Electromagnetic nondestructive evaluation (XI)

ELECTROMAGNETIC NONDESTRUCTIVE EVALUATION (XI)

Studies in Applied Electromagnetics and Mechanics Series Editors: K. Miya, A.J. Moses, Y. Uchikawa, A. Bossavit, R. Collins, T. Honma, G.A. Maugin, F.C. Moon, G. Rubinacci, H. Troger and S.-A. Zhou

Volume 31 Previously published in this series: Vol. 30. Vol. 29. Vol. 28. Vol. 27. Vol. 26. Vol. 25. Vol. 24. Vol. 23. Vol. 22. Vol. 21. Vol. 20. Vol. 19. Vol. 18. Vol. 17. Vol. 16. Vol. 15. Vol. 14. Vol. 13. Vol. 12.

S. Wiak, A. Krawczyk and I. Dolezel (Eds.), Advanced Computer Techniques in Applied Electromagnetics A. Krawczyk, R. Kubacki, S. Wiak and C. Lemos Antunes (Eds.), Electromagnetic Field, Health and Environment – Proceedings of EHE’07 S. Takahashi and H. Kikuchi (Eds.), Electromagnetic Nondestructive Evaluation (X) A. Krawczyk, S. Wiak and X.M. Lopez-Fernandez (Eds.), Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering G. Dobmann (Ed.), Electromagnetic Nondestructive Evaluation (VII) L. Udpa and N. Bowler (Eds.), Electromagnetic Nondestructive Evaluation (IX) T. Sollier, D. Prémel and D. Lesselier (Eds.), Electromagnetic Nondestructive Evaluation (VIII) F. Kojima, T. Takagi, S.S. Udpa and J. Pávó (Eds.), Electromagnetic Nondestructive Evaluation (VI) A. Krawczyk and S. Wiak (Eds.), Electromagnetic Fields in Electrical Engineering J. Pávó, G. Vértesy, T. Takagi and S.S. Udpa (Eds.), Electromagnetic Nondestructive Evaluation (V) Z. Haznadar and Ž. Štih, Electromagnetic Fields, Waves and Numerical Methods J.S. Yang and G.A. Maugin (Eds.), Mechanics of Electromagnetic Materials and Structures P. Di Barba and A. Savini (Eds.), Non-Linear Electromagnetic Systems S.S. Udpa, T. Takagi, J. Pávó and R. Albanese (Eds.), Electromagnetic Nondestructive Evaluation (IV) H. Tsuboi and I. Vajda (Eds.), Applied Electromagnetics and Computational Technology II D. Lesselier and A. Razek (Eds.), Electromagnetic Nondestructive Evaluation (III) R. Albanese, G. Rubinacci, T. Takagi and S.S. Udpa (Eds.), Electromagnetic Nondestructive Evaluation (II) V. Kose and J. Sievert (Eds.), Non-Linear Electromagnetic Systems T. Takagi, J.R. Bowler and Y. Yoshida (Eds.), Electromagnetic Nondestructive Evaluation

Volumes 1–6 were published by Elsevier Science under the series title “Elsevier Studies in Applied Electromagnetics in Materials”. ISSN 1383-7281

Electromagnetic Nondestructive Evaluation (XI)

Edited by

Antonello Tamburrino University of Cassino, Italy

Yevgen Melikhov Cardiff University, UK

Zhenmao Chen Xian Jiaotong University, China

and

Lalita Udpa Michigan State University, USA

Amsterdam • Berlin • Oxford • Tokyo • Washington, DC

© 2008 The authors and IOS Press. All rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without prior written permission from the publisher. ISBN 978-1-58603-896-0 Library of Congress Control Number: 2008932761 Publisher IOS Press Nieuwe Hemweg 6B 1013 BG Amsterdam Netherlands fax: +31 20 687 0019 e-mail: [email protected] Distributor in the UK and Ireland Gazelle Books Services Ltd. White Cross Mills Hightown Lancaster LA1 4XS United Kingdom fax: +44 1524 63232 e-mail: [email protected]

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LEGAL NOTICE The publisher is not responsible for the use which might be made of the following information. PRINTED IN THE NETHERLANDS

Electromagnetic Nondestructive Evaluation (XI) A. Tamburrino et al. (Eds.) IOS Press, 2008 © 2008 The authors and IOS Press. All rights reserved.

v

Preface The 12th International Workshop on Electromagnetic Nondestructive Evaluation (ENDE’07) was held from 19th–21st June 2007. The Workshop was hosted by the Wolfson Centre for Magnetics at Cardiff University, Cardiff, Wales, UK with sponsorship from Cedrat SA, Serco Assurance, Rolls-Royce plc, Welsh Assembly Government, Computer Simulation Technology, The Japan Society of Applied Electromagnetics and Mechanics, Engineering and Physical Sciences Research Council. The organizers gratefully acknowledge their support. The aim of this annual workshop is to bring together engineers and scientists from universities, research institutions and industry to discuss and exchange the latest ideas and findings in basic research and development as well as industrial applications of Electromagnetic Nondestructive Evaluation. After the introductory welcoming remarks from Dr. David Grant (Vice Chancellor of the Cardiff University), Prof. Hywel Thomas (Head of the School of Engineering, Cardiff University) and Prof. David Jiles (Chairman of the Workshop), the technical program of the Workshop commenced with a plenary talk “NDE Research Makes a Difference” by Prof. Chris Scruby, Director, UK Research Centre in NDE, Imperial College London, U.K. Four distinguished invited speakers discussed the challenges and achievements in various fields of ENDE. Prof. J. Bowler (Iowa State University, USA), gave a talk titled “Integral methods for calculating the interaction of eddy currents with cracks”. Prof. K. Miya (Keio University, Japan), presented the second invited talk on “The Start of a New Field of Electromagnetic and Mechanical Maintenance Engineering”. Prof. G. Dobmann (Fraunhofer-Institute for Non-destructive Testing, Germany), was invited to present “Industrial Applications of 3MA – Micromagnetic Multiparameter Microstructure and Stress Analysis”. Finally Prof. N. Takahashi (Okayama University, Japan) presented an invited talk on “3D Nonlinear Eddy Current Analysis of Electromagnetic Inspection of Defects in Steel”. A total of 75 technical papers were divided into 30 oral and 45 poster presentations. The oral presentations were organized into 7 sessions covering a variety of topics on both theoretical and experimental aspects of NDE in eddy currents, magnetic measurements, magnetic flux leakage, Barkhausen methods, new methods and inverse problems for crack detection. These sessions were chaired by experts in the field including Profs. S. Udpa, L. Udpa, D. Jiles, C. Scruby, P. Nagy, T. Moses, G. Dobmann, K. Miya, S. Takahashi, A. Tamburrino and others. During closing remarks it was announced that the next ENDE Workshop (ENDE2008) will be held June 10–12, 2008 in Seoul, Korea. The ENDE Workshop 2009 will be held in Dayton, Ohio, U.S.A. The conference concluded with remarks from the chairman Prof. David Jiles. A total of 73 participants from 16 countries were registered for the Workshop. The short versions of the papers were published in the Workshop digest and 39 reviewed full papers were accepted for publication in this proceeding. The organizers would like to thank all the participants for their contribution and all the referees for their role in reviewing the full papers. Lastly, the editors gratefully acknowledge the help and hard work of Ms. Linda Clifford in putting this volume together.

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List of Referees J. Aldrin Z. Badics J. Bowler N. Bowler T. Chady M. Chan Z. Chen W. Cheng G. Dobmann Y. Gotoh R. Grimberg X. Hao H. Huang G. Hwang L. Janousek H. Kikuchi S. Kobayashi F. Kojima J. Lee D. Lesselier L. Li Y. Melikhov V. Melapudi O. Mihalache T. Moses G. Ni J. Pávó P. Ramuhalli G. Rubinacci O. Stupakov J. Taggart A. Tamburrino T. Takagi N. Takahashi S. Takahashi T. Theodoulidis G.Y. Tian I. Tomas Y. Tsuchida L. Udpa S. Udpa M. Vaidhianathasamy S. Ventre

Computational Tools, USA Rhythmia Medical, Inc, USA Iowa State University, USA Iowa State University, USA Technical University of Szczecin, Poland Michigan State University, USA Xi’an Jiaotong University, China Tsurumi R&D Center, JAPEIC, Japan Fraunhofer-IZFP University, Germany Oita University, Japan National Institute of R&D for Technical Physics, Romania University of Birmingham, United Kingdom IIU Corporation, Japan Shanghai Jiaotong University, China University of Zilina, Slovakia Iwate University, Japan Iwate University, Japan Kobe University, Japan Chosun University, Korea Supélec, France Tsinghua University, China Cardiff University, United Kingdom Michigan State University, USA JAEA, Japan Cardiff University, United Kingdom Zhejing University, China Budapest University of Technology and Economics, Hungary Michigan State University, USA Università degli Studi di Napoli “Federico II”, Italy Tohoku University, Japan Serco Assurance, United Kingdom University of Cassino, Italy Tohoku University, Japan Okayama University, Japan Iwate University, Japan University of Western Macedonia, Greece University of Newcastle upon Tyne, UK Institute of Physics, Czech Republic Oita University, Japan Michigan State University, USA Michigan State University, USA University of Newcastle Upon Tyne, United Kingdom University of Cassino, Italy

viii

M. Versaci F. Villone J. Wilson L. Xin N. Yusa Z. Zeng

Università “Mediterranea” di Reggio Calabria, Italy University of Cassino, Italy University of Newcastle Upon Tyne, United Kingdom Michigan State University, USA IIU Corporation, Japan Michigan State University, USA

ix

Organizing Committees International Committee Chairman

• S. Udpa, Michigan State University, USA

Members

• • • • • • • • • • • • • • • • • •

J.R. Bowler, Iowa State University, U.S.A. N. Bowler, Iowa State University, U.S.A. Z. Chen, Xian Jiaotong University, China G. Dobmann, Fraunhofer Institute for NDT, Germany H.K. Jung, Seoul National University, South Korea F. Kojima, Kobe University, Japan D. Lesselier, DRE-LSS CNRS-SUPELEC-UPS, France K. Miya, Keio University, Japan G.Z. Ni, Zhejing University, China J. Pavo, Budapest University, Hungary G. Pichenot, CEA SACLAY, France A. Razek, LGEP CNRS-SUPELEC-UPS-UPMC, France G. Rubinacci, Universita di Napoli Federico II, Italy S.J. Song, Sung Kwan University, Korea T. Takagi, Tohoku University, Japan S. Takahashi, Iwate University, Japan A. Tamburrino, Universita degli Studi di Cassino, Italy L. Udpa, Michigan State University, U.S.A.

Organizing Committee

• • • • • • • • •

Tony Dunhill, Rolls Royce Plc Keith Jenkins, Cogent Power David Jiles, Cardiff University (Chairman) Chester Lo, Iowa State University Tony Moses, Cardiff University Ian Nicholson, TWI Ltd Allan Rogerson, Serco Assurance Plc Chris Scruby, Imperial College London Gui Yun Tiann, University of Huddersfield

Local Committee

• • • • • •

Phil Anderson Jeremy Hall Eugene Melikhov John Snyder Paul Williams Stan Zurek

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xi

List of Participants Mr. Kavoos Abbasi Tohoku University, Japan [email protected]

Dr. Dagmar Faktorova University of Zilina, Slovak Republic [email protected]

Prof. Purnachandra Rao Bhagi Indira Ghandi Centre for Atomic Research, India [email protected]

Mr. Fabrice Foucher CEDRAT, France [email protected]

Prof. John Bowler Iowa State University, USA [email protected]

Dr. Raimond Grimberg National Inst. of R & D for Technical Physics, Romania [email protected]

Dr. Nicola Bowler Iowa State University, USA [email protected]

Dr. Xinjiang Hao Birmingham University, UK [email protected]

Dr. John Burd JB Consulting Ltd, UK [email protected]

Dr. Jeremy Hall Wolfson Centre for Magnetics, UK [email protected]

Hee Jun Chen Sungkyunkwan University, Korea [email protected]

Mr. Jiseong Hwang Chosun University, Republic of Korea [email protected]

Dr. Zhenmao Chen Xian Jiaotong University, China [email protected]

Dr. Richard Ireland QinetiQ, UK [email protected]

Prof. Gerd Dobmann Fraunhofer-Institut IZFP, Germany [email protected]

Dr. Ladislav Janousek University of Zilina, Slovak Republic [email protected]

Mr. David Edgar University of Nottingham & Qinetiq, UK [email protected]

Dr. Mohan Jayawardene CST, UK/Germany [email protected]

Dr. Christiaan Eggink Shell Global Solutions Int., Netherlands [email protected]

Dr. Steve Jenkins Current Enterprises, UK [email protected]

xii

Prof. David Jiles Wolfson Centre for Magnetics, UK [email protected]

Dr. Dmitriy Makhnovskiy University of Plymouth, UK [email protected]

Dr. Tonphong Kaewkongka Chulalongkorn University, Thailand [email protected]

Dr. Eugene Melikhov Wolfson Centre for Magnetics, UK [email protected]

Mr. Yuchiro Kai Oita University, Japan [email protected]

Prof. Kenzo Miya IIU, Japan [email protected]

Dr. Hiroaki Kikuchi NDE & SRC Ueda, Japan [email protected]

Prof. Tony Moses Wolfson Centre for Magnetics, UK [email protected]+D70

Mr. Jeremy Knopp Air Force Research Laboratory, USA [email protected]

Dr. Shoichiro Nagata University of Miyazaki, Japan [email protected]

Dr. Satoru Kobayashi NDE & Science Research Centre, Japan [email protected]

Prof. Peter BN Nagy University of Cincinnati, USA [email protected]

Prof. Fumio Kojima Kobe University, Japan [email protected] Dr. Yann Le Bihan LGEP- SUPELEC, France [email protected] Prof. Jinyi Lee Chosun University, Republic of Korea [email protected]

Severine Paillard CEA, France [email protected] Dr. Manuele Papais University of Udine, Italy [email protected] Dr. Grégoire Pichenot CEA, France [email protected]

Dr. Yohan Le Diraison ENS-CACHAN, France [email protected]

Mr. Grzegorz Psuj Szczecin University of Technology, Poland [email protected]

Dr. Dominique Lesselier SUPELEC, France [email protected]

Mr. Brian Radtke Iowa State University, USA [email protected]

Prof. Li Luming Tsinghua University, China [email protected]

Miss Alicia Romero Ramirez Swansea University, UK [email protected]

xiii

Dr. Cyril Ravat ENS-CACHAN, France [email protected]

Prof. Norio Takahashi Okayma University, Japan [email protected]

Dr. Alan Rogerson Serco Assurance, UK

Prof. Seiki Takahashi Iwate University, Japan [email protected]

Dr. Adriana Savin National Inst. of R & D for Technical Physics, Romania [email protected]

Prof. Antonello Tamburrino Daeimi University of Cassino, Italy [email protected]

Prof. Chris Scruby Imperial College, UK [email protected]

Dr. Alan Tassin ENS-CACHAN, France [email protected]

Dr. Gongtian Shen CSEI, China [email protected]

Dr. Theodoros Theodoulidis University of West Macedonia, Greece [email protected]

Prof. Young-Kil Shin Kunsan National University, South Korea [email protected]

Prof. Gui Yun Tian Newcastle University, UK [email protected]

Dr. Anastassios Skarlatos CEA, France gregoire.pichenot.cea.fr

Mr. Yuji Tsuchida Oita University, Japan [email protected]

Dr. Sung-Jin Song Sungkyunkwan University, Korea [email protected] Mr. Giuseppe Sposito Imperial College, UK [email protected] Dr. Vladamir Syasko Constanta, Russia [email protected] Dr. John Taggart Serco Assurance, UK [email protected] Prof. Toshiyuki Takagi Tohoku University, Japan [email protected]

Dr. Lalita Udpa Michigan State University, USA [email protected] Prof. Satish Udpa Michigan State University, USA [email protected] Dr. Tetsuya Uchimoto Tohoku University, Japan [email protected] Dr. Moorthy Vaidhianathasamy Newcastle University, UK [email protected] Dr. Haitao Wang Nanjing University of Aeronautics & Astronautics, China [email protected]

xiv

Dr. Casper Wassink Applus RTD, The Netherlands [email protected]

Mr. John Wilson Newcastle University, UK [email protected]

Mr. Chris Ward University of Nottingham/RWE NPower, UK [email protected]

Mr. Chen Xing Tsinghua University, China [email protected]

Dr. Paul Williams Wolfson Centre for Magnetics, UK [email protected]

Dr. En Tao Yao Nanjing University of Aeronautics & Astronautics, China [email protected]

xv

Contents Preface

v

List of Referees

vii

Organizing Committees

ix

List of Participants

xi

Invited Speakers A Start of New Field of Electromagnetic and Mechanical Maintenance Engineering Kenzo Miya NDE Research Makes a Difference C.B. Scruby

3 10

Industrial Applications of 3MA – Micromagnetic Multiparameter Microstructure and Stress Analysis Gerd Dobmann, Iris Altpeter, Bernd Wolter and Rolf Kern

18

3D Nonlinear Finite Element Analysis of Electromagnetic Inspection of Defects in Steel N. Takahashi and Y. Gotoh

26

Magnetic Materials Evaluation of Irradiation Embrittlement in Fe-Cu-Ni-Mn Model Alloys by Measurements of Magnetic Minor Hysteresis Loops Satoru Kobayashi, Hiroaki Kikuchi, Seiki Takahashi, Katsuyuki Ara and Yasuhiro Kamada Analysis of Barkhausen Noise Characteristics and Mechanical Properties on Cold Rolled Low Carbon Steel Hiroaki Kikuchi, Tomoki Koshika, Tong Liu, Yasuhiro Kamada, Katsuyuki Ara, Satoru Kobayashi and Seiki Takahashi A Bridge Between NDE and Charpy Impact Testing Seiki Takahashi and Satoru Kobayashi ND-Materials Characterization of Neutron-Induced Embrittlement in German Nuclear Reactor Pressure Vessel Material by Micromagnetic NDT Techniques Gerd Dobmann, Iris Altpeter, Melanie Kopp, Magdalena Rabung and Gerhard Hübschen Evaluation of Chill Contents in Flake Graphite Cast Irons Using AC Magnetization Method Tetsuya Uchimoto, Jun Matsukawa, Toshihiko Abe, Toshiyuki Takagi, Takeshi Sato, Hiroyuki Ike, Takahito Takagawa and Noritaka Horikawa

37

42

46

54

62

xvi

Characterisation of Microstructures in Heat Treated Maraging Steel Using Eddy Current and Barkhausen Emission Techniques K.V. Rajkumar, B.P.C. Rao, B. Sasi, S. Vaidyanathan, T. Jayakumar and Baldev Raj

70

Novel Acoustic Barkhausen Noise Transducer and Its Comparison with Electromagnetic Acoustic Transducer John Wilson, Gui Yun Tian, Rachel S. Edwards and Steve Dixon

78

Modelling and Measurement of Decarburisation of Steels Using a Multi-Frequency Electromagnetic Sensor X.J. Hao, W. Yin, M. Strangwood, A.J. Peyton, P.F. Morris and C.L. Davis

86

Assessment of Grinding Damage on Gear Teeth Using Magnetic Barkhausen Noise Measurements Moorthy Vaidhianathasamy, Brian Andrew Shaw, Will Bennett and Peter Hopkins Evaluation of Contact Fatigue Damage on Gears Using the Magnetic Barkhausen Noise Technique Moorthy Vaidhianathasamy, Brian Andrew Shaw, Will Bennett and Peter Hopkins

90

98

Inverse Problems 3D Reconstruction of Flaws in Metallic Materials by Eddy Currents Inspections Alessandro Pirani, Marco Ricci, Antonello Tamburrino and Salvatore Ventre

109

Multi-Frequency Eddy Current Imaging for the Detection of Buried Cracks in Aeronautical Structures Yohan Le Diraison and Pierre-Yves Joubert

117

A Comparative Study of Source Separation Techniques for the Detection of Buried Defects in the EC NDE of Aeronautical Multi-Layered Lap-Joints Alan Tassin, Yohan Le Diraison and Pierre-Yves Joubert

125

Fundamental Feature Extraction Methods for the Analysis of Eddy Current Data Jeremy S. Knopp and John C. Aldrin

133

Inversion of Potential Drop Data for the Reconstruction of Crack Depth Profiles Giuseppe Sposito, Peter Cawley and Peter B. Nagy

141

Automatic Classification of Defects with the Review of an Appropriate Feature Extraction Alicia Romero Ramirez, Neil Pearson and J.S.D. Mason

148

Microwave Nondestructive Detection of Longitudinal Cracks in Pipe with U-Bend and Prediction of Its Location by Signal Processing Kavoos Abbasi, Satoshi Ito and Hidetoshi Hashizume

154

Some Experiences with Microwave Investigation of Material Defects Dagmar Faktorová

162

xvii

Modeling Effect of Crack Closure on Quantitative ECT Inspection of Closed Fatigue Cracks Zhenmao Chen, Noritaka Yusa, Kenzo Miya and Hideaki Tokuma Toward the Reconstruction of Stress Corrosion Cracks Using Benchmark Eddy Currents Signals Maxim Morozov, Guglielmo Rubinacci, Antonello Tamburrino, Salvatore Ventre and Fabio Villone Evaluation of Subsurface Cracks in Riveted Aluminium Joints Using Industrial Eddy Current Instrumentation Maxim Morozov, Guglielmo Rubinacci, Antonello Tamburrino and Salvatore Ventre Design of a System for the Long Defects Detection with Advanced Methods for Eddy-Currents Analysis E. Cardelli, A. Faba, A. Formisano, R. Martone, F.C. Morabito, M. Papais, R. Specogna, A. Tamburrino, F. Trevisan, S. Ventre and M. Versaci

171

179

187

195

Theory of Four-Point Alternating Current Potential Drop Measurements on a Layered Conductive Half-Space Nicola Bowler and John R. Bowler

203

Integration of Tilted Coil Models in a Volume Integral Method for Realistic Simulations of Eddy Current Inspections Theodoros Theodoulidis and Gregoire Pichenot

211

Modeling of Flawed Riveted Structures for EC Inspection in Aeronautics S. Paillard, G. Pichenot, Y. Choua, Y. Le Bihan, M. Lambert, H. Voillaume and N. Dominguez Numerical Modeling of Eddy Current Nondestructive Evaluation of Ferromagnetic Tubes via an Integral Equation Approach Anastassios Skarlatos, Grégoire Pichenot, Dominique Lesselier, Marc Lambert and Bernard Duchêne Design of Reflection Type Pulsed Eddy Current Nondestructive Testing Young-Kil Shin, Dong-Myung Choi and Hee-Sung Jung

217

225

231

Applications Noninvasive Characterization of Bjork-Shiley Convexo-Concave Prosthetic Heart Valves Using an Electromagnetic Method Raimond Grimberg, Shiu C. Chan, Adriana Savin, Lalita Udpa and Satish S. Udpa Remote Field Eddy Current Control Using Rotating Magnetic Field Transducer. Application to Pressure Tubes Examination Adriana Savin, Lalita Udpa, Rozina Steigmann, Alina Bruma, Raimond Grimberg and Satish S. Udpa

241

249

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Lifetime Prediction of Pressure Tubes in PHWR Nuclear Power Plants Using Eddy Current Data Raimond Grimberg, Adriana Savin, Rozina Steigmann, Aurel Andreescu, Nicoleta Iftimie and Marius Mihai Cazacu Electromagnetic Non-Destructive Evaluation of Reinforced Concrete Rebars Maxim Morozov, Guglielmo Rubinacci, Antonello Tamburrino and Salvatore Ventre

257

263

Advanced Probe with Array of Pick-Up Coils for Improved Crack Evaluation in Eddy-Current Non-Destructive Testing Ladislav Janousek, Klara Capova, Noritaka Yusa and Kenzo Miya

271

Observation of Stress Loaded Ferromagnetic Samples Using Remanent Flux Leakage Method Tomasz Chady, Grzegorz Psuj and Ryszard Sikora

276

Evaluation of Complex Multifrequency Eddy Current Transducer Designed for Precise Flaw Depth Measurements Tomasz Chady, Piotr Baniukiewicz, Ryszard Sikora and Grzegorz Psuj

283

Comparative Study of Coil Arrangements for the EC Testing of Small Surface Breaking Defects Cyril Ravat, Yann Le Bihan, Pierre-Yves Joubert and Claude Marchand

288

Author Index

295

Invited Speakers

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Electromagnetic Nondestructive Evaluation (XI) A. Tamburrino et al. (Eds.) IOS Press, 2008 © 2008 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-58603-896-0-3

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A Start Of New Field Of Electromagnetic And Mechanical Maintenance Engineering Kenzo MIYA1 IIU, Corp., 2-7-17-7F, Ikenohata, Taitoku, Tokyo, 110-0008, Japan

Abstract. Maintenance to ensure the integrity of structures is one of the most important issues in modern industry, but more so in the nuclear power industry. This is primarily because complete prevention of all degradation of industrial materials is not possible, at least not in a realistic way. Consequently it is extremely important to detect degradation before machines start to loose their ability to function which may lead to harmful failures. Usually there is some kind of significant interval between the start of material degradation and failure; in other words, degradation usually progresses slowly with time. The problem is whether we can detect precursors of failure in the interval or not. If it is possible, we can have economic as well as safety related benefits because we are able to stop the machine before a functional failure and prevent an accident initiated by the failure of the machine. The benefits are not restricted to the nuclear power industry because it can be applied to any other heavy industry. There are many reasons why many conferences, such as ENDE, have been established to discuss and promote the progress of nondestructive inspection techniques. Whereas nondestructive inspection plays an important role in maintaining structural integrity and the performance of nondestructive inspection techniques should be enhanced in that sense, we need to regard it as one of several components composing “maintenance engineering.” Moreover, although nondestructive inspection is a proactive measure of maintenance, it is not a predictive tool. In fact, it is effective for detecting existing defects and does not say anything about the temporal evolution of defects. On the other hand, a condition monitoring system can offer significantly more useful information as mentioned above. In this paper I would like to introduce the concept of maintenology as a new science and technology in contrast to conventional maintenance engineering and to present several important results on electromagnetic maintenance for nuclear power plants as condition monitoring techniques (CMT). In particular, the introduction of electromagnetic maintenance is expected to play a very promising role in abnormality predictions of many dynamic machines that are required to be inspected regularly by law. Application of the technique would change conventional wisdom in thinking that machines should be taken apart and inspected regularly based on regulations. In many cases, this TBM (time based maintenance) is not too conservative in achieving an optimal maintenance approach.

Introduction The nuclear energy renaissance is occurring not only in advanced countries but also in developing ones like China, India and Brazil, due to demands for renewable energy sources and to protect the earth against abnormal climate caused by the green house effect. Nuclear power plants are one of the greenest sources of energy, and operated

4

K. Miya / A Start of New Field of Electromagnetic and Mechanical Maintenance Engineering

safely, can provide energy reliably to meet base loads. Thus, there is considerable interest in the safe and economic operation of nuclear power plants (NPPs). Maintenance engineering is extremely important to achieve these two goals. Two approaches are usually pursued: time-based maintenance (TBM) and condition-based maintenance (CBM). Optimal maintenance may be achieved by planning the best mix of the two approaches. The development of CBM techniques is greatly needed to enhance the safety level of NPPs. In this paper we explain the possibility of using electromagnetic methods and the application of the technology to maintenance operations at NPP. The essential part of electromagnetic maintenance technology is the utilization of u x B electromagnetic motive force (u: vectored velocity, B: magnetic field). In principle, diagnostics based on the technique can be applied to rotating machines at present although application could be extended to static components in future. Theoretical issues underlying the approach and experimental work associated with electromagnetic maintenance will be introduced first. Numerical simulations and experiments will then be presented.

1. Construction of maintenance engineering as a new field Maintenance issues comprise two different aspects, one is related to human behaviour and another relates to technical matters. Complicated human behaviour relating to maintenance of machines is considered to consist of three principles, as shown in Figure 1: the selection principle, connection principle and projection principle. Their relationship can be understood well if we imagine a process of making a sentence where proper words are selected first (selection principle), words are properly arranged to meet grammatical requirements (connection principle), and the intended meaning is realized by the sentence. The grammatically correct arrangement of words is called a projection principle. Concept of such a view is translated into maintenance activities like words corresponding to various kinds of technology supported by natural science, sociology, codes and standards, the connecting principle corresponding to maintenance scheme, and projection principle corresponding to the selection of necessary techniques from existing technological systems. These basic principles should be favourably applied to planning the maintenance scheme. In Fig. 2, a flow chart of maintenance activities is shown schematically. They start from the selection of the component to be maintained followed by the selection of the maintenance method, i.e. TBM or CBM, and then finally we proceed to the inspection process. This, in general, is the most universal process. In Fig. 3, concepts of maintenology are newly defined and explained to introduce a new approach to conventional maintenance engineering. The new approach consists of three principles depicted in Fig. 1; the basic form of maintenance action is shown in Fig.2. This recognition may contribute to the construction of revised maintenance engineering by applying theoretical aspects.

2. Electromagnetic maintenance engineering Principles of electromagnetic maintenance may be called the EM method. It is associated with the following processes: 1) Creation of a static magnetic field in a region of rotating components

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K. Miya / A Start of New Field of Electromagnetic and Mechanical Maintenance Engineering

2) Measurement of a dynamic magnetic field created by eddy currents 3) Diagnosis of conditions of rotating parts inside, which can not be observed from the outside 4) Understanding the precursor of component abnormalities Measurements were carried out for real pumps, real fans, bearings, generating motors, etc. It was surprising to observe signals through thick casing of components overcoming the skin effect due to very low frequency. Simulation software was developed to predict eddy current distribution in components allowing one to judge whether conditions are normal or abnormal. This is a classical inverse problem but a very difficult one to solve due to ill-posedness. Ԙ Selection Principle

ԙ Projection principle

Ԛ Connection principle

System s

Component

㪪㫋㫉㫌㪺㫋㫌㫉㪼

ԘSelection of applicable engineering theories

Equipments

ԙReflection ԙReflection of maintenance technology on planning

Select appropriate technical knowledge from the engineering science system Codes&standards Sociology, economy Engineering science

Maintenanology

humanities

Ԛmaintenance scheme= Flow of maintenance activities

A-B-C-D-E-F…

Three elements of maintenance

1RGTCVKQP

Corrective actions

Characteristics of Aging (predictable㧛 unpredictable)

ԙAnalysis ࡮Evaluation Check࡮ Evaluation Investigations of root causes

Natural science

Component attribution Design Operation

+PUGTXKEG

ԚActions/Measures

ԘUnderstand the current state Inspections࡮ Tests Monitoring

㪘㪾㫀㫅㪾㩷㫆㪽㩷㪪㪪㪚

࡮࡮࡮࡮࡮࡮࡮࡮࡮

Maintenance engineering

Nuclear facilities

㪧㪸㫉㫋㫊

Classifications of maintenance methods Options

Logic of choice for maintenance methods

Inspection plans

Maintenance methods : Decomposition testing : ࡮ Nondestructive testing : ࡮ Function tests : ࡮ Condition monitoring : ࡮ Corrective Maintenance

Safety Safety Operation Operation

Figure 1. Principles underlying maintenance activities Maintenance Maintenance Engineering 1. 2. 3. 4. 5.

Maintenance Engineering

Maintenance Science Maintenance Engineering & Technology Maintenance Sociology M ethodology of optimization Codes and Standards development

Figure 2. Flow Chart of Maintenance

Theoretical Approach 1. 2. 3. 4. 5.

Theoretical Approach

Internal form of maintenance activities Basic form of maintenance action Academic development Application of P-D-C-A Theory of code and standard

Figure 3. Structure of maintenology

Figure 4. Eddy current distribution in blades (The largest eddy current will be generated in the area of the blade near the exciting coil. Due to this, magnetic flux changes in the direction coil are large. The excitation flux is constant and is not measured)

Casing

Impeller

Blades

Figure 5. Impeller model and meshes

Figure 6. Eddy current in ball bearings

K. Miya / A Start of New Field of Electromagnetic and Mechanical Maintenance Engineering

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Figure 7. Signals from sensor. (1. Decrease of signal amplitude by 1/10 when distance becomes longer, from 5 to 10 mm. 2. Effect of a holder on signal is not significant, about 10% decrease) 3.00E-08 2.00E-08

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Figure 9. Signals from defect

In Figure 4, four blades rotate around an axis which is not shown in the static magnetic field created by a permanent magnet (not shown here). Eddy current distribution induced in blades is shown in the figure together with a pick-up coil. If a crack is present or the blade is greatly deformed, we measure some changes in signals when abnormalities are present. In Figure 5 the finite element mesh for the impeller of a pump is shown. The finite element method is employed to evaluate eddy currents in the impeller. In Figure 6 ball bearings witness an orbital motion. The rotational eddy current is not significant, but the orbital motion produces a considerable amount of eddy currents in the balls. Thus, defects in a ball bearing may be easily detected by the method. If worn particles are present between bearings and steel plates, the speed of the orbital motion will change and this change can be detected using this method. Simulation results are shown in Fig. 7 for two cases: one is without a holder and the other is with a holder. Eddy currents in these cases are not different from each other indicating small effects of the holder. In the figure, “U” is a measure of distance between a bar magnet and surface of a casing. The measured signals largely depend on the distance, which is easily estimated by the decrease in the field due to the distance. The number of signal oscillations corresponds to the number of blades. In Fig. 8, the possibility of the detection of two notches on the surface of balls was tested by numerical simulation. The notches are in horizontal and vertical direction as shown in the figure. Results are shown in Fig.9. In the case of the vertical notch, differences from the case without a notch are evident but are difficult to find. This result can be explained from the magnitude of eddy currents due to positional differences of the two notches. Therefore, it becomes essentially important to optimize the relative position of a magnet and rotating blade.

K. Miya / A Start of New Field of Electromagnetic and Mechanical Maintenance Engineering

7

3. Experimental results The numerical results above were introduced on the basis of the explained concept to apply electromagnetic phenomena to defect inspection of rotating machines. The numerical results showed that there is a valid basis for the concept. The next step is to show experimental verification of the concept. Up to now, our research group has conducted many experiments with a small fans and pumps. We have also measured electromagnetic signals generated by rotating parts of real machines. When we can set a sensor and magnet close to the rotating parts, we can successfully measure a signal. However, when access is limited, it is difficult to obtain a useful signal. In Fig.10, measurement results are shown for the case of a fan. The signals were obtained as a function of distance between the sensor and the rotating part. When the distance is 5 mm, the signal is the largest and in the case of 20mm distance, the signal is the smallest. These results are from the set-up without fan casing. But, the 20mm distance result indicates that the measurement with a set-up that includes fan casing is possible. Results with the casing are not shown here, but a sufficient number of signals were obtained. Cyclic signals are obtained for 5 blades. There is the possibility that the smaller signal on the inside is due to a weight. The major purpose of this study is to verify the possible application of electromagnetic phenomena to proactive detection of various types of defects. Extensive studies must be conducted to find useful relations between signal changes and the condition of defects. Useful information must be provided to make engineering decisions on whether operation of the machine should be stopped for repair or continued with careful monitoring. With this in mind, we carried out an experiment with a notched blade as shown in Fig. 11. Two curves are shown corresponding to two types of bar and U-magnets. It is possible to see the movement of the 5 blades from both results. One of the blades was machined with the notch and signals reflecting an existence of the notch are observed in both results. Through a two-way excitation method, a crack of 1/3 the width was easily detected. Significant differences in signals were seen for cracks 1/10 the width. In Fig.12, three pictures of a casing of the real pump, location of a sensor and a pick-up coil, and an impeller are shown. The casing is cast iron and shows magnetic property. The rod type permanent magnet is attracted to the casing. 0.08

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K. Miya / A Start of New Field of Electromagnetic and Mechanical Maintenance Engineering

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Figure 11. Detection of a defective blade

In Fig. 13, measurement results are shown. A careful examination shows that the number of impellers is 5 and the rotation cycle is 0.02 seconds since a motor operates at 50 Hz in the Kanto area in Japan. In addition to this, we can recognize a small difference in the amplitude of the measured voltage corresponding to the difference in size of the 5 blades. Since the signal amplitudes are different this suggests that the method can be applied to test for the dimension of axis and impellers, as well as their condition of motion. The wave form is not sinusoidal and shows a small tooth. The reason for the tooth is not clear until we see the inside of the pump after opening the casing. This small observation indicates that the detailed structure inside a rotating machine will be made clear after we accumulate knowledge on dimensional information and defects signals in the future.

Figure 12. Casing and impellers (real pump)

K. Miya / A Start of New Field of Electromagnetic and Mechanical Maintenance Engineering

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Figure 13. Signal with rod type permanent magnet sensor

3. Conclusion The author would like to note that there are many challenging problems in the diagnostics of rotating machines and that there is a strong need for developing methods of detecting abnormality precursors as a prognosticator of functional failure. There are well-known methods of condition monitoring. These include vibration monitoring methods, oil analysis, thermography, etc. These methods will be useful if they are used properly; however, there are several important problems to be solved in identifying the root causes of malfunctions occurring in a machine. Electromagnetic methods have shown their superiority over conventional methods in being able to locate defects and in identifying conditions at specific locations in rotating parts. Extensive studies are required to establish the relationship between the measured signal and the nature of defects. Efforts are urgently needed to translate R&D efforts to industrial applications.

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Electromagnetic Nondestructive Evaluation (XI) A. Tamburrino et al. (Eds.) IOS Press, 2008 © 2008 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-58603-896-0-10

NDE Research Makes a Difference C B SCRUBY UK Research Centre in NDE, Imperial College London, SW7 2AZ UK

Abstract. This paper discusses the development of research in NDE and its impact on industry. Examples will be given of past research projects that have been translated into solutions to industrial inspection problems, and present day challenges to industry and the NDE research community. Recurring themes include the need for quantification, and physical models to give scientific understanding and hence improved confidence for product quality and safetycritical application. Timely technology transfer is a continuing challenge and lessons from past experience will be discussed. Finally, the author will discuss future research strategy, including opportunities for interdisciplinary collaboration in order to integrate NDE more effectively into the engineering life cycle. Keywords. Non-destructive evaluation, NDE, electromagnetic.

Introduction There has been steady growth in non-destructive evaluation (NDE) research since the 1950s, reflecting the increasing demand for greater safety and environmental protection by the public. NDE research has always been particularly challenging. Firstly, the NDE field makes use of multiple technologies & disciplines, including magnetic, electrical, ultrasonic, radiographic, optical, and thermographic methods. Secondly, NDE is used for a wide range of materials (from metals to plastics, ceramics and composites) & applications (manufacturing process control, in-service inspection, defect sizing, corrosion measurement, and degradation monitoring). NDE is used in most sectors of industry: aerospace, power, oil & gas, transportation, infrastructure, built environment, manufacturing, nuclear, process, defence, electronics, packaging, etc., which have vastly different products and assets to be inspected – everything from electronic devices and foodstuffs through to entire rail networks and huge refineries. To enhance the challenge there is a complex supply chain to take new technologies from university research through to routine use, involving research and technology organizations (RTOs), service companies, equipment suppliers, certification and standards authorities, trainers and consultants (Figure 1). However, on the positive side, there is much commonality and overlap at the research stage in terms of techniques and generic applications. Many universities and RTOs have begun to recognize the benefits of an interdisciplinary approach to NDE research. Until the late 1980s much research was funded by government research laboratories and state-owned industries, especially in the nuclear and defence sectors. There were then changes due to privatisation that made a major impact on the funding of NDE research. Although the value of an NDE solution to an individual company or single industry sector may be too small to justify large investment, there are significant opportunities for collaborative funding to increase benefit, share risk and reduce cost.

C.B. Scruby / NDE Research Makes a Difference

Technique development

Service suppliers

Product development

Equipment suppliers

11

Asset owners and operators

Research

Product Manufacturers

Figure 1. The technology supply chain for NDE

Furthermore, generic research may attract government funding through its research councils, while pre-competitive, inter-sectoral, research collaborations lever public funding via for instance EU’s Framework Programmes. There are several key common themes affecting the effective application of NDE, and which are the drivers for research in NDE. The major ones are: coverage, overall inspection speed, quality of information delivered (sensitivity, accuracy, resolution, etc), accessibility of region to be inspected, reliability of the NDE measurement, applicability to a wide range of damage processes, materials and applications, reducing the need for skilled operator intervention (which implies autonomous inspection or monitoring systems), and of course the reduction of costs of the whole NDE process. The UK Research Centre in NDE (RCNDE) has a wide portfolio of NDE research within most of these theme areas.

1. The Research & Innovation Process for NDE The innovation process for NDE is no different from any other area of technology. Strong relationships in the supply chain (Figure 1) aid idea generation. As Figure 2 shows, there is usually some pioneering or opportunistic research before a more substantial research programme is undertaken. This is often followed by trials to evaluate the likely industrial benefits of the research. Depending upon the outcome, this may be followed by further, more applied research and development. If successful the new technology needs to be transferred or “translated” from research into product, a crucial and vulnerable step that will be discussed again. Commercialization, involving development of a market and sales, follows. However, development of the full potential of a product (or service), market penetration and acceptance, tends to be hindered if the technology is not embodied into standards and routine inspection procedures. Note that both scientific “push” and industrial “pull” are needed to drive this process; they need to overlap to ensure successful innovation. For a variety of reasons product development and commercialization sometimes accelerates beyond what can be supported by the market or the scientific foundation. As a result the technology is oversold which may lead to disillusionment. The only way forward is a realistic evaluation of both the underlying science and the proposed market, followed (if the conclusion is positive) by further research, development, optimization of the product to match industrial requirements, and hence through standardization into market acceptance.

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230

Acceptance

Standardisation Commercialisation Product development 100 Further research & development

Trials & evaluation Research Pioneers 1

Technology development

121

-30

Scientific push Industrial pull

Figure 2. Research and innovation process for NDE

Within the defence and aerospace sectors of industry the innovation process is often described in terms of technology readiness levels (TRLs), as shown in Figure 3. Here the inventive phase is described as technology assessment. This may take place in an industrial R&D laboratory or an university. Production implementation is the remit of the end-user company. The challenge is the intermediate steps from 4 to 7; there is a need not only for organizations to undertake work at TRLs 5 and 6, but also to interact effectively with the organizations who carry out TRLs 1-4 on the one hand and TRLs 7-9 on the other. Experience has shown that the most risky part of the process is this translation from research to production. This may be because research and production are carried out by organizations with different objectives and cultures. The NDE industry has a relatively complicated supply chain for new technology (Figure 1) because the technology is used in both production and operation, and operators often sub-contract to service companies. There need to be routes to market for NDE services as well as products. In either case, improved ways are needed to facilitate the movement of new technology from left to right along the chain.

2. Case Studies of NDE Research and Innovation There are many potential examples within the field of electromagnetic NDE, but only a small number can be examined here with a view to understanding the process whereby a research idea is converted into an industrial technology. The examples are selected from the knowledge and experience of the author, and selection or omission is not a value judgment of the product in question. Alternating Current Field Measurement (ACFM) [1] is a current perturbation technique related to, but different from eddy current testing methods. Its development followed closely the pattern described by Figure 2. Thus there was scientific push in the form of university research at University College London (UCL) including

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Proven Method

9. Track record established through successful applications 8. Production system qualified through test and demonstration

7. System prototype demonstration in an operational environment

6. Inspection optimised for capability and speed

Pre-Production

5. Inspection validated in relevant environment (prototype equipment)

4. Inspection validated in laboratory environment

Technology Assessment and Proving

Development

Production Implementation

3. Experimental proof of concept completed 2. Technology concept or application vetted or demonstrated 1. Basic principles observed and reported

Idea

Figure 3. Innovation process described in terms of Technology Readiness Levels

substantial modelling from 1987-9. This was followed in 1991 by application trials on model offshore nodes supported in part by the oil & gas industry, demonstrating growing industrial pull. In 1993 ACFM was licensed to TSC (a small university spinout company), with (1993) a royalty agreement to cover the UCL developments needed to commercialize the technology. 1994-8 saw the development of an applications market, mainly in oil & gas sector. This was supported by applications R&D in both university and company (1996-2000) with strong industrial pull. Standards for ACFM were published in 2003, and from 2004 onwards the focus was growing the application market and moving into the rail and nuclear sectors as the technology gained acceptance. The development was over a shorter period than some other examples, initial research to standard taking some 16 years. This was perhaps partly because the risk was reduced by the existence of an established market for eddy current technology. There was a good combination of scientific push and industrial pull for most of the development phase. But also, significantly, a strong supply chain based on close organizational and individual relationships was established early on. A second example is Pulsed Eddy Currents (PEC). It is based upon pioneering research at Argonne National Laboratory (USA) in 1950 with nuclear applications in mind. It was then picked up by the aerospace industry for detecting cracks in aluminium. In 1987 PEC was adapted by ARCO in their TEMP instrument (a pulsed eddy current device) to detect steel corrosion under insulation (CUI) for the oil and gas industry. In 1990 TEMP was licensed to RTD in Holland, being commercialized as INCOTEST. In 1994 Shell investigated PEC for detecting CUI, but found some shortcomings. However, at the same time, Shell carried out a laboratory investigation of PEC for other industrial applications. This led in 1996 to the launch of a commercial PEC system for a range of oil and gas applications, such as corrosion under fireproofing. There are no standards for PEC at the time of writing. The research from the 1980s onwards mainly took place in companies rather than universities, which ensured a strong industrial pull through most of development of PEC and a good potential market, once the target applications had been identified [2]. Basic research into eddy currents was started at RAE Farnborough (MoD) in collaboration with Surrey University in the 1970s. In the 1980s this moved on to eddy

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current research using Hall sensors, while from 1985-9 industrial pull joined scientific push and a prototype EddyScan system for crack detection in aircraft was developed. The scientific focus then moved to transient eddy currents in the 1990s [3], as further research was undertaken, first on the technique and then (1995-2000) on applications as industrial pull increased. Activity switched to a product and the TRECSCAN system was developed from 2000-3, addressing aircraft inspection needs in the defence and aerospace sectors. Like ACFM and PEC, the development of transient eddy currents was heavily dependent upon background research into electromagnetic induction and eddy currents in particular. Here the early work benefited from collaboration between a government laboratory and a university. There was a requirement to deliver useful research outputs to the MoD customer in the early days of this development, but industrial pull appears to have strengthened progressively. This is consistent with the growing market for methods to prolong the life ageing aircraft. The first three examples build on related research into eddy currents. Apart from isolated pieces of pioneering research in various countries, the next example is of a technology developed from first principles, and it is therefore not surprising that it is still some way from acceptance, even though about 20 years have passed. In 1982-9 some fundamental scientific studies of magnetic methods for materials and stress characterisation were undertaken at Oxford University and Harwell Laboratory [4]. This led on to a programme of research into NDE stress measurement, 1989-93, with progressively stronger industrial pull and support from the oil and gas industry; this led to trial applications of what became known as MAPS in 1993-5. The early applications demonstrated the need for further research into the technique as well as its application (1995-00). It was found necessary to implement further refinements to the underpinning physical model as well as to the MAPS instrument (2000-7), while at the same time beginning to commercialise the technology for niche applications in the oil and gas and rail sectors. The early stages of the development showed the importance of collaboration between university, RTO and end-user industry. Industrial pull waned in the middle period of the development and this, coupled with privatisation and successive company reorganisations, may have delayed the innovation process. The final example is of an important ultrasonic innovation, time-of-flight diffraction (TOFD), rather than another electromagnetic technique. Maurice Silk started research into TOFD [5] at the NDT Centre, Harwell Laboratory (UKAEA) in 1974 using ideas from previous research into neutron time-of-flight spectrometry. During the ensuing years (1974-82) the work was mainly laboratory research (scientific push). Other scientists became involved and the theory of ultrasonic diffraction was developed in 1981-83. The first major industrial application was to UKAEA’s Winfrith Reactor 1982-4. Soon afterwards (1983-4) TOFD used by UKAEA for their nuclear defect detection trials. Almost simultaneously (1984-90) there was further industrial pull when TOFD was developed for offshore and undersea use as an early activity of Harwell’s HOIS project. The first commercialisation came 1982-4 when Zipscan was developed and licensed. Soon afterwards in 1984, TOFD started to be used for major industrial inspections, especially nuclear pressure vessels and offshore structures. The first TOFD standard was published in 1993 and TOFD was soon accepted as a mainstream NDE method across industry. TOFD took about 20 years to move from initial research idea through to an industry standard. It is salutary to wonder how long exploitation would have taken had it not been for strong industrial pull in the mid-1980s from two separate energy sectors. TOFD had little input from the university research base in its early days, reflecting the strength of public sector

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laboratories then, a different situation from the 21st century. Throughout the central period of development there was strong collaboration between researchers, developers and end-users, helped by national imperatives in the nuclear case and a well-established and effective joint industry collaborative project (HOIS) in the other. Another important element was the utilisation of ideas and technology from other fields. A common theme in all of these and similar developments has been the need to develop physical models of the technique under investigation. In many cases using models to perform predictive or interpretive calculations was a major exercise, with more limited computing facilities prior to the 1990s. A model was vital to understand the amplitude variations in TOFD data, as it has been for example to interpret the electrical signals from ACFM, TRECSCAN and PEC techniques. In the case of MAPS, modelling the effects of stress on magnetic parameters from first principles involves very difficult physics as well as computational power. However difficult or timeconsuming, robust physical models are, in the author’s view, vital for any new technology. They are needed, not only to interpret the data and design the best way to use it, but also to give credibility within the scientific and engineering communities.

3. Lessons to be learnt From the author’s experience and knowledge, there are a number of barriers to or brakes that slow down effective NDE research, i.e. research whose results make a positive difference to industrial practice. Two important hurdles are, on the one hand lack of understanding by researchers of industrial needs and culture, and on the other hand lack of understanding by industry of scientific issues and research culture. Research itself, or the development process that follows can be hindered by the wrong level of funding, more commonly too little but occasionally too much at a time when the team is unable to deliver what is anticipated. This leads on to the importance of correctly managing expectations. Often researchers are over-optimistic about what they will achieve and their speed of progress in order to secure funds. When they fail to meet their customer’s expectations the development may be dropped for the wrong reasons. Intellectual property (IP) can cause problems. Sponsors of research may insist on IP rights that are too restrictive and stifle creativity, while loose IP arrangements can dissuade companies from investing in technology. As already stated, a serious issue concerns gaps in the supply chain, i.e. between researchers, developers and end-users. In terms of TRLs, the problems usually arise when progressing from level 4 to level 7. Especially during the past 10 years, members of the NDE supply chain have undergone reorganisations, changes of status, mission and objectives. Staff have been lost, working relationships destroyed and the supply chain disrupted. Finally, human factors always play a part, the biggest hurdles being lack of trust and poor communication for whatever reason. The Engineering Doctorate in NDE is a very encouraging recent development, already proving its worth in terms of technology transfer from research to application. Accountable to both university and company, the student (research engineer) begins to bridge that TRL gap. What lessons can be learnt of the ingredients for successful NDE research? The following list is not exhaustive, nor is every ingredient always necessary: 1. Adequate resources - people, facilities, environment, timely funding 2. Scientific excellence - creativity and lateral thinking balanced against penetration and focus; correct fundamentals essential for robust application

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3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

Technology push balanced against industry pull throughout Interdisciplinary collaboration, networking and international links Import of ideas, results & technology from other fields Industrial pull founded on sound business needs or regulatory imperatives Supportive organisational structures with long-term vision Viable exploitation route along “joined up” technology supply chain Committed individuals to champion and drive innovation process Trust, good communication and shared objectives within the whole “team” Proprietary secrecy balanced against publication and scientific credibility Good timing, grasp of opportunity, achievable timescales

The author is tempted to add: serendipity, since chance events often seem to unlock research and stimulate vital creative leaps; patience, since it is difficult to predict what research will produce and when.

4. Concluding Remarks Before discussing strategy for successful research in NDE, it is important to capture the present trends in the field of NDE. Encouragingly, most recent market surveys have predicted a steady growth in use of NDE by industry. This is driven ultimately by the needs of society for greater assurance of the safety of engineering structures. Linked with this is a heightened awareness of the need for environmental protection. New materials & new designs are being used that require new inspection technology. There is also a move towards greater automation, and the willingness to invest in high technology solutions to reduce inspection costs, improve quality, speed up inspection and sentencing. In some cases the move is towards reducing the need for inspections that interrupt service by new strategies such as structural health monitoring (SHM).

Mathematics Materials characterisation

Physics

Manufacturing & product quality Techniques

Technology & science transfer Mechanical engineering Materials science

NDE Research Applications

Supply chain

Electronic engineering

In-service structural integrity & assessment

Condition & health monitoring

Other disciplines Figure 4. NDE research and linked engineering disciplines

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17

As a long-term strategy there is a desire to integrate NDE more strongly into the engineering life cycle, so that the benefits of NDE are weighed against reductions in the whole life cost of an asset. To do so requires the development of linkages with material science, engineering design, structural integrity and assessment. NDE sits at the centre of a complex network of engineering disciplines as Figure 4 shows; these needs to be understood and exploited. Recent years have seen large changes not only in the large users of NDE technology, but also in the supply chain. Equipment supply and inspection service companies have changed hands, merged and in some cases been bought by large companies. Such changes are likely to continue in the future. Without any doubt the NDE industry will continue to encounter technical challenges that can only be solved by consistent, high quality research. What are likely to be the main elements of a future NDE research strategy? The following list indicates some of the likely priorities: 1. Modelling, always essential for scientific understanding and to give confidence in product quality and for safety-critical applications 2. Improved quantification of results, characterisation and discrimination 3. More advanced data analysis, imaging and visualisation 4. Greater understanding of and improvement to reliability 5. Raising inspection speeds and reducing human factors through automation and autonomous systems 6. Incorporation of technological advances from other fields 7. Addressing new materials, designs, difficult applications & environments 8. Earlier detection of materials & structural degradation & failure 9. Technologies and strategies to facilitate reliable SHM This is a very full and challenging list. It can only be achieved through greater collaboration & integration with other disciplines & fields. It also requires the long term education and training of high calibre engineers for all stages of the research and innovation process. The UK Research Centre in NDE is a university-industry partnership that was established nearly 5 years ago to harness the UK’s research base to meet these longterm challenges, building on and learning from past experience, and hopefully avoiding some of the pitfalls. Its vision is to make a lasting difference to NDE technology through well-planned world-class research, and to invigorate the NDE profession through the provision of highly trained engineers. To conclude, NDE research does make a difference. It is impossible to respond to the challenges of tighter regulation, new materials and applications, new products and plant, more stringent operational conditions, longer life, higher accuracy, reliability, long terms global trends, changes in industry, rising public expectation of safe and environmentally secure operation, and the commercial drivers of faster, better, cheaper products without research.

References [1] [2] [3] [4] [5]

W.D.Dover, R.Collins and D.H.Michael, Phil. Trans. R. Soc. Lond. A320, (1986) 271-283. P.Crouzen, Proceedings of 9th European Conference on NDT, Berlin, (2006) in press S.K.Burke, G.R.Hugo and D.J.Harrison, Review of Progress in Quantitative Non-Destructive Evaluation, 17A, (1998) 307-314 D.J.Buttle, C.B.Scruby, J.P.Jakubovics and G.A.D.Briggs, Proc Roy Soc Lond. A414, (1987) 469 497. M.G.Silk and B.H.Lidington, Harwell Report, AERE-R7774 (1974).

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Electromagnetic Nondestructive Evaluation (XI) A. Tamburrino et al. (Eds.) IOS Press, 2008 © 2008 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-58603-896-0-18

Industrial Applications of 3MA – Micromagnetic Multiparameter Microstructure and Stress Analysis Gerd DOBMANN1, Iris ALTPETER1, Bernd WOLTER1, Rolf KERN1 1 Fraunhofer IZFP, Germany

Abstract. Micromagnetic NDT techniques like the measurement of the magnetic Barkhausen noise, the incremental permeability and the harmonic analysis of the tangential magnetic field allow deriving inspection procedures to online monitoring and control machinery parts and components in production processes in order to characterize mechanical properties like hardness, hardening depth, yield and tensile strength. These types of inspection procedures continuously were further developed in the last two decades so that today the second generation of system hard and software is in industrial use. The application is in steel industry where steel sheets in hot-dip-galvanizing lines were annealed after cold rolling but also in heavy plate rolling mills where after thermo-mechanical rolling special textures and texture gradients can occur. An increasing number of applications are also to find in the machinery building industry and here especially in case of machinery parts of the car supplying industry. Besides mechanical hardness determination the measurement of residual stresses and the detection of inhomogeneities in the surface of machined parts is an inspection task. In different case studies the advantage to implement a micromagnetic NDE technique into the industrial processes is discussed. Keywords. Micromagnetic NDE, hardness, hardening depth, residual stresses, yield strength, steel industry, steel sheets, heavy plates, machinery building, automotive

Introduction The reason to develop 3MA (Micromagnetic-, Multiparameter-, Microstructure-, and stress-Analysis), starting in the late seventies in the German nuclear safety program, was to find microstructure sensitive NDT techniques to characterize the quality of heat treatments, for instance the stress relieve of a weld. George Matzkanin [1] just had published a NTIC report in the USA to the magnetic Barkhausen noise. The technique was sensitive to microstructure changes as well as to load-induced and residual stresses. Therefore a second direction of research started in programs of the European steel industry and the objective was to determine residual stresses in big forgings. Beside the magnetic Barkhausen effect also a magneto-acoustic-one became popular [2]. The technique has based on acoustic emission measurements during a hysteresis cycle and was – because of the high amplification – also sensitive to electric interference noise. Therefore the acoustic Barkhausen noise technique has never found a real industrial

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application. Later further micromagnetic techniques were developed: the incremental permeability measurement, the harmonic analysis of the magnetic tangential field and the measurement of the so-called dynamic or incremental magnetostriction by use of an EMAT [3, 4]. The methodology of the Micromagnetic-, Multiparameter-, Microstructure-, and stress- Analysis (3MA) in detail is described in [4]. On the basis of a multiple regression model, describing target quantities like hardness or yield strength as a function of measured micromagnetic quantities, the unknown model parameters are determined in a calibration step. By using a least squares approach the unknown parameters are the solution of a system of linear equations. 3MA only can be applied at ferromagnetic materials. Here the techniques are especially sensitive to mechanical property determination as the relevant microstructure is governing the material behavior under mechanical loads (strength and toughness) in a similar way as the magnetic behavior under magnetic loads, i.e. during the magnetization in a hysteresis loop. Because of the complexity of microstructures and the superimposed stress sensitivity there was a need to develop the multiple parameter approach. Whereas the first generation of 3MA equipments was basing on the magnetic Barkhausen noise and magnetic tangential field analysis only, 3MA equipment exist now in the forth generation also integrating incremental permeability and eddy current impedance measurements (see Figure 1). More than 100 installations are in use in different industrial areas. This mainly covers the steel and machinery building industries.

Figure 1. TCP-IP-based 3MA equipment and software in combination with a laptop

1. Applications in the steel industry 1.1 Steel Strip Inspection A lot of experiences with 3MA in the last 2 decades were to the continuous mechanical property determination at steel strips, designed to produce car bodies [5, 6], running with a speed of 300m/minute for instance in a continuous galvanizing and annealing line. Yield strength (Rp0.2), tensile strength (Rm), planar and vertical anisotropy parameters (rm, 'r) are in the focus of quality assurance measures [4], all of them are defined by destructive test and cannot be measured continuously. Therefore 3MA correlations were calibrated. Figure 2 shows a yield strength profile along a coil of 2.5 km length [5]. At the beginning and the end an unacceptable increasing of strength is detected higher than

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G. Dobmann et al. / Industrial Applications of 3MA

the upper acceptance level (blue line). The strength values are calculated by the 3MA approach from measured micromagnetic data. The red dots indicate the selection of specimens taken to destructive verification tests after performing NDT. The residual standard errors found by validation are in the range 4-7 % concerning the yield strength. Figure 3 shows a 3MA installation in the line of a strip producer; a robot is used to handle the transducer.

Figure 2. 3MA predicted Yield strength [5]

Figure 3. 3MA probe with robot at a strip line

1.2 Heavy plate Inspection

1600

1600

Elastic limit R p0.2 [MPa] (3MA)

Tensile strength R m [MPa] (3MA)

Ongoing research is to heavy plate inspection. The steel producer asks for the measurement of geometrical and mechanical properties, which have to be uniform along the product length and width, especially in the case of high-value grades used in off-shore application. Destructive tensile and toughness tests are performed by highly qualified and certified personnel according to codes and delivery conditions. The tests cannot be integrated into online closed loop control with direct feedback. To reliably test the mechanical hardness the surface must be carefully prepared by removing scale and decarburized surface layers and residual stresses are to relieve. The extraction of the test pieces and testing is very time and cost extensive. Costs in the range of several thousands Euro per year arise in a middle-sized heavy plate plant only by destruction of the test pieces. 1400 1200 1000 800 600 400 200 0

1400 1200 1000 800 600 400 200 0

0

200

400

600

800 1000 1200 1400 1600

Tensile strength R m [MPa] (destructive)

Figure 4. Tensile strength predicted by 3MA [6]

0

200

400

600

800 1000 1200 1400 1600

Elastic limit or yield strength Rp0.2 or R EH [MPa] (destructive)

Figure 5. Yield strength predicted by 3MA [6]

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In case of a mother plate of several meters length the edges are usually subjected to other cooling conditions than the rest. Indeed, especially the plate ends are known to cool faster, generating an undesired increase in tensile strength Rm and yield strength Rp0.2. State-of-the-art is to cut-off the plate edges with non-conform properties based on empirical values concerning the cut-off length. As the destructive tensile test follows directly after the cut-off process of the edges, only the result of these tests can reveal the selection of a not appropriate cut-off length. This results in high costs due to reworking, pseudo-scrap and delayed shipment release; the European steel producers estimate their annual costs in the range of 11 million Euros. Knowing exactly the contour of the zone with unacceptable material properties would allow an open loop control of the cut-off process. Therefore heavy plate producers will replace the destructive quality inspection of test pieces by a NDT technology [6] applying 3MA (see Figure 4 and 5). By a manufacturer-specific calibration residual standard errors of 10 MPa (Rm), 20 MPa (Rp0.2), and 4HB in the Brinell hardness can be obtained. It should mention here that in the 3MA calibration also other measuring quantities can be integrated so far they provide other independent information, for instance elastic properties. By using ultrasonic waves propagating in thickness direction, i.e. a compressive wave excited by a piezoelectric transducer (index L) and two linearly polarized shear waves (polarized in, index SHR, and transverse, index SHT, to the rolling direction) excited by a EMAT, normalized time-of-flight quantities can be derived describing crystallographic texture effects. Taking into account these quantities (tSHR/tL, tSHT/tL, (tSHR-tSHT)/tL) together with the micromagnetic parameters then a regression result is obtained again reducing the residual standard error.

2. Application in Automotive and Machinery Building Industry 2.1 Car Engine casting To reduce the weight of the power supply unit the car combustion engines cylinder crankcases can be made of cast iron with vermicular graphite (GJV), because this material in a Diesel engine allows a higher loading pressure even by reduced wall thickness. However, the service live of machining tools is during processing an engine block made from GJV substantially smaller compared with a block from cast iron with lamellar (flake) graphite (GJL). work on - relevant range

lamellar graphite

GJL

transition zone

vermicular graphite

GJV

Figure 6. Microstructure gradient obtained in a cylinder region of a cast engine [7]

This disadvantage can be eliminated by an innovative casting technology that produces a continuous microstructure gradient in the cast iron from lamellar graphite at

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the inner surface of the cylinders to vermicular graphite in radial direction. By implementing some chemical additives into the core of the mould which can diffuse in the cast iron during the solidification process in the mould the gradient with a continuous transition from lamellar graphite and finally vermicular graphite is obtained. However, the technology can only be used by the casters so far the gradient quality can be characterized and monitored by NDT. Figure 6 documents in a micrograph such a gradient beginning at the left side with cast iron (inner cylinder surface) and lamellar graphite followed by a transition region and vermicular graphite on the right side. 3MA techniques always cover a certain analysing depth depending on the magnetising frequency and geometrical parameters of the magnetisation yoke, etc. So far the gradient has different graphite compositions within the analysing depth, 3MA quantities should be influenced. Based on measurements at an especially designed calibration test specimen set 3MA quantities were selected to image the gradient with optimal contrast. As reference quantity to calibrate 3MA the local thickness of the GJV-layer was evaluated by using micrographs and optimized pattern recognition algorithms in the microscope. A special designed transducer head was developed to scan the cylinder surface by line scans in hoop direction and rotating the head, then shifting the head in axial direction to perform the next line scan. Figure 7 and Figure 8 show as example the coercivity images derived from the tangential field strength evaluation[3] (HC0 in A/cm) and line scans covering an angle range of 190°.

Figure 7. Coercivity image of a reference block made from GJV

Figure 8. Coercivity image of block with GJV/GJL gradient

Combining different 3MA quantities in a multiple regression the thickness of the GJL layer was predicted. A regression coefficient of R2= 0.93 and a residual standard error of V = 0.06 mm was obtained [7]. 2.2 Wheel Bearing Inspection The fixation of the inner ring of wheel bearings is performed by a wobble riveting process. As a consequence a residual stress is built up in the ring which may not exceed a limit value of about 300 MPa to get a perfect quality. The usual technique to inspect the residual stress state is x-ray diffraction which is destructive in nature because it requires a preparation of the test location. Furthermore it can only be performed statistically. The 3MA technique allows a fast non-destructive estimation of the residual stress level (Figures 9, 10). After a calibration step by using x-ray reference values a 100% quality inspection of these parts is possible. The calibration procedure requires a coincidence of the 3MA and x-ray calibration positions

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because residual stress varies along the circumference. That means the 3MA data have to be recorded in a first step before the x-ray test location is prepared by etching. According to Figure 10 the residual standard error in the calibration is in the 20 MPa range. Besides the residual stress additionally the surface hardness can be measured. 250

Analysing Depth: 100 μm

Residual Stress [MPa] (X-ray)

200

150

100

50

0

Adj.R² = 0.941 1 = 19.0 MPa

-50 -50

0

50

100

150

200

250

Residual Stress [MPa] (3MA)

Figure 9. 3MA-Probe at test location

Figure 10. Residual stress calibration

2.3 Evaluation of Microstructure and Stress Gradients Machined parts in most of the cases have more or less steep gradients in their properties near the surfaces. To improve the lifetime of mechanical highly stressed machinery components the bearing areas are surface-hardened from the μm- up to the millimetre range depending on the requirements and on the hardening technology. 80 70

3MA / Nht 700 [μm]

Adj R² = 0,8211

60 50 40

Adj R² = 0,9151

30 20

3MA Value

10

Nht700 Value

0 0

10

20

30

40

50

60

70

Optical Result [μm]

Fig.11. Comparison of nitrating hardening depth measured by 3MA and Nht 700 (Vickers) versus optical result

Additional surface finishing by grinding can superimpose surface near defects of microstructure and residual stresses which can result in a part breakdown. To inspect the production quality in many cases not only the properties immediately at the surface but also information of the properties below the surface are desired. 3MA is an effective tool to investigate the properties near the surface as well as the range below the surface up to several millimetres in depth. One example of a 3MA application in industry is the determination of nitrating hardening depth NHD of piston rings on the flank side and on the tread surface. Typical values of nitrating hardening depth are between 60 and about 100 μm. It is found by the user that the reproducibility of the non-destructive values of hardness and hardening depth in piston rings is better than the conventional testing by a

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G. Dobmann et al. / Industrial Applications of 3MA

metallographic Vickers hardness test (Nht700), as can be seen in Figure 11 [8]. The reason of that behaviour seems to be the difference in the lateral resolution of the conventional and the non-destructive testing method. Due to a diameter of the 3MA receiver coil of about 2 mm the 3MA values are covering a much larger inspection area. Fast data evaluation by 3MA allows a complete production feedback control. The occurrence of grinding defects, e. g. in gear wheels, is a main problem since many years which is caused by too much heat input during the grinding process. Modern grinding tools allow much higher grinding speed compared to former machines but on the other side this can result in more defects. To get information on the quality of grinded microstructure states the common method in industry is the nital etching technique. Grinding defects are indicated by the discoloration of the surface. This technique is effective as long as the surface information is sufficient to estimate the quality. But it fails if in a preceding production step defects are produced below the surface which are covered in the next production step by a perfect finishing. Several examples of defective gear wheels investigated by hole drilling method and x-ray diffraction have shown that in a depth of 100 μm high tensile stresses up to several 100 MPa can be present whereas at the surface a perfect compressive state of several hundred MPA has been found. These hidden defects cannot be detected by nital etching. As a consequence after some time small cracks are covering the surface due to stressrelieve even without a mechanical load.

Figure 12. Hardness calibration at various depths; hardness values determined by 3MA versus target values

Figure 13. Residual Stress calibration at various depths; RS values determined by 3MA versus X-ray reference values

Since several years IZFP has gained experience in the non-destructive detection and quantitative evaluation of such grinding defect gradients by 3MA in cooperation with industrial partners and in different research and development projects [9, 10]. After a calibration step 3MA can be used to evaluate different target values simultaneously, especially the hardness and the residual stress at the surface and in several depths below the surface (Figures 12 and 13). To get unambiguous results calibration must be done carefully. Calibration is mainly determined by well defined calibration specimens and only valid to the target ranges available by calibration. In most cases calibration is restricted e. g. to the material, to the actual machining parameters and even to the 3MA probe in use. If any variation occurs, its influence on the validation of the existing calibration has to be checked and if necessary a recalibration or extension of the existing calibration has to be performed to include any disturbances. These limitations and the calibration effort may be seen as a disadvantage of 3MA. But if an optimal calibration is developed the fast non-destructive

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determination of various quality parameters which is desired concerning expensive security related parts justifies this effort.

3. Conclusion 3MA is a matured technology and a wide field of applications is given. However, besides the success story we also can find critical remarks from industrial users. These are mainly to the calibration efforts and problems of recalibration if a sensor has to be changed because of damage by wear. Therefore actual emphasis of R&D is to generalize calibration procedures.

4. Acknowledgements The authors very much appreciate to acknowledge the contribution to the result by companies as ThyssenKrupp Stahl AG, Duisburg, ArcelorMittal Research, Metz, Dillinger Hütte GTS AG, Dillingen, Halberg Guss GmbH, Saarbrücken, and Schaeffler KG, Schweinfurt.

