass cullet and industrial waste is shown in Table 1. Table 1: % (w/w) FeO Fe2O3 MnO Ni-Co
SiO2 CaO MgO Al2O3 Na2O K2O Cr2O3 SO3
Electric Furnace Fe-Ni Slag 41.10 2.60 0.14 33.70 3.30 3.40 9.30 4.30 0.85
Chemical composition of cullet, fly ashes and slags. Electric Furnace Steel Slag 17.00 7.50 16.00 41.00 4.50 7.00 0.56 6.63
Lignite Meg. Fly Ash 8.44 51.26 11.82 2.27 19.39 0.53 1.81 2.91
Lignite Ptol. Fly Ash 5.10 30.16 34.99 2.69 14.93 1.01 0.4 6.28
Amber cullet
Green cullet
0.35 71.20 10.35 2.60 1.90 13.15 0.60 0.06 0.30
0.45 70.50 10.15 2.75 1.80 12.95 0.45 0.25 0.25
Flint cullet
0.45 70.65 10.70 2.45 1.75 13.25 0.55 0.45
Green, amber and flint containers were ground in a roller mill and in a mortar grinder and separated into the appropriate fractions depending on the application. The slag was ground in ball mills and their particles passed the 90 µm sieve (DIN 4188). The fineness of fly ash is measured using Laser Granulometre (CILAS GRANULOMETRE 715 D314) and it was found that Megalopolis fly ash samples have a retained amount of 60% on 48 µm, while Ptolemais fly ash samples have an average retained amount of 25% on 48 µm. Ordinary Portland Cement (OPC) and sand according to ASTM C778 were used for the pastes and the mortars. A solution of NaOH 1M was used as alkali activator. The x-ray analysis XRD (Siemens D5000 diffractometer, Cu Ka radiation, Ni Filter) of the glass cullet and electric furnace Fe-Ni slag spectrums revealed an amorphous material, while the spectrums of both fly ashes and electric furnace steel slag presented as well crystalline phases.
WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
332 Computational Methods and Experiments in Materials Characterisation III 2.2 Experimental procedure For the production of cement mortars the used glass cullet is ground and separated in two fractions: –200 µm +90 µm and –90 µm, so as to study the influence of the granulometry of glass in the mixtures. In order to evaluate the colour effect on the hydration of cement paste and the degree of substitution of cement by cullet, glass-cement pastes and mortars were prepared with the -90 µm glass fraction fluctuating from 5% to 25% by volume. Additional samples containing 5% glass cullet and 5% fly ash were prepared in order to examine the potential promote of pozzolanic activity due to the presence of a highly reactive material. For the production of cement plasters glass cullet is separated in fractions similar to the conventional aggregates. In order to estimate the pozzolanicity of glass cullet as well as of fly ashes and mixtures of fly ash and cullet Chapelle test is carried out [5]. All the sediments of the above test were examined using X-Ray Diffraction (Siemens D5000 diffractometer, Cu Ka radiation, Ni Filter) and Thermal Analysis TG (Mettler TGA/SDTA851e). The potential alkali-silica reaction of the mortars containing cullet was assessed according to ASTM C1260. Specimens have been prepared with 25% substitution of cement by cullet of each colour having a granulomentry 90 µm. The used aggregates were according to ASTM C778 and are not prone to alkalisilica reaction. Common masonry plasters with white cement was selected in order to evaluate the influence of glass cullet in widely used commercial cementitious products. All samples were prepared using flint, green and amber glass cullet as a partial replacement for both aggregate and filler. The properties under examination, except from the mechanical strength measurements, were the properties of the fresh plasters. In particular, retained water (EN 1015-8), air content (EN 1015-7), specific weight (EN1015-6) and table flow tests (EN 1015-3) were estimated. For the production of foam glass, glass cullet was powdered and separated by screening into fractions of 312-250 µm, 250-200 µm, 200-160 µm, 190-90 µm, 90-71 µm, 71-45 µm, <45 µm. The foaming agents used were SiC and MnO2 with an average grain size of 45 µm and added for an amount 1-5% wt. Soda lime glass and foaming agents were dry mixed and compacted by light cold pressing before being subjected to the heating treatment. The optimal thermal treatment adopted was heating up to 900oC with rate of 10oC/min, and holding at that temperature for 30 min, followed by heating to 950oC and holding for 30 min. For the production of glass and glass-ceramic approximately 60 g of each waste were placed in fire resistant ceramic crucible and heated in air at 1450oC for 2 h. The resulted melt poured in a mould and allowed to cool to room temperature. The compositions of the batches are shown in table 2. Glassceramics were prepared by sintering of the glasses in air at a temperature in the range 900 to 1000oC, held for 120 min and then cooled to room temperature. After heat treatment, the samples were ground to a particle size <45 µm and Xray diffraction data were obtained. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
Computational Methods and Experiments in Materials Characterisation III
Table 2:
333
Percentage of the raw materials used in every specimen for the production of glass and glass-ceramics. %
Lignite Megalopolis Fly Ash Lignite Ptolemais Fly Ash
G-1
G-2
G-3
100
80
60
G-4
G-5
100
80
Electric Furnace Fe-Ni Slag
G-7
G-8
100
60
100
Steel Slag Amber glass
G-6
40 20
Green glass
40 20
In order to characterize the produced glass and glass ceramics based on its physicochemical characteristics, samples hardness was measured. In order to comply with current legislation a low leachability of hazardous components from the glass or glass-ceramic matrix must be achieved. Therefore, leaching tests were performed on both glass and glass – ceramics according to DIN 38414 S4. The ability of produced glassy materials to be crystallized is assessed by differential thermal analysis. The crystalline phase composition of the produced glasses and glass ceramics was investigated using X-ray powder diffraction. In order to estimate the resistance of the produced glass to chemical attack the standard test method for the resistance of glass containers to chemical attack (ASTM C 225-85) was employed.
3
Results and discussion
The results of the compressive strength of the mortar prisms showed that the ones with 90 µm glass cullet perform better behavior than 200 µm cullet [5]. The outcomes of pozzolanic reaction, according to the Chapelle test, are reinforced by the compressive strength. It is obvious that the two Greek fly ashes performed better behaviour that the glass cullet, which also performed lower pozzolanicity. It is worthy to mention that fly ash has smaller particle size in comparison to used glass cullet, which is a factor immediate associated with the reactivity of the materials. It was apparent that the green and the flint glass perform better behaviour than both the amber glass and mixed colour. Therefore, the development of the pozzolanic activity is not only influenced by the granulomentry but also by the chemical structure [6]. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
334 Computational Methods and Experiments in Materials Characterisation III Very promising was the lack of expansion due to the alkali-silica reaction. All specimens who underwent the ASTM C1260 test exhibited minus expansion in comparison with the blank specimen [5]. In order to evaluate the maximum percentage of substitution, mortars were made containing up to 20% glass cullet. The granulometry of 90 µm is selected own to the better performance of finely ground glass. The results indicated that the maximum substitution of cement in mortars is 15% when 90 µm ground glass cullet is used (Figure1). Pastes containing cement-glass-fly ash performed high compressive strength at 28 days, while the opposite outcomes aroused at 360 days (Figure 2), a fact which is under further investigation. Unexpectedly, the activated samples performed lower compressive strength than the non-activated ones. An explanation might be the low molarity of the alkali solution [7]. The application of the glass cullet in the cementitious plasters significantly improved their compressive strength, especially when it was used as filler in white cement plasters, without any notable affection to the properties of the fresh mortars. A negative factor was the decrease of the fresh glass-cement plaster workability. This phenomenon might be owed to the angular shape of the glass particles, which favours the creation of interlocks and consequently decrease the workability of the produced plasters [8]. SiC powder was found to be very effective in producing foamed glass when mixed to the glass powder with a concentration ranging from 1 to 5% by wt (Figure 3). The oxidation of SiC is the main reason of powdered glass cullet foaming. The final structure of the foamed glass is depending on the variation of glass viscosity to temperature, the heating rate, the access of oxygen to the SiC powder and the glass powder size. It was shown that the foaming process is halted if particles of glass waste are coarse. As the particle size of the glass cullet is decreasing the expansion of the pallet, the homogeneity of the final material is increasing. The results of the pallet with MnO2 are not similarly satisfying. The final product acquired a black colour and inhomogeneity of the size and the pore distribution could be observed. The obtained highly porous material can serve as an aggregate in the production of lightweight concrete or as a trench filling material for thermal insulation. Concerning glass and glass-ceramic production, the X-ray analysis revealed that all the products after the thermal treatment at 1450oC were amorphous except from those derived from Fe-Ni slag. It is possible that Fe-Ni slag produces crystalline phases during the thermal treatment at 1450oC. In figure 4 all the x-ray diffraction spectrums of the crystallized glasses at 1000oC are illustrated. Due to the crystallization of Fe-Ni slag at 1450oC not district changes are observed during the de-vitrification process. Regarding glass-ceramics from vitrified Megalopolis Lignite Fly Ash the main crystalline phase that could be recognized from the XRD spectrums is anorthite. All the vitrified mixtures with Electric Furnace Steel Slag have shown analogous crystalline formation. The main crystalline phases were diopside, anorthite and albite calcian. The resulted glass-ceramic from Lignite Fly Ash and WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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Electric Furnace Steel Slag was alike to that made from Electric Furnace Steel Slag. Nevertheless, the addition of glass cullet seems to deduct the crystallization, as could be revealed from the spectrum of G-1 sample compared to sample G-2. This phenomenon may occur due to the presence of Na2O and K2O in the glass cullet as fluxes which it is possible to suppress crystallization. 2 days
7 days
Compressive Strength (MPa)
50 45 40 35 30 25 20 15 10 5 0
28 days
G.5 A.5 F.5 G.10 A.10 F.10 A.15 F.15 G.20 A.20 F.20 Samples name-Percentage of substitution
Figure 1:
Compressing strength of mortar prisms. 2 days 7 days 28 days
360 days
100 80 60 40
Cement
G5%+M5%
A5%+M5%
F5%+M5%
G10%
A 10%
F10%
G 5%
0
A 5%
20
F 5%
Compressive Strength (MPa)
120
Name of the sample-percentage of substitution
Figure 2:
Compressive strength of the pastes at 2, 7, 28, 360 days.
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336 Computational Methods and Experiments in Materials Characterisation III
Foam glass produced by 90 µm glass cullet with 3% SiC.
2400
Figure 3:
G-8
G-7
counts
G-6 G-5 G-4
G-3 G-2
0
G-1 15
20
25
30
35
40
45
50
55
60
65
2ș
Figure 4:
XRD spectrums of the produced glass-ceramics (devitrification at 1000oC).
Concerning Ptolemais Lignite Fly Ash specimens, no tendency towards crystallization is observed. The development of well crystallized crystals in the glass–ceramics can improve their mechanical strength. Moreover, diopside is the preferable crystalline phase than anorthite from the viewpoint of the mechanical properties of these glass-ceramics [9]. There was no significant leachability of all the samples, according to DIN 38414 S4, for Cr, Mn, Ni, Cd, Cu, Fe, Zn, but concerning the leaching of Fe, Mn, it was not negligible, possible due to the extra fine granulometry of the testing material. All values were under the limits of the European Legislation. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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Moreover, the results of the resistance of glass to chemical attack were similar to soda lime flint glass, which shows an average value 7.67 mL sulphuric acid per 10g glass. The higher values have been received from the vitrified Fe-Ni slag which in some samples slopped the limits. An explanation is the incapability of the aforementioned slag to be vitrified. The presence of glass formers and modifiers is needed in order the desirable vitrification is achieved. The glasses derived from the slags exhibited higher hardness values. The devitrification process seems to favours the hardness of the final product. As it was prospective, no alteration of the Fe-Ni slag hardness, during the devitrification process was observed.
4
Conclusions
Finely ground coloured glass cullet could be used as a partial substitute of cement in mortars especially for substitutions up to 15%. The green and the flint cullet performed a better behaviour than the amber glass. More satisfactory were the outcomes from the cullet application as an aggregate or as filler in cementitious plasters, with a negative factor, the reduction of workability of the fresh plaster. The utilization of cullet in white cement plasters revealed final products with increased mechanical strength. As a final conclusion, the utilization of glass cullet in cementitious materials seems feasible especially for decorative products. Moreover, waste glass can serve as raw material for the production of lightweight aggregate. The parameters which have important influence on the foaming process are the particle size of the starting material, foaming agents and the temperature range of foaming. The selected additives MnO2, and SiC were proven to be suitable for the foaming of glass; among them SiC was the best resulting in highly porous structure. In addition the possibility of fabricating sintered glass-ceramics from vitrified industrial waste that was capable of bulk crystallization has been demonstrated. Suitable glasses and glass-ceramics can be obtained only if the proper ratio between glassy network former and modifier elements exists. The present work tried to demonstrate several applications for the utilization of glass cullet. Whilst economic and technical factors may ultimate exclude some of these outlets, it is essential that this diversity is preserved wherever possible if a dynamic and sustainable market is to be created for the material.
References [1]
[2]
Dhir, R.K, Dyer, T.D, Maximising Opportunities for Recycling Glass, Proc Inter Conf Sustainable Waste Management and Recycling: Glass Waste, eds. M. C. Limbachiya, J.J. Roberts, Thomas Telford: Kingston University, London, pp. 1-16, 2004 Meyer, C., Recycled glass- from waste material to valuable resources, Proc.Int.Symp. Recycling and Reuse of Glass Cullet, eds. R. K. Dhir, M. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
338 Computational Methods and Experiments in Materials Characterisation III
[3] [4] [5]
[6]
[7]
[8]
[9]
C. Limbachiya, T. D. Dyer, Thomas Telford: Dundee,UK, pp. 179-188, 2001. Strnad, Z., Glass-Ceramic Materials, Glass science and technology v.8, Elsevier, 1986 Frugier, P., Godon, N., Vernaz, E., Larche, F., Influence of composition variations on the initial alteration rate of vitrified waste incineration flyash, Waste Management, 22, pp. 137-142, 2002. Moutsatsou, A., Chaniotakis, E., Papageorgiou, D., Karamberi, A.: Treatment and Recycling of Vitrified Fly Ash and Coloured Cullet in Cement Mixtures, Proc. of the International Congress Rec’2002, Geneva, February 2002 Moutsatsou, A., Chaniotakis, E., Papageorgiou, D., Karamberi, A., Participation of coloured cullet to the hydration and the development of compressive strength of cement, Proc. of the Sixth International Conference on Concrete Technology for Developing Countries, eds. M. Resheidat, al-Balqa: Amman, Jordan, pp. 43-50, 2002. Moutsatsou, A., Kerimis, M., Karamberi A., Pozzolanic Behaviour of Glass Cement and Glass Cement Activated Mixtures, Proc. of the 7th Inter. Confer. on Concrete Technology, eds. H. Al-Mattarneh, A. Ibrahim, Z. Ahmad, UPENA: Kuala Lumpur, Malaysia, pp. 147-156, 2004. Karamberi, A., Chaniotakis, E., Papageorgiou, D., Moutsatsou, A., Application of Glass Cullet in Cement Mortars, Proc. of the 7th Inter. Confer. on Concrete Technology, eds. H. Al-Mattarneh, A. Ibrahim, Z. Ahmad, UPENA: Kuala Lumpur, Malaysia, pp. 157-164, 2004. Toya T., Kameshima Y., Yasumori A., Okada K., Preparation and properties of glass-ceramics from wastes (Kira) of silica sand and kaolin clay refining, J. Eur. Ceram. Soc., 24, pp. 2367–2372, 2004.
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In situ dynamic characterization of soils by means of measurement uncertainties and random variability G. Vessia & C. Cherubini Department of Civil and Environmental Engineering, Polytechnic of Bari, Italy
Abstract In situ dynamic characterization of natural granular soils by means of VS values is accomplished by direct and indirect investigation techniques. Integration among those types of field test are encouraged by Eurocode 8 through correlations amongst VS and NSPT but this does not suggest the best correlation formulation among the ones presented over the last thirty years. Besides such correlations can provide highly disperse values of VS. Thus a rational design of investigation campaign and measurement interpretation and calculations appears to play an important role in dynamic characterization of granular soils accomplished by in situ tests. It should rely on selecting the best fitting correlation formulations site by site according to soil types, their random structures and the characteristics of investigation techniques measured dynamic soil properties. An application of statistical approach to the issues previously sketched is carried out in the Pomigliano d’Arco urban area where Down-Hole and Standard Penetration tests were performed for dynamically characterizing the foundation soils. Assessment of uncertainties in VS values should allow the performance of hazard analyses and reliability-based design in seismic areas. Keywords: Down-Hole tests, SPT, model uncertainty, NSPT-VS relations, measurement errors.
1
Introduction
Dynamic characterization of granular soils at low strain level is the first step of seismic response analyses or of soil basement dynamic classification whenever is needed for building designing activity in urbanized areas. Various “in field” WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/MC070341
340 Computational Methods and Experiments in Materials Characterisation III techniques have been developed and enhanced to that scope as Down-Hole and Standard Penetration Test or similar tests. The first device allows to directly record arrival times and convert them into VS and VP; whereas the second one gives indirectly the velocity VS by means of correlations, developed by different authors over the years, with the number of blow counts NSPT. Such direct and indirect techniques for VS estimation are concerned with uncertainties and suffer the inherent variability and heterogeneity that granular soil deposits show. Accordingly it should be useful to recognize the most affecting sources of uncertainties for the two types of investigation techniques in order to make them more reliable whenever geostatistical approach is employed. The study presented below deals with the proposal of statistical methods to improve the reliability of VS values both from direct and indirect measure. As indirect device concerns, that are NSPT measurements, the uncertainties in NSPT values and uncertainties given by the transformation models will be taken into account.
2
VS direct measurements and their interpretation
A common geotechnical in field test to measure shear wave velocity (VS) is the Down-Hole test. It is a punctual investigation and it exploits the theory of refraction of waves in order to measure the first arrival times of S and V waves.
Figure 1:
Down-Hole tests setting at Pomigliano d’Arco town.
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Besides geophysics investigates the real soil deposits with a lot of approximations and simplifications because they are very complex and heterogeneous media in spite the theory of refraction and propagation of elastic waves within a homogeneous and elastic medium. Hence, the interpreting phase of recorded arrival times play a fundamental role even though it is heavily influenced by the operator judgement. This is the most relevant issue why the application of reliability approach to that dataset is a hard work. Let us now consider the case of five Down-Hole tests performed in the urban area of Pomigliano d’Arco, a town near Naples (Italy), where a microzonation activity was recently carried on (fig. 1). Five borings of 30m depth were investigated and five Down-Hole tests were performed. Direct analyses of soil samplings over the five profiles show successions of pyroclastic sandy deposits from 0 to 16m depth and lava and sand alternate levels from 16m to 30m. This evidence can be caught from the five time vs. depth diagrams illustrated in fig. 2. Time (ms) 0
20
40
60
80
100
120
140
1 3
DH1 DH2
5
DH3
7
DH4
9
DH5
Depth (m)
11 13 15 17 19 21 23 25 27 29 31
Figure 2:
Time versus depth diagram for the five Down-Hole tests performed in Pomigliano d’Arco town.
As can be pointed out at 16m a change in arrival times is evident but more variability can be drawn deeper. Furthermore some differences in resulting VS values can be read, affecting seismic strata distribution, whether different methods are employed. Table 1 shows VS values according to the following two interpretation procedures of time vs. depth diagrams: (1) it considers interval velocities and defines a seismic stratum where rapid variations occur; (2) it searches for a linear trend on time vs. depth diagram then sketches bounds where the trend visibly changes. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
342 Computational Methods and Experiments in Materials Characterisation III Table 1:
VS values (m/s) calculated by means of method (1) and method (2) from the five Down-Hole tests. DH1
Depth (m) 1 4 5 10 11 12 14 15 16 17 18 19 21 22 23 24 25 28 29 30
DH2
DH3
DH4
DH5
1
2
1
2
1
2
1
2
1
2
240
227
211
278
278
250
281
264
196
212
258 185
208 146 1121 1126
191
1167 1020
1204 1176
1040 1064 1053 1034
441
282 1212
1209 258
236 281 230
286
233
251
227
Table 1 shows different seismic strata and different VS values. Even when seismic strata for the two methods correspond, there are no way to rationally lead to unique VS values. This subjectivity cannot be solved and its final dispersion in VS values cannot be treated or reduced in any way. In order to address this issue Cherubini and Vessia [5] suggested using statistical techniques on time vs. depth diagram to derive a trend and residuals that recognize vertical variability structure of the deposit. That approach would be useful whenever Down-Hole tests are performed in the nearby and eventually supported by seismic refraction tests in order to get also horizontal variability structure. On the contrary, as can be seen in fig. 1, in Pomigliano d’Arco those five seismic tests are set far each other. For that reason only their vertical variability structures shall be considered. Thus another procedure is presented here with the scope of defining VS values from time vs. depth diagrams in a unique and repeatable fashion. The technique applied was proposed by Vivatrat WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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[6] and it was born and developed for continuous vertical measurements performed in bore holes as cone penetration test (CPT). Here it is successfully applied to Down-Hole tests. 2.1 Vivatrat procedure applied to VS estimation The Vivatrat filtering procedure allows to statistically treat measures by selecting those data which result to be odd values and affect the mean trend and the variability of the data set. The Vivatrat procedure can be sketched in the following items: (1) To plot the unfiltered measures (arrival time) versus depth. (2) To divide the complete dataset of measures in layers of extension D: it is suggested to vary from 0.5m to 2.5m. In this case, the space lag between measures is 1m, thus it is assumed D=1m not to reduce the resolution of measures for “outlying peak” detection. (3) Calculation of mean Pi and standard deviation si for each sub-layer identified. (4) Calculation of the “representative dispersion” Sr which is the minimum value among the following expressions: Sr
1 S i 1 S i 2
(1)
Sr
1 S i 1 S i 2
(2)
1 S i 1 S i 1 2
(3)
Sr
where Si-1, Si and Si+1 are the standard deviations calculated for sub-layers i-1, i and i+1 respectively. (5) To filter the measures which lie beyond the following limit values: P i r A Sr
(4)
where Pi is the mean value within the sub-layer i, Sr is the characteristic standard deviation and A is the coefficient of the limiting band which can assume a value belonging to the interval (0.5; 2.5). In this case, four value of A were attempted: 0.5m, 1m, 1.5m and 2m. Thus for final results just A=1m is accounted for due to the fact that 0.5m eliminates quite all of the data, 1.5m filters as much data as 1m; finally 2m allows quite all of the data set to be accounted for. Accordingly table 2 summarizes results for the five Down-Hole shear wave velocities filtered by means of the Vivatrat procedure. Comparing table 1 and table 2 differences into seismic strata and VS values can be found but they are not so relevant. Nevertheless from a methodological point of view, the Vivatrat procedure shows a real advantage because of its objectivity and repeatability. Moreover such method reduces the number of seismic strata making them more strictly correspond with lythological interfaces.
