Electromagnetic Nondestructive Evaluation (X) (Studies in Applied Electromagnetics and Mechanics)

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ELECTROMAGNETIC NONDESTRUCTIVE EVALUATION (X)

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 28 Previously published in this series: 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. Vol. 11. Vol. 10. Vol. 9.

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 H. Tsuboi and I. Sebestyen (Eds.), Applied Electromagnetics and Computational Technology A.J. Moses and A. Basak (Eds.), Nonlinear Electromagnetic Systems T. Honma (Ed.), Advanced Computational Electromagnetics

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 (X)

Edited by

Seiki Takahashi Iwate University, Morioka, Iwate, Japan

and

Hiroaki Kikuchi Iwate University, Morioka, Iwate, Japan

Amsterdam • Berlin • Oxford • Tokyo • Washington, DC

© 2007 The authors. 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 978-1-58603-752-9 Library of Congress Control Number: 2007927275 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]

Distributor in the USA and Canada IOS Press, Inc. 4502 Rachael Manor Drive Fairfax, VA 22032 USA fax: +1 703 323 3668 e-mail: [email protected]

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 (X) S. Takahashi and H. Kikuchi (Eds.) IOS Press, 2007 © 2007 The authors. All rights reserved.

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Preface The 11th International Workshop on Electromagnetic Nondestructive Evaluation (ENDE) was held at the Hotel APPI Grand in Hachimantai-shi, Iwate, Japan, on June 14th–16th, 2006. The workshop was organized by NDE & Science Research Center, Faculty of Engineering, Iwate University, and financially supported and co-sponsored by Japan Society of Maintenology, the Iron and Steel Institute of Japan and the Japanese Society for Non-Destructive Inspection, and sponsored by the Japan Society of Applied Electromagnetics and Mechanics, the Institute of Electrical Engineers of Japan and the Magnetic Society of Japan. Following welcoming remarks by Prof. Seiki Takahashi, workshop chair, there were 46 presentations given at the workshop: 3 invited talks, 29 oral and 14 poster presentations. Three invited talks were given by Dr. Masaaki Kurokawa, Mitsubishi Heavy Industries Ltd., Prof. Anthony Moses, Cardiff University, and Dr. Gábor Vértesy, Hungarian Academy of Sciences. The workshop was organized into 9 oral sessions and 1 poster session: “ECT modeling” chaired by D. Lesselier, A. Tamburrino, “ECT Modeling and Simulation” chaired by G. Rubinacci, T. Takagi, “Eddy Current Testing” chaired by J. Pàvò, T. Theodoulidis, “New Methods” chaired by K. Ara, S. Udpa, “Industrial Applications”, Y. Tsuchida, T. Uchimoto, “NDE by Magnetism I” chaired by D.G. Park, G.Y. Tian, “NDE by Magnetism II” chaired by P. Novotný, S. Takahashi, “Inverse Problem” chaired by Z. Chen, L. Janousek, “Inverse Problem and Benchmark” chaired by G. Berthiau, F. Kojima. The workshop was concluded with closing remarks by Prof. Fumio Kojima. The main theme of the ENDE workshop has been on “Eddy Current Testing” to identify cracks in metals and alloys. Since the first ENDE workshop was held in London 1995, the seeing of workshops have contributed the technical advance in ECT through our competition and collaboration. ECT is put to practical use in industry now as one of the approved methods of crack detection in steels and metallic structures. We added the new topics in APPI meeting, i.e. magnetic NDE method according to the concept of NDE & Science Research Center. Two of three invited talks are on the magnetic NDE. Forty-eight participants were registered for this workshop from different parts all over the world; France, Italy, Hungary, China, Korea, UK, USA, Czech Republic, Germany, Greece, Poland, Slovakia and Japan. Short versions of all contributed papers have been published in the workshop abstracts, and 33 full papers were accepted after review and are published in “Electromagnetic Nondestructive Evaluation (X)” published by IOS Press in the series “Studies in Applied Electromagnetic and Mechanics.” We could concentrate our interest on the academic exchange and the sincere discussion for three days, since APPI is located in an out-of-the way place. All the participants enjoyed the beautiful green, fresh air, good taste water and the lovely concert. The workshop organizers gratefully acknowledge the financial support of the sponsors and would like to thank the session chairs and the participants. Thanks are also due to the members of the standing committee. The editors are truly thankful to

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referees listed below, especially regional editors, Professors G. Rubinacci, T. Takagi and S.S. Udpa. The next ENDE meeting will be held from June 19th to 21st 2007 in Cardiff under the auspices of Wolfson Center for Magnetics Technology, Cardiff School of Engineering, Cardiff University. Seiki Takahashi Iwate University Morioka, Iwate, Japan Workshop Chair and Co-Editor

Hiroaki Kikuchi Iwate University Morioka, Iwate, Japan Co-Editor

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List of Referees K. Ara – Iwate University, Japan K. Arunachalam – Michigan State University, USA J. Bowler – Iowa State University, USA N. Bowler – Iowa State University, USA Z. Chen – Xi’an Jiaotong University, China G. Dobmann – Fraunhofer-IZFP Institute, Germany M. Hashimoto – Polytechnic University, Japan H. Hashizume – Tohoku University, Japan Y. Kamada – Iwate University, Japan S. Kanemoto – Aizu University, Japan H. Kikuchi – Iwate University, Japan F. Kojima – Kobe University, Japan K. Koyama – Nihon University, Japan D. Lesselier – DRE-LSS CNRS-SUPÉLEC, Ecole Superieure d’ectricite, France C. Lo – Iowa State University, USA V. Melpaudi – Michigan State University, USA O. Mihalache – Japan Atomic Energy Agency, Japan A.J. Moses – Cardiff University, UK N. Nair – Michigan State University, USA J. Pávó – Budapest University of Technology and Economics, Hungary G. Pichenot – CEA/DRT/LIST/DETECS/SYSSC/LSM, Centre CEA de Saclay, France P. Ramuhalli – Michigan State University, USA A. Razek – LGEP CNRS-SUPÉLEC, Ecole Superieure, France G. Rubinacci – DIEL, Università degli Studi di Napoli Federico II, Italy M.J. Sablik – Southwest Research Institute, USA S.J. Song – Sung Kwan University, South Korea T. Takagi – Tohoku University, Japan S. Takahashi – Iwate University, Japan A. Tamburrino – DAEIMI, Università degli Studi di Cassino, Italy I. Tomáš – Institute of Physics, ASCR, Czech Republic Y. Tsuchida – Oita University, Japan T. Uchimoto – Tohoku University, Japan L. Udpa – Michigan State University, USA S.S. Udpa – Michigan State University, USA G. Vértesy – Hungarian Academy of Sciences, Hungary F. Villone – Università degli Studi di Cassino, Italy N. Yusa – International Institute of Universality, Japan Z. Zeng – Michigan State University, USA

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Editors S. Takahashi – Iwate University H. Kikuchi – Iwate University

Regional Editors G. Rubinacci – Universita di Napoli Federico II, Italy T. Takagi – Tohoku University, Japan S.S. Udpa – Michigan State University, USA

Standing Committee G. Rubinacci – Universita di Napoli Federico II, Italy R. Albanese – Universita Reggio Calabria, Italy J. Bowler – Iowa State University, USA N. Bowler – Iowa State University, USA G. Dobmann – Fraunhofer Institute for NDT, Germany R. Grimberg – National Institute of R&D for Technical Physics, Romania H.K. Jung – Seoul National University, South Korea F. Kojima – Kobe University, Japan D. Lesselier – DRE-LSS CNRS-SUPELEC-UPS, France V. Lunin – Moscow Power Engineering Institute, Russia K. Miya – Keio University, Japan G.Z. Ni – Zhejing University, China J. Pávó – Budapest University of Technology and Economics, Hungary A. Razek – LGEP CNRS-SUPELEC-UPS-UPMC, France T. Sollier – CEA Paris, France T. Takagi – Tohoku University, Japan S. Takahashi – Iwate University, Japan L. Udpa – Michigan State University, USA S.S. Udpa – Michigan State University, USA V. Vengrinovich – Institute of Applied Physics, Belarus

Organizing Committee S. Takahashi, Workshop Chairman – Iwate University T. Takagi – Tohoku University F. Kojima – Kobe University Y. Ogura – Japan Probe Co., Ltd. T. Imanaka – Iwate University M. Kurokawa – Mitsubishi Heavy Industries, Ltd. N. Sato – Asahi Kasei Engineering Co., Ltd. K. Ara – Iwate University Y. Kamada – Iwate University H. Kikuchi, Secretariat – Iwate University S. Kobayashi – Iwate University

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List of Participants Mr. Kavoos Abbasi Department of QSE, Tohoku University, Japan Dr. Katsuyuki Ara NDE & SRC, Faculty of Engineering, Iwate University, Japan Dr. Hossein Bayani Department of Applied Science for Electronics and Materials, Kyushu University, Japan Dr. Gérard Berthiau Research Institute in Electrotechnology and Electronics of Nantes Atlantique, France Dr. Pierre Calmon CEA-LIST, France Prof. Zhenmao Chen School of Aearospace, Xian Jiaotong University, China Dr. Weiying Cheng NDE Center, Japan Power Engineering and Inspection Corporation, Japan Prof. Masato Enokizono Faculty of Engineering, Oita University, Japan Dr. Szabolcs Gyimóthy Budapest University of Technology and Economics, Hungary Dr. Yusuke Imai National Institute of Advanced Industrial Science and Technology, Japan Dr. Satoshi Ito Department of QSE, Grad. School of Eng., Tohoku University, Japan

Dr. Ladislav Janousek Department of Electromagnetic and Biomedical Engineering, Faculty of Electrical Engineering, University of Zilina, Slovakia Dr. Yuichiro Kai Faculty of Engineering, Oita University, Japan Dr. Yasuhiro Kamada NDE & SRC, Faculty of Engineering, Iwate University, Japan Dr. Hiroaki Kikuchi NDE & SRC, Faculty of Engineering, Iwate University, Japan Dr. Satoru Kobayashi NDE & SRC, Faculty of Engineering, Iwate University, Japan Prof. Fumio Kojima Graduate School of Science and Technology, Kobe University, Japan Dr. Masaaki Kurokawa Mitsubishi Heavy Industries, Ltd., Japan Dr. Ken Kurosaki Division of Sustainable Energy and Environmental Engineering, Graduate School of Engineering, Osaka University, Japan Prof. Jinyi Lee Department. of Inf., Cntl and Inst./Chosun University, South Korea Dr. Dominique Lesselier Laboratoire des Signaux et Systemes – Departement de Recherche en Electromagnetisme, France

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Prof. Luming Li Aerospace School, Tsinghua University, China

Prof. Seiki Takahashi NDE & SRC, Faculty of Engineering, Iwate University, Japan

Dr. Ovidiu Mihalache Japan Atomic Energy Agency, Fast Breeder Reactor Research and Development Center, Japan

Prof. Tokuo Teramoto Graduate School of Systems & Information Engineering, University of Tsukuba, Japan

Dr. Kenzo Miya Japan Society of Maintenology, Japan

Prof. Theodoros Theodoulidis Department of Electrical Engineering/Technological Educational Institute of West Macedonia, Greece

Prof. Anthony Moses Wolfson Centre for Magnetics Technology, School of Engineering, Cardiff University, Wales, UK Dr. Pavel Novotný Institute of Chemical Technology Prague, Czech Republic Dr. Toshihiro Ohtani Ebara Research Co. LTD, Japan Dr. Duck-Gun Park KAERI, South Korea Dr. József Pávó Budapest University of Technology and Economics, Hungary Dr. Stéphane Perrin IIU, Japan Dr. Gregoire Pichenot CEA, France Dr. Madalina Pirlog Materials Characterization/Fraunhofer-Institut IZFP, Germany Prof. Guglielmo Rubinacci Dipartimento di Ingegneria Elettrica, Università degli Studi di Napoli Federico II, Italy Prof. Toshiyuki Takagi Institute of Fluid Science, Tohoku University, Japan

Prof. Gui Yun Tian School of Electrical, Electronic and Computer Engineering, Newcastle University, UK Dr. Haiyan Tian Institute of Fluid Science, Tohoku University, Japan [email protected] Prof. Masaaki Tsushima Iwate University, Japan Prof. Hajime Tsuboi Department of Information Engineering, Fukuyama University, Japan Dr. Yuji Tsuchida Faculty of Engineering, Oita University, Japan Prof. Antonello Tumburrino DAEIMI, Italy Dr. Tetsuya Uchimoto Institute of Fluid Science, Tohoku University, Japan Prof. Lalita Udpa Department of Electrical and Computer Engineering, Michigan State University, USA Prof. Satish Udpa Department of Electrical and Computer

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Engineering, Michigan State University, USA Dr. Gábor Vértesy Hungarian Academy of Sciences, Research Institute for Technical Physics and Materials Science, Hungary Prof. Shinsuke Yamanaka Division of Sustainable Energy and

Environmental Engineering, Graduate School of Engineering, Osaka University, Japan Mr. Tomoharu Yasutake Department of Electrical and electronic Engineering, Graduate School of Engineering, Oita University, Japan

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Contents Preface Seiki Takahashi and Hiroaki Kikuchi

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List of Referees

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Organization

viii

List of Participants

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Invited Talks Inspection Experience of Steam Generator Tubes with Intelligent ECT Probe Masaaki Kurokawa

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Origin, Measurement and Application of the Barkhausen Effect in Magnetic Steel Anthony J. Moses and David C. Jiles

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A New Initiative: Universal Network for Magnetic Non-Destructive Evaluation Gábor Vértesy

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ECT Modeling and Simulation Skin and Proximity Effects in ECNDT Sensors Vincent Doirat, Gérard Berthiau, Javad Fouladgar and Anthony Lefevre

13

Eddy Current Modelling for Inspection of Riveted Structures in Aeronautics S. Paillard, G. Pichenot, M. Lambert and H. Voillaume

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Numerical Modeling of a Phase Sensitive Eddy Current Imaging System Guglielmo Rubinacci, Antonello Tamburrino, Salvatore Ventre, Pierre-Yves Joubert and Jean Pinassaud

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Developments in Modelling Eddy Current Coil Interactions with a Right-Angled Conductive Wedge Theodoros Theodoulidis, Nikolaos Poulakis and John Bowler Volumetric and Surface Flaw Models for the Computation of the EC T/R Probe Signal Due to a Thin Opening Flaw Léa Maurice, Denis Prémel, Jozsef Pàvò, Dominique Lesselier and Alain Nicolas Application of Eigenfunction Expansions to Eddy Current NDE: A Model of Cup-Cored Probes Hossein Bayani, Theodoros Theodoulidis and Ichiro Sasada