References [1]

G.A. Matzkanin, et al., The Barkhausen Effekt and its Application to Nondestructive Evaluation, NTIAC report 79-2 (1979) (Nondestructive Testing Information Analysis Center, San Antonio, Texas) 1-49. [2] W.A. Theiner, E. Waschkies, Method for the non-destructive determination of material states by use of the Barkhausen-effect (in German), Patent DE 2837733C2 (1984). [3] G. Dobmann et al, Barkhausen Noise Measurements and related Measurements in Ferromagnetic Materials; in Volume 1: Topics on Non-destructive Evaluation series (B.B. Djordjevic, H. Dos Reis, editors), Sensing for Materials Characterization, Processing, and Manufacturing (G. Birnbaum, B. Auld , Volume 1 technical editors), The American Society for Non-destructive Testing (1998) ISBN 1-57117067-7. [4] I. Altpeter, et al., Electromagnetic and Micro-Magnetic Non-Destructive Characterization (NDC) for Material Mechanical Property Determination and Prediction in Steel Industry and in Lifetime Extension Strategies of NPP Steel Components, Inverse Problems 18 (2002) 1907-1921. [5] M. Borsutzki, Process-integrated determination of the yield strength and the deep drawability properties rm and 'r on cold-rolled and hot-dip-galvanized steel sheets (in German); Ph.D. thesis, Saar University, Saarbrücken, Germany, 1997. [6] B.Wolter, G. Dobmann, Micromagnetic Testing for Rolled Steel, European Conference on Nondestructive Testing (9) (2006) Th. 3.7.1, 25.-29. 09. 2006, Berlin. [7] M. Abuhamad, I. Altpeter, G. Dobmann, M. Kopp, Non-destructive characterization of cast iron gradient combustion engine cylinder crankcase by electromagnetic techniques (in German), DGZfPAnnual Assembly (2007), Fürth (to be published). [8] IZFP Annual Report, (2004), Saarbrücken, Germany. [9] W. A. Theiner et al., Process Integrated Nondestructive Testing For Evaluation Of Hardness; in the proceedings of the 14th World Conference on Nondestructive Testing (14th WCNDT), (1996) 573, New Delhi, India. [10] B. Wolter et al., Detection and Quantification of Grinding Damage by Using EC and 3MA Techniques, in the proceedings of the 4th International Conference on Barkhausen Noise and Micromagnetic Testing, 03-04 July 2003, Brecia, Italy, 159-170.

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Electromagnetic Nondestructive Evaluation (XI) A. Tamburrino et al. (Eds.) IOS Press, 2008 © 2008 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-58603-896-0-26

3D Nonlinear Finite Element Analysis of Electromagnetic Inspection of Defects in Steel N.Takahashi 1 and Y.Gotoh 2 Abstract. The electromagnetic inspection technology is commonly used to evaluate defects in steel in various power generation plants because of its ability to detect quickly. In this paper, the electromagnetic inspection methods using an ac magnetic field, or a biased ac field are proposed. The behavior of the flux in steel is examined using 3-D FEM that takes into account the initial magnetization curve, hysteresis (minor loop) and eddy currents in order to improve the inspection method. Keywords. Electromagnetic inspection, 3-D nonlinear FEM, hysteresis, magnetization curve, opposite side defect in steel

1. Introduction The electromagnetic inspection method offers the possibility of quick detection of various kinds of defects, such as the outer side defects and plural cracks [1]. Since the permeability of the steel is usually not uniform, the electromagnetic inspection of steel has a magnetic noise. Therefore, a strong magnetic field is used for the inspection of defects in a ferromagnetic material, such as a steel wall of the oil tank or the steel tube etc. [2]. The non-uniformity of permeability in steel is reduced when a magnetic field is increased. Therefore, the ac or dc strong magnetic field is used for the inspection method using dc field and eddy current testing or the magnetic flux leakage testing (MFL) etc. [3,4]. In order to improve these inspection methods, the detailed analysis of 3-D flux and eddy current distribution should be performed. However, a detailed examination of the behavior of flux distribution etc. under the electromagnetic inspection using a strong magnetic field is difficult, because the magnetic property of steel is nonlinear and eddy currents are induced. Although there has been a lot of research in defect detection analysis [5-7], little work has been done in the 3-D analysis when the material is magnetic. In this paper, problems of 3-D finite element analysis in electromagnetic inspection, such as the inclusion of minor loops for the detection under ac and dc excitation, are discussed. The electromagnetic inspection method using a dc magnetic field and a minute alternating magnetic field has been proposed [8]. The behavior of flux in steel is examined using a 3-D finite element method that takes into account hysteresis (minor loop) and eddy currents. It is shown that the detection of a defect is possible by the differential permeability of the minor loop as its position in the BH plane is affected by 1 Norio Takahashi is with Department of Electrical and Electronic Engineering, Graduate School of Natural Science & Technology, Okayama University, 3-1-1 Tsushima, Okayma 700-8530, Japan. (telephone: +8186-251-8115, fax: +81-86-251-8258, e-mail: [email protected]. jp). 2 Yuji Gotoh is with Department of Mechanical and Energy Systems Engineering, Faculty of Engineering, Oita University, 700 Dannoharu, Oita, 870-1192, Japan. (telephone: +81-97-554-7795, fax: +81-97-554-7790, e-mail: [email protected]).

N. Takahashi and Y. Gotoh / 3D Nonlinear Finite Element Analysis of Electromagnetic Inspection

27

the existence of the defect. The flux and eddy current distribution in steel, having plural cracks, are analyzed and it is shown that the detection of plural cracks, when the distance between them is very short, is possible using the differential type two search coils which is set parallel to the steel plate [9]. Steel tubes are used in the heat exchanger in petrochemical plants. Since these steel tubes are grouped in a bundle, it is necessary to inspect the existence of defects from the inside of each tube. Therefore, the possibility of detection of outer side defects in steel tubes using an inner coil in the alternating flux leakage test is examined by analyzing the detailed behavior of flux and eddy current distribution [10]. 2. Evaluation of Detection Method of Opposite Side Defect using DC Field and Minute AC Field Taking Account of Minor Loop 2.1 Model and Method of Analysis Figure 1 shows the model of 1/2 the domain needed to analyze the detection of the opposite side defect in a steel plate. This model is composed of the yokes for dc and a minute ac magnetic field and a search coil. The dc exciting current is 3A and the minute ac exciting current is 0.5A (1kHz). The flux density B in the steel is produced by the dc magnetic field and the minute ac magnetic field. The magnetic field is analyzed using 3-D edge-based hexahedral nonlinear FEM and the step-by-step method taking account of hysteresis (minor loop) and eddy currents in the steel plate. The basic equation of eddy current analysis using the A-Imethod is given by: · § wA Jo  V ¨  gradI ¸ ¹ © wt ­ § wA ·½ div ® V ¨  gradI ¸¾ 0 ¹¿ ¯ © wt

rot (QrotA)

(1) (2)

where A is the magnetic vector potential, I is the scalar potential, v is the reluctivity, Jo is the current density and V is the conductivity. The minor loop is modeled using these upper hysteresis curves (SS400) [1]. It is assumed that the obtained B and H are at the point b (Hmin, Bmin) on the upper loop as shown in Figure 2. If the calculated flux density Bc at the Newton-Raphson (N-R) iteration is larger than Bmin, then Bc should be located at the point d (Hd, Bc) on the lower minor loop. Hd on the lower minor loop is given by the following equation, if the upper loop is symmetrical with respect to the middle point e: Hd

H g  2H e  H g .

(3)

2.2 Behavior of Minor Loop and Inspection of Opposite Side Defect Figure 3 shows the calculated result of a minor loop at a surface point in the steel with and without an opposite side defect. The figure indicates that the dc flux density near the defect in steel is increased when there exists an opposite side defect and a minor loop is generated at the high flux density on an initial magnetization curve. The figure shows that the differential permeability of the minor loop becomes small, when there exists an opposite side defect in the steel. Figure 4 shows the distribution of the differential relative permeability Pd on a minor loop with and without an opposite side defect. Figure 4 (a) shows that the differential relative permeability is increased near the surface of the steel plate when there are no

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N. Takahashi and Y. Gotoh / 3D Nonlinear Finite Element Analysis of Electromagnetic Inspection

22

52.5

.5

.5 16 20

19

dc-yoke dc-exciting coil (3A)

B

2

initial magnetization curve upper minor curve

29

33

steel plate (SS400)

3.35

1.35 7.65

lift-off=0.1 3

x

f (Hf, Bf)

=

=

150 ac-exciting coil (1kHz, 0.5A)

g (Hg, Bg)

=

z y

a (Hmax, Bmax) 2.7 9 1.4 4 ac-yoke search coil 10.18 0.56

4.28

4.7

10 5

=

c (Hc, Bc)

2.95

e (He, Be) d (Hd, B䌣)

Dd=1

opposite side defect

b (Hmin, Bmin) Dw

lower minor curve

0

H

Dw=0.5

Figure1. Inspection model of steel plate with outer side defect (1/2 domain). 2

Figure 2. Explanation of minor loop. ac-yoke

search coil (40turns) differential Pd

1.6

1200

B (T)

with an opposite side defect

1000

1.2

800

without an opposite side defect

600

0.8

400

z

initial B-H curve

200

0.4 0

0

x

0

2000

4000 6000 H (A/m)

8000

steel plate (SS400)

(a) without an opposite side defect

differential Pd 1200

Figure 3. Effect of opposite side defect on minor loop (calculated).

1000 800 600 400 200 0

opposite side defect

(b) with an opposite side defect Figure 4. Distribution of the differential relative permeability Pd on a minor loop in the steel plate with and without an opposite side defect (dc=3A, ac=1kHz, 0.5A).

defects. However, the permeability between the opposite side defect and the surface of the steel is reduced as shown in Figure 4 (b). Since the dc flux is distributed near the surface of the steel plate, the minute ac flux density dose not penetrate as far as the opposite side defect. During the inspection, the dc and ac yokes are moved along the x-direction by 1mm pitch, keeping the lift-off at 0.1mm. Figure 5 shows the measured inspection result of the change of ac flux density 'B detected by the search coil due to the outer side defect. 'B is defined by  'B=|B| (at defect position)-|B| (at no defect position, x=10mm)

(4)

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N. Takahashi and Y. Gotoh / 3D Nonlinear Finite Element Analysis of Electromagnetic Inspection

'B in the search coil is calculated by 3-D non-linear FEM taking account of hysteresis (minor loop) and eddy current. After 35 steps (about 2 periods), almost steady state result can be obtained. The figure shows that the measured and calculated peak values of 'B are almost in good agreement. Moreover, 'B is decreased near the position of the opposite side defect. This is due to the fact that the dc flux density near the position of the opposite side defect in steel plate is increased and as a result, the permeability of the steel is decreased. The figure suggests that it is possible to detect the opposite side defect in a steel plate by using the proposed inspection method. measured

0

'B (x10-4T)

calculated -20

-40

Dd=1

-60 -10 -7.5 -5 -2.5

0

2.5

5 7.5 10 position x (mm) opposite side defect

Dw=0.5

Figure 5. Change of flux density 'B when there exists an opposite side defect (dc=3A, ac=1kHz, 0.5A).

3. Alternating Magnetic Flux Leakage Testing for Detection of Plural Cracks 3.1 Inspection Method and Modeling Figure 6 (a) shows a model of the alternating magnetic flux leakage test that detects plural cracks. The amplitude of the current is 1A(rms). The gap between the leg of the yoke and the surface of the steel is 0.2mm. Figure 6 (b) shows the proposed differential type search coils for detecting the parallel component Bx of leakage flux from plural cracks. The leakage flux Bx which is uniformly distributed over the steel surface is measured using the search coil E. The local leakage flux Bx from the cracks is measured using the search coil D. The difference between Bx obtained by the search coil D and that by the search coil E is used for detecting the number and the size of plural cracks. The sizes of these coils were optimized using the evolution strategy. The search coils (thickness < 0.1mm) can be located under the legs of the yoke. The frequency is chosen as 1kHz, resulting in a skin depth of 0.15mm (the relative permeability is assumed to be 2500).

yoke Yoke

z

Plate

Distance L:0.5mm y

29

E

w=S

16.5

Sw -

3

52

2

29

Steel plate steel plate (SS400)

22 .5

19

2

52.552.5

19

56.5

exciting Exciting coilcoil

10 5

D

Bx search coil E

SlSl-E=59 =59

  0.1

0.06

x

150

search coils Search coil y

z

Crack (Width Cw:: 0.01mm)

Depth Cd:1mm :1mm

Bx search coil D

Position of search coil D (D)

x

(a) bird’s eye view (1/2 region) (b) search coils for detecting plural cracks Figure 6. Model for alternating flux leakage testing of plural cracks.

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N. Takahashi and Y. Gotoh / 3D Nonlinear Finite Element Analysis of Electromagnetic Inspection

Cd=1

Bx [x10-4 T]

100 80

Cd=0.5

60

Cd=0.1

40 20 0 -20 -1.5

No-crack -1

-0.5

0

L=0.5

Figure 7. Detection of Bx using differential search coil (Cw=0.01mm, Cd=1mm, L=0.5mm, 1kHz, 1A, calculated, with hysteresis).

0.5

1 1.5 Position [mm]

Crack position (Cw=0.01)

Figure 8. Effect of depth of cracks on Bx (1kHz, 1A, calculated, with hysteresis)

3-D FEM using the 1st order hexahedral edge element is applied. The flux and eddy current are analyzed by the step-by-step method taking account of the non-linearity of the steel plate. In order to obtain the steady state result, the calculation is carried out for 2.5 periods (=160 steps). The time interval Ǎt of the step-by-step method is chosen as 1.5625x10-5 sec. 3.2 Detection of Plural Cracks using Horizontal Coils The detection characteristics are analyzed by a nonlinear calculation using the hysteresis curves. Figure 7 shows the distribution of Bx of one, two and four cracks detected using the differential type coil. The figure illustrates that it is possible to evaluate plural cracks by using the amplitude of the parallel component Bx of leakage flux detected by the differential search coil. Figure 8 shows the effect of the depth of the cracks when there are two cracks. The figure shows that the amplitude of Bx is increased as the crack depth grows. 4. Electromagnetic Inspection Method of Outer Side Defects on Steel Tubes using an Inner Coil 4.1 Inspection Model and Conditions Figure 9 shows the inspection model of the outer side defect of a steel tube (SUS430). The proposed inner inspection probe is also shown in the figure. The inspection probe is composed of a yoke, an exciting coil and a search coil for detecting the perpendicular component |Bx| of leakage flux due to the outer side defect. The outer side defect is a circumferential one. The frequency is chosen as 60Hz (commercial frequency) resulting in a skin depth equal to 2.31mm (maximum relative permeability (=434) in the steel tube is used for the calculation of the skin depth). The exciting current is 5A(rms). The conditions of analysis and experiment are as shown in Table 1. 4.2 Outer Side Defect in a Steel Tube Figure 10 shows the distribution of calculated and measured |Bx| in a search coil. |Bx| is obtained by moving the inspection probe in the z-direction inside the steel tube at the

N. Takahashi and Y. Gotoh / 3D Nonlinear Finite Element Analysis of Electromagnetic Inspection

Table 1. Condition of analysis and experiment 202 turns, 60Hz, 5A (rms) 50 turns, Width (Sw)=3mm, Height (Sh)=1.65mm, Length (Sl)=2.56mm, Lift-off (Lo)=0.2mm SUS430, V=1.82x106 S/m, Diameter=25I, Thickness (t)=1.5mm, Pr-max=434 SS400, V=7.51x106 S/m, Maximum relative permeability Pr=3000 Width (Dw)=2mm, Depth (Dd) =0.5mm, Circumference defect 88095, 83232 N-R method: 1.0x10-3 T, ICCG method: 1.0x10-5

Exciting coil Search coil Steel tube Yoke Outer side defect Nodes and elements Convergence criterion

5

steel tube (SUS430, 25㱢) exciting coil (202turns)

70 60

-4

search coil (Bx)

Bx [x10

Sw=3

80 59.6

50turns

me asured 40 30 20

4.5 Sl=2

20.4

calculated

50 T]

10.5

31

.56 S

5 1.6 h=

yoke (SS400)

10 0 -10

-5

0

z t=1.5

y

x D w=2

Figure 9. Inspection model for outer side defect of steel tube (1/4 domain).

5

10 position z [ mm]

position of outer side defect

Figure 10. Inspection waveform of leakage flux (60Hz,5A).

lift-off of 0.2mm. The calculated result is in agreement with measurement. The figure illustrates that the outer side defect in the steel tube can be detected using the proposed inspection method. 4.3 Application to the Steel Tube with Aluminum Cooling Fin In a petrochemical plant, the steel tube is sometimes used with aluminum cooling fins. Therefore, the possibility of applying the proposed inspection method for detecting the outer side defects on a steel tube with cooling fin is examined. Figure 11 shows the inspection model of the steel tube (SUS430) with aluminum cooling fin. The outer side defect width (Dw), defect depth (Dd) and defect length (circumference direction, Dl) are 0.5mm, 0.5mm and 10mm, respectively. The nonlinear analysis was carried out. The non-uniformity of permeability and conductivity in steel is neglected. The conductivity V of the aluminum fin is 3.5x107 S/m. Figure 12 shows the eddy current distributions in the steel tube with and without fin. The figure shows that the eddy current density is maximum at the inner boundary of the fin with high conductivity. The maximum flux density |B|max in the steel tube with fin is 1.68T and |B|max without the fin is 1.51 T. The flux density in the steel tube is increased when the fin is put on the tube because of the opposing flux due to the eddy currents. Figure 13 shows the average flux density |Bx| in a search coil calculated along the zposition inside the steel tube with and without the fin. The results under the dc excitation are also shown. The figure shows that the leakage flux from the steel tube with the fin is larger than that without the fin under ac excitation. The leakage flux is increased due to the larger than that without the fin under an ac excitation. The leakage

32

N. Takahashi and Y. Gotoh / 3D Nonlinear Finite Element Analysis of Electromagnetic Inspection steel tube (SUS430, 25㱢)

1 .5

2.5

2 2

search coil (Bx)

tube fin

yoke fin of aluminum

exciting coil

exciting coil (202turns) yoke (SS400)

outer side defect Dw=0.5, Dd=0.5, Dl=10

z y

x

27.5

Figure11. Inspection model of the steel tube with the aluminum fin. eddy current [x105 A/m2] 14 12 10 8 6 outer side defect

4 2

z

0

x

steel tube (SUS430)

1.5 2.5

fin of aluminum

(a) without fin  (b) with fin Figure 12. Distribution of eddy current density in steel tube with the aluminum fin (60Hz,5A, Dw=0.5mm, Dd=0.5mm). with fin (60Hz) 30

without fin (60Hz)

15

with fin

20 10

with fin and without fin (DC) : with fin : without fin

5

0 -8

-6

-4

-2

0

2

10

without fin

4 6 8 position z [mm]

position of the fin of aluminum position of outer side crack (Dw=0.5, Dd=0.5, Dl=10) 2

Bx [x10-4 T]

Bx [x10-4 T]

20

0 0

20

40

60 80 100 120 140 160 180 200 exciting frequency [Hz]

2

Figure 13. Effect of aluminum fin and alternating magnetization (5A, Cw=0.5mm, Cd=0.5mm, calculated).

Figure 14. Effect of exciting frequency (5A, calculated).

N. Takahashi and Y. Gotoh / 3D Nonlinear Finite Element Analysis of Electromagnetic Inspection

33

increased due to the eddy current in the steel tube and the fin. The ac excitation at 60Hz is appropriate from the viewpoint of the amplitude of the output signal as compared with the dc excitation. Figure 14 shows the maximum flux density in a search coil calculated by changing the exciting frequency in a model with and without fin when the exciting current is 5A (rms). As seen in the figure, the exciting frequency that is suitable for the inspection is around 20Hz – 60Hz. 5. Conclusions The results obtained are summarized as follows: (1) The principle of the inspection method of opposite side defects with ac and dc excitations is clarified by analyzing the magnetic property of the material. When the large dc magnetic field is impressed on a steel plate with the opposite side defect, the dc flux in steel bypasses the defect because of the magnetic saturation. As a result, the flux density between the opposite side defect and the surface of the steel is increased. The differential permeability of the minor loop due to the minute ac magnetic field is therefore decreased. This phenomenon can be used for the inspection of opposite side defects. (2) It is possible to evaluate plural cracks by using the amplitude of the parallel component Bx of the leakage flux detected by the differential search coil. (3) The alternating flux leakage test method using an inner coil at commercial frequency is able to detect the outer side defect in steel tubes with or without aluminum cooling fin. The ac excitation is more suitable than the dc excitation. References [1] Y.Sun, “An introduction to electromagnetic nondestructive testing”, Applied Electromagnetics and Mechanics, vol.13, pp.145-152 (1998). [2]N.Kasai㧘K.Sekine, and H.Maruyama, “Non-destructive evaluation method for far-side corrosion type flaws in oil storage tank bottom floors using the magnetic flux leakage technique", J. Jpn. Petrol. Inst., vol.46, no.2, pp.126-132 (2003). [3] H.Fujiwara, T.Sakamoto, T.Nishimine, and K.Kokubo, “Development of ac magnetic leakage flux testing system”, Proc. Int. Symp. Applied Electromagnetics and Mechanics, pp.527-528 (2001). [4] S.Nishino, “Development of magnetizing eddy current pipeline inspection tools”, The First US-Japan Symposium on Advances in NDT, pp.254-258 (1996). [5] G.Chen, T.Sugibayashi, M.Shiwa, and H.Yoneyama, “Investigation of subsurface flaw detectability of magnetic flux leakage testing”, Proc. Int. Symp. Applied Electromagnetics and Mechanics, pp.525-526 (2001). [6] K.Sekine, Y.Zhang, A.lizuka, and K.Nonaka, ”A Theoretical analysis of magnetic force acting on magnetic particles in the Immediate vicinity of surface flaws”, The First US-Japan Symposium on Advances in NDT, pp.396-401 (1996). [7] M.Katoh, K.Nishio, T.Yamaguchi, and S.Mukae, “FEM study on magnetic test of square bar by direct contact method”, Proc. FENDT ’94 and ROCSNT 9th Annu. Conf., pp.79-85 (1994). [8] Y.Gotoh and N.Takahashi, “Evaluation of detecting method with AC and DC excitations of opposite side defect in steel using 3D non-linear FEM taking account of minor loop ”, IEEE Trans. Magn., vol.44 (2008). [9] Y.Gotoh and N.Takahashi, “Detection of plural cracks in steel using horizontal coils – 3D FEM analysis considering hysteresis and non-uniformity of steel –”, IEEJ Trans. FM, vol.125, no.10, pp.835-840 (2005). [10] Y.Gotoh and N.Takahashi, “3D FEM analysis of electromagnetic inspection of outer side defects on steel tube using inner coil”, IEEE Trans. Magn., vol.43, no.4, pp.1733-1736 (2007).

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Magnetic Materials

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Electromagnetic Nondestructive Evaluation (XI) A. Tamburrino et al. (Eds.) IOS Press, 2008 © 2008 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-58603-896-0-37

37

Evaluation of Irradiation Embrittlement in Fe-Cu-Ni-Mn Model Alloys by Measurements of Magnetic Minor Hysteresis Loops Satoru KOBAYASHI a,1 , Hiroaki KIKUCHI a , Seiki TAKAHASHI a , Katsuyuki ARA a and Yasuhiro KAMADA a a NDE and Science Research Center, Faculty of Engineering, Iwate University, 4-3-5 Ueda, Morioka 020-8551, Japan Abstract. Magnetic minor hysteresis loops of neutron-irradiated Fe-Cu-Ni-Mn model alloys varying Cu and Ni contents have been measured. For almost alloys minor-loop coefficients which are in proportion to internal stress decrease after neutron irradiation to a maximum fluence of 0.44 × 1019 n cm−2 . The decrease of the coefficients is strongly enhanced for alloys with high Cu and high Ni contents. Both magnetic and mechanical properties are correlated with each other and the coefficients are roughly in inverse proportion to yield strength. Keywords. Neutron irradiation, Magnetic minor hysteresis loops, precipitates

Introduction Neutron irradiation induces microstructural changes associated with an increase in a number density of nanoscale defects including vacancies, dislocation loops and precipitates, and makes materials brittle and more susceptible to fracture [1]. Currently, the irradiation embrittlement of pressure vessels in nuclear reactors is evaluated by ductilebrittle transition temperature (DBTT) obtained in Charpy impact tests. However, the stock of Charpy specimens preinstalled in the reactors is diminishing and nondestructive evaluation of the irradiation embrittlement has become an urgent matter of study. Recently, we measured magnetic minor hysteresis loops of some neutron irradiated Fe-Cu-Ni-Mn model alloys with high Ni content to investigate the influence of neutron irradiation on magnetic properties [2]. It was found that minor-loop coefficients which are obtained from power-law relations between minor-loop parameters and are sensitive to internal stress [3], decrease with fluence. This shows the reduction of internal stress during neutron irradiation and was explained as being due to a compensation of internal stress of dislocations by Cu precipitates grown around the dislocations. Nevertheless, dependence of elemental content on the coefficients as well as their relation with mechan1 Corresponding Author: Satoru Kobayashi, NDE and Science Research Center, Iwate University, 4-3-5 Ueda, Morioka 020-8551, Japan, E-mail: [email protected] .

38

S. Kobayashi et al. / Evaluation of Irradiation Embrittlement in Fe-Cu-Ni-Mn Model Alloys

Table 1. Chemical compositions of measuring samples. (wt %) Sample

Cu

Ni

Mn

OV4

0.05

0.8

1.6

OV5

0.05

1.6

1.6

OV6 OV7

0.1 0.1

0.8 1.6

1.6 1.6

OV8

0.05

1.6

1.6

OV17

0.2

1.6

1.6

P

Si

0.025

0.5

Table 2. Neutron irradiation conditions in this study. Fluence Φt (1019 n cm−2 )

Effective fluence Φteff (1019 n cm−2 )

Flux φ (1012 n cm−2 s−1 )

Flux regime

T29

0.89

high

0.44

0.44

T30

0.07

low

0.02

0.07

T31 T32

0.72 0.26

high intermediate

0.06 0.02

0.07 0.04

ical properties were not investigated in detail. In this paper, we study the influence of Cu and Ni contents on minor hysteresis loops in neutron-irradiated Fe-Cu-Ni-Mn model alloys.

1. Experimental Neutron-irradiated tensile test samples with dimensions of 24 × 5 × 0.5 mm 3 were prepared by Odette group of University of California Santa Barbara (UCSB). Fe-Cu-NiMn model (OV) alloys with variable combinations of Cu and Ni contents listed in Table 1 were neutron irradiated at 290 ◦ C. We examined four irradiation conditions with fluence Φt up to 0.44 × 10 19 n cm−2 and with neutron flux φ in the range 0.07-0.89 × 10 12 n cm−2 s−1 as listed in Table 2. A set of magnetic minor hysteresis loops with various field amplitudes H a was measured at room temperature using a closed magnetic circuit with a sample sandwiched between two magnetic yokes. A cyclic magnetic field with a frequency of 1 Hz and H a up to 6 kA/m was applied along the long axis of the sample. Our analysis showed that there exist several power-law relations between minor-loop parameters in a limited range of Ha in which irreversible movement of Bloch wall mainly contributes to magnetization [3]. From the relations, minor-loop coefficients in proportion to internal stress were determined. In this study, we paid attention to the minor-loop coefficient W F0 , obtained from the power-law relation, given by  ∗ nF Ma ∗ 0 WF = WF , (1) Ms where Ma∗ and WF∗ are magnetization and hysteresis loss of a minor hysteresis loop and Ms are saturation magnetization [3]. From least-squares fits of W F∗ − Ma∗ curves to equation (1), the exponent of n F = 1.70 ± 0.03, which is independent of chemical compositions and neutron fluence, as well as W F0 were determined. Here, minor loops

S. Kobayashi et al. / Evaluation of Irradiation Embrittlement in Fe-Cu-Ni-Mn Model Alloys

39

with μ0 Ma∗ = 0.3−1.3 T were used for the fits. The obtained coefficient was typically averaged over 2 - 3 samples for each alloy-irradiation condition and an experimental error of WF0 mainly results from the sample dependence. To compare W F0 obtained with various neutron fluxes, an effective neutron fluence t Φeff , given by Φ teff = Φt (φr /φ)1/2 , was introduced [2,4]. Here, φ r is a reference flux and φr = 0.89 × 10 12 n cm−2 s−1 was assumed. This equation was originally proposed to normalize a flux-dependent change of yield strength [4] and is also useful for magnetic properties; on the Φ teff scale, all minor-loop coefficients obtained for various neutron fluxes fall in the same smooth curve, although lower flux tends to shift the coefficients to lower Φt [2].

2. Results and Discussion Figure 1 shows WF0 as a function of Φ teff . For all OV samples, the behaviour of W F0 seems to be classified into two groups. One is a behaviour seen for OV6 and OV7 that W F0 increases at low fluence, shows a maximum around Φ teff = 0.05 × 10 19 n cm−2 , and then gradually decreases with fluence. The other is a behaviour that W F0 shows a monotonic decrease with fluence (OV5, OV8, OV17) or is almost constant against fluence (OV4). For OV5, OV7, and OV17, both Ni and Mn contents are 1.6 wt% and only the Cu content is different from each other. The decrease of W F0 after irradiation to Φ teff = 0.44 × 10 19 n cm−2 is proportional to Cu content and is most pronounced for OV17 with 0.2 wt% Cu.

Figure 1. WF0 as a function of effective neutron fluence.

On the other hand, a behaviour of W F0 is also influenced by Ni content. For OV4 and OV6 with 0.8 wt% Ni, W F0 is weakly dependent on fluence and the decrease after

40

S. Kobayashi et al. / Evaluation of Irradiation Embrittlement in Fe-Cu-Ni-Mn Model Alloys

irradiation is largely reduced compared with that for OV5 and OV7 with 1.6 wt% Ni, respectively. There observations clearly show that the higher level of Cu and Ni inclusion enhances the decrease of internal stress during neutron irradiation. Note that Si inclusion also seems to enhance a decrease in W F0 after irradiation when data for OV5 and OV8 are compared. The effects of Si inclusion on minor-loop properties are subjects for further study. We now examine a relation of W F0 to yield strength σy obtained by tensile tests performed by UCSB group. Figure 2 shows relations between W F0 and a change in yield strength Δσy for all fluences. Since Δσ y generally increases with fluence, higher Δσ y corresponds to that for higher Φ teff . For all OV samples, WF0 is almost constant or linearly decreases against Δσy . Moreover, the higher Cu and Ni contents the larger a change both in WF0 and Δσy . This correlation implies that a decrease in W F0 originates from the same irradiation mechanism as that for the increase of yield strength.

Figure 2. Relation between WF0 and Δσy at all measuring fluences.

For all materials, neutron irradiation induces changes in mechanical properties. These changes are primarily due to the formation of irradiation defects such as Cu rich and Cu-Mn-Ni precipitates [5]. Since these defects act as obstacles to the movement of Bloch wall, minor-loop coefficients will increase with fluence and Cu and Ni contents. However, WF0 rather decreases with fluence, whereas for some OV samples a peak appears at low fluence. This implies the presence of two irradiation mechanisms that affect magnetic properties; the first mechanism is due to the formation of irradiation defects in the matrix and contributes to an increase in minor-loop coefficients and the other is a mechanism that contributes to their decrease. One of possible mechanism to explain such decrease is the preferential formation of Cu rich and/or Cu-Mn-Ni precipitates on dislocations [6,7]; precipitates are preferentially formed on dislocations to minimize the elastic energy and reduces the internal stress around the dislocations. With increasing Cu and Ni contents, the volume fraction of precipitates also increases [5]. This would enhance the precipitation around the dislocations, resulting in a large decrease of W F0

S. Kobayashi et al. / Evaluation of Irradiation Embrittlement in Fe-Cu-Ni-Mn Model Alloys

41

for OV17 with high Cu and high Ni contents. This enhanced precipitation, on the other hand, makes the material mechanically harder [1], which is reason why W F0 is inversely proportional to Δσ y . In conclusion, we have shown that the minor-loop coefficient is roughly in inverse proportion to yield strength, which is an important mechanical property related with irradiation embrittlement. This result clearly shows that magnetic method using minor hysteresis loops is useful for nondestructive evaluation of irradiation damage in nuclear reactor pressure vessels.

Acknowledgements This research project has been conducted under the research contract with the Japan Nuclear Safety Organization (JNES). We thank Prof. G. R. Odette of UCSB for allowing us to measure neutron irradiated samples.

References [1] [2] [3] [4] [5] [6] [7]

G. R. Odette, G. E. Lucas, Radiat. Eff. Def. Solids 144 (1998) 189. S. Kobayashi, H. Kikuchi, S. Takahashi, K. Ara, Y. Kamada, Studies in Applied Electromagnetic and Mechanics 28 (2007) 217. S. Takahashi, S. Kobayashi, H. Kikuchi, Y. Kamada, J. Appl. Phys. 100 (2006) 113908. G. R. Odette, T. Yamamoto, D. Klingensmith, Philos. Mag. 85 (2005) 779. S. C. Glade, B. D. Wirth, G. R. Odette, P. Asoka-Kumar, J. Nucl. Mater. 351 (2006) 197. S. Takahashi, H. Kikuchi, K. Ara, N. Ebine, Y. Kamada, S. Kobayashi, M. Suzuki, J. Appl. Phys. 100 (2006) 023902. M. K. Miller, K. F. Russell, M. A. Sokolov, R. K. Nanstad, J. Nucl. Mater. 361 (2007) 248.

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Electromagnetic Nondestructive Evaluation (XI) A. Tamburrino et al. (Eds.) IOS Press, 2008 © 2008 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-58603-896-0-42

Analysis of Barkhausen Noise Characteristics and Mechanical Properties on Cold Rolled Low Carbon Steel Hiroaki KIKUCHI a,1, Tomoki KOSHIKA a , Tong LIU a , Yasuhiro KAMADA a, Katsuyuki ARA a, Satoru KOBAYASHI a and Seiki TAKAHASHI a a NDE & SRC, Faculty of Engineering, Iwate University, 4-3-5 Ueda, Morioka, Iwate, 020-8551, Japan

Abstract. Low carbon steel specimens cold rolled at ratios of 0 - 40 % have been examined comprehensively by magnetic Barkhausen noise (MBN) method, and their microstructure were studied by transmission electron microscope. In order to correlate MBN parameters with those mechanical properties, Vickers hardness and ductile-brittleness transition temperature (DBTT) were also evaluated. MBN energy and rms voltage rise rapidly with cold rolling below 10 %, and saturate at higher rolling ratio. This phenomenon is attributed to the combined effects of cell texture and dislocation density. It is also found that good correlation between MBN parameters and Vickers hardness, DBTT. Keywords. Barkhausen noise, Microstructure, Vickers hardness, DBTT

1. Introduction Magnetic Barkhausen noise (MBN) has been widely used to study the ferromagnetic materials nondestructively and there have been investigations of MBN changes under various conditions including fatigue, irradiation, stress and so on [1-3]. It has been proved to be sensitive to grain size, composition, hardness and so on [4, 5]. Therefore, this method is becoming a potential tool for many nondestructive evaluation (NDE) applications. However, the effect of microstructure changes induced from cold rolling on MBN has been rarely investigated. Though Atherton’s group has studied MBN properties in cold rolled nuclear vessel steel [6], their specimens possessed an easy axis in the unrolled state as a result of crystallographic texture, which made the exclusive study of rolling texture by MBN method very difficult. For practical uses, it is important to investigate that effect and a relation between MBN parameters and mechanical properties. In this work, low carbon steel plates with negligible crystallographic texture before deformation by cold rolling were investigated to understand the origin of MBN dependence on rolling texture, and to correlate those MBN parameters with those mechanical properties.  1 Corresponding Author: Hiroaki Kikuchi, NDE & Science Research Center, Faculty of Engineering, Iwate University, 4-3-5 Ueda, Morioka 020-8551, Japan; Phone:+81-19-621-6350; Email: [email protected]

H. Kikuchi et al. / Analysis of Barkhausen Noise Characteristics and Mechanical Properties

2. Experimental Procedure

43

Excitation coil

Low carbon steel (S15C) plates were prepared and then annealed at 1173 K for one hour, followed by air-cooling. Then, 50 mm 40 mm 13 mm Fi-Si those steels were deformed by cold rolling 60 mm with different reduction ratios of 0, 5, 10, Fig. 1 Schematic view and dimensions of yoke 20 and 40 %. The steel contains 0.15– probe. 0.20wt.%C, 0.15–0.35wt.%Si, 0.30– 0.60wt.%Mn and Fe in balance. For MBN measurement, five kinds of specimens were ground into the same dimension 40 × 60 × 10 mm3. In order to evaluate ductile-brittleness transition temperature (DBTT) Charpy impact test pieces, 10 × 10 × 55 mm3, were machined from each plate along the rolling direction. Disk specimens were Fig. 2 MBN measurement setup. also prepared to evaluate microstructures by Philips-tecnai 30 transmission electron microscope (TEM). The plate specimens were magnetized parallel to the rolling direction by a triangle wave of 1 Hz using a yoke probe. The yoke probe was composed of a U-type Fe-Si yoke and an excitation coil as shown in Fig. 1. MBN signals were detected by a MBN sensor, i.e., an air-core coil with 305 turns and 10 mmI, attached on the surface of specimens. The measurement system is illustrated in Fig. 2. The original MBN signals were amplified (60 dB), filtered (10-100 kHz), and finally sampled at 380 kHz. The MBN results of each sample were measured 10 times and averaged. The MBN parameters dependencies on the cold rolling ratio were studied in terms of MBN energy and rms voltage. MBN energy, EMBN, and rms voltage, Vrms are defined as follows.

EMBN

T

2

³0 VMBN dt

(1)

1 T 2 (2) ³ VMBN dt T 0 where VMBN is original MBN signal and T is half period of excitation field. The absorption energy of the Charpy impact test pieces was obtained by using the Charpy test machine at temperatures between 200 and 360 K. The ductile-brittleness transition temperature (DBTT) was estimated from the absorption energy temperature dependence of the Charpy impact test pieces [7]. The Vickers hardness of the specimens was also measured using a Vickers hardness meter with a load of 500 g. Vrms

3. Results and Discussion Fig. 3 shows typical time dependent of MBN signals and the excitation current applied to the yoke probe for 0% and 40 % reduction ratio specimens. From these profiles, MBN energy and rms voltage was calculated using equations (1) and (2). MBN parameters were plotted as a function of reduction ratio in Fig. 4. They rise rapidly in

H. Kikuchi et al. / Analysis of Barkhausen Noise Characteristics and Mechanical Properties

MBN energy EMBN (mV2)

480

32 MBN energy rms voltage

400

28

320

24

240

20

160

16

80

rms voltage Vrms (mV)

44

12 0

10

20

30

40

50

Reduction ratio (%)

(a) 0 % reduction ratio

Fig. 4 The relation between MBN energy, rms voltage and reduction rate.

the beginning with reduction ratio below 10%, and then slightly increase above 10% cold rolling. In Artherton’s work [6], cold rolling brought about the increase of MBN parameters. The authors attributed these phenomena to crystalline anisotropy before rolling. In our work, on the other hand, Xray analysis revealed that the crystalline anisotropy is not observable before rolling (b) 40 % reduction ratio and the surface residual stress effect is also Fig. 3 typical time dependent of MBN signal and negligible after a surface grinding process. excitation current applied to yoke probe. Fig. 5 shows the micrograph of TEM observation. One can see that dislocations are distributed homogeneously for 0% cold rolling and a large amount of dislocations are generated with the increase of reduction ratio. A cell substructure also comes into being gradually during this rolling process and aligns with the direction parallel to the rolling direction. The formation of rolling texture <110> was observed by X-ray analysis. The dislocation density Uestimated by the Ham method [8] is 5 × 109 cm-2, 2 × 1010 cm-2, and 6 – 10 × 1010 cm-2 for 0%, 5%, and 10% reduction ratio, respectively; for higher reduction, is not shown because of the formation of cell structures, which makes it difficult to estimate a reliable value of U. It is proposed that the increase of MBN parameters is attributed to the combined effects of cell structure and dislocation density. TEM observation reveals that dislocations tend to aggregate at the boundary of cell structure during the cold rolling, and the dislocation density inside the cell texture is relatively low so that the domain wall can come across. Consequently, increases in dislocation density with cold rolling lead to sensitive increases in the domain wall gradient at pinning site, resulting in a larger MBN response up to 10 % reduction ratio. On the other hand, above 10 % increases in dislocation density becomes not significantly, whereas a higher rolling ratio induces a large number of smaller cell structures, namely the boundary area increases, which results in low MBN signal. Therefore, the total MBN response tends to saturate at high reduction ratio. This MBN analysis method shows a potential application in evaluating microstructure changes nondestructively in cold rolled steel. The relations between MBN parameters and mechanical properties, DBTT and Vickers hardness, are shown in Fig. 6. DBTT and Vickers hardness increases as reduction ratio increases due to work hardening. MBN parameters rise rapidly with increasing mechanical parameters below 10 % reduction ratio, and then they increase

45

H. Kikuchi et al. / Analysis of Barkhausen Noise Characteristics and Mechanical Properties

(a) 0 % (b) 5 % (c) 10 % Fig. 5 TEM micrographs showing dislocations in S15C steel.

24

300

22

260

20

220

18

180

16

140 130

140

150 160

170

180 190 200

Vickers hardness (Hv)

MBN energy EMBN (mV2)

340

26

380 340



24

300

22

260

20

220

18

180

16

140 245

14 210

MBN Energy rms voltage

250

255 260

265

270 275

280

rms voltage Vrms (mV)

26 MBN Energy rms voltage

rms voltage Vrms (mV)

MBN energy EMBN (mV2)

380

(d) 40 %

14 285

DBTT (K)

(a) MBN parameters vs. Vickers hardness (b) MBN parameters vs. DBTT Fig. 6 The relations between MBN parameters and mechanical properties, DBTT and Vickers hardness.

gently over 10 % reduction ratio. Though the relation between MBN parameters and mechanical parameters is not simple proportional, MBN parameters shows the increases monotonically as function of mechanical parameters. Thus, these results represent a possibility of NDE for the mechanical properties using the Barkhausen noise technique.

4. Conclusion The MBN and mechanical properties of cold rolled low carbon steel were studied. MBN energy and rms voltage rise sharply in an initial stage of cold rolling and gently over 10% cold rolling ratio. The Vickers hardness and DBTT exhibits the same tendency as MBN parameters. Dislocations increase with the increase of the rolling reduction, which cause the increase of Vickers hardness and DBTT. The formation of cell texture and the changes in dislocation density dominated the MBN properties. Good correlations between MBN parameters and mechanical parameters were derived, which show the Barkhausen technique is a good candidate of NDE for the mechanical properties of cold rolled steel.

References [1] C. C. H. Lo, J. Paulsen and D. C. Jiles, IEEE Trans. Magn., 40 (2004) 2173-2175. [2] S. Palit Sagar, N. Parida, et al., Int. J. Fatigue, 27 (2005) 317-322. [3] V. Moorthy, B. A. Shaw, S. Day, Acta Mater., 52 (2004) 1927-1936. [4] J. Anglada-Riveraa, L. R. Padoveseb, J. Capó-Sáncheza, J. Magn. Magn. Mater., 231 (2001) 299-306. [5] O. Saquet, J. Chicois, A. Vincent, Mater. Sci. Engineering, A269 (1999) 73–82. [6] C. G. Stefanita, L. Clapham, J. K. YI, D. L. Atherton, J. Mater. Sci., 36 (2001) 2795-2799. [7] Y. Kamada, T. Nakano, S.Takahashi, et al., J. Magn. Jpn., 28 (2004) 409–412. [8] R. Ham, Philos. Mag., 6 (1961) 1183–1184.

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Electromagnetic Nondestructive Evaluation (XI) A. Tamburrino et al. (Eds.) IOS Press, 2008 © 2008 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-58603-896-0-46

A Bridge Between NDE and Charpy Impact Testing Seiki TAKAHASHI 1 and Satoru KOBAYASHI NDE and Science Research Center, Faculty of Engineering, Iwate University, Morioka 020-8551, Japan Abstract. Charpy impact test is explained from the viewpoint of the transition of hammer’s energy to the kinetic energy of dislocations. Ductile-brittle transition temperatureT is represented as a simple function of the nucleation energy of dislocations Hn, the dislocation density U, the maximum density of mobile dislocations Uo and the interaction energy of obstacles with dislocations Uob; kT = UobҏUo +(Uo-U)Hn when U< Uo, while kT = UobҏUm when U> Uo, where k is Boltzmann constant and Um is the density of mobile dislocations. The relationship is compared with the experimental results for cold rolled S15C steels and neutron irradiated low and high copper A533B steels of nuclear reactor pressure vessel materials. The experimental results are qualitatively explained by the present model. Keywords. Charpy impact test, dislocations, ductile-brittle transition, plastic deformation, neutron irradiation

1. Introduction Charpy impact test is an useful and reliable method to get information on ductility of materials and has been traditionally used for a long time in the engineering field.[1,2] The surveillance test of nuclear reactor pressure vessels (NRPVs) has been carried out by Charpy impact method and the obtained ductile-brittle transition temperature (DBTT) decides the lifetime of NRPV. The mechanism of age degradation in NRPV has been investigated from the viewpoint of microstructure and it is widely accepted that copper precipitates with size of 2-3 nm, which nucleate and grow by the neutron irradiation, make material brittle.[3,4] On the other hand, the nucleation mechanism has been recently investigated by magnetic method in NRPV material and it was suggested that copper precipitates gathering around dislocations through the elastic interaction also contribute to the degradation.[5] Currently, the degradation in NRPV is evaluated by DBTT obtained by Charpy impact test that is a macroscopic property. Nevertheless, there exist few ideas to connect the macroscopic property with the microscopic one and its physical meaning is vague at present. We need a bridge between the microstructure of irradiation damages and the traditional mechanical properties for the practical use. The relationship between DBTT and magnetic properties has been investigated experimentally and it was found that coercive field increases in proportion to DBTT.[6] Charpy impact method is a destructive test, whereas the magnetic method has a characteristic of non-destructive evaluation. We need the physical model of DBTT to explain the relationship of DBTT with magnetic properties. The purpose of the present 1 Corresponding Author: NDE&Science Research Center, Faculty of Engineering, Iwate University, 4-3-5 Ueda, Morioka 020-8551, Japan; Phone:+81-19-621-6431; Email: [email protected]

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47

study is to give physical explanation for the DBTT and absorption energy from the microscopic viewpoint. In this study, we introduce a dislocation model representing the absorption energy versus temperature and express DBTT by physical properties. The experimental results are analyzed and DBTT and upper shelf energy are explained on the basis of the present dislocation model in the neutron irradiated low carbon steels.

2. Charpy impact test Ductile and brittle states are examined by Charpy impact test in which a hammer accelerated by gravity potential collides with a test piece and the hammer energy lost by the collision is measured. The lost energy is very small in the brittle state, whereas in ductile state the hammer energy is absorbed into the test piece. The metallic materials are brittle at low temperatures but change to ductile above the critical temperature. This critical temperature is called ductile-brittle transition temperature. The value of DBTT depends on the kinds of materials and increases with the progression of degradation. The absorption energy in the ductile state also depends on the degree of degradation and the ductility of materials is therefore evaluated by both DBTT and the upper shelf energy. [1,2] Samples are deformed plastically in the ductile state when a hammer collides. The hammer’s energy is consumed for plastic deformation and is then transformed into thermal energy. Plastic deformation is cause of the nucleation and motion of dislocations from the microscopic viewpoint. On the other hand, in the brittle state dislocations cannot move and the samples are broken down without the dislocation motion.

3. Absorption energy and dislocations In the ductile state, most of a potential energy of a hammer are transferred to a kinetic energy of dislocations during the collision that is the main part of the absorption energy in Charpy impact test. The mechanism of the energy transition depends on the dislocation density. If there exist many dislocations enough to receive the hammer’s energy, the interaction of dislocations with their obstacles decides the energy transition. If dislocations do not exist enough, the hammer’s energy would be consumed for nucleation of dislocations and their kinetic energy. If the energy transformation is adiabatic, though transformation in actual Charpy impact test is not adiabatic, the absorption energy is represented as a step function of temperature as shown in Figure 1. The energy is discontinuously transformed at the transition temperature T. The absorption energy of the step function can be approximately expressed by the equation Eabs = Uo exp[- (U/kT)n] ,

(1)

where n = f. Here, Uo is an upper shelf energy, k is Boltzmann constant and U is the transition energy. The transition temperature T is given by

48

S. Takahashi and S. Kobayashi / A Bridge Between NDE and Charpy Impact Testing

Absorption energy Eabs/ U0

1.2 adiabatic (n=п) 1 n = 50 n = 30 n = 15

0.8 0.6 0.4

static (n = 1)

0.2 0 0

0.5

1

1.5

2

T/T   Figure 1. Energy transition processes for n = 1 (static), 15, 30, 50, f (adiabatic) cases.

U = kT

(2)

and is not the same value as the definition of DBTT. Another extreme case of energy transformation is the quasi-static transition where the energy is transformed at the constant temperature near T, during the infinite time. In this case, the absorption energy is written as Eabs = Uo exp[-(U/kT)],

(3)

which is represented in Figure 1. The actual transition in Charpy impact test is represented as a model of the intermediate of two examples, taking an adequate n in Equation (1), and an absorption energy for n = 15, 30, 50 is plotted in Figure 1 as an example. The energy transition in Charpy impact test is explained under supposition that any phase transition does not occur in the temperature range of the measurement. The hammer’s energy is transformed into the kinetic energy of dislocations during the collision. The energy transition is performed perfectly near Twhen the dislocation density is high enough to receive the potential energy and their mean free path is long enough for dislocations to accumulate their kinetic energy. However, there exist a lot of obstacles against the dislocation motion in real materials. The obstacles interact with dislocations and restrict the dislocation motion. The interaction of obstacles with dislocations is represented as an interaction energy Uob that depends on the strength of the interaction, the density and distribution of obstacles. Dislocations themselves act as the obstacles, make the mean free path short and the number of mobile dislocations small near and above T. When the dislocation density is not enough to receive the hammer’s energy, the dislocations would be nucleated by the energy supplied from the hammer during the collision. The absorption energy is written as, neglecting the obstacle effect, Eabs = Uo exp[- ((Uo - U)Hn/kT)n] ,

(4)

where U is the dislocation density before the collision, Hn is the nucleation energy of dislocations per unit length and Uo is the maximum dislocation density to receive the

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49

potential energy of the hammer. Generally, materials include obstacles and both obstacles and the dislocation density contribute to the absorption energy. When U is lower than Uo, dislocations with density of Uo-U should be nucleated and the absorption energy would be represented by Eabs = Uo exp[-((Uob̓ Uo +(Uo - U)Hn)/ kT)n]

(5)

On the other hand, when U is higher than Uo, the absorption energy is represented as Eabs = Uo exp[-(Uob̓ Um/ kT)n].

(6)

Here, Um is the density of mobile dislocations that is lower than Uo. Uo is the maximum of Um. The dislocation density is not included in Equation (6) explicitly but Uob is related to the density and distribution of dislocations, because dislocations play an important role as obstacles even in the initial stage of plastic deformation. The upper shelf energy Uo depends on the density of mobile dislocations and their mean free path in the collision. Uo is the kinetic energy of dislocations; i.e.

Uo F't

p2 U m ҏ, 2m

'( pU m ) p

m

(7)

U m 'p  p'U m 'x 't

,

(8)

,

(9)

where p is the momentum of a dislocation per unit length and depends on the mean free path x. m is the effective mass of a dislocation and F is the force acting on dislocations during collision time 't. Dislocations are accelerated during 't. When x is long enough, the momentum would become large. If the density of mobile dislocations Um is small and x is short, 't would become short and the material is brittle. Uo depends on Um. The strength of interaction energy and the test temperature restrict the density Um; dislocations get over obstacles through the thermal activation process and the external force F that is decided by the external conditions of a hammer.

4. Comparison with experimental results The relationship between DBTT and dislocations has been investigated in S15 C steel, where the dislocations are induced by cold rolling with 0, 5, 10, 20 and 40% strain. The chemical composition of S15C steel is listed in Table 1. The absorption energy was measured by use of Charpy impact test pieces with the standard size of Table 1.

Chemical compositions of S15C steel.

S15C

C

Si

Mn

Fe

wt.%

0.16

0.20

0.44

balance

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S. Takahashi and S. Kobayashi / A Bridge Between NDE and Charpy Impact Testing

10×10×55 mm. The impact tests were carried out with a pendulum of 27.6 kG and lift angle of 138.5° in the temperature range of 200-363 K. Five V-notched Charpy samples were tested at each temperature and both the largest and smallest values of absorption energy were eliminated when averaging the data. Figure 2 shows the temperature dependence of absorption energy. The lines are obtained by fitting the experimental results to Equation (1). The value of n changes from 15 to 30 depending on plastic deformation; it increases with rolling reduction initially, takes the maximum for 20% rolling reduction and decreases above 40% reduction. The dislocation density is not enough before cold rolling, whereas obstacles are present. The hammer’s energy would be consumed by the two processes; the nucleation of dislocations and climbing over obstacles. The dislocation density becomes enough by 5% rolling reduction and the process becomes only climbing of obstacles. The value of n increases from 15 to 30. The dislocations play the roll of obstacles above 20% rolling reduction. The pinning processes of dislocations increase and the value of n decreases from 30 to 15.  The value of DBTT was obtained experimentally as the temperature at which the upper shelf energy becomes a half. Figure 3(a) shows the relation between DBTT and rolling reduction, which is compared with the calculated value of T and the upper shelf 250

0% 5% 10% 20% 40%

Absorption energy (J)

200

150

100

50

0 180 200 220 240 260 280 300 320 340 360 380

    

Temperature(K)



Figure 2. Temperature dependence of absorption energy in cold rolled S15C steel. The carved lines are calculated results n = 15, 31, 61, 25 and 11 correspond to H = 0, 5%, 10%, 20%, and 40% in strain, respectively.

(a)

180

270

160

260

140

250 120 240 100 230

600

0

10

20

30

40

Rolling reduction (%)

50

U0

DBTT, T (K)

280

200

Coercive field Hc (A/m)

290

(b) 500

400

300

200 240

250

260

270

280

290

DBTT (K)

Figure 3. (a) DBTT and theoretical values of T and Uo as a function of rolling reduction in S15C steel. The solid and open circles, and triangles denote DBTT, T and Uo, respectively. (b) The relation between DBTT and coercive field of S15C steel.

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S. Takahashi and S. Kobayashi / A Bridge Between NDE and Charpy Impact Testing

Table 2.

Chemical compositions of A533B steel.

A533B

C

Si

high Cu

0.19

0.19

1.47

0.16

0.64

0.51

0.14

balance

low Cu

0.19

0.18

1.46

0.05

0.64

0.50

0.14

balance

Table 3.

Mn

Cu

Ni

Mo

Cr

Fe

n, T and U0 of A533B steels before and after neutron irradiation.

T.

n

A533B

Uo (J) 223 ± 75  

high Cu (before)

7±2

232 ± 5

    (after)

4±2

312 ± 30

low Cu (before)

11 ± 4

215 ± 6

 174 ± 27

    (after)

12 ± 4

238 ± 4

 153 ± 11

181 ± 50

energy Uo. The relation between DBTT and coercive field obtained in our previous work[6] is also given in Figure 3(b).   DBTT has been measured before and after the neutron irradiation in NRPV A533B steels with low and high copper contents. Their chemical contents are shown in Table 2. The neutron radiation was performed at 563 K in helium atmosphere in a 50 MW nuclear reactor of Japan Materials Testing Reactor(JMTR). The radiation effect that yields the brittleness has been examined after the neutron fluence to 5 × 1019 cm-2. The number of test pieces is limited to two for each temperature. Figure 4(a) shows the temperature dependence of absorption energy in high copper A533B steel. The lines are obtained by fitting the experimental results to Equation (6). The values of n , Tand Uo ̓change by the neutron radiation, from 7 ± 2 to 4 ± 2, 232 ±5 K to 312± 30 K and 223±75 J to 181± 50 J, respectively as listed in Table 3. Figure 4(b) shows the temperature dependence of absorption energy in low copper A533B steel. The values of

250

250

(a)

high Cu

unirradiated

Absorption energy (J)

Absorption energy (J)

300

200 150 100

irradiated

50 0 150

200

250

300

350

Temperature (K)

400

450

(b)

low Cu

200

unirradiated

150

irradiated 100

50

0 150

200

250

300

350

400

450

Temperature (K)

Figure 4. Temperature dependence of absorption energy in A533B steel with (a) high copper and (b) low copper contents, before and after neutron irradiation to a fluence of 5 × 1019 cm-2. The solid lines through the data shows the least squares fits.

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S. Takahashi and S. Kobayashi / A Bridge Between NDE and Charpy Impact Testing

n ,Tand Uo ̓change by the neutron radiation from11 ± 4 to 12 ± 4, 215 ± 6 K to 238 ± 4 K and 174 ± 27 J to 153 ± 11 J, respectively as listed in Table 3. The large deviation of n , Tand Uo is attributed to the lack of data points and the shortage of test pieces. Neutron radiation would not exert any remarkable influence on the distribution of dislocations as well as the dislocation density but on the interaction energy Uob. The change of properties due to neutron radiation is smaller in low copper A533B steel than in higher copper one.

5. Discussion In cold rolled S15C steel, the transition temperatures DBTT and T show similar change against rolling reduction though the value of DBTT is slightly larger than that of T as shown in Figure 3. The obstacles to the dislocation motion are dislocations themselves and their interaction would be proportional to the applied stress. The value of T shows a gentle increase from 5% to 40% in rolling reduction, whereas it increases rapidly from 0 to 5% in rolling reduction. The upper shelf energy U0 decreases monotonically from 0 to 40% reduction. The monotonic decrease of U0 indicates that the mean free path would decrease and the density of mobile dislocations would not change remarkably. The dislocation density of A533B steels is higher than 1010 cm-2 before neutron radiation and dislocations make cell structure. The dislocations that do not contribute to the cell structure can move the same distance as the size of a cell, because there exist little dislocations inside of the cell. Therefore, the mean free path would be large, whereas the value of Um is small. Recently, it was suggested by the magnetic method that the copper precipitates and dislocation loops created by neutron radiation would gather around dislocations and disturb the dislocation movement.[5] Since copper precipitates have stress field and edge dislocations include both compressive and repulsive stress field, copper precipitates gathering around the dislocations would compensate the stress field of dislocations in order to reduce the elastic energy. The copper precipitates strongly disturb the dislocation movement and makes high copper A533B steel brittle. On the other hand, copper precipitates inside of cells also disturb the dislocation movement and make the mean free path x decrease. Since the value of Um would not change by the neutron radiation, the value of Uo decreases as is listed in Table 3. Copper precipitates make the value of Uob increase and their inhomogeneous distribution makes the distribution of Uob wide. This results in a decrease of n due to neutron radiation in the high copper A533B steel. The amount of copper precipitates nucleated by neutron radiation is small in A533B steel with low copper content in comparison with that for high copper content. The change of T (DBTT) is 18 ± 5 K in low copper A553B steel that is much smaller than 80 ±30 K in high copper A533B steel. The difference of the change in T is attributed to the number of obstacles, which decide the value of Uob. The value of n does not change remarkably by the radiation in low copper A533B steel. This result indicates that the obstacles distribute homogeneously. The change of Uo due to neutron radiation in low copper A533B steel is also smaller than that of the high copper A533B one, being consistent with the results of T. The main obstacles to dislocation motion in A533B steels are copper precipitates and their amount depends on the copper contents. DBTT gives us the direct information about ductility and brittleness from a macroscopic viewpoint and can be qualitatively explained by the dislocation theory. On

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53

the other hand, dislocations also interact with magnetic domain walls and influence their movement. According to earlier theory for micromagnetism, arrangement of magnetization is determined so as to minimize magnetic Gibbs free energy consisting of exchange energy, magnetocrystalline anisotropy energy, magnetostatic energy and magnetoelastic energy.[7] In ferromagnetic materials including dislocations, the Gibbs free energy is lowered when domain walls are located at dislocations and dislocations act as obstacles to the domain wall motion, yielding changes in magnetic properties. Therefore, both magnetic and mechanical properties have an intimate connection with each other through dislocations as is seen in the simple relation between DBTT and coercive field in Figure 3(b). Such connection is also true for NRPV steel irradiated by neutron where various kinds of lattice defects such as precipitates which disturb dislocation motion are formed; these irradiation defects interact with domain walls as in the case of dislocations.[7-9] However, the crucial difference between these properties is the fact that magnetic properties can be obtained by nondestructive measurements whereas Charpy impact test is destructive one. The practical application of magnetic methods to NDE is therefore expected for the pressure vessel of nuclear reactors exposed to neutron radiation.

Acknowledgements The authors express thanks to Dr. Y. Kamada, for the Charpy impact test measurement, Dr. H. Kikuchi, K. Ara and N. Ebine for the operation of the nuclear reactor. This research was supported by a Grant-in-Aid for Scientific Research (S), Grant No. 14102034, from the Ministry of Education, Culture, Sports, Science and Technology of Japan.

References [1] E. R. Parker, in Brittle Behavior of Engineering Structure, (John Wiley & Sons, 1957). [2] D. Francois, in From Charpy to Present Impact Testing, (ESIS Publication, 2002) [3] J. Koutský and J. Kocík, in Radiation Damage of Structural Materials, (Elsevier Science Publishers, 1994). [4] G. R. Odette and G. E. Lucas, JOM 53 (2001) 18. [5] S. Takahashi, H. Kikuchi, K. Ara, N. Ebine, Y. Kamada, S. Kobayashi and M. Suzuki, J. Appl. Phys. 100 (2006) 023902. [6] S. Takahashi, S. Kobayashi, Y. Kamada, H. Kikuchi,, J. Appl. Phys. 100 (2006) 113908. [7] H. Kronmüller and M. Fähnle, in Micromagnetism and the Microstructure of Ferromagnetic Solids (Cambridge, 2003). [8] L. J. Dijkstra and C. Wert, Phys. Rev. 79 (1950) 979. [9] J. B. Goodenough, Phys Rev. 95 (1954) 917.

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Electromagnetic Nondestructive Evaluation (XI) A. Tamburrino et al. (Eds.) IOS Press, 2008 © 2008 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-58603-896-0-54

ND-materials characterization of neutroninduced embrittlement in German nuclear reactor pressure vessel material by micromagnetic NDT techniques Gerd DOBMANN1, Iris ALTPETER1, Melanie KOPP1, Magdalena RABUNG1, and Gerhard HÜBSCHEN1 1 Fraunhofer IZFP, Germany

Abstract. Depending on the neutron fluence and the special design of the pressure vessel of nuclear power plants (NPP) the microstructure of the steels change by neutron induced embrittlement. Embrittlement is on the basis of vacancies and Curich precipitates which in the size range of 1-3 nm contribute with coherent residual stresses of the 3rd kind to an increase in hardness and strength (yield strength and tensile strength) as well as with a reduction of the upper shelf value of Charpy energy and a shift in the brittle-to-ductile transition temperature to higher temperatures. Micromagnetic investigations sponsored by the German minister of economics were performed at full Charpy specimen and material of the last generation of German NPP in order to characterize the material degradation. The contribution reports to the results obtained by the application of the Micromagnetic-, Multiparameter-, Microstructure-, and stress-Analysis (3MA) and the magnetostrictive excitation of ultrasound using an EMAT. Both technologies document potential to be further developed to an in-service inspection technique.

Keywords. Neutron irradiation, embrittlement, pressure vessel material, micromagnetic NDE techniques, multiple regression, calibration

Introduction In the year 2003 IZFP has participated in the EURATOM project GRETE where the characterization of neutron degradation of pressure vessel material was one project task. Materials came from surveillance and irradiation programs. All specimens were investigated in the hot cells of the research reactor in Petten, the Netherlands. The specimens were half Charpy specimens obtained after the performance of the Charpy impact energy test, i.e. the specimen have had plastic deformation and residual stresses

G. Dobmann et al. / ND-Materials Characterization of Neutron-Induced Embrittlement

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as disturbing influences. Concerning micromagnetic NDT techniques proposed by IZFP the effects strongly influence the results. However, performing the so-called 3MA-approach (Micromagnetic, Multiparameter, Microstructure and stress Analysis) [1] after calibration correlation coefficients in the 0.98 range were obtained with a residual standard deviation of 16°C when, for instance, the shift – compared with the non-irradiated material state - of the ductile to brittle transition temperature 'T09 was predicted. When ISO-v-notched specimen, for instance according to the ASTM standard A370 are tested in the Charpy impact test in order to evaluate the Charpy impact energy as function of temperature, each half of the broken specimen has shear lips in the fracture plane, i.e. the broken specimen shows a broadening compared with the initial state. The broadening is defined as the difference value between the specimen width with shear lips after break and the initial width value. T09 is derived from the fitted and averaged Charpy impact energy versus temperature curve as the special temperature where the broadening meets the value 0.9mm. However, a verification test of the approach by independently selected specimen resulted in much larger deviations because of the above mentioned disturbing effects [2, 3].

1. Material Selection

Figure 1. Neutron fluence in a German NPP of the last generation as function of lifetime

As directed by the German minister of economics – responsible for nuclear safety – a project was performed where the objective in a feasibility study was to demonstrate the potential of micromagnetic NDT techniques to characterize the material degradation by neutron irradiation when the neutron fluence is much smaller compared to the former discussed European project. Background is that in Germany (see Figure 1), according to the German codes, the design lifetime is 32 years and the fluence is restricted to values of 5×1018 n/cm2 (Energy >1MeV). This design end-of-life value (green curve in Figure 1.) is one order

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G. Dobmann et al. / ND-Materials Characterization of Neutron-Induced Embrittlement

in size smaller than in other countries and is obtained by a much larger gap between PV-wall and core internals in the German design compared with others. When the real behavior of the material is discussed resulting from fluence measurements then the fluence curve follows (in an extrapolation) the red curve. After 48 years of full power service only a value of 3.35×1018 n/cm2 is obtained documenting also the potential of a possible lifetime extension. The materials selected to perform the non-destructive tests were from the two steel types 22NiMoCr37 and 20MnMoNi55. The important contents of the elements Cu, P and Ni are indicated in Table 1 where also the available fluence values are documented. As can be seen, the specimens named P16 with the highest Cu, P, and Ni-content have the highest fluence values, i. e. they have the highest degree in degradation. Table 1 Steel grades selected for materials characterization Indication

P140

Weld Material /Base Material

Cu [%]

WM

0,07

P [%]

Ni [%]

Fluence [n/cm²]

0,009

0,9

3,72E+18 7,55E+18 1,04E+19 3,71E+19

P141

BM

0,06

0,008

0,8

3,78E+18 7,66E+18 1,05E+19

P16

WM

0,08

0,012

1,7

4,15E+18 8,04E+18 1,16E+19 5,22E+19

According to Figure 2 the materials P 16 and P 141 show normal behavior, i.e. an increase of the of the shift (dt41) of the brittle-to-ductile transition temperature with fluence, whereas the P 140 material documents a recovery annealing, first increasing then decreasing. The arrows in Figure 2 indicate the tendency. In this case the transition temperatureT 41 in contrast to T09 is discussed which is derived from the fitted and averaged Charpy impact energy curve as function of temperature exactly where the curve meets the value of 41J. P16 – weld metal P 16 WM

P 141 BM

P140 – weld metal

P141- base metal P 140 WM

Neutron fluence times 10E18 Figure 2. Shift in the brittle-to-ductile transition temperature (dt41) as function of the fluence (abscissa) of the three materials

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2. Measurements with 3MA Techniques and Correlation with Toughness Parameters The 3MA measurements were performed in the hot cell of AREVA whereas only the magnetic yoke transducer was inside the hot cell and the electronic equipment outside. The Charpy specimens were handled by a manipulator. A special adaption piece made by an Al-alloy was applied to guarantee reproducibility in positioning of the specimen at the yoke pole shoes. The 3MA-approach is described in detail elsewhere [1]. However, a short explanation is given here (Figure 3). With 3MA different micromagnetic quantities are measured. These are derived by analysis of the magnetic Barkhausen noise M(Ht), the incremental permeability μ(Ht) as function of a tangential magnetic field Ht which varies as function of time (t) according to a sinusoidal time function. In Figure 3, in a sketch, the different measuring quantities are illustrated: In the middle a magnetic hysteresis (induction B(H) versus the magnetic field H), in the upper left part the Barkhausen noise M which is an electrical voltage received by integrating the magnetic flux excited by Bloch wall jumps and rotational processes of the magnetization vectors of the domains. In the upper right part the incremental permeability which is the inclination of the small inner loop (see hysteresis) 'B/'H and proportional to the impedance of an eddy current coil superimposing to the hysteresis loop the small incremental magnetic field 'H of a frequency, at minimum, a factor 10 higher than the hysteresis frequency. H, respectively Ht are measured in A/cm, the time t in s and the induction B in T. In the lower left part of Figure 3 the harmonic analysis of the tangential field strength is shown and how, for instance, a distortion factor K can be derived by measuring the odd harmonics up to order of seven. The lower right part of Figure 3 documents an additionally performed eddy current impedance measurement with three different frequencies. The 3MA-approach correlates a target value like, for instance, the dt41 transition temperature shift in a multiple regression model with the micromagnetic measuring quantities and estimates the unknown parameters of the model by applying a least squares algorithm.

Figure 3. The 3MA approach

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G. Dobmann et al. / ND-Materials Characterization of Neutron-Induced Embrittlement

In the least squares algorithm only one part of the set of specimens is used for calibration of the model, the other independently selected part is applied to check the quality of the model (verification test).

Figure 4. 3MA result at the P16 specimens

In Figure 4 as one result the shift in the brittle-to-ductile transition temperature (dT41) is compared with the predicted values by 3MA. The red colored dots indicate the calibration specimens, the green colored the verification specimens. The regression coefficient from the calibration is 0.93 with a residual standard error of 12.8°C. However, because of the inhomogeneous microstructure in the weld material P16 (multiple-path welding under submerged arc) the residual standard error concerning the verification specimens 24.8°C is nearly a factor 2 larger. In the base material the obtained standard errors are much smaller. This is documented in Figure 5 in case of the material P 141. The regression coefficient after the calibration is 0.986; the residual standard error in the verification is only 1.2°C.

Determination of the shift of the ductile to brittle transition temperature dT41 by the 3MA-technique Base material P141

r2 = 0.986 Standarderror = 0.35 (Calibration) Standarderror = 1.2 (Verification)

Figure 5. 3MA result at the P141 material

The future plan is to develop an ISI inspection technology to examine the pressure vessel from the inner side by a 3MA approach. However, in that case the inspection has to be performed through the austenitic stainless steel cladding which itself has certain G-ferrite content, a ferromagnetic phase. Therefore the influence of the cladding on a micromagnetic technique like Barkhausen noise was investigated. Figure 6 documents the result. Shown are Barkhausen noise profile curves [1] which are obtained when the

G. Dobmann et al. / ND-Materials Characterization of Neutron-Induced Embrittlement

59

received electrical voltage (ordinate) as time signal in a (x,y)-presentation on the oscilloscope is visualized versus the time signal of the magnetic field (abscissa). Even through the 10 mm thick austenitic plate the Barkhausen noise from the ferritic plate can be recorded. The thickness of the austenitic plate influences the inspection mainly by a larger lift-off effect. However, there is also a higher eddy current damping because of the electrical conductivity of the cladding.