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344 Computational Methods and Experiments in Materials Characterisation III Table 2: Depth (m) 1 14 15 17 18 21 22 24 25 30
3
Shear wave velocity values (m/s) and seismic strata subdivision from Vivatrat procedure for five Down-Hole tests. DH1 231
1037
DH2 202
DH3 219
DH4 229
1135
1176
DH5 225
1025 266
1136 236
217
VS estimation by means of standard penetration tests
International building codes for seismic areas as Eurocode 8 [1] and the Italian “Testo Unico” [2] indicate the possibility of performing a dynamic soil characterization by means of the measurements performed over 30m depth of three parameters as shear wave velocity (VS), blow count from standard penetrometer tests (NSPT) and undrained shear strength (su). Besides, for granular soils only VS and NSPT are useful and from now on we will deal only with them. Then parameter values should be converted into shear modulus at low strain rate, G0 in order to carry out dynamic geotechnical analyses. At this stage VS values are needed. That is the main reason why numerous correlation expressions between VS and NSPT are raised provided that standard penetrometer tests are widely performed and VS is the most used parameter for in situ G0 estimation. Those empirical expressions are derived by means of different NSPT and VS database from all over the world but none provides high correlation coefficients. One well known expression is that by Ohta and Goto [4], whose database refers to alluvial plains in Japan: VS
0.17 69 N SPT z 0.2 EF
(5)
where z= depth (m); E= the geological epoch factor: 1.0 (Holocene), 1.3 (Pleistocene); F= soil type factor: 1.0 clay, 1.09 fine sand, 1.07 medium sand, 1.14 coarse sand, 1.15 gravely sand, 1.45 gravel. They provided their best relation between NSPT and VS (eqn. (5)) with a correlation coefficient R2 equal to 0.86 with a probable error of 19.7%. Moreover it is worth noticing that Ohta and Goto also proposed to take into account different variables as effective stress, depth, soil type, geological epoch or only the NSPT value formulating other empirical expressions reported within [7]. Accordingly they found that the equation where VS depends only on NSPT WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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variable has a correlation coefficient slightly different from those considering geological epoch, soil type and depth as the eqn. (5) (R2=0.719, 27.4% for probable error). Over the years numerous were the researchers tried to manage the possible correlation between NSPT and VS but each formulation has not a wide applicability and problems on correspondence of VS measured and estimated values are still opened. In this study the eqn. (5) has chosen, amongst the others, and applied to NSPT measures performed at Pomigliano d’Arco in five boreholes where Down-Hole tests were carried out (see table 3). Table 3 reports NSPT values over 16m depth because of the presence of lava and sands alternate levels under 16m for which standard penetration test results are often unreliable. Table 3:
NSPT values measured over five soundings where Down-Hole tests were performed. Depth (m) 1 2 2.5 4 5 6 7.5 8 9 10.5 11 12 12.9 14.5 15 16
NSPT S1
S2
S3
S4
S5
20 5 15 25 53 49 16 29
10
49 26 24
17
27 27 63 1
Shear wave velocity estimates from the application of eqn. (5) to the pyroclastic medium sands over the first 16m depth are illustrated in table 4 and compared with VS measures from Down-Hole tests filtered by Vivatrat procedure. As can be seen differences in values are registered even though they don’t show systematic trend. In fact sometimes VS measured values are higher than the estimated one but other times the contrary is true. Moreover often the two types of values are near each other but not always and this occurrence apparently cannot be related to the depth or to the estimation errors. Thus VS indirect estimation would become a very uncertain activity which could lead to an unreliable geotechnical design if variability and uncertainties concerning to NSPT measures and transformation models are not investigated. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
346 Computational Methods and Experiments in Materials Characterisation III Table 4: Depth (m) 1 2 2.5 4 5 6 7.5 8 9 10.5 11 12 12.9 14.5 15
4
VS values estimated by NSPT and Vivatrat procedure applied to VS (m/s) measurements performed by Down-Hole tests. VS1 DH1 VS2 DH2 VS3 DH3 VS4 DH4 VS5 DH5 183 152
270
264
255
219
231 229
219
233
219
266
219
201
225
278
225
267
225
280
225
231
231
231
289
276
215
202
202 331
165
229
229
202
Uncertainties concerning with SPT measurements
Standard penetration test (SPT) is a common tool for geotechnical characterization of building sites due to its economy and simplicity. Nevertheless most of the sources of uncertainties concerned with the NSPT measures have not sufficiently quantified. A detailed list of 27 sources of uncertainties are illustrated by Zekkos et al. [3] but only three out of them can be taken into account by means of reliability analyses: 1. Soil inherent variability 2. Equipment uncertainties due to hammer efficiency, borehole diameter and sampler 3. Procedure uncertainties Phoon and Kulhawy [7] summarized measurement errors and random variability commonly found for in situ tests. As regard NSPT values three coefficient of variation (COV (%)) ranges are outlined for the three sources of uncertainties itemized above: 1. Random variability for clay and sand: 12%y50%; 2. Equipment uncertainty: 5%y75%; 3. Procedure uncertainty: 5%y75%. In the case studied the NSPT values are not enough for carrying out a variability soil characterization. Accordingly in order to assess the reliability of VS estimation by means of NSPT measures and eqn. (5) by Ohta and Goto, the minimum values of the COV ranges reported are taken for the study. Moreover the variance related to the transformation model is calculated by the formulation of probable error (E) indicated by [4]: WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
Computational Methods and Experiments in Materials Characterisation III
SD2m
n
¦
Vc Vo 2
i 1
ln E 1 0.071 0.675
n
347 (6)
where SD2m is the variance that represents the “model error”; Vc is the shear wave velocity calculated by eqn. (5); V0 is the corresponding shear wave velocity in situ measured; n is the number of measures and E is the calculated probable error that is 19.7% for eqn. (5). In order to measure the reliability of VS estimated values by means of NSPT measures and eqn. (5) variability and uncertainties are combined consistently using the second-moment probabilistic approach, reported by [7]. According to such approach the mean value and the variance characterizing an estimated variable [d is given by the following expressions: m[d | T t , 0 2
2
(7) 2
§ wT · § wT · § wT · 2 2 2 SD [2d | ¨ (8) ¸ SD w ¨ ¸ SD e ¨ ¸ SD H © ww ¹ © we ¹ © wH ¹ where T() is the “transformation model” or the correlation equation eqn. (5) for the case studied; t is the deterministic trend function or the mean value; SD2w, SD2e and SD2H introduce variances concerned to inherent soil variability, measurement error and transformation uncertainty respectively. Results from the application of the second-moment probabilistic technique are presented in table 5. The total coefficient of variation measures the reliability of estimate at each depth. Hence, for those values of COV higher than 50% the estimate results to be unreliable whereas those values of COV lower than 50% should be considered as reliable as the NSPT values result to be.
Table 5:
VS1 152 270 264 255
5
Total coefficient of variation related to VS estimated values by means of Ohta and Goto expression in terms of NSPT measures from five boreholes. COV 83% 14% 25% 41%
VS2 COV 289 16% 276 28% 165 >100%
VS3 183 229 233 266
COV VS4 COV VS5 COV 25% 215 59% 201 37% 25% 331 14% 278 16% 40% 267 28% 30% 280 28%
Conclusions
In the paper two reliability studies are carried out on shear wave velocity determination by means of in situ tests: Down-Hole and Standard Penetration Tests. The first one is related to depth vs. arrival time diagrams from Down-Hole measures: a filtering procedure is applied in order to suggest a standard method by means of seismic strata detection and VS value calculation.
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348 Computational Methods and Experiments in Materials Characterisation III The second issue attains the evaluation of reliability in estimation of shear wave velocity from NSPT measures by means of Ohta and Goto relationship. The analysis considers the contributions of measurement errors in SPT, inherent variability of soil and transformation model error from eqn. (5) to the final VS values. The study shows that often the reliability of VS estimation, for the case studied, can be considered acceptable and can justify the differences in values between measured and estimated VS. Results from such work can be reviewed as a contribution to a more objective method for dynamic characterization of soils aimed at dealing with both foundation designing and local seismic response analyses.
References [1] [2] [3]
[4] [5]
[6] [7]
Eurocode 8. Design of structures for earthquake resistance. Part 1: General rules, seismic actions and rules for buildings. UNI ENV 1998 – 1, 2005. Testo Unico. Norme tecniche per le costruzioni. Ministero delle Infrastrutture e dei Trasporti, 29 settembre 2005. Zekkos D.P., Bray J.D. & Der Kiureghian A., Reliability of shallow foundation design using the standard penetration test. Proc. ISC-2 on Geotechnical and Geophysical Site Characterization, Viana da Fonseca & Mayne eds., Millpress: Rotterdam, pp. 1575-1582, 2004. Ohta Y., Goto N., Empirical shear wave velocity equations in terms of characteristics soil indexes, Earth. Eng. Struct. Dyn., 6, pp. 167-187, 1978. Cherubini C. & Vessia G., A Stochastic Approach to Manage Variability from in Situ Test Data, Proc. of the Joint Specialty Conference on Probabilistic Mechanics and Structural Reliability, ASCE, 26-28 July, Albuquerque, 2004. Vivatrat V. Cone Penetration in clays, Ph.D. Thesis MIT Cambridge, Mass. (USA), 1979. Phoon K.K. & Kulhawy F.H., Characterization of geotechnical variability, Can. Geotech. Journal, 36, pp. 612-624, 1999.
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A natural and biodegradable scaffold of electrospun eggshell membrane W. D. Kim, T. Min, S. A. Park, J. H. Park & G. H. Kim Bio-mechatronic Division, Department of Future Technology, Korea Institute of Machinery and Materials (KIMM), Korea
Abstract A successful tissue-engineering scaffold must have a highly porous structure and good mechanical stability. High porosity and optimally designed pore size provide structural space for cell accommodation and migration and enable the exchange of nutrients between the scaffold and cell culturing environment. The pore structures should be interconnected with each other for cell growth and proliferation. Soluble eggshell membrane protein (SEP) was prepared from eggshell membrane (ESM) and mixed with poly(İ-caprolactone) (PCL) solutions. SEP/PCL micro-size-fibre web was fabricated using electrospinning process with the help of a dual nozzle and auxiliary cylindrical electrode. The web was characterized with water contact angle (WCA) and cellular behaviour. The SEP/PCL web, which showed feasibility to fabricate scaffold having adequate hydrophilicity and suitable pore distribution, was a good example mimicking the natural biomaterial. Keywords: biomimic, soluble eggshell protein, poly(İ-caprolactone), nanofibre.
1
Introduction
Natures generate remarkable materials such as abalone nacre, sea mussel adhesive, and spider silk, which is an extremely strong material and is on weight basis stronger than steel. Biomimic is a science, which takes inspiration from Natures’ designs and processes to solve engineering problems [1]. Scientists and engineers are reverse engineering many of animals’ performance characteristics using these advances. These research areas include materials, actuators, sensors, structures, functionality, control, intelligence and autonomy [2]. Recently, these technological trends using the nature-inspired technology were expanded in the WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/MC070351
350 Computational Methods and Experiments in Materials Characterisation III field of biological areas. Realistic achievements have been obtained at the interface of nano-materials and biology, including the fabrication of nanofibre materials for three-dimensional scaffold and tissue engineering, the creation of living micro-lenses, and the synthesis of metal nano-wires on DNA templates [3]. As stated by previous researchers [4, 5], the scaffold consisting of nanofibres overcomes the limitations of conventionally fabricated scaffolds due to their high surface area and high porosity. According to Buckley and O’Kelly [6], ideal scaffolds should possess the following characteristics to bring about the desired biological response: (1) highly porous with an interconnected pore network and flow transport of nutrients and metabolic waste, (2) biodegradable with a controllable degradation, (3) suitable surface chemistry for cell attachment, (4) mechanical properties, and (5) be easily processed to form a variety of shapes and sizes. Considering the previously stated technical points of ideal scaffolds, eggshell membrane (ESM) has interesting structures and functions, such as interconnected porous structure, good hydrophilic surface property, and transporting function of nutrients to the chick’s embryo. The ESM was composed with a double-layered structure in which outer structure is randomly entangled micro-size fibres with the average diameter of 3 Pm (figure 1). Despite of various researches for the applications using the biological composition of the ESM, few applications were reported for the biomimical regeneration of the unique structure of the membrane. We used in this paper poly(İ-caprolactone) (PCL), which presents good mechanical properties relative to other biomaterials and has been developed as a biomaterial scaffold having biodegradability and bioreabsorption properties [7]. In this work, we imitate the natural micro-fibrous structure of the eggshell membrane as a biomedical scaffold. In order to obtain this goal, firstly we analyse the structure of eggshell membrane, such as pore size, porosity, and water contact angle (WCA). The soluble eggshell protein (SEP) was extracted from the eggshell membrane, and it was used to fabricate micro-fibre web using electrospinning process. To increase the processability of the process, SEP was co-extruded with a biocompatible PCL. The mixture was electrospun using a dual nozzle and auxiliary electrode to achieve stable initial jets at a nozzle tip. The fabricated bio-composite was characterized in WCA and cellular behaviour. The growth characteristic of human dermal fibroblasts (HDFs) cultured on the spun mat showed the good attachment relative to pure PCL webs.
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Experimental method
2.1 Materials The extraction of SEP from ESM was followed by the experimental method of Yi et al. [8]. The protein was acquired dissolving raw ESM in aqueous 3-mecaptopropionic acid and 10% of acetic acid, and the solution was heated to 85°C for 12 h. After cooling the traces of insoluble solid in the solution was removed WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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by centrifuging. The solution was adjusted to pH 5 with 5 mol/L of NaOH. The white precipitate was acquired by filtration and washed with ethanol. 2 wt% of SEP solutions were prepared by dissolving 0.2% of aqueous NaOH with prepared SEP. Yi et al. [8] used poly(ethylene oxide) (PEO) to increase the spin-ability of this process. However, SEP/PEO solution was difficult to accumulate spun fibre on a dielectric surface due to the surface charges of the electrospun fibres. Moreover, the PEO cannot conduct a role as a matrix of a SEP/PEO web because of its great solubility to water during cell culturing. For that reason, we used poly(İ-caprolactone) (PCL, Sigma–Aldrich) which could be used for increasing spin-ability. 8 wt% of PCL was dissolved in a solvent mixture of methylene chloride (MC)/dimethyl formamide (DMF) at a ratio of 20/80. The each solution was injected into the dual nozzles with a 20 mL glass syringe. The flow rates of the solutions were controlled using two syringe pumps (KDS 230; NanoNc Inc., Seoul, Korea).
Figure 1:
SEM images of ESM, (a) for inside surface structure and (b) outside surface of the membrane.
2.2 Electrospinning Micro/nanofibres could have been fabricated using an electrospinning technique. The principle of electrospinning is that a Taylor cone is formed by applying an electric field to polymer solution hanging from a capillary tip, which causes jets of electrically charged solution to be emitted when the applied electrostatic force is stronger than the surface tension of the solution. The jets of solution erupt from the apex of the cone at a nozzle and travel toward an electrically grounded target on which they are stacked as a nonwoven mat. The SEP/PCL nanofibres were fabricated using an electrospinning technique with a cylindrical auxiliary electrode and dual nozzle system. The cylindrical electrode and nozzle were connected by a copper wire and could be charged simultaneously as the fluid passed through the spinneret. In the dual nozzle, the two different solutions were injected into the capillaries of the nozzle. Outer part (S1) was fed with the PCL and inner nozzle (S2) with SEP. The feeding rates for the solutions of SEP and PCL were 0.25 and 0.5mLh-1, respectively. The poly(ethylene terephthalate) (PET) film covered a grounded electrode as a WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
352 Computational Methods and Experiments in Materials Characterisation III collector. The detailed shape and geometry of the auxiliary electrode and dual nozzle are shown in figure 2. The cylindrical electrode served to reduce the instability of the initial jet leaving the apex of the Taylor cone. More details on the role of the electrode are described below. The syringe was subjected to the same applied voltage (19.2 kV) with a distance of 100 mm between the target and needle tip, and a high-voltage power supply (SHV300RD-50K; Convertech, Korea) was used to control the applied voltage. The initially spun jet was photographed using a digital camera (E-300; Olympus, Tokyo, Japan). The spun fibres were deposited on a PET film covering a copper target.
Figure 2:
Schematic of the electrospinning setup with an auxiliary cylindrical electrode and dual nozzle. The cylindrical electrode has a radius of 11 mm and is 0.4 mm thick.
2.3 Cell culture and experiment Primary fibroblasts were isolated from sterile biopsies of normal skin. The specimens were minced in tissue culture dishes and cultured in an atmosphere of 5% CO2 and 37ଇ. The nanofibre scaffolds were sterilized with 70% ethanol and exposed to UV light for 1 hour to eliminate contamination. And, they were prewarmed with Hank’s balanced salt solution (HBSS) for 4 hours. Human dermal fibroblasts (HDFs) were cultured in Dulbecco’s Modified Eagle Medium (DMEM) supplemented with 10% fetal bovine serum (FBS) and 1% antibiotics (penicillin/streptomycin). The cells were maintained up to passage 7. Isolated fibroblasts were seeded on each sample (1 × 1 cm) at a density of 5.0 × 104 cells/nanofibre and cultured for up to 3 days. The cells were fixed with 4% glutaraldehyde for 1 hour at room temperature, and dehydrated through a series of ethanol dilutions. The samples were sputter-coated with Pt. Cell morphology and growth was observed using a scanning electron microscopy (FE–SEM, Sirion; FEI, Hillsboro, OR, USA). 2.4 Structural morphology The morphology of the electrospun mat of the mixture (SEP/PCL) was observed using an optical microscope (BX FM-32; Olympus) and SEM. Before WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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observation, the scaffolds were coated with gold using a sputter coater. The pore size, total pore volume, pore area, and porosity were characterized with the AutoPore III mercury porosimeter (Micromeritics Instrument Co., Norcross, GA). Sample preparation and procedures for measurement were conducted following the instructions provided by the manufacturer.
3
Results and discussion
3.1 The characterization of ESM It has been well known that surface roughness and chemical structure of polymeric scaffolds are key roles on cell growth and proliferation [9]. Figure 3 shows the WCA of ESM. The comparison of the measured contact angle between the inner and outer surface of eggshell membrane, which was shown in figure 1, shows dramatically different result. The outer surface of ESM shows good hydrophilic property, but hydrophobic for the inner surface. Since the specific surface property of the membrane, the eggshell membrane may have been researched for a selective filtering system [10].
Figure 3:
Photographs taken during WCA measurements: (a) inner surface of ESM (WCA = 95o at t = 1sec, 93o at t =10 sec), (b) outer surface of ESM (WCA = 80o at t = 1sec, 33o at t =10 sec).
In figure 4, assessment of structural pore property of ESM was determined with the use of a mercury porosimeter. The porosity of the ESM was 59.62%. Total pore volume was 2.09 mL/g and total pore size was 232.96 m2/g. The plot against pore size diameter indicated that the pore size had broad range from 0.005 to 500 Pm. As shown in the figure 1, ESM has consisted of two layers and the composition of the membrane can be separated into two parts, insoluble and soluble. According to the pre-treatment of ESM, the yield of the soluble protein, WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
354 Computational Methods and Experiments in Materials Characterisation III SEP, was less than 63% and it means the insoluble part can be exist in some structure. Figure 5 shows an image of insoluble remnant after 24 h of chemical treatment. The transmission microscope images show the diameter of the ESM fibres was dramatically decreased after removing the soluble protein. From the result, we can find that the soluble and insoluble part is coexisted with fibrous forms. In summary of the analysis of ESM, the detail structure and surface properties are described in Table 1.
Figure 4:
Plot against pore size diameter of ESM. The differential intrusion means the relative quantity of pores of a specific diameter.
Figure 5:
The images taken by the transmission optical microscope. (a) is pure ESM and (b) is insoluble remnant of ESM which was chemical treated.
3.2 Regenerations of structure of ESM To mimic the topography of the outer eggshell membrane, we fabricated SEP/PCL nanofibres using a specially designed electrospinning process, in WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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which a dual nozzle is attached to the syringe pumping system and a supplementary cylindrical electrode. When various electric-field conditions and processing conditions enforced to the solution, the size-controllable micro/nanosized fibres were obtained (figure 6). Figures 6(a) and (b) show the contours of the electric field with the same electric field scale near the nozzle for a standard electrospinning and the process supplemented using a cylindrical electrode. The distribution of the electric field inferred from the shape of the auxiliary electrode was analysed using the commercial software ANSYS/Emag for the electromagnetic analysis. The numerical models consisted of two-dimensional Plane121 elements and 8-Node charge-based electric elements. From the calculated and experimental results, the auxiliary electrode altered the distribution of the electric field near the nozzle tip. In the normal nozzle without the auxiliary electrode, the direction of the initial spun solution at the nozzle tip was instable, due to near environmental conditions, figure 6(a). In contrast, with the supplementary electrode, the initial direction of the solution was very stable and the jet toward the counter electrode was straight, figure 6(b). Table 1:
Properties of ESM. Eggshell membrane inner surface outer surface
Structure diameter (average)
2 µm (bead)
3 µm (fibre) 2
pore size (total) pore volume porosity
232.96 m /g 2.09 mL/g 59.62%
*
WCA t = 1s t = 10s
95ԕ 80ȋ
93ȋ 33ȋ
*: Water contact angle.
Figure 7 shows transmission optical microscope images of the electrospun PCL and SEP/PCL fibres deposited on the PET film. The electrospun webs were consisted of randomly distributed non-woven fibres and the diameters of the PCL and the mixture are similar each other, showing an average diameter 2.3 Pm. To check the increase of hydrophilic property of the mixture (SEP/PCL), the measurements of the WCA were performed. Figure 8 shows the contact angles of the samples electrospun with and without SEP solution. It is clear that the spun web coextruded with the eggshell protein solution and PCL solution leads to a lower contact angle, i.e. higher hydrophilic property, which may be one of the reasons for enhancing the attachment of the seeding cells. According the results, SEP injected to the inner nozzle was mixed with PCL rather than forming a coreWIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
356 Computational Methods and Experiments in Materials Characterisation III shell structure. It is because the SEP solution may disperse during the spinning process, so that the spun jets appear to be not coated with PCL solutions, even though SEP was injected inside of nozzle. Resultantly, we can conclude that the nanofibre web of the mixture has hydrophilic property relative to that of pure PCL nanofibre web.
Figure 6:
(a) and (b) are the contours of the electrical fields using without and with an auxiliary electrode and photographs of the Taylor cone at the nozzle tip: (a) normal electrospinning and (b) cylindrical auxiliary electrodes under the same applied electric voltage of 15 kV.