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49

57

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Eddy Current Testing and Technique Experimental Extraction of Time-of-Flight from Eddy Current Test Data Antonello Tamburrino, Naveen Nair, Satish Udpa and Lalita Udpa

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A Probe Array for Fast Quantitative Eddy Current Imaging Carmine Abbate, Maxim Morozov, Guglielmo Rubinacci, Antonello Tamburrino and Salvatore Ventre

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Superposition of Several Phase-Shifted Exciting Fields for Crack Evaluation Ladislav Janousek, Noritaka Yusa and Kenzo Miya

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Automatic Discrimination of Stress Corrosion and Fatigue Cracks Using Eddy Current Testing Stéphane Perrin, Noritaka Yusa and Kenzo Miya

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Conductivity and Permeability Evaluation on Type IV Damage Investigation by Electromagnetic Method Haiyan Tian, Tetsuya Uchimoto, Toshiyuki Takagi and Yukio Takahashi

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Industrial Applications and New Methods Evaluation of Fatigue Loaded Conducting Structures Using Selected Electromagnetic NDT Methods Tomasz Chady, Ryszard Sikora, Grzegorz Psuj, Przemysław Łopato, Masato Enokizono and Yuji Tsuchida Evaluation of Circumferential Crack Location in Pipes by Electromagnetic Waves Kavoos Abbasi, Satoshi Ito, Hidetoshi Hashizume and Kazuhisa Yuki Inspection of Cement Based Materials Using Microwaves Kavitha Arunachalam, Vikram R. Melapudi, Lalita Udpa and Satish S. Udpa Defect Profiling Using Multi-Frequency Eddy Current Data from Steam Generator Tubes Kavitha Arunachalam, Oseghale Uduebho, Ameet Joshi, Shiva Arun Kumar, Lalita Udpa, Pradeep Ramuhalli, Satish S. Udpa and James Benson Electromagnetic Reading of Laser Scribed Logistic Markers on Metallic Components Szabolcs Gyimóthy, József Pávó, Imre Kiss, Antal Gasparics, Zoltán Kalincsák, Imre Sebestyén, Gábor Vértesy, János Takács and Hajime Tsuboi Design of a Remote Field Eddy Current Probe Dedicated for Inspection of a Magnetic Tube from Its Outer Surface Tomas Marek, Daniela Gombarska, Ladislav Janousek, Klara Capova, Noritaka Yusa and Kenzo Miya

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117 125

131

139

147

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Application of Thermoelectric Power Measurement to Nondestructive Testing Shinsuke Yamanaka, Yasuhiro Kawaguchi, Toshihiro Ohtani and Ken Kurosaki

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NDE by Magnetism and Magnetics Accurate Detection of Material Degradation of Stainless Steel by ECT Sensor Tokuo Teramoto Micromagnetic Characterization of Thermal Degradation in Cu-Rich Alloys and Results of Neutron-Irradiation Madalina Pirlog, Iris Altpeter, Gerd Dobmann, Gerhard Hübschen, Melanie Kopp and Klaus Szielasko

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Challenges in Quantifying Barkhausen Noise in Electrical Steels Anthony J. Moses, Harshad V. Patel and P.I. Williams

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Magnetic Adaptive Testing: Influence of Experimental Conditions Gábor Vértesy, Tetsuya Uchimoto, Toshiyuki Takagi and Ivan Tomáš

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Magnetic and Acoustic Barkhausen Noise for the Characterisation of Tensile Deformation and Stresses in Steel Gui Yun Tian, John Wilson and Jiri Keprt

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Electromagnetic Acoustic Resonance to Assess Creep Damage in a Martensitic Stainless Steel Toshihiro Ohtani

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NDE Method Using Minor Hysteresis Loops in Ferromagnetic Materials Seiki Takahashi, Satoru Kobayashi, Yasuhiro Kamada, Hiroaki Kikuchi and Katsuyuki Ara Investigation of Neutron Radiation Effects on Fe Model Alloys by Minor-Loop Analysis Satoru Kobayashi, Hiroaki Kikuchi, Seiki Takahashi, Katsuyuki Ara and Yasuhiro Kamada

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Numerical Analysis for Non-Destructive Evaluation of Hardening Steel Taking into Account Measured Magnetic Properties Depending on Depth Yuichiro Kai, Yuji Tsuchida and Masato Enokizono

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Development of Metal Detection System for Reuse of Dismantled Wood from Houses Tomoharu Yasutake, Tomasz Chady, Yuji Tsuchida and Masato Enokizono

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Inverse Problem and Benchmark Nondestructive Evaluation for Material Degradation of Steel Sample Using Minor Hysteresis Loop Observations Fumio Kojima and Ryou Nishiyama Identification of Defects from ECT Signals Using Linear Discriminant Function Weiying Cheng, Shigeru Kanemoto and Ichiro Komura

243 251

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Sizing of Volumetric Stress Corrosion Crack from Eddy Current Testing Signals with Consideration of Crack Width Zhenmao Chen, Noritaka Yusa and Kenzo Miya Reconstruction of Fatigue Cracks Using Benchmark Eddy Currents Signals Maxim Morozov, Guglielmo Rubinacci, Salvatore Ventre and Fabio Villone

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2D Axisymmetric ECT Simulation of the World Federation’s First Eddy Current Benchmark Problem Ovidiu Mihalache, Masashi Ueda and Takuya Yamashita

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Author Index

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Invited Talks


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Inspection Experience of Steam Generator Tubes with Intelligent ECT Probe Masaaki KUROKAWA Takasago R/D Center, Mitsubishi Heavy Industries, Ltd., Japan

An intelligent ECT probe was developed to perform a high speed and accurate inspection of SG tubes. The probe consists of an ordinary bobbin probe and a newly developed thin-film probe in which nine to twelve drive coils and pick-up coils are arrayed along the circumferential outer surface of the probe to face the inner surface of the SG tube. This multi-coil system can carry out high-performance flaw detection without probe rotation. Field tests were experienced in Japan, USA and Taiwan, and the intelligent ECT technique was qualified by the Japanese regulatory authority in August ’03, and has been adopted for actual inspection since December ’03 in 13 units in total. The total number of inspected tube has reached about 120,000 in Japan. After field tests in USA and Taiwan, the intelligent ECT technique obtained EPRI Appendix H qualification of the residual damage mechanisms and was selected to perform all tube inspection with full length in Taiwan. (summarized by reviewer, K. Ara)

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Origin, Measurement and Application of the Barkhausen Effect in Magnetic Steel a

Anthony J. MOSESa and David C. JILESa Wolfson Centre for Magnetics, Cardiff University, Wales, UK

Introduction The magnetic Barkhausen effect was discovered towards the beginning of the last century [1] but its origin and interpretation is still open for debate. It is generally accepted to be due mostly to microscopic discontinuities in domain wall motion due to the presence of defects. Various methods of measurement have been developed although quantification of results obtained using different sensor approaches is tenuous. The phenomenon is very sensitive to internal stress and microstructure and the direct correlations found between such parameters and Barkhausen emissions has made it a useful tool in Non Destructive Evaluation (NDE). Today we have more powerful data collection and analyzing systems which, combined with sensors capable of accurate measurements, gives us the opportunity to exploit the effect in a broader field of applications This paper reviews the origin of the effect and challenges in its measurement and interpretation. Applications of the Barkhausen effect, particularly in magnetic steels, are then briefly discussed.

1. Origin of Barkhausen Noise The Barkhausen noise (BN) is produced in a magnetic material while its magnetization is being changed. There are several contributing factors to Barkhausen effect emissions and these include: domain wall motion, domain rotation, domain nucleation and annihilation. The effect is largely due to interaction of moving domain walls with defects in the material. This action produces time varying irregularities in the shape and instantaneous velocity of walls on a microscopic scale. The associated flux change within the material in turn causes small electromotive forces (emfs) to be randomly generated. This is usually schematically illustrated as discontinuities in the B-H curve of the material [2]. In fact the Barkhausen emissions have both deterministic and stochastic components [3], and it is the irreproducibility and randomness of the stochastic component that causes the most difficulty in describing Barkhausen effect using a theoretical model. Early workers were able to estimate the magnetization changes due to single Barkhausen jumps from the size of emf pulses produced during BN activity and

A.J. Moses and D.C. Jiles / Origin, Measurement and Application of the Barkhausen Effect

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concluded reversals were occurring in volumes in the nanometer range [4] It is interesting to note that Weiss [5] effectively predicted the existence of domains in 1907, Barkhausen published his experimental results in 1918 but apart from indirect evidence from emf.s induced in coils embracing magnetic wires and rods containing large moving domain walls, the existence of domains was not confirmed until the powder pattern work of workers such as Hámas and Thiessen [6] and by Bitter [7] in the early 1930’s. The discontinuities were attributed to rotation of magnetization within a domain but now it is accepted that the discontinuous domain boundary motion is the most significant effect [3, 8]. Energy is dissipated at the time of a Barkhausen jump. It is normally assumed that this event takes place on a time scale over which the applied field does not vary significantly so it is independent of the field rate of change [9]. From this it might be assumed that the BN per cycle, although non-repeatable from cycle to cycle, does not depend on the magnetization frequency, i.e. it is frequency independent. In practice BN does vary with magnetizing frequency [10] simply because domain activity, such as bowing, nucleation, annihilation, etc themselves vary with frequency. Therefore the area of domain walls interacting with an individual dislocation varies with frequency and hence the BN per cycle increases with frequency far more than would be expected just from its stochastic nature. It is also possible that when clusters of submicron domains are redistributed during the magnetization process they cause BN like emissions which add to the static BN, effectively meaning the process comprises a nano-scale frequency independent component and a micro scale frequency dependent component Some correlation has been found between BN measured in electrical steel magnetized at 50 Hz and static hysteresis loss obtained by extrapolating curves of loss per cycle against frequency to zero frequency. A linear increase in BN with hysteresis loss of non-oriented steels endorses this finding and suggests the phenomena have similar origins. 2. Measurement of Barkhausen Noise An emf is induced in a search coil wound around a magnetized sample due to the internal flux changes that constitute the BN. The effect is conveniently demonstrated by connecting a loud-speaker via an amplifier to such a coil and listening to the acoustic noise output as the magnetizing field is slowly changed. The emf is small so it is a challenge not only to accurately measure it but also to ensure that what is measured is due solely to BN. For example, because BN is stochastic in nature, it is important to distinguish it from other forms of radiated or conducted noise in the measurement system. The BN has mostly been studied at very low frequency (at exciting field frequencies of less than 5 Hz). However now there is more attention being placed on higher frequency measurements because of its potential for indirect assessment of the characteristics of electrical steels at power frequency. In either case the Barkhausen signal is captured within a given frequency bandwidth typically around 3 kHz to 300

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kHz to avoid high and low frequency noise errors. Some BN signal is undoubtedly lost this way but it is not believed to be a significant factor in interpreting or practically using the phenomenon since most BN activity occurs in this region. When the enwrapping search coil method of measurement is used under A.C. magnetizing conditions the BN emf must be separated from the normal Faraday emf whose magnitude, at 50 Hz, is more than a thousand times higher than the average BN signal. A convenient way of eliminating the Faraday emf is to connect two search coils in series opposition so their output voltage ideally is just due to BN. The signals induced in the coils are very similar when the coils are placed very near to each other whereas a progressive decrease of their correlation occurs when the coils are moved apart [11]. Recent improvements in digital technology, particularly with data acquisition cards, make the AC measurements accurate and more convenient to process and analyze. Questions over the necessary specification of magnetization waveform quality and data sampling rate still need to be considered. Typically AC BN signals are captured at rates of 100-200 kHz and there is no advantage in using higher values since under constant magnetizing conditions the measured BN becomes constant at higher frequencies [12]. The IEC standard for single sheet testing of electrical steel stipulates that the form factor of the secondary induced voltage should be maintained to within ±1 % of 1.11 to ensure sufficiently accurate magnetic measurement. However, for Barkhausen noise measurements this is not sufficient since even this small deviation from a perfect controlled sinusoidal flux density is sufficient to cause poor repeatability of the measured BN. Incorporating digital feedback into the measurement system to reduce the form factor variance to within ±0.01 % of 1.11 results in a significant improvement for Barkhausen analysis. There are several ways in which the BN signal can be analyzed. Today data acquisition systems can be used to analyze a signal in terms of an average value, its RMS value, a power spectrum, summation of BN peaks, etc. It is impossible to relate any of these quantities directly to the number of BN events occurring in any particular region of a test sample but they do all normally follow similar trends as magnetizing field or frequency is changed or when one sample is compared with another. Other methods which have been found to be useful in interpreting Barkhausen noise data include the mean, standard deviation, pulse height distribution, and FFT [13]. An alternative method for Barkhausen measurement is to use a wound ferrite core whose detection coil axis is placed perpendicular to the surface of the sample [14]. The ferrite core essentially acts as a magnetic amplifier of the Barkhausen signal induced in the coil. A localized BN measurement can be made or the complete surface of a steel sample can be scanned. Other high initial permeability materials such as amorphous alloys have been successfully demonstrated as the probe core [15]. The magnitude of the detected BN signal depends on the core dimensions and permeability as well as the number of coil turns but it is interesting that the variation of BN obtained using probes follows similar treads to those found using enwrapping search coils in the same region of a specimen under the same magnetizing conditions.


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Other methods reported for measuring Barkhausen noise include the use of a commercial magnetic head sensor [16] and a commercial system supplied by Stresstech Inc, the Rollscan 200-1 [17].

3. Applications The BN effect has been used in many NDE applications already [18] and competes strongly with ultrasound and eddy current testing in many cases. Its sensitivity to microstructure including dislocations, and grain boundaries are the basis for its use in internal stress and hardness measurement. It’s potential for use in assessment of indepth properties such as in case hardening has been demonstrated widely. There are many opportunities for fully exploiting BN measurements and analysis as a competitive NDT tool. However, more research is necessary to assess its full potential in studies of magnetic steels under AC magnetization. It is a strong candidate for use in measurement of magnetic properties such as power loss and physical properties such as localized regions of irregular grain structures or mechanical hardness of such materials where other techniques are difficult to apply or do not produce sufficient information.

4. Conclusions In conclusion, although there are many factors which contribute to BN it has been found to correlate closely with mechanical stress and microstructure. The various sensing techniques used to detect BN picks up different features of the phenomena. BN measurement at power frequency in electrical steel may help in obtaining a better understanding of loss processes and surface imperfections which affect the magnetic properties. The BN signal is rich in information and undoubtedly reflects many aspects of the magnetizing process [9]. Better knowledge of its underlying features may lead to greater understanding of effects of material parameters on magnetizing processes which in turn may lead to improved magnetic materials as well as identifying further applications of BN in NDE.