Figure 6. Barkhausen-noise M as function of a tangential magnetic field Ht at a ferritic plate (left), through 8 mm austenitic (middle) and 10 mm austenitic (right) plate with G-ferrite simulating the cladding

3. Magnetostrictive Electromagnetic Excitation of Ultrasound (EMUS) G. Ahlers had previously proposed to excite a standing, low frequency (10 kHz, O=320 mm) ultrasonic wave by a magnetostrictively working electromagnetic acoustic transducer (EMAT) [4] in the interface between the austenitic cladding and the ferritic material of the PV wall propagating in thickness direction. In Figure 7 the principle of such an inspection is shown which up to now is not yet realized for ISI-technology. A dc- or low frequency ac-electromagnet magnetizes locally the pressure vessel wall from the inner side through the cladding. A high-frequency (HF)-current tone burst is exciting a HF-eddy-current coil; the magnetic field is controlled by a Hall probe. The principle was investigated using cladded test pieces. Figure 8 gives a view on the experimental set-up using a Bruker water-cooled laboratory electro-resistance dcmagnet with a maximum magnetic induction field of 1.5 T. transmitter coil

receiver coil

poleshoes of electromagnet

Figure 7. Principle of the magnetostrictive excitation of a standing wave in thickness direction

Figure 8. EMAT transmitter-receiver prototype transducer at a cladded test piece

60

G. Dobmann et al. / ND-Materials Characterization of Neutron-Induced Embrittlement

The HF-coil was designed as transmitter receiver coil with adopted coil windings; the burst frequency was 50 kHz. The cladded test piece was set-up at the pole shoes of the laboratory magnet. It was shown that G-ferrite changes in the cladding doesn’t change the results very much. This is documented in the Figures 9 and 10. In the case of Figure 9 the standing wave was excited in a ferritic plate with wall thickness 30 mm but with a lift-off of the transducer of 8 mm whereas in Figure 10 the test piece was a 30 mm thick cladded material with a cladding thickness of 8mm. Insonification was performed from the cladded surface. The electrical signals were obtained by an excitation with a burst length of 10 cycles of a 50 kHz tone-burst at a magnetic field strength of 260 A/cm. It is obvious; the cladding is mainly influencing the signal with a lift-off effect. There were also investigations concerning the influence of the inhomogeneous microstructure of a ferritic butt weld beneath the cladding on the magnetostrictive excitation. This situation occurs at pressure vessels along an inspection path in the direction of the circumferential welds. By scanning with the EMAT along such a weld and measuring the resonance amplitude as function of the different positions only a standard deviation of < 4%, compared with the average value, has been observed. This reflects the change of magnetostriction with the microstructure of a multilayer submerged arc weld. This value has to be compared with the measuring effect obtained at neutron irradiated material. Because the dynamic magnetostriction is sensitive to lattice defects it was assumed that the resonance amplitude of the standing wave also reflects the neutron embrittlement and first experiments were also performed with a special designed magnetostrictive transducer at Charpy specimen in the hot cell of AREVA in order to principally document the potential.

Figure 9. Magnetostrictive excitation of the standing wave in a ferritic plate, lift off of the transducer 8 mm in air (abscissa is the time scale, the ordinate is the electrical voltage induced in the EMAT by the ultrasonic wave)

Figure 10. Magnetostrictive excitation of the standing wave excited beneath the cladded surface, cladding thickness 8 mm (abscissa and ordinate like in Figure 9)

The EMAT especially optimized to test the small geometry of Charpy specimens operates at 1.2 MHz. The echo sequence of the excited standing wave was recorded by varying the superimposed magnetic field. The time signal was time gated (Figure 11) and in the gate the peak amplitude was registered. The so obtained measuring quantity was named E60, indicating that the measurement was performed at the 60% amplitude level of the maximum magnetic field strength. This is an operating point of the magnetic field at which the magnetostrictive excitation has not yet obtained its maximum. It is obvious, at the higher operating frequency of 1.2 MHz the efficiency of transduction and receiving is better than in the lower frequency range (10 kHz) used at

G. Dobmann et al. / ND-Materials Characterization of Neutron-Induced Embrittlement

61

the plates. In Figure 12 by testing the P16 material the measuring quantity E60 shows a linear decreasing with the dT41 values. This behavior is expected with the increase of lattice defects. The scatter in the data documents the natural scatter in the microstructure of similar irradiated material but different specimens and can also be observed in the Charpy test data. Compared with the amplitude dynamic as function of the brittle-to-ductile transition temperature this scatter is smaller than 17%. The influence of an inhomogeneous weld microstructure which was measured with < 4% amplitude variation is much smaller.

Time gate Figure 11. Echo sequence recorded at a Charpy specimen (abscissa time scale, ordinate the electrical voltage which is induced in the EMAT by the ultrasonic wave)

Figure 12. Measuring quantity E60 as function of the shift of the brittle-to-ductile transition temperature dT41 at P16 material

Conclusion Micromagnetic NDT techniques show a high potential when neutron degradation is characterized. The combination and data fusion of micromagnetic measuring quantities in a 3MA-approach is suitable to early detect material degradation. The evaluation of a magnetostrictively transmitted and received ultrasonic wave propagating in the pressure vessel wall thickness direction as a standing wave has special potential to enhance ISI. The two techniques are under development.

References [1] [2] [3] [4]

I. Altpeter, et al., Electromagnetic and Micro-Magnetic Non-Destructive Characterization (NDC) for Material Mechanical Property Determination and Prediction in Steel Industry and in Lifetime Extension Strategies of NPP Steel Components, Inverse Problems 18 (2002) 1907-1921. G. Dobmann, et al., Electromagnetic Characterization of Materials Degradation due to Neutron Irradiation and Fatigue, Applied Electromagnetics and Mechanics (2003), 30-31. G. Dobmann, et al., Aging Material Evaluation and Studies by Non-Destructive Techniques (AMESNDT) - a European Network Project, Nuclear Engineering and Design 26 (2001) 373-374. I. Altpeter, et al., Review of Progress in Quantitative Nondestructive Evaluation. 22A, Melville, New York, American Institute of Physics (AIP) (2003) 15-21.

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Electromagnetic Nondestructive Evaluation (XI) A. Tamburrino et al. (Eds.) IOS Press, 2008 © 2008 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-58603-896-0-62

Evaluation of Chill Contents in Flake Graphite Cast Irons Using AC Magnetization Method Tetsuya UCHIMOTO a,1, Jun MATSUKAWAb, Toshihiko ABEa, Toshiyuki TAKAGIa Takeshi SATOa, Hiroyuki IKEb, Takahito TAKAGAWAc and Noritaka HORIKAWAd a Institute of Fluid Science, Tohoku University, Japan b Graduate School of Engineering, Tohoku University, Japan c Iwate Industrial Research Institute, Japan d Graduate School of Engineering, Hokkaido University, Japan Abstract. In this study feasibility of evaluation for chill contents in flake graphite cast iron is investigated based on AC magnetization method, which is one of the electromagnetic nondestructive evaluation methods. Magnetic properties of flake graphite cast iron samples with different chill contents were measured by a B-H loop analyzer in order to discuss their relation to chill contents. It was found that some magnetic parameters of the flake graphite cast iron depend on the contents of matrices and graphite. Especially, the hardness, which reflects chill contents, has good correlation with the area of hysteresis loop at relatively high frequencies. Focusing on the finding, AC magnetization method was applied to evaluation for the chill contents. Through the experiment, it was found that there is a correlation between hardness of flake graphite cast irons with chill and signals. In consequence, AC magnetization method has a capability of evaluating chill contents in flake graphite cast irons. Keywords. cast iron, AC magnetization method, nondestructive evaluation, chill

1. Introduction In foundry industry, thin-walled mechanical components of cast irons provide weight saving of automobiles, resulting in realization of energy saving vehicle. However, thinwalled components of cast iron leads to the increase in cooling rate during solidification of the cast irons, so that chill, namely proeutectic cementite microstructure, is crystallized. Chill deteriorates the mechanical properties because cast irons including chill are hard and brittle [1]. In contrast, it was reported that chill improves wear resistance, and it can be applied to sliding parts of automobile components such as cylinder bores and piston rings to be endured in severe wear conditions [2]. Therefore, it is highly required in foundry industry to evaluate and 1 Corresponding Author: Institute of Fluid Science, Tohoku University, 2-1-1 Katahira, Aoba, Sendai, Miyagi 980-8577 Japan; E-mail: [email protected]

T. Uchimoto et al. / Evaluation of Chill Contents in Flake Graphite Cast Irons

63

control chill contents. At present, visual test of fracture surface, microscopic observation and indentation test are applied to evaluate chill contents. However, they are all destructive testing and total inspection is impossible by these methods. For the reason, there is a requirement for establishment of the method to evaluate chill contents nondestructively and quantitatively. Cast iron is composed of graphite and matrices consisting of ferrite, pearlite, chill and so on. Therefore, it is indispensable to extract the information concerned with chill contents from other information including that of graphite and other matrices contents when nondestructive evaluation is applied to estimation of chill contents. Focusing on the difference of electromagnetic properties of each matrix and graphite, some attempts have been done to estimate hardness, other mechanical properties, ratio of ferrite to pearlite in ductile cast iron and graphite size in flake graphite cast iron by the method based on electromagnetic phenomena [3-6]. Feasibility of evaluation for chill contents in ductile cast iron was reported [7]. This work proposes an evaluation method of chill contents by means of the electromagnetic nondestructive method. In this paper, firstly, the contents of matrices and graphite in the flake graphite cast irons with different contents of chill are quantified from the analysis of microstructure. Secondly, the relations between electromagnetic characteristics and the contents of each matrix and graphite are discussed. Finally, focusing on the relation, AC magnetization method is applied to evaluation for chill contents.

2. Cast Metals The flake graphite cast irons which have chemical composition listed in Table 1 were prepared. Materials without chill were divided into three groups: FC150, FC200 and FC250 (JIS standard). In addition, each group has three types of materials depending on three kinds of heat treatments: as cast, furnace cooling and air cooling. In the case of furnace cooling and air cooling, the cast material was reheated at 850 oC in the furnace for one hour. Then, the material was cooled in the furnace or in air, respectively. Therefore, there were 9 materials in the group of the flake graphite cast irons without chill. There were other sets of flake graphite cast iron materials which include chill: I-1 and I-2. They included different contents of chill. The molten metal of cast iron in the group of I-1 and I-2 was same as FC250 and FC150, respectively. In order to obtain chill, following casting process were carried out. Source material, consisting of pig iron, ferrosilicon, electrolytic manganese and electrolytic iron, was melted at 1500 oC. The chemical composition of materials was controlled by retention time of molten metals at 1500 oC. As retention time of the molten metal at 1500 oC increase, CE value, which is defined by 1 CE mass %C  ( mass % Si  mass % P ) (1) 3 was decreased, and chill was obtained more easily. Chill contents were increased from I-1-1 material to I-1-3 one. It is same on the group of I-2 materials. There was no inoculant into molten metals. Microstructures of the flake graphite cast iron materials were observed by optical microscope to evaluate the size, the shape and the contents of graphite and matrices in

64

T. Uchimoto et al. / Evaluation of Chill Contents in Flake Graphite Cast Irons

them. Pearlite was etched by picric acid ethanol. Some representative photographs are shown in Figure 1. The photos of all materials were analyzed and the areas of each matrix and graphite were quantified. Graphite area was calculated from the photos of the microstructure before etching, and that of matrices was quantified from the picture of microstructure after etching. The contents of graphite and matrices in the materials are summarized in Table 2.

Table 1 Chemical composition of materials. C%

Si%

Mn%

P%

S%

CE%

FC150

3.77

2.78

0.78

0.025

0.015

4.71

FC200

3.36

2.15

0.69

0.018

0.01

4.08

FC250

3.13

1.66

0.72

0.017

0.002

3.69

I-1-1

3.40

1.81

0.66

0.016

0.008

4.01

I-1-2

3.23

1.84

0.66

0.016

0.009

3.85

I-1-3

3.01

1.84

0.66

0.016

0.009

3.63

I-2-1

3.99

2.59

0.77

0.025

0.011

4.86

I-2-2

3.78

2.62

0.77

0.025

0.010

4.66

I-2-3

3.48

2.63

0.76

0.024

0010

4.36

Table 2 Contents of graphite and matrices in each material. Graphite%

Ferrite%

Pearlite%

Chill%

FC150 as cast

11.8

11.3

72.4

0.00

FC150 furnace

13.6

69.3

17.1

0.00

FC150 air

11.1

8.85

71.0

0.00

FC200 as cast

8.25

6.60

85.2

0.00

FC200 furnace

6.45

78.5

15.1

0.00

FC200 air

6.45

4.45

89.1

0.00

FC250 as cast

4.33

3.50

92.2

0.00

FC250 furnace

4.65

40.5

54.9

0.00

FC250 air

4.50

5.20

90.3

0.00

I-1-1

0.45

0.00

68.2

22.9

I-1-2

0.17

0.00

71.5

28.3

I-1-3

0.25

0.00

76.8

31.4

I-2-1

16.4

0.00

75.5

8.1

I-2-2

6.54

0.00

78.5

15.0

I-2-3

1.78

0.00

77.0

21.2

T. Uchimoto et al. / Evaluation of Chill Contents in Flake Graphite Cast Irons

(1)G FC150 as cast sample (before etching)

65

(2)G FC150 as cast sample (after etching)

(3)G I-1-1 sample (before etching) (4)G I-1-1 sample (after etching) Figure. 1 Microstructure in flake graphite cast iron.

3. Magnetic Properties Magnetization curve was measured by the B-H analyzer. The B-H analyzer is composed of pickup coils and an exciting coil. Cylindrical sample is inserted in pickup coil. AC current flowing in an exciting coil generates uniform magnetic field around a sample. Magnetization process in the sample is obtained by a signal of pickup coil. Some parameters such as loop area, remanence and coercivity are calculated from the hysteresis curves obtained by the B-H loop analyzer. The cylindrical samples were processed from the materials. Length and diameter of samples were 30 mm and 3 mm, respectively. Hysteresis curve was measured at the frequencies of 10 Hz and 100 kHz. In the case of 10 Hz, we consider that the measurements are quasi-static, and demagnetizing field correction was made to measured loops. In the case of 100 kHz, no correction was made, which means that the loops should be compared relatively. Figure 2 shows hysteresis curves of some samples at the frequency of 100 Hz. Shape of Magnetization loop depend on the contents of matrices and graphite. Especially, magnetic flux density of the sample without chill at relatively high magnetic field increases with decreasing graphite contents. However, magnetic flux density of I-1-1 sample is relatively small in spite of its low graphite contents. It was found that the sample with chill possesses specific difference from other sample without chill in

T. Uchimoto et al. / Evaluation of Chill Contents in Flake Graphite Cast Irons

/ CIPGVKEHNWZFGPUKV[ ) 

    

(% CUAECUV (% CUAECUV (% CUAECUV + +

       









 

/ CIPGVKE(KGNF 1 G

Figure 2. B-H characteristics at the frequency of 10Hz.



.QQRCTGC ,O 

  

(% CUECUV (% HWTPCEG (% CKT (% CUECUV (% HWTPCEG (% CKT (% CUECUV (% HWTPCEG

   

(% CKT + + + + + +

        

* CTFPGUU* 8

Figure 3. Relation between loop area and hardness at the frequency of 10Hz. 

 / CIPGVKEHNWZFGPUKV[ ) 

66

 

(% CUAECUV (% CUAECUV (% CUAECUV + +

     



   / CIPGVKEHKGNF 1 G



Figure 4. B-H characteristics at the frequency of 100 kHz.

T. Uchimoto et al. / Evaluation of Chill Contents in Flake Graphite Cast Irons

67



 (% CUAECUV (% CKT (% HWTPCEG + (% CKT + (% CUAECUV + (% HWTPCEG + (% CKT + (% CUAECUV + (% HWTPCEG

 



.QQRCTGC,O 



  



  * CTFPGUU* 8 





Figure 5 Relation between loop area and hardness at the frequency of 100kHz.

magnetic characteristics. Hardness of a cast iron mainly depends on both chill and graphite contents. Focusing on the fact, the loop area calculated from hysteresis curve was evaluated as function of hardness of the sample. There is little correlation between the hardness and loop area of each specimen. Figure 4 presents hysteresis curves of the same sample shown in Figure 2 at the frequency of 100 kHz. Shape of magnetization loop is also related to the contents of matrices and graphite. Loop area of hysteresis curve of each sample was also evaluated as function of hardness in Figure 5. In contrast with the relation at 10 Hz, they decreased linearly as hardness increases. The set of samples plotted in Figure 5 includes flake graphite cast iron samples without chill structure, FC150, FC200 and FC250 as well as ones with chill structure. In addition, each series of FC150, FC200 and FC250, which has different graphite shapes, includes samples with different matrices owing to heat treatments. Therefore, hardness of the samples reflects chill contents, graphite shapes and matrices, which implies that loop area at relatively high frequencies depends on chill contents, graphite shapes and matrices. Since there is no correlation between loop area and hardness at low frequency, linear correlation between them at relatively high frequencies is due to effects of eddy currents which depends on permeability and conductivity. Permeability and conductivity of all samples were measured the by BH analyzer and four-terminal method, respectively. Both of them do not have any correlation with hardness. Its mechanism should be complicated since eddy currents flows in heterogeneous media consisting of different types of matrices and graphite structures, which will be discussed in future.

4. AC Magnetization Method Based on the finding acquired from the evaluation of magnetic properties by means of B-H analyzer, AC magnetization method was applied to evaluation for chill contents, and its feasibility was discussed. Schematic drawing of experimental setup is shown in Figure 6. The probe consists of two coaxial pancake coils with a ferrite core; upper coil is an exciting coil, and lower one is a pickup coil. A ferrite core is put to obtain

T. Uchimoto et al. / Evaluation of Chill Contents in Flake Graphite Cast Irons

Function generator

FFT analyzer PC

exciting ferrite exciter detector sample pickup Figure 6 Experimental setup for AC magnetization method.

2 KEMWR 8 



(% CUECUV

         'ZEKVG 8 





Figure 7. Hysteresis equivalent curve at the frequency of 3kHz.

13.0

FC150 as_cast FC150 furnace FC150 air FC200 as_cast FC200 furnace FC200 air FC250 as_cast FC250 furnace

12.5 2

Loop area (V )

68

FC250 air I-1-1 I-1-2 I-1-3 I-2-1 I-2-2 I-2-3

12.0

11.5

11.0

100

200

300

400

500

Hardness HV

Figure 8. Relation between loop area of lissajous and hardness.

T. Uchimoto et al. / Evaluation of Chill Contents in Flake Graphite Cast Irons

69

stronger magnetic field. AC current flowing in exciting coil induces AC magnetic field into a sample. Magnetization process of the sample is detected by the voltage of a pickup coil. Changes of hysteresis curve were easily acquired by plotting lissajous waveform composed of signals of an exciter and a detector (hysteresis curve equivalent), and amplitude of 3rd harmonic wave acquired by a signal of pickup coil. The samples were large enough not to neglect edge effect of them. Outer and inner diameter of exciting coil and pickup one is 8.4 mm and 5.4 mm, height is 4.25 mm and turn number is 150. Applied voltage was 5 V, and measurement was carried out at 3 kHz. Figure 7 shows hysteresis curve equivalent measured from the sample of FC150 as cast. We investigated relationship between the amplitude of 3rd harmonics and hardness. Correlation between them was not confirmed. Figure 8 shows relation between hardness and loop area calculated from the hysteresis curve equivalent obtained from each sample. Tendency of decrease in loop area accompanied with decrease in hardness indicates the feasibility of evaluation of hardness. It is expected that correlation between hardness and loop area improves due to accurate evaluation of loop area accomplished by optimization of the measurement condition.

5. Summary In this paper, dependence of chill contents on magnetic properties was discussed through investigation of magnetic properties of flake graphite cast iron with different chill contents. Based on the insight obtained from the investigation, AC magnetization method was applied to evaluation for chill contents. As the results, it was found that the loop area of hysteresis curve equivalent has correlation with hardness which reflects chill contents, which implies the feasibility of nondestructive evaluation for chill contents by AC magnetization method. Acknowledgements This work is partially supported by New Energy and Industrial Technology Development Organization, Japan, Industrial Technology Research Grant Program, “Characterization of microstructure of advanced cast iron for energy-saving automobile based on multi-scale electro magnetic approach”, 04A48512. The author appreciates many supports by Tsutomu Watanabe and technical staffs in the Institute of the Fluid Science in processing the samples prepared in this study. References [1] [2] [3] [4]

Handbook of foundry engineering (MARUZEN). J.JFS, 2002, 227 T. Nagai, M. Uemura, J. Fujioka, H. Hattori. J.JFS. 2004, 76(6), 440-446 T. Abe, T. Uchimoto, T. Takagi, S. Tada. J.JFS. 2003, 75(10), 675-681 T. Uchimoto, T. Takagi, S. Konoplyuk, T. Abe, H. Huang and M. Kurosawa. Journal of Magnetism and Magnetic Materials, 2003, 1(258-259), 493-496 [5] S. Konoplyuk, T. Abe, T. Uchimoto, T. Takagi, M. Kurosawa, NDT&E International, 2005, 38(2005), 623-626 [6] G. Vértesy, T. Uchimoto, T. Takagi, I. Tomáš, O. Stu-pakov, I. Mészáros, J. Pávó, Physica B, 372(2006), 156-159 [7] M. Kurosawa, T. Uchimoto, T. Abe, T. Takagi, T. Sato, H. Kage, T. Noguchi, J.JFS. 2005, 77(12), 826832

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Electromagnetic Nondestructive Evaluation (XI) A. Tamburrino et al. (Eds.) IOS Press, 2008 © 2008 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-58603-896-0-70

Characterisation of Microstructures in Heat Treated Maraging Steel using Eddy Current and Barkhausen Emission Techniques K.V. Rajkumar, B.P.C. Rao, B. Sasi, S. Vaidyanathan, T. Jayakumar and Baldev Raj Nondestructive Evaluation Division, Indira Gandhi Centre for Atomic Research, Kalpakkam 603102, India; Phone: 91 44 27480232; Fax: 91 44 27480356; email: [email protected] Abstract. The effects of ageing induced microstructural changes in M250 Maraging steel widely used in aerospace industries are characterized using electromagnetic nondestructive evaluation (NDE) methods. Eddy current and magnetic Barkhausen emission parameters have been studied and the results are compared with hardness, XRD and transmission electron microscopy (TEM). Keywords. Maraging steel, NDE, Eddy current, Barkhausen emission, Microstructure

Introduction Maraging steel is one of the most preferred structural materials for critical application in aerospace industries due to its excellent mechanical properties [1]. The aging behaviour of the maraging steels has been extensively studied [2-6]. M250 maraging steel components are subjected to solution annealing (SA) at 1093 K for 1 h followed by aging at 755 K for 3-10 h. This heat treatment produces the best combination of mechanical properties i.e. ultra high strength coupled with good fracture toughness due to the precipitation of intermetallic phases in low carbon soft martensitic matrix [5-6]. The early aging period comprises of recovery of martensitic structure and hardening due to precipitation of hexagonal Ni3Ti intermetallic precipitates. The intermediate aging duration is characterized by reversion of austenite accompanied by precipitation of hexagonal Fe2Mo intermetallic phase. As these two processes occurring during the intermediate aging drastically affect the hardening in opposite manner, overall hardening levels off after reaching a maximum. Decrease in hardening, observed during longer aging durations is attributed essentially to the formation of reverted austenite rather than the precipitate coarsening. The amount of reverted austenite is reported to increase with increase in aging temperature (upto ~ 900 K) and time [2]. Hence, this regime is of great technological importance. Quantitative characterization of microstructures using particularly, electromagnetic (NDE) methods is of much practical interest. These techniques exploit measurements of changes in

K.V. Rajkumar et al. / Characterisation of Microstructures in Heat Treated Maraging Steel

71

electrical and magnetic properties of materials. Among others eddy current (EC) and magnetic Barkhausen emission (MBE) techniques are preferred, essentially because they are non-contact in nature, sensitive, versatile and field employable. The present study attempts to investigate the effects of aging induced microstructural changes on the eddy current and Barkhausen emission measurements for exploring the possibility of using these methods in shop-floor for verifying the adequacy of heat treatment. Observations of the electromagnetic methods are correlated with hardness, X-ray diffraction (XRD), selected area diffraction (SAD) and transmission electron microscopy (TEM) data.

Figure1. Schematic of experimental setup used for eddy current testing and detailed dimensional drawing of T/R probe.

1. Experimental The chemical composition (wt %) of the maraging (M250) steel used in this study is as follows: 17.89 Ni, 8.16 Co, 4.88 Mo, 0.43 Ti, 0.05 Mn, 0.05 Cr, 0.05 Si, 0.05 Cu, 0.096 Al, 0.003 C, balance Fe. A plate of M250 maraging steel was solution annealed at 1093 K for 1 h followed by air cooling. Specimens of dimensions 30x25x7 mm3 cut from the solution annealed plates, were encapsulated in quartz tubes under vacuum and aged at 755 K for different durations of 0.25, 1, 3, 10, 30, 40, 70 and 100 h followed by water quenching. The eddy current measurements were carried out at 100 kHz using a transmitreceive coil (T/R) type eddy current probe (Figure 1). The EC measurements were carried out after balancing the probe in air and phase angle of induced voltage was adjusted such that the signal of reference stainless steel (SS) 304 specimen was along the positive side of the X-axis [7, 8]. For MBE measurements, the samples were subjected to a continuously varying cyclic magnetic field in an electromagnetic yoke with a period of 10 s. The current from the sweep controller circuit was fed to a bipolar high current generator to generate a symmetrical bipolar triangular field. The applied magnetic field H A was measured at the centre of the yoke using a Hall probe (Walker Scientific) connected to a Gauss meter (MG-50 Walker Scientific). The maximum field was set to 1500 Oe for complete magnetic saturation of the specimen. This corresponds to magnetization field strength (H) of 1,20,000 A m-1. Calibration of HA was made with respect to the current applied

72

K.V. Rajkumar et al. / Characterisation of Microstructures in Heat Treated Maraging Steel

to the yoke. The tangential magnetic field HT was measured near the sample surface. Magnetic Barkhausen emission measurements were performed using an encircling pick up coil (5000 turns). The MBE signal was amplified using a low noise pre-amplifier and a post amplifier (80 dB). The magnetic flux density was measured using a 20 turn coil closely wound on the sample connected to a flux meter (Walker Scientific MF5DP). The output voltage signals for all the magnetic parameters were suitably conditioned for digitization using PC based data acquisition. XRD measurements were carried out for estimation of volume fraction of reverted austenite using MAC Science MXP18 X-ray diffractometer with Cr Kα radiation in the complete angular range of 60-130°. Vicker’s hardness measurements were carried out on these specimens at 10 kg load. Averages of five hardness measurements have been made for each specimen. The maximum scatter in the hardness measurements was found to be ± 5 HV10.

2. Results and Discussion Variation in hardness, volume fraction of reverted austenite and resistivity reported in [3] with aging time are shown in Figure 2. The resistivity curve shows continuous decrease up to 40 h and then leveling off at long aging duration (beyond 40 h). The initial decrease is attributed to the recovery (that includes the removal of quenched in point defect and annihilation of dislocations) in martensite matrix and due to accumulation of solute atoms on dislocations in martensitic matrix. Further decrease in the resistivity and increase in permeability at intermediate durations is attributed to the intermetallics precipitation which is also accompanied by increase in the hardness. The leveling off, observed at longer aging periods (beyond 40 h) is attributed to net manifestation of two opposing mechanisms occurring simultaneously i.e. precipitation and austenitic reversion (decreases hardness).

30

1

10

100

1000

Vol.% of austenite Hardness Resistivity

SA

20

Hardness, HV10

Vol. % of austenite

25

15 10 5

650

0.65

600

0.60

550 500 450

Resitivity (μohm-M)

0.25

35

0.55 0.50 0.45

400

SA

0.40

0 0.25

1 10 Aging time, h

100

350

Figure 2. Variation of hardness, electrical resistivity and volume percent of austenite with aging time (resistivity data is taken from [3]).

Imaginary component of induced voltage, volts

K.V. Rajkumar et al. / Characterisation of Microstructures in Heat Treated Maraging Steel

73

2.5

μr

2.0 Ferrite

SA 0.25h 1h 3hrs 10hrs 30hrs 40hrs 70hrs 100hrs Reference

ρ

1.5 1.0

Carbon steel

0.5 θ

0.0

SS 304

Air

Al 3003

-0.5 -1.0

-0.5

0.0

0.5

1.0

1.5

2.0

ρ 2.5

Real component of induced voltage, Volts

Figure 3. Variation of EC induced voltage in receiver coil with aging time. The complex plane diagram of induced voltage obtained for heat treated maraging steel specimens is shown in Figure 3. The induced voltage is segregated into two distinct clusters marked in square and oval and they are found to be in the second and first quadrant, respectively. The location of these two clusters confirms that the specimens are ferro-magnetic. Cluster in the second quadrant (marked as square) corresponds to ferromagnetic induced voltage of specimens aged up to 10 h and the cluster in the first quadrant (marked as oval) correspond to samples beyond 10 h of aging. Formation of two clusters is essentially due to two distinct microstructural evolution taking place during aging and the associated changes in the resistivity and the permeability. The magnitude and phase angle of the induced voltage are determined and are shown in Figure 4a for various specimens. It can be seen that both magnitude and phase angle are influenced by microstructure changes and their trends are nearly identical. The EC induced voltage is found to increase initially from solution annealed (SA) condition to 0.25 h of aging and then continued to decrease gradually upon aging further up to 10 h. Aging between 10h and 30 h showed a drastic drop in magnitude and phase angle of induced voltage and which continued to drop further gradually in the aging regime of 30-70 h. Beyond 70 h, a drastic drop in induced voltage was noticed. The changes observed in EC parameters can be explained as follows: The initial aging regime (SA-10h) is primarily characterized by dislocation annihilation and precipitation of Ni3Ti intermetallics typically shown in Figure 5a by TEM studies. Annihilation of dislocation is attributed to increase magnetic permeability and reduction in resistivity. Increase in magnetic permeability (associated with dislocation annihilation), as reported by Sablik et al. [9], tries to increase the induced voltage while decrease in resistivity, associated with the precipitation of intermetallics and dislocation

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annihilation, tries to decrease the induced voltage. The changes in induced voltage observed for initial aging regime from SA-10 h hence, can be understood in terms of net manifestation of two opposing mechanisms i.e. dislocation annihilation and intermetallic precipitation. The larger decrease in EC parameters for specimens aged to 30h is attributed to initiation of non-magnetic reverted austenite in addition to the continuous precipitation of intermetallics (Ni3Ti and Fe2Mo). Non-magnetic austenite phase lowers the overall permeability and simultaneous precipitation of intermetallics decreases the resistivity, both contributing to drastic decrease in EC parameters. The presence of reverted austenite has been reported detrimental to toughness due to the deformation concentration at softer austenite, which reaches its critical strain of fracture at early stage. Hence, the microstructures containing austenite are avoided and this can be ascertained by using either of the EC parameters with appropriate thresholds. The regime of technological importance (3h-10h) can also be identified by specifying the corresponding EC parameters as they exhibit monotonous decrease in this regime in Figure 4a. Between 30h and 70h, the EC induced voltage again changed very gradually showing that the microstructural feature changes occurring do not influence the EC induced voltage substantially. This is attributed to subtle increase in the volume fraction of reverted austenite formed along with the precipitation, as evident from austenite and hardness measurements in Figure 2. For the aging regime 70-100 h, since the resistivity values Figure 2 remain almost constant, the observed drastic decrease in the EC parameters is attributed to larger reduction in overall permeability due to larger volume fraction of reverted austenite as evident from the XRD results in Figure 2. This study reveals that both magnitude and phase angle of induced voltage can be used as NDE parameters for characterization of the microstructures of M250 steel. Further, time for each measurement is less than 1 second. As compared to phase angle, measurement of magnitude of induced voltage is accurate and easy. It is also easy to implement the EC method in production line using portable eddy current instruments and probes. Thus, this method holds a great promise for quick and reliable characterization of microstructures in components in shop-floor for ensuring heat treatment adequacy. 2.4

1

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(a) (b) Figure 4. (a) Variation of induced voltage magnitude and phase angle with aging time and (b) variation in rms voltage of MBE signal with aging time.

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(A)

(B) (C)

0.5 μm (a)

0.5 μm (b)

Figure 5. (a) Bright field TEM image of specimen solution annealed at 1093 K for 1 h followed by air cooling (showing high dislocation density) (b) Bright field image of the specimen thermally aged at 755 K for 100 h followed by water quenching, showing long and patchy austenite (marked as A), patchy Ni3(Ti, Mo) (marked as B) and globular Fe2Mo (marked as C). The MBE rms peak voltage was found to vary with aging time as typically shown in Figure 4b and the MBE trends were almost identical to eddy current measurements. The MBE rms peak voltage remained almost constant from solution annealed condition to 10 h of aging and dropped drastically on further aging. The solution annealed microstructure is characterized by the martensitic lath/grain boundaries. In this condition, the magnetic domains have to cross several martensitic lath/grain boundaries before they give a detectable signal at the sensor coil. The constant MBE rms peak voltage obtained from SA condition to 10 h of aging can be attributed to the two opposing mechanisms taking place simultaneously i.e. dislocation annihilation and intermetallic precipitation. Martensitic recovery, due to the annihilation of dislocations occurring during initial aging is expected to increase the MBE by reducing the number of pinning sites for domain wall motion. However, this regime is also characterized by the continuous precipitation of intermetallics. Aging in this regime results in increase in the precipitates which act as strong pinning sites to domain wall motion, thereby reduction in MBE rms peak voltage is expected. The drastic decrease in MBE rms peak voltage beyond 10 h of aging is attributed to the initiation of the reversion of non-magnetic austenite phase. It is evident from the TEM studies that austenite is formed at martensitic lath /grain boundaries. The austenite formed at these lath and grain boundaries make these region nonmagnetic, which cannot be easily surmounted by the growing/moving magnetic domains. Moreover, the non-magnetic austenite phase is expected to be surrounded by stable closure domains. Under these conditions, magnetization reversal can only advance in

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limited volume fraction of the specimen at any given instant and the actual fraction depends on the amount of reverted austenite. Aging for longer durations results in increase in the volume fraction of the austenite, which further decreases the MBE rms peak voltage. The evidence for increase in austenite volume percent is obtained from XRD analysis (Figure 2) and TEM studies (Figure 5b). Hardness and magnetic parameters exhibited different behaviour upon aging. Hardness increased with the precipitation of intermetallic phases and decreased with the reversion of austenite. The MBE rms peak voltage was found to be highly sensitive to austenite reversion and was however insensitive to intermetallics precipitation during aging. Hardness was found to be influenced more by the intermetallic precipitates as compared to austenitic phase reversion. The reversion of austenite at 30 h of aging could not be identified by the hardness due to simultaneous precipitation of intermetallics, which tend to increase the hardness. The regime of technological importance 3-10 h could not be identified by hardness or MBE parameter alone. However, the study clearly revealed that the combination of these two parameters, i.e. by specifying a minimum hardness (564 VHN) and a minimum MBE rms peak voltage (1.8V) can be used for unambiguous characterization of the microstructure of technological importance in M250 maraging steel [10].

3. Conclusion The present study investigated the influence of microstructural features evolved upon aging of M250 maraging steel at 755 K for different durations on electromagnetic NDE (eddy current and MBE) parameters. In eddy current method both magnitude and phase angle of induced voltage of receiver coil were found to be sensitive to the microstructure changes through electrical conductivity and magnetic permeability. The EC parameters could distinctly identify the over-aging due to austenite reversion, a non-magnetic phase in magnetic matrix. The dislocation annihilation and intermetallics precipitation were also found to influence the EC parameters. For the first time, it has been observed that using EC parameters it is possible to study the recovery (i.e. removal of quenched-in point defect and annihilation of dislocations) during initial aging which increases the magnetic permeability and decreases resistivity. The monotonous decrease in EC parameters can be effectively used to identify the aging regime of technological importance (3-10h) at 755 K. The MBE rms peak voltage was also found to be highly sensitive to austenite reversion and was however insensitive to intermetallics precipitation during aging. Hardness was found to be influenced more by the intermetallic precipitates as compared to the austenitic phase reversion. The reversion of austenite at 30 h of aging could not be identified by the hardness due to simultaneous precipitation of intermetallics, which tend to increase the hardness. The regime of technological importance 3-10 h could not be identified by hardness or MBE parameter alone. However, the study clearly revealed that the combination of these two parameters can be used for unambiguous characterization of the microstructure of technological importance in M250 maraging steel. The study also established that electromagnetic non destructive methods hold good promise for shop floor assessment of heat treatment adequacy.

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Acknowledgements Authors thank Dr. P. Shankar, Dr. Anish Kumar and Mr. S. Mahadevan of Indira Gandhi Centre for Atomic Research (IGCAR), Kalpakkam, India for many useful discussions. References [1] [2] [3] [4] [5]

G.P. Miller, W.I. Mitchell, J. Iron Steel Inst. 203 (1965) 899-904. D.T. Peters, C.R. Cupp, Trans. Met. Soc. AIME 236 (1966) 1420-1429. V.K. Vasudevan, S.J. Kim, C.M. Wayman, Metall. Trans. A 21, (1990) 2655-2668. W. Sha, A. Cerezo, G.D.W. Smith, Metall. Trans. A 24 (1993) 1221-1232. R.F. Decker, S. Floreen, IN: R.K. Wilson (Ed.), Maraging Steels: Recent Developments and Applications, TMS-AIME, Warrendale, PA, (1988) 1–38. [6] Z. Guo, W. Sha, D. Vaumousse, Acta Mater. 51 (2003) 101-116. [7] B.P.C. Rao, Introduction to eddy current testing, Narosa Publishing, New Delhi, April, 2007 [8] K.V.Rajkumar, B.P.C. Rao, B.Sasi, Anish Kumar, T.Jayakumar, Baldev Raj and K.K. Ray, Materials Science and Engg. A 464 (2007) 233-240. [9] M.J. Sablik, J. of Appl. Phys. 89 (10) (2001) 5610-5613. [10] K.V. Rajkumar, S. Vaidyanathan, Anish Kumar, T. Jayakumar, Baldev Raj and K.K. Ray, J. of magnetism and magnetic materials 312 (2007) 359-365.

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Electromagnetic Nondestructive Evaluation (XI) A. Tamburrino et al. (Eds.) IOS Press, 2008 © 2008 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-58603-896-0-78

Novel Acoustic Barkhausen Noise Transducer and its Comparison with Electromagnetic Acoustic Transducer John WILSON1, Gui Yun TIAN1, Rachel S. EDWARDS2 and Steve DIXON2 School of Electrical, Electronic and Computer Engineering, Newcastle University, NE1 7RU, 2Department of Physics, University of Warwick, Coventry, CV4 7AL

1

Abstract

The analysis of magnetic Barkhausen noise (MBN) has been used to provide information about the stress state and microstructural properties of ferromagnetic materials. Recent work has shown that a technique using acoustic Barkhausen noise (ABN) detection can provide the similar capabilities as traditional MBN along with additional information for defect characterisation and thickness measurement in a single system. Because the detection of ABN using a piezoelectric sensor can be carried out at any point on the material surface, as well as analysing ABN for microstructural characterisation, the interaction of the surface propagating waves with defects can also be analysed and used for defect characterisation, along with frequency analysis for thickness measurement. As with electromagnetic acoustic transducer (EMAT) systems, the ABN technique applies totally different physical principles to traditional ultrasonic methods and couplant is not needed for excitation. The work is carried out through experimental investigations of calibrated steel samples with machined defects using the ABN system, in comparison to readings taken using an EMAT system. Test results show that the ABN technique has potential applications in providing a comprehensive system for material and stress characterisation along with the additional capabilities of defect characterisation and material thickness measurement.

Introduction The inspection of ferromagnetic structures such as oil and gas pipeline [1], rail track [2] or ferromagnetic components in manufacturing is a common requirement in industry, and there is wide need for accurate defect detection and characterisation apparatus for the prediction of failure in ferromagnetic engineering structures and components. This is to some degree addressed by current inspection techniques, but each method has drawbacks, for example magnetic flux leakage (MFL) has good detection capabilities, but there is difficulty in extracting accurate characterisation data [1], although the recently introduced pulsed MFL (PMFL) system has improved the potential capabilities of MFL [3]. A reasonable standard of detection and characterisation can be achieved with ultrasonic testing [2, 4-12], but with some limitations for standard contact ultrasonic measurements. This has led to the development of alternative non-contact excitation techniques.

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Acoustic sources for ultrasonic NDE fall into two categories: contact techniques requiring direct acoustic coupling between the source and the material under inspection, and non-contact techniques. The major drawback of contact transducers is the need to provide acoustic coupling between the element and the material under inspection, so real world inspections usually require extensive surface preparation and removal of coatings adding to time and expense. There are clear advantages in techniques where physical contact between transducer and the area under inspection is not required. Techniques used to address the problem include guided wave technology [4], where the sensors are located remotely to the area under inspection, water coupled systems [5, 6], where the material and transducer are immersed in a water tank, pulsed laser generation of ultrasonic sources [7, 8] and air coupled systems [9,10]. The major drawback of an air-coupled system is the miss-match in acoustic impedance between air and solid materials [9], meaning that overall path losses for an air coupled system can be 100dB + higher than water coupling, with the greatest losses occurring with ferrous metals [10]. In contrast to other non-contact techniques, electromagnetic acoustic generation opens up opportunities for ultrasonic generation without direct access to the material surface [11]. As coupling between transducer and material is provided electromagnetically, inspection through coatings and corrosion layers is possible and coupling can be established to materials with irregular surface geometry. The most commonly used electromagnetic ultrasonic source is the electromagnetic acoustic transducer (EMAT) [2, 11, 12]. EMAT transducers consist of an excitation coil driven by a current pulse in the presence of a static magnetic field. In non-magnetic conductive materials such as aluminium, application of a current pulse to the coil in presence of the permanent field causes Lorentz forces in the material, which in turn generate acoustic waves. In magnetic and conductive materials such as steel, magnetostrictive effects occur in addition to Lorentz forces. Although EMATs provide a solution to the coupling problem in electrically conductive and magnetic materials, the ultrasonic generation efficiency of an EMAT is much lower than that of a piezoelectric transducer. In this paper, a new electromagnetically generated acoustic source for ferromagnetic materials is proposed utilising acoustic Barkhausen noise (ABN). As well as providing a non-contact excitation method for ultrasonic investigation, ABN uniquely carries information about the stress and microstructure of the material within the signal itself. The technique has the potential to provide an affordable, low power, non-contact solution for electromagnetically induced acoustic defect assessment with the potential to also supply stress and material characterisation data.

1. Experimental Investigation of ABN for Acoustic Source Generation When a time varying magnetic field is applied to a ferromagnetic material, the induced magnetism is not continuous; rather, it is made up of jumps in magnetisation corresponding to domain wall movement, this can be detected by a pick-up coil or magnetic field sensor and is known as magnetic Barkhausen noise (MBN) [13]. This domain wall motion also causes a release of elastic energy which manifests itself as an acoustic pulse and can be measured using a piezoelectric sensor; this is known as magneto-acoustic emission (MAE) [14] or ABN [15]. As magnetic domain structure is

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intrinsically linked material microstructure, MBN and ABN are sensitive to material stresses and changes in microstructure [13-15]. This work extends ABN beyond microstructure and stress characterisation to provide defect assessment capabilities using broadband excitation. In contrast to EMATs and most other excitation techniques, the frequency of the measured signal is dependant, not on excitation frequency, but on the frequency of the elastic energy released by domain wall movement. Low frequency excitation can be used, thus dramatically reducing the comparative power consumption of the system.

(a)

(b)

Figure 1: a) Probe design, b) One repetition of positive half cycle of pulsed ABN and excitation signal, with calculated signal profile

The experimental probe is shown in figure 1a. A ferrite core is mounted on the sample under inspection. A piezoelectric sensor is mounted on the material surface with petroleum jelly used to provide acoustic coupling between the sensor and the material. Pulsed excitation is applied to the ferrite core and data acquired from the sensor and the excitation current simultaneously at a sample frequency of 2MHz. In this work, a piezoelectric Physical Acoustics R15I-AST integral preamplifier acoustic emission receiver is used; the sensor is resonant at 150kHz, with a useable frequency range of around 50kHz – 200kHz and a total gain of 72dB is applied to the signal. Figure 1b shows one repetition of the positive half cycle of the pulsed excitation waveform and the associated ABN signal. Several signal processing techniques are used in the work; the most basic of these is calculation of the signal profile or envelope by rectification followed by a moving average calculation as shown in figure 1b. 1.1. Characterisation of ABN signal In an ultrasonic defect detection system, the minimum detectable defect depth is proportional to the wavelength of the signal being measured, so knowledge of the frequency range of the acoustic source is vital for the developed system, but the frequency spectrum of ABN has not been widely studied. Figures 2a and 2b show FFT envelopes for two different materials; a 60mm x 60mm x 1000mm steel block and a 1mm thick mild steel sheet. Sine wave excitation was used in the test, with the ABN signal from six different frequencies from 2Hz to 1kHz recorded for comparison. It can be seen from the plots that the basic distribution of frequency components remains the

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same regardless of excitation frequency, although there is a change in amplitude over the excitation frequencies used. This is as expected, as the frequency spectrum of ABN is dependant on the frequency of the elastic wave released by the motion of the domain wall, not the excitation frequency. FFT ENVELOPES: SINE EXCITATION, STEEL PLATE -2 10

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Comparison of figures 2a and 2b show that, although material properties will certainly play a part in the ABN frequency response, for these unstressed samples, material dimensions have a much greater influence on the frequency spectrum of the induced signal than excitation frequency. With the thicker sample, the lower frequency portion of the signal is enhanced. This is due to the reinforcement of frequency components with wavelengths corresponding to the material dimensions. So at an estimated signal velocity of 3000 m/s, with the 60mm sample the frequency component corresponding to a wavelength of 60mm is 3000 / 0.06 m = 50 kHz and the frequency component corresponding to half the wavelength is 100 kHz. It can be seen from the plot that these areas of the plot are indeed enhanced for the thicker sample. For the thinner sample, the frequency component corresponding to a wavelength of 1mm is 3000 / 0.001 m = 3 MHz, well out of the measured range, so the plot for this sample is much smoother, without the reinforcement of wavelengths corresponding to the thickness of the sample. ABN RMS amplitudes for the frequencies used in the tests are shown in figure 2c. It can be seen from the plot that the ABN amplitude increases as the excitation

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frequency increases. This is due to increasing overlapping of clustered random event outputs as the excitation frequency increases [16]. This increase in ABN amplitude will not continue indefinitely as frequency increases, rather the rate will decrease as the skin-depth effect becomes apparent [16].

2. Application of ABN to defect detection An experiment was set up to assess the capabilities of the system to provide depth information for perpendicular defects in steel. Two samples, shown in figure 3a and 3b, were used, measuring 60mm x 60mm x 600mm (sample 1) and 60mm x 60mm x 1000mm (sample 2). The blocks, contain five 1mm wide defects, with depths of 0.5mm, 2mm, 2.5mm, 3.5mm and 10mm. The test set-up is shown in figure 3c. In these tests a single sensor is used at different distances (d) with respect to slot position, with excitation apparatus kept at a constant distance to the slot. d is given as the distance between the sensor rim closest to the slot and the slot under inspection, at no time in the tests is the sensor actually over the slot. The peak signal strengths for sensor positions from d = 10 to d = -10 are shown in figure 3e. It can be seen from figure 3e that the peak amplitude for all but the 2mm slot shows a maximum at d = 0 or d = 1. The EMAT normalised signal amplitude on approaching a 3mm deep slot in a steel sample is shown in figure 3f [11]. A signal enhancement is also observable in EMAT systems close to material voids where reflections and mode conversions from the slot interfere with the direct signal, as shown in figure 3f [11]. The proportion of transmitted surface wave energy will depend on the crack depth and the wavelengths within the broadband signal, through the transmission coefficients [12]. FFTs were calculated from the AE sensor signals, for four slot depths, and the mean frequencies calculated, as shown in figure 3d. It can be seen from the plot that for the 2.5mm, 3.5mm and 10mm slots the mean frequency decreases in a fairly linearly as the slot depth increases. This indicates that as slot depth increases, more of the lower frequency signal component is reflected back to the sensor. As defect depth increases, the wavelengths which can be reflected by the defect increase, thus lowering the mean frequency of the reflected wave. As the capabilities of an ultrasonic system with respect to measurable slot depth are dependant on the frequency range of the system, it may be that characterisation of the 2mm slot is beyond the capabilities of the ABN system using this particular sensor. With ultrasonic measurements using a wideband Rayleigh wave pulse, the calculated cut-off frequency of the measured signal has been shown to be proportional to slot depth [12].

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Figure 3: a) Test sample 1, b) Test sample 2, c) Defect location test set up, d) Mean ABN frequency for four slot depths, e) ABN peak amplitude over slot area, f) EMAT amplitude approaching a 3mm deep slot in a steel sample

3. Discussion and Conclusions Several parameters, summarised in figure 4, influence the form of the ABN signal, with the greatest influences coming from material properties, sample geometry and excitation waveform. The peak position of the ABN signal with respect to the excitation cycle is influenced by the excitation signal itself and the domain structure of the material, which affects the domain wall activity at different stages in the hysteresis cycle. By far the greatest influence on ABN frequency spectrum comes from the geometry of the sample, through internal reflections of the acoustic signal, but the domain structure will also have some influence through the types of domain wall which are active in the sample. The overall ABN amplitude is influenced by all three parameters, through the amount of domain activity in the sample, reinforcement of the signal through sample geometry and magnetic field intensity in the sample through the amplitude of the excitation signal. The decay of the ABN signal is greatly influenced by sample geometry through reflections received by the sensor after the main domain wall activity has ceased. ABN peak amplitude is of course affected by the overall amplitude of the ABN signal, but also by the excitation waveform. The higher the rate of change of the signal, the more ABN activity will be contained within the same time period, leading to overlapping of acoustic events.

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Figure 4: Contribution of various factors to ABN signal characteristics

ABN can work as an acoustic source which also carries information on material properties, which is a distinct advantage over current acoustic NDT. Although preliminary test results show that ABN has some promise as an acoustic source, there are several problems with technique; the ABN signal intensity is relatively weak; the signal frequency spectrum is dependent on the frequency of elastic energy from domain wall, not excitation frequency – this could be a problem due lack of controllability, but also means that low frequency excitation tuned to the optimal frequency for maximum power transfer can be used to excite high frequency ABN source; unlike the ultrasonic measurements using EMATs, the mode of propagation of the signal is not fully understood; the ABN signal is made up of many different acoustic events – this could be problematic for processing. A piezoelectric sensor is used for present tests, but for true non-contact operation, a non-contact ABN receiver should be developed. Future tests will be made with “real world” defects such as cracks, voids and dislocations and the limitations of the system ascertained. Although the technique will have limitations in terms of the interaction between the wavelength of the excited signal and defect depth, the change in the ABN signal caused by the interaction between domain walls and defects will be incorporated into future measurements.

References [1]

[2]

[3] [4]

[5]

A.A. Carvalho, J.M.A. Rebello, L.V.S. Sagrilo, C.S. Camerini and I.V.J. Miranda, MFL signals and artificial neural networks applied to detection and classification of pipe weld defects, NDT & E International, Volume 39, Issue 8, December 2006, Pages 661-667. Y. Fan, S. Dixon, R.S. Edwards and X. Jian, Ultrasonic surface wave propagation and interaction with surface defects on rail track head, NDT & E International, Volume 40, Issue 6, September 2007, Pages 471-477. J.W. Wilson and G.Y. Tian, Pulsed electromagnetic methods for defect detection and characterisation, NDT & E International, Volume 40, Issue 4, June 2007, Pages 275-283. A. Demma, P. Cawley, M. Lowe, A. G. Roosenbrand and B. Pavlakovic, The reflection of guided waves from notches in pipes: a guide for interpreting corrosion measurements, NDT & E International, Volume 37, Issue 3, April 2004, Pages 167-180. X. Jian, J.P. Weight and K.T.V. Grattan, Miniature wideband ultrasonic transducers to measure compression and shear waves in solid, Sensors and Actuators A: Physical, Volume 127, Issue 1, 28 February 2006, Pages 13-23.

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R.E. Green, Non-contact ultrasonic techniques, Ultrasonics, Volume 42, Issues 1-9, April 2004, Pages 9-16. B.B. Djordjevic, D. Cerniglia, and C. Cosenza, Guided wave non-contact ultrasonic for NDE, WCNDT 2004. Y. Hong, S.D. Sharples, M. Clark and M.G. Somekh, Rapid and accurate analysis of surface and pseudo-surface waves using adaptive laser ultrasound techniques, Ultrasonics, Volume 42, Issues 19, April 2004, Pages 515-518. E. Blomme, D. Bulcaen and F. Declercq, Air-coupled ultrasonic NDE: experiments in the frequency range 750 kHz–2 MHz, NDT & E International, Volume 35, Issue 7, October 2002, Pages 417-426. J. Buckley, Air-coupled Ultrasound - A Millennial Review, WCNDT 2000. R.S. Edwards, A. Sophian, S. Dixon, G.Y. Tian and X. Jian, Dual EMAT and PEC non-contact probe: applications to defect testing, NDT & E International, Volume 39, Issue 1, January 2006, Pages 45-52. R.S. Edwards, S. Dixon and X. Jian, Depth gauging of defects using low frequency wideband Rayleigh waves, Ultrasonics, Volume 44, Issue 1, January 2006, Pages 93-98. V. Moorthy, B.A. Shaw and P. Hopkins, Surface and subsurface stress evaluation in case-carburised steel using high and low frequency magnetic barkhausen emission measurements, Journal of Magnetism and Magnetic Materials, Vol. 299(2), Apr. 2006, pp. 362-375. D. O'Sullivan, M. Cotterell, D.A. Tanner and I. Mészáros, Characterisation of ferritic stainless steel by Barkhausen techniques, NDT & E International, Volume 37, Issue 6, September 2004, Pages 489-496. G.Y. Tian, J. Wilson and J. Keprt, Magnetic-acoustic Emission for Stress and Material Characterisation, ENDE 2006. H.C. Kim and C.G. Kim, Effect of magnetising frequency and stress on magneto-acoustic emission from 3% Si-Fe crystals, Journal of Physics D: Applied Physics, Volume 22, Issue 1, pp. 192-198 (1989).

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Modelling and Measurement of Decarburisation of Steels Using a Multifrequency Electromagnetic Sensor X.J. HAOa,1 , W. YINb, M. STRANGWOODa, A.J. PEYTONb, P.F. MORRISc and C.L. DAVISa a Department of Metallurgy and Materials, University of Birmingham, Birmingham, B15 2TT, UK b School of Engineering, University of Manchester, Manchester, M60 1QD, UK c Corus plc. Swinden Technology Centre, Moorgate, Rotherham, S60 3AR, UK

Abstract. Decarburisation of high carbon steel has been simulated, using composite samples comprised of a 316 stainless steel (paramagnetic) core and a surrounding tube of ferritic steel (ferromagnetic) with thicknesses between 100 and 600 μm, for determining the potential for on-line measurement during steel processing. Decarburization samples have also been generated, for off-line measurements, by heat treatment of an Fe-0.8 wt% C steel for various times in air at 1000 – 1200°C. A multi-frequency (10 – 106 Hz) electromagnetic sensor was used to determine variations in inductance (due to differences in permeability) as a function of decarburisation depth. The relationship between sensor output and decarburised layer type/thickness has been modelled using finite element software.

1. Introduction The heat treatment and hot processing of steel usually requires the material to be heated into the austenite phase field, in the temperature range of 800~1200oC. At these temperatures, carbon at the surface can be removed by reaction with oxygen in the surrounding atmosphere and this process is known as decarburisation. Loss of carbon from the surface is more rapid than replenishment by solid-state diffusion, causing a gradient in carbon level from bulk to surface. This effect is greater in higher carbon steels. Loss of carbon at the surface can have a significantly detrimental effect on mechanical properties of products, since hardness, fatigue, strength, and wear properties are strongly dependent on carbon content. Commercially the depth and extent of decarburisation is controlled, which needs accurate measurement of this phenomenon. Currently, measurement of decarburisation is by destructive methods, such as metallographic observation or hardness tests on a cross section of samples after processing. These methods are time consuming and cannot be applied during the production process. This study aims to develop a multi-frequency electromagnetic (EM) sensor to monitor the decarburizing process on-line, and to measure decarburisation depth off-line. Below the Curie temperature (§ 770°C for carbon steel) austenite is paramagnetic and ferrite is ferromagnetic. EM sensors work on the basis of 1

Corresponding author: X.J. Hao, E-mail: [email protected]

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detecting the difference in relative permeability, μR, and conductivity, V, between microstructural phases or due to changes with temperature. An air cored multifrequency EM sensor can measure the ferrite fraction in steel over the entire ferrite fraction range: from 0-40% ferrite fraction through low frequency inductance; and from 40-100% ferrite fraction through the zero crossing frequency, by the differences in effective permeability of the dual phase microstructure [1,2]. Decarburising at high temperature induces a carbon gradient from surface to interior. During cooling from austenite, the surface layer, with low carbon content, transforms first to ferrite whilst the interior transforms to pearlite later. An EM sensor should therefore be able to measure the decarburisation depth by detecting the ferrite fraction gradient. For on-line measurement, if the EM sensor is placed above the steel when it is between the Curie and eutectoid temperatures, any ferromagnetic ferrite surface layer may be detected compared to the paramagnetic austenite core. For off-line measurements differences in permeability between ferrite and pearlite, which are much less than between ferrite and austenite, would need to be detected.

2. Experimental On-line measurement has been simulated using composite samples comprised of a 316 stainless steel (austenite, paramagnetic) core and a surrounding tube of ferritic steel (0.17 wt% C, ferromagnetic). 316 stainless steel bars, 8mm diameter, were inserted into the ferritic steel tubes (8mm inner diameter, 1mm wall thickness) and then cold drawn to 6.7mm (composite bar outer diameter) to increase contact between core and outer layer. The composite bars (300mm length) were straightened and center-less ground to get ferritic layers with thicknesses of about 100, 200, 300 and 600 μm. For off-line measurements, decarburisation samples were generated, by heat treatment of Fe-0.8 wt% C steel bars (10mm diameter, 150mm length) in an air furnace at 1000°C for various times (10min to 5 hours) then cooled in air. Any loose surface oxidation layer was removed by gentle tapping. Transverse microstructures from each sample were examined by optical microscopy after sectioning, polishing and etching using 2% nital. A multi-frequency electromagnetic (EM) sensor was used to determine variations in inductance (due to differences in permeability) as a function of decarburisation depth. Samples were measured by inserting them into the air-cored cylindrical sensor, which had a length of 10mm and diameter of 20mm and was driven using an impedance analyser at frequencies from 10 to 106 Hz. The relationship between sensor output and decarburised layer type / thickness was modelled by finite element method (FEM) using COMSOL Multiphysics [3] software. Sensor 3. Results and discussion

Austenite Hot on-line testing was simulated using the composite bar samples. Microstructure Ferrite: observation of the composite bars has confirmed that the ferrite layer makes good contact with the austenite. The setup for sensor measurement is Figure 1. Setup of sensor/sample shown in Fig. 1, which was used to model the for experiments and modelling

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sensor output with decarburisation depth. -4

10

a

Inductance (H)

8 6 4 2

b

Frequency: 100Hz

1.0

Ferrite layer thickness (Pm) 0 100 200 300 600

10

Normalized Inductance

12

0.8 0.6

Pr

0.4

50 200 1000

0.2

measured

0 -2 1 10

0.0 2

10

3

10

4

10

Frequency (Hz)

5

10

0

6

100

10

200

300

400

500

600

Decarb thickness (Pm)

Figure 2. (a) Measured inductance vs. frequency for composite bars and (b) comparison between measured and modelled results. 5.0

a

10

-4

b

4.8 4.6

Inductance (H)

4.4 4.2 4.0 3.8 3.6 3.4

200Pm

o

At 1000 C for: 10min Increasing 1hr decarburisation 2hrs 5hrs

3.2 3.0 1 10

2

Frequency

10

Figure 3. (a) Microstructure of Fe-0.8wt%C steel after decarburising at 1000C for 2 hours showing surface ferrite (white) and pearlite (black), and (b) measured inductance change with frequency for samples after various decarburising times at 1000°C. The EM sensor output, in terms of inductance versus frequency is shown in Fig. 2(a). The magnetic field produced by an EM sensor acts on a ferromagnetic target in two ways. First it tends to magnetise the metal, which increases the coil’s inductance. Second, the alternating current magnetic field also induces eddy currents in the metal, which tend to oppose the driving current and reduce the coil’s inductance. At low frequencies, magnetisation dominates the inductance. As the frequency is increased, the effects of eddy current become more dominant and the inductance decreases, eventually approaching a constant value at high frequencies. As shown in Fig. 2(a), the inductance value increases with increasing decarburisation thickness (ferrite layer thickness) at low frequencies. This indicates that the low frequency inductance value is a good parameter for measuring decarburisation thickness. Therefore, the measured and modelled inductance values (normalized for the sample before centre-less grinding, 600μm decarburisation depth, for comparison) at low frequency (100 Hz) versus decarburisation thickness are shown in Fig. 2(b). As the relative permeability of ferrite could not be experimentally determined (and varies considerably with carbon content), three values over a large range (50, 200 and 1000) have been chosen for FEM modelling. Both the measured and modelled results show that inductance changes with decarburisation thickness in a non-linear manner. With increasing decarburisation thickness from zero, the inductance increases quickly, and then tends towards saturation. This phenomenon is due to the demagnetising field effect. When a finite size ferromagnetic sample is magnetised in an applied magnetic field, a demagnetising field appears in the sample, which is opposite to the applied field. For the sample with

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the largest relative permeability (1000), the demagnetising field effect is the most significant. It should be noted that the measured and modelled results are not in perfect agreement. This may be due to non-uniformity of ferrite layer thickness along the rod after grinding, and / or the plastic deformation introduced in the ferrite layer, which affects its permeability [4]. The simulation of on-line testing has shown that the EM sensor has the ability to detect decarburisation depth based on the fact that the relative permeability of ferrite is hundreds of times larger than that of austenite. For off-line testing, the sensor needs to be able to distinguish between the surface ferrite and core pearlite. The relative permeability ratio of ferrite/pearlite is much smaller than ferrite/austenite because pearlite is also a ferromagnetic phase. Thompson and Tanner [5] have shown that the initial relative permeability of pearlite (0.87 wt% C) is 56, whereas ferrite with a small amount of pearlite (0.17 wt% C) is 280. Modelling work determined that the EM sensor should have the ability to detect the difference between ferrite and pearlite even with such a small relative permeability ratio. Fig. 3(a) shows the microstructure from a Fe-0.8 wt% C sample after decarburising treatment of 1000°C for 2 hours, which consists of a surface ferrite zone, with a ferrite and pearlite mixed zone followed by fully pearlite on moving into the sample core. The sensor measured results in Fig. 3(b) show that inductance increases with increasing decarburising time (and hence decarburised depth) over the whole measured frequency range used (10 to 100 Hz). At a frequency of 10 Hz, the sensor could not readily distinguish the two samples with the least amount of decarburisation: decarburisation times of 10min (containing no separate ferrite layer but only a thin mixed zone), and 1 hour (containing a thin ferrite layer and a thicker mixed zone). By increasing the frequency these samples become distinguishable. Therefore, to detect thin decarburised layers, such as seen in industrial processing, the appropriate frequency needs to be chosen. This is understandable from the point of view that at very low frequency, if the skin depth is much larger than the thin decarburisation layer thickness, the contribution to the inductance from the decarburisation layer is too small compared to that from the core pearlite. On the other hand, if the skin depth is smaller than the decarburisation layer thickness, the variation of decarburisation layer thickness cannot be detected.

4. Conclusions Experiments and modelling show that decarburisation in steel rod samples can be measured using an EM sensor on-line during hot processing (by differences in permeability between surface ferrite and bulk austenite) or by off-line cold testing (by differences in permeability between surface ferrite and bulk pearlite). Appropriate testing frequency needs to be selected dependent on the decarburisation depth and whether on-line or off-line testing is being carried out to optimise signal output.

References [1] Papaelias MP, Strangwood M, Peyton AJ, Davis CL, Metall Mater Trans A 2004 (35A) 965-72 [2] Haldane RJ, Yin W, Strangwood M, Peyton AJ, Davis CL, Scripta Mater 54 (2006) 1761-65 [3] http://www.comsol.com/ [4] Thompson SM, Tanner BK, JMMM 132(1994) 71-78 [5] Thompson SM, Tanner BK, JMMM 123(1993) 283-298

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Assessment of Grinding Damage on Gear Teeth using Magnetic Barkhausen Noise Measurements Moorthy VAIDHIANATHASAMY, Brian Andrew SHAW, Will BENNETT*, Peter HOPKINS* Design Unit, Newcastle University, Newcastle upon Tyne, UK *Ministry of Defence (Navy), Bristol, UK

Abstract. The marine Gears made with Case-carburised En36 steel were subjected to grinding damage during manufacturing. The MBN measurements have been made on different Gear teeth using three different methods, namely, High Frequency, Medium Frequency and Low frequency MBN measurements with the optimised measurement device and parameters so that the MBN signal from different depth ranges can be detected and analysed. The MBN measurements on these Gear teeth have shown that the grinding damage near the surface (< 10μm depth) can be detected using High frequency MBN, any sub-surface damage (within ~40μm depth) can be detected using Medium frequency MBN and the damage in the deeper layers (> 40μm depth) can be detected using Low frequency MBN measurements. The thermal damage caused by Grinding Burn is also clearly revealed by the shifting of the Low frequency MBN peak to lower magnetic field. Keywords. Magnetic Barkhausen Noise, Gears, Grinding damage.

1. Introduction The grinding damage induced during the final stage of manufacturing is a major concern affecting the quality and hence the fatigue life of Gears. It is known that the grinding damage is associated with alterations in Residual Stress (RS) distribution and the microstuctural state caused by thermal effects such as Burning or Rehardening. Conventionally, the grinding damage is assessed using Nital Etching method which reveals only microstructural changes on the surface. Often, the depth and the extent of the grinding damage may vary at different locations of the Gear teeth. In Casehardened steel Gears, it has often been found that the surface of the material may not reveal severe damage due to immediate cooling of the surface. But, the thermal damage and deformation may have altered the microstructure and RS in the sub-surface severely [1]. Since, the Magnetic Barkhausen Noise (MBN) signal is generated by the magnetization process which is strongly influenced by the microstructural and stress states of the ferromagnetic material, the MBN technique is considered as a potential NDT method to evaluate the grinding damage in ferromagnetic steels [2]. The MBN measurements can be made with different set of parameters, varying the maximum level and the excitation

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frequency of external magnetic field strength, the sensitivity of MBN pick-up coil, the analysing frequency range etc. All these factors decide the range of magnetisation and the depth from which the MBN signal is detected. In this study, three different MBN measurement methods have been compared for evaluating the depth range and extent of Grinding damage in carburised steel Gears. An attempt has been made to relate the three different MBN measurements with RS alteration below the surface at different depth ranges and also qualitatively assess the extent of thermal damage.

2. Experimental procedure The helical gears made from case-carburised En36 steel were subjected to different levels of damage during final grinding process. Small portions (25 mm long) of the teeth were cut from different locations of these Gears so that the Residual Stress (RS) – Depth profiles and the MBN measurements can be made using the existing X-ray diffraction system and the MBN devices at the Newcastle University. The three different MBN measurement methods, namely, High, Medium and Low frequency MBN measurements were made using three different set of measurement devices (electromagnetic yoke and MBN pick-up coil) and parameters (excitation frequency fex, maximum applied magnetic field Hmax and analysing frequency range, and signal amplification). The High frequency MBN measurements were made with MBN system and Gear probe supplied by Stresstech, Finland. The Medium and Low frequency MBN measurements were made with the MBN system and devices developed at Design Unit, Newcastle University, UK. The details of the High frequency MBN measurements (fex=125 Hz, Hmax= ±70 Gauss) and Low frequency MBN measurements (fex=0.2 Hz, Hmax=±300 Gauss) are given elsewhere [2-4]. The Medium frequency MBN measurements were made at 20 Hz magnetic excitation with maximum applied magnetic field strength of ±140 Gauss. The MBN signal was filtered using a 2 kHz high pass frequency filter and amplified to a Gain of 40 dB. The MBN signal profile is used for analysis. The skin depth, from which the MBN signals are detected, strongly depends on several measurement parameters such as the fex, Hmax, frequency response of the MBN pick-up coil, analysing frequency range of the MBN signals etc. in addition the effect of permeability and conductivity of the test materials. Due to the complex and synergistic influence of these factors, it is not possible to precisely determine the skin depth theoretically. However, it is well known that the skin depth of the MBN detection decreases with the increase in frequency of external magnetic excitation and the analyzing frequency range of MBN signals due to electromagnetic attenuation of the MBN signals within the test material. Previous studies [2-5] using the High and Low frequency MBN measurements made with differents set of parameters revealed that the high frequency MBN measurements did not detect changes in material properties beyond 10 μm depth whereas the low frequency MBN measurements detect changes in material properties to a depth of 600 μm. Based on the previous experiences, the High, Medium and Low frequency MBN measurements are expected to reveal the changes in material properties in the near-surface (<10 μm), subsurface (<40 μm) and deeper subsurface (upto ~ 400 μm).

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3. Results and Discussions It is expected that the comparison of High, Medium and Low frequency MBN measurements would indicate the possible distribution of residual stresses (RS) in the depth direction due to different skin-depth of the MBN signals generated in these measurements. In this paper, the comparison is shown with two examples. As an example 1, the MBN profiles measured using the three different types of measurements on a set of three different teeth from Gear S1 and their RS – Depth profiles are shown in Figure 1. The High frequency MBN profile shows no significant change in MBN peak among these three teeth indicating no significant variations in RS near the surface which is also supported by the RS-Depth profile. However, both the Medium and Low frequency MBN profiles show significant variations between them. The highest MBN peak for the Tooth-M indicates that it would have higher tensile RS in the subsurface region compared to other teeth. This is also evident from the RSDepth profiles shown in Figure 1(d).

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94

M. Vaidhianathasamy et al. / Assessment of Grinding Damage on Gear Teeth

300

Gear S1

-

(d)

Residual Stress, MPa

200 100 0 0

10

20

30

40

50

-100 Tooth N -200

Tooth M Tooth W

-300 Depth, Pm Figure 1. The MBN profiles measured with (a) High, (b) Medium and (c) Low frequency measurements and (d) RS-Depth profiles for three teeth from Gear S1. As an example 2, the comparison of High, Medium and Low frequency MBN profiles and the RS-Depth profiles for two teeth from Gears T1 and T3 are shown in Figure 2. In both the high and medium frequency MBN measurements, the T3-L tooth shows higher MBN level than T1-1 tooth. But, the low frequency MBN profiles show the opposite that the T1-1 tooth has higher MBN peak than T3-L tooth. The variations in high and medium frequency MBN profiles suggests that the T3-L tooth may have less compressive or more tensile RS than T1-1 tooth in the near-surface region (within 30μm depth). It can also be observed that the variation in high frequency MBN peak height shows a difference of ~ 40% and the variation in medium frequency MBN peak shows a difference of ~ 65% between for T1-1 and T3-L teeth. The larger difference shown by medium frequency MBN measurement indicates the presence of extended difference in RS profile even in subsurface layers (up to ~ 30 μm depth). It can be clearly seen from the RS-depth profiles that the T3-L tooth has more tensile RS than T1-1 tooth even at 20μm depth. But, at 40μm depth, the T1-1 tooth has tensile RS value while T3-L tooth has compressive RS value. The presence of more tensile RS in the deeper region is clearly reflected by the higher MBN peak value for T1-1 tooth than T3-L tooth in the low frequency MBN measurements. The distinct variations in the peak position of the Low frequency MBN profiles clearly show the extent of thermal damage resulting in microstructural softening among these Gear teeth. The higher applied magnetic field strength in the Low frequency MBN measurement maximizes the magnetisation range and hence reveals the extent of thermal damage by distinct shifting of the position of MBN profiles.