Figure 7:
The images show the electrospun fibres of (a) PCL and (b) SEP/PCL: an average diameter of the fibres is 2.3 Pm.
3.3 Cell culturing The surface property of the biomaterial can control cell adhesion, shape, proliferation and function. Figure 9 shows SEM observation of HDFs on the PCL and SEP/PCL nanofibre web. Cell morphology in the SEM images had a multiple cell attachments on the webs. At 3 days, large area of confluence, which WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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was tightly packed with the cells, was observed on the SEP/PCL web relative to the PCL web. As the cultured images are compared in viewpoint of the cell attachment of HDFs, the SEP/PCL web provides more uniformly distributed cells, while those were not in the PCL web. The result of cell culture can be elucidated by the contact angle results. As shown in the figure 8, the electrospun SEP/PCL web had a lower WCA than that of PCL web and this phenomenon is effective in the cell attachment. It is because the hydrophilic SEP is appropriately well mixed with the PCL through the electrospinning process and the nanofibrous web-structure provides a high level of surface area for the cell attachment. Also, improved protein adsorption can enhance cell attachment to the substrate.
Figure 8:
WCAs for (a) PCL and (b) SEP/PCL nanofibre web and (c) a compared plot against time.
Figure 9:
SEM images of the cultured HDFs on (a) PCL and (b) SEP/PCL nanofibre webs at 3 days.
4
Conclusions
In this paper, we tried to mimic the eggshell membrane, which has the characteristics of a biomedical scaffold such as interconnected porous structure, good hydrophilic surface property, and transportation system of nutrients. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
358 Computational Methods and Experiments in Materials Characterisation III Although the ESM has various advantages as a scaffold, it has been difficult to change to adaptable shapes like an example of “tailor-made” scaffolds. To achieve the shape-ability of the ESM, we used electrospinning process to be able to generate various size fibres and shapes. To increase processability of SEP and conduct a role as the insoluble matrix of ESM, the biocompatible PCL was co-extruded. The solutions were electrospun using a dual nozzle and auxiliary cylindrical electrode. The SEP/PCL was easily fabricated into a nanofibrous web consisted of uniform sized fibres, and the fibrous web showed a good hydrophilic property like the ESM. From cell culturing experiments, the web enhanced the cell attachment relative to pure PCL nanofibre web, as observed in SEM images. In this paper, we only used HDFs for cell culture. Since cell attachment and cellular behavior within scaffold are generally dependent on cell type, we need to further studies dealing with the cell attachment using various cell types to confirm the feasibility of ESM as cell culturing.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
Benyus, J. M. Biomimicry, Innovation Inspired by Nature. William Morrow and Company. New York 1997. Bar-Cohen, Y & Breazeal, C. Biologically Inspired Intelligent Robotics. Proceedings of the SPIE Smart Structures Conference, 5051-02, 2003. Zhang, S. Emerging biological materials through molecular self-assembly, Biotechnology Advances 20, 321–339, 2002. Li, W-J, Laurencin, C.T., Caterson, E.J., Tuan, R.S. & Ko, F.K. Electrospun nanofibrous structure: A novel scaffold for tissue engineering, J Biomed Mater Res 60, 613-621, 2002. Zong, X., Bien, H., Chung, C-Y., Yin, L., Fang. D., Hsiao, B.S., Chu, B. & Entcheva, E. Electrospun fine-textured scaffolds for heart tissue constructs. Biomaterials 26, 5330-5338, 2005. Buckley, C.J & O’Kelly, K.U. Regular Scaffold Fabrication Technique for Investigations in Tissue Engineering (Prendergast, P.J and McHugh P.E. Eds.), Topics in Bio-Mechanical Engineering, 147-166, 2004. Pitt CG. Poly-epsilon-caprolactone and its copolymers. In: Chasin M, Langer, R, editors. Biodegradable polymers as drug delivery systems. New York: Marcel Dekker; 1990. p71-120. Yi, F., Yu, J., Guo, Z., Zhang, L. & Li, Q. Natural Bioactive Material: A Preparation of Soluble Eggshell Membrane Protein, Macromol. Biosci. 3, 234237, 2003. Kaufmann, P.M., Heimrath, S., Kim, B.S. & Mooney, D.J. Highly porous polymer matrices as a three-dimensional culture system for hepatocytes. Cell Transplant, 6, 463-468, 1997. Ishikawa, S., Suyama, K., Arihara, K., & Itoh, M., Uptake and recovery of gold ions from electroplating wastes using eggshell membrane. Bioresources Technology 81, 201-206, 2002.
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Section 9 Computational methods – discrete computational methods
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Characterization of cementitious materials by advanced concurrent algorithm-based computer simulation systems Z. Q. Guo, M. Stroeven, W. Yang, H. He & P. Stroeven Faculty of Civil Engineering and Geosciences, Delft University of Technology, The Netherlands
Abstract The traditional discrete element computer simulation system in concrete technology is based on random generators referred to as sequential random (particle) addition (SRA) systems. They generate particles that are not spaced according to situations met in the actual material. This paper indicates the technological relevance of upgrading the concurrent algorithm-based discrete element computer simulation system SPACE discrete element facilities into a new discrete element system, HADES, which can encompass arbitrary particle shapes. The generation of particles is described as is the way particulate structure is formed. The technologically relevant fields are briefly indicated requiring exploration by this concurrent algorithm-based system. Such activities will be undertaken on short terms at Delft University of Technology. Keywords: arbitrarily shaped particles, concurrent algorithm-based system, cementitious materials, discrete element, and finite element.
1
Introduction
Cementitious materials are of particulate nature on different structural levels. The aggregate is compacted in the fresh concrete into the jammed state. It is a strong and hard material, under such conditions roughly taking up three-quarter by volume of the material body, and constituting a load-bearing skeleton that can provide the normal concretes with high compressive strength. The stability of the skeleton is guaranteed by the cementitious “glue”, the cement paste. Moreover, the paste’s quality, which is directly influenced by its fineness and by the water to cement ratio, governs the actual composite’s compressive strength level. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/MC070361
362 Computational Methods and Experiments in Materials Characterisation III Additionally, it gives the material its tensile strength. Modern high performance concretes are produced at low water to cement ratio, so the volume content of the cement in the paste may be as high as 60%. The latter is achieved by addition of chemical and fine mineral admixtures, which can also be employed for replacing part of the Portland cement (PC) and can be of pozzolanic or inert nature. All composing parts of the material have influence on engineering characteristics of the composite that will change as a function of time, in the first place as a result of hydration, however also due to complicated interaction processes with the environment. Material optimization would ask for very large numbers of specimens. Certain aspects have been investigated in trial testing and structural research programs, but it would be economically attractive to have reliable computer simulation methods available. The traditional discrete element computer simulation system in concrete technology is based on random generators to disperse inside the container aggregate particles on meso-level in a cementitious matrix, or cement and eventually other types of mineral admixture particles on micro-level in the watery environment during the fresh state. These systems are referred to as sequential random (particle) addition (SRA) systems. As stipulated elsewhere, they generate particles that are not spaced according to situations met in the actual material on both structural levels [5,7]. As a result, the processes of pore de-percolation, underlying concrete durability, and damage evolution, governing the materials residual strength capacity, will be incorrectly generated; biases declining fortunately during such processes. The latter field was so far the territory of “numerical concrete” [8], which is SRA-generated concrete subjected to finite element analysis. Additionally, SRA systems cannot produce particulate systems with the aforementioned high volume densities. Therefore, we have applied the concurrent algorithm-based discrete element computer simulation system SPACE with success on both structural levels, as witnessed by our two papers [12,13]. A drawback of all these systems is that only spherical particles can be generated. For aggregate of fluvial origin this may be considered not too dramatic. This can also be argued for cement or silica fume, as popular mineral admixture. However, aggregate grains of non-spherical shape are known to lead to lower densities in the jammed state. This has consequences for engineering strength. However, the impact on the nodes in the pore network model [13,14] that can be designed for estimating durability performance could be more dramatic. Realistic packing research on different structural levels with discrete element computer simulation system therefore requires facilities to also generate non-spherical particles. This is pursued by the HADES toolbox. With this package, particles can be of any shape and contacts are force-based rather than impulse-based, as in SPACE system. The surface of objects is no longer described by a mathematical function (such as in case of a sphere), but by a set of interconnected surface elements. In this way any shape can be described. The present paper briefly sketches the actual state of developments and indicates typical fields of application that will be explored in the very near future.
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Structure generation
2.1 Single particle To be able generating a particle assembly that corresponds to some actual mixture, one needs to characterize shape first. Once shape has been described by a set of shape parameters, probability curves have to be provided for each parameter so that it becomes possible to predict the probability of a certain shape (i.e., combination of shape parameters) in a mixture. Basically, HADES is designed to handle arbitrary shapes as long as the surface is tessellated by triangular or square surface elements of which the nodes are located on the surface. So far, ellipsoidal shaped and multi-facetted particles have been implemented [18]; more complicated shapes are under development. Ellipsoids are particularly interesting because with only 3 parameters a variety of shapes, ranging from oblate to oblong can be described, as shown in fig. 1. Two extra parameters are introduced that allow a range of differentlyshaped particles derived from the ellipsoids fig. 1a-c, namely, maximum size of surface element and maximum angle between the normal vectors to neighbouring surface elements at a node. The latter parameter controls how much the surface mesh follows the actual mathematical shape. Single examples out of ranges of shapes derived from fig. 1a-c are displayed in fig. 1d-f, by changing the maximum size and the maximum angle. In fig. 1d-f for all three cases, the maximum size of surface element and maximum angle are 20 and 60º, which are 2 and 10º for the cases in fig. 1a-c, respectively.
Figure 1:
(a)
(b)
(c)
(d)
(e)
(f)
Differently shaped ellipsoids. The lengths of the three semi-axes are 6, 8, 10 in (a), 3, 20, 22 in (b) and 3, 4, 16 in (c), respectively. (d), (e) and (f) are derived from corresponding ellipsoids in (a), (b) and (c).
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(a)
(b)
(f) Figure 2:
(c)
(g)
(d)
(h)
(e)
(i)
Particles with multi-facetted surfaces. (a) tetrahedron, (b) and (c) pentahedron, (d) and (e) hexahedron, (f) and (g) heptahedron, (h) and (i) octahedron.
A specific group of shapes with 4-8 facetted surfaces are proposed to represent the crushed rock by Guo Wen’s [16] based on his investigation. This proposal greatly simplifies the simulation of crushed rock since only two parameters are needed to determine shape and size. One extra parameter of maximum size of surface element is required only by numerical algorithm of interaction between particles and this parameter will not influences the shape of particles with multi-facets. Fig. 2 illustrated the particles with different number of facets. 2.2 Multiple particles Next, a set of particles (ellipsoids or polyhedron) is generated by using size and shape distribution curves that approximate the composition of an actual mixture. The individual particles are than positioned in a non-overlapping, but rather dilute way in some region or container. This region can be defined by periodic boundaries, rigid boundaries or partly periodic and partly rigid boundaries. Each particle is given a random initial linear and angular velocity. The particles are than, iteratively displaced to a position that is obtained by integrating the velocity over some (very small) time period. Similarly, the velocity of a particle at the next iteration, or time, is calculated by integrating the force (linear) or torque (angular) that acts on each particle. Currently gravitational forces, paste friction and contact forces between particles mutually or between particles and other objects in the simulation have been implemented. Moreover, the boundaries, periodic or not, can be dynamically moved according to the user-defined function. In this way, a number of experiments can be simulated. For example, by providing some sinusoidal motion of the container, shaking can be simulated, and along with it, size segregation of the WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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particles (under the influence of gravitational force), as show in fig.3. Dense packing can be obtained in this way, but it is also possible to move the periodic or rigid walls of the container towards each other thereby increasing the volume density of the mixture. By measuring the force or stress that is exerted by the particles on these container walls one can decide when the 'jammed state' is reached.
Figure 3:
3
Highly compacted system of ellipsoidal particles of type (a) generated by HADES in container with periodic boundaries.
Possible applications
3.1 Optimum mix design How do we do that, making concrete in virtual ‘reality’? What characteristics of the complex, particulate material should be incorporated in this so-called compucrete? Such questions must have been at the minds of those coming up with the first systems in the 70s of the previous century, such as that of Roelfstra [3], which formed the starting point of the “numerical concrete” concept of Zaitsev and Wittmann [15]. Basically, these and later developed systems in concrete technology rely on random RSA algorithms [1,2,9]. In RSA systems, particles are placed proceeding from large to small on preconceived positions of a Poisson field. Violation of physical conditions by overlap leads to rejection and re-generation. So, part of the Poisson field positions cannot be exploited, since spacing with other points is insufficient. The consequences are that, firstly, new positions should be randomly assigned to remaining particles until overlap is avoided. This is a time-consuming process, whereby the number of regenerations dramatically increases when the volume fraction is approaching a level of only 35%. In Williams and Philipse [7] an upper limit of 38.5% for spherical particles is mentioned, which is in qualitative agreement with Ballani [10] where in most cases the production of compucrete with 40% spherical aggregate failed. So, practical arguments plea for application to low density grain mixtures only. Secondly, instead of having series of particles close together in compucrete, in conformity with Poisson point processes, on average a more uniform dispersion is obtained. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
366 Computational Methods and Experiments in Materials Characterisation III Clustering, a natural phenomenon in particulate matter [4], is therefore very poorly represented by RSA systems. On the contrary, the concurrent algorithmbased computer simulation systems SPACE and HADES imitate the production conditions of concretes and have been demonstrated realistically incorporating the clustering phenomenon in compucrete. The SPACE and HADES systems realize compaction by a dynamic algorithm, which is also supposed to imitate the production stage of the material, as stipulated earlier. The forces added to the particles can be manipulated, so that “sticky” particle contacts (or particle repulsion) during the production of the model material can be simulated. Also gravity effects can simply be included. River gravel and broken rock aggregates compact to different densities in the jammed state at equal grading (obtained by sieving), so HADES generation of compucrete will be required for simulation of crushed aggregate. SPACE application for this purpose in case of river gravel aggregate has resulted in good agreement with experimental observations [12]. 3.2 Dynamic effects on particle mixtures The study on the effect of compaction energy (in the construction industry as well as in laboratory testing) on possible size segregation can be pursued by HADES system. Although the concurrent algorithm in SPACE is based on a dynamic Newtonian stage, but it is impulse-based, this does not automatically allow studying effects of vibration characteristics (frequency, amplitude) on particle packing. The latter phenomenon is widely denoted as “Brazil nut effect” (BNE) in the international literature, and recognized as a relevant phenomenon in many branches of industry where they deal with transport or vibration/shaking of particles. The situation is shown quite complicated, and received intense attention in many articles issued during the present century in leading journals. Apart from the normal BNE, the reversed BNE is reported (Nature 429, May, 2004, 352-353), and even the horizontal BNE (Physics News Update, nr 653 #3, Sept. 2003). Relative densities and frequency details play a role, but the phenomenon is far from established, and some of the mechanisms are still of speculative nature. Effects of shape have been reported relevant for aggregate grains and binder particles. The shape effect was extended to fibres in Physical Review papers; so that fibre reinforcement in compacted concrete will basically be subjected to this effect, too. A wide variety of fibres (in size, aspect ratio and material) are used, as well as types of aggregate (with a wide range in volumetric densities). Also workability is low for precast elements and can be quite high for on-site placement of concrete. The assessment of safe ranges for compaction conditions should therefore be established for a variety of compositions. This would be of high economic relevance, since segregation may negatively affect performance. It will add to our studies of other size segregation phenomena inflicted by rigid surfaces during compaction (mould for aggregates, and aggregate grains for cement particles). This size segregation phenomenon finally leads after hydration to the location of percolated porosity in a thin zone immediately neighbouring all the aggregate’s surfaces, and thus to a spatial interconnected network structure WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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that governs durability issues [13]. On the somewhat longer run, it will be scientifically highly interesting and technologically extremely relevant to see whether BNE will interfere and how with such size segregation phenomena. Fig. 4 demonstrates the simulation of typical dynamic granular effects such as size segregation by vibration (the so called BNE) as generated by HADES system in 2D.
Figure 4:
Brazil Nut Effect simulated by HADES in 2D.
3.3 Workability The methods for workability and compactability testing are numerous and highly uncorrelated. The methodology can be characterized by a large degree of pragmatism, and a minor scientific basis. Specific solutions have been developed for sub-sectors of the concrete technology field, whereby simplicity under given conditions (either on-site or for laboratory testing) prevail. Some methods with overlapping fields of usage have been compared as to ease of use, simplicity of equipment, and stability or reproducibility of outcomes. The “Summary of concrete workability test methods” [17] offers a good survey. Computer simulation would allow for an economic approach to such problems and could unify (at least partly) the methodology on fundamental issues. Compucrete is employed for the purpose, whereby the effect of the existing equipment on the compucrete can be simulated. Cementitious materials contain high amounts of aggregate, so particle interference will be a major mechanism governing workability of the mixture. Conventional RSA-based systems cannot (or, cannot economically) simulate particulate materials in this high-density range. This application of HADES will require adaptations of the computer simulation methodology. A selection of most promising methods will be simulated and outcomes mutually compared. Only a small number of the methods in vogue employ vibration, thereby better resembling workability during compaction. Vibration is necessary for workability testing of SFRC (because of thixotropy). This situation will certainly be covered. The common used slump test is simulated for fresh concrete with different fluidities as shown in Fig. 5. The calibration work will be done in near future.
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368 Computational Methods and Experiments in Materials Characterisation III 3.4 Strength and damage estimation SPACE and HADES have been extended with the possibility to generate unstructured finite element meshes in which the material structure is explicitly modelled. Within these meshes, three components can be distinguished: aggregates, the cement matrix and the interfacial transition zones (the thin cement layer around each particle of which mechanical properties are different from those in bulk cement). Fig.6 shows all three components. These meshes can be constructed because SPACE and HADES provides a full description of the material structure. Consequently, it is possible to provide the mesh generator with a function that defines the element size as a function of the distance to the nearest aggregate surfaces, for example. In this way, the interfacial transition zone (ITZ)––important for many mechanical properties in concrete––can be modelled with relative small elements while the elements within aggregates can be taken much larger.
(a)
(c) Figure 5:
(b)
(d)
Slump simulation tests. (a) fresh concrete before test; (b) slump tests of concrete with low fluidity; (c) slump test of concrete with medium fluidity; (d) slump test of concrete with high fluidity.
Figure 6 presents a simple example of mechanical analysis. A specimen consisting of 9 particles and matrix is generated by HADES. The data are sent to mesh generator Gmsh [19], whereupon the displacement distribution (Fig.6a) and stress distribution (Fig.6b) under simple tension loading are analyzed by finite element analysis program FEAP [20]. Further studies on strength and damage estimation are foreseen for the near future.
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(a) Figure 6:
369
(b)
Displacement (a) and stress field (b) in HADES generated particulate system.
3.5 Durability estimation Production of computer-simulated compucrete can reduce time and efforts bestowed on assessment of geometrical properties of material structure. Results are reliable in so far compucrete’s geometric properties that are under investigation are realistic. Aggregate in concrete takes up about three-quarters of the material’s volume. This high density cannot be realized by conventional SRA systems. Moreover, particle dispersion (configuration) at lower produced densities is far from realistic. Both deficiencies can be overcome with concurrent algorithm-based SPACE and HADES systems, as is experimentally demonstrated in our paper [12]. A complete and operational system for structure analysis particularly focusing on pore characteristics is elaborated in our paper [13]. The developed methodology will be applied to concrete for pore structure analysis by means of the pore network model for concrete durability. Different technical parameters and production conditions can be incorporated into this physics model.
4
Discussion
SPACE allows investigating hard core particle packing problems up till the jammed state inside and outside concrete technology whereby particles can be considered spherical. Internal forces that govern the packing process can be emphasized. Hydrated states in concrete technology are covered as well, allowing for studies such as self-healing capacity [11] and pore de-percolation [5]. Particle systems that change their packing due to external static or dynamic forces (resulting in flow), and the inclusion of arbitrary shape that has shown to have impact on the density of aggregate at the jammed state enforced the development of HADES. Its 3D version is gradually becoming operational, and will be used for exploration of the territories indicated herein.
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5
Conclusions
This paper demonstrates that the concurrent algorithm-based discrete element computer simulation systems SPACE and HADES are capable of exploration of fields of major technological and economic relevance, the mechanical and durability properties of concrete. They allow for tackling material optimization problems whereby particle packing is especially a major issue; the new version incorporates arbitrary particle shape, and allows the simulation of effects of external forces on the particulate material.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
Breugel K. VAN, Simulation of hydration and formation of structure in hardening cement-based materials, PhD Thesis, DUP, Delft, 1991. Meakawa K., Chaube R. & Kishi T., Modeling of concrete performance – hydration, micro-structure formation and mass transport, E&FN Spon, London, 1999. Roelfstra P.E., A Numerical Approach to Investigate the Properties of Numerical Concrete, PhD Thesis, Lausanne, EPFL-Lausanne, 1989. Stroeven P., Some aspects of the micro-mechanics of concrete, PhD Thesis, DUP, Delft, 1973. Stroeven P. & Guo Z., Modern routes to explore concrete’s complex pore space. Image Analysis & Stereology, 25(2), pp. 75-85, 2006. Stroeven P. & Stroeven M., Assessment of particle packing characteristics at interfaces by SPACE system. Image Analysis & Stereology, 19, pp. 8590, 2000. Williams S.R. & Philipse A. P., Random packings of spheres and spherocylinders simulated by mechanical contraction. Physical Review E, 67(051301), pp. 1-9, 2003. Wittmann F.H., Roelfstra P.E., & Sadouki H., Simulation and analysis of composition structures. Materials Science and Engineering, 68, pp. 239248, 1984. Bentz D.P., Garboczi E.J. & Stutzman P.E., Interfaces in Cementitious Composites. Computer modeling of the interfacial transition zone in concrete. E&FN Spon, London, pp. 107-116, 1993. Ballani F., A case study: Modeling of self-flowing castables based on reconstructed 3D images. Proc. of 9th European Congress Stereology Image Analysis Polish Society Stereology, Krakow, pp. 282-288, 2005. He H., Guo Z., Stroeven P., & Stroeven M., Self-healing capacity due to unhydrated cement in concrete, Proc. of ICS XII, France (submitted), 2007. Stroeven P., Guo Z., & He H., On discrete element packing simulation of concrete aggregate. Proc. of ICS XII, France (submitted), 2007. Stroeven P., Guo Z. & Hu J., Pore modelling methodology. Proc. of ICS XII, France (submitted), 2007.