References [1] H.Barkhausen, Two phenomena uncovered with help of the new amplifiers Phys Z., 20, (1919), 401-3 [2] D.Jiles, Introduction to magnetism and magnetic materials, Second edition, Chapman and Hall, London, 1998. [3] D.C.Jiles, Dynamics of domain magnetization and the Barkhausen effect, Czechoslovak Journal of Physics, 50, 893, 2000. [4] E.P.T.Tyndall, The Barkhausen effect, Phys. Rev., 24, (1924) 439-51 [5] P.Weiss, Hypothesis of the molecular field and ferromagnetic properties, J. Phys., [4], 6, (1907), 661-90 [6] L.Hámos and P.A. Thiessen, Making visible the regions of different magnetic states in solid bodies, Z. Physik, 71, (1931), 442-4

8


[7] F.Bitter, On homogeneities in the magnetization of ferromagnetic materials, Phys. Rev., 38, (1931), 1903-5 [8] K.Schroeder and J.C.McClure, The Barkhausen effect, CRC Critical Reviews of Solid State Science, 6, 45, (1976), 45 [9] G.Bertotti, Hysteresis in magnetism, Academic Press, San Diego, 1998 [10] A.J.Moses, F.J.G.Landgraf, K.Hartmann and T.Yonamine, Correlation between angular dependence of A.C. Barkhausen noise and hysteresis loss in non-oriented electrical steel, Stahleisen, (2004), 215-9 [11] E.Puttin, M.Zani, and A Ventura, A double coil apparatus for Barkhausen noise measurement, Rev. Sc. Instrum.,72, (4), (2001) [12] B.Zhu, M.J.Johnson, C.H.Lo and D.C.Jiles, Multifunctional magnetic Barkhausen emission measurement system, IEEE Trans. Magn., 37, (3), (2001), 1095-1099 [13] H.V.Patel, A.J.Moses and P.I.Williams, The dependence of AC Barkhausen noise measurement on data acquisition parameters Proc. of 9th Int. Workshop on 1 and 2 Dimensional Magnetic Measurements and Testing Czestochowa ,Poland, (2006), 68-69 [14] D.M.Stewart, K.J.Steven, and A.B.Kaisser, Magnetic Barkhausen noise analysis of stress in steel, Current Applied Phys., 4, (2004), 308-311 [15] J.Pal’a, J.Bydzovsky, and P.Svec, Influence of magnetising frequency and construction of pick-up coil on Barkhausen noise, J. of Electrical Eng., 55, No 10/S, (2004), 38-40 [16] A.J.Perez-Benitez, L.R. Padovese, J.Capo-Sanchez, and J.Anglada-Rivera, J Investigation of the magnetic Barkhausen noise using elementary signals parameters in 1000 commercial steel, J. Mag. Magn. Mater. 263 (2003) 72-77 [17] M.Lindgren and T.Lepisto, Effect of cyclic deformation on Barkhausen noise in a mild steel, NDT&E International 36 (2003) 401-409. [18] D.C. Jiles, Review of magnetic methods for nondestructive evaluation, NDT International, 21, 311, 1988.


9

A new initiative: Universal Network for Magnetic Non-destructive Evaluation Gábor VÉRTESY Research Institute for Technical Physics and Materials Science, Hungarian Academy of Sciences H-1525 Budapest, P.O.B. 49, Hungary

Objective Magnetic measurements are suitable for characterization of changes in structure of ferromagnetic materials, because their magnetization processes are closely related to the microstructure of the materials. This fact also makes magnetic measurements an evident candidate for non-destructive testing, for detection and characterization of any modification and/or defects in materials and manufactured products made of such materials. Structural non-magnetic properties of ferromagnetic materials have been non-destructively tested by several magnetic methods for a long time with fair success. However, the application of magnetic methods in everyday nondestructive inspection practice is not satisfactory. Because if this an informal network of many research workers in many countries all over the World, interested in this area, has been organized on Prof. Seiki Takahashi’s (Iwate University) initiative (http://www.ndesrc.eng.iwate-u.ac.jp/UniversalNetwork/). Main goal of the Universal Network is to concentrate research power in this important area, to improve efficiency of the information exchange, to prove applicability of magnetic ND methods, to develop new methods, to investigate theoretically the observed phenomena, to find new application possibilities, to fasten cooperation with industrial companies, to organize workshops for experts in this area and to organize new projects for introduction of magnetic methods into industrial application. The main research directions are to clarify and quantify the relationship between microstructure and magnetism in materials and to investigate and develop in-situ magnetic inspection techniques for quantitative nondestructive evaluation of components and structures including: i) Methods for evaluating performance-related properties of materials from their structure-sensitive magnetic properties, ii) New techniques and instrumentation for evaluation of material condition using magnetic properties and iii) Models for description of magnetic properties and their dependence on structure. NDE of steel degradation before any crack initiation would be one of the targets in Universal Network concerning nuclear plants, thermal electric plants, chemical plants, mass transportation, bridges and gas pipelines.

10

G. Vértesy / A New Initiative: Universal Network for Magnetic Non-Destructive Evaluation

Methods A large number and quite different methods exist in this area. They are the following: Magnetic hysteresis loop measurements (including classical methods and the recently developed minor-loop analyzing method (MAM) and Magnetic Adaptive Testing (MAT)), Barkhausen noise measurement, magnetic acoustic emission (MAE), micromagnetic, multiparameter, microstucture and stress analysis (3MA), magnetic flux leakage measurements, combination of conventional eddy current technique with magnetic field measurement, magnetooptical methods, magnetostrictive delay line technique and classic low frequency ac magnetometry. Planned Projects Pressure Vessel The age degradation in pressure vessels is one of the most important and urgent problems in the world. No NDE methods exist for the ductile-brittle transition. Magnetic method seems to be an effective and good solution for this problem. However only few magnetic data, concerned with neutron irradiation, exist. Within this project the facilities of Halden reactor are going to be used. Measurements before and after neutron irradiation are planned to be performed. Among magnetic measurements Barkhausen noise, hysteresis loops measurement (MAT, MAM), magnetic acoustic emmission, microstucture and stress analysis will be performed, together with the investigation of mechanical properties (Vickers hardness, tensile deformation, Charpy impact test). Defects (precipitates, dislocation loops, vacancies, interstitial, void (neutron irradiation damages) will also be studied. Degradation of Gas Pipelines, Railways, Bridges and Other Steel Constructions The aim and methods of this project is similar to the previous one, but its target is to study age degradation in low carbon steels by magnetic NDE and to observe defects (dislocations and micro-cracks induced by metal fatigue test and tensile deformation) by magnetic methods. TEM, SEM, FMM and other observations will also be performed. Standardization of Magnetic Properties The aim of the project is: standardization of magnetic properties connected with degradation in steels. Fundamental study will be performed on the relationships between magnetic properties and defects. Urgency of this project is motivated by the fact that only few models exist, which are proved theoretically as well as experimentally, and frequently experimental data depend on the investigators. It means that we need a standardized data base of the magnetic properties. We want to compose the quantitative relationships between them depending on the standard data and give the physical meaning to the relationships. The project has already started, three series of round robin samples have been prepared, which are now being circulated among the participating laboratories. The same series of samples (prepared and distributed according an agreed time-table and order) were, are or will be measured by each lab within the network. Each member performs his own measurements by use of the same samples and all the measuring results will be compared.

ECT Modeling and Simulation



13

Skin and Proximity Effects in ECNDT Sensors DOIRAT Vincent a , BERTHIAU Gérard a,1 , FOULADGAR Javad a , LEFEVRE Anthony a a 37 Bd de l’université, BP 406, 44602 Saint Nazaire, France Abstract. A semi-analytical forward model based on the electromagnetic coupled circuits method is presented. This model allows to simulate the impedance variation of a ferrite-cored sensor above a controlled material. The computational speed is increased by determining the current density in coil using the Kelvin analytical distribution. This forward model provides a good accuracy with respect to experimental measurements.

1. Main Objectives ECNDT is generally used in such frequency domain that intrinsic skin and proximity effects of the sensor are rather important (freq. between 100Hz and some MHz). Most of well-used models do not consider these effects which can change considerably the impedance of the sensor [1,2]. Using Finite Element Method (FEM) in nodal formulation does not well evaluate the potential gap due to the ferrite core of the sensor. In edge element formulation, there is an increased number of unknowns and it is heavier to proceed. Semi-analytical Dodd & Deeds’ formulation [3] is fast and accurate but does not take into account neither the skin and proximity effects nor the presence of ferritic core. In this paper, we propose therefore a semi-analytical forward model which takes into account these phenomena. Our axisymmetrical model is based on the Coupled Circuits Method (CCM) [4]-[7] which allows to determine the sensor impedance. As this model is fast-running, we can use it in an inversion process in order to calculate the lift-off distance between the probe and the controlled plate and/or the material conductivity. For the probe discretization, we propose a formulation which largely reduces the number of unknowns without accuracy degradation.

2. Model Description The CCM is used to solve axisymmetric configurations. The sensor is constituted of a ferrite core and a bobbin with N w wires. The bobbin is supplied by a sinusoidal current with constant amplitude (I bob ) and pulsation (ω). That sensor is above a metallic plate (μ = μ0 ,σ). The CCM consists in associating the integral form of the solution to a sub1 Corresponding Author: Gérard Berthiau, 37 Bd de l’université, BP 406, 44602 Saint Nazaire, France; Email: [email protected]

14

V. Doirat et al. / Skin and Proximity Effects in ECNDT Sensors

division in elementary coils. The unknowns are the current densities in the different parts of the system (Q ⇒Bobbin, K ⇒Ferrite and P ⇒Plate). To determine these unknowns, material (Bobbin+Ferrite+Load) are discretized in elementary loops with constant current densities [6]. The ferrite core is discretized only on the surface Fig. 1)[7,8]. Each Axis of symmetry Bobbin (σ)

Ferrite (μ)

Only sector discretization

Layer and sector discretization

Load (σ, μ)

Lift-off

Figure 1. System discretization.

Axis of symmetry M

b Sb

a

R2

c

i2

i1

L2

L1

R1

U1

Discretization 1

Discretization 2 Sa

Figure 2. Equivalent circuit for two discretizations.

Bobbin

Ibob

Ubob

Wire Nw

Wire 2

Wire 1

RB1,1

LB1,1

RB1,2

LB1,2

Q1,1 Q1,2

RB2,1

LB2,1

RB2,2

LB2,2

RB2,Ndw

LB2,Ndw

Q2,1

RBNw ,1

LBNw ,1

Q2,2

RBNw ,2

LBNw ,2

QNw ,1 QNw ,2

MB12 ,B1Ndw RB1,Ndw

LB1,Ndw U1

RL1

LL1

RL2

LL2

RLNdc

LLNdc Load

Q1,Ndw

MB1Ndw ,L1

MB2Ndw ,BNw Ndw

U2 LF1

K1

P2

LF2

K2

PNdc

LFNdf

P1

Ferrite

KN df

• • • • • • • • • •

RBNw ,Ndw LBNw ,Ndw

Q2,Ndw

Nw Ndw Ndl Ndf Qi,j Ki Pi L R M

: : : : : : : : : :

QNw ,Ndw

UNw

Number of wires in a bobbin Number of discretizations in a wire Number of discretizations in the load Number of discretizations in the ferrite Constant current density in the (i, j)th Bobbin discretization Constant current density in the (i)th Ferrite discretization Constant current density in the (i)th Load discretization Self inductance of a discretization Resistance of a discretization Mutual inductance between two discretizations

Figure 3. Equivalent electrical scheme.


15

elementary loop is in magnetic interaction with itself and with the other ones. The interaction between two loops can be explained with the electric transformer model (Fig. 2). The resistances (R1 , R2 ), self inductance (L 1 , L2 ) and mutual inductance (M ) depend on the geometrical parameters (a, b, S a , Sb , c) and physical characteristics (σ, μ) of the discretization. Our discretization system is an extension of this electric transformer model. So, the coils inductive components are computed according to the equivalent electrical scheme (Fig. 3)– all the mutual inductances are not represented to increase clarity. The magnetic component of the bobbin is constituted by the summation of the self inductances and all the mutual inductances for each discretization element. For the bobbin’s resistance, we determine the active power in the complete system in order to get a better accuracy than with the Ohm’s law. 2.1. Skin Effect in a Cylindrical Wire We aim at determining the current density distribution Q(r) in the cylindrical wire, with external radius R, depending on the distance from the axis r : H=

1 r

r

Q(x)x dx

(1)

0

Differentiating (1) with respect to the radius r and using the Maxwell-Faraday’s law, we obtain : d2 Q 1 dQ + − jωσμQ = 0 dr2 r r.

(2)

where ω is the angular frequency, μ the magnetic permeability and σ the electrical conductivity. With k 2 = ωσμ, (2) can be written as a differential equation (3), the general solution of which is a linear combination of zero-order Bessel function (4): d2 Q 1 dQ + − jk 2 Q = 0 dr2 r r.

(3)

Q = AJ0 (k r j 3/2 ) + BK0 (k r j 1/2 )

(4)

where J0 is the zero order Bessel function and K 0 the zero order modified Bessel function. Considering the boundary conditions and the phase origin at the conductor surface (R : external radius), (4) becomes the Kelvin distribution [9,10]: Q(r) = Q0

M0 (k r) j θ0 (k r) e M0 (k R)

(5)

where M0 (X) is the modulus of J 0 (X j 3/2 ), θ0 (X) the angle and Q 0 the current density M0 (k r) on the surface of the wire. Q 0 M represents the current density magnitude in the 0 (k R) conductor. The Kelvin distribution is used in this work to reduce the discretization number of the bobbin (section 3). Fig. 4 and Fig. 5 present the ratio of inner current density to surface current density r versus the normalized radius ( R ). The higher are the frequencies, the more important is

16

V. Doirat et al. / Skin and Proximity Effects in ECNDT Sensors 1

1 25 kHz

0.9 0

Normalized current density |Q(r)/Q |

Normlized current density |Q(r)/Q0|

0.9 0.8 0.7

50 kHz

0.6 0.5 100

kHz

0.4 0.3 0.2 0.1 0 0

200

kHz

300

kHz

400 kHz 0.4 0.6 Normalized Radius r/R

50 kHz

0.8 0.7

200 kHz

0.6 0.5

300 kHz

0.4

400 kHz

0.3

500 kHz

0.2 0.1

500 kHz 0.2

25 kHz 100kHz

0.8

0 0

1

Figure 4. Outer Radius R = 0,5mm.