Average MBN level, % of 5V

M. Vaidhianathasamy et al. / Assessment of Grinding Damage on Gear Teeth

Carburised Gears T1 and T3 fex = 125 Hz 'fa = 70-200 kHz

30

(a)

20

25

95

Tooth-T3-L Tooth-T1-1

15 10 5 0 -100

-50

0

50

% of voltage applied to electromagnet

100

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Carburised Gears T1 and T3

(d)

Residual Stress, MPa

100 0 -100 0 -200 -300 -400

10

20

30

40

50

Tooth-T3-L Tooth-T1-1

-500 -600 -700 Depth, Pm

Figure 2. The MBN profiles measured with (a) High, (b) Medium and (c) Low frequency measurements and (d) RS-Depth profiles for teeth from Gears T1 and T3.

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4. Conclusions This study clearly shows that the difference in the RS distribution in the near-surface, subsurface and deeper regions can be identified by comparing the MBN profiles obtained from these three different MBN measurements. It is more appropriate to relate the MBN peak position to the extent of thermal damage and the peak height to the average RS variation over a certain depth depending on the type of MBN measurement and the parameters used. However, since the High and Medium frequency MBN measurements have limited effective magnetic field penetration resulting in smaller magnetisation range and they could not isolate thermal damage from the RS variations. References: [1] [2] [3] [4] [5]

B.A.Shaw, J.T.Evans and D.E.Yates, The influence of Grinding on the formation of Residual Stress Distribution in Ground Surfaces, Conference on Drives and Controls., Kamtech Publishing, UK, 1996, 21-26. V.Moorthy, B.A.Shaw, P.Mountford and P.Hopkins, Magnetic Barkhausen emission technique for evaluation of residual stress alteration by grinding in case-carburised En36 steel, Acta Materialia, 53 (2005) 4997-5006. V. Moorthy, B.A. Shaw and P. Hopkins, Surface and subsurface stress evaluation in case-carburised steel using high and low frequency magnetic Barkhausen emission measurements, J. Magnetism and Magnetic Materials, 299, 2006, 362-375. V. Moorthy, B.A. Shaw and P. Hopkins, Magnetic Barkhausen emission technique for detecting the overstressing during bending fatigue in case-carburised En36 steel, NDT&E international, 38, 2005, 159-166. V. Moorthy, B.A. Shaw, and K. Brimble, Evaluation of case depth in case-carburised gear steels using magnetic Barkhausen emission technique, Materials Evaluation, 62 (5) May 2004, 523-527.

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Evaluation of Contact Fatigue Damage on Gears using the Magnetic Barkhausen Noise Technique Moorthy VAIDHIANATHASAMY, Brian Andrew SHAW, Will BENNETT*, Peter HOPKINS* Design Unit, Newcastle University, Newcastle upon Tyne, UK *Ministry of Defence (Navy), Bristol, UK Abstract. Gears made from Case-carburised SAE8620H steel were subjected to contact fatigue testing at different contact stress levels in the Gear Test Rig facility at Newcastle University. The High frequency Magnetic Barkhausen Noise (MBN) measurements were made at different intervals of fatigue cycles. The MBN signal level gradually increases with progressive fatigue cycles and the rate of change in MBN level systematically increases with the increase in contact stress level. However, at higher contact stress levels, the MBN level quickly reaches a maximum value and then starts to decrease with further fatigue cycles. This maximum MBN level may be considered as an indication of the critical stage of fatigue life beyond which a gear may be expected to fail soon. With increasing numbers of fatigue cycles, the large MBN activity occurs at lower magnetic field strength which clearly indicates the formation of soft magnetisation regions near the surface. This may be attributed to the deformation induced transformation of paramagnetic retained austenite into ferromagnetic martensite. Key words: Barkhausen Noise, Contact fatigue, Gears.

1. Introduction One of the most common modes of Gear failure is the contact fatigue damage which is commonly manifested as the initiation and progression of micro-pitting on the flanks of gear teeth. The progress of micro-pitting damage alters the Micro-geometry of Gear profile which in-turn alters the contact pattern of the Gear. This would introduce nonuniform high stress contact points and makes the Gear rotation more noisy, less efficient and prone to fatigue failure of the Gear teeth. The contact fatigue failure of the Gear normally occurs by the sudden breakage of the tooth by the crack propagation initiated from the Gear flank. Hence, the monitoring of contact fatigue using NDE method would be very useful in assessing the Gear condition and predicting the remaining life of the Gear.

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The Magnetic Barkhuasen Noise (MBN) is the voltage pulses induced in the pick-up coil placed on the surface of the ferromagnetic material which is subjected to discrete changes in magnetization by the external varying cyclic magnetic field. It has been widely reported in the literature [1-3] that the MBN signal is very sensitive to changes in microstructural and stress states of the ferromagnetic steels. Since many medium and large size gears are manufactured using ferromagnetic steels, the MBN technique is considered as a potential NDT method for assessing the contact fatigue damage in Gears. This study has been carried out to understand and evaluate the variation in the MBN signal in response to progressive contact fatigue damage in case-carburised steel gears.

2. Experimental The contact fatigue tests have been carried out at Design Unit, Newcastle University, using 8 mm module, 20 teeth Varigears (Spur Gears with symmetrically varying toothwidth around the circumference – Figure 1) made with Case-carburised and Tempered SAE8620H steel [1], at 3000 rpm speed using OEP-80 Oil at 50qC as lubricant. Typical contact stresses for different tooth-width and torque levels are shown in Table 1.

Figure 1. Photograph of a VariGear

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Table 1. Typical contact stresses for different tooth width and torque levels

Tooth Width, mm

Contact stress at 1300 Nm

Contact stress at 1900 Nm

MPa

MPa

28

1301

1517

25

1352

1581

23

1404

1645

21

1457

1711

19

1506

1773

18

1559

1848

The high frequency MBN measurements were made with commercially available MBN system and the Gear sensor containing ferrite-cored electromagnet and ferrite cored MBN pick-up coil supplied by Stresstech, Finland. The measurements were made at a magnetic excitation frequency of 125 Hz. Normally the MBN signals from a ferrite cored pick-up coil are generated in a wide frequency bandwidth ranging from excitation frequency to 1 MHz. Generally, avoiding the interference from higher harmonic contents of the excitation frequency and neglecting very small amplitude signals at high frequency end, the MBN signal is acquired in a appropriate frequency bandwidth. In this study, the MBN signal were acquired and analysed within the frequency range of 70-200 kHz considering the dominance of contact fatigue damage close to the surface. The total RMS voltage of the MBN signal multiplied by 200 represented as “MBN Display M value” and the average MBN signal profiles are used for analysis.

3. Results and Discussions The variations in MBN levels measured on six different teeth having different width and hence different contact stresses are shown in Figure 2 with progressive number of cycles at 1900 Nm and 1300 Nm Torque levels respectively. It can be observed that the MBN level increases rapidly in the initial stage and then slowly with progressive number of cycles. At higher stresses >1773 MPa, the MBN level reaches a maximum and then decreases in the later stages of fatigue life. With increase in number of fatigue cycles, the cyclic contact plastic deformation results in progressive micro-pitting of the gear surface as shown in Figure 3(a-c). The micro-pitting initiates micro-cracks on the surface against the sliding direction of the gear which grows into macro-crack below the surface along the rolling direction of the gear as shown in Figure 3(d). This results in macro-pit or failure of the gear teeth. This mechanism is influenced by other

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complex gear running conditions such as changing contact stress distribution, lubrication condition, temperature, maximum bending stress, material quality and micro-geometry of the gear. This unpredictable failure event is evident from Figure 4 which shows only micro-pits on one tooth and a macro-pit above the pitch line on the adjacent tooth. This suggests that the catastrophic failure of the gear can occur without any prior warning.

MBN Display 'M' Value, A.U.

180 160 140

Tooth Width, mm Contact Stress, MPa

120

T1-28mm-1517 T2-25mm-1581

Gear- 4S Torque = 1900Nm MBN GAIN = 60

100 80

T3-23mm-1645 T4-21mm-1711 T5-19mm-1773

(a)

T6-18mm-1848

60 0

80

20 30 Number of million cycles

70 65

50

40

Gear- 5S Torque = 1300Nm MBN GAIN = 30 (b)

75 MBN Display 'M' Value, A.U

10

60

Tooth Width, mm Contact Stress, MPa

55

T11-28mm-1301

50

T12-25mm-1352

45

T13-23mm-1404

40

T14-21mm-1457 T15-19mm-1506

35

T16-18mm-1559

30 0

10

20

30 40 Number of million cycles

50

60

70

Figure 2. The variations in MBN level with progressive number of cycles at (a) 1900 Nm and (b) 1300 Nm on six different teeth having different widths and contact stresses. Note the MBN signal amplification gain for (a) is 60 while it is 30 for (b).

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Figure 3. The photographs of the flank of 18 mm width tooth of the gear- 4S showing the progressive micro-pitting (Grey strain area) after (a) 8m, (b) 20m and (c) 34m cycles at 1900 Nm and (d) micro-graph showing typical crack growth below the gear flank surface.

Figure 4. The photograph of gear showing only micro-pitting on one tooth and a large macro-pit failure on the adjacent tooth.

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Normally, a gear is considered as failed either when there is loss of 20μm thickness of gear flank profile caused by micro-pitting or when there is greater than 4% area of macro-pits on the gear. However progressive contact fatigue damage has not been directly related to changes in metallurgical properties such as hardness or microstructure, even though, they may be affected and causes changes in MBN level. Hence, this study attempts to monitor the changes in MBN level with progressive contact fatigue. The variations in the MBN level with progressive number of cycles at lower contact stresses (in the range of 1301 to 1559 MPa) clearly suggest that the initial increase in MBN level is also very gradual and systematic in response to stress level with progressive number of cycles. This suggests that the contact fatigue damage can be detected in this type of gear steels at very early stage using the MBN technique well before the development of any visible surface damage. Since the nature of gear failure is highly unpredictable and catastrophic in many cases, the transition of MBN level from a maximum may be considered as an indication of the critical stage beyond which the failure can occur at any time depending on other unknown parameters. The high frequency MBN profiles measured at the dedendum of 28 mm and 18 mm width teeth at different number of cycles are shown in Figure 5. It can be observed that the high frequency MBN level increases with number of cycles in 28 mm width tooth whereas in 18 mm width tooth, the MBN level reaches a maximum after 8 m cycles and then decreases with progressive number of cycles. Also, in both cases, initially the MBN peak position shifts to lower applied voltage (magnetic field) and then again shift back to slight higher field. The increase in MBN with shifting of peak to lower field could be due to the combined effects of deformation induced transformation of retained austenite into martensite and fatigue softening. The carburised gear surface contains about 25% volume fraction of retained austenite phases which is a paramagnetic meta-stable phase. During running, the gear surface is subjected to micro-plastic deformation which transforms the metastable retained austenite into martensite. Since, the transformed martensite is a ferromagnetic phase, it results in nucleation and movement of additional magnetic domain walls which effectively contribute to increase in MBN level. The initially hard tempered martensite poses high density of tangled dislocations. The cyclic deformation could cause this tangled dislocation to rearrange into dislocation cells. The domain walls can move with relatively less restraint within the dislocation cells compared to tangled dislocation structure. This could contribute to increased MBN level with peak shifting to lower field. The reduction in MBN from maximum level and the shifting of peak position back to slightly higher field could be due to the effects of cyclic plastic deformation induced formation of more compressive residual stresses and cyclic hardening of the microstructure. After certain number of cycles at a given stress level, the transformation of retained austenite to martensite would be completed. Normally, the number of fatigue cycles required for complete transformation of meta-stable retained austenite increases with decrease in contact stress level. This also depends on other factors like temperature, lubrication condition etc. Once the phase transformation is complete, the continued cyclic plastic deformation of near-surface could generate additional dislocations which could accumulate around the dislocation cell walls and that results in the reduction of size of dislocation cell interior. This could cause decrease in the displacement length of magnetic domain walls and stronger pinning of

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domain walls at the dislocation cell walls. This could contribute to the decrease in the MBN level from maximum and shifting of the MBN peak back to higher field. The effect of contact stress level on the rate of changes in the material behaviour introduced by these deformation processes is clearly reflected in the MBN profiles (Figure 5). At lower stresses, the effect of transformation of retained austenite into martensite would dominate and cause gradual increase in the MBN level. However, at higher contact stresses, the phase transformation would complete after smaller number of cycles. With progressive number of cycles, the cyclic-plastic deformation and the residual stress alteration would have dominant effect. Hence, the MBN level would increase to a maximum after certain number of cycles and then would decrease with progressive number of cycles as observed in Figure 5.

Figure 5. The high frequency MBN profiles measured at the dedendum of (a) 28 mm and (b) 18 mm width teeth at different number of cycles.

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Even though this explanation seems to be appropriate, very large (> 100%) increase in MBN level compared to smaller volume fraction (~25%) of retained austenite indicates that some predominant form of magnetic softening taking place in this steel by complex dislocation substructure evolution with progressive contact fatigue deformation. It requires other metallurgical investigations to answer this anomalous and surprise MBN behaviour.

4. Conclusions This study shows that the MBN technique can be used to detect the changes in the Gear caused by contact fatigue damage even at very early stages of fatigue life. The effect of variation in the contact stress level is also clearly reflected by gradual and systematic changes in the MBN level and its rate of change with progressive number of fatigue cycles. The overall response of the MBN suggests that the MBN level increases to reach a maximum level and then slowly decreases with progressive number of fatigue cycles. This is attributed to the initial deformation induced transformation of retained austenite to martensite and fatigue softening followed by cyclic plastic deformation induced hardening. References [1] [2] [3]

T.R. Hyde, J.T. Evans, B.A. Shaw, Effect of stress and heat treatment on magnetic Barkhausen emission in case-carburised steels, Mater. Eval., 58(8)(2000) 985-990. L.P.Karjalainen, M.Moilanen, Fatigue softening and hardening in mild steel detected from Barkhausen Noise, IEEE Trans. Magn., MAG-16 (3) (1980) 514-517. V.Moorthy, B.K.Choudhary, S.Vaidyanathan, T.Jayakumar, K.Bhanu Sankara Rao, Baldev Raj, An assessment of low cycle fatigue damage using magnetic Barkhausen emission in 9Cr-1Mo ferritic steel., Int J. Fatigue, 21 (1999) 263-269.

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Inverse Problems

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Electromagnetic Nondestructive Evaluation (XI) A. Tamburrino et al. (Eds.) IOS Press, 2008 © 2008 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-58603-896-0-109

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3D Reconstruction of flaws in metallic materials by eddy currents inspections Alessandro PIRANIa, Marco RICCIa, Antonello TAMBURRINOb, Salvatore VENTREb,1 a Polo Scientifico Didattico di Terni, Università degli Studi di Perugia, Via Pentima Bassa 21, Terni 05100, Italy b Ass. EURATOM/ENEA/CREATE,DAEIMI, Università degli Studi di Cassino, Via G. Di Biasio 43, Cassino 03043, Italy

Abstract. This work is focused on the image reconstruction of defects in metallic materials using time-harmonic eddy currents testing measurements. The proposed approach combines an efficient numerical model of the probe-defect interaction and a least square error regularized procedure for solving the inverse problem. The method has been successfully tested to detect multiple volumetric defects on multiple layers of a planar conductive material. The regularization term is the total variation, selected to “encode” the a priori information that defects are supposed to be “blocky”. In this manner, the method is potentially capable of treating on the same foot several defects type such as EDM, fatigue crack, stress corrosion crack etc. Keywords. Eddy currents, nondestructive evaluation, total variation regularization, numerical simulation.

1. Introduction Eddy currents non-destructive techniques are widely used in the field of electromagnetic inspection of metallic structures to determine their composition and to detect possible flaws. In this framework, a main issue is the ability to assess the 3D conductivity profile of the sample under test. The major difficulty encountered to achieve this aim is the non-linearity and ill-posedness of eddy currents inverse scattering models. In the present work, we tackle this issue by combining an efficient numerical model of the probe-defect interaction and a total variation procedure for solving the inverse problem and reconstructing the 3D conductivity profile of flawed samples. Our approach exploits a multi-position and a multi-frequency measurement system and it has been tested on synthetic noisy data as preliminary proof in the perspective of an experimental application to real defects. Here we assume that the defects are volumetric with a finite resistivity. The modeling of volumetric defects, as opposed to the modeling of zero-thickness defects, is more intriguing and is receiving increasing attention [1]–[7]. Here we present an efficient integral numerical model where the unknown is 'J, the eddy current variation due to the presence of defects. The methods is in the same line of the approaches 1 Corresponding Author: Salvatore Ventre, Università degli Studi di Cassino, Via G. Di Biasio 43, Cassino 03043, Italy; E-mail: [email protected]

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presented in [1] and [8] where perfectly insulating volumetric and zero-thickness defects are treated. The numerical calculation of 'J combines several advantages, among them: (i) requires a local discretization in a neighborhood of the defect only, (ii) the integral formulation involves the static free-space Green function. The inverse problem in cast in term of minimization of the discrepancy, that is the least square error between the experimental and numerical computed data. Due to the intrinsic ill-posedness of the problem, we include a proper penalty term “encoding” a priori information about the defects. Our choice is fall on the Total Variation (TV) regularization term that penalizes functions with great spatial variability with respect to “blocky” functions, while preserving the edges [9-11]. The TV has been chosen because it accounts for the a priori information that the anomalies are blocky. The paper is structured as follows: the finite element method used to solve the forward electromagnetic problem is presented in Section 2, the inversion algorithm is presented in Section 3 and numerical results are presented in Section 4.

2. Forward Problem The numerical method here proposed has been developed in order to treat efficiently the typical situation encountered in eddy current testing where anomalies are present in an a priori known sub-region VT of a conducting domain VC. The anomalies perturb locally the induced eddy current J and, therefore, it is very efficient [1, 8] to assume as unknown 'J=J-J0 where J0 is the eddy current when the material is flawless. Specifically, by combining the electric field expressed in terms of the vector and scalar potentials with the constitutive relationship we obtain:

KJ K0J 0

 jZA>J @  ’M  jZA ext , in VC

(1)

 jZA 0 >J 0 @  ’M 0  jZA ext , in VC

where J, J 0  L2div VC , ’ ˜ J A : vr o

P0 4S

’˜J0

0 in VC J ˜ nˆ

vr '

³ r  r' dV ,

0, J 0 ˜ nˆ

0 on wVC ,

(2)

VC

K is the electrical resistivity of the conductor (in the presence of the defect), Aext is the vector potential produced by the inducing coil, M is the scalar potential, the subscript 0 refers to the configuration in the absence of defects (defects are modeled as a perturbation 'K of the electrical resistivity, i.e. K=K0+'K). From (1) it follows the equation for 'J: K'J  jZA>'J @ 'KJ 0  ’'M , in VC

(3)

where 'M=M-M0. The related numerical model is based on [12]. Specifically, the unknown is represented as 'J ¦kAE 'I k ’ u Tk where Tk is an edge-element shape function, and AE is a

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proper subset of the edges of the graph made by nodes and edges of the finite element mesh. Choosing properly this subset it is possible to impose the gauge and boundary condition. Moreover, since 'J is localized in a neighborhood of the defect, it is possible to use a local discretization of the conductive material thus achieving a great reduction in the computational cost [1, 8]. The numerical model is, finally, obtained by imposing (3) in weak form:

³

VCLOC

’ u N k ˜ (K'J  jZ A>'J @)dV

³

VCLOC

’ u N k ˜ 'KJ 0dV

N k .

(4)

In (4) VCLOC is a local region in a neighborhood of the tentative region VT

V



 VCLOC Ž VC where 'J is not vanishing, and we exploited that the term involving 'M gives no contribution thanks to the solenoidality of the test functions and their vanishing normal component on the boundary. The corresponding linear system is: T

Z 0  'R 'I

'RI 0

(5)

where, Z0=R0+jZL, 'I is the column vector of the coefficients representing the expansion of 'J and L ij

'R ij

P0 4S

’ u N i ( x) ˜ ’ u N j ( x' )

³ ³

x  x'

VCLOC VCLOC

³’uN

i

³’uN

i

(7)

˜K 0’ u N j dV

(8)

˜ J 0 dV

(9)

VCLOC

I 0,k

³’uN

k

(6)

˜ 'K’ u N j dV

VCLOC

R 0,ij

dV dV '

VCLOC

Once the induced current density perturbation 'J has been computed, it is possible to compute the related voltage induced on the coil. Finally, it is worth noting that the unperturbed current density J0 can be computed analytically for canonical geometries or numerically for more complicated configurations.

3. Inverse Problem We assume that the measurement consists of the value of time-harmonic measurements of the (complex) voltages induced on the exciting coil due to the presence of the anomalies. Specifically, the data is the column array V * consisting of measurements collected at different locations and frequencies (we simultaneously process all of them to retrieve the overall 3D conductivity profile).

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The proposed inversion method cast the problem in terms of minimization. Specifically, the solution of the inverse problem is the minimizer of E x

2

V *  V x  DTV x

(10)

where x is the column vector containing the parameters describing the conductivity V=K-1 (here assumed uniform in each element of the finite element mesh) V * and V x are the measured and numerically computed voltages variation due to the presence of anomalies, D is the regularization parameter and TV is the total variation regularization term [9-11] defined as TV x

³

VT

’V dV

(11)

where V is the conductivity represented by x. The total variation penalty term, introduced as regularization term, penalizes function with great spatial variability but preserving the edges [9-11] and, therefore, it is indicated when the unknown is “blocky” as in the present problem. The implemented inversion algorithm update iteratively the current solution x(n) at step n with the following rule: x n 1

x n  'x n

(12)

where 'x n minimizes E n 1 'x



2



V *  V x n  S n 'x  DTV x n  'x



(13)

S n being the sensitivity map arising from the linearization of V x in a neighborhood

of x(n). The elements of the “sensitivity” matrix S n represent the derivatives of the probe voltage with respect to the voxels’ conductivity. In the present work we compute the sensitivity by using the method described in [13], that results in a first-order Born approximation of the electric field inside voxels [14]. A closed expression for 'x n that minimize E n  1 is not available, thus for each iteration n of the overall inversion algorithm, a further iterative minimization procedure, labeled henceforth by the index Q must be carried out. In the present work we employ the Lagged Diffusivity Fixed Point Iteration Method introduced by Vogel and Oman [10, 11]. The choice of a suitable value for the regularization parameterD is of utmost importance. We applied the L-curve method for choosing the regularization parameter (see figure 1(left)). Specifically, defining Deq as the value that balances the LSE and the TV regularization term, we found that the point of highest curvature, giving the value of the regularization parameter, is close to 10-3 uDeq.

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Figure 1. Left: L-curve analogous for the TV regularization. Right: Typical graph of the TV error vs. the TV parameters. Both graphs refer to defect type I.

We have also analyzed the behaviour of E n  1 when D and Q are varied, setting 'x to the value that minimizes the overall error in the spanned range of parameters D and Q. Figure 1 (right) show the typical error trend where the solid curve identifies the value D* that minimizes E n  1 . We found that D* is resulted to be very close to the value provided of the regularization parameter provided by the L-curve method. Figure 1 refers to defect type I (see figure 3). Similar results have been attained for a wide variety of numerical cases with different defect types and noise levels. Since the data are provided by a multi-frequency measurement system, we have properly weighted each frequency in order to gain useful information from all of them. To accomplish this aim, we operated a frequency dependent normalization of V and S. Usually the weights are related to the energy of the signal at the corresponding frequency, on the contrary we carry out a normalization based on a SVD analysis of the sensitivity matrix at single frequencies. This normalization is modified to take into account the presence of additive synthetic noise: in this case the weights are determined both from the SVD analysis and from the data noise variance. Finally, to avoid instabilities in the reconstruction, as well as to enhance the convergence speed, we introduce a priori information about the conductivity range of values. Specifically, when in a given element the conductivity (represented by x(n)) is greater than the value of the host material, we set it to the value of the host material. A similar processing is carried out when the conductivity assumes negative values.

4. Numerical Results In this section we consider an Aluminium plate (thickness 3mm, V=37.7u106S/m) and we focus on the conductivity retrieval in a small region (VT) of 12mmu12mmu3mm, modelled with a 3D regular grid of cubic voxels having the edge of 1mm. Defects are approximated by a well defined number of voxels with fixed conductivity. The probe consists of a coil with the following characteristics: inner radius 0.5mm, outer radius 2mm, height 3mm, 200 turns, lift-off 0.5mm. In the procedure the probe is placed in 25 different positions, whose centres build up a regular grid of points oriented at 45 degrees respect to the x axis and equally spaced at a distance of about 2mm that

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corresponds to the coil outer radius, guaranteeing data independence and optimal covering of the voxel region. The multi-frequency excitation is contextually exploited in order to inspect the specimen with varying resolution and to examine its inner structure at different depths. Since any frequency is associated to a specific skin depth penetration G, we adopt three different values (670, 1500, 6000 Hz) whose skin-depths correspond to the layer depths. In eddy-currents applications the coil voltage variation due to a defect may be a very small part (0.01%- 0.0001%) of the absolute coil voltage. Since the eddy currents intensity is proportional to the excitation frequency, as the inspection depth increases, i.e. the operation frequency decreases, the relative voltage variation decreases and the SNR tends to be determined mainly by the unavoidable limitations of the measuring apparatuses, usually determined from its operating range. In order to be consistent with these considerations, we have introduced a synthetic noise, in the numerically computed voltages vector, represented by an uncertainness circle in the voltage complex plane which radius is proportional to the coil voltage in air, Vair. Henceforth * * V * VNF  n , where VNF (n) is the noise free data array (noise array) and noise level stands for the ratio between the uncertainness circle radius and the magnitude of Vair. To gain insight about the actual noise magnitude compared to the defect signal contribution, Table 1 reports some indicative values concerning defect types I and II for the noise level adopted (noise level = 0.0005 % ). Specifically, for a given frequency, * * signal level is the ratio between the L1-norm of the voltage variation GV * VNF  VBG due to the defect and the coil voltage in air, whereas relative noise is the ratio between * the L2-norm of the noise n and GV * . Here VBG is the so-called background voltage, that is the coil voltage when defects are not present. Figure 2(left) shows the trends of the total normalized error LSE versus the overall iteration index n, having rescaled to one the value at n=1. As expected, the LSE tends to decrease as the iterations go on. Usually, in order to stop the overall inverse procedure, a proper LSE error threshold, related to the value of the actual precision of the experimental measurement, is prescribed. For noisy data, the error asymptotic value mainly depends on the chosen noise level, and then the threshold has been selected once a time. In figure 2(right) we report a plot of D* vs. Deq for different defect types and noise levels: we note that D* always belongs to a neighbourhood of 10-3uDeq. Moreover, as the noise level increases, the parameter Deq tends to assume a constant value for all tests. Figure 3 shows some reconstructed conductivity maps with and without additive noise. The contribution of a deep defect to the total error is weaker than the one of a superficial defect and, at a fixed depth of inspection, high-conductivity defect is harder to reconstruct than a low-conductivity one. Nevertheless the results show that the conductivity profiles are satisfactory assessed in few iterations. Table 1. Signal level and Relative Noise

Signal level Freq.[Hz] 670 1500 6000

Defect Type I 0.00573 % 0.0192 % 0.0995 %

Defect Type II 0.00279 % 0.00830 % 0.0154 %

Relative noise Defect Type I 12.8 % 3.2 % 0.8 %

Defect Type II 25.4 % 7.1 % 4.5 %

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Figure 2. Left: typical trends of the error LSE vs. the iterations, for no-noise and noisy data: the square signs and the circle ones refer to the defect type I and type II respectively (see also Figure 3). The noisy data are obtained with a noise level equal to 5u10-6. Right: plot of D vs. Deq for different defect types and noise levels. The marks refer to no-noise tests (squares), noise levels 10-6 (triangles), 5u10-6 (stars) and 10-5 (circles).

Figure 3. Examples of reconstructed conductivity map for two defect types: 1st column reports the actual maps; 2nd and 3rd columns report the maps obtained by processing no-noisy data for a threshold fixed at 10-4 and 10-6 respectively; in the 4th column we show the maps obtained at the stop iteration (6th and 4th) by processing noisy data with a noise level of 0.0005 %. The stopping iterations refers to a threshold fixed at 5u10-4 and 5u10-3 respectively.

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5. Conclusions In this work we have addressed the imaging of 3D volumetric defects by eddy current testing. Specifically, we have proposed an efficient integral numerical formulation where the unknown is 'J, the eddy current variation due to the presence of defects. The method combine several advantages: (i) it requires a local discretization in a neighborhood of the defect only and (ii) the integral formulation involves the static free-space Green function. The inverse problem, on the other hand, has been cast in term of minimization of the LSE plus a Total Variation regularization term. The Total Variation term accounts for the a priori information that the defect are piecewise constant.

Acknowledgements This work was supported in part by the Italian Ministry of University (MIUR) under a Program for the Development of Research of National Interest (PRIN grant # 2004095237) and in part by the CREATE consortium, Italy.

References [1]

[2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]

[13]

[14] [15]

M. Morozov, G.Rubinacci, A.Tamburrino, S.Ventre, “Numerical Models of Volumetric Insulating Cracks in Eddy-Current Testing With Experimental Validation”, IEEE Trans. Mag., Vol. 42, No. 5, May 2006, pp. 1568-1576. J. R. Bowler, S. A. Jenkins, L. D. Sabbagh, and H. A. Sabbagh, “Eddy current probe impedance due to a volumetric flaw,” J. Appl. Phys., vol. 70, no. 3, pp. 1107–1114, 1991. Z. Badics, J. Pavo, H. Komatsu, Y. Matsumoto, and K. Aoki, “Fast flaw reconstruction from 3d eddy current data,” IEEE Trans. Magn., vol. 34, no. 5, pp. 2823–2828, Sep. 1998. Z. Badics, J. Pavo, Y. Matsumoto, and H. Komatsu, “Forward solution speed-up for 3D eddy current inversion,” IEEE Trans. Magn., vol. 36, no. 4, pp. 1124–1127, Jul. 2000. D. Reis, M. Lambert, and D. Lesselier, “Eddy-current evaluation of three-dimensional defects in a metal plate,” Inverse Problems, vol. 18, pp. 1857–1871, 2002. D. Prémel and A. Baussard, “Eddy-current evaluation of three-dimensional flaws in flat conductive materials using a Bayesian approach,” Inverse Problems, vol. 18, pp. 1873–1889, 2002. Y. Li, L. Udpa, and S. Udpa, “Three-dimensional defect reconstruction from eddy-current NDE signals using a genetic local search algorithm,” IEEE Trans. Magn., vol. 40, no. 2, pp. 410–417, Mar. 2004. R. Albanese, G. Rubinacci, F. Villone, “An integral computational model for crack simulation and detection via eddy currents”, J. of Comp. Phys., Vol. 152, pp. 736-755 (1999). L. I. Rudin, S. Osher , and E. Fatemi, Nonlinear total variation noise removal algorithms, Proc. of the 11th Annual International Conference the center for Nonlinear Studies, 60, (1992) 259-268. C. R. Vogel and M. E. Oman, Iterative methods for total variation denoising, SIAM J. Sci. Comput. 17 (1), (1996) 227–238. C. R. Vogel, Computational Methods for Inverse Problems, SIAM: Frontiers in Applied Mathematics 23, (2002) R. Albanese and G. Rubinacci, “Finite element methods for the solution of 3D eddy current problems” in Advances in Imaging and Electron Physics, Peter W. Hawkes (ed.), vol. 102, (Academic Press), 1998, pp. 1-86. D. N. Dyck, D. A. Lowther, and E. M. Freeman, A Method of Computing the Sensitivity of Electromagnetic Quantities to Changes in Materials and Sources, IEEE Trans. On Magnetics, 30, 5 (1994). S. M. Nair and J. H. Rose, Reconstruction of three-dimensional conductivity variations from eddy current (electromagnetic induction) data, Inverse Problems, 6, (1990) 1007-1030. R. Fletcher and C. M. Reeves, Function minimization by conjugate gradients, The Computer Journal, 7 (2), (1964) 149-154.

Electromagnetic Nondestructive Evaluation (XI) A. Tamburrino et al. (Eds.) IOS Press, 2008 © 2008 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-58603-896-0-117

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Multi-frequency Eddy Current Imaging for the Detection of Buried Cracks in Aeronautical Structures Yohan LE DIRAISON and Pierre-Yves JOUBERT SATIE, ENS Cachan, CNRS, UniverSud 61 av. du President Wilson, 94235 CACHAN Cedex, FRANCE Abstract. The authors present a signal processing method dedicated to the detection of defects buried next to rivets in aeronautical lap joints. The method is based on a multi-frequency principal component analysis and is applied to the images provided by an original eddy current imager. The optimization of the method is carried out thanks to an experimental approach, and validated with the detection of buried defects, ranging from 2mm to 8mm long and 2mm to 8mm deep. An extension of the method to a classification scheme is also considered. Keywords. Eddy currents, magneto-optical imaging, multi-frequency, buried defect detection, aeronautical riveted lap joints

Introduction Magneto-optical and eddy current imagers (ECI) are very promising for the efficient NDE of ageing aircrafts since they simultaneously reduce inspection time and enhance characterization possibilities [1]. In this paper, the authors implement an original ECI [2] and propose a buried defect detection method, based on the principal component analysis. The efficiency of the method is characterized and optimized through an experimental multi-frequency approach, and its extension to a classification scheme is considered.

1. The Experimental Set-Up The ECI used in this study was developed for the characterization of defects in aeronautical riveted lap joints and was presented in [2]. It is constituted of an EC inductor designed to create a uniformly oriented EC flow in the inspected structure and a linear magneto-optical (MO) set-up used to image the normal distribution of the magnetic field at the surface of the structure, thanks to a linear MO sensor film used with a light modulation approach [3]. Finally, this device provides true in-phase and in-quadrature EC images of a large inspection area (up to 76mm diameter), with a resolution of 100μm × 100μm. In this study the ECI was implemented for the inspection of a laboratory made riveted lap joint mock-up, constituted of five interchangeable aluminum plates featuring a thickness

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of 2mm each and an electrical conductivity of 35M S.m−1 . The defects are placed next to the rivet holes at various depths. They are 0.5mm wide, 2mm high and their length ranges from 2mm to 8mm (see Figure 1 for an example). EC images obtained in the configuration depicted in Figure 1 are given in Figure 2 as an illustration.

Figure 1. Lap joint mock-up with a defect in the third Figure 2. EC images (600Hz) of Figure 1 configuraplate. tion with a 6mm long defect.

2. Signal processing method As seen in Figure 2, the EC signatures due to the buried defects are rather difficult to analyze from the raw EC images, firstly because they are masked by the presence of the rivets, and secondly because of the attenuation of the EC density with the penetration depth in the material. Considering the rivets and the defects are two different sources which are mixed to constitute the EC signal, the objective of the signal processing method is to find a more adequate representation space in which these sources can be separately visualized. To that purpose, a method based on a principal component analysis (PCA) is a good candidate [4,5,6]. 2.1. Basic Principle Let us assume that the transfer function of the device can be expressed by the following linear expression: ⎛ ⎞ s1 ⎟ ⎜  ⎜ s2 ⎟ (1) M = T S = t1 t2 · · · tr ⎜ . ⎟ ⎝ .. ⎠ sr where M is the measurement matrix, T is the unknown transfer matrix, and S is the matrix of the sources. M is constituted of r lines of p elements. r is the number of measurements used, gathering the in-phase and in-quadrature measurements obtained at r 2 different frequencies. Each line is the lexicographical concatenation of the lines of the measurement images and contains p elements. The dimensions of T is r × r and the dimensions of S is r × p. Assuming the sources to be independent and centered, the source covariance matrix SS t reads:

Y. Le Diraison and P.-Y. Joubert / Multi-Frequency Eddy Current Imaging

⎛

σs21 ⎜ 0 ⎜ SS t = ⎜ . ⎝ .. 0

0 σs22 .. . 0

⎞ ··· 0 ··· 0 ⎟ ⎟ . . .. ⎟ . . ⎠ · · · σs2r

119

(2)

where σs2i is the mean square (energy) of the source si . Furthermore, assuming the row vectors of T to be orthogonal, T reads: ⎞ t1  0 · · · 0 ⎜ 0 t2  · · · 0 ⎟ ⎟ ⎜ T = QT DT = QT ⎜ . .. . . .. ⎟ ⎝ .. . . ⎠ . 0 0 · · · tr  ⎛

with QT QtT = Ir

(3)

where QT is a rotation matrix. Considering the assumptions expressed in Eqs. 2 and 3, the covariance matrix M M t reads: ⎛  2 2 ⎞ t1  σs1 0 ··· 0 ⎜ ⎟ 0 t2 2 σs22 · · · 0 ⎜ ⎟ t t t t M M = T SS T = QT ⎜ (4) ⎟ QT .. .. . . . . ⎝ ⎠ . . . . 0 0 · · · tr 2 σs2 r

Besides, the singular value decomposition (SVD) of the matrix M reads: ⎛

λ1 0 · · · ⎜ 0 λ2 · · · ⎜ M M t = V DV t = V ⎜ . . . ⎝ .. .. . .

0 0 .. .

⎞ ⎟ ⎟ t ⎟V ⎠

(5)

0 0 · · · λr where V is the matrix of the singular vectors vi and D is the diagonal matrix of associated singular values λi , arranged by decreasing order. Therefore, by a formal identification between Eqs. 5 and 4, one can note that matrix QT and matrix V generate the same representation space. Therefore, sources S are then estimated by V t M , so that: ⎛

⎞⎛ ⎞ ⎛  ⎞ sˆ1 t1  0 · · · 0 s1 ⎜ 0 t2  · · · 0 ⎟ ⎜ s2 ⎟ ⎜ sˆ2 ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟ V t M = (V t QT )(DT S) = ⎜ . .. . . .. ⎟ ⎜ .. ⎟ = ⎜ .. ⎟ = Sˆ ⎝ .. . . ⎠⎝ . ⎠ ⎝ . ⎠ . sr 0 0 · · · tr  sˆr

(6)

Moreover, the singular values λi are relative to the mean square value (i.e. the energy) of the estimated sources sˆi . λi = σsˆ2 = ti 2 σs2i i

(7)

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2.2. Implementation In this study, the rivets and the defects are considered to be the only two sources of interest. Since the SVD sorts the singular values by decreasing order, the estimated sources are expected to be constituted of sˆ1 (rivets) featured by a high λ1 (high energy of the rivet signatures), and sˆ2 (defects), featured by a smaller λ2 (low energy of the defect signatures). As an example, the source separation was carried out on the EC images of Figure 2, and are shown in Figure 3. This example validates the signal processing approach, since it is clearly seen that estimated source sˆ1 is relative to the presence of the rivet, and estimated source sˆ2 is relative to the presence of the defect, separated from the rivet. In order to characterize the efficiency of the source separation for each rivet, a separation ratio is defined as follows: SRrivet =

σsˆ22 λ2 = σsˆ21 λ1

(8)

This ratio is expected to be minimum for a sound rivet (equal to zero in ideal case), and maximum for large defects. In the example shown in Figure 3, the computation of this ratio for the sound rivet gives SRsound = 0.03 and SRf lawed = 0.08 for the flawed rivet.

Figure 3. Results of the signal processing method applied to images of Figure 2.

3. Frequency Optimization The implementation of the signal processing approach requires the acceptance of the assumptions expressed above, which are not a priori obvious to assume. However, if the assumptions are not entirely verified, it is known that the PCA allows a source rejection - rather than an actual separation - to be achieved [5]. The rejection (of the rivet) is sufficient here as it is a posteriori verified by the obtained results. Moreover, the choice of the excitation frequency is particularly important so that the linearity and the orthogonality of the model can be approached (if not entirely fulfilled), and the defect detection can be optimized. To this end, the ECI was implemented for the inspection of defects buried in the 2nd , 3rd , and 4th plate, using excitation frequencies ranging from 200Hz to 4kHz. Then, the separation ratio defined in Eq. 8 was computed for each rivet. Separation re-

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121

sults obtained for that configurations are presented in Figures 4 to 6, and feature the optimum excitation frequencies gathered in Table 1. The existence of these optimum frequencies can be explained as follows: a low frequency implies a deep EC penetration and a non-linear mixing of the rivet and defect sources; conversely, a high frequency implies a reduced EC penetration depth, and therefore a poor buried defect detection. However, an intermediate frequency features a limited EC penetration, so that the presence of the defect hardly modifies the EC signature of the rivet. For this particular frequency a linear model can be approached, and the separation is more efficient. Furthermore, one can note that for each plate, the optimum excitation frequency roughly corresponds to a phase-shift Δφ = −90˚ between the surface EC density and the EC density at the depth d of the defect. Indeed, considering that the excitation is a plane wave, Δφ can be expressed as [7]: Δφ = −d πf μσ (9) where f the frequency, μ is permittivity and σ the conductivity of the material. This feature is consistent with the assumption of orthogonality of the transfer matrix of the ECI, required for an efficient source separation.

Figure 4. Representation of the separation ratio Figure 5. Representation of the separation ratio against the frequency, for sound and flawed rivets in against the frequency, for sound and flawed rivets in the 2nd plate. the 3rd plate.

Figure 6. Representation of the separation ratio against the frequency, for sound and flawed rivets in the 4th plate.

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Table 1. Optimum separation frequencies in each plate, and corresponding penetration depth relative to a 90˚phase-shift of the EC density. Plate

Optimum frequency (Hz)

Depth for Δφ = −90˚ (mm)

2nd (2mm → 4mm)

f2 = 1200

3.9

3rd (4mm → 6mm) 4th (6mm → 8mm)

f3 = 600 f4 = 300

5.5 7.7

4. Multi-Frequency Detection The determination of the three optimum frequencies presented in Section 3 allows an efficient multi-frequency detection method to be implemented for unknown configurations. Indeed, let us consider the multi-frequency measurement matrix M constituted of  q ) at the three frequencies so in-phase EC signals (m  p ) and in-quadrature EC signals(m that: ⎞ ⎛ m  p (f2 ) ⎟ ⎜m ⎜  q (f2 ) ⎟ ⎟ ⎜m (f )  p 3 ⎟ M =⎜ (10) ⎟ ⎜m (f )  ⎜ q 3 ⎟ ⎝m  p (f4 ) ⎠ m  q (f4 ) The PCA of M leads to estimated source matrix Sˆ in which sˆ1 is relative to the rivets, sˆ2 is relative to the defects (whatever its length or depth), and the other sources are undefined. Indeed, for each considerated rivet configuration, the implementation of this multi-frequency detection algorithm leads to the same orientation of singular vector v2 . Therefore, the best defect detection will always be obtained on estimated source sˆ2 . As an example, EC signals obtained at frequencies f2 , f3 and f4 for a four rivet configuration, summarized in Table 2, are presented in Figure 7 to 9, and the results of the multifrequency PCA are given in Figures 10. One can note the good defect results obtained on source sˆ2 . Furthermore, the computation of the scalar products between singular vectors v2 single obtained with the SVD for each rivet and v2 total obtained with the SVD for the four rivet configuration (presented in Table 2), shows that these vectors are collinear. This feature validates the multi-frequency detection approach. Table 2. Four rivet configuration and corresponding scalar product between singular vectors v2 . Rivet 1

Rivet 2

Rivet 3

Rivet 4

Defect length Defect plate

4mm 2

none none

8mm 3

6mm 4

v2 single · v2 total

0.990

0.994

0.996

0.984

5. Towards Classification of Buried Defect For a further characterization of the defects according to their length and depth, we consider the mono-frequency detection carried out in each plate using the optimized fre-

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123

Figure 7. EC signals obtained at 1200Hz for the in- Figure 8. EC signals obtained at 600Hz for the inspection of the four rivet configuration of Table 2. spection of the four rivet configuration Table 2.

Figure 9. EC signals obtained at 300Hz for the in- Figure 10. Results of the PCA for the inspection of spection of the four rivet configuration Table 2. the four rivet configuration Table 2.

quencies f2 , f3 and f4 . For each frequency, a normalized separation ratio was defined as: N SR =

SRf lawed SRsound

(11)

The N SR was computed and plotted against the defect length, as presented in Figure 11 for frequency f2 , Figure 12 for f3 , and Figure 11 for f4 . The normalized separation ratio is greater than 1 for every considered defect, i.e. all the defects can be detected when using f2 in plate 2, f3 in plate 3 and f4 in plate 4 (except for the defects shorter than 3mm in the 4th plate, at f4 = 300Hz). Moreover, the ratio is monotonously increasing with the length of the defect, which enables the classification of the defects according to their length in a considered plate. However, ambiguities may appear between large and deeply buried defects and small surface defects. To overcome this drawback, the detection procedure should be successively carried out at frequencies f2 , f3 and f4 and the obtained results should be correlated to build a defect classification according to length and depth.

6. Conclusion The proposed multi-frequency signal processing approach shows great efficiency for the detection of buried defects (down to 3mm long and 6-8mm deep), placed next to the rivets in multi-layered riveted structures, and is very promising for classification purposes. Further works will focus on the implementation of the automatic classification algorithm using for example a maximum likelihood approach. Also, the method will be extended to a 2D processing for the enhanced characterization of buried defects of any orientation.

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Figure 11. Evolution of the normalized separation ra- Figure 12. Evolution of the normalized separation ratio against the length of the defects at f2 = 1200Hz. tio against the length of the defects at f3 = 600Hz.

Figure 13. Evolution of the normalized separation ratio against the length of the defects at f4 = 300Hz.

References [1] P. Joubert, J. Pinassaud, G. Rubinacci, A. Tamburrino, S. Ventre, Numerical modeling of a continuous level Eddy Current Imager, in E NDE, Electromagnetic Non-destructive Evaluation (X), S. Takahashi and H. Kikuchi (Eds.), pp. 33-40, IOS Press, 2007. [2] P.-Y. Joubert, J. Pinassaud, Linear magneto-optic imager for non-destructive evaluation, Sensors and Actuators A: Physical, Volume 129, Issues 1-2, 24 May 2006, Pages 126-130. [3] R. Grechishkin, S. Chigirinski, M. gusev, O. Cugat, N. Dempsey, Magnetic Imaging Films, Sringer, 2007 [4] P.-Y. Joubert, Y. Le Diraison and J. Pinassaud, Eddy Current Imager for the Detection of Buried Flaws in Large Metallic Structures, In proceedings of 9th Conference on NDT, Berlin, September 25-26, 2006. [5] G. Saporta, Théories et méthodes de la statistique, Institut Français du Pétrole, Technip. br. in 8. 386 p, 1978. [in French] [6] K.V. Mardia, J.T. Kent and J.M. Bibby, Multivariate Analysis, Academic Press, 1979. [7] H.L. Libby, Introduction to Non-destructive Test Methods, Robert Kriegger Publiesher Compagny, NY 1979.

Electromagnetic Nondestructive Evaluation (XI) A. Tamburrino et al. (Eds.) IOS Press, 2008 © 2008 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-58603-896-0-125

125

A Comparative Study of Source Separation Techniques for the Detection of Buried Defects in the EC NDE of Aeronautical Multi-Layered Lap-Joints Alan TASSIN, Yohan LE DIRAISON and Pierre-Yves JOUBERT SATIE, ENS Cachan, CNRS, UniverSud, 61 Avenue du Président Wilson, 94235 CACHAN Cedex, France

Abstract. The authors present a multi-coil EC sensor dedicated to the rapid inspection of aeronautical riveted lap joints, and compare the efficiency of two signal processing methods based on principal component analysis and independent component analysis, to enhance the detection of buried defects appearing next to the rivets. Keywords. Eddy current multi-sensor, buried defects, aeronautical riveted lapjoints, source separation techniques, principal component analysis, independent component analysis.

Introduction The detection of buried defects growing next to the rivets in aeronautical riveted lapjoints is a major preoccupation for the NDE of ageing aircrafts. NDE techniques should be fast, since aircrafts feature a large amount of rivets, and reliable, since buried defects are particularly difficult to detect. In this context, the authors propose a dedicated eddy current (EC) sensor, associated to source separation techniques, for an enhanced detection of buried defects.

1. Experimental Set-Up In this study, an EC sensor was designed for the rapid inspection of riveted lapjoints. The sensor is constituted of an EC inductor featuring a large coil winded within a magnetic cup-core, and 2 pairs of pickup coils, connected in series and in phase opposition, so that a differential measurement can be carried out along the x-axis and the y-axis (Figure 1). Each pair of coils is constituted of two flat 8-layer PCB coils and is placed under the exciting coil so that no EC signal is provided in absence of defect when the sensor is placed above the inspected rivet (Figure 1). This specific configuration enables the inspection of each rivet to be achieved in a single EC acquisition.

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In this study, the sensor was implemented for the inspection of a laboratory made riveted lap-joint mockup, constituted of five aluminum based alloy plates featuring a 35MS.m-1 electrical conductivity, a 2mm thickness, and various defects placed next to the rivets in the 2nd or 3rd plates (Figure 1). The defects are rectangular notches oriented along the main direction of the lap-joint (x-axis). They feature a 0.5mm width, a 2mm height, and their length ranges from 1mm to 10mm. The EC data acquisitions were carried out thanks to a PC controlled impedance analyzer HP4192A, and the sensor was moved by a PC controlled 3-axis robot, so that the influence of the sensor mispositioning (lift-off and tilt) can be considered as negligible. y

Exciting coil x

Pickup coils

Magnetic core 2mm

12mm Plate

1 2 3 4 5

6mm

Defect length

40mm

Figure 1. Structure of the riveted lap-joint mockup and of the dedicated EC sensor.

PCA results

Raw EC signals

ICA results

-10

0.01

8

Sˆ12

In-phase

0.005 0

4 2

0

20

40

60

1

0

80

0.5

0

20

40

60

0

80

0

20

(mm)

(mm) -9

Sˆ22

0.005

40

60

80

60

80

(mm) -9

x 10

0.01

In-quadrture

x 10

Sˆ12

6

-0.005 -0.01

-9

x 10

x 10

Sˆ22

1

1

0 0.5

-0.005 -0.01

0

20

40

(mm)

60

80

0

0.5

0

20

40

(mm)

60

80

0

0

20

40

(mm)

Figure 2. Raw EC signals (1200Hz) obtained along the x-axis, PCA and ICA result components along the xaxis. Two averaged sound rivets centered at x = 20mm and x = 60mm (dotted lines). Flawed rivet centered at x = 60mm (solid line). The defect is 5mm long and placed in the second plate.

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The sensor was implemented in two different modes: the scanning mode (S-mode) in which the EC signals are provided while the sensor is moving along the x-axis, and the punctual mode (P-mode) in which the sensor is only operating above the inspected rivet, for a rapid lap-joint inspection (Figure 1). Since only defects oriented along the x-axis are considered in this study, only the pair of pickup coils placed along the x-axis (Figure 1) is used.

2. Source Separation Techniques for the Enhanced Detection of Buried Defects As shown in Figure 2, the EC signatures of the defects are rather difficult to analyze from the raw signals, firstly because of the attenuation of the EC density with the depth of the defect, and secondly because their EC signatures are masked by the rivets. In order to enhance the detection of the defects, the authors consider two source separation techniques: the principal component analysis (PCA) and the independent component analysis (ICA). In both techniques, the EC signals are assumed to be constituted of linear mixings of different sources, and the sensor modeling is therefore expressed by: G G ­ m1 ½ ª t11 t12 º ­ s1 ½ M TS œ ® G ¾ « (1) »®G ¾ ¯m2 ¿ ¬t 21 t 22 ¼ ¯s2 ¿ where the rows of M are the EC signals (in-phase and in-quadrature signals shown in Figure 2), T is the unknown transfer function of the EC sensor, and the rows of S are the two sources of interest (rivet and defect sources). Both techniques perform the estimation of the sources S from the measurements M, but under different assumptions. 2.1. PCA Basic Principle In the PCA method, the sources are assumed to be centred and uncorrelated, so that:

ªV 12 0 º . « 2» ¬« 0 V 2 »¼

SS T

(2)

Furthermore, the column vectors of T are assumed to be orthogonal, which means that T can be decomposed as the product of a rotation matrix R and a dilatation matrix D: T

RD

ªcosT « sin T ¬

 sin T º ªd1 « cosT »¼ ¬ 0

0º . d 2 »¼

(3)

Under these assumptions, the variance-covariance matrix MMT is expressed by:

MM T

TSS T T T

ªd 2V 2 R« 1 1 ¬« 0

0 º

» d 22V 22 ¼»

RT .

Besides, the singular value decomposition of MMT leads to:

(4)

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A. Tassin et al. / A Comparative Study of Source Separation Techniques

MM T

ªO V« 1 «¬ 0

0º T »V O2 »¼

(5)

where V is the matrix of the singular vectors of M associated to the singular values O1 and O2. According to Eqs. (4 and 5), the rotation matrix R can be identified to matrix V. Finally, the PCA consists in the computation of VTM which leads to the estimation of the sources S, since: T

V M

T

V (T S )

T

(V R)( D S )

G ª d1s1 º «d sG » ¬ 2 2¼

Sˆ .

(6)

Since the vectors of R and T appear in an unknown order, the sources of S are rather separated than estimated. Besides, the vectors of V are chosen to be arranged by decreasing order according to their singular values [1]. Therefore, in this study, the implementation of the PCA will carry out a source separation in which the first row Dž1 of Dž is expected to be relative to the rivet (the rivet features a high contribution to the EC signals) and the second row Dž2 is expected to be relative to the defect (the defects feature a low contribution to the EC signals). 2.2. PCA Implementation The efficiency of the source separation techniques is related to the acceptance of the assumptions expressed in section 2.1. which are not obvious. However, if the assumptions are not entirely verified, the PCA is known to carry out a good rejection of the higher source (rivet) while estimating the source of lower energy (defect) [1,2], which is quite satisfactory in the case of defect detection. Furthermore, the excitation frequency can be optimized so that the assumptions can be approached, if not entirely fulfilled [3]. In this study, frequency f2 = 1200Hz is chosen for the detection of 2nd plate defects, and f3 = 600Hz for the detection of 3rd plate defects, according to the frequency optimization presented in [3]. As an example, the PCA was implemented on the EC signals obtained at frequency f2 for the inspection of a sound rivet and of a flawed rivet in plate 2. The raw EC signals and PCA results are shown in Figure 2, in which one can note that the second PCA component (Dž2) allows the presence of the defect to be highlighted, over the whole rivet signature (S-mode) or only over the central peak of the signature (P-mode). In order to characterize the efficiency of the method, the authors define a defect detection ratio U , expressed by:

U

Sˆ 2d

2

Sˆ 2s

2

flawed rivet

(7) sound rivet

where the numerator is the norm of Dž2 computed over the signature of a flawed rivet (in S-mode or P-mode), and the denominator is the norm of Dž2 computed over the signature of a reference sound rivet (in S-mode or P-mode).

A. Tassin et al. / A Comparative Study of Source Separation Techniques

129

Amplitude of the detection ratio U for T = 90°

As an illustration, the detection ratio was computed for the detection of 10 defects buried in the 2nd plate, ranging from a 1mm length to a 9mm length, and inspected in Smode at f2 = 1200Hz. The obtained results are plotted in Figure 3, as a function of the rotation angle T, for which T = 0 is relative to the direction of the first vector of V (rivet source) and T = S/2 is relative to the direction of the 2nd vector of V (defect source). One can note that the PCA provides a maximum detection ratio U = Umax > 1 for T = S/2 (i.e., as expected, the defects appear on the second PCA component Dž2), and that U | 1 for T = 0 (i.e. only the rivet source appears on the first PCA component Dž1).

2.5

9mm 7mm 5mm 4mm 3mm 1mm

2 1.5 1

U

0.5

T°

0 -0.5 -1 -1.5 -2 -2.5 -3

-2

-1

0

1

2

3

Amplitude of the detection ratio U for T = 0°

Figure 3. Defect detection ratio U (defined in Eq. 7) as a function of the projection angle T, in polar coordinates (U : radius, T : angle). Acquisitions made at f2 = 1200Hz, defects placed in the 2nd plate and lengths ranging from 1mm to 9mm.

2.3. ICA principle and implementation The ICA method is based on an extension of the Central Limit Theorem [4], which states that the distribution of the linear mixing of two independent sources is more gaussian than the distribution of each source. The gaussianity of a signal s can be estimated by the kurtosis criterion [4], expressed in Eq. (8), which tends to zero for a gaussian signal:

kurt ( s)

E[(s  s ) 4 ]  3( E[ s  s 2 ]) 2 .

(8)

Therefore, the estimation of non-gaussian independent sources is achieved by finding the linear combinations of the considered signals which maximize the absolute value of the kurtosis [4]. However, the comparison of the kurtosis values of different signals is only consistent for signals which are centred and of unity variance. Therefore, the implementation of the ICA requires a previous whitening step [4] by the means of a PCA of the variance-covariance matrix MMT of the measurements, and expressed by:

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A. Tassin et al. / A Comparative Study of Source Separation Techniques

~ M

ªO V« 1 ¬« 0

0º » O2 ¼»

1 / 2

VTM

(9)

~ in which M are the whitened measurements. The implementation of the ICA then consists in the research of the optimum rotation angle T = Topt, so that: kurtmax

ªcosT opt º ~ kurt ( « »M ) ¬ sin T opt ¼

(10)

Finally, the ICA estimation of the sources then reads: Sˆ

ªcosT opt « sin T opt ¬

 sin T opt º ~ M cosT opt »¼

(11)

In this method, the estimated sources are not likely to appear in a predefined order. Therefore, the identification of the sources requires a calibration step obtained on known flawed situations. In this study, the source relative to the rivet is chosen to be placed in Dž1 and the source relative to the defect (which maximizes the detection ratio defined in Eq. 7) is chosen to be placed on Dž2, for the sake of comparison with the PCA results. As an illustration, the ICA was implemented for the processing of the raw EC signatures of a sound rivet and a rivet featuring a 5mm long defect buried in plate 2. The results are compared to the raw EC signatures and to the PCA results in Figure 2. One can note that Dž2 is mainly relative to the defect, and that Dž1 is mainly relative to the rivet alone, in S-mode or P-mode.

3. Detection results using PCA and ICA

The PCA and ICA based defect detection methods were implemented using the EC signals provided by the inspection of 10 flawed rivets in plate 2, 10 flawed rivets in plate 3 and 10 sound rivets, in S-mode and in P-mode, at f2=1200Hz and f3=600Hz. The PCA and ICA were carried out using each flawed rivet signature separately (PCA2, ICA). The PCA was also carried out on a reference sound rivet signature obtained by the averaging of 10 sound rivet signatures (PCA1), so that the determination of the rivet source Dž1 is less influenced by the presence of the defect. Then, the detection ratio U was computed as expressed in Eq. (7), in each detection case, as a function of the defect length. The results obtained for defects in plate 2 are presented in Figure 4, and defects in plate 3 in Figure 5. In each case, detection ratio U = 0dB is relative to the defect detection method applied to the reference sound rivet. In addition, a detection threshold was computed. This threshold corresponds to the

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A. Tassin et al. / A Comparative Study of Source Separation Techniques

highest value of U z 0dB (wrongly) obtained for the inspection of sound rivet samples. Above this threshold, defects are correctly detected without false alarm. 14

4.5 4

S-mode EC acquisitions Defects in plate 2

PCA 1

12

PCA 2

P-mode EC acquisitions Defects in plate 2

PCA 1

3.5 PCA 2

10 Detection ratio in dB

Detection ratio in dB

3 ICA 2.5 2 1.5

8

6 ICA 4

1

2

0

0 -0.5 0

Detection threshold

Detection threshold

0.5

1

2

3

4 5 6 Defect length in mm

7

8

9

-2 0

10

1

2

3

4 5 6 Defect length in mm

7

8

9

10

Figure 4. Detection ratio versus defect length for PCA and ICA based detections of defects buried in the 2nd plate. Acquisition carried out at f2=1200Hz in S-mode (left) and P-mode (right).

The detection results obtained in plate 2 (Figure 4) show that defects longer than 1mm are detected without false alarm. However, one can note that the detection ratio decreases for the longer defects. This feature can be attributed to a poor verification of the linearity assumptions for long defects (i.e. a reduced efficiency of the source separation methods) and to the distance between the 2 pickup coils (12mm) which is not optimum for defects longer than 5mm. Finally, one can note that best detection results are obtained with the PCA applied on P-mode EC signals, which enables a higher rejection of the rivet signature. 1.8 1.6

12

S-mode EC acquisition Defects in plate 3

PCA 1

1.4

10

P-mode EC acquisitions Defects in plate 3

PCA 2

PCA 2

PCA 1

8

1

Detection ratio in dB

Detection ratio in dB

1.2 ICA

0.8 0.6 0.4

6

4 ICA

Detection threshold 2

Detection threshold 0

0.2 -2

0 -0.2 0

1

2

3

4 5 6 Defect length in mm

7

8

9

10

-4 0

1

2

3

4 5 6 Defect length in mm

7

8

9

10

Figure 5. Detection ratio versus defect length for PCA and ICA based detections of defects buried in the 3nd plate. Acquisitions carried out at f3=600Hz in S-mode (left) and P-mode (right).

Same conclusions can be derived from the results obtained in plate 3 (Figure 5), except that defects longer than 2mm can be detected without false alarm in S-mode, and longer than 5mm in P-mode. The ICA is inadequate for the detection of defects in P-mode and less efficient than PCAs in S-mode. These results can be explained by the high source rejection possibilities provided by the PCA [1,2] when estimating the source of low

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energy. This feature is not operative with the ICA because of the whitening step expressed in Eq. (9). Also, one can note that the results obtained in PCA1 and PCA2 are quite similar: indeed, the directions of the first eigenvectors are quite identical in both approaches, since the presence of the deeply buried defects hardly modifies the EC signatures of the rivets. Finally, the presented results exhibit some scattering of the data relative to small defects and sound rivets, which leads to non-detection or false alarms. This feature can be attributed to the poor accuracy of the machining of both the used mockup and sensor array, and to the possible presence of air gaps between the lap joint plates, since they are not fastened with real rivets.

Conclusion

In this paper the authors have presented and compared the implementation of two source separation techniques (PCA and ICA) used for the detection enhancement of buried defects growing next to the rivets. The methods were implemented on the EC signals provided by a specific eddy current sensor dedicated to the rapid inspection of riveted lap-joints. The sensor was used in scanning mode and in punctual mode, in the case of buried defects placed in the 2nd or 3rd plate of a riveted lap-joint mockup. The obtained results show that the sensor could be optimized so that all defect lengths can be considered with equal detectability. Also, the PCA appears to be more efficient than the ICA, thanks to its ability to reject the source of higher energy (rivet) when estimating the source of lower energy (defect). Further works will focus on the extension of the signal processing technique to 2D EC signals, in order to detect defects of any orientation, and to reject the possible edge effect occurring in the inspection of rivets placed near the edges of the lap-joint. Finally, a multi-frequency approach will be developed in order to extend the detection technique to a classification scheme.

Acknowledgements

This work was supported by grants from Région Ile-de-France in the framework of the competitiveness cluster SYSTEM@TIC PARIS-REGION (Digital Production project).

References [1] [2] [3] [4]

T. Jolliffe, Principal Component Analysis, Springer Verlag, New York, 2002 S. Hermosilla-Lara, P.-Y. Joubert, D. Placko, Identification of thermal and optical effects for the detection of open-cracks in photothermal non destructive testing, Eur. J. Appl. Phys. 24, 223-229 (2003) Y. Le Diraison, P.-Y. Joubert, Multi-frequency Eddy Current Imaging for the detection of buried cracks in aeronautical structures, in proceedings of ENDE 2007, 19-21 June 2007, Cardiff, United Kingdom. A. Hyvärinen, J. Karhunen, E. Oja, Independent Component Analysis, John Wiley and sons, 2001

Electromagnetic Nondestructive Evaluation (XI) A. Tamburrino et al. (Eds.) IOS Press, 2008 © 2008 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-58603-896-0-133

133

Fundamental Feature Extraction Methods for the Analysis of Eddy Current Data Jeremy S. KNOPPa,1 and John C. ALDRINb a

Air Force Research Laboratory, USA b Computational Tools ,USA

Abstract. Features are investigated in eddy current data that are sensitive to corrosion and fatigue cracks in airframe structures while invariant to other NDE noise factors. To investigate subsurface corrosion characterization at the faying surface, a series of eddy current studies were performed using an analytical model for varying total subsurface thickness loss and percentage of the thickness loss occurring in each layer. Results for the simulated studies are presented demonstrating a novel feature for corrosion characterization using first and second order derivatives of the impedance response with respect to frequency. For characterization of subsurface cracks around fastener holes in structures, numerical simulations and experimental studies are presented. Unique features in the measurement response in circumferential direction were found to be sensitive to subsurface cracks around fastener holes and invariant to irregular geometric factors such as fastener fit and probe tilt. Multifrequency eddy current data combined with circumferential (spatial) measurement features were found to be promising for characterizing subsurface cracks in terms of length and depth. Keywords: eddy current, feature extraction, material loss, cracks

Introduction The detection and characterization of subsurface cracks and corrosion in multi-layer airframe structures is a common practical problem and also a challenging research problem in NDE. Eddy current and ultrasonic methods have been applied with some success for detecting and quantifying damage. Reliable second layer crack detection using eddy current is still in its infancy [1,2]. Dual frequency eddy current techniques have been shown to be effective in detecting second layer corrosion even in cases 1 Air Force Research Laboratory (AFRL-MLLP), Wright-Patterson AFB, OH [email protected]

45433, USA,

Email:

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where there is a variable air gap between layers [3]. Pulsed eddy current with giant magnetoresistive (GMR) sensors in conjunction with advanced data processing has also been used to detect and estimate some properties of subsurface corrosion [4]. Likewise, GMR sensors and advanced feature extraction techniques have been employed to detect subsurface cracks around fastener holes [5,6]. On-board in-situ eddy current sensors have also been considered [7]. Although an asymmetric response observed for a hole feature in an eddy current image from 2D raster scan data is typically used to distinguish crack and no crack conditions, there are a variety of potential sources of coherent noise features that produce similar asymmetric responses. In particular, misdrilled holes cause the fasteners to be skewed and irregular gaps to exist between the fastener and the hole. Variability in probe lift-off related to the scanning system hardware alignment or part surface conditions can cause variability in the signal. The consistency of windings in eddy current probes due to difficulty in manufacturing can also be a source for measurement asymmetry. Lastly, the response from adjacent fastener sites can mask an asymmetric response due to a crack. Clearly, the presence of coherent noise can increase false call rates, limit crack detectability, and ultimately decrease the prospects for crack sizing. Thus, there is a need to develop advanced data analysis approaches and find reliable features that are sensitive to the crack condition yet invariant to such coherent noise signals also present in real data. The use of invariant features has been shown to be valuable for other problems in eddy current nondestructive evaluation. A basic approach to reduce sensitivity to liftoff during EC measurement of surface breaking cracks concerns adjusting the phase during calibration so as to isolate liftoff to the horizontal measurement component while a threshold is applied to the vertical measurement component in order to make a call. Advanced feature extraction methods have also been developed to address a wide variety of problems. For example, feature extraction methods were developed to address unknown permeability variation through an invariance transformation of flux density measurements incorporating radial basis functions [8]. The performance of neural network classifiers were found to significantly benefit from the use of such invariant signal features. This paper focuses primarily on two concepts related to feature extraction in eddy current NDE. The first concept concerns the use of multifrequency analysis of eddy current data. In particular, a novel feature involving the second derivative of the reactance component of the impedance change with respect to frequency is investigated. The second concept concerns the use of a feature related to circumferential gradients in the reactance component at a particular radius from the center of an embedded cylinder. These two concepts are essentially applied to estimate parameters related to the aspect ratio of subsurface cracks at fastener holes.

1. Frequency Domain Feature Extraction for Characterization of Thickness and Depth of Material Loss A series of simulations using the analytical solution for layered media were performed varying total subsurface thickness loss, and depth of the thickness loss as illustrated in Figure 1. Several different features were discovered that can be used to determine total thickness loss and depth. Figure 2(a) shows the real part of the change in impedance as

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a function of frequency for a variety of thicknesses and depths. At approximately 1.5 KHz, “bands” form that provide a good measure of total thickness loss. This measure is also insensitive to the depth of the loss. Figure 2(b) shows a similar plot of the imaginary part of the change in impedance as a function of frequency. For a particular thickness loss, the imaginary component decreases as the depth of the air gap increases. Figure 3 shows the second derivative of the imaginary component of the change in impedance as a function of frequency. Again, “bands” are visible that provide a good measure of total thickness loss as observed for the real part of the change in impedance. Inner Diameter = 2.438 mm Outer Diameter = 4.42 mm 30% IACS

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Figure 2. (a) Resistance and (b) reactance component for varying percent material loss (6%,8%,10%) and percent of material loss in 2nd layer (0%, 50%, and 100%).

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Figure 3. Second derivative of reactance component for varying percent material loss (6%,8%,10%) and percent of material loss in 2nd layer (0%, 25%, 50%, 75%, 100%).

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2. Spatial Domain Feature Extraction for Improved Crack Detection Recently, the difficult problem of distinguishing crack responses from other non-flaw asymmetric features, gaps between the fastener and hole, probe liftoff variation, and probe skew, was investigated [9,10]. The fruit of this investigation was a promising feature that is invariant to several irregular non-flaw conditions listed in the introduction to this paper. Earlier work proposed a method to determine optimal probe location for crack detection around a fastener hole [9]. Once the probe location is determined, data is collected, and if necessary, interpolated at a fixed radius around the center of the fastener site. Figure 4(a) shows the imaginary component of the change in impedance as a function of the polar angle around the fastener hole. The noticeable Gaussian shaped response is the feature that is used for crack detection. To obtain a measure of this localized crack feature, an approach was developed using a fit of a characteristic function

f T

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through nonlinear least squares estimation where the localized Gaussian response, B, can be used as a crack measure separate from the sinusoidal noise feature as shown in Figure 4(a). A model-based optimization approach was implemented to evaluate the best signal processing algorithm design to distinguish crack size. In addition, experimental studies were performed to further explore the reliability of this feature in the presence of experimental noise and adjacent holes in close proximity. Through the development of an automated algorithm to quantify this feature, results in Figure 4(b) for the experimental study demonstrate the ability to detect small cracks around fasteners while maintaining a low false call rate [10]. Although the proposed circumferential feature extraction methodology is beneficial for distinguishing crack features in the presence of certain asymmetric hole features, liftoff and probe tilt, other complex features of aircraft structures can hinder the direct application of the approach. For general inspections, the presence of adjacent fastener sites and part edges in close proximity can hinder the detection of cracks located at certain angular locations around the hole of interest. In addition, they can also contribute to the eddy current response in crack regions and thus decrease -3

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prospects for sizing. There is a clear need for model-based feature extraction schemes that also compensate for adjacent fastener sites and part edges. New feature extraction methods were developed to address fitting approximate models to data associated with geometric part features including adjacent fastener sites and panel edges. The solution strategy focuses on three steps: 1) a heuristic approach using a physical understanding of the sources of greatest error, 2) a least-square estimation approach to solving for the polynomial response quickly and accurately, and 3) an iterative approach to improve model solutions for overlapping fastener site and part edge regions. Figure 5(a) displays an image plot of the original measurement data for the in-phase component (Vx) containing 10 fastener sites (9 of titanium, 1 of steel). Figure 5(b) displays an image plot of the processed data with both hole and part edge feature extraction. For this specimen with three cracks located around fastener sites, the crack features are clearly observed. A complete automated process performs this feature extraction algorithm in approximate 60 sec for a 10 hole panel, providing far greater accuracy and a 10X improvement in speed over prior experience with direct global estimation methods [11].