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[14] [15] [16] [17] [18] [19] [20]
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Stroeven P., Hu J., & Chen H.S., On connectivity of porosity. Proc. of Brittle Matrix Conference 8, Warsaw, pp. 25-34, 2006. Zaitsev J.W. & Wittmann F.H., Crack propagation in a two-phase material such as concrete. Fracture 3, ICF4, Waterloo, Canada, pp. 1197-1203, 1977. Guo W., Some material parameters on numerical statistical continuum mechanics of concrete. TU Delft Report: 25-88-38, 1988. Koehler E.P., Fowler D.W., Summary of concrete workability test methods. International Center for Aggregate Research, Report 105-1, 2003. Yang W. & Guo Z., Generation of three-dimensional particles of arbitrary shape and granular material simulation. TU Delft Report: 22.1.06.01, 2006. http://www.geuz.org/gmsh/ (http://www.ce.berkeley.edu/~rlt/feap/)
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A simulation of the behaviour of propane bulks on a grid platform A. Lagan`a & A. Costantini Department of Chemistry, University of Perugia, Italy
Abstract The increasing interest for the Ozone hole problem has prompted the European Union to ban the use of CFCs and HCFCs before the year 2015 (Copenaghen amendments). For this reason, intense research is presently being carried out to find alternative refrigerant fluids. Propane is one of these fluids and in order to understand its properties we carried out molecular dynamics simulations. In this paper we examine the results of our simulations and the difficulties met when implementing in parallel the suite of codes used for the molecular dynamics studies. Keywords: propane, frigorigen fluids, molecular dynamics, thermodynamic properties
1 Introduction Due to the recently approved Copenhagen amendments, the use of CFCs and HCFCs will be definitively banned before the year 2015. Hydrocarbons (HC) are being considered as an appropriate alternative. In particular HCs are considered as a long-term alternative refrigerant with no impact on global environment and in particular on stratospheric ozone depletion and global warming. Propane (also called R-290) is among them. It is therefore of great interest to carry out accurate computational simulations of propane bulks in order to rationalize their macroscopic properties and to single out in an ab initio way the theoretical foundations of their behaviour. Unfortunately this requires an amount of computing resources which is not always available. At present, a technology able to offer prospective affordable solutions to such a problem is Grid computing [1]. For this reason we decided to start a computational investigation aimed at constructing in an a priori fashion the state diagram of propane [2] on the EGEEWIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/MC070371
374 Computational Methods and Experiments in Materials Characterisation III Grid platform [3]. To this end the DL POLY [4] parallel software package was used in which the OPLS/AMBER all-atoms potential [5] was implemented. The paper is organized as follows: in section 2 the theoretical and computational machinery is sketched; in section 3 some indications on the performance of the used grid platform are given; in section 4 the results of the calculations are illustrated; in section 5 some conclusions are drawn.
2 The theoretical and computational machinery The simulation is based on a Molecular Dynamics (MD) approach. In MD approaches the time evolution of an appropriate ensemble of particles is computed in order to work out from the microscopic behaviour of the system an estimate of the macroscopic properties. As already mentioned, in our investigation MD calculations were carried out using the DL POLY suite of codes developed by W. Smith at the Central Laboratory for High Performance Computing of Daresbury [4]. As also already mentioned, the other pillar of our theoretical and computational machinery is the adoption of the OPLS/AMBER force field [5]. The OPLS/AMBER force field represents the nonbonded interactions as a combination of Coulomb plus a Lennard-Jones pair of terms as follows: mol.a 12 6 mol.b qi qj e2 σij σij + 4ij (1) fij VOP LS = 12 − r6 rij rij ij i j where qi and qj are the charges of atom i and j respectively, e is the charge of the electron, ij , σij and rij are the depth, the equilibrium and the actual distance respectively between atom i and j. In eq. (1 fij is always taken equal to 1 for all the ij interactions. The same expression is used for intramolecular nonbonded interactions between all pairs of atoms separated by three or more bonds. The intermolecular interaction for angular (eq. (2)) and torsional (eq. (3)) motions is represented as 2 Kθ (θ − θeq ) (2) Vangle = angle
with θ, the bending angle, having an equilibrium, θeq , value of 109.5◦ and Vdihedral =
Vi 1
i
2
[1 + cos (φi )] +
V2i [1 + cos (2φi )] + 2 +
V3i [1 + cos (3φi )] 2
(3)
with φi , being the dihedral angle and V1 , V2 and V3 the coefficients of the Fourier series. In the present system all the bonds have been considered constant and the total energy is taken as V = VOP LS + Vangle + Vdihedral WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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The value of the parameters used in the adopted OPLS/AMBER potential is given in Tables 1 and 2 [5].
Table 1: Values of the parameters of the OPLS/AMBER bending and torsion potentials of the Propane system. Bending Group
θeq /◦
Kθ /kcal mol−1
H −C −H H −C−C
109.5 109.5
35.00 35.00
C−C −C
109.5
40.00
Torsion Group
V1 /kcal mol
H −C−C −H H −C −C−C
V2 −1
V3
/kcal mol
0.000 0.000
−1
/kcal mol−1
0.000 0.000
0.318 0.366
Table 2: Parameters for the OPLS/AMBER nonbonded potential of the Propane system. q/e−
σ/A˙
/kcalmol−1
C, RCH3
−0.180
3.650
0.0635
C, R2 CH2 H
−0.120 0.060
3.650 2.585
0.0635 0.0287
Atom
3 Performances of the used grid platform To evaluate the performance of the used platform, six different EGEE-Grid computer clusters were used. In order to evaluate the elapsed time of each simulation and the related speed-up for each cluster, we ran the calculations sequentially on one node and in parallel on 2 and 4 nodes. Measured elapsed times and speedups are plotted in Fig. 1 and 2 respectively. As shown by the figures the parallel performance of some clusters of the EGEE-Grid is very close to the WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
376 Computational Methods and Experiments in Materials Characterisation III ideal value due to their dedicated usage. Deviations from it occurring in the other clusters are mainly due to the time sharing regime adopted by them. This means that the parallel performances of each EGEE-Grid cluster strictly depend on the adopted regime. In order to evaluate more in detail the parallel performance of each cluster and the waiting time intercurring between the scheduling and the running of a process we restricted parallel calculations to two nodes. To carry out a statistical analysis we ran 50 parallel jobs (see Table 3). As apparent from the table, more than 70% of the jobs ran properly and only 26% were aborted. Abortion is due for 62% of the cases to communication errors between the nodes of the same cluster, for 23% to errors internal to DL POLY occurred during the running and for 15% a wrong scheduling.
Figure 1: Elapsed time measured on six different EGEE-Grid clusters (listed in the right hand side of the graph) plotted as a function of the umber of processors used.
4 Calculations and results All the calculations were carried out using the same npt statistical ensemble at two different pressures and temperatures in order to simulate the liquid phase at the equilibrium and out of equilibrium conditions for a bulk system of 288 molecules of propane. All the simulations were performed for a time duration of 1 ns. As shown by Table 4, the calculated value of the density of the system gets closer to the experimental data given in literature (582 Kg m−3 at T=230 K at P=1.013 bar [6]) when going from 10 bar to 1 bar. An important aspect to single out here is the fact that the pressure calculated at the end of the simulation does not agree with the imposed pressure (0.8 bar larger). From values reported in Table 4 it appears clearly that this difference (∆P ) is not constant. ∆P decreases, in fact, as WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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Figure 2: As in Figure 1 for speedups.
Table 3: Statistics on EGEE-Grid submissions out of 50 jobs. Job status
Number
%
Success Aborted
37 13
74 26
Cause for abort
Number
%
Communic. error
8
62
DL POLY error Scheduler error
3 2
23 15
the pressure increases. Another set of calculations was carried out at 100 K at a different pressure in order to evaluate the property of the system out of equilibrium (Table 5). As shown by the Table, also the density of the system out of equilibrium decreases in going from 10 bar to 1 bar. However the effect of the pressure on the system seems to be stronger if the temperature decreases. Further calculations are being carried out to single out the microscopic reasons for such an effect.
5 Conclusion We have studied the propane system in liquid phase using the OPLS/AMBER definition of the force field on the EGEE-Grid platform in order to reproduce the properties of the system and, at the same time, to evaluate the performance of the parallel calculations. We found that the calculated value of the density of the system gets closer to the data given in literature (when going from 10 bar to 1 bar) and we also found a substantial difference between the calculated average pressure and imposed pressure values since the former strongly dependent from the temperature and the density of the system. Further investigations suggested by our WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
378 Computational Methods and Experiments in Materials Characterisation III
Table 4: Thermodynamic properties of Propane bulk system calculated after 1 ns of simulation time at 230 K. Pressure / bar
Density / Kg m−3
∆P/bar
1.0035 ± 28
584.2 ± 4.4
0.8705
1.9768 ± 27 3.9590 ± 28
585.2 ± 5.6 585.4 ± 5.3
0.8568 0.8394
7.9393 ± 26 9.9444 ± 28
585.2 ± 5.4 585.7 ± 6.6
0.8196 0.8243
Table 5: Thermodynamics properties of Propane bulk system calculated after 1 ns of simulation time at 100 K. Pressure / bar Density / Kg m−3
∆P / bar
1.0509 ± 25 2.0362 ± 23
722.9 ± 4.7 723.9 ± 5.3
0.9179 0.9162
4.0492 ± 25 8.0334 ± 24
724.2 ± 5.6 724.5 ± 5.2
0.9292 0.9134
10.047 ± 26
725.0 ± 5.8
0.9273
results are those aimed at understanding whether this difference is due to the nature of the repulsive interaction adopted by the model potential. We found also high statistical errors which affect the pressure values. Other investigations suggested by our results are those concerned with the need for increasing of the simulation time in order to obtain a better average value of pressure, a better definition of the variation of ∆P using a more extended range of temperatures and pressure and a tuning of the force field of the system in order to exert a better control of the effect of the pressure on the system.
Acknowledgements This work has been supported financially by MIUR, ASI, CNR and COST CMST (action D37 GRIDCHEM). Specific mention needs to be made to the Italian MIUR FIRB Grid.it project (RBNEOIKNFP) on High Performance Grid Platform and tools and to the MIUR CNR Strategic Project L 499/97-2000 on High Performance Distributed Enabling Platforms. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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References [1] Storchi, L., Manuali, C., Gervasi, O., Vitillaro, G., Lagan`a, A., Tarantelli, F.: Lecture Notes in Computer Science 2658 (2003) 297-306 [2] Costantini, A., Lagan`a, A., Pirani, F.: Lecture Notes in Computer Science 3980 (2006) 738-743 [3] EGEE website: http://public.eu-egee.org [4] Smith, W., Forester, T.R.: DL POLY2: a general-purpose parallel molecular dynamics simulation package. J. Mol. Graph. 14 (3) (1996) 136-141 [5] Jorgensen, W. L., Maxwell, D.S., Tirado-Rives, J.: J. Am. Chem. Soc. 118 (1996) 11225-11236 [6] Air liquid group website: http://www.airliquide.com
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Section 10 Computational methods – damage mechanics
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Failure characterisation of Ti6Al4V gas turbine compressor blades A. Kermanpur1, H. Sepehri Amin1, S. Ziaei Rad2, N. Nourbakhshnia2 & M. Mosaddeghfar3 1
Department of Materials Engineering, Isfahan University of Technology, Isfahan 84156, Iran 2 Department of Mechanical Engineering, Isfahan University of Technology, Isfahan 84156, Iran 3 Isfahan Regional Electric Company, Isfahan, Iran
Abstract In this study, the failure process of Titanium compressor blades of an industrial gas turbine was investigated. Several premature failures occurred in the high-pressure section of the compressor due to the fracture of the blade roots. Macro- and micro-fractographic investigations were carried out on the fracture surfaces. Optical and scanning electron microscopy of the blade airfoil and root were also performed. Mechanical properties of the blade alloy were evaluated and compared with the standard specifications. Next, a 2D finite element model of the blade root was constructed and used to provide accurate estimates of stress field in the dovetail blade root and to determine the crack growth initiation in the dovetail. Based on the normal service operation of the compressor, the centrifugal and shear forces applied to the blade-disc configuration were considered in the model. The experimental results showed no metallurgical and mechanical defects for the blade materials. Microstructure of the blade root and airfoil, and hardness and tensile properties were all comparable with those reported in the standard specification. Fractography experiments clearly showed multiple crack initiation sites and fatigue beach marks. Debris particles were observed on the fracture surfaces and in the mouth of initiated cracks. The blade surface in contact with the disc in the dovetail region showed a higher surface roughness than the other surfaces. The numerical model clearly showed stress concentration at the corner on the contact facet of the blade dovetail between the blade dovetail and the wheel dovetail. Based on the results obtained, the fretting fatigue mechanism was proposed for the premature failures. Keywords: fretting fatigue, compressor blade, fractography, finite element method, computer simulation. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/MC070381
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1
Introduction
The phenomenon of ‘fretting fatigue’ has been recognized and studied well for over a century. Fretting is defined as the wear process occurring between two surfaces that have an oscillatory motion of small amplitude, on the order of tens of microns [1]. It has been responsible for a large number of service failures across a wide range of applications. For example, fretting in railway axles was reported by Maxwell et al. [2] in 1967, yet remains a cause for concern in forty years later [3]. For obvious reasons, fretting fatigue is particularly important in safety-critical industries such as aerospace or nuclear power generation. The recent High Cycle Fatigue (HCF) initiative [4] in the USA has provided a focus for fretting research in the aerospace sector, particularly in aircraft engine applications. These include the ‘dovetail’ roots of compressor blades (Nowell, [5]), where failure may have serious consequences for engine integrity (Xi et al., [6]). Furthermore, wherever two or more turbine components are in tight contact, fretting fatigue becomes a relevant failure mechanism. Yoshimura et al. [7] evaluated the fretting fatigue life of titanium alloy dovetails by using stress singularity parameters. They also used the finite element method to show that there exists stress concentration and high stress gradient in the zone of crack initiation under work condition. Arrieta and his coworkers [8] focused on identifying the driving factors for fretting damage on blade-disk attachment under real engine conditions. Two-dimensional finite element contact calculations were carried out to quantify the influence of the key factors on mechanical quantities such as stress and strain. Special attention was paid to material models and surface interaction (friction coefficient and contact conditions) in order to balance computational effort with result’s accuracy. Nowell [9] reviewed a number of recent developments, starting with attempts to apply multi-axial initiation criteria to the fretting problem. The importance of the size effect was highlighted and an analogy was made between fretting and notch fatigue. Methods for characterising crack initiation using asymptotic analysis were discussed, together with short crack arrest concepts which provide a means of predicting fretting fatigue limits from plain fatigue data. Golden and Calcaterra [10] evaluated a fracture mechanics based crack growth life prediction methodology for dovetail fretting fatigue laboratory experiments. They considered contact loads and bulk stress calculated from finite element method as input to the stress and life estimation analysis. Their analysis showed that propagation consumes a majority of the total life and was investigated to a large range of initial crack sizes. In this paper, several premature failures of Ti alloy compressor blades were characterised by both experimental observations and 2D finite element modelling. Characteristics of the fretting fatigue mechanism are also discussed.
2
Materials and procedures
2.1 Experimental Several premature failures were occurred in the high pressure compressor of gas turbines of Hesa power plant due to the fracture of the blade roots. The plant is WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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working under nominal output power 29MW with the rotating speed 8500rpm in the high pressure compressor. The failures were experienced at the 9th, 10th, and 12th stages of the compressor. Table 1 lists only the working history of the fractured blades in the 9th stage. First, chemical composition and mechanical and metallurgical properties of the blades were characterised. In order to perform optical microstructural investigations, metallographic tests were carried on different samples prepared from the root and airfoil of blades. Hardness test on the root and airfoil of the blades was performed using Hauser 292DR machine. Tensile test was carried on the sub-sized specimens, which were prepared from root of blades according to JIS-Z 2201 standard by Instron-8500 machine. Macro-fractography was performed on the surface of the samples by digital camera. In one of the fracture occurrences, a blade was left inside the disc with a crack in the root region. The fracture surface of the blade was also investigated along with the other completely fractured blades. Micro-fractography studies were carried out on all the failed samples by SEM Philips X230 machine equipped with EDS chemical analysis. Table 1:
Working history of the failed blades of stage 9.
Number 1 2
Date March 2005 May 2005
Working hours 7653 7669
2.2 Simulation Figure 1 shows a schematic of the forces acting on the blade-disc configuration. The simulation was carried out in two phases. First, a fluid analysis was carried out to estimate the aerodynamic force exerted on the blade. Then, the calculated aerodynamic forces together with the centrifugal force were used to obtain the stress analysis and to determine the stress concentration in the contact regions.
Aerodynamic force
Centrifugal force
Contact force
Figure 1:
The forces acting on the rotating blade.
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386 Computational Methods and Experiments in Materials Characterisation III 2.2.1 Fluid flow calculations A 2D fluid flow analysis was performed to estimate the forces acting on the blade under steady-state work condition. Simulation was made using the commercial software FLUENT. One static vane and one rotating blade were considered in the model. In the fluid calculation, the vane movement was assumed to be zero. The blade velocity was set to be rȦ, where Ȧ is the compressor rotating speed and r is the average distance of the blade from the disk centre. The fluid was assumed compressible and viscose. The k-İ equation was used to model the turbulence. 2.2.2 Stress calculations A 2D finite element analysis was conducted to evaluate stress concentration in the system. To apply the centrifugal force, the origin of coordinate system was located at the disk centre, and an angular velocity of 8500 rpm was applied to the disk-blade structure. The dovetail region was modelled using the finite element software ANSYS. Figure 2a shows the meshing created on the blade and disk. The mesh consisted of 525 2D plane stress four-node elements as well as 169 surface-to-surface contact elements. A close-up of the mesh near the interface between contact surfaces is shown in Figure 2b. The disc material was made of steel and the blade material was Ti-6%V-4%Al. All the centrifugal, contact and aerodynamic forces were considered in the model.
Figure 2:
3
a) Finite element model of the blade and a part of disc in the dovetail region; b) Details of the mesh in the contact area.
Results and discussion
3.1 Experimental results Table 2 shows chemical composition of the blade material compared with the standard limits of Ti6Al4V alloy. It confirms that the composition of the fractured blade is in fact Ti6Al4V alloy. The microstructures of the blade root
Computational Methods and Experiments in Materials Characterisation III
387
and airfoil with different work hours are presented in Figure 3. It is consisted of predominantly equiaxed Į grains, lamellar transformed Į plates, and fine intergranular ȕ phases. It should be noticed that this microstructure is common in Ti-alloy compressor and fan blades, with equiaxed portion providing good tensile ductility and hence good resistance to crack initiation, while the lamellar portion is responsible for increasing resistance to crack propagation. Table 2: Composition Standard Blade
Figure 3:
min max Mean RSD
Chemical composition of the blading alloy.
Al
V
Fe
Zr
Mn
Mo
Sn
Nb
Pd
Ti
5.50 6.75 5.18 1.95
3.50 4.50 3.91 1.31
--0.30 0.15 17.9
----<0.10 ---
----<0.10 ---
----<0.50 ---
----<0.50 ---
----<0.50 ---
----0.19 0.74
Rem
a
b
c
d
88.16 0.08
Microstructure of the fractured blades: a,b) root & c,d) airfoil; a,c) 1st & b,d) 2nd fractures. Table 3:
Vickers hardness of the blade’s root and airfoil. Number 1st fracture 2nd fracture
Position Airfoil Root Airfoil
HV 359.33 335.8 353.25
Root
338.17
Hardness values of the root and airfoil of two failed blades are presented in Table 3. The root and airfoil both had the same hardness. Tensile properties of the samples with different work hours are shown in Table 4. It can be seen that the mechanical and metallurgical properties of the blade material are in the standard range and no deviation in these properties were detected.
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388 Computational Methods and Experiments in Materials Characterisation III Table 4:
Mechanical properties of different fractured blades.
Sample Standard (min) 1st fracture nd
2 fracture
Figure 4:
YS [MPa] 862
UTS [MPa] 931
Elongation [%] 10
Reduction of Area [%] 25
961
1093
11.8
39.2
984
1025
16
33
Fracture surfaces of the: a) 1st and b) 2nd failure. Note that three distinct regions are numbered and the main position for crack initiation are identified by an arrow.
Figure 4 shows macro-fractography images of the 1st and the 2nd failures. Three different regions are remarkable in each fracture surface. In the first and second regions, beach marks are clearly detectable. Moreover, several radial lines can be revealed in each fracture surface. The position of the main crack initiation from the front edge of contact (EOC) of both blades are shown (Figure 4). It is seen that the characteristics of the fracture surfaces and the position of crack initiation are more or less similar for both failures. Micro-fractography tests were performed on different fracture surfaces as shown in Figure 5 for the 1st fracture. Figure 5a shows the main crack, beach marks and radial lines in region 1 of fracture surface. Figure 5b illustrates the fatigue appearance in region 2. The image of EOC and multiple micro crack initiation are observed in Figure 5c. The brittle fracture mode can be clearly seen in the fracture surface as shown in Figure 5d. Many debris particles as an indication of wear were found on EOC and in the mouth of cracks (Figure 6). EDS analysis (Table 5) of the debris particles showed a high amount of oxygen confirming oxidation of Ti during the service, which is responsible to form abrasive TiO2 particles in the fracture surface. Debris also shows some Fe content coming from the steel disk. Sever sliding and rough surfaces were observed in EOC in the blade roots as shown in Figure 7. It is believed that the coating of blade root and disk in the contact region were damaged making these surfaces so rough which can directly influence the crack initiation. The results of roughness measurements are listed in Table 6. As it can be seen, the maximum surface roughness is achieved in the EOC region.
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Computational Methods and Experiments in Materials Characterisation III
Figure 5:
(a)
(b)
(c)
(d)
Micro-fractography of the 1st fracture surface: a) region 1, b) transition to region 2, c) EOC, and d) brittle manner of material.
Table 5: Location Matrix Debris
389
Ti 89.39 32.24
EDS analysis of the blade alloy and debris on EOC. Al 7.75 5.89
Si 0.25 2.43
V 2.61 1.52
Fe --2.42
Mo 1.18 1.18
Na --0.48
P --0.4
O --52.8
According to all experimental results, existence of multiple crack initiation at EOC, presence of debris in the contact region, severe sliding wear, and high roughness at EOC, proposed that the main reason for failure phenomenon in the premature fractures of Ti alloy blades is the fretting fatigue mechanism. 3.2 Simulation results The fluid analysis was carried out to estimate the aerodynamic force exerted on the blade. The dynamic and static pressure distributions around the stator vane and the rotor blade were evaluated. According to the fluid flow analysis, the WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
390 Computational Methods and Experiments in Materials Characterisation III values of total forces exerted on the rotor by gas (the aerodynamic forces) in x, y and z directions are estimated to be: 0, -858.0 and 509.5 kPa, respectively. These values were used in the stress model as the aerodynamic forces.