0.2

0.4 0.6 Normalized Radius r\R

0.8

1

Figure 5. Outer Radius R = 0,25mm.

the skin effect. Consequently, as ECNDT works on high frequencies (some 100kHz), the sensor impedance evaluation must take into account the skin effect because it generates an increasing variation of the conductor resistance. 2.2. Proximity Effect in a Multi Coil Sensor The second main effect to be taken into account is the proximity effect of the coil wires. First of all, we consider a circular sensor with N w elementary coils and without ferritic core. Each coil is discretized in layers and sectors (N dw discretizations) in order to determine the current density distribution using the CCM. So, the total number of unknowns is Nw × Ndw . With respect to Fig. 6, the magnetic potential vector A ϕ (which only has the azimuthal component) generated in P by the current I bob which circulates around C is: μ0 Ibob Aϕ = k1 π

a k12 1− L1 (k1 ) − L2 (k1 ) b 2

(6)

4ab where k1 = (a+b) 2 +c2 , L1 , L2 are Legendre elliptical integrals. • The mutual and self inductancies are computed with magnetic potential vector (6): Φ = M= Ibob

section

Ibob

BdS

=

C

Adl

Ibob

(7)

However, the unknown in the CCM presented in this paper is the current density. So we used the next inductance formulation where the "surface" of the discretization element (Sd ) is used: √ k12 2μ0 ab L1 (k1 ) − L2 (k1 ) Sd 1− Ms = k1 2

(8)

If both layer and sector discretization are used, the current in the surface can be supposed constant. In this case, S d is the real surface of the element. This method however, leads to a great number of unknowns. To reduce the calculation time, one can suppose that radial variation of current is defined by Kelvin function (5). In this case, the discretization is done only in sectors. The current is supposed to be constant on the circle’s arc and the

17


dA

z C

P(b,0,c) y c 0 C

dl a a

Ibob

b

H

x

dl

Figure 6. Circular coil inducing the magnetic potential vector dA in P.

inductance M s is calculated by integrating (7) with respect to r. The "surface" S d in (8) is then given by : 3

Sd =

2πR J1 (k R j 2 ) 3

(9)

3

ns kj 2 J0 (k R j 2 )

where ns is the number of sectors. In order to avoid numerical singularities in the integration computing, the Gauss X-point integration formula is used, taking care that the Gauss points do not coincide with the discretization barycenter points. • The "resistance" for each discretization is computed with: Rs =

2πr σ

(10)

where r is the distance between the barycenter of the discretization and the revolution axis (a in Fig 2 for example). Finally, the "impedance" full square matrix (Z) is built using (10) and (8). Then, in each coil the current is: Ibob =

N dw

Sdi,k Qi,k

(11)

k=1

where Ndw is the number of discretization by coil, Q i,k the unknown current density in the ith coil and the k th element with the surface S di,k . The surface matrix S Nw ×(Nw .Ndw ) is built from (11) :

0 Sd1,1 . . . Sd1,Ndw 0 . . . . . . S= 0 . . . . . . 0 SdNw ,1 . . . SdNw ,Ndw

(12)

Considering the voltage constant between all discrete elements of the same coil (eg. coil i), the difference of potential between the two elements (eg. element 1 and k ∈ (2, Ndw )) is null (13) and we finally get the following system (14): (Rsi,1 + j ωMsi,1 )Qi,1 − Rsi,k Qi,k −

Nw N dw p=1 q=1

j ωMsp,q Qp,q = 0

(13)

18

V. Doirat et al. / Skin and Proximity Effects in ECNDT Sensors T

T

T

[[S] [D]] [Q1,1 · · · QNw ,Ndw ] = [I · · · I 0 · · · 0]

(14)

Then, this system is solved to obtain the current densities for each sector of each coil. Fig. 3 shows the repartition of the current density in the coils of the sensor. The skin effect is visible and, the proximity of the conductors also has an influence on the current repartition as far as the neighbors are concerned.

3. Main Interest The CCM needs the inversion of a quasi full square matrix the dimensions of which are linked to the discretization number. So, it is important to reduce this number while keeping the accuracy as best as possible. To do this, the coils are only discretized in sectors where the unknown current density is on the conductor’s surface. The current densities inside the conductors are then calculated with the Kelvin distribution (5). By introducing the Kelvin distribution rather than discretizing the wire in layers, we obtain a remarkable reduction of the discretization number and then the computational time is divided by a factor 36 for similar accuracies (Fig.3, Tab.1). The measurements are obtained with an "Agilent 4294" impedance analyser. SimuR program on a computer (Pentium 4, CPU 2.8GHz, lations are obtained with a Matlab RAM 1G). Altitude [mm]

×105

4

4

Altitude [mm]

×105

4

4

3.5

3.5

3.5

3.5

3

3

2.5 2.5 2

2.5

2

2.5

1.5

2

1

1.5

3

3

2 1.5 1

1.5

0.5 1

0.5 1

9

9.5

11 10 10.5 Radius [mm]

11.5

12

9

(a) Layer and sector discretization.

9.5

11 10 10.5 Radius [mm]

11.5

12

(b) Only sector discretization.

Figure 7. Distribution of current density in the bobbin: Skin and proximity effects.

Table 1. Reduce discretization results and comparison with the experiment. Nb discretization

Resistance (Ω)

Reactance (Ω)

Inductance (μH)

time(s)

Layer and sector

1800

1,3

40,97

13,04

170

Only sector

300

1.22

40,99

13,05

4.7

Measures

×

1.34

41

13.05

×

19


3.1. Introduction of a Ferritic Core Most of EC sensors have a ferritic core to focus the magnetic flux, so it is important to be able to take it into account in a model. We considered the magnetic permeability of the ferritic core as linear, homogeneous and isotropic and its electrical conductivity as null (no EC loss). The core surface is discretized and N df fictitious surface currents K’ are considered [7,8]. In this part, only the system "bobbin+ferritic core" is taken into account. The characteristic magnetic equation of the system can be written as: 1 μr + 1 (μ0 K’(M )) + n × 2 μr − 1

dB’ = −n × B0s

(15)

(l)

which corresponds to a second kind Fredholm equation in K’. The magnetic induction B0s on the ferritic core surface is generated by the sensor coils (sensor discretization in sectors) and B’ by the ferritic core itself (fictitious current K’) as shown on Fig. 8. This gives the following discrete relation: 1 μr + 1 (μ0 K’(M )) + 2 μr − 1 Ndf

k=1

n × dB’

=−

(lk )

N dw k=1

n × dB0

(16)

(lk )

For this determination, we used the expression of the magnetic potential vector (6) for each coil given by: dB’r =

μ0 k1 c √ [−J1 (k1 ) + C J2 (k1 )]K’(M ) dl 4π b a b

(17)

dB’z =

μ0 k1 √ [J1 (k1 ) + D J2 (k1 )]K’(M ) dl 4π a b

(18)

2

2

2

2

2

2

a +b +c a −b −c with C = (a−b) and D = (a−b) 2 +c2 2 +c2 Finally, we have to solve the following matrix system representing the set "ferritic core + bobbin" :

T [[[S] [0]] [D] [F ]]T Q1,1 · · · QNw ,Ndw K1 · · · KN = [I · · · I 0 · · · 0]T df Axis of symmetry Inductor

Ferritic core K(M)

n dB0(M)

c J0

dB (M) a

b

Figure 8. Inductor + Ferritic core contributions to magnetic induction.

(19)

20


3.2. Addition of a Load A conducting plate, which can be constituted by several layers (i) (σ(i), μ(i)), is set under the sensor. The load length is long enough in order to have no boundary effect. The discretization mesh is refined in the interesting zones under the sensor. Thus, the load is considered as a set of rectangular section circular coils where the voltage is constant in each discretization part. As previously, the matrix system (19) is completed by addition of the impedance matrix of the load (C). In the system (20), P represents the current densities in load discretization parts. [[[S] [0]] [D] [F ] [C]]

T

T T Q1,1 · · · QNw ,Ndw K1 · · · KN P · · · P = [I · · · I 0 · · · 0] 1 N dl df (20)

4. Discretization Number The accuracy of the CCM method depends on the discretization number. However, if the discretization number is very important, this method can not be use in an inversion process. We should do then a compromise between the precision and the computation time. • As far as the bobbin is concerned, the number of discretization has been reduced by using the Kelvin distribution (section 3). The impact on the computational time is remarkable since it has been divided by a factor 36. • As far as the ferrite core is concerned, the number of elements and the type of discretization have an effect on accuracy. On figure 9(a), discretization is equally distributed

0

12 10 8 6 4 2 0

Altitude [mm]

Altitude [mm]

12 10 8 6 4 2 0

3 4

2 1 2

4

5 6

8

10

12

14

16

18

20

Radius [mm]

(a) Discretization of the ferrite with w = 1.

3 2

4 5

1 0

2

4

6

8

10

12

14

16

18

20

Radius [mm]

(b) Discretization of the ferrite with w = 2.

Figure 9. Influence of the discretization sort to the ferrite core (Ndf = 100).

on the whole surface. On figure 9(b), a weighting coefficient w is used to discretize finely the segment 1 to 5 in which the field gradient is more important. The number and the type of discretization’s impact on the resistance and the inductance simulation are presented on Fig. 10. The resistance and the inductance variations versus the number of discretizations are presented on 10(a) and 10(c), respectively. The resistance and inductance relative deviation from the measures versus the number of discretizations are presented on 10(b) and 10(d), respectively. We notice that the accuracy increases with the number of discretizations. Table 2 shows the number of discretizations which are used to reach a 5% accuracy as far as resistance and inductance measures are concerned. It also notifies

21


62 Measurement 60

10 Simulations w=1 w=1.5 w=2

9 [%]

[m :]

58 56

8

Simulation w=1 w=1.5 w=2

7 6

54

5 52

4 50

0

200

400 600 800 Number of discretizations

1000

(a) Resistance versus discretization number.

3

240 0


1000

14 12

54

10

52

48

[%]

Simulations w=1 w=1.5 w=2

50

[P H]

474

314

(b) Relative erreur of the resistance between measures and simulations.

Measurement

56

200

Simulations w=1 w=1.5 w=2

8 6

46

4 44 42 40

0

200


1000

(c) Inductance versus discretization number.

2

202

273

0 0

200


422 1000

(d) Relative erreur of the inductance between measures and simulations.

Figure 10. Influence of the ferrite discretization number on the resistance and the inductance.

the simulation time. The bobbin used in the ferrite core is constituted of 5*5 coils, which are discretized in 6 sectors only (using Kelvin distribution). The results prove that simulation time and ferrite discretization number have been divided by 2 because segments 1 to 5 have been given priority. • As far as the load is concerned, the number of discretization could be very great. But the interesting zone is localized underneath the sensor. This zone is discretized finely according to the radius and the elements are enlarged after the external sensor radius. Moreover, the higher are the frequencies, the more important is the skin effect. Thus, the current densities are located on the surface of the metallic plate. So, an exponential discretization which depends on the skin depth is used according to the thickness (Fig. 1). Table 2. Ferrite discretization to obtain an uncertainty of 5% between measurement and simulation. w=1

w = 1.5

Discretization number to R

474

314

w=2 240

Discretization number to L

422

273

202

times (s)

7.5

4.6

3.6

22


12

Altitude [mm]

10 8 6 4 2 0

10 Radius [mm]

5

0

2

4

6

8

15

10

20

12

25

14

16

×104

Figure 11. Currents density in the load and the bobbin.

Lift Off = 1 mm Lift Off = 0.5 mm Lift Off = 0 mm

Resistance (Ohm)

Reactance (Ohm)

10

50

5 0 0 10

200

400

600

5

0 0 100

200

400

600

200

400

600

50

0 0 10

200

400

600

5

0 0 100 50

0 0

200 400 Frequency (kHz)

600

0 0

200 400 Frequency (kHz)

600

Figure 12. Measure(–) and simulation(+).

5. Measurements and Simulations Tests have been carried out on different conducting materials. The sensor is built with 25 coils (wire diameter 1mm), so skin effects are not negligible for frequencies greater than 50 kHz. In the following example, a 2mm thick copper plate has been used (Fig. 11). A comparison between measured and simulated resistance and reactance is presented on Fig. 12. The frequency moves from 1kHz to 500kHz and three different lift-off (0mm, 0,5mm and 1mm) have been taken into account. The relative error is less than 2% for reactance and 5% for resistance.

6. Inversion Process The presented model allows to take into account the coil intrinsic skin and proximity effects. This forward model is fast-running and accurate; it can be used easily in inversion process to determine geometrical and/or physical parameters (lift-off, conductivity,. . . ). Optimization methods with a gradient were discarded, because a gradient cannot be accurately computed in the case of non-analytical objective functions, as its first derivative is not assured to be continuous. In this perspective, we implemented a Particle Swarm Optimization which is a recent heuristic [11,12] able to escape from local minima. PSO is a population based on the stochastic optimization technique developed by Eberhart and Kennedy in 1995, inspired by the social behavior of bird flocking or fish schooling. PSO shares many similarities with evolutionary computation techniques such as Genetic Algorithms (GA). The system is initialized with a population of random solutions and searches for optima by updating generations. However, unlike GA, PSO has no evolution operators such as crossover and mutation. In PSO, the potential solutions, called particles, fly through the problem space by following the current optimum particles. Most of evolutionary techniques have the following procedure: • Random generation of an initial population • Reckoning of a fitness value for each subject. It will directly depend on the distance to the optimum. • Reproduction of the population based on fitness values.

23


• If requirements are met, then stop. Otherwise go back to 2. In our case, the optimization problem consists in determining sensor geometrical characteristics (distance between the bobbin inner radius and the ferritic core(Rint), varnish thickness (ev), wire diameter (Dcu),...) with respect to measurements (Fig.13). On Fig.14, we have represented the resistance and the inductance of a sensor. The typical intrinsic data given by the manufacturer for the sensor have been taken as initial parameters in the model (crosses), the solid line shows the measurements and the circles illustrate the result obtained after optimization using PSO and our forward model. Resistance (Ohm)

ev

Inductance (μH)

1.4

Dcu

15.5

1.2

15

Measurements Initial Optimal

1 14.5 0.8 14 0.6 13.5 0.4 0.2 0 0

Rint

Figure 13. Parameters optimization.

Measurements Initial Optimal

200 Frequency (kHz)

400

13

12.5 0

200 Fréquency (kHz)

400

Figure 14. Impedance variation before and after optimization.

Table 3 shows that the optimization process allows to reduce the gap between simulations and measurements, providing the sensor parameters are closer to the real values.