3. Model-based Data Analysis in Spatial and Frequency Domains for the Fastener Crack Problem In order to fully characterize sub-surface corner cracks at fastener sites in multilayer structures, additional measures with sensitivity to all important crack dimensions are needed. In particular, the sizing of corner cracks initiating from the near surface of the second layer shown in Figure 6 requires values in the measurement data that are well correlated to varying crack length (a) and crack depth (b). Multifrequency eddy current methods have been investigated for many NDE applications that require the characterization of various damage states from part characteristics of varying depth [12]. Multifrequency eddy current data have also been used with imaging [13] and inversion methods [14,15] to improve the detection and characterization of cracks and corrosion conditions. In this work, a model-based feature extraction method of the eddy current response in the spatial domain is coupled with multifrequency data analysis for improved sensitivity to corner crack size and aspect ratio. To obtain measures with sensitivity to the localized crack dimensions, the approach uses a fit of a characteristic function for a fastener site and radial crack:

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Figure 6. Diagram of fastener crack problem with varying notch length and depth: (a) a = 1.27 mm, b = 1.27 mm, (b) a = 2.54 mm, b = 1.27 mm, (c) a = 1.27 mm, b = 2.54 mm, (d) a = 2.54 mm, b = 2.54 mm.

f T , r, f

Ar, f cosT  B r, f exp D r, f T 2  C r, f

(2)

for varying radial location and frequency. The localized Gaussian response, B, is evaluated as function of frequency and radial extent from the fastener site center and used as a crack measure. To investigate the viability of this approach, simulated studies in VIC-3D® [16] were performed. Cracks were modeled as notches of finite width with a quarter ellipse profile. The crack length and depth were each varied over two levels in the study (1.27 mm and 2.54 mm) as shown in Figure 6. The frequency ranged from 50 Hz to 2000 kHz. Additional details on the probe model and multilayer structure properties can be found in prior work [10]. Figure 7 presents the simulated results for the local crack characteristic response, B, as a function of radial location and frequency for the four combinations of varying notch length and depth: (a) a = 1.27 mm, b = 1.27 mm, (b) a = 2.54 mm, b = 1.27 mm, (c) a = 1.27 mm, b = 2.54 mm, (d) a = 2.54 mm, b = 2.54 mm. The response as function of the radial direction provides a characteristic valley and peak moving away from the hole center. The magnitude of these local minima and maxima as a function of frequency were estimated using interpolation and investigated further for sensitivity to crack length and depth. Figure 8 presents (a) the minimum response and (b) the maximum response as a function of the frequency and the four combinations of notch length and depth. The minimum and maximum response measures are partially correlated to the cross-sectional area of the corner crack (=Sab/4). Both the minimum and maximum responses also exhibit some varying sensitivity to the crack length and depth with respect to frequency. Processing these minimum and maximum responses can help distinguish the crack length and depth parameters. For example, normalization of the maximum response with respect to the minimum response [as in Figure 8(c) at lower frequencies] and the maximum response at 500 Hz [as in Figure 8(d) at higher frequencies] provides the means to distinguish the two levels of crack depth. A combination of these feature measures can thus be used to help distinguish between these classes of crack length and depth and provide promise for accurate crack sizing.

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4. Conclusions And Recommendations Features have been demonstrated to quantify subsurface material loss, detect subsurface cracks around fastener sites, and estimate parameters related to subsurface cracks around fastener sites. Experimental studies will be conducted to study the impact of measurement noise on second derivative features.

5. Acknowledgements Funding was provided by the Air Force Office of Scientific Research. The authors thank Dr. Harold Sabbagh and Dr. Matthew Golis for the input they provided.

References [1] D. Hagemaier and G. Kark, “Eddy Current Detction of Short Cracks Under Installed Fasteners”, Mat Eval, Vol 55 (1), pp. 25-30, (1997). [2] J..S. Knopp, J. C. Aldrin, E. Lindgren, and C. Annis, “Investigation of a Model-Assisted Approach to Probability of Detection Evaluation”, Rev. Prog. Quant. Nondestr, Vol 26, pp. 11775-1782, (2007). [3] J.G. Thompson, “Subsurface Corrosion Detection in Aircraft Lap Splices Using a Dual Frequency Eddy Current Inpsection Technique”, Materials Evaluation, Vol 51 (12), pp. 1398-1401, (1993). [4] Y.A. Plotnikov, W. J. Bantz, and J. P. Hansen, “Enhanced Corrosion Detection in Airframe Structures Using Pulsed Eddy current and Advanced Processing”, Mat Eval, Vol 65 (4), pp. 403-410. (2007). [5] B. Wincheski , J. Simpson, M. Namkung, D. Perey, E. Scales, and R. Louie, “Development of Giant Magnetoresistive Inspection System for Detection of Deep Fatigue Cracks Under Airframe Fasteners”, Rev. Prog. Quant. Nondestr, Vol 21, pp. 1007-1014, (2002). [6] N.V. Nair, V. Melapudi, H. Jimenez, X. Liu, Y. Deng, Z. Zeng, L. Udpa, T. Moran, and S. Udpa, “A GMR Based Eddy Current System for NDE of Aircraft Structures”, IEEE Transactions on Magnetics, Vol 42 (10), pp. 3312-3314 [7] N. Goldfine, V. Zilberstein, A. Washabaugh, D. Schlicker, I. Shay, and D. Grundy, “Eddy Current Sensor Networks for Aircraft Fatigue Monitoring”, Mat Eval, Vol 61 (7), pp. 852-858, (2003). [8] S. Mandayam, L. Udpa, S. Udpa, and W. Lord, “Invariance Transformations for Magnetic Flux Leakage Signals”, IEEE Transactions on Magnetics, Vol 32 (3), pp. 1577-1580, (1996). [9] J. S. Knopp and J. C. Aldrin, “Numerical Studies of Eddy Current NDE for Small Crack Detection around Fasteners in Multi-Layer Structures”, Rev. Prog. Quant. Nondestr. Eval., Vol 24, pp. 417-424, (2005). [10] J. C. Aldrin and J. S. Knopp, “Crack Characterization Method with Invariance to Noise Features for Eddy Current Inspection of Fastener Sites”, Journal of Nondestructive Evaluation, 25 (4), pp. 165-181, (2006). [11] J. C. Aldrin and J. S. Knopp, “Case Study for New Feature Extraction Algorithms Automated Data Classification, and Model-Assisted Probability of Detection Evaluation”, Rev. Prog. Quant. Nondestr. Eval. 26, pp. 257-264, (2007). [12] H. L. Libby, Introduction to Electromagnetic Nondestructive Test Methods, John Wiley, (1971). [13] T. Chady, M. Enokizono, and R. Sikora, “Crack Detection and Recognition Using an Eddy Current Differential Probe”, IEEE Transactions on Magnetics, Vol. 35 (3), pp. 1849-1852, (1999). [14] J. C. Aldrin, H. Sabbagh, E. Sabbagh, R. Murphy, M. Concordia, D. Judd, E. Lindgren, and J. Knopp, “Methodology Using Inverse Methods for Pit Characterization in Multilayer Structures”, Rev. Prog. Quant. Nondestr. Eval. Vol. 25, pp. 767-774, (2006). [15] N.C. Haywood, and J. R. Bowler, “Eddy Current Imaging of Buried Cracks by Inverting Field Data”, IEEE Transaction on Magnetics, Vol 28 (2), pp. 1336-1339, (1992). [16] R. Murphy, H. Sabbagh, A. Chan, and E. Sabbagh, “A Volume-Integral Code for Electromagnetic Nondestructive Evaluation”, Proceedings of the 13th Annual Review of Progress in Applied Computational Electromagnetics, (1997).

Electromagnetic Nondestructive Evaluation (XI) A. Tamburrino et al. (Eds.) IOS Press, 2008 © 2008 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-58603-896-0-141

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Inversion of Potential Drop Data for the Reconstruction of Crack Depth Profiles Giuseppe SPOSITO a, Peter CAWLEY a and Peter B. NAGY a,b Non-Destructive Testing Group, Department of Mechanical Engineering, Imperial College London, London SW7 2AZ, UK b Department of Aerospace Engineering and Engineering Mechanics, University of Cincinnati, Cincinnati, OH 45221

a

Abstract. This paper considers the inverse problem of estimating the depth profile of an unknown defect from measurements of transfer resistance. The results of both finite-element analyses and experimental tests on specimens with EDM notches of various shapes and sizes were used to develop a simple inversion algorithm that allows a good reconstruction of the depth profile. A synthetic focusing technique is applied which improves the quality of the reconstruction. Keywords. Potential Drop, inverse problem, crack sizing, focusing

1. Introduction Estimating the shape and size of a defect is a problem of major interest in many industrial applications, since the depth of a crack is often a key parameter in calculations of structural integrity. The potential field created on the surface of a testpiece by the injection of direct or alternating currents for Potential Drop (PD) measurements has been obtained analytically for simple geometries in the absence of defects [1]; previous studies have also shown that a simple three-dimensional Finite Element (FE) model is able to give an accurate solution to the direct problem of predicting the response of a probe to a surface-breaking defect of known geometry [2]. Most previous work on the inverse problem of using values of transfer resistance measured at a number of different locations to calculate the depth profile of an unknown defect have assumed a priori knowledge of the defect shape, or made use of parameters to be evaluated heuristically [3-6]; crack gauges are commercially available that assume the defect has a semi-circular form. However, this assumption is not always correct. The aim of the present study is to develop an inversion technique of more general validity.

2. Experimental Setup Used for Measurements For the present study a linear array probe having the dimensions shown in Figure 1 was manufactured, its dimensions being chosen so that if current is injected at the outer pins the distribution across the measurement electrodes is fairly uniform. The 5 mm spacing between the lines of measurement electrodes was chosen to give reasonably high

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60 5 j=-2 j=-1 j=0 j=1 j=2

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sensitivity to cracks (the fractional increase in resistance due to a defect is roughly proportional to the defect depth as a fraction of the electrode spacing) while not being overly sensitive to errors in the pin positioning. However, the whole system is reciprocal and it is much more practical to multiplex the healthy input currents (~130 mA) than the very small measured voltages (order 1 ȝV). Therefore when running the tests it was decided to measure the voltage across the two outer electrodes of Figure 1 and inject current across pairs of inner electrodes on opposite sides of the defect position in turn. The excitation signal is generated by the internal oscillator of a lock-in amplifier and driven by a differential circuit: the symmetry of the signal is ensured by two scaling amplifiers whose gain, initially set as equal and opposite, is automatically adjusted to compensate for any differences between the contact resistances of the electrodes. A multiplexer then routes the signal to one of the pairs of inner electrodes at a time. The voltage difference measured at the outer electrodes is amplified by a lownoise preamplifier, and the values are read on the same lock-in amplifier used to generate the excitation signal. The instruments are remotely controlled via a simple LabView routine. Relatively small currents (as little as 130 mA) could be used, as opposed to the large currents (up to the order of 100 A) often required in commercially available DCPD systems, thanks to the high sensitivity of the lock-in amplifier used for the experiments, which is capable of measuring signals of the order of a nV. However, it must be mentioned that the signal to be measured, i.e. the voltage difference between the two sensing electrodes (differential signal), is typically much smaller than the voltage at either electrode (common signal), and therefore, in addition to the differential driving mentioned earlier, a very high Common Mode Rejection Ratio (CMRR) is required; the preamplifier used for the experiments had a CMRR in excess of 110 dB, which means that the differential part of the signal is amplified by a factor at least 3 · 105 times more than the common signal. The electronic noise introduces oscillations of less than 0.1% in the measured signal, and it is negligible compared to the variations due to the uncertainty in the positioning of the probe.

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Figure 2. Current distribution along the centreline of the array probe (x=0) for focusing with 1, 3 and 5 pairs of electrodes.

3. Focusing The thin line in Figure 2 shows the current distribution across the centreline of the array when a unit current I0 is injected between the two central electrodes. The wide lateral spread of current causes an averaging effect that would ‘smear’ rapid variations in the depth profile of a defect. The array of Figure 1 gives the possibility of producing ‘focused’ currents. If a negative current was applied to the pairs of electrodes j=±1 in Figure 1 adjacent to the central pair (j=0) which was driven with the positive current that yielded the thin-line distribution of Figure 2, it would be expected that part of the wide lobe could be cancelled out, thus ‘squeezing’ the current into the centre of the array. The thick and shadowed curves of Figure 2 show the resulting current distribution if this concept is applied to three and five pairs of electrodes respectively: the peak is considerably narrower, as desired; as a side effect the current at the centre is reduced. The optimum weightings of currents applied to the pairs are different depending on the number of pairs used, and they are also a (weak) function of frequency. The distributions shown in Figure 2 are for low frequency (DC) and are obtained by injecting I±1=-0.33 at the electrode pairs j=±1 for 3-pair focusing, or I±1=-0.39 at j=±1 and I±2=+0.04 at j=±2 for five pairs. These values, scaled to the positive unit current I0 injected at the central pair, are those that minimise the value of the integral J x ( y) dy , x (0)

³J

(1)

where Jx is the axial current density at the centreline of the array, as plotted in Figure 2, and the integral is calculated over the centreline along the entire width of the specimen.

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In practice the focusing was done synthetically: measurements were taken by applying the same current to each electrode pair in turn, and the focused results were computed later by combining the weighted data. This procedure is analogous to SAFT (Synthetic Aperture Focusing Technique), commonly used in ultrasound and radar.

4. Notch Profile Reconstruction Using Focused Array Tests were run on 150-mm long, 50-mm wide, 10-mm thick blocks of SS304. In addition to experimental measurements, FE simulations were run using the commercial FE software Abaqus and the simple quasi-three-dimensional model presented in [2]. Both experimental and numerical results on a notch-free specimen (baseline) and on three specimens with EDM notches of different shapes (rectangular, triangular, circular arc) but identical length and maximum depth are shown in Figure 3. It should be noted that no focusing has been applied at this stage. Three array positions were required to cover the full block width, which explains the three groups of points in the graph for each specimen; some variation would be expected across the array even in an infinitely wide plate, because the outer electrodes are fixed and only directly in line with the central pair of the array. This effect is predicted satisfactorily by the FE model, as is the much larger variation towards the edges of the specimen; both effects are removed once results relative to the baseline are considered. As an example, the reconstructed profile of the triangular notch is shown in Figure 4. At each measuring point the estimated depth is given by d

T˜

V  V0 , V

(2)

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where T is the block thickness and V and V0 are the voltages measured on the notched specimen and on the baseline, respectively. This formula is easily derived assuming that at low frequency the potential drop is inversely proportional to the remaining thickness T-d ‘seen’ by the current. It is therefore important that the lateral spreading of the current be small, as achieved by focusing. The results of Figure 4 show that focusing the currents synthetically does in fact yield a very good reconstruction of the depth profile already for three pairs. Note that the same number of electrodes must be used for both V and V0 if focusing is used. 4.0 1 pair

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Distance from edge [mm]

Figure 6. Reconstructed profiles of a 10-mm long, 3-mm deep circular arc notch. FE predictions (solid lines) and measurements (points) compared with the real profile (dashed line).

The reconstruction of the rectangular notch (see Figure 5) is less satisfactory: focusing, while sharpening the representation of the step at the extremities of the notch, causes an overestimation of the maximum depth. Defects of such shape, however, are very unlikely to occur in practice; in fact, previous studies on this subject often made the assumption that cracks have a semi-circular or semi-elliptical shape (see for example [3] and [6]). A circular arc is therefore a fairer approximation of a real crack. The results for this notch are shown in Figure 6: as for the triangular notch, the reconstruction is very good if focusing with three or five pairs.

5. Conclusions A FE model was used to determine a simple formula for the inversion of Potential Drop measurements. This was subsequently applied to experimental data obtained with an array probe on specimens with EDM notches of various shapes, and it has been shown to give a good reconstruction of the notch depth profiles. The improvement in the results introduced by synthetic focusing of the injected currents has also been discussed. Future work will be aimed at exploring the range of applicability of the formula used for the estimation of crack depth, by extending the study to notches of different aspect ratios and blocks of different geometry.

References [1]

N. Bowler, “Analytical Solution for the Electric Field in a Half-Space Conductor Due to Alternating Current Injected at the Surface”, J. Appl. Phys. 95(1), 344-348 (2004)

G. Sposito et al. / Inversion of Potential Drop Data for the Reconstruction

[2] [3] [4] [5] [6]

147

G. Sposito, P. Cawley, and P. B. Nagy, “Crack Profile Reconstruction by Means of Potential Drop Measurements”, Review of Progress in Quantitative Nondestructive Evaluation 26A, 733-740 (2006) D. H. Michael, R. T. Waechter, and R. Collins, “The Measurement of Surface Cracks in Metals by Using AC Electric Fields”, Proc. R. Soc. Lond. A 381, 139-157 (1982) M. P. Connolly, D. H. Michael, and R. Collins, “The Inversion of Surface Potential Measurements to Determine Crack Size and Shape”, J. Appl. Phys. 64(5), 2638-2647 (1988) M. McIver, “Characterization of Surface-Breaking Cracks in Metal Sheets by Using AC Electric Fields”, Proc. R. Soc. Lond. A 421, 179-194 (1989) K. Ikeda, M. Yoshimi, and C. Miki, “Electrical potential drop method for evaluating crack depth”, Int. J. Fracture 47, 25-38 (1991)

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Automatic classification of defects with the review of an appropriate feature extraction Alicia ROMERO RAMIREZ, Neil PEARSON and Dr. J. S.D. MASON Swansea University, SA28PP, UK. Email: [email protected]

Abstract. A novel method for the automatic classification of defects using magnetic flux leakage inspection is presented. A technique based on geometric measures to distinguish between different defects due to petro-chemical tank corrosion is presented. In order to characterize a defect, a process of feature extraction is proposed. Principal component analysis is then used to select the most powerful set of features. The performance is compared using two different methods: k-nearest neighbor and support vector machine. The results show an accuracy of 91% with which automatic classification is possible on unseen test examples on steel plates.

Introduction Petro-chemical storage tanks are important objects in the industrial sector. The servicelife of a storage tank is between 20-40 years, although in some cases this life is reduced to 2-3 years due to failures within the storage tank [1]. The importance of predicting a possible tank failure for the industry is not only the value of the tank content, which in the case of petroleum tank is very high, but also the environmental damage that the tank failure can cause and consequently, fines the industry would potentially face. The main cause of failure of steel storage tanks is corrosion [2]. Magnetic flux leakage (MFL) can reliably detect metal loss due to corrosion, permitting a quantitative evaluation of the size of the defect [3]. MFL tools are equipped with sensors to collect information about the state of the floor tank. It is suggested in [4] that a deeper understanding of the shape of the MFL signals could be beneficial to find more effective type-of-defect separation methods. Once a defect is detected, its shape and size is not easy to predict. This is the topic of this paper. In recent years there has been much interest in the development of automatic classification of defect patterns and many are using neural networks, for example [5-9]. Some successful work in the use of ultrasonic approaches is reported in [5,8,9] and automatic defect classification using MFL is reported in [7] for pipe welds achieving a success classification rate of 71% across 3 classes namely spheres, parallelepipeds and cylinders. In [6] eddy current signals are used for defect classification in aluminium plates with a reported error rate of 10%.

A. Romero Ramirez et al. / Automatic Classification of Defects

1.

149

Data acquisition

MFL testing machines require a mapping of magnetic fields onto flaw geometry. The machine used for the development of this work, measures magnetic flux signals and converts them into estimates of percentage of volumetric loss. A discussion about the reliability of this method can be found in [3]. Each prospective or potential defect is represented by a matrix of data ([m x n]), in which the geometry of the defect is not easily determined. In very simple terms the defect classification could be in terms of the number of rows and the number of columns ([m x n]) for which the signal exceeds some threshold. The percentage of metal-loss could be a suitable integration of these values. However we show here that more useful classification is possible.

2.

Feature extraction and feature transformation

Defect characterization and pattern recognition are essential for the development of an automatic classifier. The goal is to highlight similarities between defects from the same class and to draw attention to the differences between defects from different classes. A number of geometrically derived features are considered. These include: relation between length and width, position of the maximum and minimum, angle of the slopes, gradient of the channel with the maximum, mean values, area from the top view, volume and length relations. In total, the number of extracted features per defect is 50. By examining a number of examples and studying the different classes, there have been identified that lead to good classification performance. Clearly, there is significant redundancy across the set of 50 chosen features. Hence in an attempt to reduce this redundancy, principal component analysis (PCA) [11] is used. Figure 1 shows the results of the PCA analysis on a preliminary training data set. Note subsequent experimental results are performed on data test sets that do not direct overlap with this PCA set. In Figure 1 it is shown that by selecting the 30 most significant components the percentage of information lost is below 1%.

Figure 1. % of information versus PCA components retained. Experiment on preliminary data set.

150

3.

A. Romero Ramirez et al. / Automatic Classification of Defects

Classification

The overall objective of the work is to determine that an incoming signal belongs to a specific category from among a finite set of possibilities. This is referred to as identification and is a 1-from-n classification task. Alternatively verification can be considered; this is a 1-from-2 class task and can be regarded as a special case of identification. The choice of classes form a closed set was made taking into consideration the shape of real defects appearing in a petro-chemical storage tank. Due to the width of the platforms (between 6-12 mm) undercutting defects are unlikely to appear [15]. Consequently the shapes of our defects are restricted. Defects are assumed to have a profile similar to the ones shown in Figure 2, namely pipe, conical and lake.

Figure 2. Different defect profiles.

4.

Experimental work

The assessment of the classifier is reported in two different ways. The first uses a multi-class classifier with three classes and the second uses three binary classifiers (one per class). The arrangements are shown in Figure 3. In both cases a ‘signal to test’ gives rise to three scores (Ps, Pc, Pl) and these are subjected to a single decision threshold. The relative performance is shown on a detection error tradeoff (DET) curve [14] as the decision threshold is varied. In addition accuracy scores are given.

Signal to test

Signal to test

Multi class classifier

Probability of being a pipe defect. (Ps) Probability of being a conical defect. (Pc) Probability of being a lake defect (Pl)

Pipe classifier

Probability of being a pipe defect. (Ps) Probability of NOT being a pipe defect.

Conical classifier

Probability of being a conical defect. (Pc) Probability of NOT being a conical defect.

Lake classifier

Probability of being a lake defect (Pl) Probability of NOT being a lake defect

Figure 3. Experimental setup.

151

A. Romero Ramirez et al. / Automatic Classification of Defects

DET curves are frequently used to measure the verification performance of a classification algorithm. Verification addresses a two-class problem where the expected answer is either true or false. Here we focus on verification so that the assessment is independent of the number of classes. For each trial, the score is thresholded and a decision is made. The DET curve shows the variation of this threshold. Such an approach gives a robust indication of performance. Figure 4 presents the scheme of a feature vector entering the classifier which produces a score which is them threshold. Moving the threshold changes the distribution of the error rates as indicated in the DET plots.

Threshold 2.5

2

Classifier

SCORE

1.5

Density

Feature Vector

1

0.5

0 −1

−0.5

0

0.5 Critical values

1

1.5

2

Figure 4. A feature vector enters the classifier which produces a score which is then thresholded. The 2 distributions represent actual in-class and out-of-class scores.

Due to the difficulty of having real data from the field with accurate ground truth, emulated corrosion has been used. Thirty defects in total representing three classes (pipe, conical, lake) were created in steel plates. The profiles and sizes are shown in Table 1. The data set contains 816 records of a total of 30 defects classified as: pipe (121), conical (330), lake (365). It is worth noting that the recordings were made on 7 different dates. The reason for having fewer samples of pipe defects is due to a limitation of the scanning tool, which captures only defects with a volume-loss larger than 20%. The data set is divided into two groups: a) training (408 recordings), b) testing (408 recordings). There is no data overlap in between the two.

Table 1. Description of emulated defects. Profile

Type

Thickness of plate

Pipe

6 [mm]

Conical

6 [mm]

Lake

6 [mm]

Diameters [mm] x maximum depth [mm] 2.0 x 2.0 2.0 x 4.0 10 x 1.2 17.3 x 4.2 20 x 1.0 20 x 2.0

3.0 x 2.0 3.0 x 4.0 12.1 x 1.8 18.2 x 4.8 30 x 1.0 30 x 2.0

4.0 x 2.0 4.0 x 4.0 13.7 x 2.4 10 x 1.2 40 x 1.0 40 x 2.0

5.0 x 2.0 5.0 x 4.0 15.1 x 3.0 13.7 x 2.4 50 x 1.0 50 x 2.0

6.0 x 2.0 6.0 x 4.0 16.3 x 3.6 16.3 x 3.6 100 x 1.0 100 x 2.0

152

A. Romero Ramirez et al. / Automatic Classification of Defects

Performances with SVM

Performances with KNN

Table 2. Experimental results for K-nearest neighbour and support vector machine classifiers. The SVM with three verification classifiers seem to give the best results.

Accuracy using “multiclass” classifier: 85.75 % Accuracy using three binary classifiers: 90.25 %

Accuracy using “multiclass” classifier: 87.46 % Accuracy using three binary classifiers: 91.44 %

The experimental results in Table 2 show the accuracy and the DET curves using two different classifiers, namely K-nearest neighbour and support vector machine. In both cases there is a discontinuous profile which corresponds to the ‘multiclass’ experimental setup and a continuous profile that correspond to the three binary classifiers experimental setup. The number of scores used per profile is 1224 scores.

A. Romero Ramirez et al. / Automatic Classification of Defects

5.

153

Conclusion

Classification of emulated corrosion based on the proposed approach has been successfully achieved with accuracy over a 90% when classifying pipe, conical and lake defects. The final goal of this work is the characterization of real defects appearing in storage tank floors. Here a simplification of the problem based on emulated corrosion is presented. The feasibility of using emulated corrosion as data to train the classifier for real inspections is currently being tested.

Acknowledgements The work is funded by European Social Funds in collaboration with Silverwing Ltd.

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]

M.L. MEDVEDENA and T.D. TIAM. Classification of corrosion damage in Steel Storage Tanks. Chemical and Petroleum Engineering.Vol.34. Nos 9-10. 1998 GEYER W.B Handbook of storage Tank Systems: Codes, Regulations and Designs. K.REBER, A.BELANGER. Reliability of Flaw Size Calculation based on Magnetic Flux Leakage Inspection of Pipelines. ECNDT 2006 Till SCHMITTE. Modelling of Magnetic Flux Leakage Measurements of Steel Pipes. ECNDT 2006 Oleg KARPASH, Maksym KARPASH, Valentine MYNDJUK. Development of Automatic Neural Network Classifier of Defects Detected by Ultrasonic Means. ECNDT 2006 Adam DOCEKAL. Signal Preprocessing Methods for Automated Analysis of Eddy Current Signatures during Manual Inspection. ECNDT 2006 A.A.CARVALHO. MFL signals and artificial neural networks applied to detection and classification of pipe weld defects. NDT &E International. June 2005. J.B. SANTOS. Automatic defects classification-a contribution. NDT &E International.. June 2000. A.MASNATA. Neurual network classification of flaws detected by. ultrasonic means.NDT & E International. October 1995 K. MANDALY, D.L. ANTHERTON.A study of magnetic flux-leakage signals. July 1998 LINDSAY I SMITH. Principal component analysis. February 2002. V.N Vapnik, Statistical Learning Theory. Adress: New York: Wiley, 1998. C.J.C BURGES. Discov., vol2, no 2, pp.1-47, 1998. NIST, “DET-Curve Plotting software for use with MATLAB”. Software available at http://www.nist.gov/speech/tools http://www.corrosion-doctors.org/Forms-pitting/Pitting.html

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Microwave Nondestructive Detection of Longitudinal Cracks in Pipe with U-bend and Prediction of its Location by Signal Processing a

Kavoos ABBASIa,1 , Satoshi ITOa , Hidetoshi HASHIZUMEa Dept. of Quantum Science and Energy Engineering, Tohoku University, Sendai, Japan

Abstract. A circular electromagnetic TE11-mode is used for detection of longitudinal crack in a stainless steel pipe. To show the capability of microwave nondestructive testing for detection of cracks in large and complex piping systems such as steam generator (SG) tube, inspected pipe including U–bend are examined in this study. The crack location is determined through time of flight (TOF) of the reflected wave and group velocity of electromagnetic signal. The TOF is evaluated in the time domain via Inverse Fast Fourier Transform (IFFT) of the wave spectrum. Then, two different methods of signal processing are applied to obtain TOF more accurately. Keywords. Microwave, longitudinal crack, Time of flight (TOF)

Introduction Steam generator (SG) tubing in pressurized water reactors (PWRs) is subject to a variety of degradation processes that can lead to tube cracking, wall-thinning, and potential leakage or tube rupture [1]. In order to avoid the tube failure, the piping systems of the reactors must be routinely inspected to guarantee the safety of operations. Hence detection of defect in complex piping systems in early stage of degradation with a high-speed and high-accuracy inspection method is serious matter in the operation of pressurized water reactor. At present, the typical methods for detecting defects are eddy current testing (ECT) and ultrasonic testing (UT). Even though these methods have high accuracy, they need point-by-point inspection and therefore, they are time/cost–consuming for the inspection of long pipes [2, 3]. Hence it is desirable to develop another high-speed technique for crack detection. One of the most promising techniques which might reduce the time/cost of long-range inspection is the NDT method using microwaves. The experimental results show that, due to propagation of an electromagnetic wave above cutoff frequency in waveguides without significant attenuation loss it is possible to inspect lengthy pipes [4, 5]. In our previous studies, detection of circumferential and longitudinal cracks by using TM01 and TE11 modes were experimentally verified in a short straight tube [6, 7]. In this study to show the potential of this method for inspection of large and complex piping system, the microwave NDT method is applied to detect a longitudinal crack in a long pipe including U-bend. The obtained experimental results are analyzed by two different signal processing methods. 1Corresponding

Author: Kavoos Abbasi, Tohoku University, Aramaki-Aza-Aoba 6-6-01-2, Sendai, Japan; E-mail: [email protected]

K. Abbasi et al. / Microwave Nondestructive Detection of Longitudinal Cracks

155

1. Background and Experimental Setup

This study is carried out to detect longitudinal crack in a pipe with U-bend by using circular TE11-mode which is suitable for detection of longitudinal crack in the pipe. The TE-modes are characterized by fields with Ez = 0 and Hz z 0, where z indicates the direction of propagation (In the case of cylindrical pipe, z corresponds to the axial direction of the pipe). When an electromagnetic wave is propagated in the pipe, an electric surface current with a circumferential component is produced at the inner surface of the pipe. Once this surface current flows in the pipe with a longitudinal crack, the crack prevents proper flow of the surface current. Consequently, part of the incident wave is reflected, which has information about the crack. A schematic diagram of the experimental setup is given in Fig.1. The network analyzer is used as the generator of the electromagnetic wave. The generated wave passes through the mode converter via the coaxial line. The mode converter is formed by joining the rectangular waveguide (C-band) to the circular waveguide in order to transform the rectangular TE-modes to the circular TE- and TM-modes.

pipe 2

Crack

Matched load Plunger position

E

Tapered waveguide F

110.9 mm

Circular waveguide

l

C B 69.5 mm D 298.8 mm U-bend

126 mm

A

pipe 1

85 63 A

SPE C TR U M AN A L YZ E R

9 kH z - 26.5 G H z

65 mm

Rectangular waveguide

Mode converter

Coaxial line

Network Analyzer 10 MHz ~ 40 GHz

Fig.1. Experimental system for detection of axial crack The first dominant circular TE-mode is TE11-mode which can be resonated in the system by moving the plunger in the circular waveguide. The conditions to resonate or to damp the mode are given by the following equations:

156

l

l

K. Abbasi et al. / Microwave Nondestructive Detection of Longitudinal Cracks

m (for resonating) 2 2m  1 (for damping) Og . 4

Og .

(1) (2)

where l is the distance between plunger and center of rectangular waveguide and m is an integer. The Og is the wave length of the electromagnetic wave as is guided in the circular waveguide. Group velocity of the wave, which is an important parameter for calculating the crack locations, is also given by the following equation.

vg

c

PRH R

§f · 1  ¨¨ c ¸¸ © f ¹

2

(3)

wherein c, PR, HR are light velocity, relative permeability and relative permittivity, respectively. The inspected pipe made of SUS-304 has inner and outer diameters of 34 mm and 38 mm respectively. As seen from Fig.1, the inspected pipe is made of three parts, two straight pipes and U-bend pipe. The length of pipe 1, pipe 2 and U-bend is 3000 mm, 800 mm and 1200 mm respectively. The crack is a longitudinal slit whose length is 40 mm and width is 0.3 mm and made by cutting blade from the outer surface of the pipe to the inner surface. The position of the created crack is indicated by point F in Fig.1. To reduce environmental noise and to absorb the transmitted wave, a matched load which is made of paraffin and graphite is mounted at the end of the pipe. The electromagnetic modes can be resonated or reduced by changing the plunger position from 90 mm (minimum position) to 180 mm (maximum position). The experiment is performed for pipes without fluid in them.

2. Results and Discussions 2.1 Evaluation of results at plunger position of 90 ~180 mm Two experiments are carried out for two crack positions CF = 4200 mm and 4600 mm separately, where CF is the length from point C to point F in Fig.1. The TE11-mode is the first and dominant circular mode in any circular waveguide. The cutoff frequency of this mode in the inspected pipe is 5.17 GHz. The next circular mode is TM01-mode with cutoff frequency of 6.755 GHz. To avoid generation of TM01-mode in the system, frequency range of 5.2 ~ 6 GHz is chosen in this experiment. Figures 2(a) and (b) show the results for the crack located at 4180 mm in frequency and time domain, respectively when the plunger position is changed from 90 mm to 180 mm. Fig.3 shows the same results for a crack located at 4580 mm. These results are obtained by subtraction of reflection coefficient signal (Ƚ) of the pipe with and without crack. The color bar in each figure shows these differences of two signals (ǻī). Reflection coefficient is defined as the ratio of the reflected signal voltage to the incident signal voltage as the following equation.

K. Abbasi et al. / Microwave Nondestructive Detection of Longitudinal Cracks

*

Vreflected Vincident

157

(4)

-3

|'*| [x10 ]

As observed from Fig.2 and Fig.3, ǻī reaches the maximum value in several plunger positions. This means that the TE11-mode is resonated at those plunger positions. Dashed-line indicates TOFs obtained by the calculation at frequency of 6 GHz.

Calculated time at 6 GHz

(a)

(b)

-3

|'*| [x10 ]

Fig.2. Difference of reflection coefficient (ǻī) at different plunger positions for the crack located at 4180 mm (a) frequency domain (b) time domain

Calculated time at 6 GHz

(a)

(b)

Fig.3. Difference of reflection coefficient (ǻī) at different plunger positions for the crack located at 4580 mm (a) frequency domain (b) time domain

158

K. Abbasi et al. / Microwave Nondestructive Detection of Longitudinal Cracks

2.2 Evaluation of results at one plunger position

0.10

0.10

0.08

0.08

0.06

0.06

0.04

0.04

0.02

0.02

'*

'*

The obtained results in Fig.2(b) and Fig.3(b), indicated that large response of the electromagnetic waves are occurred in several plunger positions such as 90 mm, 125 mm and 155 mm (almost center of area with large intensity). Herein, As an example, the result when plunger located at 125 mm is investigated. Figure 4 displays ǻī in frequency domain and Fig.5 displays ǻī in time domain for two crack locations. The signals shown in Fig.5 are obtained by taking the IFFT (Inverse Fast Fourier transform) of the signal shown in Fig.4.

0.00

0.00

-0.02

-0.02

-0.04

-0.04

-0.06

-0.06

-0.08

-0.08

-0.10 5.2

5.4

5.6

5.8

-0.10 5.2

6.0

5.4

5.6

5.8

6.0

Frequency [GHz]

Frequency [GHz]

(b

(a

1.0

0.5

0.5 -3

' * [x10 ]

1.0

-3

' * [x10 ]

Fig.4. Difference of reflection coefficient (ǻī) in frequency domain for plunger position of 125 mm and (a) crack located at 4180 mm (b) crack located at 4580 mm

0.0

0.0

-0.5

-0.5

-1.0

-1.0 0

20

40

60

80

Time [ns]

100

120

140

0

20

40

60

80

100

120

140

Time [ns]

(a) (b) Fig.5. Difference of reflection coefficient (ǻī) in time domain for plunger position of 125 mm and (a) crack located at 4180 mm (b) crack located at 4580 mm

K. Abbasi et al. / Microwave Nondestructive Detection of Longitudinal Cracks

159

In Fig.2 (b) and Fig.3 (b), the shortest times are measured as TOFs (Time of Flight) for the each crack location since the highest frequency (6 GHz) in the operation frequency range has the shortest time of flight. In order to calibrate the experimental result, the TOF is calculated at a frequency of 6 GHz. The obtained TOFs from the calculations for the two aforementioned crack locations, 4180 mm and 4580 mm, are 62 ns and 67.2 ns, respectively. The calculated TOFs are denoted in Fig.5 (a) and Fig.5 (b) by solid arrows. Figure 6 is obtained by a applying Hilbert transform filter upon the signal shown in Fig.5. As is seen from this figure, the response of electromagnetic waves to the crack becomes clearer than before and noise as displayed in each graph (from 0 to ~60 ns) is mostly canceled out. The solid arrows in Fig. 6 indicate the calculated TOFs. One might take for granted that the two sharp peaks with large amplitudes in Figs.6 (a) and (b) with their related times (75 ns and 80 ns) can be considered as the TOF of the electromagnetic wave for each crack location. However, it is not a correct assumption for the maximum frequency (6 GHz) in the frequency range considered has the shortest TOF. Later on, we will show that the TOF is actually the time when ǻȽ starts to increase rather than the time related to those large peaks. Hence, in the next step another method is applied to the signal shown in Fig.5 so as to tell which time should be considered as the real TOF of the crack. In this method a cut-off value is defined with regard to the maximum value of ǻȽ as given by the following equation. Cut off value = E × ('ī) max where the threshold factor (E) is changed from 0.05 to 0.3 (such values are extracted from the experimental error). The results obtained via such a signal processing are shown in Fig.7 (a) and Fig.7 (b). In this analysis the signals are cut off until the response of electromagnetic waves becomes larger than the cut-off value. As observed from these figures, for two crack locations, the TOF remains almost constant when the threshold value changes from 0.1 to 0.3. The obtained TOFs by this method for two crack locations are 66.45 ns and 71. 㧝 ns. There is also a small discrepancy between these TOFs and those calculated (62 ns and 67.2 ns). These differences for two crack locations (4180 mm and 4580 mm) are 4.45 ns and 3.9 ns. From Fig.4, it is seen that the amplitude of the signal in frequency range of about 5.9 ~ 6 GHz is rather smaller than at other frequencies (5.2 ~ 5.9 GHz). This means that the response of the electromagnetic wave within this frequency range is too small to be detected. This is why the calculated time is a little different from the one predicted.

160

K. Abbasi et al. / Microwave Nondestructive Detection of Longitudinal Cracks

5

4.0 3.5

Calculated time = 62 ns

Calculated time = 67.2 ns

3.0 -6

3

_'*_ [x10 ]

-6

_'*| [x10 ]

4

2

2.5 2.0 1.5 1.0

1

0.5 0 0

20

40

60

80

100

120

0.0

140

0

20

Time [ns]

40

60

80

100

120

140

Time [ns]

(a)

(b)

80

80

70

70

60

60

Time [ns]

Time [ns]

Fig.6. Difference of reflection coefficient (ǻī) in time domain for plunger position of 125 mm after applying Hilbert transform and (a) crack located at 4180 mm (b) crack located at 4580 mm

50 40

Predicted TOF

30

50

30

20

20

10

10

0 0.05

0.10

0.15

0.20

E

0.25

0.30

Predicted TOF

40

0 0.05

0.10

0.15

0.20

0.25

0.30

E

(a) (b) Fig.7. Difference of reflection coefficient (ǻī) in frequency domain for plunger position of 125 mm and (a) crack located at 4180 mm (b) crack located at 4580 mm The times as calculated at frequency of 5.9 GHz are 64.94 ns and 70.47 ns and differences with those predicted are 1.51 ns and 0.63 ns. The calculated crack locations at this frequency are 4173 mm and 4618 mm, which are closer to the predicted ones. The predicted TOF and predicted crack location are summarized in Table 1.

K. Abbasi et al. / Microwave Nondestructive Detection of Longitudinal Cracks

161

Table 1: predicted TOFs and Crack location Crack locations

Frequency range (GHz)

Calculated TOF (ns)

Predicted TOF(ns)

Predicted crack location (mm)

4180

5.2 ~ 6

62

66.45

4517

4580

5.2 ~ 6

67.2

71.1

4871

4180

5.2 ~5.9

64.94

66.45

4173

4580

5.2 ~5.9

70.47

71.1

4618

3. Conclusions In this study, a NDT method using high frequency electromagnetic waves is used to detect a longitudinal crack in a piping system including U-bend. The results show that the circular TE11-mode is a suitable mode to detect longitudinal cracks. To infer information about the existence of a crack and its location, two different signal processing methods are introduced. From our results the response of electromagnetic waves to the crack is clearly exhibited. The signals in the time domain are obtained by applying IFFT onto the signals in the frequency domain. TOFs follow quite accurately by performing two different signal processing methods. Then, we show that by knowing both TOF and group velocity of electromagnetic waves, the position of crack can be determined. Although the open crack with depth as same as the thickness of test pipe was detected in this study, however ,due to this fact that skin depth of microwave in the inner surface of the pipe is too small (in microscale), the ID crack with depth of micrometer can be detected by this technique. There was a limitation to make a crack with width smaller than 0.3 mm, however we looking for a way to create crack with smaller width. The detection of crack with small length will be investigated in the next experiment.

References [1] [2] [3] [4]

[5] [6]

[7]

P.E. MacDonald, V.N. Shah, L.W. Ward, P.G. Ellison, Steam generator tube failures. NUREG/CR6365, INEL-95/0393 (1996). M. V. Brook, D. K. Ngoc, J. E. Eder, Ultrasonic Inspection of Steam Generator Tubing by Cylindrical Guided Waves, Review of Progress in Quantitative Nondestructive Evaluation, 9 (1990), 243-249. K. Sugawara, H. Hashizume, S. Kitagima., Development of NDT method using electromagnetic waves, JSAEM Studies in Applied Electromagnetic and Mechanics 10 (2001), 313-316. H. Hashizume, S. Kitajima, T. Shibata, Y. Uchigaki and K. Ogura, Fundamental study on NDT method based on electromagnetic waves, ENDE2003, Saclay, Studies in Applied Electromagnetics and Mechanics 24 (2003), 263-270. H. Hashizume, T. Shibata and K. Yuki , Crack detection method using electromagnetic waves, International Journal of Applied Electromagnetics and Mechanics 20 (2004), 171-178 K. Abbasi, S. Ito, H. Hashizume, K. Youki, Crack detection by using electromagnetic waves, EPRI 5th International conference on NDE in relation to Structural Integrity For Nuclear And Pressurized Components 2006. K. Abbasi, S.ito, H.Hashizume, Microwave detection of longitudinal crack in straight pipe, ICONE 15, Nagoya, 2007.

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Electromagnetic Nondestructive Evaluation (XI) A. Tamburrino et al. (Eds.) IOS Press, 2008 © 2008 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-58603-896-0-162

Some Experiences with Microwave Investigation of Material Defects Dagmar FAKTOROVÁ University of Žilina, Faculty of Electrical Engineering, Slovak Republic

Abstract. The paper deals mainly with microwave measurement of deeper cracks in metal samples while an attempt to describe the crack as a part of the microwave line is set out. Information about the crack’s properties is obtained from the reflected signal directly measured and also by means of impedance measurement. Keywords. Non-destructive testing, microwaves, crack depth, waveguides, rust

Introduction The article is engaged in detection of cracks in metals from the microwave theory standpoint, and so it tends to basic research. Nevertheless an example about more versatile using of Maxwell´s equations is presented on a practical case at the detection of a defect in metal, a smaller one comparing with the detector’s wavelength. On the assumption starting from the wave theory applied in microwave technique a proof is given that a seeming unreability of the defect detected in such configuration is in a fact one case of electromagnetic wave spreading out in the rectifying surroundings. On the experiments with artificial defects it is demonstrated how general relations for impedance can be used at the determining of the defect geometry. On the basis of measurements also the influence of dielectric splits on the measuring signal is quantitatively presented.

1. Theoretical basis and applied formulae As to general approach to the problems, Maxwell equations provide the basis to solution and for the experimental part we have chosen the waveguide technique making use of the same theoretical basis. For the transversal electric field having a sinusoidal character with the angular frequency ω we can write

∂ 2 E&

& ∂ 2E

∂ 2 E&

ω2 & E = 0, ∂x 2 ∂y 2 ∂z 2 c 2 _______________________________________________ +

+

+

University of Žilina, Univerzitná 8215/1, 010 26 Žilina, Slovak Republic; E-mail: [email protected].

(1)

D. Faktorová / Some Experiences with Microwave Investigation of Material Defects

163

ω 2π where E& is the phasor – vector of electric field intensity, is the phase constant = λ c for the transversal electromagnetic (TEM) waves and λ is the wavelength in free space. On the assumption that the change of the E& in dependence on coordinate x has the form

& ∂2E ∂x

2

& = −β 2 E

where β =

(2)

2π is the propagation constant and λ g is the wavelength in the waveguide, λg

we get

∂ 2 E& ∂y 2

+

⎞ ∂ 2 E& ⎛⎜ ω 2 + 2 − β 2 ⎟ E& = 0 . 2 ⎜ ⎟ ∂z ⎝c ⎠

(3)

For experiments we use transversal electric (TE) waves and they are based on the reflected signal from defects. Our measurements and calculations are based on this reality exploiting the waveguide technique, where the complex reflection coefficient ρ& can be measured and it is given as

ρ& =

E& − , E& +

(4)

where E& + and E& − are intensities of reflecting and incident waves, respectively. When we take in account expressions of E& + and E& − by means of propagation constant β we have

ρ& = ρ& 0 e j(φ0 + 2βx ) ,

(5)

where φ 0 is the phase of ρ& in the point x = 0 and ρ& 0 is absolute value of ρ& in the same point. The incident and reflected wave create the standing wave. Standing wave ratio (SWR) s

s=

& E min &E

(6)

max

& &. can be measured and from the E min position it is possible to determine the phase of ρ Seeing that ρ& is a complex quantity we can determine complex impedance of defect Z& like terminative impedance of waveguide in the component form

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D. Faktorová / Some Experiences with Microwave Investigation of Material Defects

Z& = Z& 0

1 − ρ&

2

2

1 + ρ& − 2 ρ& cos φ

+ jZ& 0

2 ρ& sin φ 2 1 + ρ& − 2 ρ& cos φ

,

(7)

where φ is the angle of ρ& and Z& 0 is the characteristic impedance of waveguide. As all quantities on the right hand of Eq. (7) are measurable, [1] Z& can be evaluated.

2. Experimental results The experiments were carried out on the standard laboratory microwave equipment with the connection in the schematic illustration in Figure 1. As a source of microwave signal was used the reflex klystron modulated with 1 kHz signal. The measurements were carried out on frequencies from the ranges X and G band on the wave TE10 . The measured quantities were detected on the selective amplifier on the end of the line. The switch enables measuring both SWR and direct reflections in the same connection. The measurements of standing wave ratio (SWR) in waveguide were taken with the switch position to the open waveguide (OW). The SWR was measured for every depth at each frequency by the standing wave detector. CL

A CD CL

SA

FM

KPS

A

CL

CL

sample

OW

CD WRS K IM

FI

VA

MT

SWD FC

CD

MSH

Figure 1. Experimental set up for inhomogenities measurement, K – reflex klystron, KPS –klystron power supply, IM- impedance match, VA – variable attenuator, MT – magic T, A – adapter, FM – frequency meter, FI – ferrite isolator, CL – coaxial line, FM – frequency meter, WRS – waveguide rotation change–over switch, SWD – standing wave ratio measurement line, FC – ferrite circulator, CD – crystal detector, OW – open waveguide, SA – selective amplifier, MSH – movable sample holder

Samples were made in such way to be as much as possible similar to the real crack and simultaneously to provide a possibility for quantitative processing and evaluation. That is, the samples were made from steel plates 5x4x1,5 [cm]. Their areas should have overlapped the waveguide cross-section (22,5x10 [mm]) and in every sample there was filed a slot with the width 1 mm and length 20 mm representing an artificial crack (the depth of individual cracks are given in Figure 2). These samples were located in front of

165

D. Faktorová / Some Experiences with Microwave Investigation of Material Defects

SWR [-]

the empty waveguide without any other termination (open waveguide - OW) at the distance of 1mm and their longitudinal sections were parallel to the longer side of the waveguide. The measured and calculated values are plotted in the Figure 2. The successive curves for individual defects show quasiresonant course but in fact they represent values of waveguide terminating impedance in the waveguide–defect contact position. It is possible to assume, that individual samples with defects at particular frequencies behave as a quarter–wave transformers. The quarter–wave transformer effect manifests itself at λg . individual frequencies at three multiple of 4 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 0

2

4

f=10,20GHz f=8,40GHz

6

8 10 12 14 16 18 20 22 deph of defect [mm] f=10,03GHz f=7,70GHz

f=9,61GHz f=4,92GHz

f=9,20GHz

Figure 2. Dependence of SWR on the defect depth at seven frequencies

For the more complex assessment of the measured results from the point of view of quantities with which the microwave technique operates the values of complex impedance were calculated, Eq. (7) and plotted their dependences on the defect depth at the frequency 9,23GHz, Figure 3. An illustrative image about impedance course for the defect quarter–wave transformer affords Figure 3, where closed curves belongs to the defect depths

λg 4

f=9,23GHz 600

Im{Z}

400

200

0 0

200

400

600

Re{Z}

Figure 3. Lissajouse curve of various depths of defects

, and 3

λg 4

.

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D. Faktorová / Some Experiences with Microwave Investigation of Material Defects

From the Figure 2 it can be seen declining SWR amplitude for n = 1 what shows that the defect behaves as a loss waveguide section. To point this fact we carried out another measurement on a purpose-built sample. This sample was manufactured from two steel plates. The arrangement was adapted for setting desired different lengths widths and depths of the artificial crack. Thereafter for one series of measurement there was sideways delimited width and the depths were set for every measuring. Individual depths could be set accurate to 0,01mm. This arrangement was used at measurements, the results of which are plotted in Figure 4 and Figure 5. In order to show to what extends the defect depth can influence the reflected signal amplitude we took two measurements, Figure 4, where f=10,1 GHz

100

amplitude [a.u.]

80 60 40 20 1

2

0 0

20

40

60

80

100

120

140

crack depth [mm]

Figure 4. Dependence of the reflected signal amplitude on the depth of the crack

curve 1: the reflected signal measurement in the lossless waveguide, curve 2: the reflected signal measurement on the sample with adjustable depth. The reflected signal was measured through the ferrite circulator, Figure 1 and measurement were carried out for such position of the piston in the lossless waveguide which were identical with the corresponding crack depths. The comparison of the both measurements is in the Figure 4. From this graph it is possible to form a conception about the decreasing amplitude of the reflected signal at the determining of the crack depth with

(2n + 1)

λg

distant maxima. 4 For the reason of more complex evaluation of the defect character as a special waveguide section we also followed the shift of the SWR minimum with the enlarging defect depth. The corresponding values of the complex impedance were calculated from Eq. (7) and the dependence of complex impedance imaginary component and SWR shift on the depth of defect is in the Figure 5. From the point of view of microwave theory the presented results bring an additional proof of the fact that for the defect investigation the microwave method can be used as well as a tried and tested microwave practice.

D. Faktorová / Some Experiences with Microwave Investigation of Material Defects

167

f=10,1 GHz 500

5

100 0 -100 0

10

20

30

40

50 -5

-300 -500

minimum shift [mm]

Im{Z} [Ω]

300

posun minima [mm]

10

-10

crack depth hĺbka defektu [mm][mm] Im {Z}

posun minima

Figure 5. Dependence of complex impedance imaginary component and standing wave minimum shift on the depth of defect

With the open waveguide it could be possible to obtain information about the defect orientation. Changing the angle between the waveguide H–plane and the straight line passing along the defect we measured the reflected signal amplitude and the dependence of signal amplitude on angle of defect rotation is in the Figure 6.

amplitude [a.u.]

f=9,23 GHz

90 70 50 0

50

100

angle of rotation [°]

Figure 6. Dependence of signal amplitude on angle of defect rotation

At defects detection it is necessary to admit that an older crack is partly or wholly filled with rust or another deposit and also can be covered with paint, rust or with their combination. Additional crack filling can also be water or various water solutions. These materials signify from the microwave defectoscopy point of view dielectrics which will have an influence on the defect viewed as a part of the microwave network. We followed these conditions experimentally and the obtained results are in Figure 7. In the Figure 7 there are demonstrated courses of the reflected signal from the defect gradually being filled with rust layers (width of defect - 1mm, depth of defect - 10mm). In the Figure 7 we also present for a comparison the curve of the reflected signal course from the empty crack (curve “e”). The curve “f” represents the course of the reflected signal from the defect filled with pertinax, the curve “g” from the empty defect covered with a paint, the curve “h” from the defect filled with water and the curve “i” from the defect filled with paint.

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D. Faktorová / Some Experiences with Microwave Investigation of Material Defects

f = 9,3 GHz 100

80

80

amplitude [a.u.] amplitúda [a.u.]

amplitude [a.u.]

amplitúda [a.u.]

f = 9,3 GHz 100

60 40 20

60 40 20 0

0 -10

-5

0

5

10

-10

-5

a

b

c

d

e

0

5

10

polohaposition sondy [mm] probe [mm]

poloha sondy [mm] [mm] probe position

e

f

g

h

i

Figure 7. Dependence of reflected signal amplitude from defect gradually filled with the rust layers (a – one layer, b – two layers, c – three layers, d – defect filled with rust, e – empty defect) and form the presence different dielectrics in the volume and on the defect surface

3. Conclusions Our goal was to find an interface of practical testing knowledge with the theory which is at disposal in microwave domain. The acquired experiences can be summarized in several points indicating possibilities of microwave NDT: 1. to find out the defect (with a waveguide or a coaxial probe), 2. to determine the defect orientation, 3. to obtain information about the defect width, [2] and about presence dielectrics, 4 to determine the defect depth (according to the defect impedance), 5. to fix the defect depth utilizing the quarter-wave transformer effect and the attenuating characteristics, [2]. It is worth also saying that microwaves offer additional possibilities, with regard to expanding their utilization as well sensibility and accuracy. These goals can be achieved by using higher frequencies (around 100 GHz) and more sophisticated techniques (e.g. cavity resonators).

Acknowledgement The author would like to thank MSc. Pavol Žirko director of High School for Agriculture and Fishing in Mošovce for technical help at realization of experiments.

References [1] [2]

M. Pastorino, A. Massa, S. Caorsi, A Global Optimization Technique for Microwave Nondestructive Evaluation, IEEE, Transaction on Instrumentation and Measurement, 51, (2002), 666-673. D. Faktorová: Using of Microwaves at Investigation of Solid Materials Inhomogenities, Conference proceeding APCNDT 2006, 12th Asia - Pacific Conference on Non-Destructive Testing Auckland, New Zealand, http://www.ndt.net/article/apcndt2006/index.htm.

Modeling

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Electromagnetic Nondestructive Evaluation (XI) A. Tamburrino et al. (Eds.) IOS Press, 2008 © 2008 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-58603-896-0-171

171

Effect of Crack Closure on Quantitative ECT Inspection of Closed Fatigue Cracks Zhenmao CHEN a1, Noritaka YUSA b Kenzo MIYA b and Hideaki TOKUMA c a School of Aerospace, Xian Jiaotong University, China, b International Institute of Universality, Japan c Nuclear Power Engineering Department, Tokyo Electric Power Company, Japan

Abstract. In this paper, the feasibility to apply a closed fatigue crack as a substitute of a Stress Corrosion Crack (SCC) is investigated aiming at applications to ECT crack sizing. Several testpieces of closed fatigue cracks are fabricated, and ECT signals are measured after selected bending loads being applied to close the crack. From the measured signals, the crack profiles are reconstructed by using a deterministic inversion technique, and the sizing results are compared with the true crack profiles in order to evaluate the effect of crack closure. The results reveal that the closing load does not give significant influence on the crack sizing precision. Therefore, to simulate SCC with a fatigue crack closed by 3 point bending testing is not a suitable way from the view point of ECT inversion. Keywords. Fatigue crack, Crack sizing, Eddy Current Testing, Crack Closure

1. Introduction In practical NDT applications such as in Performance Demonstration (PD) activities, various kinds of TestPieces (TP) are necessary for calibrations, inspector training and etc. TP of artificial Stress Corrosion Crack (SCC) with known profile is indispensable in PD because the SCC is a major concern of many critical mechanical structures, e.g. a nuclear power plant. The fabrication of SCC, however, is high cost and time consuming due to difficulties to control the crack initiation and propagation. Recently, a strategy using closed Fatigue Crack (FC) as a substitute of SCC is proposed in the ultrasonic NDT applications because the signal features of an SCC and some closed FCs are similar [1]. This strategy is promising not only because of the low fabrication cost, but also because the profile of a fatigue crack is much easier to be controlled in the fabrication procedure. In several papers the crack closure effect on the UT signals has been studied [2]-[5]. The influence of crack closure on the ECT signals is also investigated by some researchers [6],[7],[8]. The feasibility to apply closed FC as a substitute of SCC in ECT inspection, however, is not clarified yet especially for the quantitative ECT inspections. In this paper, effect of crack closure on the quantitative ECT inspection is studied ___________________________________ 1 Corresponding author, MOE Key Laboratory for Strength and Vibration, Xi’an Jiaotong University, 28 West Xianning Road, Xi’an, 710049, China, Tel/Fax: 86-29-82663973, E-mail: [email protected].

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Z. Chen et al. / Effect of Crack Closure on Quantitative ECT Inspection of Closed Fatigue Cracks

by inspecting and sizing fatigue cracks in different closure state that is adjusted by using a mechanical loading system. 6 fatigue crack TPs of two sizes are fabricated through 3 point bending fatigue testing in different loading conditions. Bending loads from 13kN to 31kN are applied to the TPs to change the closure state of cracks after the cracks are introduced. A pluspoint ECT sensor is adopted to inspect the TPs that are unloaded from the test machine after selected maximum bending load being applied. From the detected ECT signals, the crack sizes are reconstructed based on a deterministic ECT inversion technique. All the TPs are destructed after detailed ECT inspections to observe the true crack profiles. The correlations between the ECT signals, the sizing results and the bending loads are analyzed through comparing the observed and reconstructed crack information. The results show that closure states of fatigue cracks do not give significant influence on the ECT signals and consequently, the sizing precision. In other words, application of closed FCs to replace SCC is not suitable in the quantitative ECT inspection in view of that the signal of an actual SCC is much smaller than that of an FC of similar size.

2. Fatigue crack TPs and ECT inspection system Two kinds of fatigue crack TPs are fabricated with type SUS316 austenitic stainless steel. The fatigue cracks in one kind of them are introduced with a relative larger strain range (tension-tension) and smaller number of loading cycles. The sizes of these TPs are 400 mm in length, 120 mm in width, and 15mm in thickness. The maximum bending load and the loading range are 29 kN and 25 kN respectively. The fatigue tests are terminated at 40,000 (TP L1), 50,000 (TP L2) and 60,000 (TP L3) of loading cycles respectively. For another kind of TPs, relative smaller loading range and large number of loading cycles are selected. The loading cycles used for these TPs are 0.52 million (TP S2), 0.88 million (TP S3) and 1.0 million (TP S3) respectively. The final sizes of the second kind of TPs are 200 mm in length, 100 mm in width and 8 mm in thickness. Figure 1 shows the loading system for both the fatigue testing and applying closing loads to the TPs. In all TPs, the fatigue cracks can be confirmed through visual observation. In Fig.2, a zoom up view of a fatigue crack initiated at the two ends of the initial slit is given. The initial EDM slit of 0.5 mm depth, which is introduced for guiding the location of cracking, is removed by grinder machining after fatigue testing.

Fig.1 Jigs for closing loading and fatigue testing Fig.2 Zoom up of a fatigue crack

Z. Chen et al. / Effect of Crack Closure on Quantitative ECT Inspection of Closed Fatigue Cracks

173

A pluspoint sensor of relative large size is selected for the ECT inspection (C scan). The sensor is scanned around the crack with a range of 40 mm in width and 60 mm in length. Three frequencies, 10 kHz, 20 kHz and 50 kHz, are chosen for the ECT inspection. Figure 3 shows a flowchart of the ECT testing system. After plastic deformation is introduced to the TP by applying bending load of selected maximum value for closing the crack, the TPs are unloaded and set to the scanner for ECT and TOFD (Time of Flight Diffraction, an UT method) inspections. Both the ECT signals and the position information are inputted to a computer through the A/D converter. The structure and size of the Pluspoint sensor are shown in Fig.4. In order to correspond crack depths in wide range, a relative large sensor size is adopted. Table 1 List of TPs TP Number

Loading Cycles

TP Thickness (mm)

TP Size (mm)

L1 L2 L3 S2 S3 S4

60,000 50,000 40,000 1,000,000 880,000 520,000

15 15 15 8 8 8

400/120/15 400/120/15 400/120/15 200 /100 /8 200 /100 /8 200 /100 /8

7.5

Side View side view

PC

aect2000s

12.5

front view Front View

A/D converter 2.5

2.5

7.5

7.5

12.5

12.5

stage contoller View tTop op view

XYZ stage

Fig.3 Flowchart of the inspection system

Fig.4 Structure of the Plus-point sensor

(a) SCC image (b) FC image (before loading) (c) FC image (after loading) Fig.5 Comparisons of TOFD images of SCC and closed FC cracks

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Z. Chen et al. / Effect of Crack Closure on Quantitative ECT Inspection of Closed Fatigue Cracks

Figure 5 shows a comparison of TOFD (Time of Flight Diffraction, an UT method) inspection results (B scope images) for an artificial SCC TP and the fatigue crack TP L1. Due to bridging between the crack surfaces, many echoes appear inside the crack region in case of the SCC TP (Fig.5 a). For the fatigue crack, however, there is no such echo recognized before closing load being applied (Fig.5 b). After applying plastic deformation to close the crack, however, similar echoes appear inside the fatigue crack region. These results demonstrate that to simulate SCC with FC is valid in case of UT (TOFD) inspection.

3. Inspection Results of Eddy Current Testing Figure 6 depicts a typical ECT C scan signal for the fatigue crack TP L1 to show the quality (high S/N ratio) of inspection signals. In Fig.7 and Fig.8, the ECT signals measured at each loading step are compared for the TP L1 and TP S3 respectively. Only signals along the crack line are given in the figures. For TP L1, loads of 7 conditions (10kN, 20kN, 22kN, 24kN, 26kN, 28kN and 30kN) are selected to adjust the closure state of crack. ECT signals are measured before and after each loading step. There is no significant change observed in the measured signals for the TP L1. Figure 8 shows results of the small TP S3 in which a crack has been introduced by 880,000 cycles of fatigue testing. The signal changes due to closing loads are also not significant though it is bigger than the case of TP L1. From the signals, it is difficult to extract a simple correlation between the loading value and the change of signal amplitude. Similar observations are also found for other TPs.

Fig.6 A typical C scan signal of ECT inspection for a fatigue crack

4. Sizing of fatigue cracks with a deterministic optimization strategy To evaluate the effect of crack closure on the sizing precision, the ECT signals for fatigue cracks at different loading conditions are applied to reconstruct the crack profiles for each TP. A deterministic inversion technique – the Conjugate Gradient (CG) method is employed in the sizing procedure [10, 11]. The database approach for fast simulation of crack signals is adopted to calculate the crack signals in the inverse analysis [12]. In the sizing procedure, the crack is supposed nonconductive and in a rectangular or a semi-elliptic shape respectively.

175

Z. Chen et al. / Effect of Crack Closure on Quantitative ECT Inspection of Closed Fatigue Cracks 0.9

0.35 noload 18kN 20kN 22kN

0.3

0.7

24kN 26kN 28kN 30kN

0.6

0.2 0.15 0.1

0.5 0.4 0.3

0.05

0.2

0

0.1

-0.05 -0.1 -30

’noload 18kN 20kN 22kN

0.8

Signal (V)

Signal (V)

0.25

24kN 26kN 28kN 30kN

0

-20

-10

0

10

20

30

-0.1 -30

-20

-10

0

10

20

30

x (mm)

x (mm)

(a) Real (b) Imaginary Fig.7 Comparison of ECT signals at different closing loads (TP L1) 2

3

noload 12kN 14kN 15kN

1.5

noload 12kN 14kN 15kN

2.5

Signal (V)

Signal (V)

2

1

0.5

1.5 1 0.5

0 0

-0.5 -30

-20

-10

0

x (mm)

10

20

30

-0.5 -30

-20

-10

0

10

20

30

x (mm)

(a) Real parts b) Imaginary parts Fig.8 Comparison of ECT signals measured after different closing loading (TP S3) As example of sizing results, Fig.9 shows reconstructed crack depths for TP L1 under different conditions of closing loads. The two block lines in the figure denote results using the rectangular and semi-elliptic crack model respectively. The true crack depth and length, which are obtained through destructive observation, are depicted in the figures as dot lines. One can read that the reconstructed crack profiles are in a satisfactory agreement with the measured ones for all closing loads. The rectangular crack model gives better predictions for crack depth, while the crack lengths obtained by using the semi-elliptic crack model are in better agreement with the true value. Figure 10 gives the comparison of the measured crack signals and the simulated signals due to the reconstructed crack for TP L1. The signals are in good agreement. In Fig.11 and Fig.12, the sizing results for another TP (S2) are presented. Similar to the results of TP L1, the predicted crack depth and length are near the true crack profile and do not show simple dependence on the load values. In Fig.13 and Fig.14, reconstruction results for all the 6 TPs and load values are summarized. Figure 13 shows a comparison of results for crack depth. The error between the true and reconstructed crack depth is less than 20%. For crack length, the sizing precision is much better (Fig.14). These results verify that treating FCs as a nonconductive notch is reasonable for FC sizing. The results also demonstrate that the CG method is efficient for profile reconstruction of FCs. It is well known that the signal of an SCC is much smaller than that of a fatigue crack of similar size [7], [9]. The results of this study, however, reveal that the closure state of an FC does not significantly influence the ECT signals. Therefore, we have to conclude that an FC closed by simple 3 point bending testing is not appropriate to simulate SCC in applications of crack sizing.

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Z. Chen et al. / Effect of Crack Closure on Quantitative ECT Inspection of Closed Fatigue Cracks

There are several reasons can be listed to interpret why the ECT signals do not decrease significantly, e.g., residual stress introduced by the 3 point bending testing may actually not be in a state closing the whole crack, or simply due to oxidation at the crack surfaces. Further studies are necessary to clarify these questions [13]. 5. Concluding Remarks From the research work described above, the following conclusions are obtained. 1) The nonconductive crack model and the deterministic inverse analysis strategy are feasible for the reconstruction of fatigue cracks. The sizing error is acceptable for the crack depth and is much better for sizing of the crack length. 2) The maximum load of 3 point bending does not significantly influence the crack signals and the consequent crack sizing results. 3) The fatigue crack closed by applying plastic deformation with 3 point bending testing is not suitable to simulate SCC in the ECT crack sizing application. Acknowledgements This work was supported in part by the National Natural Science Foundation and National Basic Research Program of China through Grand No.50677049, No.2006CB601206 and No. 2007CB707702, and Program for New Century Excellent Talents in University. Rectangular

Rectangular

Elliptic

2

Crack Length (mm)

Crack depth (mm)

Elliptic

12

2.5

1.5 1

0.5

10 8 6 4 2 0

0 0

18

20

22

24

26

29

30

0

31

18

20

22

24

26

29

30

31

Load (kN)

Load (kN)

(a) Results for crack depth (b) Results for crack length Fig.9 Reconstructed crack profiles for the TP L2 80

80

Measured (real) Reconstructed (real) Measured (imag) Reconstructed (imag)

60

40

Signal (μV)

Signal (μV)

40

20

0

20

0

-20

-20

-40

-40

-60 -0.03

Measured (real) Reconstructed (real) Measured (imag) Reconstructed (imag)

60

-0.02

-0.01

0

x (m)

0.01

0.02

0.03

-60 -0.03

-0.02

-0.01

0

0.01

0.02

x (m)

(a) Rectangular crack model (b) Semi-elliptic crack model Fig.10 Comparison of true and reconstructed crack signals (TP L2)

0.03

Z. Chen et al. / Effect of Crack Closure on Quantitative ECT Inspection of Closed Fatigue Cracks

Rectangular

Rectangular

elliptic

elliptic

40

6

35

C ra ck d epth (m m )

C rack leng th (m m )

5 4 3 2 1

30 25 20 15 10 5 0

0 0

12

14

0

15

12

14

15

Load (kN)

Load (kN)

(a) Results for crack depth (b) Results for crack length Fig.11 Reconstructed crack profiles for different closing load (TP S2) 0.5 Reconstructed(squre Re) Reconstructed(squre Im) Reconstructed(ellipse Re) Reconstructed(ellipse Im)

0.4

Measured(Re) Measured (Im)

Signal (mV)

0.3

0.2

0.1

0

-0.1

-0.2 -0.03

-0.02

-0.01

0

0.01

0.02

0.03

x (m)

Fig.12 Comparison of true crack signals and that due to reconstructed crack 㪍

Reconstructed (mm)

㪌

㪋

elliptic Rect.

㪊

㪉

㪈

㪇 㪇

㪈

㪉

㪊

㪋

㪌

㪍

True (mm)

Fig.13 Reconstruction results for crack depth for all TPs and load values

177

178

Z. Chen et al. / Effect of Crack Closure on Quantitative ECT Inspection of Closed Fatigue Cracks

Reconstructed (mm)

㪋㪇

㪊㪇

elliptic

㪉㪇

Rect.