Figure 6:
Micro-fractography of the 1st cracked blade fracture surface showing the appearance of main crack and compact debris in mouth of crack.
Figure 7:
Micro-fractography of the 2nd fracture surface showing sliding marks on EOC. Table 6:
Roughness at different regions of the blade.
Roughness
Airfoil (convex side)
Airfoil (Concave side)
Root, no contact
Root, EOC, near crack
Root, EOC
Ram (µm) STDEV
0.863 0.09
0.950 0.06
1.183 0.15
2.493 0.94
3.770 1.98
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Figure 8:
391
Contact pressure distribution in the contact surface.
a
b Figure 9:
Distribution of von misses stress in the a) blade, and b) contact region of disc and blade.
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392 Computational Methods and Experiments in Materials Characterisation III In the stress analysis, the centrifugal, contact and aerodynamic forces were applied to the model. Figure 8 indicates the high contact pressure at the EOC between blade dovetail and wheel dovetail. Figure 9 shows the von misses stress distribution and stress concentration in the contact surfaces. It can be seen that the maximum stress of about 195 MPa has achieved in the corner on EOC, the position that is in agreement with the experimental characterisation. It was concluded that this stress concentration has been caused by either unsuitable curvature ratio of the disk dovetail, incorrect design of the blade or tight contact between the blade root and the disk in dovetail region. It seems that the aforementioned factors as well as abnormal vibration have caused the fretting fatigue failure of the 9th stage compressor blades. The simulation model is under development to consider the fatigue feature of the aerodynamic force as well.
4
Conclusions
A fretting fatigue mechanism as the main cause of several premature fractures of Ti alloy compressor blades was characterised. All fretting characteristics were distinguished in the fracture surfaces. The developed 2D numerical model clearly showed that stress concentration is happened at the corner of EOC. The high stress at the dovetail region can be either due to the unsuitable curvature ratio of the disk dovetail, incorrect design of the blade, insufficient distance between the blade root and the disk in dovetail region, or abnormal vibration, causing the fretting fatigue failure of the 9th stage compressor blades which eventually leads to the complete failure of the blade and its separation from the disk.
Acknowledgement The authors would like to acknowledge Isfahan regional electric company for financial support of this work under contract 100/31911-113.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
Hutson, A.L. et al., Int. J. Fatigue, 24, pp.1223-34, 2002. Maxwell, W.W. et al., Proc. I. Mech. E, 182, pp.89-108, 1967. Hirakawa, K. et al., Int. J. Fatigue, 20(2), pp.135-144, 1998. Burns, C., Proc. 7th Nat. Turbine Engine HCF Conf., Dayton, Ohio, 2002. Nowell, D., Proc. Prog. in Structural Mechanics, Univ. of Seville, 61, 2000. Xi, N.S. et al., Engineering Failure Analysis, 7(6), pp.385-392, 2000. Yoshimura, T. et al., J. of Mate. Sci. Soc. of Japan, 40(6), pp.41-46, 2003. Arrieta, H.V. et al., H., Technical Report, RTO-MP-AVT-109, 2003. Nowell, D., Recent Developments in the Understanding of Fretting Fatigue, Department of Engineering Science, University of Oxford, 2004. Golden, P.J. & Calcaterra, J.R., Trib. Int., 39(10), p.1172, 2006. Mazur, Z. et al., Engineering Failure Analysis, 13, p.1338, 2006. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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Seismic damage assessment of steel components A. Benavent-Climent Department of Structural Mechanics, University of Granada, Spain
Abstract This paper discusses a new approach to the assessment of damage in structural steel components under cyclic inelastic loading stories of the type experienced in earthquakes. The approach is based on a new damage model proposed by the author. It is shown that the seismic performance of a steel component depends on two structural performance parameters: b and m. The parameter b is influenced by the material properties, the prevailing loading condition and the geometry of the steel component. The parameter m reflects the influence of the structural system, hysteretic behavior and characteristics of the earthquake. This approach takes into account that the cumulative damage—in addition to being affected by the total amount of dissipated energy, the maximum deformation and the number and amplitude of the cycles of deformation—is also path-dependent. Keywords: damage model, fatigue, seismic damage, steel component.
1
Introduction
The great damage caused by recent earthquakes, such as Northridge (1994) or Kobe earthquakes (1995), has highlighted that code design for life safety does not protect adequately the structure adequately against damage; performance goals other than life safety (e.g. damage control) must be taken into account explicitly in the seismic design of new structures (performance-based seismic design). In the field of earthquake engineering, there is an increasing trend toward employing damage as a measure of seismic performance in the assessment and design of structures [1-3]. To this end, accurate damage models that take into account cumulative damage effects (cumulative models) are needed for quantifying realistically the expected damage under different design earthquakes. These models can also provide the basis for judging the safety of existing structures and reference for retrofit decision making.
WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/MC070391
394 Computational Methods and Experiments in Materials Characterisation III The issue of structural damage characterization under seismic actions has received much attention, and several approaches have been proposed. One approach is based on the classical Manson–Coffin model for metallic materials [4, 5] and Miner’s linear damage accumulation rule [6], which governs low-cycle fatigue behavior of metals [7-12]. Manson–Coffin’s model postulates that, under constant amplitude cycling, the number of cycles to failure, Nf, can be related to the plastic deformation range of the cycle (in terms of strain, rotation, deflection etc.), 'Gp, by an equation of the type:
Nf
1
(1)
c
C ('G p )
where C and c are the structural performance parameters. The damage per cycle of amplitude 'Gp is 1/Nf. If the loading history consists of a sequence of n1,n2,.., nN closed cycles of different amplitudes 'Gp1,'Gp2..., 'GpN, respectively, Miner’s rule postulates that the accumulated damage, D, is:
D
ni 1 N fi
N
¦
i
N
c
C ¦ [ni ('G pi )] .
(2)
i 1
Failure is predicted when D=1. If the response history consists of arbitrary individual excursions (i.e. in the case of a seismic response history), cumbersome cycle counting methods (i.e. the rain-flow method) must be applied to convert the individual excursions into a sequence of closed cycles of constant amplitude so that Eq. (2) can be applied. This is one of the shortcomings of this approach. Another approach accounts for damage as a combination of maximum deformation and dissipated energy [13-16], and here the model proposed by Park and Ang [14] is the most widely used. Park and Ang’s model defines the damage index D by: D
Pmax EW , Qy Gu Pu
(3)
where Pmax (=Gmax/Gy) is the maximum deformation Gmax normalized with respect to the yield deformation, Gy; Pu (=Gu/Gy) is the normalized ultimate deformation Gu under monotonic loading; W is the dissipated hysteretic energy; Qy is the yield strength; and E is a parameter characterizing the damage contribution due to cumulative plastic strain energy. In this model, Pu and E can be viewed as the basic structural performance parameters. This model also presents important shortcomings: (1) the methodology for determining the “key” parameter E is not well stated; (2) failure is not identified by a single value of D; and (3) the model assumes that the response of the structure up to the limit state is path independent, that is, not influenced by the distribution of the plastic cycles during the deformation history. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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The shortcomings mentioned above endanger the consistency and reliability of these methods in predicting the level of damage and the closeness to failure of a structural steel component subjected to seismic actions. This paper discusses a different approach for assessing the structural performance of steel components subjected to arbitrarily applied stress reversals, such those induced by earthquakes. This approach is based on a new energy-based damage model proposed by Benavent-Climent [17]. In this model, structural performance is governed by two parameters, b and m. The former, b, depends on the material properties, the prevailing loading condition and the geometry of the steel component. The latter, m, is influenced by factors such as the structural system, the hysteretic behavior, and the characteristics of the earthquake. In contrast to existing methods, which consider damage as a combination of the total amount of dissipated energy and maximum deformation, the proposed model represents damage as a combination of: (a) the total dissipated energy and, (b) the portion of the total dissipated energy consumed on the skeleton part of the loaddisplacement curve. This paper shows that the model can easily be extended to other types of prevailing stress conditions. The model is intended to be used either for quantifying the level of damage in performance-based seismic design of new structures, or for evaluating the safety of existing buildings and establishing a framework for making decisions about seismic retrofitting.
2
Damage model
The load-displacement, Q-G, curve of a steel component subjected to an arbitrarily changing history of deformation can be decomposed, in each domain of loading, into three parts: the skeleton part, the Bauschinger part and the unloading part [18]. The skeleton part, Q-SG, is constructed by connecting sequentially each loading path that exceeds the load level attained in preceding cycles in the same loading domain. The Bauschinger part, Q-BG, begins at Q=0 and terminates at the maximum load level previously attained in preceding cycles in the same loading domain. The rest of the curve is the unloading part. Fig 1 shows an example of decomposition for a steel component subjected to constant amplitude flexure deformations. Akiyama et al. [19] and Benavent-Climent et al. [20] applied the concept of this decomposition to investigate experimentally the ultimate energy dissipation capacity (UEDC) of structural steel components subjected to forced flexure and shear cyclic deformations in the plastic range. In total, 49 round steel rods and 10 rectangular steel plates with slits were subjected to bending and shear under statically applied cyclic loads up to failure. Each Q-G curve obtained from the tests was decomposed into the skeleton and the Bauschinger parts as explained above. The skeleton part was approximated by the trilinear curve shown with dotted lines in Fig. 1b, which is defined by the yielding load, Qy, the yielding displacement, Gy, the plastic stiffness Kp1 and Kp2, and the load QB that determines the transition point from Kp1 to Kp2. The plastic strain energy dissipated in the positive and negative loading domains in the skeleton part, SWu+
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396 Computational Methods and Experiments in Materials Characterisation III and SWu, and in the Bauschinger part, BWu+ and BWu, was computed and expressed in a non-dimensional form as follows:
SȘ
Wu ; SK Qy į y
SWu
S
QyG y
;
BWu
BK
;
QyG y
_ BK
BWu
QyG y
(4)
Next, the total plastic strain energy dissipated in the positive and negative load domain up to failure was expressed by the following ratios: K
S
;
K BK
K
S
K BK
(5)
From the results of the tests, it was concluded that at the ultimate state, and for each domain of loading,CSK andCK can be related by the following expressions: Kd
W B2 1 :
K!
W B2 1 :
S
S
K
2k p1
2k p1
K
K
S
K
S
7.33 k p1
> 2k
@
K 1 1 0.5b
p1 S
(6)
º k k 7.33 ª« 2k p2 SK W B2 p2 (W B2 1) W B p 2 (W B 1)» 0.5b (7) k p2 « k p1 k p1 » ¬ ¼
where kp1=Kp1/Ke, kp2=Kp2/Ke, Ke=Qy/Gy, WB=QB/Qy and b is a non-dimensional coefficient that depends on the type of steel, the loading condition (flexure, shear etc.) and the geometry of the steel component. Qy, Gy, WB, kp1 and kp2 can easily be predicted analytically from the stress-strain relationship of the steel. b is the “key” structural performance parameter governing the UEDC of the steel component. It can be obtained by testing one specimen under constant amplitude cyclic loading [19] and is very sensitive to the detailed shape of the steel component in the region of plastic deformations. For the purposes of illustration, Eqs.(6) and (7) are drawn with dotted lines in Fig. 2 in the normalizedCK versusCSK space, for mild steel rods subjected to flexure. It is worth noting in Eqs.(6) and (7) that the total amount of plastic strain energy that the steel component can dissipate up to collapse,CK, depends on the amount of energy consumed on the skeleton partCSK, rather than on the maximum deformation Gmax. To clarify this point, let us consider for example a mild steel rod subjected to flexural cyclic deformations up to a given instant ti, at which it reaches the maximum deformation in the positive domain G+max for the first time. The condition of the rod at t=ti can be represented by a point with coordinates (CSKi,CKi ) in theCK versusCSK space shown in Fig. 2. Let us consider that after this instant ti, the rod is forced to undergo more cycles of plastic deformation with amplitude less than or equal to G+max in the positive load domain. The total amount of energy that the rod can dissipate in this domain until failure,CKu, varies according to the path followed by the rod from t=ti in theCK versusCSK, space. That is, if the path is such that the energy consumed on the skeleton part,CSK, does not increase in the positive load domain (i.e. path M in Fig.2), the rod will fail whenCK=CKu,1; otherwise failure will occur for a value WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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ofCK, smaller thanCKu,1. The minimum value thatCK can attain isCKu,2 (i.e. the path N in Fig.2), which corresponds to the situation in which after instant ti the rod continues deforming monotonically in the positive domain of loading, thus consuming only the skeleton part. The intermediate situation between path M and path N is represented by pathe, in which after instant ti the rod continues deforming cyclically and consuming energy in both the skeleton and the Bauschinger parts.
a)
K Wu/(QyGy)
Q
Skeleton part Bauschinguer part Unloading part
Wu
Qy
B Gmax
Gy
Wu
Q QB Kp1 Qy Ke SWu/(QyGy)
K
Gy Approximate skeleton curve
c) K
B
_ BWu _
K Wu/(QyGy)
SWu
S
G
Onset of strength degradation (assumed point of failure)
b)
Gmax
Kp2
+ SWu
G
S
K + SWu+/(QyGy)
S
Q
_ BWu/(Qy y)
G
G
K
B
Figure 1:
B + W B u + + B u y y
W /(Q G )
Decomposition of the load-displacement curve: a) original curve; b) skeleton part; c) Bauschinger part.
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398 Computational Methods and Experiments in Materials Characterisation III
K
900
Ultimate Limit State (failure) Equation (6) Equation (7)
Path 1
Ku1
Path 3
600
(SKu,Ku)
Ku2
300
Pa t h
2
Pa th
0
(SKi,Ki)
0
Figure 2:
K
S 100
200
Energy consumption path of the steel component.
Path e represents the general situation of a steel component with stable hysteretic response like that shown in Fig. 1, subjected to seismic loadings. It is important to point out that along this path e, due to the strain hardening effect of the steel, the maximum load attained by the rod in a given loading domain for the first time that it reaches the maximum displacement, Gmax, can increase in successive cycles even if Gmax is not exceeded. As these increments of maximum load in successive cycles involve additional consumption of energy on the skeleton part, it follows thatCSK can increase even if the maximum deformation Gmax is not exceeded. As stated by Eqs.(6) and (7), the UEDC of the memberCK decreases asCSK increases. In other words, the UEDC of the steel component depends onCSK rather than on Gmax. This experimentally demonstrated fact is contrary to the assumption implicit in the Park and Ang model, which holds that if the structure is subjected to the same normalized maximum displacement (Pmax/Pu), it will dissipate the same amount of normalized plastic strain energy (EW/QyGu). This is the case irrespective of the portion of this energy that is consumed on the skeleton part,CSK, which depends on the path followed by the member up to collapse. This path-independent characterization of ultimate state implicitly assumed by the Park and Ang and other damage models constitutes an important shortcoming, as mentioned in the introductory section of this paper. On the basis of this experimental background, Benavent-Climent [17] proposed a new model that defines the damage index of the steel component at a given stage i (prior to failure) characterized by (SKi,CKi ) as follows: WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
Computational Methods and Experiments in Materials Characterisation III
IDi
max{ IDi , IDi }
399 (8)
where IDi and IDi are the index of damage in the positive and negative domains defined by:
I Di
Ki Ku
(9)
This index measures the level of damage between 0 (no damage) and 1 (failure). As explained above, the value ofCKu at a given stage i depends on how the energy dissipated by the steel component is distributed between the skeleton part and the Bauschinger part. The distribution of energy between these two parts changes through the entire duration of the response and is strongly influenced by the structural system and the characteristics of the earthquake. This makes the prediction ofCKu for design purposes a cumbersome problem that is addressed in next section.
3 Energy demand for performance assessment A seismic damage assessment based on the model given by Eqs. (5) and (6) requires information on the energy demand ratio Ș / S Ș imposed by an earthquake on a steel component. Previous research [21, 22] showed that this ratio is influenced by parameters such as the properties of the structural system (yield level, period etc.), the hysteretic behavior of the component (which, in turn, depends on the axial force acting on the component, the prevailing stress condition etc.), and the characteristics of the earthquake. Through dynamic response analyses allowing for the Bauschinger effect, Akiyama and Takahashi [21] found that for the particular case of beams and columns in steel moment-resisting frames (flexural systems),CSK andCK can be approximately related by:
K/ S K
m
m
(1 p) (0.39 1.09 p )
(10) (11)
where p is the axial force ratio, i.e. p=N/Afy (here N is the axial force, fy the yield stress of the steel, and A the cross section of the member). Eqs. (10) and (11) provide an average value of the responses obtained from the dynamic analyses. For illustrative purposes, in Fig. 3 the relation betweenCSK andCK given by Eqs.(10) and (11) is compared with the actual response obtained from dynamic response analyses for p=0 (indicated by the symbol D).
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400 Computational Methods and Experiments in Materials Characterisation III As observed in Fig. 2, Eq. (7) is very close to Eq. (6); thus, for the sake of simplicity, Eq. (7) can be adopted for the entire range ofCSK. By substituting the ordinateCKu of the point where the line defined by K Ki m ( SK SKi ) intersects the ultimate limit state curve given by Eq. (7) in Eq. (9), the damage index IDi in a given domain of loading is: ID i
Ki 2 º ½° 7.33 kp2 mF 40k p2 7.33m ° 1 ª 7.33 7.33 2 k p1 k p2 bk p2 ( W B 7.33) 53.73 » ¾ « ®F 2 0.5(m 1) m 1 ° k p2 « m 1 k p1 k p1 ( 1 ) m »¼ °¿ ¬ ¯
(12) F
SKi
7.33
Ki 7.33m
WB 1 k p1
WB k p2
b 14.66
(13)
The “key” structural performance parameters that govern the damage model given by Eq. (12) are b and m. b reflects the influence of the material properties, prevailing loading condition and geometry of the steel component. m reflects the influence of the structural system, the hysteretic behavior and the characteristics of the earthquake. The rest of variables, i.e. kp1, kp2 andWB, simply define the shape of the skeleton curve and (in comparison to b) have minor influence on the structural performance of the steel component. Further research is needed to clarify the relation betweenCSK andCK for structural systems other than the flexural system described above. A comprehensive statistical evaluation of the ratio Ș / SȘ is in progress for bracing systems.
K
1200 s
p=0
1000 800
Eqs.(10),(11)
600 400 200 0
Figure 3:
4
0
K 500
1000
1500
2000
2500
Comparison of Eqs. (8), (9) with the actual response obtained from numerical simulations.
Conclusions
In this paper a new approach to the seismic damage assessment of structural steel components is discussed. The approach is based on a low-cycle fatigue damage WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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model proposed by the author. In this approach, the structural performance is governed by two “key” parameters: b and m. b reflects the influence of the material properties, prevailing loading condition and geometry of the steel component. m reflects the influence of the structural system, the hysteretic behavior and the characteristics of the earthquake. In its current form, the formulation is applicable to steel flexural systems with stable hysteretic response governed by bending/shear (whether or not combined with axial forces). Further research is needed to extend this formulation to other structural systems, such as bracing systems. The methodology can be used to quantify the level of damage in performance-based seismic design of new structures or to evaluate the safety of existing buildings and make decisions about seismic retrofitting.
Acknowledgements The research reported in this paper was funded by the Spanish Ministry of Education, through the grant BIA2005-00591. The research received funds from the European Union (Fonds Européen de Dévelopment Régional).
References [1]
[2]
[3] [4] [5] [6] [7] [8]
Kunnath, S.K., Reinhorn & A.M., Lobo R.F., IDARC version3.0: a program for the inelastic seismic analysis of RC structures, Technical Report NCEER-92-0022 State University of New York: Buffalo, N.Y., 1992. Krawinkler, H. & Nassar, A.A., Seismic design based on ductility and cumulative damage demands and capacities. Nonlinear Seismic Analysis and Design of Reinforced Concrete Buildings, eds. P. Fajfar & H. Krawinkler, Elsevier: New York, pp. 77-95, 1992. Fajfar, P. & Gaspersic, P., The N2 method for the seismic damage analysis of RC buildings, Earthquake Engineering and Structural Dynamics, 25, pp. 31-46, 1996. Manson, S.S., Behavior of materials under conditions of thermal stress. Heat Transfer Symposium, Engineering Research Institute, University of Michigan: Ann Arbor, pp. 9-15, 1953. Coffin, L.F., A study on the effect of cyclic thermal stresses in ductile metals, Transactions of the American Society of Mechanical Engineers, 76, pp. 931-950, 1954. Miner, M.A., Cumulative damage in fatigue, Journal of Applied Mechanics, 12, pp. 159-164, 1945. Kasiraj, I. & Yao, J.T.P., Fatigue damage in seismic structures, Journal of Structural Engineering ASCE, 95(8), pp. 1673-1692, 1969. Suidan, M.T. & Eubanks, R.A., Cumulative fatigue damage in seismic structures, Journal of Structural Engineering ASCE, 99(5), pp. 923-943, 1973.
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402 Computational Methods and Experiments in Materials Characterisation III [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]
[19] [20]
[21] [22]
Krawinkler, H. & Zhorei, M., Cumulative damage in steel structures subjected to earthquake ground motions, Computers and Structures, 16(1-4), pp. 531-541, 1983. Cosenza, E., Manfredi, G. & Ramasco, R., The use of damage functionals in earthquake engineering: a comparison between different methods, Earthquake Engineering and Structural Dynamics, 22, pp. 855-868, 1993. Ballio, G. & Castiglioni, C.A., A unified approach for the design of steel structures under low and/or high cycle fatigue, Journal of Constructional Steel Research, 34, pp. 75-101, 1995. Daali, M.L. & Korol, R.M., Low-cycle fatigue damage assessment in steel beams, Structural Engineering and Mechanics, 3, pp. 341-358, 1995. Banon, H. & Veneziano, D, Seismic safety of reinforced concrete members and structures, Earthquake Engineering and Structural Dynamics, 10, pp. 179-193, 1982. Park, Y.J. & Ang, A.H.S., Mechanistic seismic damage model for reinforced concrete, Journal of Structural Engineering ASCE, 111(4), pp. 722-739, 1985. Park, Y.J., Ang, A.H.S. & Wen, Y.K., Seismic damage analysis of reinforced concrete buildings, Journal of Structural Engineering ASCE, 111(4), pp. 740-757, 1985. Fajfar, P., Equivalent ductility factors taking into account low-cycle fatigue, Earthquake Engineering and Structural Dynamics, 22(10), pp. 837-848, 1992. Benavent-Climent A., An energy-based damage model for seismic response of steel structures, Earthquake Engineering and Structural Dynamics, 36, (in press), 2007. Kato, B., Akiyama, H. & Yamanouchi, H., Predictable properties of structural steels subjected to incremental cyclic loading, Symposium on Resistance and Ultimate Deformability of Structures Acted on by Well Defined Loads, IABSE: Lisbon, 1973. Akiyama, H., Takahashi, M. & Shi, Z., Ultimate Energy Absorption Capacity of Round-Shape Steel Rods Subjected to Bending, Journal of Structural and Construction Engineering AIJ, 475, pp. 149-158, 1995. Benavent-Climent, A., OH, S.H. & Akiyama, H., Ultimate Energy Absorption Capacity of Slit-Type Steel Plates Subjected to Shear Deformations. Journal of Structural and Construction Engineering, Transactions of the Architectural Institute of Japan 1998; 503: 139-147. Akiyama, H, Takahashi, M. Influence of Bauschinger Effect on Seismic Resistance of Steel Structures, Journal of Structural and Construction Engineering, AIJ, pp. 49-57, 418, 1990. Benavent-Climent, A., Seismic Design of Structures by Using Brace-Type Hysteretic Dampers, Doctoral Thesis, University of Tokyo: Tokyo, 1998.