Table 3. Optimization result. Rint (mm)

Dcu (mm)

ev (μ m)

erRmean (%)

erXmean (%)

Initial

8,75

1

50

5.6037

1.2532

Optimal

8,789

0,972

77,3

1.9396

0.4051

7. Concluding Remarks The presented model can be used for probe coil design (e.g. geometrical parameters), for implementation of industrial NDT methods (e.g. frequency choice), for evaluation of the influence of perturbation parameters (e.g. lift-off) and/or for physical properties evaluation of a controlled material (σ, μ), thus limiting the number of experimental tests. As it is fast running, it can be also driven by an optimization heuristic like Particle Swarm Optimization for inversion problem in respect with measurements. In our inversion case, the results for sensor geometrical parameters have been achieved due to the accuracy and speed of the forward model and to the relevant choice of the objective functions allowing to fit the measurements provided by the sensor with accuracy less than 2%.

24


References [1] F. Buvat et al., Eddy-current modeling of ferrite-cored probes, Review of Progress in Quantitative Nondestructive Evaluation, Vol. 24, pp. 463-470, 2004. [2] G. Berthiau, B. de Barmon, MESSINE : Eddy current modeling in CIVA, 15th WCNDT, Roma, pp. 15-21, Oct 2001. [3] C. V. Dodd, W. E. Deeds, Analytical Solution to Eddy-Current Probe-Coil Problems, J. Appl. Phys, Vol.39, No.6, pp.2829-2838, may 1968 [4] A. Lefèvre, L. Miègeville, J. Fouladgar, G. Olivier, 3-D Computation of transformers overheating under nonlinear loads, IEEE Trans. on Magn., Vol. 41, No. 5, May 2005. [5] B. Maouche, M. Feliachi, N. Khenfer, A half-analytical formulation for the impedance variation in axisymmetrical modelling of eddy current non destructive testing, Eur. Phys. J. Appl. Phys, Vol.33, pp.59-67, 2006. [6] D. Delage, R. Ernst, Prédiction de la répartition du courant dans un inducteur à symétrie de révolution destiné au chauffage par induction MF et HF, RGE No.4/84, pp.225-230, Apr. 1984 [7] R. Ernst, A. Gagnoud, I. Leclercq, Etude du comportement d’un circuit magnétique dans un système de chauffage par induction, RGE No.9, pp.10-16, Oct. 1987 [8] E.Durand, Magnétostatique, Ed. Masson et Cie, 1968 [9] A. Angot, Compléments de Mathématiques à l’usage des ingénieurs de l’électrotechnique et des télécommunications, Ed. Masson et Cie, Edition 6, 1972 [10] G. Gaba, M. Abou-Dakka, A simplified and accurate calculation of frequency dependence conductor impedance, IEEE/PES and NTUA 8th International Conference of haronics and quality of power(ICHQP’98), pp. 939-945, Athens, Oct. 1998 [11] Kennedy, J. and Eberhart, R. C. Particle swarm optimization. Proc. IEEE int’l conf. on neural networks Vol. 4, pp. 1942-1948. IEEE service center, Piscataway, NJ, 1995. [12] R. C. Eberhart, J. Kennedy, A new optimizer using particle swarm theory. Proceedings of the sixth international symposium on micro machine and human science pp. 39-43. IEEE service center, Piscataway, NJ, Nagoya, Japan, 1995.

25


Eddy Current Modelling for Inspection of Riveted Structures in Aeronautics S. PAILLARD a,1 , G. PICHENOT a , M. LAMBERT b , H. VOILLAUME c a CEA/LIST, CEA Saclay 91191 Gif-sur-Yvette France b L2S (CNRS-Supélec-UPS), 3 rue Joliot-Curie, 91192 Gif-sur-Yvette France c EADS CCR, DCR/SP/PN, 12 rue Pasteur, 92152 Suresnes France Abstract In the framework of a collaborative project with EADS, a semi-analytical model based on a volume integral method has been developed to simulate eddy current (EC) inspection of riveted structures in aeronautics. The model handles a layered structure by considering a dyadic Green’s approach where a fastener and a flaw are introduced as a variation of conductivity in a stack of slabs. Experimental data are used to validate the model. Keywords. Eddy Current Testing, Aeronautic inspection

1. Introduction EC technique is currently the operational tool used for fastener inspection which is an important issue for the maintenance of aircraft structures. The industry calls for faster, more sensitive and reliable NDT techniques for the detection and characterization of potential flaws nearby rivets. In order to reduce the development time, to optimize the design and to evaluate the performances of an inspection procedure, CEA and EADS have started a collaborative work aimed to extend the modelling features of the CIVA non destructive simulation platform to the simulation of multilayer assembly with fasteners. CIVA

(a) Bobbin coil placed inside a conducting tube

(b) Bobbin coil placed on a configuration defined by CAD

(c) Three ferrite cores placed on a conducting slab

Figure 1. Representation of several configurations affected by a parallelepiped flaw in the CIVA user interface. 1 Corresponding Author: Séverine Paillard, CEA/LIST, CEA Saclay 91191 Gif-sur-Yvette France; E-mail: [email protected]

26

S. Paillard et al. / Eddy Current Modelling for Inspection of Riveted Structures in Aeronautics

is a powerful multi-technique platform for industrial NDT (see [1,2,3]). The developed EC simulation models are mainly based on the volume integral method using the dyadic Green’s formalism detailed in [4]. Several examples of CIVA for eddy current testing are presented in Fig. 1. This paper describes the progress in developing a 3D computer code for fastener modelling based on the volume integral equations which has the capability to quickly predict the response of an eddy current probe to 3D flaws.

2. Description of the Model 2.1. Theoretical Formulation A typical configuration of interest is depicted in Fig. 2. It consists of a layered planar structure with a fastener and a semi-elliptical flaw nearby the lower part of the rivet. The EC probe is moved along the surface, above the fastener assembly. This configuration

Figure 2. Typical aircraft configuration.

can be attacked in two steps: (i) modelling the response of a probe to a layered structure with fastener without flaw; (ii) taking into account the flaw. Results of the first step are given below. Those of the second one are not yet obtained and will be presented later. The configuration is described as follows : the space is divided in two air half-spaces numbered 0 and N + 1 with, in between, a N -layer slab, each layer being numbered i and having a conductivity σ i (all materials are supposed to be non magnetic and of air permeability μ0 ). The slab is affected by a defect of volume Ω and conductivity σ (r) crossing one or more layers (as depicted Fig. 2). Let us denote with index m (resp. n) the first (resp. last) layer affected by the defect n (m < n), the latter being sliced into as many layers as necessary such as Ω = k=m Ωk (note that, in the case of a rivet crossing the N layers without his foot, m = 1 and n = N ). An exemple of the Ω domain for a two-layered slab is shown in Fig. 3(a). A time-harmonic source (circular frequency ω and implied time-dependence exp (jωt)) –a coil probe for example– is placed in the upper half-space 0. The so-called 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 onto 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 G kl (r, r’) the electric-electric dyadic Green’s functions defined as the field response for a unit point source and solution of (0) Ek (r)

(ee)

S. Paillard et al. / Eddy Current Modelling for Inspection of Riveted Structures in Aeronautics (ee)

(ee)

∇ × ∇ × Gkl (r, r’) − kk2 Gkl (r, r’) = δkl Iδ(r − r’).

27

(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 dyadic and δ kl stands for the Kronecker delta. kl is the wave number in the l th layer defined as kl2 = jωμ0 σl . The Green’s dyad satisfies the 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 is obtained via the reciprocity theorem, where I 0 is the feeding current of the probe, as I02 ΔZ =

n l=m

Ωl

(0)

[σl − σ(r)] El (r) · El (r)dr.

(3)

2.2. Numerical Considerations Once the model has been chosen and the equations established, the numerical formulation can be implemented. Equation (1) is discretized using a Galerkin’s version of the method of moments where the contrast zone Ω is sliced in N cell parallelepipeded voxels. The voxels are chosen in order to have an homogeneous conductivity inside each voxel, and in each voxel, the electric field is a constant-valued. This approach leads to 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 i th region of the sliced rivet onto itself and where G i,j are the mutual coupling terms of the j th over the ith . An example is given for a two-layered slab (n = 1 and m = 2) in Fig. 3. The rivet illustrated in Fig. 3(a) is here sliced into two parts, each one entirely contained in a single layer of conductivity σ k . The self-coupling terms G i,i with i ∈ {1, 2} are represented in Fig. 3(a) and the mutual-coupling terms G i,j with (i, j) ∈ {1, 2} and i = j are represented in Fig. 3(b).

(a) Rivet and the contrast zone Ω sliced in two inhomogeneity zones

(a) Self-coupling

(b) Mutual coupling

Figure 3. Example of a rivet in a two-layered slab.

For building this multi-layer model, two main improvements have been made:

28


• Self-coupling terms: the planar stratification of the work piece is taken into account by introducing generalized reflection and transmission coefficients at each interface in the Green’s dyads. • Mutual coupling terms: the mutual Green’s functions are written in explicit analytical expressions [4] and implemented to reconstruct the entire matrix of equation (4). In the applications which we are interested in, the typical size of the domain Ω may be more than ten skin-depths which leads to a large number of voxels and to a too large 2 linear system to invert (the memory size can be estimated as O (9 N cell )). 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 4/3 allows us to treat larger defects by reducing the memory size to O (9 N cell ).

3. Validations On one hand, the model is developed to handle a defined configuration –a rivet within a laminated slab– and from this point of view, we have to validate the two first aspects of the fastener modelling illustrated in Fig. 4. On the other hand, this model is a multi-layer model –an inhomogeneity zone embedded in a laminated work piece– and therefore, we have to validate this multi-layer modelling also. In order to focus on these different aspects, and to avoid errors in rivet shape simulation, the rivet with its typical flat head shape is assumed in all validations to be a cylindrical through-wall hole. The flat head shape of the rivet can be obtained by introducing volume ratios in the calculation zone. Several validations have been done to improve the two approaches -handle a fastener in

(a) Rivet in one slab

hole

(b) Rivet crossing a multi-layer slab

(c) Rivet in a multi-layer slab and a flaw nearby

Figure 4. Different aspects of fastener modelling.

a laminated slab and a multi-layer configuration- of this multi-layer model: • Fastener approach: through-wall inhomogeneity zone in one slab (first aspect, Fig. 4(a)) and in a two-layer slab (second aspect, Fig. 4(b)). The third aspect (Fig. 4(c)) is not treated yet. • Multi-layer approach: inhomogeneity zone contained successively in the different layers of a two-layer slab. For all such studies, the same air-cored probe is used (an inner radius of 1 mm, an outer radius of 1.6 mm, a lift-off of 0.32 mm and a height of 2 mm with 320 turns) and is displaced along the diameter of the hole.


29

Figure 5. Cylindrical through-wall hole in one layer of aluminium (— experimental data, +++ CIVA results).

3.1. One-Layer Validation An impedance meter HP4194 is used to measure the impedance of the air-cored probe working in absolute mode at the frequency of 10 kHz on a through-wall hole in an aluminium slab (Fig. 5, left). The hole diameter is 4.9 mm and the slab thickness is 4 mm with a conductivity of 30 MS/m. The agreement between the model and the experimental data is better than 1% for the amplitude and 8 ◦ in phase (Fig. 5, right). 3.2. Multi-Layer Validations The multi-layer modelling has been validated on a two-layer slab (mock-up inconelaluminium) described as follows: an inconel slab with a conductivity of 1 MS/m and a thickness of 1.27 mm lies above an aluminium slab with a conductivity of 30 MS/m and a thickness of 4 mm. A cylindrical hole of 4.9 mm is crossing one (inconel slab, Fig. 7(a)) or the other (aluminium slab, Fig. 8(a)) or both (Fig. 9(a)). The air-cored probe is working here at 75 kHz. 3.2.1. Calibration In most industrial applications, the measured EC signal is calibrated over a reference flaw. Preliminary to these validations, a calibration experiment has been made; the reference flaw is a surface breaking notch in an inconel slab with a conductivity of 1 MS/m. The EDM notch is 0.1 mm in width, 20 mm in length and 0.93 mm in depth and the thickness of the slab is 1.55 mm as shown in Fig. 6 (left). The impedance variation measured in the impedance plane calibrated at 500 mV and 135 ◦ is presented in Fig. 6 (right).

Figure 6. Response of the probe to a breaking notch in a slab (— experimental data, +++ CIVA results).

30


(a) Cylindrical hole in the inconel layer with perfect matching

(b) Cylindrical hole in the inconel layer with imperfect matching

(c) Calibrated signals in the impedance plane Figure 7. Cylindrical hole in the inconel layer of a two-layer slab perfectly matched (— experimental data, *** CIVA results with perfect matching, +++ CIVA results with imperfect matching).

3.2.2. Imperfect Matching Slabs Influence For the hole in the inconel slab (like for the others but we will come back to them later on), the result is not completely satisfactory (Fig. 7); even if the agreement for the measurement of the EC signal in the impedance plane between the model and the experimental data is better than 4% for the amplitude and 2 ◦ in phase, the shapes of the signal are different (Fig. 7(c)). One of the reasons can be that the simulated configuration does not correspond exactly to the reality of the experimental configuration. As a matter of fact, in the experiment, the two slabs could not be fastened in perfect fashion (like on the Fig. 7(a)), causing the occurrence of a thin air layer in between. A study has been carried out to evaluate the thickness of the layer of air to be taken into account and the best results have been obtained with a thickness of 50 μm (Fig. 7(b)). All the results presented in the next subsection take into account this air gap. 3.2.3. Results of Validations For the hole in the inconel slab, the agreement between the model and the experimental data is better than 6% for the amplitude and 2 ◦ in phase (Fig. 7(c)) whereas, for the hole in the aluminium slab, the agreement is better than 4% for the amplitude and 3 ◦ in phase (Fig. 8(b)). For the through-wall hole in the two-layer slab (Fig. 9), the agreement between the model and the experimental data is better than 2% for the amplitude and 3 ◦ in phase (Fig. 9(b)).


(a) Hole in the aluminium layer with imperfect matching

31

(b) Calibrated signals in the impedance plane with imperfect matching

Figure 8. Cylindrical hole in the aluminium layer of a two-layer slab (— experimental data, +++ CIVA results).

(a) Hole crossing a twolayer slab with imperfect matching

(b) Calibrated signals in the impedance plane with imperfect matching

Figure 9. Cylindrical through-wall hole in a two-layer slab (— experimental data, +++ CIVA results).