㪈㪇

㪇

㪇

㪈㪇

㪉㪇 True (mm)

㪊㪇

㪋㪇

Fig.14 Reconstruction results for crack length for all TPs and load values References [1] Savahn PH, Hogberg K, Defect simulation for interdendritic stress corrosion cracks in Alloy 182 welds, CD-ROM Proceedings of the 16th World Conference on NDT (available at NDT.net). [2] Clark R, Dover WD, Bond LJ. The effect of crack closure on the reliability of NDT predictions of crack size. NDT&E international, 20(1987), 269-275. [3] Salam Akanda MA, Saka M. Relationship between closure stress of small fatigue crack and ultrasonic response. J. Nondestr. Eval. 23(2004), 37-47. [4] Buck O, Thompson RB, Rehbein DK. The interaction of ultrasound with contacting asperities: applications to crack closure and fatigue crack growth. Journal of Nondestructive Evaluation, 4(1984), 203-212. [5] Mihara T, Nomura S, Akino M, Yamanaka K. Relationship between crack opening behavior and crack top scattering and diffraction of longitudinal waves. Materials Evaluation, 62(2004), 943-947. [6] Kurokawa M, Kamimura T, Fukui S. Relationship between electric properties and width of cracks of Inconel alloy. In: Proceedings of the 13th International Conference on NDE in the Nuclear and Pressure Vessel Industries, Kyoto, Japan, 1995, 261-265. [7] Villone F, Harfield N. Simulation of the effects of current leakage across thin cracks. Electromagnetic Nondestructive Evaluation (IV). S.S. Udpa, T. Takagi, J. Pavo and R. Albanese (Eds.). IOS Press (1999), 79-86. [8] Badics Z, Matsumoto Y, Aoki K, Nakayasu F, Kurokawa A, Finite element models of stress corrosion cracks (SCC) in 3-D eddy current NDE problems. Nondestructive Testing of Materials. R. Collins, W.D. Dover, J.R. Bowler and K. Miya (Eds.). IOS Press (1993), 21-29. [9] Ohshima, K., Hashimoto, M., Research on numerical analysis modeling of SCC on eddy current testing. Journal of the JSAEM, 10 (2002), 384-388. [10] Chen Z and K.Miya, ECT inversion using a knowledge based forward solver, Journal of Nondestructive Evaluation, 17(1998), 167-175. [11] Yusa N, Chen Z, Miya K, Uchimoto T, Takagi T. Large-scale parallel computation for the reconstruction of natural stress corrosion cracks from eddy current testing signals, NDT&E international, 36(2003), 449-459. [12] Chen Z, Miya K. and Kurokawa M., Rapid prediction of eddy current testing signals using A-Phi method and database, NDT&E International, 32(1999), 29-36. [13] Yusa N., Perrin S., Mizuno K., Chen Z. and Miya K. , Eddy current inspection of closed fatigue and stress corrosion cracks, Meas. Sci. Technol. 18(2007), 3403-3408.

Electromagnetic Nondestructive Evaluation (XI) A. Tamburrino et al. (Eds.) IOS Press, 2008 © 2008 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-58603-896-0-179

179

Toward the Reconstruction of Stress Corrosion Cracks Using Benchmark Eddy Currents Signals Maxim MOROZOV a, Guglielmo RUBINACCI b, Antonello TAMBURRINOc,11, Salvatore VENTRE c and Fabio VILLONE c a CREATE Consortium, Naples, Italy b Ass. EURATOM/ENEA/CREATE, DIEL, Università degli Studi di Napoli Federico II, Italy c Ass. EURATOM/ENEA/CREATE,DAEIMI, Università degli Studi di Cassino, Italy

Abstract. This paper concerns numerical modelling of stress corrosion cracks in Inconel600 plates using experimental data of benchmark eddy current measurements. The problem is considered from a broad perspective, in view of its integration with algorithms for solving the inverse problem. The accuracy and efficiency have been particularly considered. The computational technique applied for modeling the crack is based on an integral formulation of the eddy current problem. The cracks are treated as either penetrable volumetric or zero-thickness (surface) defects enabling some electric current flowing through them. Real stress corrosion crack have been considered in this study where measured and simulated eddy current signals due to the cracks are presented. Keywords. Eddy currents, nondestructive evaluation, stress corrosion cracks, numerical simulation.

Introduction This paper is in the framework of Electromagnetic Non-Destructive Evaluation (ENDE) of real defects by means of conventional Eddy Current (EC) instrumentation. The main objective of the present work has been to validate an original method for modeling the electromagnetic response of stress corrosion cracks (SCC) which have certain conductivity and therefore enable some electric current flowing through them [2]. The numeric method is based on an integral formulation in terms of a twocomponent current density vector potential expanded over edge-elements [3]. The exploitation of superposition and a proper choice of the current density degrees of freedom gives rise to a very efficient numerical implementation. As discussed in [4], a fast numerical method for the forward problem is essential to reconstruct the defect with an iterative method minimizing the discrepancy between the simulated and measured EC signals. Experimental data comprising eddy current responses to several SCC flaws and fatigue cracks (FC) in Inconel600 plates, as well as the respective crack profiles found by destructive metallographic examination, have been offered as a 1

Corresponding Author: Antonello Tamburrino, DAEIMI, Università degli Studi di Cassino, V. G. di Biasio 43, Cassino, 03043-Italy; E-mail: [email protected]

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benchmark to the scientific community by a research team of International Institute of Universality, Tokyo, Japan [5]. The experimental data are available for various EC probes, however in this paper we focus on the modeling of SCC flaws from signals obtained with an absolute type pancake coil. Reconstruction of thin FC flaws has been discussed in [6]. Reconstruction of SCC flaws presents actual challenge due to their volumetric nature, complex geometry and conductivity distribution within a crack [7, 8].

1. Numerical method: Forward analysis for partially conducting cracks The numerical method consists in an integral formulation of the eddy currents problem in terms of a two-component electric vector potential [9]. This integral formulation allows us to discretise only the conducting domains where the eddy currents are induced and automatically enforcing regularity conditions at infinity. In addition, the introduction of the electric vector potential T, such that the eddy currents density is J=’uT, ensures that J is solenoidal and the choice of the two-component gauge minimizes the number of discrete unknowns required. The equations to be solved are the standard eddy current equations in the frequency domain. The electric field is: E = jZA’M

(1)

where M is the scalar electric potential and A is the magnetic vector potential given by: A(x, t )

P0 4S

J ( x' , t ) dV '  A 0 (x, t ) x  x' VC

³

(2)

where P0 is the magnetic permeability of the vacuum, VC is the conducting domain and A0 is the contribution due to the external current density. The integral equation is, then, obtained by combining (1) and (2) with the constitutive equation KJ E in VC , K being the electrical resistivity. From the numerical point of view, the formulation is solved using finite elements: a mesh of VC is given, and an edge element basis functions Nk is introduced for T: T

¦I N k

k

k

Ÿ

J

¦I

k

’ u Nk

(3)

k

It is worth noting that the choice of edge elements allows us to enforce the right continuity conditions of the various electromagnetic quantities and to impose easily both for the gauge and boundary conditions. The numerical model is, finally, obtained by imposing the constitutive relationship in weak form by using the Galerkin approach:

³

Vc

’ u N k ˜ (KJ  jZ A)dV

0 N k

(4)

The term involving the electric scalar potential gives no contribution thanks to the solenoidality of the test function. Finally, using (2) we obtain:

M. Morozov et al. / Toward the Reconstruction of Stress Corrosion Cracks

ZI=U

181

(5)

Where, Z=R+jZL, I = ^Ik`, U = ^Uk` and L ij

R ij

P0 4S

³³

’ u N i ( x) ˜ ’ u N j ( x ' ) x  x'

VC VC

dV dV '

˜ K’ u N j dV

(7)

 ³ ’ u N i ˜ jZ A 0 dV

(8)

³’uN

i

VC

Ui

(6)

VC

In modeling SCC, it is important to exploit that the defect occupies, usually, a small volume VD of the conducting domain VC. Therefore, the eddy current density J undergo a local perturbation G J in a neighborhood of VD requiring, from the computational viewpoint, a “small” and local mesh in a neighborhood of VD. Let K, K0 and 'K be the total, background and perturbation resistances, respectively: K=K0+'K: and let R, 'R and R0 be the corresponding matrices defined in (7). From (5), it follows that the eddy current perturbation can be numerically computed by solving:

Z 0  'R GI where Z 0

'RI 0

R 0  jZL , I 0 k

(9)

³’u N

k

˜ J 0 dV and J0 is the unperturbed current

VC

density that, for canonical geometries, can also be computed analytically (see [10] for the analytical calculation in planar geometries). The impedance variation due to the presence of the flaw can be expressed as GZ = UTGI/Is2

(10)

where U is defined in (8) and Is is the impressed current flowing in the excitation coil. There are situations that may be encountered in practice where one dimension of the defect is negligible. This type of defects is termed as zero-thickness (surface) defects. Equations (9) and (10) are still valid but 'R, involving an integral extended to the volume VD of the defect, must be defined in the limit of zero thickness defect [11]. Specifically, let d and 6D be the thickness and the surface of the defect. In the limit do0, matrix 'R (and, consequently GI ) is vanishing if 'K is finite. On the other hand, if 'K=+f we have a perfectly insulating defect. Therefore, we assume that do0 and d'K=const. Under this condition, it follows that [11] 'R ij o d'K ³ (’ u Ti ˜ nˆ )(’ u T j ˜ nˆ ) dS 6D

(11)

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Finally, we assume that the discretization is such that 6D is the union of facets of the finite elements mesh. Finally, the numerical model (9), regardless the type of anomaly that can be either volumetric or surface, can be significantly improved in term of efficiency by introducing the concept of tentative region, that an a priori known region VT where the defect is contained (VDŽVT) and the Woodbury’s algorithm [1], [4].

2. Experimental data and samples The studied EC test specimens represent Inconel600 plates with stress corrosion cracks [5]. The electric resistivity K0 of Inconel600 is assumed to be 1 P:m and its relative magnetic permeability Pr | 1. The dimensions of the specimens (mm) are given in Figure 1. SCC was produced into the plates by loading the plate with three-point bending and immersion into polythionic acid solution. SCC fabrication conditions are given in Table 1. EC signals due to the SCC were obtained with an absolute type pancake coil probe, shown in Figure 2. The excitation frequency of EC testing with the pancake coil was 100 kHz and its lift-off above the surface of a sample was 1 mm. After EC testing, crack profiles were found by destructive metallographic examination. A cross section of specimen SCC4 is shown in Figure 3. Since by conditions of the benchmark test neither the excitation current flowing through the coil, nor the phase shift and amplification of the measured signals are known, the measured results have been calibrated with respect to an artificial notch produced by Electrical Discharge Machining (EDM).

Figure 1. Specimen layout (dimensions in mm)

Figure 2. Absolute pancake coil (dimensions in mm)

Table 1. SCC flaws fabrication conditions Specimen

Duration (hours)

SCC1 SCC3 SCC4 SCC5

75 50 50 165

Crack Length (mm) 14 12 21 29

Figure 3. Metallographic cross section of specimen SCC4

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183

Figure 4. Measured and simulated eddy current signal obtained by a pancake coil due to an EDM notch. 2D indicates that the crack was considered as a zero-thickness defect whereas 3D stands for volumetric model

Figure 5. Dependence of crack signal on crack resistivity (signals have been normalized to the absolute value of the crack signal when the crack resistivity is infinite)

The EDM notch has a rectangular profile of 10 mm in length, 0.3 mm in width, and 5.0 mm in depth. The calibration process consists in finding a magnitude scaling factor and an appropriate phase shift at which the numeric simulation result is in agreement with the measured signal for the EDM notch. Then, the same scale factor and phase shift found by calibration is applied to measured signals for the SCC flaws.

3. Results of SCC flaws modeling The volumetric cracks search regions have been modelled as regular parallelepipeds with width of 0.3 mm for EDM notch and 1.5 mm for SCC flaws. In all the cases a flaw comprised two mesh elements in the transversal direction. Results of simulation of EC signals for volumetric cracks model, hereafter termed as 3D, have been compared with corresponding signals obtained by simulating cracks as zero-thickness defects (width | 0, see [6]), hereafter termed as 2D. The calibration signal (represented as the real and imaginary components) due to the EDM notch is shown in Figure 4, with a magnitude scaling factor and an appropriate phase shift being applied to the measured result in order to bring it to agreement with the simulated signal. Error of 9.4% between volumetric flaw simulation (3D) and measured signal occurs due to background noise in the measured signal (low-pass filtering was applied to reduce this noise).

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(a)

(d)

(b)

(e)

(c)

(f)

Figure 6. Crack profiles in specimens SCC1 (a) and SCC4 (d) and respective EC signals: real (b) and imaginary (c) parts for SCC1, real (e) and imaginary (f) parts for SCC4

Discrepancy between zero-thickness flaw simulation (2D) and measured signal is big which might be due to significant thickness of the EDM notch (0.3 mm). The magnitude scale factor and phase shift found by calibration on the basis of 3D simulation are maintained when numerically reconstructing the SCC flaws. However, in contrast to completely non-conducting EDM notch, natural SCC flaws have certain conductivity and therefore enable some electric current flow across their surface [2,7,8]. Consequently, partial conductivity of a crack, denoted by grey facets, should be introduced when reconstructing fatigue cracks. Dependence of a crack signal on the crack resistivity is shown in Figure 5, with the response values being normalised to the absolute value of the crack signal when the crack resistivity is infinite. The crack’s resistivity Kc = 2.5 P:m corresponds to the optimum correlation between SCC4 flaw profile and EC signal (Figure 6 e, f). Metallographic profiles of various SCC flaws and the respective numerically reconstructed profiles, as well as comparison of the corresponding measured and simulated EC signals are given in Figures 6-7. The figures representing SCC flaws profiles (Figures 6a, 6d, 7a) show discretisation of crack search

M. Morozov et al. / Toward the Reconstruction of Stress Corrosion Cracks

185

(a)

(b)

(c)

Figure 7. Profile of SCC5 flaw (a) and the respective EC signals: real part (b) and imaginary part (c)

regions in the crack plane, where white elements correspond to undamaged material, light grey elements belong to the crack and have resistivity Kc = 2.5 P:m, dark grey elements belong to the crack and have zero conductivity. The thick line approximately denotes cracks metallographic boundaries. The value Kc = 2.5 P:m follows from the experience on previous SCC whereas the perfectly insulating elements (dark grey elements) have been individuated by a search and trial approach.

4. Conclusions and outlook A numerical method has been presented for simulating EC signals of partially conductive volumetric cracks in conductive materials. The method enables fast and accurate reconstruction of fatigue cracks on the basis of measured signals obtained with conventional EC instrumentation. Moreover, experimental tests show that a SCC can be modeled as a region of appropriate resistivity that, eventually, may be spatially varying. The future development will address: x reconstruction of defects using signals obtained with EC probes of more complex arrangement, such as uniform EC probe [7]; x integration of the numerical model with an inversion algorithm for automated crack reconstruction.

Acknowledgements The experimental data have been kindly provided by Dr. Noritaka Yusa of International Institute of Universality, Tokyo, Japan. This work was supported in part by the Italian Ministry of University (MIUR) under a Program for the Development of Research of National Interest (PRIN grant #

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2004095237) and in part by the CREATE consortium, Italy.

References [1]

M. Morozov, G.Rubinacci, A.Tamburrino, S.Ventre, “Numerical Models of Volumetric Insulating Cracks in Eddy-Current Testing With Experimental Validation”, IEEE Trans. Mag., Vol. 42, No. 5, May 2006, pp. 1568-1576 [2] N. Yusa, Z. Chen, K. Miya, T. Uchimoto, T. Takagi, “Large-Scale Parallel Computation For The Reconstruction Of Natural Stress Corrosion Cracks From Eddy Current Testing Signals”, NDT&E Intnl. 36 (2003) pp. 449–59 [3] R. Albanese, G. Rubinacci, A. Tamburrino, F. Villone, “Phenomenological approaches based on an integral formulation for forward and inverse problems in eddy current testing”, Int. J. of Applied Electromagnetics and Mechanics, Vol. 12, No. 3-4/2000, pp. 115-137 [4] R. Albanese, G. Rubinacci, F. Villone, “An integral computational model for crack simulation and detection via eddy currents”, J. of Comp. Phys., Vol. 152, pp. 736-755 (1999) [5] N. Yusa, L. Janousek, Z. Chen, K. Miya. “Diagnostics of stress corrosion and fatigue cracks using benchmark signals”, Materials Letters 59 (2005), 3656-3659 [6] M. Morozov, G. Rubinacci, S. Ventre, F. Villone, “Reconstruction of Fatigue Cracks Using Benchmark Eddy Currents Signals”, in E’NDE, Electromagnetic Non-destructive Evaluation (X), S. Takahashi and H. Kikuchi (Eds.), pp. 267-274, IOS Press, 2007. [7] N. Yusa, L. Janousek, M. Rebican, Z. Chen, K. Miya, N. Dohi, N. Chigusa and Y. Matsumoto, “Caution When Applying Eddy Current Inversion To Stress Corrosion Cracking”, Nucl. Eng. Des. 236 (2006) pp. 211-221 [8] N. Yusa, H: Huang, K. Miya, “Numerical Evaluation of The Ill-Posedness of Eddy Current Problems to Size Real Cracks”, NDT&E Intnl. 40 (2007) pp. 185-191 [9] R. Albanese and G. Rubinacci, “Finite element methods for the solution of 3D eddy current problems” in Advances in Imaging and Electron Physics, Peter W. Hawkes (ed.), vol. 102, (Academic Press), 1998, pp. 1-86. [10] C.V. Dodd, W.E. Deeds, “Analytical Solution to Eddy-Current Probe-Coil Problems”, J. Appl. Phys., Vol. 39, No. 6, 1968, pp. 2829-2838 [11] F. Villone, “Simulation of Thin Cracks with Finite Resistivity in Eddy Current Testing”, IEEE Trans. on Magnetics, vol. 36, no. 4, July 2000.

Electromagnetic Nondestructive Evaluation (XI) A. Tamburrino et al. (Eds.) IOS Press, 2008 © 2008 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-58603-896-0-187

187

Evaluation of Subsurface Cracks In Riveted Aluminium Joints Using Industrial Eddy Current Instrumentation Maxim MOROZOV a1 , Guglielmo RUBINACCI b, 1, Antonello TAMBURRINO c and Salvatore VENTRE c a CREATE Consortium, Naples, Italy b Ass. EURATOM/ENEA/CREATE, DIEL, Università degli Studi di Napoli Federico II, Italy c Ass. EURATOM/ENEA/CREATE,DAEIMI, Università degli Studi di Cassino, Italy

Abstract. This paper concerns the efficient numerical modeling of subsurface flaws emanating from a fastener hole in riveted aluminum joints on the basis of eddy current (EC) signals measured with industrial instrumentation. Modeling of EC signals from modern industrial instrumentation is a difficult task because of the typical “complex” (in term of geometry and materials) configuration of the probes. The computational technique we applied is based on an integral formulation of the eddy current problem in the presence of magnetic (the core of the probe) materials. Measured and simulated eddy current signals due to the second-layer artificial flaws of various profiles are compared. Keywords. Eddy currents, nondestructive evaluation, rivet joint, ferromagnetic core, numerical simulation.

Introduction Fast and reliable evaluation of minute cracks deeply buried beneath rivet heads in lapjoints is an important issue of the aircraft maintenance process. This paper concerns Electromagnetic Non-Destructive Evaluation (ENDE) of subsurface flaws in aluminum sandwiches on the basis of measured signals obtained with industrial Eddy Current (EC) instrumentation. This paper addresses the numerical simulation of the response due to a crack. The main objective is to experimentally validate an original method for modeling EC signals arising from industrial instrumentation. This is a challenging problem because industrial EC probes present higher sensitivity at the price of a “complex” structure in terms of geometry and materials. Moreover, due to the skin effect, the inspection for subsurface defects in aluminum must be conducted at low excitation frequencies in the range of few kHz [1, 2]. At our knowledge, this work is one of the first attempt available in literature to model an industrial EC probe. The numeric method is based on an integral formulation in terms of a twocomponent current density vector potential expanded over edge-elements [3]. The 1 Corresponding Author: Guglielmo Rubinacci, Dipartimento di Ingegneria Elettrica, Università degli Studi di Napoli Federico II, Via Claudio, 21 – 80125, Napoli, Italy; E-mail: [email protected]

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exploitation of superposition and a proper choice of the current density degrees of freedom gives rise to a very efficient numerical implementation.

1. Numerical method 1.1. Thin insulating crack The present method consists in an integral formulation of the eddy currents problem in terms of a two-component electric vector potential [3]. This approach has a number of advantages as follows. Using an integral formulation allows us to discretise only the conducting domains where the eddy currents are induced, automatically enforcing regularity conditions at infinity. The introduction of the electric vector potential T, such that the eddy currents density is J=’uT, ensures that J is solenoidal. The choice of the two-component gauge minimizes the number of discrete unknowns required. The equations to be solved are the standard eddy current equations in the frequency domain. The electric field is: E = jZA ’M

(1)

where M is the scalar electric potential and A is the magnetic vector potential given by:

J ( x' ) P0 dV '  A 0 (x) ³ 4S V x  x'

A ( x)

(2)

c

where P0 is the magnetic permeability of the vacuum, Vc is the conducting domain and A0 is the contribution of the external coil currents. From the numerical point of view, the formulation is solved using finite elements: a mesh of Vc is given, and an edge element basis functions Nk is introduced for T:

T

¦I N k

k

Ÿ J

k

¦I

k

’ u Nk

(3)

k

On the one hand, the choice of edge elements allows us to enforce the right continuity conditions of the various electromagnetic quantities; on the other hand, their properties are fully exploited both for the gauge and boundary conditions imposition. The electric constitutive equation is imposed in weak form using Galerkin approach:

³

Vc

’ u N k ˜ (KJ  jZ A)dV

0 N k

(4)

where K is the resistivity. The term involving the electric scalar potential gives no contribution thanks to the solenoidality of the test function. Using (2) we have:

(R+jZL) I = jZQi where I = ^Ik`, Q = ^Qk`, i=^ik`is the vector of the external coil currents and

(5)

Lij

M. Morozov et al. / Evaluation of Subsurface Cracks in Riveted Aluminium Joints

189

’ u N i ( x ) ˜ ’ u N j ( x' ) P0 dV dV ' ³ ³ 4S V V x  x'

(6)

c

Rij

c

³’uN

i

˜K’ u N j dV

Vc

Qik

1 ’ u N i ˜ A 0 k dV ik V³c

(7)

(8)

Supposing that the crack has a negligible thickness, it can be schematised as a surface (not necessarily planar), discretised via a set of finite element facets (defect pixels), where the normal component of the current density must vanish. In order to reduce the computational load, and exploiting linearity, we use superposition: the total current density is the sum of the solution computed in absence of crack (unperturbed solution J0) plus the perturbation GJ due to the presence of the defect (J = J0 + GJ). In particular, on the insulating crack surface, since the total current density normal component must be zero, we impose that J ˜ nˆ = 0 Ÿ GJ ˜ nˆ = J0 ˜ nˆ

(9)

where nˆ is the unit normal to the crack. This approach offers the great advantage that J0 can be calculated either analytically, or numerically using the scheme described above on a mesh that does not depend on the crack geometry. Conversely, when solving for GJ the mesh must account for the crack only, so that the mesh refinement is required only close to the crack, regardless of the position of the exciting source. Due to the properties of edge elements, the set GG of perturbation currents crossing the crack facets (that must be equal the unperturbed currents G0) can be written as [4]:

GG = P GI

(10)

where GI are the coefficients of the expansion of GJ in terms of edge elements, and P is a (m,n) sub-matrix of the edge-facet incidence matrix with coefficients 0, +1 or -1. The degrees of freedom of the edge element expansions are in fact related to the line integrals of T along the edges, and the circulation of T along a closed line gives the total current (flux of ’uT) linked with the line. We then make a change of variables [4]:

GI = K GX + P+ GG

(11)

where K is a (n,n-m) matrix given by an orthonormal basis for the null space of P, P+ is the pseudo-inverse of P, and GX is a new set of unknowns, providing no net current flowing through the crack. Galerkin’s procedure in terms of these new variables yields: KTZK GX = KTZ P+ G0

(12)

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M. Morozov et al. / Evaluation of Subsurface Cracks in Riveted Aluminium Joints

solving which we have GX, and hence GI from (11). Knowing GI it is possible to compute the reaction field. In particular, the impedance changes of the probe coils are given by

jZ [(Q k )T GI l ik  (Q l )T GI k il ] , 2ik il

GZ kl

(13)

where Qk and is the kíth column of Q, ik and il are unitary currents for all k and l.

1.2. Treatment of magnetic materials Many conventional EC probes contain ferromagnetic cores. Usually the magnetic fields encountered in EC testing are low and linearity of the magnetic material can be assumed, resulting in a significant simplification of numerical simulation. Applying superposition and using conventions defined in (3), (6), (7) and (8), the problem at steady current becomes [5]: (R+jZL) I + jZF M =ҟjZQi

(14)

· § 1  F m ¨¨ P 0 D  E ¸¸M  F T I Fm ¹ ©

Ni

(15)

where M=^Mk` is magnetization vector, Fm=Pr-1 is the magnetic susceptibility (constant after linearization), i=^ik`is the vector of the external coil currents and: Fij

Eij

P0 4S

³³

’ u Tj (x) ˜ Pi u (x  x' )

Vc Vm

P0 ³ Pi ˜ Pj dV  Vm

Dij

³

Pi ˜ P j dV

N ik

1 ik

³

Vm

Vm

x  x'

P0 4S

3

³ ³

wVmi wVmj

dV dV '

(16)

Pi (x) ˜ n Pj (x' ) ˜ n' x  x'

dS dS ' (17)

(18)

Pi ˜ B 0k dV

(19)

in which wVmi is the surface bounding the element where the shape function Pi is located and B 0k is the magnetic induction produced in the vacuum by the k-th coil. In particular, the magnetization vector is supposed to be piecewise constant, so that Pk’s are unit vector pulse functions: M = ¦k Mk Pk Hereafter

M. Morozov et al. / Evaluation of Subsurface Cracks in Riveted Aluminium Joints

191

(R+jZL*) I = jZQ*i

(20)

L*= L + F S FT,

(21)

Q*= Q + F S N,

(22)

where

S

Fm 1  F m P 0

· § Fm ¨D  E ¸¸ ¨ 1  F m P 0 ¹ ©

1

(23)

In this way the problem is put in the same form as in section 1.1, with the only difference that L* must be considered instead of L and Q* instead of Q. Hence, the techniques described above can be used also in this case. If linearization cannot be applied, it is possible to compute the field variations due to defect presence as the numerical difference between solutions obtained for unperturbed and perturbed case using the same mesh (same shape and weight functions). In spite of that the perturbations are substantially smaller than the whole solution, this method allow to obtain results of good quality, because using the same mesh systematic errors are eliminated [6,7]. For linear problems, the method is obviously equivalent to superposition. We finally notice that, in the presence of magnetic materials, the impedance changes of the probe coils are given by

GZ kl

jZ [(Q*k )T GI l ik  (Q*l )T GI k il ] 2ik il

(24)

2. Experimental setup and samples The samples are riveted aluminium-to-aluminium two layer sandwiches with countersink fastener holes. The plates are 200u200 mm2 large and 2 mm thick. The fastener hole has a diameter of 4 mm. The layers of the sandwiches are electrically insulated and this is taken into account into the numerical model by meshing separately the two layers. The samples contain Electric Discharge Machined (EDM) notches emanating from the fastener hole. The inspection cases studied represented cracks lying in the second layer under rivet head. The EDM notches have rectangular profiles of 0.15 mm in width, 2 mm in depth (passing through the second layer plate) and length of 5 and 3 mm. In order to detect subsurface flaws, a sliding probe for fastener inspection was used at low excitation frequency of 1kHz. The probe is a dual element reflection probe with a complex ferrite magnetic circuit [1, 2]. The EC inspection was performed by robotic scanning of samples along straight lines containing both the fastener hole and an EDM flaw with the sensitive axis of the sliding probe being oriented along the scanning path. The experimental setup is shown in Figure1. EC signals from the sliding probe were measured by Phasec2d EC instrument [8]. Both the robotic arm and EC instrument were controlled by a PC via RS-232 interface.

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3. Results and discussion Figure 2 shows a fragment of the finite elements mesh and the crack search region, where white facets have zero conductivity (3 mm long flaw) and black facets represent undamaged material. The EC instrument Phasec2d measures EC signals in relative units. In order to convert measured signals to Ohms the instrument output has been calibrated with respect to difference between signals from probe placed on a defect-free aluminum sandwich and probe away from a conductor. Figure 3 represents measured and calculated EC response to a fastener hole.From the measurements we have subtracted the signal coming from the probe in absence of the specimen. Figures 4 and 5 represent flaw contributions of the EC responses to flaws emanating from a fastener hole in the second layer. The flaw contribution signal is defined as the difference between the signal coming from a hole with a rivet and the signal for the same structure including a flaw. The flaw contribution, obtained as a difference between two signals of the same order of magnitude, is thus quite sensitive to noise. Moreover, the measurements setup is critical because of the need of using relatively “low” frequencies (1kHz). Nonetheless, there is a reasonably good agreement between experimental results and simulations. Since the probe contains a ferromagnetic core, a possible source of discrepancies is the estimate of the relative permeability of its core. Moreover, another critical parameter is the lift-off. Both parameters have been assessed on the basis of a comparison of the measurements with the numerical model of the reference design of the probe. A deeper analysis is therefore needed in view of a possibly more accurate simulation of the response of the probe. Finally, another source of discrepancies is the finite elements mesh discretization that, especially for the unperturbed solution, requires a “large” number of unknowns because of the probe geometry and materials. In this work, taking into account the constraints for a standard PC (CPU time and memory), we have optimized the mesh for a total of 8842 unknowns for computing the unperturbed field and 9498 unknowns for computing the effect due to the defect.

4. Conclusions and outlook A numerical method has been presented for simulating EC signals of thin cracks deeply buried beneath rivet heads in aluminum lap-joints. The method enables accurate modeling of artificial flaws on the basis of measured signals obtained with industrial EC instrumentation. The future development will address implementation of an inversion algorithm for automated crack reconstruction.

Acknowledgements The technical data of the sliding probe have been kindly provided by Hocking NDT Ltd. This work was supported in part by the Italian Ministry of University (MIUR) under a Program for the Development of Research of National Interest (PRIN grant # 2004095237) and in part by the CREATE consortium, Italy.

M. Morozov et al. / Evaluation of Subsurface Cracks in Riveted Aluminium Joints

RS-232

193

Robotic Arm

Sliding Probe

PC

RS-232 Phasec2D

Figure 1. Measurement setup.

Figure 2. The finite elements mesh (gray) and crack search region: white facets have zero conductivity (flaw) and black facets represent undamaged material

Figure 3. Response to a fastener hole with rivet, measurements vs. simulation: left - real component and right - imaginary component

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Figure 4. Measured and simulated crack contribution to an EC signal due to 100% deep (passing) 5 mm long EDM notch emanating in the subsurface layer from a fastener hole.

Figure 5. Measured and simulated crack contribution to an EC signal due to 100% deep (passing) 3 mm long EDM notch emanating in the subsurface layer from a fastener hole.

References [1] [2] [3]

[4] [5]

[6] [7]

[8]

J. Hansen and N. Thorpe, “Low frequency eddy current inspection”, Conference Proceedings, NDT 2003, Worcester, UK, BINDT, pp. 147-154 J. Hansen, “Back to basics: The eddy current inspection method”, Parts 1-4, Insight - Non-Destructive Testing and Condition Monitoring, Vol. 46, No. 5-8 (2004) R. Albanese, G. Rubinacci, A. Tamburrino, F. Villone, “Phenomenological approaches based on an integral formulation for forward and inverse problems in eddy current testing”, Int. J. of Applied Electromagnetics and Mechanics, Vol. 12, No. 3-4/2000, pp. 115-137 R. Albanese, G. Rubinacci, F. Villone, “An integral computational model for crack simulation and detection via eddy currents”, J. of Comp. Phys., Vol. 152 (1999), pp. 736-755 R. Albanese, G. Rubinacci, F. Villone, “Crack simulation in the presence of linear ferromagnetic materials using an integral formulation”, Electromagnetic Nondestructive Evaluation (V), J. Pavo et al. (Eds.), pp. 16-21, IOS press, 2001. R. Albanese, R. Fresa, R. Martone, “Accurate computation of electromagnetic fields in the presence of conducting and magnetic material”, Int. J. Applied Electromag. and Mech., Vol. 6, 1995, pp. 73-88. R. Albanese, R. Fresa, G. Rubinacci, “Assessment of the Accuracy of Electromagnetic Feld Calculations for Non Destructive Testing”, Electromagnetic Nondestructive Evauation, T. Takagi et al. (Eds.), IOS Press, 1997, pp. 17-22. Eddy Current Probes & Accessories Catalogue, GE Inspection Technologies, http://www.geinspectiontechnologies.com/download/products/ec/GEIT-50016EN_ec-probe-hi.pdf

Electromagnetic Nondestructive Evaluation (XI) A. Tamburrino et al. (Eds.) IOS Press, 2008 © 2008 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-58603-896-0-195

195

Design of a System for the Long Defects Detection with Advanced Methods for Eddy-currents Analysis1 E. Cardelli b , A. Faba b , A. Formisano c , R. Martone c , F.C. Morabito e , M. Papais a , R. Specogna a , A. Tamburrino d , F. Trevisan a , S. Ventre d , M. Versaci e a University of Udine, via delle Scienze 208, Udine, Italy b University of Perugia, via G. Duranti 67, Perugia, Italy c nd 2 University of Napoli, via Roma 29, Aversa, Italy d University of Cassino, via Di Biasio 43, Cassino, Italy e University of Reggio Calabria, via Graziella Feo di Vito, Reggio Calabria, Italy Abstract. The aim of the paper is to highlight some of the innovative methodologies, techniques and systems for non-destructive electromagnetic testing, which have been developed in the framework of the AMDE project (Applications of Methods of Diagnostics Electromagnetic) partially funded by the Italian Ministry of University and Research. In particular, we will present the feasibility design of a suitable excitingreceiving coils configuration able to detect long defects by means of eddy-currents. To solve the forward eddy-current problem, advanced analysis tools have been developed and validated. In this paper, we will also introduce the approach for numerical simulations in the detection of the surface defects. Keywords. Non destructive testing, eddy-currents, discrete approaches.

Introduction The strong international competition forced industrial companies to change dramatically the manufacturing processes, in order to reduce the overall manufacturing time. One of the conditions to be satisfied for this goal is the capability to detect very quickly the product non-conformities with respect to the assumed standards. For these reasons, there is a remarkable interest in the techniques for the surface defects detection during the hot mill rolling process of the steel bars (bars with circular cross-section and diameter that ranges from 8 to 80 mm, a longitudinal speed that changes from 5 to 100 m/s and a temperature from 800 to 1200◦ C). The capability to detect these defects permits a fast and straightforward quality assessment of the product and provides the possibility to reduce those non-conformities due to a wrong set-up of the manufacturing process parameters. The defects considered 1 This work has been supported by the Italian Ministry of Education - Scientific Program PRIN 2004-2006 AMDE (Application of Methods of Diagnostics of Electromagnetics).

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have a depth ranging from 0.1 mm to 2 mm and, even though they have quite different shapes and sizes, they generally correspond to an interruption of the material continuity (also from the electrical point of view) and lay along an almost radial direction. Two main categories of surface defects can be considered depending on their axial length L: the “short” defects, with L ranging from 1 mm to 20 mm and the “long” defects with L from a meter to tens of meters. In any case, the defect width is much smaller than the two other dimensions. Short defects can be easily detected using a differential method in which the signal, after the noise reduction, is compared to a similar signal taken few centimeters away along the rolling direction. On the contrary, so far, no practical solution has been found as regards the detection of long defects, for which a differential approach is not suitable. The motivation of this paper is to develop the feasibility design of an excitingreceiving coils configuration able to detect the long defects. The numerical simulations have been performed with a Discrete Geometric Approach [1], [2] based on the so called A − χ formulation described in [3], [6] and modified in order to represent the effect of source currents in an integral way. As second tool for numerical simulations and comparisons we used an integral formulation [5].

1. Geometrical model of the detector The geometry of the detector consists of a conducting AISI 310 steel bar, modeled as a conducting cylinder Dc . The radius of the bar is 17 mm and the conductivity is σ = 1.236·106S/m. A longitudinal perfectly insulating defect is assumed, 0.5 mm deep from the surface of the cylinder and 0.2 mm thick. A pair of source coils Ds (30 mm inner Ds

long defect

Dc

receiving coils

Figure 1. Geometric model of the detection system. It consists in a pair of transmission coils coaxial with the steel bar and 12 evenly spaced circular receiving coils.

radius, 39 mm outer radius, 1.5 mm height, 7 turns each) feeded by a sinusoidal current of I = 200 mA per turn with a frequency of f = 100 kHz. They are connected in counter series and the axial distance between the two coils is 30 mm, see Fig. 1 and 2. A set of 12 evenly spaced circular receiving coils (3 mm inner radius, 6.5 mm outer radius, 6 mm height, 400 turns, lift-off 15 mm) with axis directed as the radii of the bar, are considered. Increasing the number of receiving coils the spatial resolution will

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197

be improved but it is also more difficult to dispose the coils without modifying their geometric characteristics. y

D1

6mm

0.5

mm

4

30 ˚

il # co

15˚

9mm

coil # 5

6mm

m 14m

˚ 30

3 coil #

m 2m

0.

D2

6mm 14mm 30mm

15˚

1.5mm

100mm 17mm

15mm

x

a)

b)

Figure 2. Design of the detection system geometry.

2. Solution of the eddy-current problem 2.1. Discrete Geometric Approach (GAME code) In order to solve the eddy current problem we resort to the so-called Discrete Geometric Approach[1], [2]. The domain of interest D of the eddy-current problem, has been partitioned into a source region Ds , consisting in a pair of

current driven coils, and in a passive conductive region Dc . The complement of Dc Ds in D represents the air region Da . A pair of interlocked cell complexes is introduced in D, [1]. The cell complex is obtained meshing the model domain. The primal complex is simplicial with inner oriented cells such as nodes n, edges e, faces f , volumes v (v are tetrahedra). The dual cell complex is obtained from the primal, according to the barycentric subdivision, with outer oriented cells such as dual volumes n ˜ , dual faces e˜, dual edges f˜, dual nodes v˜. For example, a dual node v˜ is the barycenter of the tetrahedron v, a dual edge f˜ is line drawn from the barycenter of f joining the two dual nodes v˜ , v˜ in the tetrahedra v  , v  on both sides of f ; with this notation, the one-to-one correspondence between a cell and its dual is underlined. The interconnections between cells of the primal complex, are defined by the usual connectivity matrices G between pairs (e, n), C between pairs (f, e), D between pairs (v, f ). Similarly, the corresponding matrices for the dual complex are −GT (the minus sign is due to the assumption that a dual volume n ˜ is oriented by the outward normal, while a node n is oriented as a sink) between pairs (˜ n, e˜), CT between pairs (˜ e, f˜) and DT between pairs (f˜, v˜). With respect to these cell complexes, we recall the algebraic equations governing the Discrete Geometric Approach [3], [6], formulated in terms of the array A of the circulations of the magnetic vector potential along primal edges e of D and in terms of the array χ of scalar potential χ associated with primal nodes n of Dc . We obtain:

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E. Cardelli et al. / Design of a System for the Long Defects Detection with Advanced Methods

(CT νC A)e = (Is )e ∀e ∈ D − Dc (CT νC A)e + iω(σ Ac )e + iω(σG χ)e = 0 ∀e ∈ Dc iω(GT σ Ac )n + iω(GT σG χ)n = 0 ∀n ∈ Dc ,

(1)

where array Ac is the sub-array of A, associated with primal edges in Dc and Is is the array of the source currents crossing dual faces in Ds . With notation (x)k , we mean the k-th row of array x, where k = {e, n} is the label of edge e or of node n. Finally ν and σ are matrices representing the discrete counterparts of reluctivity and Ohm’s constitutive relations respectively; dim(ν) = F , F being the number of faces in D, and dim(σ) = Ec , Ec being the number of edges in Dc . 2.2. Construction of the constitutive matrices We will construct the constitutive matrices ν and σ using the Discrete Hodge technique based on Whitney’s maps, described in [7]. We will consider the elementary case of a single tetrahedron, assuming reluctance ν and conductivity σ element-wise constants. For a mesh of tetrahedra, we will add the contributions element by element. 2.2.1. Reluctance matrix Reluctance matrix relates the magnetic fluxes Φk on primal faces fk with the magneto˜ motive forces (m.m.f.s) Fi on dual  edges fi . We use Whitney’s map [1] to express the magnetic flux density field b = k wkf Φk , where wkf is the vector proxy of the Whitney’s function associated to face fk . Because of the Gauss’ Magnetic Law DΦ = 0, the field b is elementwise constant [4], and using the pointwise material law h = νb, we may compute Fi as  Fi =

f˜i

νb =

4 

ν wkf (p) · ˜fi Φk ,

(2)

k=1

where ˜fi is the dual edge vector associated with edge f˜i and p is any point in the considered tetrahedron. Then, the entry ν vik of a possible reluctance matrix ν v for tetrahedron v is ν vik = ν wkf (p) · ˜fi . 2.2.2. Conductance matrix The conductivity matrix links the electro-motive forces (e.m.f.s) Uj , with the currents Ii on dual faces e˜i . Using the Whitney’s map, we may express the electric field e as e = j wje Uj , where wje is the vector proxy of the Whitney’s function associated to edge ej . It is an affine field and from j = σe, we obtain the following expression for Ii  Ii =

σe = e ˜i

6 

σ wje (mi ) · ˜ei Uj ,

(3)

j=1

where ˜ei is the area vector associated with e˜i and mi is the center of mass of face e˜i . Finally, the entry σ vij of the conductance matrix σ v for tetrahedron v is σ vij = σ wje (mi )· ˜ei . The obtained matrix is non-symmetric, but it’s possible to demonstrate that, if the Whitney’s functions are evaluated in the barycenter v˜ of the tetrahedron, the matrix σ becomes symmetric [6].

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199

2.2.3. Integral representation of sources Thanks to the linearity of media, we can express the array A as A = Ar +As , where As is the array of circulations of the contribution to the magnetic vector potential produced by the source currents in Ds and Ar is the array of circulations of the contribution to the magnetic vector potential due to the eddy-currents in Dc . Therefore we have that (CT νC As )e = (Is )e (CT νC Ar )e = 0 ∀e ∈ Ds (CT νC As )e = 0 (CT νC Ar )e = (I)e ∀e ∈ Dc

(4)

holds, where I is the array of eddy currents crossing f˜ in Dc . Each entry (As )i of the array As can be pre-computed as (As )i = ei As · dl, where ei is a primal edge in D and As is the magnetic vector potential due to the known source current density in Ds . In our case, we have a stranded circular coils and As can be computed in closed form in terms of the elliptic integrals of the first and second kind [9]. In this way, we can rewrite the system (1) by removing the source currents from its right hand side, obtaining (CT νC Ar )e = 0 ∀e ∈ D − Dc (CT νC Ar )e + iω(σ Acr )e + iω(σG χ)e = v ∀e ∈ Dc iω(GT σ Acr )n + iω(GT σG χ)n = w ∀n ∈ Dc ,

(5)

where v = −iω(σ Ac s )e and w = iω(GT v)e . The system (5) is singular and, to solve it, we rely on CG method without gauge condition. 2.2.4. Calculation of the induced voltage For the calculation of the induced voltage we will sub-divide the coil in a series of M sub-coils. The voltage induced at the terminals of the i-th sub-coil can be determined by:  Ui = −jωΦi = −jωNi

A · dl, ci

where ci is the circumference coaxial with the coil and passing trough the barycenter of the considered sub-coil. For the calculation of the integral we use the Biot-Savart’s law: A(P ) = As (P ) +

μ0 4π

 Dc

J(P  ) dV. |P − P  |

2.3. Integral formulation (CARIDDI code) As second tool for numerical simulations and comparisons we used an integral formulation described in [5], [11], [12], and [13]. Assuming non-magnetic conductors and time harmonic fields, the integral formulation of eddy currents is governed by the following equations: μ0 ηJ(P ) = −jω 4π



J(P  ) dP  Vc |P −P  |

− jωAs − ∇φ,

(6)

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E. Cardelli et al. / Design of a System for the Long Defects Detection with Advanced Methods

 Σ

ˆ dS = 0 ∀Σ, J · n ˆ = 0 on ∂Vc , J·n

(7)

where J is the current density, As is the vector potential defined in Section 2.2.3 produced by the excitations sources, φ is the electric scalar potential, Σ is an arbitrary closed ˆ is the outward normal on ∂Vc , and η is the surface in Vc , ω is the angular frequency and n resistivity of the conducting domain Vc . The method offers the advantages to discretize only the conducting domains where the eddy currents are induced, and to automatically enforce the regularity conditions at infinity. Moreover, if we introduce the electric vector ˆ = 0), then only Equation 6 potential T, such that J = ∇ × T (and (∇ × T) · n is to be imposed. The numerical formulation is obtained n by expanding T in terms of edge-elements based shape functions Nk , as T(r) = k=1 Ik Nk (r) where Nk satisfies ˆ . The uniqueness of the electric vector potential T is achieved by imposing the ∇×Nk · n two-component gauge condition by means of the tree-cotree decomposition of the finite element mesh [11]. Imposing Equations 6 in weak form by the means of the Galerkin’s approach, we obtain:  ∇ × Nk · (ηJ(P ) + jω Vc

μ0 4π

 Vc

J(P  ) dP  + jωAs + ∇φ)dP = 0, ∀Nk . |P − P  |

The numerical system is expressed in the form: (R + jL)I = U,

(8)

where I = {Ik }, U = {Uk } and μ0 Lij = 4π





Vc

∇ × Ni (x) · ∇ × Nj (x ) dV dV  , |x − x |

Vc

 Rij =

∇ × Ni · η∇ × Nj dV, Vc

 Ui = −

∇ × Ni · jωA0 dV. Vc

Let us assume that a perfectly insulating crack with negligible thickness is present in the conductor. It can be schematized through the following condition: J · n = 0 on Σd , where Σd is the surface representing the crack and n ˆ is the normal to the crack. To reduce the computational load and enhance the accuracy we can apply the compensation method where the total current density J is written as the sum of the solution computed in absence of the defect (the so-called unperturbed solution J0 ) and of the perturbation δJ (the so-called perturbed solution) due to the presence of the defect. In terms of δJ we have: δJ · n = −J0 · n.

(9)

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201

The unperturbed solution J0 can be computed using a mesh that does not depend on the crack geometry, whereas the perturbed solution δJ requires only a local and refined mesh in a neighborhood of the crack (see [12] for details). Once δI has been computed, the impedance change due to the flaw is given by δZ = −UT δI/Is2 ,

(10)

where Is is the impressed current. Finally, we mention that this approach has been extended to 3D volumetric defects in [13].

3. Numerical results When detecting long defects, a reference signal for each coil is not available, therefore is not possible to use a differential detection system. To have an estimation of the expected voltage variations in the coils due to the presence of the defect, we computed the voltage variations ΔU = Ud − U0 . −4

1.5

x 10

Integral Formulation Diffrential Formulation

|Δ U| [V]

1

0.5

0

0

2

4

6 coil index

8

10

12

Figure 3. Voltage variation on each of the 12 receiving coils. The numerical results obtained with the GAME and CARIDDI codes are in a good agreement each other.

To this aim we need to solve a pair of eddy-current problems with the GAME code (Geometrical Approach for Maxwell Equations) [8] with the A − χ formulation and the integral representation of sources. The defect has been modeled as a volume discretized with a collection of tetrahedra. The unstructured mesh used consists of 505k tetrahedral elements, yielding 630k DoF. We apply also the CARIDDI code [5] implementing the integral formulation to the system under test, splitting the current into a perturbed and an unperturbed solution. Due to the symmetry of the excitation and pickup coils with respect to the conductive region, we can reduce memory storage and computational time by discretizing only one-eighth

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of the steel cylinder. The mesh used for the perturbed solution is localized near the flaw, allowing for both an increase of accuracy and a reduction of the numbers of unknowns. The compared results are shown in Fig. 3.

4. Conclusions The paper exploited two numerical approaches tailored to solve a non-destructive eddycurrent testing problem for the long defect detection during the hot steel-bar production. The two numerical approaches are the Discrete Geometric Approach (GAME code) and the integral formulation (CARIDDI code). The numerical results are in agreement each other and demonstrate that the two formulations can be considered as useful tools for the numerical modeling and design of eddy-current diagnostics devices.

References [1]

Bossavit, How weak is the Weak Solution in finite elements methods?, IEEE Trans. Mag. Vol 34, No. 5, 1998, pp. 2429–2432. [2] E. Tonti, Algebraic topology and computational electromagnetism, 4-th International Workshop on Electric and Magnetic Fields, Marseille (Fr) 12–15 May, pp. 284-294, 1988. [3] F. Trevisan, 3-D Eddy Current Analysis With the Cell Method for NDE Problems, IEEE Trans., Vol. 40, No. 2, 2004, pp. 1314–1317. [4] F. Trevisan, L. Kettunen, Geometric interpretation of discrete approaches to solving Magnetostatics, Vol. 40, No. 2, March 2004, pp. 361-365. [5] R. Albanese, G. Rubinacci, Integral Formulation for 3D Eddy Current Computation using Edge Elements, IEE Proceedings, vol. 135, Part A, n. 5, pp. 457–462, 1988. [6] R. Specogna, F. Trevisan, Discrete constitutive equations in A−χ geometric eddy-currents formulation, IEEE Trans. on Magn., Vol. 41, No. 4, 2005, pp. 1259–1263. [7] T. Tarhasaari, L. Kettunen, A. Bossavit, Some realizations of a discrete Hodge operator: a reinterpretation of finite element techniques, IEEE Trans. Mag. Vol. 35, 1999, pp. 1494-1497. [8] R. Specogna, F. Trevisan, The Geometric Approach to solve Maxwell’s Equations (G.A.M.E.) code http://www.quickgame.org, copyright 2003-2007. [9] E. Durand, Magnetostatique, Paris: Masson & C. 1968. [10] E. Cardelli, A. Faba, R. Specogna, F. Trevisan, Image Reconstruction of Defects in Metallic Plates Using a Multi-Frequency Detector System and a Discrete Geometric Approach IEEE Transaction on Magnetics, vol. 42, n. 4, 2007, pp. 1857–1860. [11] R. Albanese, G. Rubinacci, Finite element methods for the solution of 3D eddy current problems, Advances in Imaging and Electron Physics, vol. 102, pp. 1-86, 1998. [12] R. Albanese, G. Rubinacci, F. Villone, An integral computational model for crack simulation and detection via eddy currents, J. of Comp. Phys., Vol. 152 (1999), pp. 736-755 [13] M. Morozov, G. Rubinacci, A. Tamburrino, and S. Ventre, Numerical Models with Experimental Validation of Volumetric Insulating Cracks in Eddy Current Testing, IEEE Trans. on Magnetics, vol. 42, no. 5, pp. 1568-1576, 2006.

Electromagnetic Nondestructive Evaluation (XI) A. Tamburrino et al. (Eds.) IOS Press, 2008 © 2008 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-58603-896-0-203

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Theory of Four-Point Alternating Current Potential Drop Measurements on a Layered Conductive Half-Space Nicola BOWLER 1 , and John R. BOWLER Center for Nondestructive Evaluation, Iowa State University, USA Abstract. An analytic expression describing the complex voltage measured between the pickup points of a four-point probe, in contact with the surface of a layered metal half-space, is derived. The driving current is assumed to be timeharmonic. A Green’s function formulation leads to a result in which the voltage is expressed as a sum of two terms. One represents the potential drop due to a homogeneous half-space conductor with properties the same as those of the surface layer. The other represents the effect of the substrate and is expressed as a Hankel transform. A scheme for numerical evaluation of this term, by truncating the range of integration, is presented. An example calculation is given. Keywords. Four-point, alternating current, potential drop, layered metal half-space

Introduction Potential-drop measurements using a four-point probe are commonly used to determine bulk and surface conductivity of metals and semiconductors [1,2], and for crack sizing, and several commercial instruments are available for these purposes. Four-point methods rely on using either direct current or very low frequency alternating current for which the potential drop is essentially real, being in phase with the applied current. In this regime, the effect of permeability and conductivity separate. This means that the method is suitable for measuring the conductivity of both non-ferromagnetic and ferromagnetic materials, contrasting with eddy-current (EC) measurements in which the conductivity and permeability are not easily separated at typical EC operating frequencies, restricting EC conductivity measurements to non-ferromagnetic metals. The alternating current potential drop (ACPD) technique has been analyzed extensively for crack sizing measurements, under the assumption that the current injection points are sufficiently far apart that the applied current density at the crack is uniform [3,4]. In recent years, the four-point ACPD method of nondestructive evaluation has been developed both in the context of materials property measurements [5,6] and for crack sizing [7]. 1 Corresponding Author: Center for Nondestructive Evaluation, 279 Applied Sciences Complex II, 1915 Scholl Road, Ames, IA 50011-3042, USA; E-mail: [email protected].

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The work presented here is motivated by the need to determine the profile of conductivity and permeability in a metal as a function of depth from the surface, in applications such as nondestructive determination of the case depth in surface-hardened steels or, at higher frequencies, surface residual stress in aircraft engine alloys. It is anticipated that ACPD measurements provide greater sensitivity in measuring changes in electromagnetic material properties as a function of depth, when compared with EC testing [8,9], because injected current has a component perpendicular to the conductor surface, whereas induced eddy currents always flow parallel to the surface of an unflawed specimen. ACPD measurements also offer greater sensitivity for this application than direct current potential drop measurements [10] since the skin effect provides a mechanism for the current to be concentrated at a particular depth of interest such as the transition region between a surface-hardened layer and substrate in case-hardened steel. In contrast with earlier work, the work reported here does not rely on the assumption of uniform current density but, rather, an exact analytical solution for the measured potential drop is obtained on the assumption that the test-piece is significantly larger than the largest separation of the probe points. An example calculation shows how the ACPD voltage varies as a function of the depth of a surface layer, relative to that of a homogeneous test-piece.

1. Analysis In a four-point measurement, two current electrodes and two voltage electrodes are used. Typically they are arranged in a straight line, or on the vertices of a rectangle, and contact with the specimen is made using spring-loaded pins. The potential drop is measured between the voltage electrodes. The potential drop between the pickup points, v, may be written as the sum of four terms; the potential at each of the two measurement points due to the sources at the current injection and extraction points. With reference to Figure 1, v = v1 − v2 =

 I  f (ρ22 ) − f (ρ21) − f (ρ12 ) + f (ρ11) , 2πσ1

(1)

where I is current amplitude and f (ρ) depends on frequency and the variation of conductivity and permeability of the test-piece as a function of depth below the surface. In this article, an analytic expression is derived for the ACPD voltage measured by a four-point probe with points located at arbitrary positions on the surface of a planar

v2 r v1 r B
@  B @  ρ11
B ρ22 @
 B
ρ12 @ @ B
r  ρ21@ B +I @B @Br −I v = v 1 − v2 Figure 1. Plan view of the four electrode points on a conductor surface.

N. Bowler and J.R. Bowler / Theory of 4-Point Alternating Current Potential Drop Measurements

Air Region 1 (Layer)

σ1 , μ1

Region 2 (Substrate) σ2 , μ2

205

z=0 z=d

? z

Figure 2. Cross-section of the metal test-piece.

conductor, with a surface layer of depth d. The conductivity and permeability of each region are denoted σj and μj respectively, j = 1, 2, with region 1 being the surface layer and region 2 being the substrate, Figure 2. Assuming the field varies as the real part of e−iωt , f (ρ) for a homogeneous halfspace conductor with parameters the same as those of region j is given by [11], fhs,j (ρ) =

eikj ρ + ikj [E1 (−ikj ρ) + ln ρ] , ρ

where kj2 = iωμj σj .

(2)

Corresponding expressions for plates of various thickness relative to the probe dimensions are given in Ref. [11]. In its present form, Eq. (2) does not take into account inductive pick-up in the closed loop formed by the pick-up pins, the conductor, and associated wiring. This contribution to the measured voltage is seen in the imaginary part (in quadrature with the applied current). From the practical point of view it is important to minimize the inductive pickup by making the pick-up loop physically as small as possible, otherwise it dominates the signal as frequency increases [5]. An additional analytic term can be derived that theoretically accounts for the inductive pick-up [5] but, in this article, we are concerned with the effect of the surface layer on the voltage measured between the pick-up pins and do not deal with the inductive term explicitly. 1.1. Formulation and Solution In this work we follow the formulation of Ref. [11], in which we solve the electromagnetic field problem initially assuming a single current injection or extraction point. In this way cylindrical symmetry can be exploited. The result for current injection and extraction at two separate points is then obtained by superposition. Under certain assumptions [11], the magnetic field H is transverse magnetic (TM) with respect to the direction of the normal to the conductor surface (ˆ z ) and hence can be expressed as H = ∇ × [ˆ z ψ]

(3)

where ψ is the TM potential. With this formulation, the potential v at a point Q1 relative to that at another point Q2 , both in the plane z = 0, is found from the following expression [11],     ∂ψ  1 ∂ψ  − . (4) v= σ1 ∂z Q1 ∂z Q2 The solution is formulated in terms of the Green’s function G(r, r ) for the structure, from which the TM potential is obtained using the following relationship [11].

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N. Bowler and J.R. Bowler / Theory of 4-Point Alternating Current Potential Drop Measurements

ψ(r) =

−I∇−2 t



∂G(r , r) ∂z 

 z  =0

.

(5)

The potential drop v then follows from relation (4). In order to determine G(r, r ), express the layered half-space kernel in the following cylindrically-symmetric form, ∞ 1 

z, z  )J0 (κρ)κ dκ, (6) G(κ, G(r, r ) = 2π 0 which is a solution of (∇2 + kj2 )G(r, r ) = −δ(r − r ).

(7)

At the interface between the layer, region 1, and the substrate, region 2, the continuity of H at z = d implies that ψ is continuous there. The continuity of the tangential electric field implies that σ1 ∂ψ ∂z is also continuous at z = d. These conditions on ψ also apply to G. In addition we retain the requirements from the homogeneous half-space problem that G(r, r ) = 0 at z = 0 and that the remote dipole field vanishes (this occurs when the combined effect of current injection and extraction points is considered).

z, z  ) assumes that the source point (denoted The following general solution for G(κ, by the primed co-ordinates) is located within region 1. The solution vanishes at z = 0.  1 −γ1 |z−z  | −γ1 (z+z  ) γ1 (z−z  ) e ,1 − [1 + A(κ)] e + A(κ)e

z, z  ) = 2γ1 (8) G(κ, 1 −γ2 z−γ1 z  , 2 2γ1 B(κ)e

with γj = κ2 − iωμj σj and the root with a positive real part is taken. Applying the interface conditions gives A(κ) =

 Γe−2γ1 d (e2γ1 z − 1), 1 + Γe−2γ1 d

z  < d,

(9)

where Γ=

γ1 /σ1 − γ2 /σ2 . γ1 /σ1 + γ2 /σ2

(10)

Substituting for A(κ) from (9) into expression (8) gives 

z, z  ) = 1 e−γ1 |z−z | − e−γ1 (z+z ) + G(κ, 2γ1

 4Γe−2γ1 d  sinh(γ1 z) sinh(γ1 z ) . 1 + Γe−2γ1 d

(11)

Now note that the first two terms in (11) are simply those forming the Green’s function for a half-space, Ghs,j (r, r ), with parameters σj and μj denoted by the subscript j. Hence G(r, r ) = Ghs,1 (r, r ) + V (r, r ) where, from (6)

(12)

N. Bowler and J.R. Bowler / Theory of 4-Point Alternating Current Potential Drop Measurements

V (r, r ) =

1 π



∞

0

1 Γe−2γ1 d sinh(γ1 z) sinh(γ1 z  )J0 (κρ)κ dκ. γ1 (1 + Γe−2γ1 d )

Now, referring to Eq. (3.26) in Ref. [11] and from Eq. (5) with relation (2),  I ∂ψ  [fhs,1 (ρ) + flayer (ρ)] , =− ∂z z=0 2π

207

(13)

(14)

where flayer (ρ) = −2 0

∞

γ1 Γe−2γ1 d J0 (κρ) dκ κ (1 + Γe−2γ1 d )

(15)

since the operator ∇2t introduces the factor −κ2 in transform space. The potential drop between two points may now be computed by substituting (14) into (4). 1.2. Limiting Cases In this section it is shown that the solution obtained here reduces as anticipated in limiting cases. First, if regions 1 and 2 have identical parameters, Γ vanishes and only fhs,1 remains in Eq. (14), as expected. Similarly, as d → ∞, e−2γ1 d → 0 and only fhs,1 remains in Eq. (14). Considering the case d → 0, note first that [12] ∞ γ1 J0 (κρ)dκ. (16) fhs,1 (ρ) = κ 0 Then see that, as d → 0, ∞ 1 (γ1 σ2 − γ2 σ1 ) J0 (κρ)dκ flayer (ρ) → − σ2 0 κ σ1 = −fhs,1 (ρ) + fhs,2 (ρ). σ2 Substituting this relation into (14) it is seen that  I σ1 ∂ψ  =− fhs,2 (ρ), as d → 0, ∂z z=0 2π σ2

(17) (18)

(19)

which leads to the replacement of σ1 by σ2 in (4), as required. Finally, note that putting σ2 = 0 and μ2 = μ0 gives a representation for a plate in air. Putting σ2 = 0 makes Γ = −1 and    ∞ I γ1 1 + e−2γ1 d ∂ψ  =− (20) J0 (κρ)dκ. ∂z z=0 2π 0 κ 1 − e−2γ1 d Eq. (20) is in agreement with an expression that can be obtained from the result specifically derived for a metal plate in Ref. [13, Eq. (30)]. It is interesting to see that (20) is obtained by putting σ2 = 0, regardless of the value of μ2 . This reflects the nature of the TM excitation of the test piece; a low conductivity substrate will give the same v regardless of whether or not the substrate is magnetic. In order to observe the magnetic state of the substrate, it is necessary to excite the transverse electric mode, as in EC testing.

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N. Bowler and J.R. Bowler / Theory of 4-Point Alternating Current Potential Drop Measurements

2. Numerical Evaluation The functions in Eq. (2) are readily available in computational packages such as Matlab, but evaluation of flayer (ρ), Eq. (15), requires more work. An efficient and accurate numerical evaluation of the integral can be performed by artificially truncating the domain of the function flayer (ρ) by setting flayer (ρ) = 0 for ρ ≥ a and hence recasting the integral as a sum [14]. The value of the parameter a is chosen to be sufficiently large for this to be a reasonable approximation. A factor of 10 greater than the probe length is usually sufficient. In detail, for an integral of the form ∞ f (κ)Jn (κρ)κdκ, (21) f (ρ) = 0

including Eq. (15) with Γe−2γ1 d γ1 f (κ) = −2 2 κ (1 + Γe−2γ1 d )

(22)

and n = 0, it is assumed that the function f (ρ) can be written as the following summation: f (ρ) =

∞ 

Al f (κl )Jn (κl ρ),

(23)

n=1

where Jn (z) is the Bessel function of the first kind of order n and Jn (κl a) = 0. The coefficients Al are determined by applying the Hankel transform to Eq. (21) and truncating the domain of f (ρ) so that f (ρ) = 0, ρ ≥ a. Next, f (ρ) as given in Eq. (23) is substituted into the resulting integrand to give f (κm ) =

∞ 

Al f (κl )

l=1



a

Jn (κl ρ)Jn (κm ρ)ρ dρ,

(24)

0

for a particular κ = κm . Now apply standard integral Eq. 11.4.5 of Ref. [15] to determine a a2  2 [Jn (κl a)] δlm , Jn (κl ρ)Jn (κm ρ)ρdρ = (25) 2 0 where Jn (z) = dJn (z)/dz and δlm = 1 for l = m and 0 otherwise is the Kronecker delta function. Hence, from Eq. (24), Al = (2/a2 )[Jn (κl a)]−2 and substituting Al into Eq. (23) gives f (ρ) =

∞ Jn (κl ρ) 2 

f (κl ) 2. 2 a [Jn (κl a)]

(26)

l=1

In the particular case of interest here, following the above procedure allows Eq. (15) to be written as follows.  ∞  4  γ1 Γe−2γ1 d J0 (κl ρ) . (27) flayer (ρ) = − 2 a κ2l (1 + Γe−2γ1 d ) [J1 (κl a)]2 l=1

N. Bowler and J.R. Bowler / Theory of 4-Point Alternating Current Potential Drop Measurements

209

since J0 (z) = −J1 (z), [15, Eq. 9.1.28]. The set of zeros of the function J0 (z) are used to determine the set of κl that satisfy J0 (κl a) = 0. Once values of κl are known, the terms in Eq. (27) may be computed and summed.

3. Example Calculation and Discussion As an example consider a four-point probe, with co-linear arrangement of the points, placed on the surface of a layered test-piece with σ1 = 36 MS/m (aluminum) and σ2 = 25 MS/m (a typical aluminum alloy). The separation between the current injection and extraction points is 40 mm. That between the pickup points is 35 mm. In Figure 3 normalized relative voltage, ΔV, defined ΔV =

v − vhs,1 , vhs,1

(28)

is plotted for surface layer thickness d = 1, 2 and 3 mm. v is computed using expressions (14) and (15), whereas vhs,1 is computed using (16). From Figure 3 it is clear that the real part of the signal shows greater relative change, due to the layer, than the imaginary part. ΔV → 0 as frequency increases due to the layer appearing more like a half-space as the electromagnetic penetration depth decreases. In the case of thicker layers, ΔV → 0 at lower frequencies than for thinner layers. On this basis, broadband potential drop measurements, coupled with model-based interpretation, hold promise for determining the depth of an interface at which there is a change in electrical conductivity. In general, ΔV is enhanced if the conductivity contrast between the layer and the substrate is increased. Acknowledgement This work was supported by the NSF Industry/University Cooperative Research Program. References [1] R. K. Stanley, P. O. Moore, and P. McIntire (eds.), Nondestructive Testing Handbook, 2nd ed., vol. 9, Special Nondestructive Testing Methods. American Society for Nondestructive Testing, Columbus, OH, 1995. [2] D. K. Schroder, Semiconductor Material and Device Characterization, Wiley, New York, 1998. [3] D. H. Michael, R. T. Waechter and R. Collins, The measurement of surface cracks in metals by using AC electric fields, Proc. Roy. Soc. Lond. Ser. A 381 (1982), 139-157. [4] A. M. Lewis, D. H. Michael, M. C. Lugg and R. Collins, Thin-skin electromagnetic fields around surface-breaking cracks in metals, J. Appl. Phys. 64 (1988), 3777-3784. [5] N. Bowler and Y. Huang, Model-based characterization of homogeneous netal plates using four-point alternating current potential drop measurements, IEEE Trans. Mag. 41 (2005), 2102-2110. [6] V. A. Mitrofanov, Problems of the theory of the electric potential method of nondestructive inspection using alternating current, Russ. J. Nondestructive Testing 34 (1998), 183-189. [7] G. Sposito, F. Simonetti, P. Cawley, and P. B. Nagy, Potential drop spectroscopy for characterization of complex defects, CP820, Review of Quantitative Nondestructive Evaluation Vol. 25, ed. by D. O. Thompson and D. E. Chimenti, American Institute of Physics 2006. [8] F. Yu and P. B. Nagy, Simple analytical approximations for eddy current profiling of the near-surface residual stress in shot-peened metals, J. Appl. Phys. 96 (2004), 1257-1266.

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N. Bowler and J.R. Bowler / Theory of 4-Point Alternating Current Potential Drop Measurements

Real Normalized Relative Voltage

0.35

0.25 0.2 0.15 0.1 0.05 0 −0.05 0 10 0.1

Imaginary Normalized Relative Voltage

d = 1 mm d = 2 mm d = 3 mm

0.3

1

10

2

10

3

10

4

10

0.08 0.06 0.04 0.02 0 −0.02 0 10

1

10

2

10 frequency (Hz)

3

10

4

10

Figure 3. Calculated normalized relative potential drop ΔV, Eq. (28), for a co-linear four-point probe on a metal half space, σ2 = 25 MS/m, with a surface layer of thickness d and σ1 = 36 MS/m. [9] Y. Shen, C. Lee, C. C. H. Lo, N. Nakagawa and A. M. Frishman, Conductivity profile determination by eddy current for shot-peened superalloy surfaces toward residual stress assessment, J. Appl. Phys. 101 (2007), 014907. [10] F. Takeo, K. Nakajima, T. Baba, Y. Aonahata and M. Saka, Arrangement of probes for measuring case depth by means of four-point probes, Advances in nondestructive evaluation, Key engineering materials Vols. 270-273 82-88, Part 1-3 2004. [11] J. R. Bowler and N. Bowler, Theory of four-point alternating current potential drop measurements on conductive plates, Proc. R. Soc. A 463 (2007), 817-836. [12] N. Bowler, Analytical solution for the electric field in a half space conductor due to alternating current injected at the surface, J. Appl. Phys. 95 (2004), 344-348. [13] N. Bowler, Electric field due to alternating current injected at the surface of a metal plate, J. Appl. Phys. 96 (2004), 4607-4613. [14] T. P. Theoudoulidis and E. E. Kriezis, Eddy Current Canonical Problems, Tech Science Press, Forsyth GA, 2006. [15] Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, edited by M. Abramowitz and I. A. Stegun, Dover, New York, 1972.

Electromagnetic Nondestructive Evaluation (XI) A. Tamburrino et al. (Eds.) IOS Press, 2008 © 2008 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-58603-896-0-211

211

Integration of tilted coil models in a volume integral method for realistic simulations of eddy current inspections Theodoros THEODOULIDIS a,1 , and Gregoire PICHENOT b a University of West Macedonia, Energy Department, Greece b CEA-LIST, CEA, Saclay 91191 Gif-sur-Yvette, France Abstract. Tilted coil models are incorporated in a Volume Integral Method code for realistic simulations of eddy current inspections. The coils have either cylindrical or rectangular shapes and the configurations involve a layered conductor system with an arbitrary number of layers. Emphasis is put on the rapid calculation of the incident fields by modifying existing integral expressions to equivalent Fourier-type series expressions. In this paper we present only the cylindrical coil configuration. Theoretical results for the crack signal of a titled coil are verified by experimental measurements. Keywords. Eddy currents, analytical modelling, tilted coils, Volume Integral Method

Introduction In the application of the Volume Integral Method for the simulation of eddy current defect inspections an important part of the solution is the accurate calculation of the incident (0) electromagnetic field, that is the term Ek (r) in Equation (1), describing the numerical discretization scheme for the calculation of the electric field in the volume of a defect embedded in a multilayered conductive half-space [1] (0)

Ek (r) = Ek (r) − jωμ0

N 

¯ (ee) (r, r )[σl − σ(r )]El (r )dr G kl

(1)

l=1 Ω (0)

Here Ek (r) is the electric field with the defect present, Ek (r) is the electric field with ¯ (ee) (r, r ) is the electric-electric dyadic Green’s functhe defect absent (incident field), G kl tion defined as the field response to a unit point source, σl refers to the conductivity of the host layer, σ(r ) refers to the conductivity distribution of the defect and primed and non-primed position vectors refer to source and field cells respectively. Within the framework of a collaborative project between the University of West Macedonia, Greece and CEA-LIST, France, the incident electromagnetic field as well as 1 Corresponding Author: Theodoros Theodoulidis, University of West Macedonia, Energy Department, Bakola & Sialvera, 50100 Kozani, Greece; E-mail: [email protected].