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A visco-plastic damage model for high temperature creep of single-crystal superalloys A. Staroselsky1 & B. Cassenti2 1 2
Pratt and Whitney, USA Rensselaer at Hartford, USA
Abstract The micromechanics of the high temperature creep and damage accumulation in single crystal nickel base superalloys is important for the design of turbine blades and vanes in advanced commercial and military gas turbines. We have developed a robust predictive tool to relate single crystal macroscopic behaviour and fracture initiation to micromechanical events. A crystallographic-based model for non-isothermal high temperature cyclic deformation has been fully coupled with the damage kinetics. The model significantly improves the quality of material deformation predictions on cyclic and thermal-cyclic loading. Keywords: super-alloys, single crystal, constitutive modeling, dislocation kinetics.
1
Introduction
Historically, secondary creep effects with associated modelling techniques (Larson-Miller, etc.) were used in engineering calculations. However, during the thermal-mechanical loading of high temperature single crystal turbine parts, all three creep stages: primary, secondary and tertiary, manifest themselves and none of them can be neglected. A creep law is especially important in the case of non-homogeneous thermal loading which results in intensive stress redistribution and relaxation. Several damage mechanisms, namely multiplication of mobile dislocations, void and micro-crack growth and the scale effects caused by dislocation extrusions/intrusions and necking, have been considered. Our damage model bridges the gap between dislocation dynamics and continuum mechanics scales. Damage accumulation causes tertiary creep and shear localization around local concentrators, which is essential for airfoil life prediction. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/MC070401
404 Computational Methods and Experiments in Materials Characterisation III The constitutive model has been implemented in the commercial finite element software ANSYS as a material user routine to predict creep anisotropy and yield thermal dependence. The model is calibrated against stress-strain and crystallographic texture predictions against test data up to 25% strain. The developed non-isothermal, crystal–viscoplastic, damage mechanics model is used for creep, cyclic ratcheting and thermal mechanical fatigue (TMF) analysis.
2
Viscoplastic model
We have used standard viscoplastic power law creep with a back stress [1] to represent the response of the material. The constitutive law for the inelastic strain,
J i p , along slip plane i
Ji
will be written as
§U J0 ¨¨ m © U0
p
where J0 is a time constant,
· W i Zi ¸¸ * ¹ si
Um
n
§W Z sgn ¨¨ i * i © si
· ¸, ¸ ¹
(1)
is the mobile dislocation density,
arbitrary reference dislocation density,
Wi
U0
is a
is the slip plane resolved shear stress,
si* is the isotropic yield stress, Zi is the slip plane back stress, and ( ) is the rate *
of change with respect to time. The isotropic yield stress, s i , is assumed to be a constant throughout this discussion but is actually a variable with its own evolution equation. The back stress will be taken to evolve according to [1,2]:
Z i where
O0
§
· Up p sgn Ji Zi ¸ ss ¸ Up ¹
O0 Ji p ¨ Zf ¨ ©
is a time constant,
Zf
pinned dislocation density, and
is the steady state back stress,
U pss
(2)
Up
is the
is the value of the steady state pinned
dislocation density. The total slip shear strain, J i , includes the elastic part and can be written, for a single active slip plane, as
Ji
Wi G
Jip
(3)
where G is the shear modulus for along the slip plane. The initial conditions will be taken as
Zi
0 Ji
p
0 at t
0
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(4)
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405
Dislocation kinetics model
The mobile and the pinned dislocations will also evolve over time. We have chosen to represent the evolution as two body interactions, and have assumed that the entropy production, s , is given by [3]: n slip
s C
§ W i Zi · p ¸J i t 0 , s* ¹ 1
¦ ¨© i
(5)
where the parameter C is a constant, and n slip is the number of slip systems. Note that from equation (1) that Ji p is already a linear function of the mobile dislocation density and, hence, if the dislocation evolution equations vary linearly with the inelastic strain rate then to represent two body interactions they must also be proportional to linear combination of the mobile and pinned dislocation densities. Based on these constraints, we have chosen the evolution equation for the mobile dislocation density to be nslip
U m
2 ss 2 ss § W i Zi · p §¨ H U m U p U p H U m ·¸ D ¨ ¸J i ¸ s * ¹ ¨© U0 i 1© ¹
¦
(6)
where D is a time constant, U mss , is the saturated mobile dislocation density, 2 U ss is a positive constant. p , is the saturated pinned dislocation density, and H
Equation (6) includes the annihilation of mobile dislocations and also includes their conversion to pinned dislocations. For the pinned dislocation density we have taken the evolution equation to be n slip
U p
E
ss § W i Zi · p §¨ U p U p ·¸ ¨ ¸J i s * ¹ ¨© U0 ¸¹ 1©
¦ i
(7)
where E is a time constant. The pinned dislocations grow at a rate that is proportional to the mobile dislocation density because of the presence of the plastic strain rate term. Throughout this paper, for the initial conditions we have taken U m U 0 U p 0 at t 0 (8) Of course, they can be generalized if the need arises.
4
Damage parameters
There are several mechanisms leading to the macrocracking or high temperature rupture. We define damage parameters (up to five in the extended model) reflecting each of these mechanisms. Not all of them are equally important at all conditions. In this paper we focus on damage associated with mobile dislocations multiplication d d and briefly review effects caused by evolution of porosity WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
406 Computational Methods and Experiments in Materials Characterisation III
d v and microcracking d c on the elastic moduli. We also considered damage effects related to the interactions of dislocation loops with the free surfaces. This damage was defined through the change in the shear modulus as G (1 d s ) G 0 . In this discussion we will illustrate the development of the creep and void damage models, but the illustrations of the effects of damage will include only the changes in shear modulus. The presented damage model is based on a “damage rate conservation” assumption stating that all damage mechanisms are interconnected and caused by entropy generation as follows: (9) d i ~s .
¦
damage mechanisms
We define damage caused by the increase of the dislocation density as
dd
1
U0 Um
(10)
p The increase of d d from zero to unity causes the fast raise of J (see eq. (1)).
In turn it leads to the tertiary creep or even elimination of the secondary creep stage called sigmoidal creep. This dislocation driven mechanism does not directly affect crystallographic structure or material elastic properties. Two other major damage mechanisms are void development and microcracking. Both change the part stiffness, and can be defined through the variation of elastic parameters as follows:
E 1 Q
(1 d c )
E0 ; 1 Q 0
(11) E0 E (1 d v ) K (1 d v ) K 0 3 1 2Q 3 1 2Q 0 where E0 and X 0 are the original Young’s modulus and Poisson ratio; K 0 , is the original bulk modulus. Thus, having d c and d v calculated we are able to adjust the materials elastic response during the loading. It can be shown that E and K decrease with the increase of damage parameters. The quantity d v changes with the pore volume fraction, v , and was found from a model based on the bulk modulus variation for a sphere with central hole. Variation of effective moduli with cracking is a well known problem (e.g., [4]). Finally, relations for the damage parameters for materials with cracks and voids have the following form: 1Q 0 · § ¨ 1 2Q 0 ¸X S ln(sec( 2 f )) 2 ¹ (12) © dc( f ) 1 d X ; ( ) v S Q 1 f f ln(sec( )) 0 8 2 X 1 2Q 0 2 where f is crack volume fraction. To complete the damage model, the evolution equations are needed. It is assumed that the coalescence of voids is the source of the micro-cracks and the pile-up of mobile dislocations causes void nucleation. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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From these considerations and the damage “conservation rule” (9) the damage kinetics equations can be written in the following simplified form:
dd
n slip
§ W Zi · p 2 C1 ¦ ¨ i ¸J i (1 d d ) ; s * ¹ i 1©
(13)
Void growth obeys the Wilkinson-Ashby equation and creep crack growth is c
linearly proportional to the C * -parameter where C* ~ fH . Crack nucleation rate is proportional to the probability of the event that at least three pores coalesce along a line. The probability of pore occurrence in the fixed volume is governed by Poisson stochastic process [5]. Pore coalescence occurs when a pore appears to be inside a sphere of two average pore radii from the center of another pore. The number of crack nucleation sites is proportional to probability of the occurrence of such an event, which, in turn, is N c ~ 12 X*(8X ,3) where *() – is incomplete Gamma function. The microcrack fraction nucleation rate is equal to 13 f
N c ; therefore the final evolution relationship for the voids and cracks Nc
fractions has the form:
d v
X
wd v X; d c wX
d d X (1 X ) n C2 C V ; kk 4 2 (1 X 1 / n ) n d 1 d
void growth
f
wd c f wf (14)
void nucleation rate
X § 8X* c(8X ,3) · ¸ C 3 fHec 13 f ¨¨1
X© *(8X ,3) ¸¹ creep crack
growth
crack nucleation rate
where C1 - C4 are temperature dependant parameters and n – is the creep exponent. The last damage parameter, d TW , was defined through the change in the bulk modulus as
G
(1 d TW )G0
(15) where G0 , is the original shear modulus and will be referred to as the thinwalled debit [6] d TW , and was based on the intersection of dislocation loops with the surface. Consider a flat dislocation loop of radius R with the normal to the plane of the loop at an angle T with respect to the length of a uniaxial stress test specimen. It can be shown that the average density of dislocation loops intercepting the surface, N I , for a specimen of thickness H is
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408 Computational Methods and Experiments in Materials Characterisation III
where
R
4Um
R
cosT H is the average dislocation loop radius. NI
(16) For many dislocations
intercepting the surface, the average number moving the surface right, P , can be found from the binomial distribution as P
NI 2
(17)
N I WL 4
(18)
while the standard deviation, V , satisfies
V2
where W and L are the width and length of a surface. If each dislocation has Burger’s vector b, then average absolute distance, S each surface moved from the mean is b S N I WL (19) 2S We can approximate the change in the shear modulus by considering a panel with shear applied at the top and held at the bottom. The bottom has a length equal to the original thickness, H , and the top has length H S . The average modulus, G , can then be found from S /H . (20) G G0 1 § · ln¨ ¸ ©1 S / H ¹ The damage, d TW , becomes
d TW
5
1 G / G0
(21)
Typical response
A typical creep response, that includes many of the effects that we can represent, can be illustrated using the parameters and initial conditions shown in Table 1. The dislocation density evolution is shown in Figure 1. Initially the mobile dislocation density grows slowly, then rises as the pinned the dislocation density levels out, and finally grows exponentially toward the steady state value. In Figure 2 each of the individual damage parameters initially grows rapidly, with the damage parameters controlling the shear modulus and isotropic yield stress accelerating at around 16000 seconds. Figure 3 shows the total strain as a function of time. Clearly all three modes are present including a short primary creep interval, a fairly long secondary creep region and a steep tertiary creep region. The primary creep region is controlled by the rapidity with which the back stress and the pinned dislocations reach steady state. For Figure 3 the primary creep region is short. The tertiary creep region is very steep and is controlled the WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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damage evolution rates and the rate of mobile dislocation generation. The steady part can be lengthened or shortened by changing the rates of the primary and tertiary creep response. Clearly, the initial conditions, such as the initial pinned and mobile dislocation density and the initial back stress will also control the length each the primary, secondary and tertiary creep regions. Table 1:
Material parameters and initial conditions.
Parameters:
D
2.00E+07
E
2.00E+10
J 0 O U ss p
0.00001 1.00E+03
G/s0
100
n
3
cosT
0.57735027
Z f / s0
0.25
H b
0.15 2.00E-08
WL
/H
6.00 50.00
Initial Conditions: 5.00E+06 Um 0.00E+00 Up 5.00E+06 U
Jp Z W/s0
0 0 0.3
Figure 1:
U0 U mss
2.00E+10 5.00E+06 1.00E-04 2.00E+15
Dislocation density for data in Table 1.
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410 Computational Methods and Experiments in Materials Characterisation III
Figure 2:
Figure 3:
6
Damage parameters for data in Table 1.
Total strain for data in Table 1.
Conclusions
We have studied creep behaviour of single crystal Ni-based superalloys using a dislocation–based viscoplastic model. The model is focused on analysis of high temperature deformation and is coupled with damage kinetics allowing the prediction of tertiary creep and failure initiation at high temperature. We were able to predict generic creep response including primary, secondary and tertiary stages as well as sigmoidal creep. Varying the model damage parameters we WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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obtained different tertiary creep responses allowing sensitivity study and model parameters calibration. It is important to note that model internal state variables have clear physical meanings and were chosen in rational matter. Macroscopic parameters, such as back stress Zcreep strain rate J p and others depend on densities of mobile and pinned dislocations and their kinetics. Damage nucleation and accumulation is defined by entropy generation and is described by dislocation density, pore and micro-crack volume fractions. All introduced damage parameters are interconnected: crack nucleation is defined by pore coalescence and pore nucleation which is in turn defined by the increase in dislocation density. The simple mesoscopic model presented sheds light on the formulation and calibration of crystal – viscoplastic, damage mechanics constitutive model and allows estimates for the role of different damage mechanisms in creep and creep – fatigue modeling of single crystal materials.
References [1] [2] [3]
[4] [5] [6]
Nissley, D., Meyer, T., and Walker, K. Life Predictions and Constitutive Models for Engine Hot Section Anisotropic Materials, Pratt & Whitney, Report NAS3-23939, 1991 S. J. Basinski and Z. S. Basinski, The Nature of the Cold Worked State, in Recrystallization, Grain Growth and Texture, ASM, pp. 1-44, 1965 Staroslesky, A, and B. Cassenti, Damage Accumulation and Fracture Initiation Due to High Temperature Creep of a Single-Crystal Superalloy, in Fracture of Nano and engineering Materials and Structures, Ed. E.E.Gdoutos, Proc. 16th European Conf. of fracture, Alexandroupolis, Greece, 2006. Nemat-Nasser, S. and M. Hori, Micromechanics: Overall Properties of Heterogeneous Materials. Elsevier, 1999, 786 p. A. Freudenthal, Statistical approach to brittle fracture, in Fracture Vol II Ed. H. Liebowitz, Academic Press, 1968 pp 591-619 M. Doner and J.A. Heckler, Effects of Section Thickness and Orientation on Creep-Rupture Properties of Two Advanced Single Crystal Alloys, Proc. Aerospace Conf. SAE Technical Paper #851785, 1985
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Failure mechanics of slope slip with predestinate slip plane J. Vacek & S. Sedláþková Czech Technical University in Praha, Czech Republic
Abstract Failure of rock mass is not a static process, but has its own history. Its duration varies from several seconds to several hundred years. Rock mass movements are often measured in hundreds of metres and significantly change the formation’s original shape. Failure mechanics can be studied experimentally. On nonhomogeneous models we can observe the onset of failure (prior to and during the failure, deformations increase on sliding surfaces), the chronology of various stages of failure (cavings, slides), and the final shape of the rock mass. We can also observe influences exerted by modelled joints, adits and other features upon the failure history and shapes of cavings and slides. Research will be concentrated on the stability of internal tailings of Northern Bohemia open coal mines. Tailings will be strengthened by piles that join bed rock with tailing over the predestinated slip plane. Methods used for the study of geotechnical problems have to allow for two basic presumptions: x results must be time dependent x results must allow the creation of joints in the rock mass before the study event and during the event must allow for the moving of rock along joints, the opening of joints and creation of new joints. The direction of modelled joints must be similar to reality, i.e. their direction and inclination must be the same as the real ones. These measures make it possible to create the structure of modelled rock mass similar to real ones. Filling of cracks must be equivalent to real ones. A scale physical model from equivalent materials and mathematical solutions were used as a basic method for the study of geotechnical problems. Keywords: failure mechanics, failure history, physical model, mathematical model, stability of rock mass, jointed rock mass. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/MC070411
414 Computational Methods and Experiments in Materials Characterisation III
1
Introduction
The present study is concerned with the failure mechanics of the slope build-up on the bedrock with a smooth surface. This arrangement is typical for the internal tailings in the surface of coal mines. The experimental study was constructed in a stand enabling tilting. A scale model was constructed from equivalent materials. The smooth surface was made from a special epoxy resin. For the mathematical part, the particle flow code in 2 dimensions (PFC2D) was employed. The pile bored to the bedrock, instrumented with strain gauges, restrain the slope movement in the experimental case. Ten fixed balls were considered in the mathematical solution. Both methods have shown the slip as a time dependent process. Moreover, both methods allow one to describe a decomposition of the originally homogeneous and isotropic body into blocks (see figs 2-3) and, therefore, they treat the slip as a discontinuous deformation process. The stability of mine tailings situated on an inclined terrain is often influenced by a predestinated slip surface represented by the contact between the terrain surface and tailings. The speed of movements of Loket or VintíĜov tailings during the slip was about 1 m in a day. For strengthening of the critical shear plane, piles were bored down to the bedrock and jointed the tailings with the original terrain. In fig. 1 the case of slip of terrain along predestined slip plane (Hasen, 1969, Mencl [4]) is shown; it was created by sensitive clays.
1. Sensitive sea clays, 2. Rigid clays, 3. Sands and gravels, 4. Fall down hedge shape disconnected place, 5. Squeezing out clays
Figure 1:
Block diagram of slip along sensitive clays during an earthquake in Alaska in 1964 year.
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Experimental models
Physical scale models from equivalent materials were utilized for an experimental study of the problem. The model was built-up from three types of material: the bedrock consisted of a mixture of 100 weight parts of melted limestone, 4 w.p. of cement and 4 w.p. of water. The shear surface was created by a specifically adapted epoxy resin. The angle of internal friction and the long time cohesion equals zero. It behaves as a liquid with a high viscosity. Tailings were made from a mixture of melted limestone 100 w.p. and grease 0,5 w.p.. The pile was represented by a polyethylene pipe with an 18 mm diameter, provided with three pairs of strain gauges connected to the tensometrical bridge. This arrangement enables measure of the force with which the pile resists the tailings slip. The model dimensions were: length – 1450 mm, height – 600 mm, width – 200 mm. Before the test, the stand was tilted 10º from the horizontal plane (see figure 2).
3 Test results Figure 2 represents a photograph of the model before the test. Figure 3 shows the model at a time to + 30 minutes. Figure 4 depicts the model at a time to + 70h and figure. 5 at a time to + 140h. The photos clearly reveal the cracks in the tailing’s body. Figure 5 also shows the movements of the tailing body and the flow of the tailings material around the pile. Figure 6 shows the slip history as obtained from the experimental part of the solution by the method of a close stereophotogrammetry and depicted by a technocart device. It records the individual stages of the model. Figure 7 displaces a change of the slip surface. In Figure 8, there are seen the movements of selected points. As shown in figure 8, there are three areas with different movements during the slip. The part under the last right crack has only small, horizontal displacements. The left triangle under the last left crack moves only in the horizontal direction, and the wedge between these areas moves parallel with the last right crack.
Figure 2:
Model before test to = O.
Figure 3:
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Model at to + 30 min.
a
time
416 Computational Methods and Experiments in Materials Characterisation III
Figure 4:
Model at a time to + 70h.
Figure 6:
Figure 5:
Model at to + 140h.
Decomposition of slope during slip.
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a
time
Computational Methods and Experiments in Materials Characterisation III
Figure 7:
Changes of tailing surface during slip.
Figure 8:
Moving of selected points during slip.
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4
Mathematical part
For the numerical modeling study PFC2D software (Particle Flow Code in two dimensions) was used. In this code rock mass is composed from balls (in two dimensions from discs). Each disc has its own diameter and axial and shear stiffness. Among the discs axial and shear bonds act. When stresses in some area exceed bonds, discs are disconnected and a joint appears. Each property (diameter, stiffness...) is arbitrary and it is possible to order them properties in the conditions Gauss statistical dispersion. It is possible to fix every disc against moving or rotation. The pile was modelled as ten fixed disc, the diameters and distance was carefully studied because arrangement must allow floating disc of rock mass between them, but the pile must defend the slope slip similar to that in the physical model. Calculation runs in separate cycles (iterations). Unbalanced force is characterized after each cycle degree of slope settlement. When it reaches the request value, work is finished. In the case described it was after 800 000 cycles. Some of the calculate states are shown in fig. 9.
Figure 9:
Slip of tailings according PFC2D Code.
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Computational Methods and Experiments in Materials Characterisation III
Figure 10:
Details of the velocities of individual discs.
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Conclusions
For solving geotechnical problems, it is modern and convenient to use a coupled modeling, with a mathematical and experimental part. This arrangement makes it possible to cut down the disadvantages of each method. They thus offer a description of the problem that is much closer to reality. Both methods described allow investigation of the slope slip problem as a time-dependent process and treatment of this problem as a discontinuous deformation process (which when modelled and during slip created new cracks). The estimation of the force defended in the slope slip by the pile was also proved in the terrain.
Acknowledgement This research has been sponsored by the GAýR: 103/05/0334.
References [1] Vacek, J. (1992) Similarity in geotechnics and calibration of models from equivalent materials. Rock mechanics as a multidisciplinary science,. Oklahoma, Balkema, p. 745-754. [2] Vacek, J., Westman, E. (1996) Experimental Study of Rock Mass Decomposition During Slip. IF DDA, Berkeley, California. [3] Vacek, J., Sedláþková, S. (2006) Failure mechanics of jointed rock mass, Debris Flows, Rhodos, Witpress, Southampton, p. 251-260 [4] Mencl, V. (1974) Inženýrská geologie (Engineering geology), Academia, Praha, 507 p.