4. Application in Aeronautics Once the model has been validated, we can consider a realistic case: two identical multilayered slabs held together by a rivet. We have applied the model to the calculation of the impedance variation of a ferrite-cored probe used to test the aeronautical work piece illustrated in Fig. 10. One slab is decomposed in three thin layers of aluminium alloy,

Figure 10. Cylindrical through-wall hole in two multi-layer slabs.

bonded together with non-conductive material. The aluminium slabs are 0.3 mm in depth and the non-conductive slabs are 0.25 mm, the fastener hole has a diameter of 4.9 mm.

32


The cylindrical ferrite-cored probe used for these studies has an inner (resp. outer) radius of 3.74 mm (resp. 7.325 mm), and a height of 3.46 mm with 926 turns and works at 2.6 kHz. The results presented in Fig. 11 have to be validated with experimental data,

Figure 11. Simulated response of the probe to a cylindrical through-wall hole in two multi-layer slabs.

however they are coherent with what is expected in such a configuration: (i) when the centre of the probe is exactly above the centre of the cylindrical hole, the signals are almost null because the inner diameter of the probe is larger than the diameter of the hole, and so the currents are almost undisturbed. (ii) when the centre of the probe is at 5 mm from the centre of the hole, the signals (Fig. 11) are at their maximum (resp. minimum) for the real part (resp. for the imaginary part) corresponding to the positions where most of the winding is above the hole. 5. Conclusion and Perspectives The extension of the CIVA platform to the simulation of riveted structures is currently in progress. The multi-layer model is now validated, with a good agreement between the model and the experimental data, for a cylindrical through-wall hole in a set of two slabs, a cylindrical hole either in the top slab or in the bottom slab of the stack. A first milestone has been reached with the development of a model taking into account the presence of a rivet in a layered slab assembly. Validations with experimental data of the 3D model developed here for fastener modelling have been carried out successfully. Work is in progress to calculate the probe response due to the presence in a fastened structure of both a rivet and an embedded flaw located nearby as shown in Fig. 4(c). Acknowledgements This research is supported by the Paris Ile-de-France Region. References [1] [2]

[3] [4]

Buvat F., Pichenot G., Prémel D., Lesselier D., Lambert M. and Voillaume H., Eddy current modelling of ferrite-cored probes, in Review of Progress in QNDE Vol. 24, 2005, pp. 463-470. Sollier T., Buvat F., Pichenot G. and Premel D., Eddy current modelling of Ferrite-Cored Probes, application to the simulation of Eddy current signals from surface breaking flaws in austenitic steel, Proc. 16th World Conf. on NDT, Montreal, 2004. Pichenot G., Buvat, F., Maillot V. and Voillaume H., Eddy current modelling for non destructive testing, Proc. 16th World Conf. on NDT, Montreal, 2004. Chew W.C., Waves and Fields in Inhomogeneous Media, Van Nostrand Reinhold, New York, 1990.


33

Numerical Modeling of a Phase Sensitive Eddy Current Imaging System Guglielmo RUBINACCI a,1, Antonello TAMBURRINO b, Salvatore VENTRE b, Pierre-Yves JOUBERT c and Jean PINASSAUD c a Ass. EURATOM/ENEA/CREATE, DIEL, Università degli Studi di Napoli Federico II Italy b Ass. EURATOM/ENEA/CREATE, DAEIMI, Università degli Studi di Cassino, Italy c SATIE, ENS Cachan, CNRS, Universud, F-94230 Cachan, France Abstract. This work focuses on an innovative Eddy Current Imager dedicated to the high-speed and high-resolution non-destructive testing of large metallic structures, such as the riveted lap joints of aircrafts. The system produces time-harmonic in – phase and in – quadrature eddy current images, thanks to a specific linear magneto-optic set-up, which actually provides a true measurement of the 2-D spatial distribution of the magnetic flux density at the surface of the inspected structure. In view of quantitative imaging of defects in planar structures, an appropriate numerical model, based on an efficient integral formulation, is presented and validated against the measurements. Keywords. Eddy current imaging, nondestructive evaluation, 3D numerical modeling experimental and computed data, surface and buried defects.

1. Introduction Magneto-Optic (MO)/eddy current (EC) imagers appear to be a good alternative to conventional EC sensors such as pencil probes or array sensors, for the non-destructive evaluation (NDE) of large metallic structures such as the riveted lap joints of aircrafts. Indeed, these imagers provide real time and possibly high resolution images relative to the integrity of the structure, without intensive mechanical scanning. MO imagers dedicated to NDE were firstly introduced by [1]. However, this type of imager only provide “two-level” images resulting from the comparison to an adjustable reference threshold. These features actually limit both the efficiency and the defect characterization possibilities. In this paper, we focus on an original eddy current (EC) imager [2] able to provide true in-phase and in-quadrature EC images which are linearly related to the spatial distribution of the magnetic flux density at the surface of the inspected structure. These EC images are suitable to be processed by a quantitative inversion algorithm in order to carry out an exhaustive defect characterization. However, the success of this approach requires the precise knowledge of the interactions between the imager and the inspected structure. To this purpose, it is 1 Corresponding Author: Guglielmo Rubinacci, Euratom/Enea/Create, Dipartimento di Ingegneria Elettrica, Università degli Studi di Napoli Federico II, Via Claudio, 21 – 80125, Napoli, Italy; E-mail: [email protected]

34

G. Rubinacci et al. / Numerical Modeling of a Phase Sensitive Eddy Current Imaging System

essential to develop numerical formulations, tailored for nondestructive testing applications, that satisfy the following three requirements: (i) the numerical method has to be capable of handling different scales ranging from the defect scale (small scale) to the imager scale (large scale), (ii) numerical errors must be small enough otherwise, due to the ill-posedness of the inverse problem, they may alter significantly the reconstruction and (iii) the numerical method has to be fast enough to be incorporated into an iterative inversion procedure. Finally the numerical model should also take efficiently into account the magnetic circuit of the EC inductor. In this paper, we present the numerical simulation of a quantitative MO/EC inspection of a riveted lap joint with a surface breaking or a buried crack in the proximity of the rivet hole. The numerical model is briefly illustrated and validated against the measurements.

2. Description of the Eddy Current Imager The diagram of the imager [2] is presented in Figure 1. Its working principle is based on the combination of an EC inductor used to excite the material under inspection, with a specific MO set-up used to image the spatial distribution of the normal magnetic field at the surface of the inspected area, in real and imaginary parts. The specific configuration of the EC inductor allows a uniformly oriented eddy current flow to be generated in a large inspection area. The presence of a defect induces the rise of a non-zero normal component of the magnetic field in the vicinity of the defect. This component is sensed by a dedicated MO garnet film relying on the Faraday effect. The garnet features a linear and hysteresis free magnetization loop. It is integrated to an optical set-up so that the variation of the magnetic field is translated into the variations of the intensity of light beam measured by a CCD camera. The acquisition rate of the used camera (25 images/s) being far smaller than the excitation frequency of the EC inductor (100Hz up to 20kHz), the images are obtained using a stroboscopic approach, followed by a digital lock-in used to obtain the real and imaginary parts of the magnetic field. The EC imager prototype used in this study allows 45mm diameter images to be obtained in 15 seconds, and was designed to provide a 100μmu100μm spatial resolution.

3. The Numerical Model The numerical model here implemented is based on the numerical formulation presented in [3]-[7]. The problem under consideration is the calculation of the magnetic field perturbation induced on a conducting specimen by a time harmonic magnetic field in the presence of a perfectly insulating defect and linear magnetic materials. The direct solution of this problem may require a very heavy computational effort, since the defect size is usually smaller than the other relevant characteristics of the system (size of the specimen and of the eddy current inductor). Consequently, a proper discretization of the system calls for a very large number of unknowns. Moreover one has to take into account that the signal due to the defect is usually weak so that numerical errors can compromise the numerical solution.


35

Our approach exploits a volume integral formulation, to efficiently reduce the discretization only to the sources region, and the superposition principle, to separately compute the current density perturbation due to holes and defects. Light proof box Synchronisation board CCD camera

Light source

Polarizer

Analyzer

PC Current controlled AC power. 100Hz-20kHz

& z

Coils

& y

& x

MO sensor

2 layer lap joint mockup

EC inductor

defect

Figure 1. General diagram of the eddy current imager

In our volume integral formulation, the unknowns are the two-component vector potential T defined in the conducting region Vc (where the current density J is given by its curl) and the magnetization vector M defined in the magnetic region Vf, that in the present case does not coincide with Vc. Assuming a sinusoidal excitation, we represent the current density J in terms of edge shape functions Tk and the magnetization vector as a piecewise uniform function in terms of elementary pulse functions Pk(x) n

J (x)

¦I

m

k

u Tk (x) , M (x)

k 1

¦M

k

Pk ( x )

(1)

1

The gauge based on the tree-cotree decomposition of the mesh [8] assures the uniqueness of Tk. Applying the Galerkin's approach to the electric and magnetic constitutive equations, the following linear system of equations is obtained:

³uT

k

(KJ jZA)dV

0

Tk

(2)

Vc

³P

k

[M kB]dV

0

Pk

(3)

Vf

where B is the magnetic flux density, A is the magnetic vector potential, K is the resistivity and k P r 1 P 0 P r . A and B are calculated from J and M via Biot-Savart law. Having defined I and M as the column vectors made by the complex coefficients of the expansions (1), equations (2) and (3) lead to a linear system of equations, that * * when solved for M, reduces to ZI jZ U , where Z is a n u n full matrix, and U

36


is a n u 1 column vector related to the external sources, whose explicit expressions can be found in [3, 6]. Using superposition, the forward problem is reformulated [3], [5], [6] as the determination of the modified eddy current pattern J = J0 + GJ. Here, J0 is the unperturbed current density in the presence of the hole, whereas GJ = 6k=1,n GIk Jk is the perturbation due to the crack. The crack is assumed to be thin, so that it may be computationally convenient to treat it as a surface 6d, discretized via a set of finite element facets, with the constraint ˆ = 0, leading to GJ. nˆ = J0 . nˆ , where nˆ is the normal unit vector on the J. n face. We then make a change of variables:

GI = K GX - S G0 (4) where GX is an auxiliary variable which gives current densities with zero flux through the crack and G0 is a particular set of values giving a net flux through each facets of the ˆ = J0. nˆ . The definition of the matrices K and crack according to the constraint GJ. n S is given in [5]. Galerkin’s procedure in terms of the new variables yields: KTZK GX = KTZS G0

(5)

This approach, introduced in [3, 5], was also applied to the treatment of volumetric cracks [4, 6, 7]. The possibility of treating volumetric defect allows to efficiently compute also the effect of the hole on the unperturbed current density J0. Specifically, J0 can be represented as the superposition of J0,P and GJ0,H where J0,P is the current density when only the plate is present and GJ0,H its perturbation due to the presence of the hole. Moreover, the interaction between GJ0,H and the iron yoke is negligible (GJ0,H flows in a region that is relatively “far” from the yoke) and, therefore, the presence of the magnetic material can be limited to the computation of J0,P only. One of the advantages of the proposed approach is that it is possible to define a region where the crack could be located ad to pre-compute all the unknowns external to that region in terms of the unknowns in the tentative crack region. In this way, the magnetic field associated to any set of faces belonging to the possible crack region can be computed in a very fast way by solving a very small linear system.

4. Results The eddy current inductor is shown schematically in Figure 2a. The magnetic poles (panels) are vertical (without any tilt angle as opposed to the drawing) and directly in contact with the inspected mockup. Two induction windings are winded around 10mm diameter ferritic rods. Each winding features 2 coils of 120 turns each. (the total number of turns is 4 u 120 turns). The four windings are connected in parallel. The magnetic circuit is made out of 3C90 with a relative magnetic permeability μr| 2300 and a resistivity of 5:m, that has been assumed infinite in the numerical simulation. The active area of the MO sensor film is a circle with a diameter of 45 mm.


37

The tested mock-up is a laboratory made riveted lap joint with a thin notch (surface or buried) in the proximity of a rivet hole, simulating a crack, as shown in Figure 2b. The two 1.5 mm thick non-magnetic plates are made in Aluminium with a conductivity V| 20 MS/m, according to the manufacturer. The coils are fed with sinusoidal current, the excitation frequency being 1kHz. Due to the symmetry of the eddy current inductor and of the mock-up, the computation of the eddy currents in absence of the holes and notch can be made by discretizing only one forth of the system. The finite element mesh, shown in Fig. 3a is made of 3476 elements in the conducting region and 796 elements in the magnetic region, leading to 5106 complex Degrees of Freedom (DOF) for the eddy currents and 2388 complex DOF for the magnetization. The finite element mesh to compute the field due to the hole is again symmetric, in the hypothesis that the hole is at the center of the eddy current inductor. This is not exactly true (the holes in Figure 2b are not exactly at the center of the eddy current inductor), but it is a good approximation because the inductor produces an almost uniform field in the hole region. This finite element mesh is shown in Figure 3b and is made of 2196 elements in the conducting region, leading to 3226 complex DOF for representing the eddy current density. The magnet is discretized as in the previous case, although it has been checked that its contribution in this part of the computation is absolutely negligible, as already remarked in Section 3. A third finite element mesh is necessary for computing the crack contribution. In this case, we again assume that the crack is located at the center of the inductor, so that only half of the mock-up can be discretized. Again, this is a good approximation in the reasonable hypothesis of an almost uniform inducing field in the region of the crack and the hole. The finite element mesh is shown in Figure 3c and is made of 4320 elements in the conducting region leading to 6328 complex DOF. In this case half of the EC inductor should be discretized, leading to twice the magnetic unknowns than previously. Of course, it can be verified that also in this last case the presence of the

a) 2 Aluminium Alloy plates V | 20 MS/m ; μr=1

12 mm x 1.5 mm x 0.5mm (length x depth x width )

5 mm x 1.5 x 0.5 (length x depth x width )

1.5 mm

Notches on the first layer

4 mm diameter 1.5 mm

b)

20 mm

Figure 2. Eddy current inductor (a) and riveted lap joint mock-up (b).

38


inductor does not produce any appreciable contribution to the field. The measurements are available for the surface defect and the buried defect. The first simulation refers to the hole without defect. In particular, in Figure 4 it is shown the flux density component normal to the specimen corresponding to both experimental and numerical data on a rectangular region above the hole and along a line passing through the center of the hole in a direction orthogonal to the induced current density. The data are normalized to the maximum value of the field modulus. The computed results are also shown for another value of the conductivity, namely V| 35 MS/m, corresponding to the pure aluminum. The slight asymmetry in the measurements can be ascribed to a possible tilting of the garnet film. The results for the surface and buried defects are shown in Figures 5 and 6, showing a satisfactory agreement with the measurements. In the pictures the dimensions of each square pixel have been assumed to be actually 97.7μmu97.7μm, rather than 100μmu100μm.

c)

b)

a)

Figure 3. The finite element mesh (a) in the unperturbed case, (b) for the hole and (c) for the crack perturbation.