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T. Theodoulidis and G. Pichenot / Integration of Tilted Coil Models in a Volume Integral Method

the coil self- and mutual-impedances for uncracked conductors have been calculated in an efficient and rapid way for arbitrary cylindrical and rectangular coil orientations. The model, in turn, has been successfully included into the CIVA software, which is a powerful multi-technique platform for simulating NDT industrial configurations. In this work we outline the method for calculating the electromagnetic field from a tilted cylindrical coil located above a layered conductive and/or magnetic half-space. The existing integral expressions are modified to equivalent series expressions thus providing a way for rapid calculations and ease of implementation without any sacrifice on accuracy of results. The extension of the class of coils used in the simulations and the corresponding decrease of computation time in the Volume Integral Method calculations are the main achievements of this project. Results for the eddy current response of tilted coils using VIM have also been previously demonstrated in [2].

1. Analysis Consider Figure 1 which shows a cylindrical coil located above a layered conductor. The coil is excited by a time harmonic current varying as the real part of I exp(jωt). The coil is tilted by an angle ϕ around the y-axis, rotated by an angle θ around the zaxis and moved so that its center lies at (x0 , y0 ). Both ϕ and θ angles are positive for counterclockwise rotation. The layered conductor can have an arbitrary number of layers nl , each layer t having conductivity σt , relative magnetic permeability μt and thickness ct . In order for the field to assume a double sum than a double integral expression, the solution domain for the boundary value problem is truncated in both x and y directions. Thus, the solution domain extends from 0 to hx in the x-direction and from 0 to hy in the y-direction. These boundaries are chosen to be far from the coil and they are perfect electric insulators, i.e. Bz = 0.

Figure 1. Tilted coil configuration above a layered conductor.

The analysis of the electromagnetic field problem is based on the use of potentials. The truncated domain is divided into the conductor layers and the above air region. The

T. Theodoulidis and G. Pichenot / Integration of Tilted Coil Models in a Volume Integral Method

213

solution then takes the form of series expansions in each region and the expansion coefficients found from the continuity conditions governing the field at the interfaces between each region (layer). In the air-region above the conductor upper surface, the magnetic field can be expressed as the gradient of a scalar potential B = ∇φ where φ satisfies the Laplace equation. The potential can be considered as the superposition of the isolated coil potential φ(s) and the potential originating from the eddy currents in the conductor φ(ec) . The expressions for these two potentials are then written as: φ

(s)

(x, y, z) =

∞  ∞ 

(s)

sin(ui x) sin(vj y)eκij z Cij

0 ≤ z ≤ l0

(2)

i=1 j=1 (ec)

φ

(x, y, z) =

∞  ∞ 

sin(ui x) sin(vj y)e−κij z Dij

(ec)

z≥0

(3)

i=1 j=1

The magnetic flux density in the conductor layers (z < 0) can be written using the ˆ transverse electric (TE) part of the second order vector potential as B = ∇ × ∇ × W a z with scalar potential Wa satisfying either the Laplace or Helmholtz scalar equations according to the conductivity of the specific layer. The general expression for a particular layer is: Wa (x, y, z) =

∞  ∞ 

  (a) (a) sin(ui x) sin(vj y) eγij z Cij + e−γij z Dij

(4)

i=1 j=1

where ui = iπ/hx , vj = jπ/hy (j is index), κ2ij = u2i + vj2 , k 2 = jωμr μ0 σ (j is the 2 = κ2ij + k 2 . The electric field in a conductive layer can be derived imaginary unit), γij ˆ. Expressions for the potentials satisfy the continuity conditions from E = −jω∇ × Wa z of the field at the interface planes. A recursive use of these conditions [3], can be used (ec) for expressing the unknown coefficient Dij in air and the unknown nl coefficients (a)

(a)

(s)

Cij and Dij in the conductor layers in terms of the source coefficient Cij , which is (ec)

considered to be known. The Dij , which is needed for calculations of the magnetic field in air as well as for self- and mutual-impedances, can be written in the general (ec) (s) form as Dij = Rij Cij where Rij is a reflection coefficient that depends solely on the characteristics of the layered conductor [3]. 1.1. Self and Mutual Impedance Change The magnetic field in all regions as well as the electric field in the conductor can be calculated from the expressions that relate B and E to W. The general expression for the impedance change caused by the presence of the layered conductor can be derived by using a reciprocity relation [4]. ΔZ = (s)

∞ ∞ jωhx hy   (s) (s) κij Cij Cij Rij 2μ0 I 2 i=1 j=1

(5)

where Cij represents the source coefficients characterizing the isolated coil and Rij represents the reflection coefficient characterizing the contribution of the eddy current density induced in the layered conductor.

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T. Theodoulidis and G. Pichenot / Integration of Tilted Coil Models in a Volume Integral Method

In case the mutual impedance change between two coils is sought, Equation 5 takes the form ΔZ12 =

∞ ∞ jωhx hy   (s) (s) κij Cij,driver Cij,pickup Rij 2μ0 I 2 i=1 j=1

(6)

where now there are two source coefficients, one for the driver and one for the pickup coil. 1.2. The Source Coefficient for a Tilted Cylindrical Coil The method of calculating the source coefficient Cij is similar to the one presented in [4] and involves an integration over the coil surface and a superposition over the coil crosssection. The resulting expression for the coil of Figure 1 is  μ0 i0 2π e−κij d ej(+ui xd +vj yd ) N(ψa ) − ej(+ui xd −vj yd ) N(ψb ) (s)  Cij = (7) hx hy κij +ej(−ui xd +vj yd ) N(ψb∗ ) − ej(−ui xd −vj yd ) N(ψa∗ ) where d = l0 + r2 sin |ϕ| + (l/2) cos ϕ is the coil center height and N(ψ) = sin (lψ/2) M(ψr1 , ψr2 )/ψ 3

(8)

ψa = (ui cos θ + vj sin θ) sin ϕ − jκij cos ϕ

(9)

ψb = (ui cos θ − vj sin θ) sin ϕ − jκij cos ϕ

(10)

where i0 = N I/[(r2 − r1 )l] is the coil current density with N denoting the number of  ψr wire turns and M(ψr1 , ψr2 ) = ψr12 xI1 (x)dx with I1 (x) denoting the modified Bessel function of order 1.

2. Results Code was written in Matlab to compute the impedance change of the tilted coil above the layered conductor, the mutual impedance between combinations of cylindrical and rectangular coils, the magnetic field in air both from the isolated coil and the change due to the conductor and the incident electric and magnetic field in the conductor layers. The field can be computed very rapidly in a 3D grid (volume area), a 2D grid (surface), a 1D grid (line) by utilizing the vector capabilities of Matlab. In all of the examined cases, appropriate dimensions hx and hy for the truncated domain as well as appropriate number of terms for the double series were used. Typical values were hx = hy = 20 · max(r2 , r2 cos(ϕ) + l/2 sin(ϕ) so that whatever the coil dimensions and tilt, the coil is not located close to the boundaries and also Ni = Nj = 200 which is much larger than the rather small number of terms that is normally required. Theoretical results, produced by using CIVA, were first compared to results from the exact double integral expressions in [4] for the coil and conductor (plate) data that are given in Table 1. Accuracy was verified for the field and impedance in case of an uncracked conductor. Figure 2 shows amplitude of the eddy current density induced on the top surface of the plate for three tilt angles. Computation time for such plots is less than 1 sec.

T. Theodoulidis and G. Pichenot / Integration of Tilted Coil Models in a Volume Integral Method

215

Table 1. Coil and testpiece parameters for the results in Figure 4.

y [mm]

Coil

Testpiece

r1 r2

1.0 mm 1.75 mm

nl c1

2 1.55 mm

l N l0

2.0 mm 422 0.1 mm

σ1 σ2 μr1

1.02 MS/m 0.0 1

μr2

1

5

5

5

0

0

0

−5 −5

0 x [mm]

5

−5 −5

0 x [mm]

5

−5 −5

0 x [mm]

5

Figure 2. Eddy current amplitude contours for tilt angles ϕ = 0o , 45o and 90o .

The theoretical results were also compared to experimental measurements conducted by CEA and involved two position scans of a surface EDM notch in an Inconel plate. The notch dimensions were 0.1 × 7.0 × 1.24mm and the coil and plate data are those given in Table 1. The coil tilt was ϕ = 90o and the coil rotation was θ = 90o as shown in Figure 3. The measurements were done at 100kHz using an Agilent 4194A

Figure 3. Screenshot from CIVA showing the coil and testpiece configuration for the results in Figure 4.

impedance analyzer. The coil’s calculated inductance of 0.315mH was verified by the measured value of 0.314mH. In the first position scan the coil is moved along the x-axis and in the second position scan it is moved along the y-axis. Since the EDM notch is

216

T. Theodoulidis and G. Pichenot / Integration of Tilted Coil Models in a Volume Integral Method

ΔR/X

0

ΔX/X

0

located along the y-axis, in the first position scan the coil is moved across the notch while in the second position scan it is moved along the notch. The results for the resistive and reactive part of the impedance change due to the crack are shown in Figure 4. In both cases the agreement is very good. 0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

0

0

−0.1

−0.1

−0.2

−0.2

−0.3

−0.3

−0.4 −6

−4

−2

0 x [mm]

2

4

6

−0.4 −6

−4

−2

0 y [mm]

2

4

6

Figure 4. Comparison of theoretical (lines) and experimental results (circles) for the resistive (•) and inductive part (◦) of the impedance change as a function of position. On the left the coil is moved across the notch while on the right the coil is moved along the notch. Simulations were done with CIVA.

3. Conclusions We have incorporated further capabilities in a Volume Integral code by introducing tilted coils above a layered conductor system in absolute, differential and driver-pickup modes. We are now able to compute in a rapid manner the incident electromagnetic field, self and mutual impedances and most importantly defect signals produced by tilted coils.

References [1] S. Paillard, G. Pichenot., M. Lambert and H. Voillaume, Eddy current modelling for inspection of riveted structures in aeronautics, Electromagnetic Nondestructive Evaluation, Japan, 2006. [2] J.C. Aldrin and J.S Knopp, Crack characterization method with invariance to noise features for eddy current inspection of fastener sites, J. Nondestr. Eval. 25 (2006), 165–181. [3] W.C. Chew, Waves and Fields in Inhomogeneous Media, Van Nostrand Reinhold, New York, 1990. [4] T.P. Theodoulidis and E.E. Kriezis, Eddy current canonical problems (with applications to nondestructive evaluation, TechScience Press, 2006.

Electromagnetic Nondestructive Evaluation (XI) A. Tamburrino et al. (Eds.) IOS Press, 2008 © 2008 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-58603-896-0-217

217

Modeling of Flawed Riveted Structures for EC Inspection in Aeronautics S. PAILLARD a , G. PICHENOT a Y. CHOUA b Y. LE BIHAN b M. LAMBERT c H. VOILLAUME d and N. DOMINGUEZ e a

CEA, LIST, Gif sur Yvette, F-91191, France LGEP, CNRS UMR 8507, Supelec, Univ Paris Sud, Univ PM Curie-P6, France c L2S (CNRS-Supelec-UPS), 3 rue Joliot-Curie, 91192 Gif-sur-Yvette, France d EADS Innovation Works, NDI & SHM, 12 rue Pasteur, 92152 Suresnes, France e EADS Innovation Works, NDI & SHM, 23 bv Victor Hugo, 31770 Colomiers, France b

Abstract. Within the framework of a collaborative project between CEA and EADS, a semi-analytical model based on a Volume Integral Method (VIM) has been developed so as to simulate the Eddy Current (EC) inspection of riveted structures in aeronautics. The modeling is the one of a layered planar structure with a flaw located nearby a fastener. The VIM involving dyadic Green’s functions is considered, a fastener and a flaw being introduced as a variation of conductivity in a stack of slabs. This semi-analytical approach is compared to a Finite-Element one (FE) developed by LGEP and is validated with experimental data acquired on an aeronautical configuration. Keywords. Eddy Current Testing, Aeronautic inspection, Flawed fastener

Introduction

This contribution describes recent achievements about the simulation of EC inspections of flawed fastened structures. The model developed is mainly based on a volume integral formulation employing the dyadic Green’s formalism [1]. This model, which can quickly predict the response of an EC probe, is implemented in the NDT software CIVA ([3]). This multi-modality platform for industrial NDT also handles various eddy current testing configurations as is sketched in Figure 1. In a previous work, a multi-layer model has been investigated [2], and results compared with those provided by a finite-element approach and with experimental data. Here, we intend to extend it to the case of a flaw near a rivet in a like structure. The paper goes as follows: A flawed rivet model is presented, a method of moments is developed and its results are compared with those provided by a finite-element method and by one based on a potential formulation, experimental data being used for further, in-depth validation.

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1.a: Bobbin coil placed inside a conducting tube

1.b: Bobbin coil placed on a configuration defined by CAD

1.c: Ferrite core placed on a fastened structure

Figure 1. Representation of several configurations in the CIVA user interface

1. The semi-analytical model 1.1. Theoretical Formulation The configuration is the following one: a N -layer slab, each layer numbered i and of conductivity σi is sandwiched between two air half-spaces numbered 0 and N + 1, all materials being linear, isotropic, and non magnetic (with permeability μ0 ). The slab is affected by a defect of volume Ω and conductivity σ (r) crossing one or several layers (as depicted in Figure 2.a). One is denoted with index m (resp. n) the first (resp. last) layer affected by the  defect (m < n), the latter being divided into as many layers as necessary n such as Ω = k=m Ωk (in the case of a rivet traversing the N layers, m = 1 and n = N ). A time-harmonic source (circular frequency ω and implied time-dependence exp (jωt)), e.g., a coil probe, is set in the upper half-space. A vector domain integral formulation of the electric field Ek (r) in the layer k in such a configuration is obtained by application of the Green’s theorem to the diffusive vector wave equation and is given by (0)

Ek (r) = Ek (r) − jωμ0

n  l=m

Ωl

(ee)

Gkl (r, r’) [σl − σ(r’)] El (r’) dr’

∀r’ ∈ Ωk

(1) where is the primary field in the layer k and Gkl (r, r’) the electric-electric dyadic Green’s functions defined as the field response to an unit point source and solution of (0) Ek (r)

(ee)

(ee)

(ee)

∇ × ∇ × Gkl (r, r’) − kk2 Gkl (r, r’) = δkl Iδ(r − r’).

(2)

In the above equations k, l denote the index of the layer of the observation r and of the source r’ point, respectively, I is the unit dyad, and δkl stands for the Kronecker delta. kl is the wave number in the lth layer defined as kl2 = jωμ0 σl . The Green’s dyad satisfies appropriate boundary conditions at the interfaces between the different layers in the same way as the electric fields do. The response of the probe is given by its impedance variation and is obtained via the reciprocity theorem, where I0 is the feeding current of the probe, as

S. Paillard et al. / Modeling of Flawed Riveted Structures for EC Inspection in Aeronautics

I02 ΔZ

=

n  l=m

Ωl

(0)

[σl − σ(r)] El (r) · El (r)dr.

219

(3)

1.2. Numerical developments Once the model has been chosen and the equations established, the numerical formulation can be implemented. Equation (1) is discretized by means of a Galerkin’s version of the method of moments where the contrast zone Ω is divided into Ncell parallelepipeded voxels. The voxels are chosen in order to have an homogeneous conductivity inside each one, the electric field being assumed constant-valued within a given voxel as well. This approach yields a linear system (4) ⎤ ⎛ ⎤⎞ ⎡ ⎤ ⎡ (0) Em Gm,m · · · Gm,n Em ⎢ . ⎥ ⎜ . ⎥⎟ ⎢ . ⎥ . ⎢ . ⎥ = ⎝I − ⎢ ⎣ .. . . . .. ⎦⎠ ⎣ .. ⎦ ⎣ . ⎦ (0) Gn,m · · · Gn,n En En ⎡

(4)

where Gi,i are the electromagnetic self-coupling terms of the ith region of the divided rivet onto itself and where Gi,j are the mutual coupling terms of the j th over the ith . An example is given for a three-layered slab (n = 3 and m = 1) in Figure 2. The flawed rivet is here divided into three parts, each one entirely contained within a single layer of conductivity σk with k ∈ {1, 2, 3}. The self-coupling terms Gi,i with i ∈ {1, 2, 3} and the mutual-coupling terms Gi,j with (i, j) ∈ {1, 2, 3} and i = j are represented in Figure 2.b.

2.a: Separate parts of the calculation zone along the Z-axis

2.b: Green s dyads for a three layer slab configuration

Figure 2. Example of a flawed rivet in a three-layered slab

To propose a semi-analytical flawed rivet model, three main improvements have been made as follows. • The multi-layer model: it takes into account a contrast zone which is crossing several layers like a through-wall hole in a multi-layer slab (the model validation is detailed in [4]). The self and mutual coupling terms of the Green’s functions are written in explicit analytical fashion and implemented to reconstruct the entire matrix of equation (4). • The rivet model: considers what happens when a stack of slabs is fastened. The model takes into account the typical rivet shape, i.e., its flat cone-shaped head. It is considered via the calculation of the volume ratio in every cell of the discretiza-

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tion zone. A weighting coefficient is introduced in each cell based on the volume occupied by the head rivet compared to the one occupied by the slab (it is equal to one if the cell is entirely in the rivet or in the flaw, and zero if not). • The flawed rivet model: extends the rivet model to the case of a flaw within a fastened structure. The rivet and the flaw are included in the same calculation zone (see Figures 3.b and 3.c) with a volume ratio matrix so as to fit the geometry at best (an example is shown in Figure 3.a).

3.a: Contrast Matrix

3.b: Discretization in the X-Y-plan

3.c: Discretization along the Z-axis

Figure 3. Discretization of the full calculation zone

In the applications aimed at, the typical size of the domain Ω might be more than ten skin-depths at the frequency of operation. Few voxels per skin-depths are needed, which leads to a large number of voxels and to a too large linear system to invert (the memory 2 size can be estimated as O (9 Ncell )). Taking into account the convolution structure of the integral equation (1) with respect to the two lateral directions via appropriate fast Fourier transforms, an iterative solution of the system enables us to treat large defects by 4/3 reducing the memory size to O (9 Ncell ). 2. Comparison to a published example (Zeng et al., ACES’07) 2.1. Configurations In [5], the authors successfully compared their approach based on a potential formulation with a finite-element approach on two configurations (one is depicted in Figure 4 and the second is similar to it without flaw). It consists of a plate with a through-wall cylindrical hole with (and without) a flaw located nearby, sketched in Figure 4.b. The EC probe is moved along the surface, on a line passing by the diameter of the hole and along the length of the breaking-surface flaw, above the fastener assembly (Figure 4.a). 2.2. Results There is a good agreement in both amplitude and phase (Figure 5.a and 5.b) between CIVA and the potential formulation (which, in addition, as already said, was successfully compared with the finite-element method). These configurations involved a breakingsurface flaw, a cylindrical hole and a unique slab. These elements are still simple compared with respect to those in aeronautics. However, the good results achieved in these simple configurations have allowed us to validate the flawed rivet model for a more realistic aeronautical configuration with the following characteristics: a multi-layer configuration, a buried flaw with a thin opening, a fastener shape (with conical head), and a ferrite-core probe.

S. Paillard et al. / Modeling of Flawed Riveted Structures for EC Inspection in Aeronautics

4.a: View of the configuration with CIVA

221

4.b: Details of the hole and the flaw

Figure 4. Configuration for the data comparison

(



5.a: Amplitude of the signals CIVA, • ◦ Potential Formulation)

(



5.b: Phase of the signals CIVA, • and ◦ Potential Formulation)

Figure 5. Comparison between CIVA results and those of the potential formulation [5].

3. Calibration on the rivet In most industrial applications, the measured EC signal is calibrated over a reference configuration. The issue is to cope with discrepancies of scales, the size of the rivet and the one of the flaw differing by orders of magnitude. So, to be sensitive to the flaw response, a calibration of the signals simulated vs. the experimental one is seen as a preliminary set to the validation of the flawed rivet model. 3.1. Configuration of the calibration The reference configuration for the calibration is a rivet without flaw within a multi-layer slab as is depicted in Figure 6. It consists of a layered planar structure with a fastener hole: three aluminum layers (2.5 mm and 4 mm thick) with a conductivity of 17 MS/m are traversed by a borehole with head diameter of 12 mm and body diameter of 6.35 mm (see details in Figures 6.a and 6.b). The EC probe is moved on a line along the diameter of the rivet. The experiments have been performed with a ferrite-cored probe operating at 1.6 kHz (detailed in [6] and [7]). The probe has an inner radius of 3.74 mm, an outer radius of 7.325 mm, a lift-off of 0.09 mm and a thickness of 3.46 mm with 926 turns. The semi-analytical and finite-element results –the latter being obtained from a code

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S. Paillard et al. / Modeling of Flawed Riveted Structures for EC Inspection in Aeronautics

6.a: View of the configuration with CIVA

6.b: Details of the rivet

Figure 6. Configuration for the calibration

developed at LGEP [8]– are calibrated with respect to the complex value associated to the maximum amplitude of the experimentally recorded borehole signal. 3.2. Results of the calibration The impedance variations measured in the impedance plane calibrated on the rivet signal with the semi-analytical model, with the finite-element code and the experimental data are displayed in Figure 7.a with squares ( ), circles (•) and (–), respectively .

7.a: Impedance plane diagram

7.b: Real and imaginary parts Figure 7. Calibration

A good agreement between the semi-analytical model and the finite-element one is obtained. Nevertheless, the two simulated signals do not accurately fit the experimental one when the probe is placed right above the borehole. An explanation for this dis-

S. Paillard et al. / Modeling of Flawed Riveted Structures for EC Inspection in Aeronautics

223

crepency is that the EC probe in this configuration has a 3D ferrite core (cylindrical core with slots) which was not modeled using CIVA and the FE code. The disagreement between experimental and simulation data could be due to this specific probe as shown in [6]. 4. Validation on experimental data: Flawed Rivet 4.1. Configuration of the experimental validation Now, the model is validated in the case of a flaw near a rivet in a structure similar to the one described in section 3.1 (see Figure 8.a). The configuration (slab, borehole dimensions, probe) is the same as at the calibration case save the addition of an EDM notch of 200 μm-width, 5 mm-length and 4 mm-depth in the second layer as shown in Figure 8.b. The probe is moved on a line along the diameter of the rivet and along the length of the flaw.

8.a: View of the configuration with CIVA

8.b: Details of the rivet and the flaw

Figure 8. Flawed structure configuration

4.2. Results of the experimental validation In the following all the results are calibrated (see section 3 for the calibration procedure). In Figure 9.a the experimental data and the results obtained from the semi-analytical model are compared using an impedance plane representation whereas in Figure 9.b the latter and the finite-element results are presented. The flaw signal is obtained by subtracting the response of the probe from the flawed rivet from the one over the rivet without flaw. Due to the small amplitude of the flaw signal and to the incertitude of the experimental signal, the result of the flaw signal is here only compared to the Finite element result (Figure 9.c). It appears that the flaw signal has the same shape in the impedance plane for the semi-analytical and the finite-element results, with a discrepancy in amplitude better than 30 %. 5. Conclusion The integration of the flawed rivet model in the CIVA platform is in progress. The approach has been successfully compared with different methods (potential formulation

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S. Paillard et al. / Modeling of Flawed Riveted Structures for EC Inspection in Aeronautics

9.a: Lissajous curves (— Experimental data,  CIVA)

9.b: Lissajous curves ( CIVA, ◦ FE)

9.c: Flaw response ( CIVA, ◦ FE)

Figure 9. Lissajous curves of the rivet and the flaw

and finite-element method) for different configurations. This semi-analytical flawed rivet model is validated with experimental data on an aeronautical configuration, with good agreement. Among the questions still open, how to better account for the discrepancy between the sizes of the rivet and of the flaw appears to be one of the most compelling one. Acknowledgements This work is supported by the Paris Île-de-France Région. References [1] [2] [3] [4]

[5]

[6] [7] [8]

Chew W. C., Waves and Fields in Inhomogeneous Media, Van Nostrand Reinhold, New York, 1990. Paillard S., Pichenot G., Lambert M., and Voillaume H., Eddy current modeling for inspection of riveted structures in aeronautics, 11th International Workshop on Electromagnetic NDE, Iwate, 2006. Le Ber L., Calmon P., Sollier T., Mahaut S., and Benoist P., Advances of simulation and expertise capabilities in CIVA platform, in Review of Progress in QNDE 25, 2006, pp. 684-691. Paillard S., Pichenot G., Lambert M.,Voillaume H. and Dominguez N., A 3D model for eddy current inspection in aeronautics: application to riveted structures, Review of Progress in QNDE 26, 2006, pp. 265-272. Zeng Z., Liu X., Deng Y., Udpa L., Knopp J. S., and Steffes G., Reduced magnetic vector potential and electric scalar potential formulation for eddy current modeling, Review of Progress in ACE, Verona, 2007, pp. 773-777. Buvat F., Pichenot G., Prémel D., Lesselier D., Lambert M., and Voillaume H., Eddy current modeling of ferrite-cored probes, Review of Progress in QNDE 24, 2005, pp. 463-470. Pichenot G., Buvat, F., Maillot V., and Voillaume H., Eddy current modeling for non destructive testing, 16th World Conf. on NDT, Montreal, 2004. Choua Y., Santandrea L., Le Bihan Y., Marchand C., Thin Crack Modeling in ECT with Combined Potential Formulations, IEEE Transactions on Magnetics, 43, 2007, pp. 1789-11792

Electromagnetic Nondestructive Evaluation (XI) A. Tamburrino et al. (Eds.) IOS Press, 2008 © 2008 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-58603-896-0-225

225

Numerical Modeling of Eddy Current Nondestructive Evaluation of Ferromagnetic Tubes via an Integral Equation Approach Anastassios SKARLATOS a , Grégoire PICHENOT a , Dominique LESSELIER b , Marc LAMBERT b and Bernard DUCHÊNE b a CEA-LIST, 91191 Gif-sur-Yvette b Département de Recherche en Electromagnétisme - Laboratoire des Signaux et Systèmes (CNRS-Supélec-Univ Paris-Sud), 91192 Gif-sur-Yvette Abstract. In this contribution a Volume Integral Equation (VIE) formulation for the modeling of eddy current Nondestructive Evaluation (NDE) of ferromagnetic tubes is proposed. The method is well suited for the simulation of NDE applications involving moving probes including Remote Field Eddy Current Effect (RFEC) probes. The proposed algorithm has been integrated in the CIVA platform. Keywords. Ferromagnetic tubes, Integral Equations, Remote Field Eddy Current Effect

1. Introduction Volume Integral Equation (VIE) - based models are well established and successfully applied in the industry for nonmagnetic tubes [1,2]. Such models have also been already developed for the modeling of ferrite-core eddy-current probes [3]; however, the formulation of the problem in the more general ferromagnetic case deserves more studies. The presence of material defects in this case results in a local variation of the magnetic permeability in addition to that of the conductivity met in nonmagnetic materials. This in turn requires a system of two integral equations, one for the electric field and one for the magnetic field, in order to obtain a well determined problem. This system involves the full family of the Green’s dyads. The integral equations are solved numerically using the Method of Moments (MoM). For the latter, only the flaw region needs to be discretized. The matrix produced by the discretization of the integral equations depends only upon the geometries of the tube and the flaw and upon the frequency. Hence, once the Green’s dyads have been calculated and the MoM matrix has been constructed, the response of the flaw to a given excitation can be obtained by a simple multiplication of the discretized primary field vector (which calculation is very fast) with the inverse of the above matrix. Thus, the method is very efficient, particularly for the simulation of Nondestructive Evaluation (NDE) tech-

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niques involving moving coils, as the most important part of the computational burden relies on the computation of the Green’s dyads that have only to be computed once. In the following, the VIE formulation for the ferromagnetic problem is presented briefly and validated using experimental data obtained by means of the Remote Field Eddy Current (RFEC) technique. The discussed model has already been integrated in an expertise software for the simulation of NDE applications, i.e., the CIVA platform [4].

2. The Integral Equation Formulation Let us consider a ferromagnetic tube with conductivity σb2 and permeability μb2 . Index 2 denotes the second layer (the tube wall) of a cylindrically layered medium. The first and the third layers correspond to the inner and outer regions, respectively. The presence of a material defect inside the tube wall causes a local variation of conductivity, and/or permeability, depending upon the type of flaw. In NDE applications, we usually deal with flaws caused by corrosion or material damage (like cracks) so that a simultaneous change of both parameters is the most interesting case. Let δσ2 ( r ) = σ2 ( r ) − σb2 and δμ2 ( r ) = μ2 ( r ) − μb2 stand for the variation of conductivity and permeability inside the tube wall with respect to their background values in a non-damaged zone. The electric and magnetic fields can be expressed in the following form (the time convention e −jωt is implied) [5]:  (ee) 2 ( r ) = E inc ( r )+jωμb2 G 2 ( r  ) dV  E r, r  ) · δσ2 ( r  ) E 2 22 (  +jω

Vf (em)

G22

2 ( r  ) dV  , ( r, r  ) · δμ2 ( r  ) H

(1)

Vf

and

 (me) inc 2 ( r  ) dV  H2 ( r ) = H2 ( r )+ G22 ( r, r  ) · δσ2 ( r  ) E  Vf (mm) 2 ( r  ) dV  , +ω 2 ε˜b2 G22 ( r, r  ) · δμ2 ( r  ) H

(2)

Vf

inc , H inc denote the where the integration extents over the support of the flaw Vf . E 2 2 σb2 σb2 electric and magnetic fields in the absence of the flaw, and ε˜b2 = εb2 − jω ≈ − jω (ab)

is the complex permittivity of the medium. The dyadic Green’s functions G 22 ( r, r  ), (a, b = e, m) are defined as the field response of unit point current sources of electric and magnetic types. Their definition is given in [3,6]. The system of equations (1),(2) provides a complete description of the problem. It can be solved numerically by means of the method of moments. Let us notice that the eddy current inspection of nonmagnetic conducting tubes can be deduced from the above formulation as a subcase. Once the fields inside the damaged region have been obtained by solving the above-mentioned system, the variation of the probe mutual impedance, which is actually the physical quantity that can be measured, can be found by applying the reciprocity theorem:

A. Skarlatos et al. / Numerical Modeling of Eddy Current Nondestructive Evaluation

ΔZ12

227

  1 inc ( r  ) · E 2 ( r  ) δσ2 ( r  ) E =− Rx I1 I2 Vf

 2 ( r  ) · H inc ( r  ) dV  , + jωδμ2 ( r  ) H Rx

(3)

where I1 and I2 are the electric currents flowing in the driving and receiving coils, re inc ( r ) and H inc ( r ) denote the electric and magnetic fields induced in spectively, and E Rx Rx the unperturbed material by the receiving coil (Rx) when operating in the transmission mode.

3. Validation The above integral formulation has been validated by comparing the theoretical results with two experimental data sets. The first experimental set-up consists of a RFEC probe moving inside a steel tube with inner and outer diameters of 14 mm and 18 mm, respectively. The operating frequency is set to 250 Hz. At this frequency, the measured values of conductivity and relative permeability are 6.25 MS/m and 210, respectively. Figure 1 displays the layout of the probe and some representative results obtained for a 3 mm wide 70% deep external groove and a 5 mm through-hole. The number of grid cells used for the discretization of the integral equation is 200 for the groove and 1089 for the hole, which results in respective computation times of 23 min and 31 min on a Pentium 4 workstation operating at 3.6 GHz with 1 GB RAM, for 161 different probe positions. It must be noticed that, for both cases, the major part of the computation time for both cases is dedicated to the calculation of the dyads and to the inversion of the matrices. In the case of the through-hole, for instance, the CPU time needed for the computation of the primary field is ca. 3 min, whereas the rest of the time (28 min) is the dedicated to the calculation of the Green’s dyads and the matrix inversion. Duplicating the number of probe positions, the difference in the calculation time is less than one minute. The number of probe positions has thus a very small impact on the total calculation time. Furthermore, the simulation of a new scan does not require the recalculation and inversion of the matrix. In the second experiment, the tube has inner and outer diameters of 23.3 mm and 31.9 mm, respectively. The frequency of operation is 150 Hz. The values of the tube conductivity and permeability at this frequency are 3.5 MS/m and 100, respectively. The probe configuration and the results for a 3D defect (notch) are displayed in Figure 2. Both experimental and FEM simulation results for this given configuration are courtesy of Chen et al. [7]. 567 grid cells are used for the discretization of this problem and the CPU time reaches 13 min for 200 probe positions, 40 s being dedicated to the computation of the primary field. Tab.1,2 compare the measured values of the probe signal’s amplitude and phase to those obtained by means of the VIE model. In general, simulation and measurements are in good agreement. Some deviations in phase observed in the cases of 3D flaws (hole and notch) can be attributed to the side effects of the flaw fabrication procedure. This is evidenced in Tab.3 which displays the values measured (in the first experiment) for two identical holes produced with different fabrication techniques (one is electro-eroded and the other is drilled). It can be observed that the flaw fabrication procedure has a non-

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Table 1. Comparison of the amplitude and phase of the measured signal to that obtained by means of the VIE model (2D flaws). Flaw

Amplitude VIE

External Groove 20% (1st exp.)

Phase

Meas.

4.4 mV

VIE

Meas.

4.1 mV

-43◦

-41◦

External Groove 60% (1st exp.) External Groove 70% (1st exp.)

21.9 mV 30 mV

21 mV 30 mV

-20.6◦ -17◦

-24.1◦ -21◦

External Groove 50% (2nd exp.)

18 mV

16 mV

11◦

15◦

3 mm

35 mm

35 mm

5 mm

6.8 mm 12.8 mm

(a) 15 VIE Measurements

1

5 0

−5

−10 −15 −15

VIE Measurements

2

Im{VR} (mV)

Im{VR} (mV)

10

0

−1 VIE : 30 mV, −17° Meas: 30 mV, −21° −10

−5

°

−2 VIE : 5.0 mV, 0 Meas: 4.5 mV, 15° 0 Re{VR} (mV)

5

10

15

−2

−1

(b)

0 Re{VR} (mV)

1

2

(c)

Figure 1. (a) Probe layout in a tube with a hole. Comparison of the simulation and experimental results for: (b) a 3 mm wide 70% deep external groove, and (c) a 5 mm through-hole. The results are calibrated by using the results obtained for a 3 mm wide 40% deep external groove

negligible impact on the measurements. Furthermore, the Lissajous curves calculated by the VIE model and the FEM fit very well with each other and both present the same deviation in phase from the experimental curve (cf. Figure 2). As the two results are obtained by means of two methods quite different from one another, it seems probable that the deviation from the experimental curve is due to the local change of the magnetic permeability in the vicinity of the flaw caused by manufacturing. Table 2. Comparison of the amplitude and phase of the measured signal to the ones obtained by means of the VIE model and FEM (3D flaws). Flaw

Amplitude VIE

Through Hole (1st exp.) External Notch 50% (2nd exp.)

4.5 mV 2.4 mV

Phase

FEM

Meas.

VIE

FEM

Meas.

2.7 mV

5 mV 3.8 mV

15◦ 14◦

11.9◦

0◦ 29◦

A. Skarlatos et al. / Numerical Modeling of Eddy Current Nondestructive Evaluation 15 mm

229

5 mm

2 1.5

VIE FEM Measurements

114 mm

R

8 mm

Im{V } (mV)

1 0.5 0

−0.5 −1

VIE : 2.4 mV, 14° ° −1.5 FEM : 2.7 mV, 12 Meas: 3.8 mV, 29° −2 −2 −1

19.5 mm

15.5 mm

(a)

0 Re{VR} (mV)

1

2

(b)

Figure 2. (a) Probe layout, and (b) results for a 5 mm wide, 60 ◦ and 50% deep external notch (b). Both simulation and experimental results are calibrated by using the results obtained for a 5 mm wide 20% deep external groove. Table 3. Comparison of the measured signals for two identical through-holes made with different techniques. Flaw

Amplitude

Phase

Electro-Eroded Hole (1st exp.) Drilled Hole (1st exp.)

5 mV 4.2 mV

0◦ 6◦

4. Conclusion A Volume Integral Equation formulation for the inspection of ferromagnetic tubes has been proposed. The results of the model have been validated using experimental data. A good agreement between theoretical and experimental results has been observed. The presented model is particularly efficient for simulation of NDE applications involving moving probes. It has been already integrated in the CIVA platform and it will be available with the next release (CIVA 9.0).

Acknowledgments The authors would like to thank Prof. Chen and his colleagues from the International Institute of Universality in Tokyo, and Prof. Takagi from the Institute of Fluid Science in Sendai, Japan, for kindly supplying their experimental and FEM simulation results for the validation of our model.

References [1]

[2]

V. Monebhurrun, D. Lesselier, and B. Duchêne, “Evaluation of a 3-D bounded defect in the wall of a metal tube at eddy current frequencies: the direct problem", J. Electromagn. Waves Appl., vol. 12, pp. 315-347, 1998. G. Pichenot, D. Prémel, T. Sollier, and V. Maillot, “Development of a 3D electromagnetic model for eddy current tubing inspection: Application to steam generator tubing", Rev. Quant. Nondestr. Eval., vol. 16, pp. 79-100, 2005.

230 [3]

[4] [5]

[6] [7]

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J. R. Bowler, L. D. Sabbagh, and H. A. Sabbagh, “A theoretical and computational model of eddycurrent probes incorporating volume integral and conjugate gradient methods", IEEE Trans. Magn., vol. 25, no. 3, pp. 2650-2664, 1989. CIVA 9.0, State of the art simulation platform for NDE, 2007, www-civa.cea.fr. A. Skarlatos, G. Pichenot, D. Lesselier, M. Lambert, and B. Duchêne “Remote fi eld effect modeling via an integral equation approach”, 5ème Conférence Européenne sur les Méthodes Numériques en Electromagnétisme, Lille, pp. 139-140, 2006. W. C. Chew, Waves and fields in inhomogeneous media. New York: IEEE Press, 1995. M. Rebican, Z. Chen, N. Yusa, K. Miya, T. Uchimoto, and T. Takagi, “Investigation of numerical precision of 3-D RFECT signal simulations", IEEE Trans. Magn., vol. 41, no. 5, pp. 1968-1971, 2005.

Electromagnetic Nondestructive Evaluation (XI) A. Tamburrino et al. (Eds.) IOS Press, 2008 © 2008 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-58603-896-0-231

231

Design of Reflection Type Pulsed Eddy Current Nondestructive Testing a

a

a

b

Young-Kil SHIN , Dong-Myung CHOI and Hee-Sung JUNG School of Electronic and Information Eng., Kunsan National University, San 68, Miryong-Dong, Kunsan, Chonbuk, 573-701, Korea b R&D Institute, Sae-An Engineering Corporation, Byucksan Digital Valley II, Gasan, Geumcheon, Seoul, 153-803, Korea

Abstract. Reflection type shielded send-receive probe is designed for accurate measurement of specimen thickness by pulsed eddy current testing and when evaluating material conductivity, effects of pulse width on the signal are investigated. Results show that the best sensitivity to thickness is achieved when ferrite shields for both coils are used and when the exciter coil is located inside the sensor coil. Pulse width study suggests that the shorter pulse width is desired if the peak amplitude is used to evaluate the material conductivity, while the longer pulse width is needed if the peak time is used for the same purpose. Keywords. Pulsed eddy current, Reflection probe, Pulse width

1. Introduction Thickness and material property measurements without contacting the test object is the main advantage of eddy current testing over the other testing methods. Among eddy current testing methods, the pulsed eddy current (PEC) testing is expected to be rich of information and to have deeper penetration than conventional eddy current testing. This is because a pulse current can be transformed into infinite train of harmonically related sinusoidal waveforms so that it has wideband frequency [1-3]. There are two types of PEC testing, one is through transmission method and the other is reflection method. Both methods are known to be sensitive to thickness variation of test specimen. When the far side of test object is not accessible, the reflection type PEC testing has to be used. In this paper, a shielded send-receive type reflection probe is designed by using a self-written numerical analysis code and their performance to evaluate the thickness and conductivity of test object is investigated. Also, effects of pulse width to PEC signals are investigated when material conductivity is evaluated. The time taken to reach the peak value of the step response is first investigated and it is used as the pulse width in the PEC testing to produce the maximum PEC signal.

2. Numerical method and test design models Pulse coil current induces eddy currents in a specimen and their magnitude change continuously with time. In such a case, a transient analysis is required to predict their

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behavior so that the backward difference method is used for temporal analysis. For the spatial modeling, the finite element method is used [4,5]. An axisymmetric modeling code is written and used for the prediction of PEC signals. The governing equation for PEC testing is §1 · ’ u ¨ ’ u A¸ ©P ¹

where

Js V

P , V , J s , A are

wA . wt

(1)

permeability, conductivity, source current density vector,

magnetic vector potential, respectively. In this work, Eq. (1) is written using a cylindrical coordinate system. Applying the finite element formulation for the space, the following type of matrix equation is obtained [6]. wA

> S @^ A`  >C @ ­® wt ½¾ ^Q` ¯

(2)

¿

To treat time, the backward difference method is used where all the values are evaluated at a new time, t n1 ­ wA ½ ® ¾ ¯ wt ¿

n 1

n t  't , and the time derivative term is expressed as

^ A`n1  ^ A`n

(3)

't

where ^A`n is the magnetic potential evaluated at time t n . Rewriting Eq. (2) by using Eq. (3), the following recurrence relation is obtained and the magnetic potential at any time step can be calculated. ª1 º n 1 « 't >C @  > S @» ^ A` ¬ ¼

^Q`n1 

1 n C @^ A` > 't

(4)

The test signal in PEC testing is the electromotive force induced in the sensor coil so that it can be calculated as follows.

Vemf

^ A`n1  ^ A`n 't

2S rc

(5)

where rc is the centroidal radius of a coil. Four probe design models that use copper and ferrite shields, as shown in Figure 1, are first tested. Figure 1 shows cross section of axis symmetric test model probes and the vertical line is the axis of symmetry. The exciter and sensor coils are denoted by “E” and “S’, respectively. Later, all the shields in model 1 and model 4 are changed to ferrite and tested for thickness evaluation of copper and inconel 600 plates.

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 (a) Model 1

(b) Model 2

 (c) Model 3

(d) Model 4

Figure 1. Four test models of reflection type PEC probe using copper and ferrite shields [unit = mm]

3. Selection of probe design for thickness evaluation Figure 2 shows PEC signals obtained by model 1, peak amplitude and peak time variations as a function of thickness. Figures 3, 4 and 5 show same kind of results obtained by models 2, 3 and 4. As the thickness increases, numerical modeling results show that the peak value decreases and the time taken to reach the peak amplitude (hereafter, the peak time) increases at the low thickness, but decreases when the thickness exceeds a certain limit. When the coil spacing is increased from 3 mm (D=10) to 6mm (D=20), the peak value decreases but the peak time increases. Comparing results from model 1 and 4, and model 2 and 3, we can find that the higher peak value appears when the exciter coil is inside the sensor coil. Meanwhile, if we compare results from model 3 and 4 in which the exciter is inside the sensor, we can find that the higher peak value is obtained when the exciter coil is shielded by copper while the sensor coil is shielded by ferrite.

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(a) Signal (coil spacing = 3mm)

(b) Peak amplitude variation

(c) Peak time variation

Figure 2. Thickness variation results obtained by probe model 1

G (a) Signal (coil spacing = 3mm)

(b) Peak amplitude variation

(c) Peak time variation

Figure 3. Thickness variation results obtained by probe model 2

G (a) Signal (coil spacing = 3mm)

(b) Peak amplitude variation

(c) Peak time variation

Figure 4. Thickness variation results obtained by probe model 3

 (a) Signal (coil spacing = 3mm)

(b) Peak amplitude variation

(c) Peak time variation

Figure 5. Thickness variation results obtained by probe model 4

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Table 1. Sensitivity to thickness variation when copper and ferrite shields are used

Model 1 Model 2 Model 3 Model 4

Copper D=3mm D=6mm 53.3 % 59.78 % 51.6 % 59.4 % 46.2 % 51.15 % 56.16 % 64.76 %

Inconel 600 D=3mm D=6mm 40.7 % 47 % 44.96 % 51.7 % 40 % 47.4 % 44.7 % 52 %

In a practical sense, however, the probe sensitivity to thickness variation seems more important than peak value changes. This sensitivity is calculated by dividing peak value changes due to thickness variation from 1.8 mm to 4.5 mm by the biggest peak value, that is, when the thickness is 1.8 mm. Results are summarized in Table 1. According to this table, model 4 gives the best sensitivity and the better sensitivity can be achieved as the coil spacing is wider and as the conductivity of the test material is higher. This result seems reasonable because direct influence from the exciter would be suppressed if the coil spacing increases (although PEC signal itself is reduced) and the influence of eddy currents in the test material that reflect the condition (thickness, in this case) of test specimen would be increased if the conductivity is higher. If eddy currents are induced in the copper shield and when the conductivity of test material is very low, the influence of eddy currents in the shielding material may appear in the PEC signal. To avoid such unwanted signals, models using ferrite shields for both coils are tested. The results are shown in Figure 6 and they are much better than those from previous models. Table 2 shows that the sensitivity, as well as the PEC signal, is also much higher.

 

 (a) Signal (coil spacing = 3mm)

(b) Peak amplitude variation

(c) Peak time variation

Figure 6. Thickness variation results obtained by a probe that uses only ferrite shields (Exciter inside)

 Table 2. Sensitivity to thickness variation when only ferrite shields are used

Sensor Inside Exciter Inside

Copper D=3mm D=6mm 74.3 % 74.2 % 74.3 % 74.2 %

Inconel 600 D=3mm D=6mm 44.3 % 60.2 % 50.96 % 60.2 %

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4. Effects of pulse width variation in the evaluation of conductivity PEC signal variation due to material conductivity is investigated in conjunction with the pulse width variation. First, the response from step input current is investigated to decide the pulse width. As shown in Figure 7(a), peak amplitudes of step responses that are from various conductive materials appear at different times. The time taken to reach the peak amplitude in the step response is investigated and summarized in Table 3. The peak time increases as conductivity increases. Figure 7(b), (c) show PEC signals obtained by using different pulse widths. In Figure 7(b), the peak time of tungsten is used as the pulse width and that of copper is used in Figure 7(c). As the conductivity increases, the peak amplitude gets reduced and the peak time increases. When the pulse width is long enough, signal passes the peak point and reduces somewhat before the steep drop caused by the pulse-off. If the pulse width is too short, the peak amplitude is less than that of step response. Peak values and peak times from various conductors are investigated and effects of pulse width on them are shown in Figure 8. The steeper slope would give better signal resolution. The sensitivity to conductivity variation is also investigated and summarized in Table 4. According to these investigations, the pulse width needs to be shorter if the peak value is used to evaluate the conductivity, while the longer pulse width is desired if the peak time is used for the same purpose.



 (b) Pulse width = 180 ȝs

(a) Step responses

(c) Pulse width = 520 ȝs

Figure 7. Step responses and PEC signals obtained by model 4, except that only ferrite shields are used. Table 3. Peak time of step responses to various conductivities and thickness when ferrite shields are used

Thickness 1.8 mm 4.5 mm

Copper 520 ȝs 950 ȝs

(a) Peak value variation

Aluminum 390 ȝs 720 ȝs

Tungsten 180 ȝs 340 ȝs

(b) Peak time variation

Figure 8. Variation of peak value and peak time due to conductivity changes.

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Table 4. Sensitivity to conductivity variation when only ferrite shields are used.

Plate Thickness



1.8 mm Sensor Inside 4.5 mm 1.8 mm Exciter Inside 4.5 mm

Pulse Width

Peak Value Sensitivity

Peak Time Sensitivity

520 ȝs 180 ȝs 950 ȝs 340 ȝs 520 ȝs 180 ȝs 950 ȝs 340 ȝs

63.4 % 79.7 % 63.9 % 81.0 % 64.1 % 80.1 % 63.9 % 81.0 %

65.3 % 37.0 % 63.8 % 27.6 % 66.6 % 29.1 % 65.2 % 26.0 %

5. Summary In this paper, numerical modeling of reflection type PEC testing is performed. Results show that the best sensitivity to thickness variation can be achieved when exciter coil is located inside the sensor coil and both are shielded by ferrite. Effects of pulse width for conductivity evaluation are also studied by monitoring the peak times of step responses. Results suggest that the pulse width needs to be shorter if the peak amplitude is used to evaluate the conductivity, while the longer pulse width is desired if the peak time is used for the same purpose.

Acknowledgement This work was supported by the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korea government (MOST) (No.2007-00467).

References [1] [2] [3] [4] [5] [6]

C. J. Renken, “The use of a personal computer to extract information from pulsed eddy current tests,” Materials Evaluation, Vol. 3, pp. 356-360, 2001. M. S. Safizadeh, B. A. Lepine, D. S. Forsyth, and A. Fahr, “Time-frequency analysis of pulsed eddy current signals,” J. NDE, Vol. 20, No. 2, pp. 73-86, 2001. Gui Yun Tian and Ali Sophian, “Reduction of lift-off effects for pulsed eddy current NDT,” NDT&E International, Vol. 38, pp.319-324, 2005. R. Ludwig and X. W. Dai, “The numerical and analytical modeling of pulsed eddy currents in a conducting half-space,” IEEE Trans. Mag., Vol. 26, No. 1, pp. 299-307, 1990. Xiao-wei Dai, Reinhold Ludwig, and R. Palanisamy, "Numerical simulation of pulsed eddy-current nondestructive testing phenomena," IEEE Trans. Mag., Vol. 26, No. 6, pp. 3089-3096, 1990. Young-Kil Shin, Numerical modeling of probe velocity effects for electromagnetic NDE, Ph. D. Dissertation, Iowa State University, U.S.A., 1992.

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Applications

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Electromagnetic Nondestructive Evaluation (XI) A. Tamburrino et al. (Eds.) IOS Press, 2008 © 2008 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-58603-896-0-241

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Noninvasive Characterization of BjorkShiley Convexo-Concave Prosthetic Heart Valves using an Electromagnetic Method Raimond GRIMBERG1, Shiu C. CHAN2, Adriana SAVIN1, Lalita UDPA2, Satish S.UDPA2 1

National Institute of R&D for Technical Physics, Iasi, Romania 2 Michigan State University, East Lansing, USA

Abstract. Prosthetic heart valves Bjork-Shiley Convexo-Concave type were intense implanted during long time, being reported cases of breaking of one component of the valves which had lead to deceases. This paper presents a new method for noninvasive electromagnetic method for this type of valve, using an eddy current transducer with orthogonal coils. In vitro experiments had shown that discontinuities of outlet strut with depths equal or bigger than 0.4mm can be detected with a probability of detection of 86.4% and in the case of discontinuities with depth equal or bigger than 0.6mm with POD of 97%. Keywords: eddy current examination, nondestructive evaluation, Björk-Shiley convexo-concave prosthetic heart valves

1. Introduction Current prosthetic heart valve devices are subject to strict regulatory ([1],[2],[3]) and engineering controls in design evaluations, manufacturing quality control and in vitro verifications, and must demonstrate satisfactory results in both animal and human trials. The BSCC heart valve comprises of a flange (orifice ring), an inlet strut, an outlet strut, a disc occluder and a woven Teflon fabric sewing ring for implantation. The flange and the inlet strut are manufactured as an integral unit from a cobalt-based Haynes-25 alloy bar stock. The outlet strut is formed from a wire of the same alloy and joined to the flange by TIG welding. The occluder disc is composed of an outer Pyrolite® coating over a graphite core (Figure 1). The failure mechanism of the BSCC heart valve is not yet completely understood, many reports [1] have suggested material fatigue as the key cause of the fractures. There is, therefore, a necessity and considerable interest in developing techniques to detect cracks and single-leg separation (SLS) failures before a complete outlet strut fracture (OSF) occurs. Many detection approaches have been proposed. They generally belong to one of the three categories: high speed and energy cineradiography [4]; acoustic approaches [5]-[7]; electromagnetic approaches [6], [7].

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Figure 1. BSCC convexo-concave heart valve

This paper proposes a novel electromagnetic method for noninvasive in vivo detection of fatigue cracks in the outlet strut. In this method, an absolute send-receiver transducer [8], [9] with orthogonal coils for excitation and reception is used. Characterization of the detection system with heart valve replicas has demonstrated a high system sensitivity to crack size as small as 0.4 mm. Meanwhile, in vitro testing of 32 BSCC heart valves with various outlet strut conditions using the proposed method has demonstrated 100% accuracy in indicating SLS failures.

2. Test Specimens Two types of test specimens were used in the studies:  Replica valves made from Haynes-25 alloy with the tolerances of a 27 mm BSCC valve. On the outlet strut of each specimen, there is either no crack or an EDM notch with a depth of one of 0.2, 0.4 or 0.6 mm and 0.3mm width. The replicas do not contain occluder discs (Figure 2a). This is done without loss of accuracy since the contribution of conductivity from the disc is small, as is its influence on the results of the inspection.  BSCC heart valves with either intact or single-leg separated outlet struts (Figure 2b). The SLS cases consist of both manufactured and naturally occurring defects. In the manufactured SLS cases, a laser was used to sever one of the outlet strut legs. The occluder discs are present in these valves.

a

b Figure 2. BSCC valves: a) replicas; b) real valves

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243

3. Fatigue Growth Rate The relationship between the fatigue growth rate per cycle, da/dN, and stress intensity range 'K is given by Paris law [10]

da dN

C  'K

n

For the Haynes-25 alloy, da/dN was also experimentally determined using alloy wire samples with a diameter of 1.2 mm, immersed in Ringer’s lactate solution at 370C. Figure 3 shows a comparison between the experimental and theoretical results. According to the data from this figure, for a normal pulse of 72pulses/minut, if initially in OS a crack with 0.6mm depth exists; it will grow until OS fractures in 3 months. If it can be determined with a good probability of detection, an interval of time, long enough for the preparation of the operation of explant-implant will be obtained.

Figure 3 Comparison of experimental and theoretical results

4. Experimental Setup A test setup had been constructed to investigate the proposed approach involving the use of orthogonal coils and to demonstrate the method’s ability to accurately detect and characterize discontinuities on outlet struts of BSCC heart valves. For each test, the heart valve is rotated 400 clockwise and tilted back 600 from the vertical, with the outlet side of the valve facing “up” towards the transducer. The transducer is made from two orthogonal coils wounded on an insulator support. It is placed approximately 70 mm away from the outlet strut of the valve. This particular valve orientation and test configuration resembles the situation when the transducer is placed on the chest surface of the patient. During the heart valve inspection, the relative position and distance between the transducer and the heart valve continuously vary due to the cardiac cycle. In order to

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investigate the effects of this movement on the performance of the proposed orthogonal coils detection system, a cinegram of an unidentified BSCC heart valve patient was obtained and the in situ movement of the heart valve was traced from a series of fluoroscopic images [11]. The obtained travel path (Figure 4) was then used to program a motorized stage to simulate the relative movement between the transducer and the outlet strut (the superposition of the displacing of a point from OS along horizontal and vertical direction). In the in vitro test setup, the heart valve was held at a fixed location by a silicon holder while the transducer was mounted on and moved by the motorized stage.

Figure 4. Trajectory of a point on the outlet strut during a cardiac cycle

The experimental setup is shown in Figure 5.

a

b

c

Figure 5. Experimental setup: a)basic scheme; b) transducer - valve assembly; c) photo of equipments

The proposed detection system uses an absolute send-receiver electromagnetic transducer (remarkable sensitivity and self-nulling property) [8], [9]. The emission coil is 120 mm in diameter and has 300 turns, was excited with a 60 kHz, 40Vrms sinusoidal

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245

signal (the impedance of emission coil is 2.8k: at 40kHz). The reception coil is wounded in the plane orthogonal to the emission coil and also has 300 turns. The motorized stages simulating the relative in vivo valve-transducer movement had a repetitive frequency of 1.2 Hz, corresponding to a 72 cycles/minute cardiac rhythm. The data acquisition frequency was 100 samples/second. Figures 6a and 6b show the phase dependency of the received signal for testing the replica valves with no defect, and those with one of 0.2, 0.4 or 0.6 mm deep EDM notch, respectively.

a

b Figure 6 Experimental measurements for replica valves: a) real component; b) imaginary component

5. Experimental Results In the proposed detection system, the power spectrum is obtained for the imaginary component of the reception coil signal. The amplitude of the first harmonic of this power spectrum is then used as the indicator of BSCC valve quality state. The power spectrum of a signal U is defined as

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S

1 fft  Im U conj fft  Im U N





where N is the number of samples and fft is the Fast Fourier Transform function. The power spectrum contains N harmonics. 5.1. Determination of Probability of Detection (POD) One hundred measurements were taken on BSCC valve replicas with intact outlet struts as well as those with EDM slots of 0.2, 0.4 and 0.6 mm deep. The recorded signals were processed using the procedure described above. Examples of the processing scheme outputs are shown in Figure 7 for 12 of the measurements. From the measured data, the lower-bound for the probability of detection with a 95% confidence level [12] was determined for each slot depth. The results are summarized in Table 1. Although all the 0.6 mm cases were correctly classified, the POD was less than 100% due to the imposed 95% confidence level and the fact that the number of measurement was 100. Table 1. The lower-bound probability of detection for a 95% confidence level for various slot depths Slot depth [mm]

Probability of Detection (POD)[%]

Probability of Missing Flaw (PMF)[%]

0.2

41.3

58.7

0.4

84.6

15.4

0.6

97

3

Figure 7. Experimental results on BSCC replica valves

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6. In Vitro Testing with BSCC Heart Valves Double-blind in vitro tests using 32 BSCC heart valves were also performed. The test samples consisted of 12 valves with intact outlet struts, 10 valves with manufactured SLSs and 10 explanted valves with SLSs. The data collected are processed and the results are presented in Figure 8. In this figure, only the amplitude of the first harmonic of a signal’s power spectrum is considered. The decision threshold was obtained using the 3V law [10]: the mean plus three times the standard deviation of all the good valve data points:

Threshold

P g.v.  3V g.v.

Any valve with a data point located above this threshold was considered an SLS valve. Using this technique, the proposed detection method achieved a 100% correct classification with all the BSCC heart valves samples.

Figure 8 Results of the double-blinded in vitro test

7. Conclusion A novel electromagnetic method has been developed for noninvasive detection of cracks in the outlet strut of BSCC prosthetic heart valves. With the valve replicas, this detection method has demonstrated a POD of 86.4% for a 0.4 mm deep crack, and a POD of 97% for a 0.6 mm deep slot in the strut. In vitro tests effectuated through described method have allowed the correct classification of the valves (good valves and valves with defects)

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References [1]

P. Hedger, Important updated information for physicians about patients with Björk-Shiley convexoconcave heart valves – Dear Doctor letters, Irvine, CA: Shiley Inc. March/April, 1993. [2] ISO 5840:1996 (E) Cardio-vascular implants – cardiac valve prostheses [3] EN 12006-1:1999 Non-active surgical implants – Particular requirements for cardiac and vascular implants: Part I. Heart valve substitutes [4] W.W. O’Neil, J.G. Chandler, G.T. O’Connor, Radiographic detection of strut separation in BSCC valves, New Engl. J. Med, 333, (1995), pp. 414-419 [5] J.W. Candy, H.E. Jones, Classification of Prosthetic Heart Valve Sounds: A Parametric Approach, J. Acoustic Soc. of America, 97, 6, (1995), pp. 3675-3687 [6] S. Udpa, New electromagnetic methods for the evaluation of prosthetic heart valve, J. Appl. Phys., 90, (2002), pp. 1-5 [7] S.C. Chan, R. Clifford, S. Majunar, N. Nair, S. Ramakrishnan, Y. Li, P. Ramuhalli, L. Udpa, S. Udpa, Novel Methods for detecting fractures in prosthetic heart valves, INSIGHT, 47, (2005), pp.15-19 [8] E. Radu, R. Grimberg, A. Savin, O. Mihalache, Modeling the operation of the eddy current transducer with orthogonal coils in the presence of material discontinuities, Sensors and Actuators, A, 59, (1997), pp. 201-204 [9] R. Grimberg, A. Savin, E. Radu, O. Mihalache, Nondestructive Evaluation of the Severity of Discontinuities in Flat Conductive Materials Using the Eddy Current Transducer with Orthogonal Coils, IEEE Trans on Mag. 36, 1, (2000), pp. 299-307 [10] J. Lemaitre, J.L. Cheboche, Mechanics of Solids Materials, Cambridge University Press, 1990 [11] S C Chan, R Clifford, S Majumdar, N Nair, S Ramakrishnan, Y Li, P Ramuhalli, L Udpa, S S Udpa, Novel Methods for detecting fractures in prosthetic heart valves, INSIGHT, 47, 15-19 [12] R.C. McMaster, R.C.P. McIntire, M.L.Master, Nondestructive testing handbook (2nd Ed), 4 Electromagnetic testing, American Society for Nondestructive Testing, London, 1986.

This paper is supported by Romanian Ministry of Education and Research Research of Excellence Program, Contract no. 6110/2005 SINERMAT and CNCSIS Grant no.586/2006.

Electromagnetic Nondestructive Evaluation (XI) A. Tamburrino et al. (Eds.) IOS Press, 2008 © 2008 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-58603-896-0-249

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Remote field eddy current control using rotating magnetic field transducer. Application to pressure tubes examination Adriana SAVINa, Lalita UDPAb, Rozina STEIGMANNa, Alina BRUMAc, Raimond GRIMBERGa1, Satish S.UDPAb a

National Institute of R&D for Technical Physics, Iasi, Romania b Michigan State University, East Lansing, USA c Faculty of Physics, Al.I Cuza University, Iasi, Romania

Abstract. In this paper we propose to investigate the possibility of obtaining the remote field effect for the transducer with rotating magnetic field and to use this for detecting the artificially discontinuities practiced on un-irradiated pressure tubes samples. Keywords. Remote field effect, eddy current transducer with rotating magnetic field, propagator matrix

Introduction The remote field eddy current (RFEC) technique was originally developed for the nondestructive examination of ferromagnetic tubes [1]. Relatively recent RFEC has started to be used for examination of magnetic pipes and tubes [2] and was applied at the evaluation of metallic parts, too [3]. The RFEC technique shows few distinctive characteristics compared to those of conventional eddy current examination: they are equally sensitive to ID and OD defects; has insensitivity to probe wobble or variable lift-off, defect indications in the signal always appears double and with the same strength. In this paper we propose to investigate the possibility of obtaining remote field effect for the transducer with rotating magnetic field [3] and to use it for detecting the artificial discontinuities practiced on un-irradiated pressure tube samples.

1. Theoretical Aspects The state equations for a cylindrically layered medium can be derived from Maxwell’s equation, which are

1 Corresponding Author: Raimond Grimberg, National Institute of R&D for Technical Physics, 47 D.Mangeron Blvd., Iasi, 700050, ROMANIA, [email protected]

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’u E

jZP H

’u H

 jZH E

(1)

using a cylindrical coordinate system  U , I , z , the system (1) can be written as ª Ez º ª Ez º « » «E » d « EI » I U U « » «Hz » d U «Hz » « » « » ¬« HI ¼» ¬« H I ¼»

(2)

where U  U is a 4x4 matrix having the form

U U

ª « 0 « « « 0 « « jk n « z « ZPU « « 0 «¬



0 

1

jZH  

jk z 2

ZP

jk z n

ZPU

 jZP 

ZHU

jZP 

U

jk z 2 º ZH »» » jk z n » ZHU » » 0 » » » 1  » U »¼

jk z n jn 2

ZHU 2

0 0

(3)

The eq. (2) is a equation with own vectors, having 4 linear independently solutions. The form of own vectors can be determined if the expressions of the field created in free space by the emission part of the transducer with rotating magnetic field are inserted in eq.(2) f ª º jZP0 f k n j nI  k z EU  U , I , z dk z e  z « jA1 z H n(1) '  k U U  jA2 2 H n(1)  k U U » 2 ¦ ³ k k 4S n f f U U U ¬« ¼» (4) f f ª kz n º jZP0 1 j  nI  k z z (1) (1)  U ' U EI  U , I , z dk e A H k A H k   « » ¦ U U 1 n 2 n 2 ³ z 4S 2 n f f kU «¬ k U U »¼ f f jZP0 Ez  U , I , z ¦ ³ dkz e j nI kz z A1H n(1)  kU U 4S 2 n f f where the prime sign represents the derivation of Bessel function

A1 f

I0 J n  kU R R 1  e jnS  e

j

2S 3

Lz § L · sin c ¨ k z z ¸ f ; 2 © 2¹ 5S  jn §  jn 23S 3  e e ¨ ©

R

A2

· j 43S ¸e ¹

§ L · 2 I 0 sin ¨ k z z ¸ nf ³ J n  k U r0 dr0 © 2¹ 0

4S  jn §  jn S3 · 3  e e ¨ ¸ © ¹

I0 – the amplitude of the three phase current; Lz – the dimension of one of emission coli after z axis; 2R – dimension after U direction; k U

Z 2 P0H 0  k z 2 , with Im(kU)>0.

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The components of magnetic field created by the transducer in vacuum are immediately obtained taking into account that 1 (5) ’ u E (r ) H (r ) jZP0 Inserting (4) and (5) in (3) we obtain the eigenvectors

v1

J n (kU U ) º ª « nk » «  2 z J n (k U U ) » « kU U » « », 0 « » « jZH » J n '(k U U ) » « k ¬« U ¼»

v3

ª H n (1) (k U U ) º « » «  nk z H (1) (k U ) » U n 2 « kU U » « » , v4 0 « » « jZH » (1) « H n '(k U U ) » «¬ k U »¼

v

v2

0 º ª » « jZP « J n '(k U U ) » » « kU » « J k ( U ) n U » « » « nk z «  2 J n (kU U ) » k U »¼ ¬« U

(6)

0 ª º « jZP » (1) « H n '(k U U ) » « kU » « » (1) U H ( k ) n U « » « nk z » (1) «  2 H n (k U U ) » ¬« k U U ¼»

> v1 , v2 , v3 , v4 @

(7)

In the case in which the source is into a layered cylindrical medium, the fields in all media can be calculated using the method of “propagator matrix” [4].

ª Ez ( U ) º « E (U ) » « I » « H z (U )» « » ¬« H I ( U ) ¼»

ª Ez ( U ) º « E (U ) » 1 I » v( U )v ( U ') « « H z (U )» « » ¬« H I ( U ) ¼»

ª Ez ( U ) º « E (U ) » I » P( U , U ') « « H z (U )» « » ¬« HI ( U ) ¼»

(8)

1

P( U , U ') v( U )v ( U ') Now, equipped with the propagator, we can solve the transmission and reflection fields through a cylindrical layered medium. The field in air, created by the emission part of the transducer with rotating magnetic field was previously calculated (Eqs. (18) and (19) from [5]), the expressions of dyadic Green’s function for layered cylindrical medium (Eqs. (22), (28) and (30) from [5]) have been developed, also. To solve the forward problem, a discretization with the moment’s method in pointmatching variant has been used. The numerical code was developed in Matlab 7.0. The distance between the center of transducer’s emission part and those of the ( reception part is D, so that for the calculus of the dyadic Green’s function G21 , the supplementary factor e

jk z D

must be inserted.

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2. Numerical Simulations

The transducer with rotating magnetic field which works in RFEC conditions is made from 3 orthogonal coils making 2S/3 angle between them and supplied with a triphased current system. The pressure tubes, on which the experimental measurements were made, are confectioned from Zr 2.5%Nb alloy having inner diameter 103mm, outer diameter 111.4mm and electrical conductivity 1.89x106S/m. In figures 1 a and b we present the responses of transducer, obtained by solving forward problem for the case D=0 for a slot with 6x0.2x0.2mm placed on internal surface, and respective on external surface of pressure tube.

a

b Figure 1. The response of the transducer for D=0; 6x0.2x0.2mm slot a) slot is made on internal surface; b) slot is made on external surface

A. Savin et al. / Remote Field Eddy Current Control Using Rotating Magnetic Field Transducer

253

The condition in which the transducer functions in RFEC mode is obtained modifying D. This is obtained, in the case of pressure tubes with dimensions and electromagnetic properties mentioned above, if the distance D becomes equal to 1.8 x outer diameter of pressure tube. This situation is presented in figure2.

a

b Figure 2. The response of the transducer for D=1.8x outer diameter; slot dimensions 6x0.2x0.2mm a) the slot is made on internal surface; b) the slot is made on external surface

The analysis of the data presented in Figure 2 shows the presence of two pronounced peaks, the distance between them being a little bigger than D. The peaks have equal amplitude, being indifferent by the position of the discontinuities (on inner surface, respective on outer surface). It must be mentioned the existence of a signal placed at the middle of the distance between two peaks and having amplitude relatively small. This supplementary peak is due, probable, to the shape of the source [5].

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3. Experimental Results

In the procedures for eddy current examination of pressure tubes from PHWR reactors, CANDU type, the minimum detectable defect must be circumferential or axial slots with 6x0.2x0.2mm practiced on inner and outer surface of the tubes. With the transducer with rotating magnetic field functioning in RFEC mode and the equipment described in [3], experimental measurements were effectuated. The optimal conditions are: frequency 47 kHz, D=200mm. In Figure 3 a) we present the response of the equipment for one axial slot described in figure’s caption and in figure 3 b is presented the picture of the same slot.

a)

b) Figure 3. The signals, remote field type, delivered by a 6x0.157x0.189mm axial slot practiced on external surface of pressure tube sample: a) signals; b) Photo of discontinuity.

In Figure 4 we present the same features for a circumferential slot. The obtained experimental results confirm the righteousness of the theoretical model developed above, for the case of circumferential slot, the central peak, unusual

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255

in the case of axi-symmetric excitation, becomes well marked. This is due probable to the source.

a

b Figure 4. The signals, remote field type, delivered by a 6x0.19x0.19mm circumferential slot practiced on internal surface of pressure tube sample. a) signals; b) photo of discontinuity.

4. Conclusions

A method for calculation of the field generated by the eddy current transducer with rotating magnetic field using “propagator matrix” method was developed. The effectuated calculi allow a simpler solving of the forward problem, the optimal distance emission–reception which assures the functioning in RFEC mode being determined. The experimental measurements are in good concordance with the numerical calculus, which confirm the righteous of model.

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5. References [1] [2] [3]

[4] [5]

T.R. Schmidt, The remote field eddy current inspection technique, Materials Evaluations, 8, (1984), 225-230 D.L. Atherton, Remote Field Eddy Current Inspection, IEEE Trans on Magnetics, 31, 6, (1995), 41424147 R. Grimberg, L. Udpa, A. Savin, R. Steigmann, S.S. Udpa, Inner-Eddy-Current Transducer with Rotating Magnetic Field: Experimental Results, Application to Nondestructive Examination of Pressure Tubes in PHWR Nuclear Power Plants, Research in Nondestructive Evaluation, Springer-Verlag, New York, LLC, vol 16, issue 2, (2005), 65-78 W.C. Chew, Waves and Fields in Inhomogeneous Media, Von Nostrand Reinhold, NY, Chapter 3 and 7, 1995 R. Grimberg, L. Udpa, A. Savin, R. Steigmann , S.S. Udpa, Inner-Eddy-Current Transducer with Rotating Magnetic Field: Theoretical Model, Forward Problem, Research in Nondestructive Evaluation, Springer-Verlag, New York, LLC, vol 16, issue 2, (2005), 79-100

This paper is supported by Romanian Ministry of Education and Research - Research of Excellence Program, Contract no. 6110/2005 SINERMAT, Contract No.49/2006 ROLIGHT and Nucleus Program, Contract No. PN 06 - 38 01 03.