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Section 11 Computational methods – innovative techniques
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Back analysis of reinforced soil slopes P. Procházka1 & J. Trckova2 1 2
Czech Technical University in Prague, Czech Republic IRSM, Czech Academy of Sciences, Prague, Czech Republic
Abstract Among the most popular reinforcement in soil mechanics of slopes is anchoring and nailing. In our experiments nails are applied; they are penetrated into the slope, it is loaded only by its volume weight. The material of the nails, as well as that of the slopes, is known from laboratory tests. This circumstance influences the distribution of stresses along the length of the body of the nail. Moreover, the position of the nails to the stability of the reinforced slopes is observed. As the experiments are carried out in scale models, similarity conditions have to be obeyed. The technology of construction of experimental models is very important. Similarity rules are applied, but in this case no additional tests on physical equivalence of materials (real and that in the scale model) are necessary. As is well known that slope stability is a phenomenon which underlies the softening material behavior, i.e. the nonlinear behavior is concentrated along the slip curve. All kinds of nails are fully active after their mobilization. A different position of nails is considered to obtain the influence of this effect. In numerical analysis and a priori integration method is fully used. Its application enables one to decide relatively quickly if the slope is stable or the measure of stability, the safety margin. Originally, the method was applied to stability of both homogeneous and nonhomogeneous slopes, streaming water and pore pressure influence on the slope stability. Here the influence of nails is considered by additional slip force along the slip surface. The force is calculated from comparison with the experimental data. The nails are introduced in such a way that they are long enough to cross the most dangerous slip curve possible. Keywords: nailed slopes, scale models, a priori integration method, back analysis.
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424 Computational Methods and Experiments in Materials Characterisation III
1
Introduction
The concept of a priori integration of functionals of the classical method of slope stability assessment was published for the first time in [1] for the classical plain gravity model. Before these dates it was applied to the analysis of slope stability for the Prague Underground Railway and formed the subject of several thematic problems and improvement suggestions. Further possibilities of the method have been shown also in the solution of the earth pressure problem and a wide range of applications is found in [2]. The formulation of the method is based on the combination of variation problems with the strip methods. In practice these slice methods depend on a single argument only and make it possible to express the functionals in the variation formulation in the form of functions. If we consider the very accurate interpretation of the values of functions by contemporary computers, it is obvious that a priori integration results not only in the acceleration of computer processing of stability problems, but also in increased accuracy of computation and subsequent determination of the form of the permissible shear surface and the safety factor value with any accuracy required. The error of the method resulting from introduced assumptions will not be eliminated, naturally, but will be reduced by the possible introduction of better contact assumptions. Coupled problem have been solved in a couple of papers by Procházka and Trckova [3, 4]. Here internal parameters for a back analysis served design parameters of some optimization problems. The modeling from physically equivalent materials in stands (scale models) starts with papers [5–7]. Application of back analysis to stability of tunnel structures is described in [8], in [9], the stability of tailings (deposits) from open-pit mines is solved and in [10]. Identification of internal parameters using back analysis is studied in [11].
2
Basic principles of a priori integration method (AIM)
The idea of the AIM arose from the needs of design practice. In the design of big excavations or embankments which occurred, e.g., in the construction of the underground railway it was found suitable to base the actual design on parametric studies depending on the simplified geometry of the slope and the geotechnical parameters of the soil of which the slope consists. Computations have shows explicitly that for reasons of final assessments of slope stability it was impossible to use modern numerical methods (finite element method, boundary element method). However, classical slice methods did not appear entirely suitable, either. Modern methods need more computational time, while slice methods are numerically unstable and do not enable the application of minimization strategy for a more accurate stability coefficient computation. One of the possibilities of elimination of these shortcomings consists in the application of the AIM, e.g., to the classical plain gravity model which has the advantage of explicit expression of the stability coefficient on the given shear surface, can easily be extended to three dimensions and involve other influences on the slopes. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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Before presenting the initial formulas we introduce some symbols and assumptions. First we will deal with two-dimensional problems in Oxy coordinate system. In practice it is advantageous to locate the origin of the coordinates O at the toe of the slope. The application of the AIM consists in expressing the problem in functional form. For the classical model, for instance, we seek the stability measure (safety factor) on a concrete admissible shear surface with the understanding that the safety factor is the minimum of stability measures. Moreover, in the AIM we express the functionals for a fixed shear surface in the form of functions. This can be achieved, e.g., with the assumption (frequently used in engineering practice) that geotechnical parameters are homogeneous and isotropic by parts (by layers). In our case homogeneous medium is considered, as the influence of nails is studied in the scale model. Let y t (x ) be the boundary of the slope surface (terrain) and y f (x ) describe the shear surface the admissible form of which is a part of the circle. In order not to complicate the explanation, let us assume that f is a function, i.e. that there is just one value of y for every x within the admissible interval. The generalization of this assumption is not connected with any difficulties. Further, in accordance with the principal idea of the model (equilibrium on the fixed shear surface together with the respective denotations is shown in Fig. 1) it is possible to define the safety factor F on the shear surface as follows: F
N tan ij C T
(1)
where N and T are the normal and tangential components, respectively (with reference to the shear surface) of the unit weight of the soil above the shear surface, ij is the angle of internal friction (shearing resistance) and C is the cohesion.
Figure 1:
Equilibrium of forces on the shear surface in the gravity model.
The most probable location of the shear surface and simultaneously the safety factor value (minimum safety factor) are determined by the minimization of the values of F , i.e.
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426 Computational Methods and Experiments in Materials Characterisation III F0
(2)
minimum F
where the minimum is considered across all admissible shear surfaces, i.e. such circles for which the set of those x for which S ( x)
(3)
P [t ( x ) - f ( x )] z 0
is not empty. In the definition of the function S we have introduced the Heaviside operator P [a ] 1 for a ! 0 ,
P [a ]
0
otherwise
(4)
The condition (3) means that the diagrams of the functions t and f and intersect at least in two points and t ( x 0 ) ! f ( x 0 ) at least for one x 0 . The condition (2) determines the form (or, to be exact, the location) of the shear surface along which the slip will occur most probably, if the safety factor F0 is lower than the respective safety factor of the slope, determined either by a standard (EC7-1, DIN, CSN), or by the designer's experience. If the safety factor is higher than this number, the slope can be considered stable. Now we can express the individual terms in (1) as follows: f t( x)
T( f )
f
³ ³ Ȗ( x, y ) p( x)S ( x ) dy dx,
C( f )
f f ( x )
c( x ) S ( x ) dx q( x ) f
³
f t( x)
N tan ij( f )
(5)
³ ³ Ȗ( x, y ) tan ij( x)q( x)S ( x ) dy dx
f f ( x )
where Ȗ is the volume weight of the soil, c is the cohesion, and p( x )
x xC , q( x ) R
1 p2
(6)
where ( x C , y C ) are the coordinates of the center of the slip surface and R is its radius. Note that the functions p and q in (6) are the sine and cosine, respectively of the angle Į between the tangent to the slip surface at the point ( x, R ( R 2 ( x x C ) 2 ) and the axis x (see Fig. 2). The material constants ij and c can be entered as residual or peak values. In this way it is possible to consider also the influence of deformation. Description of the geometry and subregions, the procedure of the AIM can be applied, is seen from Fig. 2. Roman numerals denote homogeneous and isotropic subdomains (elements), Arabic WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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numerals describe the vertices of element boundaries. It can easily be verified that the formulas (5) correspond with the relations of the gravity model for the case of limit transition in the meaning of the Riemann integral definition. The cases most frequently occurring in practical computations are the cases of soil mass, the boundary of which can be approximated by a polygon and the material of the mass is homogeneous and isotropic in parts, while these parts (subdomains) are also bounded by polygons.
Figure 2:
Topological relations of the AIM.
Figure 3:
Geometry of the simple slope.
In order to study the influence of reinforcing nails, simple slope, i.e. a homogeneous isotropic slope without benches, see Fig. 3, is considered, and the slip curve meets the toe of the slope, i.e. points 1 and 4 are identical. This is the case of slopes with steeper toe angles. Our aim is the computation of the values of integrals (5) for the latter case. As in this particular case Ȗ, ij and c are constant, so that it holds that x3
x2
T
Ȗ{ t 12 ( x ) p( x ) dx t 23 ( x ) p( x ) dx
³
³
x1
x2 x2
N tan ij
12
x3
x1
³
f ( x ) p( x ) dx}
x3 x3
23
Ȗ tan ij{ t ( x )q( x ) dx t ( x )q( x ) dx
³
x1
³
x2
C
c
dx
³ q( x )
x1 x1
(7)
³ f ( x )q( x ) dx}
x3
where superscripts ij stands for abscissa or circle of the slip line i – j, i, j =1,2,3. Furthermore, in the last equations x i and y i are coordinates of point i. Substituting for the slope 1 - 2 and ridge 2 - 3 yields WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
428 Computational Methods and Experiments in Materials Characterisation III t 12 ( x )
k0 ,
t 23 ( x )
q0 ,
f ( x)
(8)
y C Rq( x )
where k0 is the value of the slope and q0 is the height of the ridge. We ascertain that the explicit expressions of T, N tan M and C is split into an algebraic sum of influences of individual abscissas forming the boundary of the slope and its individual layers and the parts of the circles forming the slip surface. Before coming to the explicit expression of influences from the integration over an abscissa or a circle it is advisable to introduce substitution (parameter p stands for sine of the angle Į ) and formulate functions:
x
xC pR
F3 ( p )
dx
R dp
arcsin p p 1 p 2 2
§¨ 1 p 2 ·¸ © ¹ 3
F1 ( p ) F4 ( p )
3
p3 F5 ( p ) 3
F2 ( p ) p-
p3 3
p2 2 F6 ( p )
arcsin p
(9) Now it easily follows that the influences from integrations below the abscissas can be expressed as (denoted by brackets): [T ] [ AF4 ( p ) BF2 ( p )]ij
[ N tan ij] [ BF3 ( p ) AF1 ( p )]ij tan ij
(10)
where A
ȖR 2 , B
ȖR( k 0 xC q0 ), and [ f ( p )]ij
f ( p j ) f ( pi ) , pi
( xi xC ) / R .
In case of circular segments are considered the following formulas can be derived: [T ] [ AF2 ( p ) BF1 ( p )]ij [ N tan ij] [ AF3 ( p ) BF5 ( p )]ij tan ij C
cR[ F6 ( p )]ij
where A ȖRy C , B ȖR 2 . The loading from above the ridge is taken into volume weight, while the influence of the nail (nails) is an additional shear force at the cross of current slip circle and the nail. The value of it follows from the experiments. If instead of a nail a geotextilie is put into the material of the slope, one force is needed to explain the influence of the reinforcement on the stability of the slope. This is not the case, so that a different number of nails is necessary to consider. The aim of the coupled modeling consists in tuning the numerical model, turned to a programming code, in such a way that the influence of the nails can be identified with high accuracy.
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Physical modeling
Physical modeling is important for the study of effects taking place in soil mass in connection with construction of underground structures. The modeling allows us to investigate mechanisms of geotechnical phenomena, predicts stress changes and their demonstration during various progress of underground construction and also during simulation of operating conditions. Basic rules of the experimental modeling and formulation of the mechanical conditions for modeling come from the principles of geometrical and physical similarity which is inferred for a consideration of dimensional analysis, [6–8]. According to the Buckingham theorem, [6], the dimensional equation for the relation between reality and the model can be reduced to the problem of finding relevant non-dimensional parameters. Equations can be determined, their arguments are dimensionless. The physical model has to obey geometrical similarity; this is the proportionality of dimensions and the identity of angles between the model and modeled object in the whole range of the model. The type of modeled geotechnical problem and its extent, possibility and technique of bringing forces, time factor and other aspects, technical possibilities, assign linear scale of the model. It is the aspect ratio in which length dimensions of the model are reduced against the reality. Note that the similarity being valid for slope stability assessment can be found in [11]. The models are constructed from mixture of various, mostly easy available materials (e.g. sand, bentonite, ballotine, gypsum, mica - vermiculite, composite mortar, cellular concrete and water). The models are constructed in stands of various dimensions in dependence of solving problem and scale of the model. Compact structure of the stand is formed by reinforced frame performing no deformation of it during the model test. Front wall of the model stand can be glassed to observe and measure deformation of the model.
4
Example
Slope 1:1.5 (length:height) is considered in the scale of 1:100. The slope obeys the similarity laws according to the previous section. Physically equivalent material is selected to be in compliance with selected real slope as: Mixture of ballotine and fat is the basic material for the laboratory tests in stands, the contents of ballotine was 99.87%, fat A00 was 0.125%. As the filling quartz sand with granularity of 1-7 mm was used. The stand is 1.5 m x 1 m x 0.5 m. Material properties of the slope are listed below: Volume weight 1.707 g/cm3 Cohesion 0.722 kPa Angle of internal friction 24° Oedometric modulus E 5 560 kPa Coefficient of compressibility 152 Tensile strength 5.1 kPa WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
430 Computational Methods and Experiments in Materials Characterisation III Density of the sand 1.93 g/cm3 Density of saturated sand 2.16 g/cm3 In the following pictures stands with different stages of loading and reinforcements are shown. The loading from above the ridge was applied to tune the material properties of the aggregate in the model (the slope created from the physically equivalent material together with a nail). The nails have been prepared from a chip of bamboo, unified in the shape and dimensions, their shear strength is known, so that the resistance force due to a nail is also given. Influence of load to the safety margin is depicted in Fig. 4.
Figure 4:
Figure 5:
Relation load and safety margin.
View of stand with the slope loaded from above and with the first position of a nail.
Two basic positions is horizontal set of nails were prepared. The first is seen in Fig. 5, it should help to stiffen the upper part of possible slip surface (curve). As is well known, this is the most advantages position, since the slopes in general start their damage along the ridge. The first loading step is also seen from this picture. In Fig. 6 the second position of reinforcement is depicted together with obvious movement of the ridge. Also in the upper right part of the slope partial damage is highlighted and according to the assumed shape of the slip curve the safety margin is derived. WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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It appears that for upper position of the nail one nail bears 12.29 kg load, two nails 16.15 kg and the necessary number of nails for higher value of the load can be extrapolated. For the lower position (second case) of the nail, one nail bears only 7.12 kg, two nails 9.78 kg etc. The bearing capacity is considered for safety margin 1.3, as most of standards consider. It is worth noting that this approach for the identification of appropriate structure of slopes with reinforcement by nails can be applied to various types of slopes, even in non-homogeneous mediums. For this case and the AIM see [11].
Figure 6:
5
The second type of reinforcement, slip curves highlighted.
Conclusions
Coupled modeling, experimental in stands and numerical using the AIM is shown on model examples of reinforced slopes by nails. This simple algorithm involves very user-friendly algorithm of the AIM and relatively simple and cheap modeling in stands. Tuning of numerical models using results from experiments enables engineers to assess this type of structures with relatively high accuracy and very fast.
Acknowledgement This paper was prepared under financial support of GA AV ýR, project No. IAA 2119402.
References [1] [2]
Procházka, P., Koudelka, P.: Slope stability analysis by the Apriori Integration Method (in Czech), Inzenyrske stavby, Vol. 28/3, 79-84 Koudelka, P., Prochazka, P.: Apriori Integration Method, Analysis, Similarity and Optimization of Slopes, Academia 2001, Prague WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
432 Computational Methods and Experiments in Materials Characterisation III [3] [4] [5] [6] [7] [8] [9]
[10] [11]
Procházka, P., Trcková, J.: Assessment and Control of Tunnel Structures based on coupled modelling. Submitted to Geotechnique Procházka, P., Trþková, J.: Coupled modeling of structural strength. Boundary Elements XXVII, eds. A. Kassab, C.A. Brebbia, E. Divo, and D. Poljak. Orlando, USA, WIT Press 2005, 155-164 Buckingham, E.: On physically similar systems: Illustrations of the use of dimensional equations. The Physical Review, Vol. IV, series II. No. 4, 1914, 345-376 Head, K.H.: Manual of Soil Laboratory Testing. John Wiley & sons. Inc. New York, Toronto, 1992 Kožešník, J.: Theory of similarity and modeling, Academia, Prague, 1983 Procházka, P., Trþková, J.: Coupled modeling of Concrete Tunnel Lining, Our World in Concrete and Structures, Singapore, 2000, 125-132 Procházka, P., Trþková, J.: Material properties of tailings of open-pit mines using coupled modeling, Proc. 5th European Conf. on Numerical Methods in Geotechnical Engineering NUMGE, ed. Mestat, Presses de IÉNPC/LCPC, Paris, 273-278, 2002 Procházka, P., Trþková, J.: Identification of material parameters in underground structures, Proc. Material Characterization, ed. C.A. Brebbia, Santa Fee, NM, USA, 2003 Procházka, P.: Slope optimization by the Apriori Integration Method, Acta Montana, IG CSAS, 82, 51-154, 1990
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Towards 3D simulation of sintering processes S. Bordère1, D. Bernard1, S. Vincent2 & J.-P. Caltagirone2 1
Institut de Chimie de la Matière Condensée de Bordeaux, ICMCB-CNRS-Université Bordeaux 1, France 2 Transferts, Ecoulements, Fluides Energétique, TREFLE-ENSCPB, France
Abstract The Monte Carlo approach based on minimisation of a potential including interface and volume energies has been implemented in the framework of a Eulerian interface tracking method in order to deal with 3D sintering of complex powder compacts. First applied to the unique spherical particle system, these new developments lead to a surface tension-induced pressure close to that theoretically given by Laplace’s law. The accuracy of this result is largely improved compared to those given by a classical fluid mechanics computation using the front tracking method. Our progress towards 3D modelling of sintering for realistic systems is illustrated by the computed stress gradients induced by surface curvature gradients within a small set of particles extracted from X-ray computed micro-tomography images of a real sample. Keywords: stochastic methods, ceramics, image analysis.
1
Introduction
As regards the recent studies in modelling sintering processes [1–4], one can notice that it still remains difficult to deal with realistic particle arrangements systems. In fact, modelling of polycrystalline material sintering has only been handled in 2D [1, 2]. The only approach which would be powerful enough to overcome that difficulty is the phase field approach which is based on a diffuse definition of the interface [2]. Applied to 3D complex microstructure evolution only involving grain growth [5], no example of 3D many particle densification has up until now been shown. In the case of amorphous particles sintering, only 2 [6, 7] or 3 particles were handled [8]. Apart from these deterministic methods, the Monte Carlo simulations based on the Potts model have exhibited 3D WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line) doi:10.2495/MC070431
434 Computational Methods and Experiments in Materials Characterisation III microstructures evolutions [4] but remain too restrictive for precise morphology characterisation and realistic kinetics. The Monte Carlo methodology based on the non-discrete potential that we have developed was shown to overcome these restrictions [9–11]. Nevertheless, this methodology was only developed for 2D and 3D axi-symmetric configurations of particles, and therefore remains restrictive to deal with realistic arrangements of particles. Based on finite element discretisation, the main numerical difficulty to extend this approach to 3D modelling was to readapt the tetrahedral mesh during calculation. So, to progress towards 3D modelling of sintering, this Monte Carlo methodology is now implemented in the framework of a Eulerian interface tracking method. We present here, the first 3D results, with the aim to show that it is possible to model sintering processes involving real particle arrangements that can be extracted from microtomography images of powder compact.
2
Simulation method
2.1 The Monte Carlo model The energetic model of the Monte Carlo methodology is defined in the canonical ensemble (closed system at constant volume and temperature) by the potential I: I J s As Ev (1) Here Js is the surface tension, As its respective surface area and Ev the total volume energy of the system which includes the volume energy of the solid phase and the vapor phase. The volume energy in eq. (1) corresponds to the sum of two terms: Ev E0 EH , where E0 is the volume energy for the two-phase coexistence involving no interface tension, and EH is the excess of volume energy which is induced by an interface tension. This capillary induced excess of volume energy is quantified in the framework of elastic strain energy: 1 (V : H )dV Ev E0 EH (2) 2 ³V where H and V are the elastic strain and stress tensors, respectively. The strain tensor H is related to the displacement vector of the fluid phase, and the stress tensor V to the strain tensor through the elastic constants: the Young’s modulus EY and the Poisson’s coefficient Q. The minimization of the potential through the Metropolis algorithm allows the calculation of the stress gradient within the volume phase in relation to the surface curvature gradients. The hydrostatic pressure can thus be deduced from the relation: 1 p trace(V ) (3) 3 This stress gradient is the driving force for volume mass transport which will allow the power compact to sinter.
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2.2 The Monte Carlo implementation The solid/vapor interface is discretized using a triangular mesh (fig. 1(a)) for a Lagrangian description of the interface motion. This discretized interface is placed within a fixed Cartesian grid (fig. 1(a)) for a Eulerian description of the two volume phases. On this grid a staggered mesh is used (fig. 1(b)). In the following displacements of the volume phase will be imposed on the u,v,w-grids for the calculation of the strain and stress tensors on the p-grid (fig. 1(b)). The I-potential is minimized using the Metropolis algorithm which proceeds in localized random changes of the total system configuration in order to induce potential variation GI m of the system. The configuration changes are accepted with the probability P( GI m ) =min (1, exp(- GI m /kBT)), (4) where kB is the Boltzmann constant and T the temperature. Two types of random changes are considered (see [12] for a complete description of the method): the first one concerns configuration changes by local elastic displacement of the two-phase system. At step m, when displacement only involves the volume phase deformation, three points located respectively on the u,v,w-grids (fig. 1(b)) are randomly chosen. Then, random displacements um, vm, wm, at step m, are respectively imposed upon these three points. For each of them (a = u or v or w), the variation of the strain tensor GHH am, c within the control volumes which are centered at the scalar points located backwards (c=b) and forward (c=f) can be calculated from the displacement vectors. The stress tensor GV V am,c can thus be deduced from elastic equation depending on the Young’s modulus EY and the Poisson’s coefficient Q. At this stage the strain and stress tensors at step index m+1 can be calculated as: H m 1 H m GH m , V m 1 V m GV m . Hence, the elastic strain energy variation G EHm which is determined from m
integration over the control volume Va ,c can be determined using the following equation:
G EHm ( a ,c )
1 Va ,c (V am,c GV am, c ) : GH am, c 2 ( u , b ),( u , f ),( v ,b ),( v , f ),( w ,b ),( w , f )
¦
(5)
At step m, in the case of interface and volume displacement coupling, a Lagrangian marker i is randomly selected among the Nf interface markers (fig. 1b) and randomly displaced ( u mf,i is the corresponding displacement vector). This displacement vector is projected onto the Eulerian grid by choosing three points located in the vicinity of the i-marker on the u-grid, vgrid and w-grid respectively (fig. 1). These three markers support the fluid displacement values u m , v m and wm along the X, Y, Z-directions respectively.