V=20MS/m

a)

b)

c)

Figure 4. The real part of Bz/max(|Bz|) for both experimental (a) and numerical data (b) on a rectangular region above the hole; The Lissajous plot (c) of Bz/max(|Bz|) along a line passing through the center of the hole. The computed results for V=20MS/m (diamonds) and V=35MS/m (crosses) are compared with the measurements.


a)

39

b)

Figure 5. The Lissajous plot of Bz/max(|Bz|) along a line passing through the center of the hole for a surface (a) and a buried (b) defect. The computed results for V=20MS/m (diamonds) and V=35MS/m (crosses) are compared with the measurements. V=20MS/m

(a)

(b)

V=20MS/m

V=35MS/m

(c)

(d)

(e)

V=35MS/m

(f)

Figure 6. The real and imaginary part of Bz/max(|Bz|) for both experimental (a), d)) and numerical data (b), c),e),f)) on a rectangular region above the hole, in the presence of a buried defect; The computed results refers to V=20MS/m (b),e)) and V=35MS/m (c),f)). V=20MS/m

(a)

(b)

V=35MS/m

(c)

V=20MS/m

(d)

(e)

V=35MS/m

(f)

Figure 7. Same as Figure 6, but in case of a surface defect.

It should be explicitly mentioned that the presence of the magnetic core in the perturbed models does not play any role, so that the computational model is very fast and the shape of the crack can be very efficiently detected with a very limited computational effort, as in the non magnetic case. For instance the field variation due

40


to the introduction in the crack shape of additional boundary facets is an almost real time computation (few ms of a PC CPU time).

5. Conclusions In this paper we have presented a numerical tool able to fully simulate a new quantitative MO/EC imager. Usually, MO/EC imagers provide only “two-level” images that are not well suited to give enough information for NDE, as in cases when one needs to discriminate surface and buried defects and evaluate their size and shape. This two-level feature actually limits both the efficiency and the defect characterization possibilities. In this paper, we have shown that the magnetic flux density data provided by a new eddy current imager can be reproduced by an effective numerical tool leading to a very fast and accurate evaluation procedure for the detection of cracks in a riveted lap joint. As a matter of fact, a linear model of the sensor has been coupled to a numerical scheme able to simulate the effects of cracks in conducting bodies in terms of magnetic field perturbation. The resulting tool is extremely useful in understanding more deeply the behaviour of the sensor in an advanced ECT application. This is fundamental if the inverse problem (given the measurements provided by the sensor, find the characteristics of the crack) must be solved.

Acknowledgments 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] G. L. Fitzpatrick et al. Magneto optic/eddy current imaging of ageing aircrafts, Mat. Eval. (1993), pp. 1402-1407. [2]. P.-Y. Joubert and J. Pinassaud, Linear magneto-optic imager for non-destructive evaluation, Sensors and Actuators A: Physical, Volume 129, Issues 1-2, 24 May 2006, pp. 126-130. [3] R. Albanese, G. Rubinacci, F. Villone, “Crack simulation in the presence of linear ferromagnetic materials using an integral formulation”, Electromagnetic NDE (V), (J. Pavo et al. Eds.), pp. 16-21, IOS press, 2001. [4] G. Rubinacci, A. Tamburrino, S. Ventre, F. Villone, Numerical Modelling of Volumetric Cracks, Int. J. Appl. Electromag. Mech, vol. 19, pp. 345-349, 2004. [5] R. Albanese, G. Rubinacci, F. Villone, “An Integral Computational Model for Crack Simulation and Detection via Eddy Currents”, J. Comp. Phys., Vol 152, 736-755, 1999. [6] 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. Appl. Electromag. Mech., vol. 12, pp. 115-137, 2000. [7] M. Morozov, G. Rubinacci, A. Tamburrino, S. Ventre, Numerical Models with Experimental Validation of Volumetric Insulating Cracks in Eddy Current Testing, IEEE Trans. Mag, Vol. 42, no. 5, May 2006, pp 1568-1576. [8] R. Albanese and G. Rubinacci., Finite Element Methods for the Solution of 3D Eddy Current Problems, Advances in Imaging and Electron Physics 102 (1998) 1-86.


41

Developments in Modelling Eddy Current Coil Interactions with a Right-Angled Conductive Wedge Theodoros THEODOULIDIS a,b,1 , Nikolaos POULAKIS a and John BOWLER c a TEI of West Macedonia, Electrical Engineering Department, Greece b University of West Macedonia, Energy Department, Greece c Iowa State University, Center for Nondestructive Evaluation, USA Abstract. Recently we presented an analytical solution for the 3D configuration of a cylindrical coil at the edge of a conductive block and calculated the impedance variation with position relative to the edge. Since then we have been seeking ways to improve and extend the analytical and numerical treatment of this canonical problem. In the present paper, several extensions to previous work are presented including a modification to the expressions for the field potentials in double series form and the generalization of the field source to coils of arbitrary shape and orientation. Experimental results involving a cylindrical coil of arbitrary tilt are shown to verify the calculations. Keywords. Eddy current testing, analytical modelling, conductive wedge

1. Introduction The problem of evaluating the impedance change of a coil at the edge of a conductive block modelled as a conductive quarter space has been solved recently by using the Truncated Region Eigenfunction Expansion (TREE) method [1]. The problem was formulated using a Cartesian coordinate system with the z-direction perpendicular to one surface of the block and the edge in the y-direction, Figure 1. The solution was made possible by introducing artificial boundaries that limit the problem domain in the x-direction. The truncated domain is divided into regions, the solution expressed as series expansions in each region and the expansion coefficients found from the continuity conditions governing the field at the interfaces between each region. The approach is based on the principle of mode matching and the creative use of truncation boundaries to find quasi-analytical solutions to boundary value problems that would be intractable without modified boundaries. Using symmetry considerations, the solution was extended to the case of a plate [2] and a through thickness slot [3]. In the present study, we report on further developments including (i) the reformulation of the problem by expressing the electromagnetic field 1 Corresponding

Author: Theodoros Theodoulidis, University of West Macedonia, Energy Department, Bakola & Sialvera, 50100 Kozani, Greece; E-mail: [email protected]

42

T. Theodoulidis et al. / Developments in Modelling Eddy Current Coil Interactions

and coil impedance in double series form which is advantageous in terms of computer implementation and convergence control and (ii) extension to a cylindrical coil of arbitrary tilt. In particular, we provide general expressions for the magnetic field, eddy current density and impedance change of the coil in terms of source coefficients that characterize the coil. These coefficients depend only on the isolated coil magnetic field and can be found by using the Biot-Savart law.

Figure 1. Problem geometry. A cylindrical coil is moved across the edge of a right-angled conductor.

2. Analysis In the new approach, the solution domain for the boundary value problem is truncated in both x and y directions. Formally the truncation was in the x-direction only [1]. Thus, the solution domain extends from 0 to hx in the x-direction and from 0 to hy in the ydirection. The presence of four boundary surfaces at x = 0, hx and y = 0, hy means that we have a wide choice of boundary condition combinations. The choices include one which defines a perfect magnetic insulator, Bn = 0 (n stands for normal component) and one which defines a perfect electric insulator, Bt = 0 (t stands for tangential component). For the case examined here where the edge at x = c as well as the coil are located far from the boundaries these choices have a negligible effect on numerical values of the coil response. However, they determine the form of expressions for the solution and the combination of eigenfunctions-eigenvalues used to represent it. In this work we consider a magnetic insulator at x = 0, x = hx , y = hy and an electric insulator at y = 0. The choice of magnetic insulation is consistent with previous work [1]. The reason for the discrepancy in the boundary condition at y = 0 is clearly logistic. In this way we end up with sines instead of cosines in the Y -dependence of the expressions for the potentials used in the solution. The use of sines means the absence of a dc term in the series which introduces a small simplification. From the physical point of view it does not have any effect on the solution since all the boundaries are located far from the source coil.


(a)

43

(b)

Figure 2. (a) Normal cylindrical coil above a conductive quarter-space (b) Tilted cylindrical coil above the edge of a conductive quarter-space.

2.1. Field Expressions Consider Figure 2 which shows a coil located above a right-angled conductive nonmagnetic quarter-space with a conductivity σ. The coil is excited by a time harmonic current varying as the real part of I exp(jωt). The analysis of the electromagnetic field problem is based on the use of potentials. In the air-region between the lowest point of the coil and the upper conductor 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 and the potential originating from the eddy currents in the conductive quarter-space φ = φ(s) + φ(ec) . The expressions for these two potentials are then written as: φ(s) (x, y, z) =

∞ ∞

(s)

cos(ui x) sin(vj y)eκij z Cij

(1)

i=0 j=1

φ(ec) (x, y, z) =

∞ ∞

cos(ui x) sin(vj y)e−κij z Dij

(ec)

(2)

i=0 j=1

The magnetic flux density in the region below z = 0 can be written using the second order vector potential as B = ∇ × ∇ × W where W = Wa x0 + x0 × ∇Wb and Wa , Wb satisfy either the Laplace or Helmholtz scalar equations according to the conductivity of the sub-region. Here x0 is a unit vector. The eddy current density in the quarter-space is written as J = −jωσ∇ × W. Expressions for the two potentials satisfy the continuity conditions on the magnetic field at the z = 0 plane and the x = c half-plane (z < 0). By ensuring continuity and satisfying the insulator boundary conditions at the truncation boundaries, it is found that ⎧ ∞ (a) ⎪ ⎪ sin(vj y) xevj y C0j + ⎪ ⎪ ⎪ j=1 ⎪ ⎨ ∞ (a) γij z ; 0≤x≤c sin(pi x)e ai Cij + (3) Wa (x, y, z) = ⎪ i=1 ⎪ ⎪ ∞ ∞ ⎪ (a) ⎪ ⎪ sin[qi (hx − x)] sin(vj y)eγij z Cij ; c ≤ x ≤ hx ⎩ j=1 i=1

44


Wb (x, y, z) =

∞

(b)

C0j cosh[k(hx − x)] cos(vj y)evj z

j=1

+

∞ ∞

(b)

cos[ri (hx − x)] cos(vj y)esij z Cij

;

c ≤ x ≤ hx

(4)

j=1 i=1 2 = where ui = iπ/hx , vj = (2j − 1)π/(2hy ), κ2ij = u2i + vj2 , k 2 = jωμ0 σ, γij 2 2 2 2 2 2 2 2 2 2 2 qi + vj + k , pi = γij − vj = qi + k , ri = (2i − 1)π/[2(hx − c)], sij = ri + vj + k 2 . A solution of (4) in the region 0 ≤ x ≤ c is not necessary since B depends only on Wa in nonconductive regions [1]. The values of qi and hence pi are sought from the continuity of the magnetic field at x = c which requires

qi tan pi c + pi tan qi (hx − c) = 0

(5)

the roots of which give the eigenvalues for Eq. (3). These complex eigenvalues do not depend on the variable vj , which means that their numerical computation needs to be carried out only once. In addition in Eq. (3) qi cos qi (hx − c) sin qi (hx − c) =− sin pi c pi cos pi c

ai =

i = 1, 2, 3, ...

(6)

and (a)

(b)

(b)

C0j = k 2 cosh[k(hx − c)]C0j = a0 C0j

(7)

The source coefficients in Eq. (1) are considered to be known and hence all other coefficients Eqs. (2)-(4) are calculated in terms of them. This is done by imposing the interface conditions at the surface z = 0, see [1] for details of the procedure. The final expressions are: (ec)

D0j =

∞ k2 (−1)i+1 (b) (ec) T (b) (sij − vj ) Cij = Rj Cj 2vj hy i=1 ri (s)

(b) C0j

hx vj C0j + =

k2

k2 2

∞ i=1

i+1

(sij + vj ) (−1) ri

(8)

(b)

Cij

cosh[k(hx − c)]cvj + k sinh[k(hx − c)]vj

(b)

(s)

(b) T

= λj C0j +Rj

(b)

Cj (9)

while the other terms (i = 0) are calculated from the solution of the following matrix system, for each value of the index j " hx ! (s) (ec) (a) u Cj + Dj = M s Cj 2

(10)

" ! " hx ! (s) (ec) (a) (b)T (b) vj Cj + Dj = vj Mc Cj + k 2 Mr sj + vj Lj Rj Cj 2

(11)

(b)

(s)

+ k 2 vj λj Lj C0j

45


" ! " hx ! (s) (ec) (a) (b)T (b) κj Cj − Dj = γ j Mc Cj + k 2 vj Mr + Lj Rj Cj 2 (b)

(12)

(s)

+ k 2 vj λj Lj C0j

The dimensions of the vectors and matrices are dictated by the number of terms Ns used in the double summation expressions that represent the electromagnetic field. In Eqs. (10)-(12) the unknown coefficients for each value of j are described by a Ns × 1 vector and Ms , Mc , Mr are square matrices Ns × Ns , the elements of which are defined by the following (here k is index) sin[(pk − ui )c] sin[(pk + ui )c] − (13) Ms [i, k] = p2k ak 2(pk − ui ) 2(pk + ui ) 2 ui cos(ui c) sin[qk (c − hx )] − qk sin(ui c) cos[qk (c − hx )] + pk qk2 − u2i Mc [i, k] = ak pk − qk Mr [i, k] =

sin[(pk − ui )c] sin[(pk + ui )c] + 2(pk − ui ) 2(pk + ui )

−qk cos(ui c) sin[qk (c − hx )] + ui sin(ui c) cos[qk (c − hx )] qk2 − u2i

(14)

rk cos(ui c)(−1)k+1 rk2 − u2i

(15)

Finally, L is again a vector Ns × 1 defined by: L[i] = cosh[k(hx − c)] +

sin(ui c) ui

(16)

−ui sin(ui c) cosh[k(hx − c)] + k cos(ui c) sinh[k(hx − c)] k 2 + u2i

Note that all of the above matrices have a common characteristic: they are independent of the variable vj and therefore they need to be formed just once. 2.2. Impedance Change The magnetic field in all regions as well as the eddy current density in the conductor can be calculated from the expressions that relate B and J to W. The general expression for the impedance change caused by the presence of the conductive edge can be derived by using a reciprocity relation and written in the following form [2]: −jω ΔZ = μ0 I 2

hx hy ∂φ(s) ∂φ(ec) − φ(s) φ(ec) dxdy ∂z ∂z z=0 0

(17)

0

Substituting from Eqs. (1)-(2) and using Parseval’s theorem for Fourier series gives ΔZ = −

∞ ∞ jωhx hy (s) (ec) (2 − δi )κij Cij Dij 4μ0 I 2 i=0 j=1

(18)

46

T. Theodoulidis et al. / Developments in Modelling Eddy Current Coil Interactions (s)

(ec)

where Cij represents the source coefficients characterizing the isolated coil and Dij represents the reflection coefficients characterizing the contribution of the eddy current density induced in the right-angled conductor.