Electromagnetic Nondestructive Evaluation (XI) A. Tamburrino et al. (Eds.) IOS Press, 2008 © 2008 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-58603-896-0-257

257

Lifetime Prediction of Pressure Tubes in PHWR Nuclear Power Plants using Eddy Current Data Raimond GRIMBERG, Adriana SAVIN, Rozina STEIGMANN, Aurel ANDREESCU, Nicoleta IFTIMIE, Marius Mihai CAZACU National Institute of R&D for Technical Physics, Iasi, Romania

Abstract: In this paper is presented a model for lifetime prediction using Markov hidden chains method, starting from the results of eddy current nondestructive evaluation using rotating magnetic field transducer. The model is trained with previous experience in pressure tubes examination and allows the determination of probability that the tubes shall be found in different imposed states.

Keywords: life time prediction, pressure tubes, degradation state.

Introduction Pressure tubes (PT) assure the cooling of the fuel channels in nuclear power plant CANDU type. During the service of nuclear power plants, it appears hydrogen due to the zirconium corrosion, which is absorbed by the material of manufactured tubes, Zr2.5%Nb alloy. The absorbed hydrogen forms the zirconium hydrides which are decreasing the materials resistance. Under the influence of hydride, the incipient cracks in pressure tubes can develop in unstable and uncontrolled forms, being named Delayed Hydrogen Cracking (DHC) phenomena. The statistically analysis is made for the existent data at the IAEA Vienna and indicates a slowly evolution to a dangerous state systems. To describe the degradation processes we use Markov processes [1]. A Markov process is a stochastic one with the properties that the given value of X(t), at time W, where W > t, are independent of the values of X(u), u < t. For N states, the probabilities of transition between all possible states pairs are given by

P

ªP « 11 «P « 21 « . «P «¬ N 1

P

12

P

22

. P

N2

P º 1N » ... P » 2N » . . » ... P »» NN ¼ ...

(1)

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R. Grimberg et al. / Lifetime Prediction of Pressure Tubes in PHWR Nuclear Power Plants

1. Markov hidden chains model Evaluating the lifetime for pressure tubes represents a probabilistic model on basis of continue Markov chains. The system consists in pressure tubes of CNE CANDU type. A Markov chain is governed by the transition matrix P, where Pjk(t) elements is the probability of transition of the system from the current state j to state k: Pjk  t



P X t

k X  0

j ; j, k  S , t ! 0



(2)

There are defined the following possible states in which we can find the PT system in function of the degree of deterioration; we define: OK- state in which PT is not degraded; D1 - state in which PT are in slowly degradation state; depth limit of defect is 0.15mm; D2 : - state in which PT has degradation in relatively major degree; the depth limit of defect is 0.5mm; F1- PT system can be in critical degradation state; the depth limit of defect is 1.6mm [2], case in which the tube is replaced. The system states D are included in two categories: states with defects detected at control effectuated D1d and D2d and states with defects undetected at control effectuated D1u and D2u. The overall failure model is presented in figure 1

Figure 1. Overall failure/maintenance model,

The transition matrix P for our model is

P

ªOK D 1u « « 1 0 « « 0 1  q1 « 0 « 0 «q 0 « 2 «q 0 « 3 « 1 0 « 0 ¬« 1

D

D

D

F

0 q

0 0

0 0

0 0

1 0

0 1 q

0 0

0 0

0

0

1 q

0

0

0

0

0

0

0

0

0

1d

1

2u

2d

2

1

3

* OK º » 0 » » 0 » » 0 » 0 » » 0 » » 0 » » 0 ¼»

(3)

Further, we introduce the probabilities that degraded states are detected by the inspection:

R. Grimberg et al. / Lifetime Prediction of Pressure Tubes in PHWR Nuclear Power Plants

259

x x

q1 - probability that state D1 of the system is detected; q2 - probability that a degraded failure is detected by the inspection; it is unknown in advance if the state D1 was reached; x q3 -probability that a degraded failure D2 is detected by the inspection; it is known in advance that the state D1 was reached. The dotted lines of Figure 1 indicate transitions at the end of the test interval.

2. Experimental results The model for prediction uses so previous experience, it means the data obtained by a inspection of high number of pressure tubes (10.000), specific data for the examination method, equipment, analysis team, characterized by probability of detection and evaluation, as well as the results of current inspection. The method was developed for the case of eddy current examination of pressure tubes using a transducer with rotating magnetic field [3] (Figure 2a) and the adequate measurement system [4], Figure 2b

a

b

Figure 2 Experimental set up: a) the transducer with rotating magnetic field; b) the control equipment

2.1. Probability of detection for discontinuities with depth of cca 0.15mm. In this scope it was used the sample ARG 1 from Argentina in frame of a Contract between NIRDTP Iasi and IAEA Vienna [5]. It was used the unirradiated PT samples with artificial flaws of different types, positions and geometrical dimensions made by EDM. The inspection defects are noted with #1, #2, #3 and #4 with dimensions and orientations given bellow. Table 1: Flaw details in ARG 1 sample Flaw #

Location and Orientation

Length (mm)

Width (mm)

Depth (mm)

Characteristics

1

ID, axial

6.1

0.3

0.136

calibration slot

2

OD, axial

6.15

0.4

0.14

calibration slot

3

ID, circumferential

6.2

0.3

0.152

calibration slot

4

OD, circumferential

6.6

0.4

0.16

calibration slot

The distribution for the estimated defect severity with depth ~0.15 mm is presented in figure 3a using a method to solve inverse problem for EC [1]. The location of defect on internal, respective external surface of the tube is established from the phase

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R. Grimberg et al. / Lifetime Prediction of Pressure Tubes in PHWR Nuclear Power Plants

information, this is reducing the number of discretization cells and is increasing the robustness of inversion algorithm. Considering the probability distribution for defects of log normal type (continue curve by figure 3) and integrating in range 0.1 – 0.3, it was a detected probability of 46% with reliability coefficient 95%. 2.2. Probability of detection for discontinuities with depth of ~ 0.5mm. The inspection defects are noted with #1 and #4 with dimensions and orientations given of KOR 1 sample. Table 2 Flaw details in KOR 1 sample Flaw #

Location and Orientation

Length (mm)

Width (mm)

Depth (mm)

Characteristics

1

OD, axial

6.0

0.3

0.47

Short notch deeper than calibration slot

4

OD, circumferential

6.0

0.3

0.41

Short notch deeper than calibration slot

The histogram and log normal distribution for estimations concerning the defect with 0.5 mm depth is presented in figure 3b.

a

b

Figure 3 The estimated distribution for flaw: a) with depth 0.15mm; b) with depth 0.47mm

Using the method described above, the probability of detection and estimation for the discontinuity with depth ~0.5mm is 70% with a reliability coefficient of 95%. The probability of detection for discontinuities with depth of ~1.63mm was 98% with reliability coefficient 95%. Using the model of life/maintenance time prediction described above, the probabilities that a PT examined by eddy current with the transducer with rotating magnetic field, shall be in one of states D1u (there are undetected discontinuities with 0.15mm depth), respective D2u (there are undetected discontinuities with depth equal or smaller than 0.5mm), has been determined. The results obtained through simulation, based on the existent statistic about the states of the PT from CANDU nuclear power plants and on the probabilities of detection, experimental determined on EDM slots practiced on unirradiated pressure tube samples are presented in the next figures. The figures 4 and 5 show the probability to detect a pressure tube to be found in the degradation state (D1u or D2u) in function of

R. Grimberg et al. / Lifetime Prediction of Pressure Tubes in PHWR Nuclear Power Plants

261

time range between the inspections. The probabilities are referred to m*day of PT with the reactor at full day exploitation.

Figure 4 The probability for state D 1u

Figure 5 The probability for state D 2u

We can see that in time range between 300-400 days is minimum time up at the inspection following. Hence, it results that in this range the chance as a flaw is undetected is minim. The decreasing of the probabilities that the PT shall be in one of states D1u and D2u is not due, evidently, to the decreasing of the number of flaws, but to the fact that, these flaws are evolution in time; these are rather in the states D1d and D2d. The input parameters for the estimation of model parameters are listed in table 3. The statistical data was taken on 10,000 pressure tubes in range time 10-12 years by IAEA Vienna. Table 3: Inputs to parameter estimation Parameter definition

Parameter

Value

Number sets

N

10 000

Length of pressure tubes

L

62 000

Number of tests/inspections 1989-2002

nTF

11.3

Number of tests/inspections 1991-2002

nTD

9

Number of days, 1989-2002

N1

4661

Number of days, 1991-2002

N2

3909

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R. Grimberg et al. / Lifetime Prediction of Pressure Tubes in PHWR Nuclear Power Plants

Length of test/inspection interval

T

360

Number of observations in state D1, (i.e. transitions from D1u to D1d)

ND1

187

Number of observations in D2 when it was not known that state was degraded, (i.e. transitions from D2u)

ND2a

238

Number of observations in D2 when it was known that state was degraded, (i.e. transitions from D1d)

ND2b

20

Number of observations in F1

NF1

83

Probability of detecting D1 failure for coefficient of 95%

q1

0.48

Probability of detecting D2 failure at test (state D1n not detected previously) for coefficient of 95%

q2

0.70

Probability of detecting D2 failure at test (state D1 already detected)

q3

0.98

Rate of detecting D2 in additional inspections; (assuming on the average two additional inspections within each interval T)

U

(2/T)* q3

From here results a conclusion with high practical importance namely that for the aim of obtaining a maximum POD for the discontinuities of PT, these must be examined at an interval of 300-350 days, when the probability of existence of the states D1u and D2u are minim. Upper 600 days in the range time between two inspections the undetected probability of the flaws can be dangerous for reactor running.

3. Conclusions It was elaborate a Markov model for the life time prediction for the pressure tubes. The initial values with which we have to work are given in table 3. We developed a soft using MATLAB 7.0 programmer which uses a series of apriority knowledge which appear as accumulated experience in the exploitation of nuclear reactors PHWR type. Another data are obtained by nondestructive testing for pressure tubes at annual outage. This model has more simplifications for interpretation of the results and to use for maintenance optimization. References [1] [2] [3] [4]

[5]

Raimond Grimberg et al. Emerging Technologies in Non-destructive Testing, ETNDN Fourth International Conference, April 2 – 4, 2007, Stuttgart, Germany; Periodic Inspection of CANDU Nuclear Power Plant Components, CAN/CSA – N285.4, (1994) R. Grimberg, Lalita Udpa, Adriana Savin, Rozina Steigmann, S. Udpa, Inner Eddy Current Transducer With Rotating Magnetic Field. Theoretical Model – Forward Problem, Research In Nondestructive Evaluation, Springer-Verlag New York, Llc, Vol 16, Issue 2, (2005), 79-100 R. Grimberg, Lalita Udpa, Adriana Savin, Rozina Steigmann, Satish S. Udpa, Inner Eddy Current Transducer With Rotating Magnetic Field; Experimental Results: Application To Nondestructive Examination Of Pressure Tubes In Phwr Nuclear Power Plants, Research In Nondestructive Evaluation, Springer-Verlag New York, Llc, Vol 16, Issue 2, (2005), 65-78, IAEA TECDOC 2005 , Report for CRP Meeting Chalk River Canada - October 2005

This paper is supported by Romanian Ministry of Education and Research Research of Excellence Program, Contract no. 6110/2005 SINERMAT and Nucleus Program, Contract No. PN 06 - 38 01 03.

Electromagnetic Nondestructive Evaluation (XI) A. Tamburrino et al. (Eds.) IOS Press, 2008 © 2008 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-58603-896-0-263

263

Electromagnetic Non-Destructive Evaluation of Reinforced Concrete Rebars Maxim MOROZOV a, Guglielmo RUBINACCI b, Antonello TAMBURRINO c and Salvatore VENTRE c, 1 a CREATE Consortium, Naples, Italy b Ass. EURATOM/ENEA/CREATE, DIEL, Università degli Studi di Napoli Federico II, Italy c Ass. EURATOM/ENEA/CREATE,DAEIMI, Università degli Studi di Cassino, Italy

Abstract. This paper concerns quantitative imaging, consisting in finding location, direction and size, of concrete rebars by means of eddy current measurements and an innovative inversion method. Owing to an accurate numerical modelling of the probe-rebar interaction, an analysis of issues to be considered for the quantitative imaging of rebars is conducted, which leads to significant simplifications in the numerical model and enables developing an accurate and computationally efficient imaging method. Results of experimental testing demonstrate favourable validity of the proposed numerical model. Keywords. Nondestructive evaluation, eddy currents, numerical simulation, reinforced concrete rebars

Introduction This paper presents critical considerations for application of an innovative inversion method to the problem of quantitative eddy current (EC) imaging of reinforced concrete rebars and optimisation of an apposite EC probe. The EC imaging is aimed to determine location, direction and size of rebars. From a broader perspective, electromagnetic imaging of concrete rebars is attracting a growing interest because of the need of monitoring the “health” of existing structures that may become unsafe or collapse when, due to corrosion or damage of reinforcement bars (rebars), they cannot longer support the tensile load how it was originally designed. Several sensing methods have been developed, among them we mention techniques based on impedance probes [1]-[4], static magnetic field measurements, such as residual magnetic flux density and magnetic flux leakage [5], microwave tomography [6, 7] and polarization resistance based techniques [8]. The respective EC commercial instrumentation (the pachometer) makes use of calibration technique performed for a set of various rebar dimensions, which is ineffective for complex configurations, such as crossed bars etc. Our method benefits from an accurate numerical modelling of the EC probe interaction with rebars. As a result the possibility of relevant simplifications in the numerical model is outlined, 1 Corresponding Author: Salvatore Ventre, Università degli Studi di Cassino, Via G. Di Biasio 43, 03043 Cassino (FR), Italy; E-mail: [email protected]

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allowing the development of an accurate and computationally efficient method. The respective numerical model is based on a integral formulation requiring the discretization of only the conducting and/or magnetic regions such as the iron rebars and eventual ferrite core of an EC probe. An efficient numerical model is essential to develop a quantitative imaging system in view of an EC probe design as well as of imaging procedures based on experimental data. The key feature of an inversion method suitable for EC imaging is the maximally possible independence on the geometrical configuration. It must be capable to work properly in non a priori known configurations consisting of, for instance, either a single or more rebars eventually interacting, non parallel and located at different depth. The choice is made of an algorithm based on a monotonicity property of the unknown-data operator recently developed by the authors. The monotonicity property, that is characteristic of systems governed by elliptic PDEs, has been exploited to develop an inversion algorithm in eddy current testing of conductors and it gives rise to a fast imaging algorithm having a computational cost associated to the solution of a number of elliptic forward problems proportional to the number of voxels used to discretize the unknowns.

1. Numerical method 1.1. Forward analysis An appropriate and effective numerical model is essential to develop a quantitative imaging system. It is essential to design the probe and during the processing (imaging procedure) of the experimental data. The modeling of the interaction between the rebars and the probe is a complex issue. First, the ferromagnetic material has a nonlinear characteristic, second the skin depth in the iron is significantly smaller already at relatively low frequencies. The first issue, potentially requiring a nonlinear numerical model, can be disregarded by noting that in the typical inspection cases the magnetic flux density produced by the inducing probe is low enough so that nonlinear effects can be neglected. The second issue asks for a refined mesh in the outermost layer of the rebars, where the fields decay rapidly to zero along distances of the order of the skin-depth. In an integral formulation, such as the one presented in the following, this can be conveniently taken into account by discretizing only this outermost layer (having a thickness of the order of the skin-depth) of the rebars, thus saving elements, unknowns and in ultimate analysis, computational time and resources. In the following we neglect the electrical conductivity of the concrete. This is possible because the typical values for the electrical conductivity are fractions of S/m, thus giving a skindepth much larger (the skin-depth at 100kHz and 1S/m is 159cm) than the typical sizes of interest (up to 40cm) of the problem. The numerical model considered in this work, and here briefly described, is based on a integral formulation [9-11] requiring the discretization of only the conducting and/or magnetic regions such as the rebars (made of iron) and the magnetic core of the probe array. As mentioned, for frequencies such that the skin-depth is much smaller that the rebars diameter, it is sufficient to discretize only an outermost layer of the rebars for a thickness of the order of the skin depth. In this formulation, the eddy currents are represented in the finite dimensional space of curl of edge element shape functions Nk‘s: J=’uT where the electric vector potential T is expanded as linear combination of Nk‘s. A two-component gauge condition [9] guarantees the uniqueness

M. Morozov et al. / Electromagnetic Non-Destructive Evaluation of Reinforced Concrete Rebars

265

of the vector potential. The magnetization vector is numerically approximated as a piecewise constant vector function (hereafter Pk stays for the k-th shape function used to represent the magnetization M). The field equations in the magneto-quasi-stationary limit (time harmonic operations) are automatically solved once that the electric field is expressed as E  jZA  ’I where the magnetic vector potential is calculated by means of the Biot-Savart law. Finally, the numerical model is obtained by applying the Galerkin method to the constitutive equations J ıE and M ( P r  1) P 0 P r B :

³P

k

˜ [M  kB]dV

0, k

(1)

Vm

³’u N

˜ (KJ  jZA)dV

k

0, k

(2)

Vc

By doing this, we obtain the following algebraic linear system:

R  jZL I  jZFM k

1



T

DE MF I

U

(3)

W

(4)

where k P r  1 / P 0 P r , I is the column vector of the complex coefficients of the expansion of the current density J in terms of the shape functions ’ u N k ’s, M is the column vector of the complex coefficients of the expansion of the magnetization in terms of the shape functions Pk‘s, and: Rij

Lij

³

Vc

’ u N i ˜ V 1’ u N j dV

P0

³³

4S

Vc Vc

P0 4S

1

r  r ' ’ u N i r ˜ ’ u N j r ' dV dV ' 1

³ ³

r  r ' Pn ,i r Pn , j r ' dSdS '

Eij

Dij 

Fij

P0 4S

Uj

 jZ ³ ’ u N j ˜ A 0 dV

Dij

³

Wj

³P

³³

Vc Vm

wVm ,i wVm , j

Vm

Pi ˜ P j dV

j

3

r  r ' ’ u N i r ˜ P j r ' u r  r ' dV dV '

Vc

Vm

(5)

˜ B 0 dV ,

(6)

(7)

(8) (9) (10) (11)

266

M. Morozov et al. / Electromagnetic Non-Destructive Evaluation of Reinforced Concrete Rebars

being A0 and B0 the vector potential and the magnetic flux density produced by the sources in the free-space, Vc and Vm the conductive and magnetic domains, respectively, and Vm,j the volume of the j-th element of the finite element mesh discretizing the magnetic domain Vm. After some manipulations, it can be possible to prove (see [12]) that the impedance variation due to the presence of the rebar can be expressed as follows:

GZ

º jZ ª « ³ J ˜ A 0 d V  ³ M ˜ B 0 dV » 2 i ¬«Vc Vm ¼»

(12)

where i is the complex amplitude representing the current circulating in the inducing coil. Similarly, when a coil array is used as a probe it can be proved that

GZ kj

jZ 2 ik i j

ª º « ³ J j ˜ A 0k  J k ˜ A 0j dV  ³ M j ˜ B 0k  M k ˜ B 0j dV » «¬Vc »¼ Vm









(13)

where iD (D=j, k) is the complex amplitude of the current circulating in the k-th inducing coil, JD, M D , A D0 and B D0 are the eddy current, the magnetization, the freespace vector potential and magnetic flux density when only the current iD circulating.

is

1.2. Inverse problem A key feature of an inversion method suitable for this class of problems is the capability to be, as much as possible, independent on the geometrical configuration. It must be capable to work properly in non a priori known configurations consisting of, for instance, either a single or more rebars eventually interacting, non parallel and located at different depth. The choice is fall on an algorithm based on a monotonicity property (see below) of the unknown-data operator recently developed by the authors. The monotonicity property, that is characteristic of systems governed by elliptic PDEs, has been first exploited to develop an inversion algorithm in the framework of Electrical Resistance Tomography [13], and then extended to Eddy Current Testing of conductors [14] and it gives rise to a fast imaging algorithm having a computational cost associated to the solution of a number of (elliptic) forward problems proportional to the number of voxels used to discretize the unknowns. In Electrical Resistance Tomography the data processed by the inversion algorithm is the N×N resistance matrix made by the self and mutual resistances between pairs of N electrodes (plus one grounded electrode) located on the boundary of the conductive specimen under test. In Eddy Current Testing of conductors the measured quantity is, similarly, the impedance matrix (self and mutual impedances between pairs of coil used to probe the conductive specimen) measured at several frequencies. Here, in the framework of rebars inspection, the measured quantity is still the impedance matrix but measured at large enough frequencies. We notice that by increasing the frequency, the magnetic flux density inside the ferromagnetic rebar vanishes. Therefore, as long as the

267

M. Morozov et al. / Electromagnetic Non-Destructive Evaluation of Reinforced Concrete Rebars

displacement current is negligible, the magnetic flux density is solution of a proper magneto-static (elliptic) problem and, therefore, ­° ZV Im® m °¯ Z

½° Z large ¾ o LVm °¿

(14)

is the measured impedance matrix, and LV

where ZV

is the inductance matrix

m

m

corresponding to the magnetostatic problem with the constraint b=0 in the ferromagnetic region Vm. Thanks to the fact that LV arises from a magnetostatic m

problem, it can be shown that DE Ž DD Ÿ G L D  G L D is positive semi - definite D

(15)

E

where G L D ˆ L )  L D , L ) is the free-space inductance matrix and L D ( L D ) is k

D

k

E

the inductance matrix related to the magnetostatic problem corresponding to the constraints b=0 in DD (DE). By reversing (15) and setting DE=Dk and DD=Vm, we have that

G L V  G L D is not positive semi - definite Ÿ Dk Ž Vm m

(16)

k

where Dk has the role of test volume and G L D is numerically computed ( G LV is m

k

measured experimentally). By properly varying the position and size of the test domain Dk, and by applying (16) to each different test domain, we can retrieve the size and position of each single rebar. Moreover, (16) holds regardless the fact that the rebars may interact or not and regardless the mutual position of the rebars. In this way we overcome the detection and sizing by means of calibration charts and assuming a priori known geometrical configurations. The first imaging algorithm based on these concepts been presented in [1]. Finally, we highlight again that G LV and G L D are N×N matrices, where N is the m

k

number of coils used to probe the rebars. Increasing the number of measurement coils (up to a certain extent), makes the test more effective due to the increase of the information content of the measurement.

2. EC probe optimisation The iron bars under test had diameter of nearly 19 mm. The electrical conductivity V of the steel bars was found to be 4.61 MS/m, and their relative magnetic permeability Pr was determined to be 85 [2]. At the same time it was confirmed that (i) nonlinear effects are negligible and that (ii) Pr is constant at the frequencies of interest.

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In order to produce the inductance matrix necessary for solution of the inverse problem the eddy-current testing of steel bars used in reinforced concrete has been conducted with an array of tree coaxial induction coils which ensures a significant mutual coupling. The diameters of the coils as well as the excitation frequencies have been numerically optimized in order to produce maximum relative response due to an iron bar with respect to the intrinsic impedance of coils in absence of a test piece. Figure 1 shows dependence of the EC response on the coil diameter at the excitation frequency of 100 kHz for different couples of the excitation/measuring coils, for various lift-offs of the array above the iron bar. According to (14) we are interested in the imaginary part of the EC response. The optimum diameter of the most inner coil appears to be 65 mm, with the successive coils having diameters 70 mm and 75 mm. The height of the coils is 5 mm.

Figure 1. Optimisation of coil diameter for inspection of an iron bar of diameter 19 mm. Target lift-off is 20 mm, excitation frequency = 100 kHz. The EC response is represented by the imaginary part.

Figure 2. Optimisation of the excitation frequency for inspection of an iron bar of diameter 19 mm, coaxial coils array of inner diameter 65 mm, lift-off 20 mm. The EC response is represented as the real and imaginary parts.

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Figure 3. Measured and simulated eddy current responses to an iron bar of diameter 19 mm, obtained with coaxial coils array of inner diameter 65 mm, lift-off 20 mm, excitation frequency = 100 kHz. The EC response is represented by the imaginary part.

Figure 2 shows dependence of the EC response on the excitation frequency for all the coupled pairs of coils with the optimized diameter of the most inner coil (65 mm), with the lift-off of the array above the iron bar being 20 mm. The optimum excitation frequency is 100 kHz. The impedance of the coil has been measured with an LF (bandwidth 5 Hz - 13 MHz) impedance analyzer HP-4192A at the optimum excitation frequency of 100 kHz. The lateral scanning of the iron bar with a coil array of the optimized size at excitation frequency of 100kHz has been conducted automatically by a Mitsubishi 6-axis Melfa robot RV-1A. The bar has been placed in the horizontal plane and the coil has been moved across the bar at various lift-offs from 1mm to

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40mm with step of 1mm. Figure 3 shows the comparison of measured and calculated signal contribution due to the iron bar, represented as the inductive part. Although there is a discrepancy for the auto inductance variation, there is a good agreement for the signals obtained due to the mutual coupling (12, 13, 23).

3. Conclusions and outlook This work has been focused on quantitative rebar detection and sizing for arbitrary geometrical configurations. The main contribution of the study are the following: (i) a critical analysis of the issues that must be considered for the quantitative imaging of reinforced concrete rebars; (ii) optimisation of an EC probe for rebars imaging; (iii) experimental validation of the numerical model and its underlying hypothesis. It has been found that the measured EC response due to an iron bar is stronger and more accurate with respect to simulation in case of mutual coupling among the probe coils rather than in case of auto-inductance. Future work will address assembling together the numerical model with the inversion algorithm for processing experimental data collected in a realistic setting.

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]

G. Rubinacci, A. Tamburrino, S. Ventre, “Concrete rebars inspection by eddy current testing”, International Journal of Applied Electromagnetics and Mechanics, Vol. 25 (2007), pp. 333–339 M. de Magistris, M. Morozov, G. Rubinacci, A. Tamburrino, S. Ventre, “Electromagnetic Inspection of Concrete Rebars”, COMPEL, Vol. 26, No. 2 (2007), pp. 389-398 G. Miller P. Gaydecski, S.Quek, B. T. Fernandes and M. A. M. Zaid, “Detection and imaging of surface corrosion on steel reinforcing bars using a phase-sensitive inductive sensor intended for use with concrete”, NDT&E International, Vol. 36 (2003), pp. 19-26. T. Chady, R. Sikora, S. Gratkowski, S. Wojtowicz and S. Nagata “Eddy current inspection of reinforcement bars in concrete structures”, Proceedings of The Tenth International Workshop on Electromagnetic Nondestructive Evaluation, Michigan State University, June 1-2 2004. J. Makar and R. Desnoyers, “Magnetic field techniques for the inspection of steel under concrete cover”, NDE&E International, Vol. 34 (2001), pp. 445-456. R. Zoughi, S. Gray and P.S. Novak “Microwave non-destructive detection of rebars in concrete slabs”, Materials Evaluation, Vol. 49, no. 11 (1991), pp 1385-88. Ch. Pichot and P. Trouillet, “Diagnosis of reinforced structures: an active microwave imaging system”, Bridge evaluation, repair and rehabilitation; Proceedings of the NATO Advanced Research Workshop on Bridge evaluation, repair and rehabilitation, Baltimore, Maryland, US, April 30 –May 2 1990. Law D.W., J. Cairns, S.G. Millard, J.H. Bungey (2004) Measurement of loss of steel from reinforcing bars in concrete using linear polarization resistance measurements, NDT&E International, 37 381-388. R. Albanese and G. Rubinacci, “Finite element methods for the solution of 3D eddy current problems”, in Advances in Imaging and Electron Physics, Vol. 102 (1998), Academic Press, pp. 1-86 R. Albanese, G. Rubinacci, F. Villone, “Crack simulation in the presence of linear ferromagnetic materials using an integral formulation”, in Electromagnetic Nondestructive Evaluation V (2001), J. Pavo et al. Eds. , IOS press, pp. 16-21 R. Albanese, G. Rubinacci, A. Tamburrino, F. Villone, “Phenomenological approaches based on an integral formulation for forward and inverse problems in eddy current testing”, Int. J. of Applied Electromagnetics and Mechanics, Vol. 12, No. 3-4 (2000), pp. 115-137 G. Rubinacci, A. Tamburrino, S. Ventre, “An efficient numerical model for a magnetic core eddy current probe”, accepted for publication on IEEE Trans. on Magnetics, 2008. Tamburrino A., G. Rubinacci, “A new non-iterative inversion method for Electrical Resistance Tomography”, Inverse Problems, Vol. 18 (2002), pp. 1809-29 A. Tamburrino, G. Rubinacci, “Fast methods for quantitative eddy-current tomography of conductive materials”, IEEE Trans. Mag., Vol. 42, No. 8 (2006), pp. 2017-2028

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Advanced Probe with Array of Pick-up Coils for Improved Crack Evaluation in Eddy-Current Non-Destructive Testing Ladislav JANOUSEK a,1, Klara CAPOVA a, Noritaka YUSA b and Kenzo MIYA b a DEBE, FEL, University of Zilina, Zilina, Slovak Republic b IIU Corp., Tokyo, Japan Abstract. The paper proposes a new probe for enhancing crack evaluation in eddy-current non-destructive testing. The probe consists of one exciting coil and two identical pick-up coils. The pick-up coils are situated at different locations relative to the position of the exciting coil for gaining signals using various depth profiles of eddy current density. The two signals are linearly superposed and a certain indication of crack’s depth is extracted from the resulting signal. Numerical as well as experimental results demonstrate the effectiveness of the new probe in the evaluation of a crack’s depth. In addition, cracks much deeper than the standard depth of penetration can be evaluated using the new probe. Keywords. Non-destructive testing, eddy-currents, pick-up coil array, signal superposition, crack’s depth evaluation

Introduction Scheduled in-service inspection (ISI) is necessary for the maintenance of structural components in many industrial fields. When a defect is found during the inspection, the cracked component can usually stay in service; however, it must be assured that the dimensions of the crack will not exceed size limitations until the next scheduled ISI [1]. Frequently, ultrasonic-based methods are used for the sizing. However, such methods are quite inefficient when inspecting cracks in certain structures, e.g. welds [2], where electromagnetic methods are reported to provide good detection sensitivity [3]. One of the conventional electromagnetic methods utilized for the inspection of conductive materials is eddy-current non-destructive testing (ECT). ECT signals are integral values and do not carry explicit information about the crack’s dimensions. Several papers proposed to use numerical inversions for sizing [4]. However, the illposedness of the problem is not yet fully revealed [5]. Further improvements in eddycurrent non-destructive evaluation are therefore still necessary. The authors have proposed to utilize various distributions of eddy currents during the inspection for enhancing crack evaluation by ECT [6], [7]. An ECT probe composed of several exciting coils and one pick-up coil has been employed. The present paper proposes a new design of an ECT probe. Only one exciting coil drives the eddy currents in a test-piece and two spatially distributed pick-up coils sense crack signals. The signals are further processed to extract indication about a crack’s depth. 1 Corresponding Author: Ladislav Janousek, Department of Electromagnetic and Biomedical Engineering, Faculty of Electrical Engineering, University of Zilina, Univerzitna 1, 010 26 Zilina, Slovak Republic; Email: [email protected]

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1. Proposal of a New ECT Probe

exciter Exciting coil: - height: 30 mm - length: 30 mm - width: 10 mm - winding thickness: 1 mm

21

pick-up 1

Pick-up coils: - inner diameter: 1 mm - outer diameter: 3 mm - width: 1 mm

pick-up 2 9 Figure 1. Design of a new ECT probe

Figure 1 displays the design of a new ECT probe. The probe consists of one rectangular exciting coil positioned tangentially relative to the surface of a tested object. Two identical pancake pick-up coils located at different positions from the exciting coil sense the signals. The two pick-up coils are situated 21 mm and 30 mm away from the centre of exciting coil along its axis, respectively. The spatial distribution of the pickup coils assures that the two sensed signals of the same crack are obtained with different depth profiles of eddy currents. The configuration and the dimensions of the probe have been designed for an inspection frequency of 50 kHz. The two signals are linearly superposed based on:

Re = C1 ⋅ Re1 − C2 ⋅ Re2 , Im = C1 ⋅ Im1 − C2 ⋅ Im2 ,

(1)

where Re1, Re2 are the real parts of the complex signals for the pick-up coils 1 and 2, respectively; Im1, Im2 are the imaginary parts of the complex signals for the pick-up coils 1 and 2, respectively; and C1, C2 are arbitrary numbers defining a ratio of the superposition α = C1 C2 . The numbers C1, C2 are changed in such a way that the ratio is increased from zero to infinity. The resulting superposed complex crack signal (Re, Im) is evaluated in respect to the value of the ratio.

2. Numerical and Experimental Results A plate specimen made of stainless steel SUS316L is inspected in this study. The electromagnetic characteristics of the material include a conductivity of σ = 1.4 MS/m and a relative permeability of μr = 1. The thickness of the specimen is 25 mm. An electro-discharge machined (EDM) notch of rectangular shape with a length of

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lc = 40 mm, a width of wc = 0.5 mm and variable depth models the crack. The EDM notch of a variable depth dc ranging from 0 to 25 mm with a step of 1 mm is numerically inspected with the probe. The probe scans right over the crack along its length; the winding of the exciting coil is perpendicular to the crack’s length and the pick-up coils sense the crack signals just over the crack along its length. The lift-off of the probe is 1 mm. Frequency of 50 kHz is adopted in the inspection. A three dimensional finite element (FEM) and boundary element (BEM) hybrid method based upon A-V formulation is used for the numerical analysis. The governing equations of the A-V formulation for the low frequency eddy-current problems are as follows:

§ ∂A · ∇2 A = σ ¨ − ∇V ¸ , μ © ∂t ¹

(2)

· § ∂A ∇ ⋅σ ¨ − ∇V ¸ = 0 © ∂t ¹

(3)

1

in the conductor region and

1

μ

∇2 A = −J 0

(4)

in the air region outside the conductor. A denotes the magnetic vector potential, V is the electric scalar potential, J0 is the vector of the exciting current density, σ is the electric conductivity and μ is the magnetic permeability. Dependences of the crack signal’s amplitude and its phase on crack’s depth obtained by the two pick-up coils are shown in Fig. 2a) and 2b), respectively. 6

-35

pick-up 1 pick-up 2

-40 -45 -50

4

phase [degree]

amplitude [mV]

5

3 2

-55 -60 -65 -70 -75

1

-80

pick-up 1 pick-up 2

0 0

5

10 15 crack depth [mm]

a)

-85 20

25

0

5

10 15 crack depth [mm]

b)

Figure 2. Dependences of crack signals on crack depth for the two pick-up coils

20

25

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8

100

dc=10mm dc=12mm dc=15mm dc=20mm

80

6

40

α ratio [a.u.] ratio [-]

phase [degree]

60

7

20 0 -20

5 4 3 2

-40 1

-60

simulation experiment

0

-80 0

2

4

6

8

10

12

14

ratio[a.u.] [-] α ratio

Figure 3. Dependences of the superposed crack signal phase on the ratio of superposition for the four cracks with depths of dc = 10, 12, 15 20 mm

0

5

10

15

20

25

crack depth [mm]

Figure 4. Dependences of the ratio of superposition on crack depth, comparison of the numerical and the experimental results

It can be observed that the dependences are different for the two pick-up coils due to different depth profiles of eddy current density in the vicinity of each pick-up coil. The two signals obtained by the two pick-up coils are linearly superposed based on (1) for each particular depth of the crack. The phase of the superposed signal is extracted for each value of the ratio. Fig. 3 displays four dependences of the superposed signal phase on the ratio of superposition for the crack with depths of dc = 10, 12, 15 and 20 mm. It can be seen that the crack signals rotate almost 180° when increasing the ratio and their rotation depend on crack’s depth. Thus, a unique feature is extracted from the characteristics. It is a certain ratio value where the crack signal rotates in half the angle of its overall rotation. Dependence for the extracted feature is shown in Fig. 4. As it can be seen, the dependence provides clear indication about crack’s depth. In addition, the dependence is almost linear and thus, cracks much deeper than the standard depth of penetration (δ = 1.9 mm in this case) can also be unambiguously evaluated. The width of crack does not influence the gained dependence; however it is affected by the length of crack. The length of crack can be estimated in advance from certain features of the signals and than appropriate dependence of the ratio on crack’s depth for actual crack length should be used. Four EDM notches introduced in a 25 mm thick SUS316L plate are experimentally inspected by the probe. The notches measure lc = 40 mm in length, wc = 0.5 mm in width and dc = 10, 12, 15, 20 mm in depth. All the parameters of the inspection and consecutive processing are the same as ones used in the numerical investigations. The extracted feature values of the ratio for the four cracks are shown in Fig. 4 along with the simulated results. Quite good correspondence between the numerical results and the experimental ones can be observed.

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3. Conclusion The paper proposed a new probe for enhancing sizing ability in eddy-current nondestructive testing. Configuration of the probe assures that two signals of the same crack are obtained using different depth profiles of eddy current density. The two signals of each crack were linearly superposed and a feature value of the ratio of superposition was extracted from the resulting signal for a corresponding crack. It was shown that the value provides clear indication about crack’s depth. Moreover, cracks much deeper than the standard depth of penetration can be sized using the new probe.

Acknowledgment This work has been partially supported by a grant VEGA No. 1/2053/05 of the Slovak Ministry of Education.

References [1] [2] [3] [4] [5] [6] [7]

ASME: Boiler and pressure vessel code, section XI, Rules for in-service inspection of nuclear power plant components, 2001. W. Cheng et al.: Ultrasonic and eddy current testing of defects in Inconel welding metals, Proceedings of the 12 MAGMA conference, Oita, Japan, 2003, 187-190. N. Yusa et al.: Application of eddy current inversion technique to the sizing of defects in Inconel welds, Nuclear Engineering and Design 235 (2005), 1469-1480. B.A. Auld and J.C Moulder: Review of advances in quantitative eddy current nondestructive evaluation, Journal of Nondestructive Evaluation 18 (1999), 3-36. N. Yusa et al.: Caution when applying eddy current inversion to stress corrosion cracking, Nuclear Engineering and Design 236 (2006), 211-221. L. Janousek et al.: Excitation with phase shifted fields – enhancing evaluation of deep cracks in eddycurrent testing, NDT&E International 38 (2005), 508-515. L. Janousek et al.: Utilization of two-directional AC current distribution for enhancing sizing ability of electromagnetic nondestructive testing methods, NDT&E International 39 (2006), 542-546.

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Observation of Stress Loaded Ferromagnetic Samples Using Remanent Flux Leakage Method a

Tomasz CHADY a,1, Grzegorz PSUJ a and Ryszard SIKORA a Department of Electrical and Computer Engineering, Szczecin University of Technology, ul. Sikorskiego 37, 70-313 Szczecin, Poland

Abstract. In this paper the results of remanent flux leakage inspections of the stress loaded ferromagnetic samples are presented. Two different magnetizing methods and several configurations of the transducers’ measuring unit are used in order to compare and chose the optimal one and to enhance the performance of the whole system. Absolute and differential GMR sensors are used as the pick-up elements. All measurements were done using specimens made of a low carbon steel SS400, tensile deformed in the longitudinal direction. Key Words. Remanent flux leakage method, GMR elements, magnetic materials

Introduction Remanent flux leakage method is frequently used to evaluate structure of magnetic materials [1]. It is based on a detection of leakage fields, caused by changes of the reluctance of ferromagnetic materials, which were magnetized in a DC field. The excitation unit can be either made of a permanent magnet or a coil driven by a DC current. The leakage magnetic fields are measured by scanning the surface of the specimen with a magnetic field sensor. The collected information can be used to detect and evaluate defects in stress loaded materials. The usage of the MFL technique for the defects detection and evaluation of stress degradation has already been researched [2]. The results of the evaluation of the stress degradation stage using MFL technique were presented in [3]. During the experiments the objects were magnetized in a uniform DC field before the measurement and the leakage field was measured by absolute GMR element. In many practical applications this type of the measuring method is not an easy task due to a complicated geometrical shape of real test objects. The alternative solution in this case can be use of an integrated local magnetizing coil. One of the purposes of this paper is to broaden the scope of the tests and to compare the results obtained using two different magnetizing methods (using the uniform DC field and the local magnetizing coil). In the literature, mostly little notice has been given to the configuration of the magnetic field sensing device. In most cases a single element such as a Hall, a flux set 1 Corresponding Author: Szczecin University of Technology, Department of Electrical and Computer Engineering, ul. Sikorskiego 37, 70-313 Szczecin, Poland; E-mail: [email protected].

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Figure 1. A view of a transducer with integrated excitation unit: 1 – pick-up section; 2 – rod ferrite core; 3 – excitation coil; 4 – sample

or a GMR is used as the field sensor. In such cases a background signal can have an essential influence on the measurement results. An absolute sensor is prone to noises while gradiometer provides low amplitude in case of signals with slow changes. In this paper several differential and absolute configurations of Giant Magnetoresistive (GMR) magnetic field sensors will be compared in order to minimize the impact of the background signals and to maximize the effectiveness of the measurements.

Concepts of the Measuring Transducers Several configuration of transducers were investigated in order to find the optimal construction of the measuring unit and enhance performance of the system. Two methods of measurements were considered. In the first method tested samples were magnetized by a uniform DC field before measurements. Next, the specimen’s surface was scanned with the pick-up transducer. In order to overcome problems with uniform magnetization of a test sample we propose to integrate a magnetization section with the pick-up element (Figure 1). Such construction allows to magnetize only the area, where the measurement will be taken in the next step. The magnetizing unit consists of a coil wounded on a rod ferrite core. The whole magnetization section is placed in a front of the pick-up transducer. The dimensions of the magnetizing coil and its distance from the pick-up element was optimized to achieve a high sensitivity to defects and a low direct influence of the magnetizing unit. An absolute (NVE AAH001-02) and a differential (NVE ABH000-01) GMR elements were used as the pick-up transducers. The AAH-series sensor is made of high sensitivity GMR elements and is very suitable to measure low magnetic fields. The ABH-series sensor is extremely sensitive to the

Figure 2. Block diagram of the measurement system

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Figure 3. The dimensions of the transducers: a) P_ABS and P_GRAD, b) P_DIFF1, c) P_DIFF2

gradient of magnetic field. More information about the GMR elements used in the transducers can be found in [4]. In order to select the optimal construction four transducers with different configuration of the pick-up sections were evaluated (Figure 2): P_ABS – transducer consisting a single absolute GMR, P_GRAD – transducer with a gradiometer GMR, P_DIFF1 – transducer consisting of two differentially connected absolute GMR placed one by another and P_DIFF2 – transducer consisting of two differentially connected absolute GMR placed one over another. The dimensions of the magnetizing unit and its distance from the pick-up element, as well as the distance between two GMR elements in transducers P_DIFF1 and P_DIFF2 are presented in Figure 3. The dimensions of the GMR elements can be found in [4].

Description of the Experiments A. Preliminary Evaluation of Transducer Performance To verify a spatial resolution and sensitivity of all described transducers, two preliminary experiments were carried out (Figure 4.). In the first one a test sample consisting of two thin (thickness less than 0.1 mm) metal strips placed within a distance of 1 and 2 mm from each other (Figure 4a) was used. During the measurements transducers were moved crosswise the strips in steps of 0.1 mm. The lift-off distance was set to 1 mm. Measured signals are plotted in Figure 5. The results give the opportunity to compare the performance of the transducers. One can observe that the P_GRAD transducer (Figure 5d) has greater spatial resolution than the P_ABS one (Figure 5a). The highest signal to noise ratio was achieved for the transducer P_DIFF2 (Figure 5c). Because of the problem with magnetizing of two metal strips to equal degree a second preliminary experiment was introduced. During this experiment a magnetic

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Figure 4. Visualization of the first (a) and the second (b) preliminary experiment

Figure 5. Results of the preliminary tests with samples consisting of two metal strips with distance between each other equal to 1 mm (continuous line -) and 2 mm (dashed line --): a) P_ABS transducer; b) P_DIFF1 transducer; c) P_DIFF2 transducer; d) P_GRAD transducer

Figure 6. Results of the preliminary tests with sample consisting of copper wire carrying a DC current of 500 mA: P_ABS transducer (continuous line –); P_DIFF1 transducer (dashed line – –); P_DIFF2 transducer (dotted line ·); P_GRAD transducer (dash-dotted line – ·)

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Figure 7. Results of the preliminary tests with sample consisting of two copper wires carrying a DC current of 500 mA with distance from each other equal 1 mm (continuous line -) and 2 mm (dashed line --) and 5 mm (dotted line ·): a) P_ABS transducer; b) P_DIFF1 transducer; c) P_DIFF2 transducer; d) P_GRAD transducer

field generated by long copper wires (diameter 0.18 mm) carrying a DC current of 500 mA was measured. The measurements were done in steps of 0.1 mm for single wire and two wires placed within the distance of 1, 2 and 5 mm from each other. The lift-off distance was set at 0.5 mm. Analyzing obtained results (Figure 6 and Figure 7) one can come to similar conclusions as in the case of the first preliminary experiment. The greatest sensitivity was achieved for the P_ABS transducer. Using P_GRAD transducer it is possible to distinguish two wires placed in the distance of 1 mm between each other. The P_DIFF2 transducer generates nonzero signal only in the case of magnetic inhomogenity, which results in optimal use of A/D converter’s dynamic range. Comparing P_DIFF1 with P_DIFF2 transducer one can see that the response of the P_DIFF1 is more complicated than the P_DIFF2. B. Results of the Measurements Final measurements were done using seven planar specimens made of the SS400 low carbon steel, tensile deformed in the longitudinal direction. The samples SS400-1, SS400-2 and SS400-3 are loaded with the maximum stress of 103.2 MPa, 206.4 MPa and 300 MPa respectively, which is lower than the yield stress (350 MPa). The sample SS400-4 was tensile deformed exactly up to the yield point. More details about the test samples and the measuring system can be found in [3] and [5]. In case of the first measuring method the leakage flux from samples was observed after magnetization in uniform field. In case of the transducer with the integrated magnetization section the excitation coil was driven by 1 A DC current. The lift-off distance was about 0.5 mm from the sample surface independently of the surface roughness. The sensitivity axis of the pick-up element was parallel to the loading direction of the sample. The measurements were done along the x-axis (the longitudinal direction) and the y-axis in steps of 1 mm. The scanning area was 120 mm x 27 mm.

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Figure 8. Results of measurements achieved using P_GRAD transducer for sample: a) SS400-3; b) SS400-4; c) SS400-5; column A – uniform magnetization of a test sample using a solenoid; column B – local magnetization utilizing coil driven by a DC current.

Figure 9. Results of measurements obtained for sample loaded below material’s yield point: a) P_ABS transducer; b) P_DIFF1 transducer; c) P_DIFF2 transducer; d) P_GRAD transducer; column A – uniform magnetization of a test sample using a solenoid; column B – local magnetization utilizing coil driven by a DC current.

First P_GRAD transducer was used in order to evaluate the stage of degradation of tested samples (Figure 8). Samples SS400-4 and SS400-5 were loaded with a maximum stress value respectively equal to and grater than the yield stress, which resulted in occurrence of Lüder bands almost in all scanned area. In order to investigate an early stage of defects forming sample SS400-3 was selected for further examination. The results obtained for the sample SS400-3 are shown in Figure 9. The P_GRAD presents an extreme high spatial resolution, but the sensitivity is low. Especially low sensitivity was observed in the case of the magnetization section integrated with the

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transducer. Moreover the interpretation of differential signal is complicated. The highest sensitivity to the defect was observed in case of the P_ABS transducer, however it measures also unwanted background signal. Connecting two absolute GMR elements in the differential way it is possible to achieve higher sensitivity than for the P_GRAD and a higher spatial resolution than for the P_ABS. The P_DIFF2 transducer presents also a low dependence on an external interfering magnetic field. Using local magnetizing coil results in obtaining lower sensitivity to defects, however the problem with uniform magnetization of a tested object is avoided. Regarding to the interpretation of measured signals, the best results were obtained for the P_DIFF2 transducer. Conclusions According to achieved results (Figure 9), one can observe that the proposed differential transducers help to enhance the flux variations caused by defects. Additionally P_DIFF2 allows for simple interpretation of the signals and has the ability to reduce influences of the external fields. The transducer with integrated magnetic sections can be more easily applied in practical cases. It presents the opportunity to magnetize each measuring part of the test object in the same way. The difference between both magnetizing methods can be seen especially in Figure 9a-c. When the sample is magnetized prior the measurements (for example in solenoid), disturbances of the signal can be observed not only in the defect’s area, but in its direct neighborhood too (column A in Figure 9a-c). The effect is significantly smaller in case of the local magnetizing coil (column B in Figure 9a-c). In the future works authors would like to propose integration of a demagnetizing section with the transducer in order to overcome a problem with unknown magnetic history of the specimen.

Acknowledgements This work was supported in part by the State Committee for Scientific Research, Poland, under the Grant no: 3T10A 017 30 (2006-2009).

References [1] [2] [3] [4] [5]

Y. Tsuchida, et al, “Evaluation of Strain Distribution of Austenitic Stainless Steels by Measuring Remanent Magnetization”, Electromagnetic Nondestructive Evaluation, IOS Press, 2005, pp 151-158 V. Babbar, L. Clapham, “Residual Magnetic Flux Leakage: A Possible Tool for Studying Pipeline Defects”, Journal of Nondestructive Evaluation, Vol.22, No. 4, 2003, pp.118-125 T. Chady, “Evaluation of Stress Loaded Steel Samples Using GMR Magnetic Field Sensor”, IEEE Sensors Journal, Vol. 2, No. 5, October 2002, pp. 488-493. GMR Sensor Application Notes, Nonvolatile Electronics, INC. [Online], Available: http://wwww.nve.com T.Chady, et. al, “Computerized System for Complex Electromagnetic Nondestructive Evaluation”, XIII International Symp. on Theoretical Electrical Engineering, ISTET’05, Lwow, Ukrain, pp. 333-336

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Evaluation of Complex Multifrequency Eddy Current Transducer Designed For Precise Flaw Depth Measurements Tomasz CHADY, Piotr BANIUKIEWICZ, Ryszard SIKORA, Grzegorz PSUJ Szczecin University of Technology, al Piastow 17, 70-310 Szczecin, Poland

Abstract. In this paper the authors propose an eddy current transducer dedicated to the precise flaw depth measurements. The transducer consists of two probes with C-shaped ferrite cores. The frequencies of the excitation currents differ for both probes. A flux generated by the big probe penetrates the material deeper than a flux from the small probe. Therefore, the bigger probe is sensitive to deep defects while the small probe is affected more by surface defects in the material. The results of measurements are presented. Keywords. Eddy current method, nondestructive testing

Introduction The rapid industry growth that has been done recently encourages new demands for safety of people and natural environment. Most of the cracks that can be observed in metals are close to notch. An eddy current (EC) method is one of the most popular electric NDT methods due to its simple hardware implementation, rapid scanning and contact-less inspection. The method is sensitive to various types of defects, mainly the surface and subsurface discontinuities with small dimensions and different shapes. This is crucial because all critical tensions, caused by fatigue of material, are concentrated on the surface of material. In the EC system, the probability of crack detection is closely related to the construction of the probe. Various probes have been proposed in literature [1]. Most of them offer high sensitivity that enables them to detect cracks located deep under the surface of the specimen. However, in particular applications it is necessary not only to detect the flaw but also to measure its depth precisely. In the case of deep flaws in thick material, most of widely used eddy current transducers are not capable to fulfill such kind of requirements [2]. Therefore, works on the new transducer started in 2003 [3]. The developed transducer achieves a very good depth resolution. It is dedicated to precise measuring the depth of the notches that may appear in thick materials.

1. Description of the Sensor and the Measuring System The proposed transducer is differential one and it is different from the other probe described in the literature [4]. The transducer, simplified view of which is shown in the Figure 1, is composed of two probes: a small probe (SP) and a big probe (BP).

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Figure 1. Simplified view of the eddy current differential transducer and the measuring system

The probes consist of the same elements and differ only in size. Both probes contain a c-shaped ferrite core. The distance between columns of a big core (FCBP) is 20 mm and in case of a small probe (FCSP) is 10 mm. Each probe consists of two exciting coils wound around the ferrite core. The coils are connected in series and supplied with the alternating current. The output signals are taken from two measuring coils wound around neighboring columns of the cores. The transducer is embedded in a plastic case and submerged in epoxy resin to prevent any mechanical damages. A flux generated by the big probe penetrates the material deeper than a flux from the small probe. Therefore, the bigger probe is sensitive to deep defects while the small probe is affected more by surface defects in the material. Selection of the excitation signals parameters, which allow us to maximize an accuracy of depth estimation, is very complicated. Distribution of the eddy currents in the specimen depends on the excitation currents ratio as well as on their frequencies. In this paper, the influence of the frequency of the excitation signals is analyzed. The big probe is under stronger influence of deep flaws than the small probe. The main task of the SP is to compensate the contribution that is brought in the output signal by the surface cracks. In this way, the transducer is affected more by the deeper located part of the crack, what results in a better depth system resolution. It is also possible to calibrate the transducer, to reach an equilibrium state, by adjusting the excitation current in the SP. The state of equilibrium is accomplished when the amplitude of output differential signal is close to zero for an unflawed specimen. The correct choice of excitation parameters is crucial. The most important parameters are frequency and amplitude of excitation currents. Too high amplitude of current causes that the output signal from the small probe is much greater than the big probe signal. Consequently, the small probe becomes dominating what, in result, rapidly decreases the depth resolution of the transducer. The transducer is powered by two function generators through the power amplifiers. The generators are coupled and triggered simultaneously from the computer. Thus, the phase shift between the excitations of the probes is constant and it can be easily adjusted. The output signals obtained from the search coils are amplified by measurement amplifiers and then filtered by band-pass filters to remove unwanted components and noise. It is done this way that, the frequency component descended from the BP excitation has to be removed from the SP output and vice versa. This guarantees that the RMS values are computed only from frequency components

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contained in the excitation signals for both probes separately. Next, both signals are converted to DC value using two true RMS/DC converters. An integrated circuit AD637 has been used as the RMS/DC converter. A single pole Sallen-key filter configuration has been chosen to measure low frequency signals, what gives us a good compromise between the conversion errors and setting time. Then, the RMS values of measured signals are subtracted using differential input operational amplifier. Finally, the output signal from the transducer is acquired by a high resolution A/D converter. As one can see, all electronic circuits used in the system are available in the form of integrated circuits. A high speed A/D converter is not required in this application due to a DC output signal from the system. Consequently, the whole measuring system can be realized as a small mobile system.

2. Measurement Results In order to verify usefulness of the proposed transducer, a set of experiments was carried out. The test specimens used for the experiments are 20 mm thick aluminum plates, which have flaws in the form of EDM notches. The flaw depth is from 7 mm to 18 mm (Figure 2). The transducer was moved over the tested specimen along a straight line parallel to the longer edge of the plate in steps of 1 mm. The lift-off was measured to be 0.5 mm. The performance of the transducer was evaluated using coefficient defined by:

k

U MAX18  U MAX16 U MAX18

˜100%

(1)

where UMAX16 and UMAX18 stand for the maximum of relative signal obtained for inner flaws with the depth of 16 mm and 18 mm respectively. At the beginning of each measurement the probe was moved towards the unflawed area of the test sample. The amplitude of the excitation current in the small probe was adjusted in order to achieve the state of equilibrium. Such adjustments have been done for each excitation frequency of SP. The parameters of the excitation signal for the big probe were not changed during the measurements. The excitation frequency of BP was 80 Hz, whereas the current amplitude was set to 100 mA. Next, the transducer was moved over the specimen with step of 1mm in order to obtain the signals for two flaws 16 mm and 18 mm deep.

Figure 2. View of the test specimen made of aluminum

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Figure 3. Relative signals obtained for flaws 16 mm and 18 mm deep and various excitation frequencies of small probe

Maximizing the coefficient k, the optimal parameters of the SP excitation were obtained. For those parameters the transducer achieves the best depth resolution what means that two inner flaws of similar depths are easily distinguishable. Figure 3 shows selected signals obtained for flaws of depth 16 mm and 18 mm for various excitation frequencies. A strong dependence between the excitation frequency of the probe SP and the depth resolution achieved by the transducer can be observed in the Figure 4. The best results were obtained when the SP was excited with the current frequency 640 Hz. Negative peaks, that occur for higher frequencies, result from the growth of the sensitivity of the SP together with its excitation frequency.

Figure 4. The depth resolution of the transducer versus excitation frequency

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D [mm]

Figure 5. Maxima of the relative signals obtained for chosen fSP versus crack depth

Figure 5 confirms that the highest depth resolution of the transducer is obtained for the optimal frequency 640 Hz. The nearly linear dependence between maximum of the signal and crack depth occurs for lower frequencies.

Conclusions The proposed transducer achieves very good depth resolution. The experiments performed on thick material show that two inner flaws of similar depths are fully distinguishable. The performance of the transducer is closely related with excitation frequency of the small probe. The best resolution, in the case of flaws 16 mm and 18 mm deep, has been achieved for frequency 640 Hz. Due to a strong influence of excitation current of the SP on the output signal, the state of equilibrium can be set very precisely. It is also possible to use the transducer as a depth discriminator. This can be accomplished by equilibrating the transducer for flaw of specified depth.

Acknowledgments This study was supported by State Committee for Scientific Research, Poland, Grant no. 3T10A01730 (2006-2009).

References [1] [2] [3] [4]

T. Chady, M. Enokizono, T. Todaka, Y. Tsuchida, R. Sikora, ”A Family of Matrix Type Sensors for Detection of Slight Flaws in Conducting Plates”, IEEE Transactions on Magnetics, 35(5), 3655-3657, 1999. F. Thollon et al., Numerical and Experimental Study of Eddy Current Probes in NDT of Structures with Deep Flaws, NDT&E International, 28(2), 97-102, 1995. T.Chady: private email correspondence 2003-07-10, 2003-08-07. L.Janousek et al., Excitation with phase shifted fields-enhancing evaluation of deep cracks in eddycurrent testing, NDT&E International, Vol.38, 508-515, 2005.

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Comparative Study of Coil Arrangements for the EC Testing of Small Surface Breaking Defects Cyril RAVAT, a,b,1 , Yann LE BIHAN a , Pierre-Yves JOUBERT b and Claude MARCHAND a a

LGEP/SPEE Labs; CNRS UMR8507; SUPELEC; Univ Pierre et Marie Curie-P6; Univ Paris Sud-P11; 91192 GIF-SUR-YVETTE FRANCE b SATIE, ENS Cachan, CNRS, UniverSud, 61 av. du President Wilson, 94235 CACHAN Cedex FRANCE Abstract. The increasing need of both reliability and speed during inspection operations requires to develop new inspection devices, such as EC multisensor arrays. In this paper, the authors consider the detection of small surface breaking defects ranging from 0.1x0.1x0.1 mm3 to 0.8x0.1x0.4 mm3 . A low-cost multilayer PCB multicoil array was implemented using different transmit/receive strategies and the detection performances were exhaustively quantified and compared, thanks to the computation of Receiver Operating Characteristics. Two strategies allow the smallest defects to be detected without false alarm. Keywords. Eddy current, non destructive testing, multicoil array, receiver operating characteristic

Introduction Eddy current (EC) sensors are widely used for non-destructive evaluation on electrically conducting materials, since they are sensitive to defects such as fatigue cracks, inclusion or corrosion, and easy to implement in industrial applications. Moreover, the use of multicoil arrays permit to increase the rapidity and the reliability of the detection and is particularly well suited to the detection of surface breaking defects. Nevertheless, the strategy of operations of the sensor has to be optimized, in order to maximize the sensitivity, regardless of the operating conditions and the defect orientation [1]. In this paper, an exhaustive and qualitative study of a 3-coil 1-D array, viewed as an elementary structure of a larger array, is proposed. After the definition of the chosen measurement strategies and the short description of the implemented experimental set-up, a quantitative comparison of the detection performances is carried out thanks to Receiver Operating Characteristic (ROC) curves. 1 Corresponding

Author: [email protected]

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1. EC Measurement Strategies The basic principle of the EC method is to induce an EC flow within the inspected material (transmission), and to measure the resulting magnetic field at the surface of the sample (reception), which is relative to the integrity of the material [2]. Actually, the EC signal is the ratio between the electromotive force generated at the terminals of the receiver (R) device, and the excitation current feeding the transmitter (T) device. Since coils can be used either as transmitter, receiver or transmitter-receiver (T&R), the following transmission-reception strategies can be defined for a 3-coil 1-D array, as depicted in Figure 1: • T/R: one T&R coil. In this case, the EC signal is actually the coil impedance. This strategy is widely used since it is the simplest to implement, despite a low sensitivity. • TR: one T coil and one adjacent R coil. This strategy is the basic structure of separate function EC measurements. The measurement is absolute, and thus quite sensitive to lift-off and tilt. • RTR: one middle T coil and two R side coils. Voltages at each R coil terminals are subtracted: the measurement is differential. • TRT+: one middle R coil and two T side coils connected so that the measured magnetic fluxes are added in the R coil. The measured signal is the superposition of two shifted TR ones. • TRT-: same as TRT+ but measured magnetic fluxes are subtracted in the R coil. This strategy can be considered as differential (the EC signal should be null in absence of defect), though not the reception but the transmission is differential. T/R

TR

TR

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Figure 1. The five T/R strategies

These five 3-coil 1-D strategies constitute all the possible relevant strategies using three adjacent coils in line and can be considered as elementary structures for the design of larger 1-D or 2-D coil arrays.

2. Experimental Set-up The three coils used in this study are 8-layer flat square coils, realized thanks to conventional PCB technology (Figure 2). Each coil features a 3x3 mm2 surface and a 1 mm thickness. The inductance and the resistance of each coil are about 2 μH and 3.5 Ω, respectively.

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The sensor array was implemented for the exhaustive inspection of a nickel based alloy mock-up featuring a magnetic permeability μ = 4π10−7 H.m−1 and an electrical conductivity σ = 0.76 MS.m−1 . 30 surface rectilinear defects were machined in the mockup. Their dimensions are 0.1, 0.2, 0.4, 0.6 or 0.8 mm in length, 0.1 mm in width and 0.1, 0.2 or 0.4 mm in depth. Since the signal amplitude and shape highly depend on the defect orientation, all the defects are available for two directions, parallel to the array main orientation (“horizontal” defect) and perpendicular (“vertical” defect). The measurements were carried out thanks to a HP4192A impedance analyzer and a PC-controlled 3-axis robot modifying the position of the sensor. The computer which controls synchronously both devices also acquires the data. In this study, the experimental set-up was adjusted so that the sensor array operates in the best possible conditions, i.e. tilt and lift-off noises were controlled and kept negligible. As the transmitter current frequency modifies the EC intensity and the penetration depth, it highly affects the detection performances. The used EC frequencies range from 500 kHz to 6 MHz. Figure 3 shows EC images obtained at 3 MHz for the 5 T-R strategies, in the case of three different defects (largest horizontal and vertical defects, and smallest defect). Spatial sampling step is 0.2 mm in both directions. All strategies allow the largest defects to be visualized with a sufficient signal to noise ratio, independently from their orientation. However, the smallest defect is hardly seen except for the RTR and TRT- strategies.

Figure 2. Eight 8-layer 3x3 mm2 flat coils in line (only 3 adjacent coils are actually used)

3. Receiver Operating Characteristic The detection performances of the multicoil array depend on the used transmissionreception strategy and EC frequency. In order to quantify and compare these performances, a detection algorithm was built and used in ROC curve representations. The detection algorithm determines whether, for a given threshold, an EC image contains a defect response or not. The defect response is basically defined as a set of adjacent pixels featuring an EC amplitude higher than the threshold. The detection matrix for the i-th defect reads Di = (EC_Imagei > t) ∗ S where ∗ designates the convolution operator, t is the threshold and S is a square matrix of ones. EC_Imagei is the matrix of the EC amplitude for the i-th defect. The dimension of S was experimentally adjusted in order to optimize the detection performances, and was fixed to 10 pixels (2 mm). The detection diagnostic denoted θ(i, t) is then expressed by

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Figure 3. EC images (EC signal signed modulus) obtained at 3 MHz with the largest horizontal defect (0.8x0.1x0.4 mm3 , first line), the largest vertical defect (second line) and the smallest defect (0.1x0.1x0.1 mm3 , third line); from left to right: T/R, TR, RTR, TRT+, TRT-; scales are in mm.

! θ(i, t) =

1 0

if ∃ (x, y) : Di (x, y) = 1 else

i varies from 1 to 30 and t ranges from tmin to tmax defined by   tmin = min min (EC_Imagei (x, y)) i  x,y  tmax = max max (EC_Imagei (x, y)) i

x,y

For each strategy and frequency, the EC images of the 30 defects are used to compute a 30-level discretized probability of detection (POD), depending on the threshold t, expressed by POD(t) =

30 1  θ(i, t) 30 i=1

Moreover, 30 EC images of defect-free areas are used to compute a 30-level discretized probability of false alarm (PFA), for the same threshold values. The ROC curve is the parametric curve which plots POD versus PFA for the different threshold values [3]. ROC curves were compared using the minimal distance from the curve to the maximum efficiency point [4], which stands for no false alarm (PFA = 0) and all defects correctly detected (POD = 1). Figure 4 presents the best curves obtained for each strategy, considering all defects (a), only horizontal ones (b) and only vertical ones (c). The TRT- and RTR strate-

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1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

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Probability of detection

Probability of detection

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gies are the most efficient and allow surface defects as small as 0.1x0.1x0.1 mm3 to be detected. Indeed, if a ROC curve passes by the maximum efficiency point, then at least one threshold allows all defects to be detected without false alarm. Figure 4 also shows that horizontal defects are far better detected than vertical ones, since a defect which is parallel to the array main orientation perturbs more the EC flow.

T/R (500kHz) TR (1MHz) RTR (4MHz) TRT+ (1MHz) TRT− (4MHz) 0.2 0.4 0.6 0.8 Probability of false alarm

1

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

1

T/R (500kHz) TR (1MHz) RTR (4MHz) TRT+ (1MHz) TRT− (4MHz) 0.2 0.4 0.6 0.8 Probability of false alarm

1

Figure 4. Best ROC curves for each strategy, considering (a) all defects, (b) only horizontal defects, (c) only vertical defects

In order to discriminate “equidistant” curves, the ratio of the largest threshold allowing all the defects to be detected to the lowest threshold allowing no false alarm to be triggered, was also calculated. In the case of the two “perfect” curves for RTR and TRT- strategies, this represents the space of choice of the correct threshold. The magnitude of this quantity quantifies the separability between detections and false alarms. The TRT- strategy has a better separability than the RTR strategy, and thus the TRT- strategy is globally the most efficient of the five implemented strategies.

Conclusion In this paper, an elementary array of 3 coils in line is studied and 5 transmit/receive strategies were carried out for the detection of small surface breaking defects. Two strategies

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permit defects as small as 0.1x0.1x0.1 mm3 to be detected without any false alarm, and the TRT- strategy is the most efficient. The influence of the tilt noise was not presented in this study, however same results were obtained for a lift-off up to 0.5 mm. The obtained results are very promising and further work will focus on 2-D multicoil array using the TRT- strategy, implemented in different orientations in order to maximize the sensitivity for defects of any orientation.

References [1]

[2] [3] [4]

P.-Y. Joubert and Y. Le Bihan, Eddy Current data fusion for the enhancement of defect detection in complex metallic structures, International Journal of Applied Electromagnetics and Mechanics, 19 (2004), 647–651. H.L. Libby, Introduction to electromagnetic non-destructive test methods, Roberty Krieger Publishing company, New York, 1979. J.P. Egan, Signal detection theory and ROC analysis, Series in cognition and perception, New York, Academic press, 1975. D. Horn and W.R. Mayo, NDE reliability gains from combining eddy-current and ultrasonic testing, NDT&E International, 33 (2000), 351–362.

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Author Index Abbasi, K. Abe, T. Aldrin, J.C. Altpeter, I. Andreescu, A. Ara, K. Baniukiewicz, P. Bennett, W. Bowler, J.R. Bowler, N. Bruma, A. Capova, K. Cardelli, E. Cawley, P. Cazacu, M.M. Chady, T. Chan, S.C. Chen, Z. Choi, D.-M. Choua, Y. Davis, C.L. Dixon, S. Dobmann, G. Dominguez, N. Duchêne, B. Edwards, R.S. Faba, A. Faktorová, D. Formisano, A. Gotoh, Y. Grimberg, R. Hao, X.J. Hashizume, H. Hopkins, P. Horikawa, N. Hübschen, G. Iftimie, N. Ike, H. Ito, S. Janousek, L. Jayakumar, T. Joubert, P.-Y. Jung, H.-S.

154 62 133 18, 54 257 37, 42 283 90, 98 203 203 249 271 195 141 257 276, 283 241 171 231 217 86 78 18, 54 217 225 78 195 162 195 26 241, 249, 257 86 154 90, 98 62 54 257 62 154 271 70 117, 125, 288 231

Kamada, Y. Kern, R. Kikuchi, H. Knopp, J.S. Kobayashi, S. Kopp, M. Koshika, T. Lambert, M. Le Bihan, Y. Le Diraison, Y. Lesselier, D. Liu, T. Marchand, C. Martone, R. Mason, J.S.D. Matsukawa, J. Miya, K. Morabito, F.C. Morozov, M. Morris, P.F. Nagy, P.B. Paillard, S. Papais, M. Pearson, N. Peyton, A.J. Pichenot, G. Pirani, A. Psuj, G. Rabung, M. Raj, B. Rajkumar, K.V. Rao, B.P.C. Ravat, C. Ricci, M. Romero Ramirez, A. Rubinacci, G. Sasi, B. Sato, T. Savin, A. Scruby, C.B. Shaw, B.A. Shin, Y.-K. Sikora, R.

37, 42 18 37, 42 133 37, 42, 46 54 42 217, 225 217, 288 117, 125 225 42 288 195 148 62 3, 171, 271 195 179, 187, 263 86 141 217 195 148 86 211, 217, 225 109 276, 283 54 70 70 70 288 109 148 179, 187, 263 70 62 241, 249, 257 10 90, 98 231 276, 283

296

Skarlatos, A. Specogna, R. Sposito, G. Steigmann, R. Strangwood, M. Takagawa, T. Takagi, T. Takahashi, N. Takahashi, S. Tamburrino, A. Tassin, A. Theodoulidis, T. Tian, G.Y. Tokuma, H.

225 195 141 249, 257 86 62 62 26 37, 42, 46 109, 179, 187, 195, 263 125 211 78 171

Trevisan, F. 195 Uchimoto, T. 62 Udpa, L. 241, 249 Udpa, S.S. 241, 249 Vaidhianathasamy, M. 90, 98 Vaidyanathan, S. 70 Ventre, S. 109, 179, 187, 195, 263 Versaci, M. 195 Villone, F. 179 Voillaume, H. 217 Wilson, J. 78 Wolter, B. 18 Yin, W. 86 Yusa, N. 171, 271

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