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436 Computational Methods and Experiments in Materials Characterisation III That volume-displacement also implies the movement u mf,l of neighboring interface markers l of the i-marker. Interface area Am+1 at step m+1 can be determined from the new position of interface markers x mf ,a1 (i ,l ) x mf , a (i ,l ) u Ef ,,am ( i ,l ) allowing the calculation of the surface energy variation G Esm at step m induced by the initial i-marker displacement G Esm J s ( Asm 1 Asm ) . As a final point, the potential variation GI m G Esm G Evm at step m induced by elastic deformation can be calculated in order to determine the probability P (GI m ) , defined by eq. (4), that the system configuration will change. the second one concerns relaxation of the distortion elastic energy generated during the previous route, which involves no pressure variation. This is done by imposing small variation GHH Dm of the deviatoric part of the strain tensor Hm. It allows the calculation of the potential variation GI m
G EHm
D
m
for the estimate of configuration change with respect to P (GI ) . The function of the second route was shown to induce mass transport in relation to stress gradient [9]. To differentiate mass transport properties between the solid and vapor phases, the location of the interface within the Eulerian grid is required. Thus, a specific variable C, the phase function, is introduced. C equals 1 in the solid phase and 0 in the vapor phase. The interface location is defined by C=0.5.
(a) Figure 1:
(b)
(a) The interface of the solid phase is discretized using a triangular mesh and is placed within a fixed Cartesian grid; (b) detailed visualization of the interfaced marker discretisation and of the staggered mesh used for the Monte Carlo calculation of the volume energy. , , , vectors parallel to the X,Y,Z-axis; scalar points.
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Validation for the single spherical particle of the 3D implementation
The Monte Carlo calculations have been performed using the following values of elastic constants for the two volume phases (EY=4x106 Pa, Q =0), surface tension (Js=2.5x10-3 N/m) and temperature (T=1K). The initial strain tensor within the two phases was H0=0. The spherical particle having a radius value R=2.5 mm is centred within the vapor phase limited to a cell of 10x10x10 mm3. At the limit of the cell imposed displacements equal zero, insuring during minimisation the condition of a closed system in which the I-potential is defined. The minimisation of the I-potential (eq. (1)) can be followed through the evolutions of p1 and p0, the mean pressures within the particle and the vapor phases, respectively (fig. 2). The equilibrium state corresponds to the large plateau at the end of the curves. The pressures within the two phases are constant and homogeneous as it is shown in fig. 2 with the 3D visualisation of an equatorial section of the particle. 2.0
p1
p0 , p1 (Pa)
1.5
1.0
'p =1.897
0.5
0.0
p0 -0.5 0
Figure 2:
50
MCS
100
150
Curves: Evolution during the Monte Carlo minimisation (MCS = Monte Carlo Steps) of the mean value of the pressure p1 within the spherical particle and p0 within vapour for the 32x32x32 grid. Centre: 3D visualisation of the pressure difference 'p=1.897 between the two phases on an equatorial plane of the particle.
To analyse the accuracy of the Monte Carlo methodology in calculating the stress response to interfacial forces, we have compared (for the final equilibrium state) the pressure difference between the two phases 'pNUM ( p1 p0 ) with the exact solution given by Laplace’s formula 'pth 2J s / RNUM , where RNUM is the numerical cylinder radius calculated from the Eulerian volume of the phase WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
438 Computational Methods and Experiments in Materials Characterisation III function C. In fig. 3, the relative error ('pNUM'pth)/'pth versus the number of scalar nodes of the mesh grid axis N is plotted. This relative error is compared to that obtained with the Front Tracking approach [13]. The comparison analysis clearly shows that both methods, Monte Carlo and Front Tracking, have first order spatial convergences. A better accuracy is nevertheless obtained with the Monte Carlo model, which corresponds, for similar mesh size, to a relative error twice lower.
relative error
1
0.1
Monte Carlo Front Tracking
0.01 1
Figure 3:
4
10
N
100
1000
The Monte Carlo relative error ('pNUM'pth)/ 'pth for the pressure difference 'pNUM ( p1 p0 ) between the two phases with respect to Laplace’s law 'pth J s / RNUM (RNUM being the radius of the phase function C), is plotted versus the scalar nodes of the mesh grid axis N and compared for equivalent criterion with the relative error obtained from the front tracking method [13].
Modelling of a real arrangement of particles extracted from microtomography image
In order to show our progress towards real material systems modelling, we have performed calculations on a four-particle system (fig. 4(b)) extracted from a 3D image of a soda-lime glass sample (fig 4(a)) obtained by X-ray computed microtomography [14]. The microtomographic acquisitions were performed at the European Synchrotron Radiation Facility (ESRF, Grenoble, France) site on the ID19 imaging and diffraction beam line. The holes on the extracted particle surface corresponding to the contact between other surrounding particles have been closed for calculation feasibility. The surface tension considered for calculations are that of the soda-lime glass material [15] i.e. Js = 0.36 J/m2. The WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
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elastic constants considered for the Monte Carlo calculation (EY=4x106 Pa, Q =0) are the same for the solid and vapour phases and thus have no physical meaning in the present case. As it can be seen on the micro tomographic image (fig. 4(a)), the glass material was characterised by a regular grain size centred around a radius of 60 Pm. The Navier Stokes resolution [16] of the microstructure evolution during sintering using the Front Tracking approach is presented in figure 5. The increase of the contact radius between particles until the contact coalescence as well as the pore closing is successfully modelled. This result highlights the numerical possibility of the coupled Eulerian/Lagrangian discretisation (fig. 1) to deal with 3D interface movements and disappearances. Nevertheless, the relevance of the calculated sintering kinetics will depend on the accuracy of the surface tension induced pressure within particles which is the driving force for mass transport. Unless very fine grids are implemented, this accuracy is difficult to reach on Eulerian grids when very small interface curvatures are involved, as it is the case at the contact zone for early sintering times. To discuss about that point, the Navier Stokes and Monte Carlo pressure fields obtained for two sections of the initial particle configuration are compared in fig. 6. One can notice that important pressure variations are located at the contact zones going from tensile values in that zone to compressive values in the direction of the outer lobe of the particles. The average value of pressure difference (p1-p0) = 1.1x104 Pa between the solid and the vapour phases at the outer lobe of the particles interface is very close to that of Laplace’s law 2Js/a = 1.2x104 Pa, considering the mean value of the particle radius a= 60 Pm.
(a) Figure 4:
(b)
(a) X-ray computed microtomography image of a glass particle compact performed at European Synchrotron Facility (ESRF, Grenoble, France) [14]. The glass material was characterised by a regular grain size of 60 Pm-radius; (b) four-particle system extracted from the powder compact for Monte Carlo and Navier Stokes calculations.
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440 Computational Methods and Experiments in Materials Characterisation III
Particle contact
Particle contact coalescence
Figure 5:
Navier-Stokes 3D evolution of the four-particle morphology during the sintering process showing pore closing and particle contact coalescence.
Now, the comparative analysis of the Monte Carlo and Navier Stokes results shows that the two tensile pressure peaks are clearly present in the three contact zones presented in fig 6 for the Monte Carlo simulation. They are sharp and located precisely just below the interface. The pressure gradient is regularly distributed in agreement with the Monte Carlo previous results based on the 2D Lagrangian volume discretisation. On the opposite, the Navier Stokes simulation leads in some cases to a unique broaden tensile peaks centred within the contact zone which are associated to no well-drawn pressure gradient distribution. On the basis of these results, the Monte Carlo calculation of the surface tension induced pressure, which results from potential minimisation involving displacement of the Lagrangian nodes, is shown to be more accurate than a method resulting from interface curvature calculation after projection on a structured grid non-conforming to the interface. The Front Tracking method thus induces an inaccurate macroscopic interpretation of the small-scale structure of interface, resulting from a simulation on a too coarse Eulerian grid.
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Computational Methods and Experiments in Materials Characterisation III
A Figure 6:
5
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B
Comparison between Navier Stokes (column A) and Monte Carlo (column B) resolution for a 64x64x64 grid of the hydrostatic pressure map within two sections of the four particle system. The pressure scale is p1=-104 Pa for white colour to p1=104 for black colour.
Conclusion
For the first time, the Monte Carlo numerical modelling dedicated to sintering processes have been implemented in an Eulerian fixed Cartesian grid framework in order to deal with 3D microstructures, the interface being tracked thanks to a Lagrangian grid. As a first step, the Monte Carlo simulations have been validated by comparisons to Laplace’s law. A first order spatial convergence, two times more accurate that the fluid mechanics Eulerian Front Tracking method, has been obtained. As a second step, the calculation of the pressure gradient within a four particle arrangement extracted from a 3D image of a real glass powder compact was shown to be accurately estimated even at the particle contact zone where low surface curvatures are involved. Our objective now is to couple stochastic WIT Transactions on Engineering Sciences, Vol 57, © 2007 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)
442 Computational Methods and Experiments in Materials Characterisation III Monte Carlo and deterministic Navier Stokes approaches in order to obtain sintering kinetics as precise as possible to be compared with experimental data from microtomography.
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J. Pan, H.N. Ch’ng, A.C.F. Cocks, Mech. Mater. 37 705-721 (2005). Y.U. Wang, Acta Mater. 54 943-961 (2006). E.A. Olevsky, V. Tikare, T. Garino, J. Am. Ceram. Soc. 89 [6] 1914-1922 (2006). H. Matsubara, J. Ceram. Soc. Japan, 113 [4] 263-268 (2005) Y. Wang, L.Q; Chen, in Methods and Material Research, Wiley, New York (2000). A. Jagota, and P. R. Dawson, J. Am. Ceram. Soc., 73 [1] 173-77 (1990). G.A.L. van de Vorst, Eng. Anal. Boundary Elem., 14 193-207 (1994). H. Zhou and J. J. Derby, J. Am. Ceram. Soc., 81 [3] 533-40 (1998). S. Bordère, D. Gendron, J. M. Heintz and D. Bernard, J. Am. Ceram. Soc., 88 [8] 2071-2078 (2005). S. Bordère, D. Gendron, and D. Bernard, Scripta Mater., 55 267-270 (2006) S. Bordère, Scripta Mater., 55 879-882 (2006) S. Bordère, S. Vincent, J.P. Caltagirone, submitted to Computers and Fluids S. Shin and D. Juric, J. Comput. Phys., 180 427-470 (2002). D. Bernard, D. Gendron, J.-M. Heintz, S. Bordère, J. Etourneau, Acta Mater., 53 121-128 (2005). H. Scholze, Le verre: Nature, Structure et Propriétés, second ed., Institut du verre, Paris, 1981. S. Vincent and J.-P. Caltagirone, J. Compu. Phys., 169 172-215 (2000)
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Author Index
Afsar M. N............................... 281 Agrianidis P. .............................. 13 Ait Aouit D. ............................. 187 Akinlade D. A............................ 85 Amobi I. U............................... 263 Anthymidis K. G........................ 13
He H. ....................................... 361 Huh H. ..................................... 319 Ibrahim I. ................................. 291 Ivanov M. A............................... 51 Jansen K. M. B. ....................... 241
Benavent-Climent A. ............... 393 Bernard D. ....................... 197, 433 Bhargava N. R. M. R. ................ 31 Bleck W. .................................... 95 Bordère S. ................................ 433 Cahoon J. R.............................. 105 Caley W. F................................. 85 Caltagirone J.-P........................ 433 Carsí M. ................................... 219 Cassenti B. ............................... 403 Castellanos J. ........................... 219 Castro G................................... 301 Chaturvedi M. C. ....................... 85 Cherubini C.............................. 339 Cizmar D.................................. 127 Climent M. A. .................. 135, 301 Costantini A............................. 373 Dantal B. R. ............................. 281 David C...................................... 13 De Baets P. .............................. 209 De Luca V................................ 273 de Vera G................................. 135 de Vreugd J.............................. 241 Ernst L. J.................................. 241 Evitts R. W. ............................... 21 Geltmacher A. B. ..................... 115 Greenberg B. A.......................... 51 Guo Z. Q. ................................. 361
Kamaruddin I............................. 61 Karamberi A. ........................... 329 Kermanpur A. .......................... 383 Khan U. A................................ 281 Kim G. H. ................................ 349 Kim S. B. ................................. 319 Kim W. D. ............................... 349 Klemm A. J.............................. 291 Klemm P.................................. 291 Kobayashi M. .......................... 177 Kobayashi T............................. 177 Korolev K. A. .......................... 281 Laganà A. ................................ 373 Lewis A. C............................... 115 Li Q.......................................... 105 Lim J. H. .................................. 319 Lissel S. L................................ 253 Luttermann T. ............................ 73 Mestrovic D. ............................ 127 Min T. ...................................... 349 Mircea I. .................................... 73 Mosaddeghfar M...................... 383 Moutsatsou A........................... 329 Muñoz J. .................................. 219 Naderi M.................................... 95 Napiah M. .................................. 61 Nourbakhshnia N..................... 383 Nóvoa X. R.............................. 301
444 Computational Methods and Experiments in Materials Characterisation III Obi E. R. .................................... 21 Oguocha I. N. A......................... 21 Ouahabi A................................ 187 Park J. H. ................................. 349 Park S. A.................................. 349 Perfumo M............................... 231 Pijnenburg J. A. C. M. ............. 241 Prasad V. V. S............................ 31 Procházka P. ............................ 423 Rao D. N. ................................... 31 Richards N. L..................... 85, 105 Rieiro I..................................... 219 Rizzo C. M............................... 231 Rowenhorst D. J....................... 115 Ruano O. A. ............................. 219 Ryszkowska J. ......................... 159 Sabia D. ................................... 273 Saigal A. .................................. 281 Salio M. P. ............................... 231 Samyn P................................... 209 Sánchez I.......................... 135, 301 Schoukens G. ........................... 209 Sedláþková S............................ 413 Sepehri Amin H. ...................... 383 Song J. H.................................. 319 Spanos G.................................. 115 Stanilovic V. ............................ 127 Staroselsky A. .......................... 393 Stefanidou M. A....................... 313
Stroeven M. ............................. 361 Stroeven P................................ 361 Sukackas V. ............................. 169 Suman K. N. S. .......................... 31 Takemura K. ................................ 3 Toda H. .................................... 177 Trckova J. ................................ 423 Tsipas D. N................................ 13 Uesugi K.................................. 177 Uzoegbo H. C. ......................... 263 Vacek J. ................................... 413 Van Driessche I. ...................... 209 Vermeltfoort A. T. ................... 147 Vessia G................................... 339 Vincent S. ................................ 433 Viot P....................................... 197 Wich T. ...................................... 73 Wilkinson D. S. ....................... 177 Yang W.................................... 361 Yao G. W................................... 43 Yasuda Y. .................................... 3 Yuen C. G................................ 253 Zhou J. T.................................... 43 Ziaei Rad S. ............................. 383 Zimmerman M. A. ................... 281
Computer Methods and Experimental Measurements for Surface Effects and Contact Mechanics VIII
Simulation of Electrochemical Processes II
Edited by: J.T.M De HOSSON, University of Groningen, Netherlands, C.A. BREBBIA, Wessex Institute of Technology, UK and S-I NISHIDA, Saga University, Japan.
This book contains papers presented at the Second International Conference in this successful series, which presents and discusses the state-of-the-art on the computer simulation of corrosion, electrochemical processes and the electrical and electromagnetic fields associated with them. Modern industry applies a wide range of electrochemical processes to protect against corrosion, provide surface treatments and to manufacture products. This book focuses on the computer modelling of these industrial processes and techniques by examining the developments of computational models and their application in practice. Featured topics include: Cathodic Protection Systems; Modelling Methodologies; Electrodeposition and Electroforming; Modelling of Coatings; Modelling Stress Corrosion, Cracking and Corrosion Fatigue; Modelling and Corrosion of Surface Coatings; Interference and Signature Control; Anodic Protection; Electrocoating and Plating; Optimisation of Control Systems; Detection and Monitoring of Corrosion; Measurement Techniques; Fuel on Photovoltaic Cells; Electrolysis Reactors; Comparison of Experimental Measurements and Computer results, Case Studies.
The importance of contact and surface problems in modern engineering and their combined effects has led to the Eighth International Conference on Computer Methods and Experimental Measurements for Surface and Contact Mechanics. Nowadays the importance of contact and surface problems in many technological fields is well understood: they are complex and inherently non-linear due to their moving boundaries and the different properties of materials, particularly along the contact surfaces. The use of surface treatments can reduce the cost of components and extend the life of the elements. Their effect is of particular importance in the case of surfaces undergoing contact, a problem which is addressed throughout the book. Topics featured: Surface Treatment; Surface problems in Contact Mechanics; Fracture Mechanics; Coupled analysis and experiments; Thin Coatings; Thick Coatings; Contact Mechanics; Material Surface in Contact; Applications and Case Studies. WIT Transactions on Engineering Sciences, Vol 55 ISBN: 978-1-84564-073-6 2007 352pp £130.00/US$235.00/€195.00
Edited by: V. De GIORGI, Naval Research Laboratory, USA, C.A. BREBBIA, Wessex Institute of Technology, UK and R. ADEY, Wessex Institute of Technology, UK.
WIT Transactions on Engineering Sciences, Vol 54 ISBN: 978-1-84564-071-2 2007 368pp £115.00/US$205.00/€172.00
Computational Methods and Experiments in Materials Characterisation II Edited by: C. A. BREBBIA, Wessex Institute of Technology, UK and A.A. MAMMOLI, The University of New Mexico, USA Bringing together the work of practitioners in many fields of engineering, materials and computational science, this book includes most of the papers presented at the Second International Conference on Material Characterisation. Compiled with the central aim of encouraging interaction between experimentalists and modelers, the contributions featured are divided under the following sections: MICROSTRUCTURES – Composites; Alloys; Ceramics; Cements; Foams; Suspensions; Biomaterials; Thin Films; Coatings. EXPERIMENTAL METHODS - Optical Imaging; SEM, TEM; X-Ray Microtomography; Ultrasonic Techniques; NMR/MRI; Micro/Nano Indentation; Thermal Analysis; Surface Chemistry. COMPUTATIONAL METHODS - Continuum Methods (FEM, FV, BEM); Particle Models (MD, DPD, Lattice-Boltzmann); Montecarlo Methods; Cellular Automata; Hybrid Multiscale Methods and Damage Mechanics. WIT Transactions on Engineering Sciences, Vol 51 ISBN: 1-84564-031-4 2005 368pp £120.00/US$195.00/€180.00 All prices correct at time of going to press but subject to change. WIT Press books are available through your bookseller or direct from the publisher.
e-Manufacturing Fundamentals and Applications Edited by: K. CHENG, Leeds Metropolitan University, UK This book begins by presenting the concepts of and an engineering-oriented approach to e-manufacturing. Next the enabling technologies and implementation issues for e-manufacturing, including topics such as Java programming, database integration, client-server architecture, web-based 3D modelling and simulations and open computing and interaction design, are reviewed. There is then an exploration of application perspectives through a number of application systems developed by the authors based on their own front-end research and first-hand engineering practices. These include Internet based design support systems, mass customization, Java based control and condition monitoring, digital and virtual manufacturing systems, e-supply chain management and e-enterprise for supporting distributed manufacturing operations. Designed for final year undergraduate elective courses on e-manufacturing and introductory courses on e-manufacturing at postgraduate level, this book can also be used as a textbook for teaching e-engineering in general. It will also provide a useful reference for design and manufacturing engineers, company managers, e-business/e-commerce developers and IT professionals and managers. ISBN: 1-85312-998-4 2005 344pp £133.00/US$213.00/€199.50
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Simulation of Electrochemical Processes Edited by: C.A. BREBBIA, Wessex Institute of Technology, UK, V.G. DEGIORGI, Naval Research Laboratory, USA and R.A. ADEY, Wessex Institute of Technology, UK This book contains most of the papers presented at the First International Conference on the Simulation of Electrochemical Processes held in Cadiz, Spain in May 2005. The meeting was organised by the Wessex Institute of Technology. The motivation for the meeting was to bring together researchers who have made significant developments in the area of Electrochemical modelling over recent years. Electrochemical processes are used by engineers to protect structures against corrosion, to apply coatings and paints, and as a manufacturing process. However, until recently, Engineers had to use experimental testing or frequent surveys to ensure the adequacy of a design as sophisticated prediction models were not available. The papers presented at this conference demonstrate the major advances that have been made in computational modelling to enable the most complex processes to be simulated. The papers in this book are divided into the following main topics: Modelling of Cathodic Protection Systems, Electrodeposition and Electroforming, Modelling Methodologies and Modelling Coatings.
Computer Methods and Experimental Measurements for Surface Effects and Contact Mechanics VII Edited by: J.T.M. DE HOSSON, University of Groningen, The Netherlands, C.A. BREBBIA, Wessex Institute of Technology, UK and S-I. NISHIDA, Saga University, Japan
WIT Transactions on Engineering Sciences, Vol 48
The research activities in the field of surface engineering have been greatly driven by the realization that the surface is usually the most important part of any engineering component. The scientific research featured deals with fundamental and applied concepts of surface engineering, in particular focusing on the interplay between applied physics, materials science and engineering, computational mechanics and mechanical engineering. The book is devoted to fundamental and applied studies of four interconnected aspects: processing, microstructural features, functional performance as well as the design of an appropriate theoretical and predictive framework of protective surfaces. This volume contains papers presented at the Seventh International Conference on Computational Methods and Experiments in Contact mechanics and Surface Treatment Effects which cover the following areas: Surface Treatments; Surface Problems in Contact Mechanics; Thin Coatings; Thick Coatings; Contact Mechanics; Material Surfaces in Contact; Applications and Case Studies.
ISBN: 1-84564-012-8 2005 264pp £92.00/US$147.00/€138.00
WIT Transactions on Engineering Sciences, Vol 49 ISBN: 1-84564-022-5 2005 416pp £145.00/US$250.00/€217.50
Surface Treatment VI Laser Metrology and Machine Computer Methods and Performance VI Experimental Measurements for Surface Treatment Effects Edited by: C.A. BREBBIA, Wessex Institute of Technology, UK, J.T.M. de HOSSON, University of Groningen, The Netherlands and S.-I. NISHIDA, Saga University, Japan Papers from the sixth international conference on this topic. Highlighting fundamental and applied concepts in this interdisciplinary field, the contributions focus on the interplay between applied physics, materials science and engineering, computational mechanics and mechanical engineering. WIT Transactions on Engineering Sciences, Vol 39 ISBN: 1-85312-962-3 2003 356pp £133.00/US$205.00/€199.50 All prices correct at time of going to press but subject to change. WIT Press books are available through your bookseller or direct from the publisher.
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Edited by: D.G. FORD, University of Huddersfield, UK Presenting the latest developments in the fields of calibration, certification and standardisation, this book features the edited proceedings for the Sixth International Conference on Laser Metrology, CMM and Machine Tool Performance. A wealth of topics including machine condition monitoring and intelligent instrumentation, gear and transmission metrology and numerical simulation and algorithm research are covered. WIT Transactions on Engineering Sciences, Vol 44 ISBN: 1-85312-990-9 2003 604pp £179.00/US$286.00/€268.50
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