3. The Source Coefficient for a Tilted Cylindrical Coil In addition to the case where the coil axis is normal to a surface of the conductor, as studied in [1], it is of interest to compute the response of a tilted coil to the presence of an edge, Figure 2(b). An analytical model for the tilted coil above a conductive halfspace was recently presented in order to study the effect of the tilt angle on the coil’s impedance and moreover its effect on surface crack inspection signals [4]. In the context of our analysis, the source coefficient of the tilted coil is (s)

μ0 i0 e−κij d 2π (2 − δi ) sin(vj yd ) · hx hy κij ψ1 l 1 ψ2 l 1 jui xd −jui xd M1 e M2 e sin + 3 sin · ψ13 2 ψ2 2

Cij =

(19)

where i0 = N I/[(r2 −r1 )l] is the excitation current density with N denoting the number of wire turns, ψ1 = ui sin ϕ − jκij cos ϕ and ψ2 = ui sin ϕ + jκij cos ϕ and Mi = ψi r 2 ψi r1 xI1 (x)dx with I1 (x) denoting the modified Bessel function of order 1. When the lift-off l0 of the coil is known, i.e. the distance of the lowest point of the coil to the upper conductor surface, the height of the coil center is given by d = l0 + r2 sin (|ϕ|) + (l/2) cos (ϕ). The tilt angle ϕ is positive for an anti-clockwise rotation. The case of a cylindrical coil, whose axis is normal to the upper surface of the conductor, can be derived from Eq. (19) by setting ϕ = 0.

4. Results Code was written in Mathematica to compute the impedance change of the tilted coil as it is moved across the edge. The issue to be decided is the extent of the truncated domain defined by hx and hy and the number of terms in the x and y-summations. Reference to the case of the half-space conductor was very helpful in this respect. Theoretical results from the double series expressions were compared to results from the exact double integral expressions in [4] and it was observed that for hx = hy = n · r2 and Ns = 2n we obtained an agreement of the order of 1% for all frequencies. Hence, for n = 15, we only need 30 terms in the series expansions and the square matrices are 30 × 30. This approach makes the quarter-space model very efficient in terms of numerical implementation since, in addition, the matrices inversions do not depend on coil position. Thus, the calculations of the whole coil-position scan above the edge (41 points), takes about a second when using Mathematica in a typical Pentium class PC. The particular value for n ensures that the coil is always far from the boundaries at x = 0, hx and thus its impedance it not affected by them. Taking into account that the coil is moved at a distance of ±20mm from the edge, the choice of n = 15 ensures that the coil is never located closer than 5r2 to the boundaries.

T. Theodoulidis et al. / Developments in Modelling Eddy Current Coil Interactions 0.04

47

0

0.035 0.05 0.03 0.025

ΔX/X

0

ΔR/X0

0.02

−0.1

0.15

0.015 0.01

−0.2 0.005 0 −20

−10 0 10 Coil center position [mm]

20

0.25 −20


20


20


20

−3

x 10

0

4.5

0.005

4

−0.01

3.5

0.015

3 0

−0.02

ΔR/X

2.5

ΔX/X0

5

0.025

2 −0.03

1.5 0.035

1 −0.04

0.5 0.045 −20

0 −20


20

−3

3.5

x 10

0

3 005

2.5 .01 ΔX/X

0

ΔR/X

1.5

0

2

015

1 .02

0.5 0 −20


20

025 −20

Figure 3. Comparison of theoretical (lines) and experimental results (circles) for the normalized resistive and inductive part of the impedance change as the coil moves across the edge. Excitation frequency is 10kHz. From page top to page bottom the tilt angle ϕ is 0, 38 and 90 degrees respectively.

48

T. Theodoulidis et al. / Developments in Modelling Eddy Current Coil Interactions Table 1. Test parameters for the numerical computations in Figure 3. Coil

Testpiece

Tilt data

r1

7.04 mm

σ

25.51 MS/m

ϕ

0o

38o

90o

r2 l

12.20 mm 5.04 mm

c

hx /2

d

4.6 mm

12.17 mm

14.0 mm

N

544

L0

5.55 mH

The theoretical results were also compared to experimental measurements for three coil orientations, Figure 3. Coil and testpiece data are given in Table 1. In all cases the coil former is in contact with the conductor upper surface and thus the distance of the coil center changes with tilt angle. Good agreement is observed for all cases except for some discrepancy in the resistive part of the tilted coil. This is attributed to the fact that it was a very small signal and thus it was subject to coil thermal drift since the position scan was time consuming.

5. Conclusions An existing model for a coil above a right-angled conductor has been extended in terms of both numerical implementation and scope. We are now able to formally express the edge effect for any coil and have given explicit expressions for a cylindrical coil of arbitrary orientation. The model is open for still further developments including (i) the use of closed form expressions for source coefficients for non-cylindrical coils (ii) the calculation of the magnetic field and eddy current density and (iii) the extension to driver pick-up probes. Furthermore, the tilted coil expressions can be combined with the plate edge analysis [2] and the through-slot model [3].

Acknowledgements The authors would like to thank Rob Ditchburn of the Defence Science and Technology Organization, Australia, for providing the experimental data. This work has been partially funded by the Greek Ministry of National Education & Religious Affairs in the framework program “Archimedes II: Promotion of Research Groups in TEI”.

References [1] [2] [3]

[4]

T.P. Theodoulidis and J.R. Bowler, Eddy current coil interaction with a right-angled conductive wedge, Proc. R. Soc. Lond. A 461 (2005), 3123–3139. J.R. Bowler and T.P. Theodoulidis, Coil impedance variation due to induced current at the edge of a conductive plate, J. Phys. D: Appl. Phys. 39 (2006), 2862–2868. F. Fu, J.R. Bowler and T.P. Theodoulidis, The effect of opening on eddy current probe response for an idealized through crack, Review of Progress in Quantitative Nondestructive Evaluation 25 (2005), 330–336. T.P. Theodoulidis, Analytical model for tilted coils in eddy current nondestructive inspection, IEEE Trans. Magn. 41 (2005), 2447–2454.


49

Volumetric and Surface Flaw Models for the Computation of the EC T/R Probe Signal due to a Thin Opening Flaw Léa MAURICE a,1 , Denis PRÉMEL a and Jozsef PÀVÒ b and Dominique LESSELIER c and Alain NICOLAS d a CEA Saclay, LIST/SYSSC, Bât. 611, 91191 Gif-sur-Yvette, France b Budapest University of Technology and Economics, H-1521 Budapest, Hungary c L2S-DRE (CNRS-Supélec-UPS), 91192 Gif-sur-Yvette Cedex, France d ECL CEGELY, 36 avenue Guy de Collongue, Bât. H9, 69134 Ecully Abstract This paper is concerned with the dyadic Green formalism in order to develop simulation tools dedicated to Eddy Current Non Destructive Testing (ECNDT). The Volume Integral Method (VIM) is useful when considering volumetric flaws. The Surface Integral Method (SIM) is more appropriate for thin opening flaws. This latter fast method provides accurate results, except in some critical Transmitting / Receiving (T/R) configurations. In such cases, we propose to combine VIM and SIM to obtain satisfactory results. Keywords. Eddy current, non destructive testing, ideal crack, CIVA software

1. Introduction The interaction between eddy currents and a thin crack has been studied by many authors in the last two decades. It is convenient to predict the EC signal due to the changes in the impedance of an absolute probe investigating a flawed region by considering an ideal crack [1]. The “ideal crack model” consists in considering that the crack width is very small compared to its other dimensions and the skin depth [1]. The surface model leads to represent the ideal crack by a current dipole surface density, which is a scalar quantity depending on two spatial variables, in the crack plane; the third spatial variable, along the thickness of the flaw, disappears. Even if this surface dipole density p is solution of an integral equation with an hypersingular kernel on the crack surface [2,3], this kernel may be evaluated in an alternative way in the spectral domain [4]. Some numerical difficulties coming from specific boundary conditions satisfied by p [5] may be overcome by using a global approximation [6]. A fast numerical model has been implemented [7], it is very favorable for the development of a commercial software dedicated to ECT engineers in probe design or in the goal to perform some parametric studies [8]. 1 Corresponding Author: Léa Maurice, CEA Saclay, LIST/SYSSC, Bât. 611, 91191 Gif-sur-Yvette, France. E-mail: [email protected]

50

L. Maurice et al. / Volumetric and Surface Flaw Models

Most of simulation results are in good agreement with experimental results, except in some critical T/R NDT configurations implying a transmitting and a receiving coil. In such a situation, we propose to combine the volumetric and surface integral approaches in order to obtain suitable results. The paper is organized as follows. A review of the volumetric (VIM) and the surface (SIM) semi-analytical models based on integral and dyadic formulations is given. Then, the hybrid method (HybM) is introduced in order to take advantage of each method and to retrieve more accurate results than those obtained by the surface model (SIM) but with a computational time smaller than the one required by using the volumetric model (VIM). In most of applications in NDT, the planar approximation gives quite good results and the integral formalism using green’s dyads provides a good accuracy and a very short computational time compared to more general FEM-BEM methods.

2. Description of the Three Models Let us consider a conducting slab, constituted by an homogeneous non magnetic media of conductivity σ 0 and permeability μ 0 . The slab is assumed to be infinite in the x and y directions with a finite depth, and it is affected by a thin crack represented by a planar defect. A driving time-harmonic current of angular frequency ω and of magnitude I T is applied to the transmitting coil. The induced primary field is denoted by E P (r). The current in the receiving coil has a magnitude of I R . The implicit time dependence is exp(iωt).

2.1. Volumetric Model The VIM model has shown its efficiency for the prediction of the probe response in presence of a volumetric flaw [9]. If we call σ(r) its conductivity, this kind of flaw is described [11] by a fictitious current density P(r) = (σ(r) − σ 0 )E(r), which is solution of the integral equation:

G(r|r ) P(r ) dr

E(r) = EP (r) + iωμ0

(1)

Vd

where G(r|r ) is the Green dyad calculated for a slab of finite thickness, and V d is the volume of the flaw. According to the reciprocity theorem [10], the probe response is obtained by: I · I ΔZ = − T

ER (r) · P(r) dr

R

(2)

Vd

where ER is the electric field which would be due to the receiving coil assumed to operate in the source mode. Since the transmitting and the receiving coils are identical in the case of an absolute probe, I T = I R and ER = EP , this leads to the usual formula of impedance [1]. A numerical model has been developed using a Method of Moments (MoM) decomposition, and a set of pulse testing functions to approximate


51

P(r). When using this model to simulate the case of a thin-opening flaw, the number of cells has to be increased to reach satisfactory accuracy, and this leads to a quite significant computational time. This is the reason why the SIM has been developed, which embodies specific assumptions enabling to significantly reduce the computational load overall. 2.2. Surface Integral Model To develop this dedicated model, an ideal crack is defined [1]: its opening is negligible, and no current is allowed to flow across it. The defect is assumed to be a void of zero conductivity : σ(r) = 0. The existence of a scalar potential quantity p(r), defined by Eq. (3), can be demonstrated [1]. − E+ t (r) − Et (r) = −

1 ∇t p(r) σ0

(3)

− where E+ t (r) and Et (r) are the tangential components of E(r) on both sides of the flaw, and ∇t is the tangential gradient. The scalar surface dipole density p(r) can be related to the projected part of P(r) on n, the unit vector orientated normal to the surface of the crack. It takes into account the fact that the idealization of the flaw means that it is equivalent to a source layer of current dipole orientated along n. Then, it can be shown that p(r) is solution of Eq. (4):

EP (r0 ) · n = −

lim

r→r0 ∈Sf

iωμ0

Gnn (r|r ) p(r )dr

(4)

Sf

where Gnn (r|r ) = n · G(r|r ) · n is the projected dyad and S f is the surface of the flaw. The probe response is then again given by: I T · I R ΔZ = −

ER (r) · n p(r) dr

(5)

Sf

with the same remarks for the case of an absolute probe as previously. A numerical model has been developed using a MoM decomposition and a global approximation [6] of p(r). It gives accurate results for the simulation of most NDT configurations in a very short time. Eq. (5) shows that only the normal component of the primary field contributes to the probe response, so we propose a hybrid model (HybM) which considers all components of the primary field. This model is built up in order to be better suited to a thin crack than VIM and less restrictive than SIM. 2.3. Hybrid Model Let us assume that we are faced with a thin planar flaw which volume V d that is perfectly non conducting. This flaw can be represented by a volumetric current density P(r) = −σ0 · ET (r) where ET (r) is the electric field due to the interaction between the primary field and the flaw. Let us approximate E T (r) with the electric field of a corresponding ideal thin crack with surface S f (a mid-cross-section of V d ) as [1]:

52


Coils Absolute mode T/R1 mode T/R2 mode

Figure 1. The EC probe is constituted by three coils.

C1 × R ×

C2 T/R T T

C3 × × R

Figure 2. The functioning mode depends on the part of each coil (Transmitter or Receiver).

G(r, r ) · n p(r )dr

ET (r) = EP (r) + iωμ0

(6)

Sf

Then, the probe response is given by : I T · I R ΔZ = σ0

ER (r) · ET (r) dr.

(7)

Vd

To perform this HybM, the SIM model must be launched in a first step in order to get the surface dipole density p(r) on S f , then the total electric field E T (r) in Vd is computed as in Eq. (6) considering a reduced VIM version. Only three dyads are required, instead of nine for VIM, and the dimensions of each matrix operators amount to N × N 1 with N = nx × ny × nz and N1 = ny × nz instead of N × N . N is the total number of discretization cells of the volumetric flaw, n x , ny and nz are respectively the number of discretization cells in the x, y and z directions. By this arrangement, the "HybM" method can get more accurate results than SIM, but with a computational time nearly comparable to the one obtained by SIM. 3. Experimental Validations Simulated data provided by VIM, SIM and HybM are then compared to experimental data. Three arrangements of three coils are tested, as illustrated in Figure 1. The table in Figure 2 summarizes three functioning modes of the probe: the first one corresponds to an absolute mode (the same coil is transmitting and receiving), the two other configurations assume a receiving coil separated from the transmitting coil. The table in Figure 2 summarizes the modes for each coil. It arises that two different T/R orientations are considered according as the axis passing by the center of the two coils is parallel or normal to the length of the flaw. These two configurations are respectively denoted by T/R1 and T/R2. Each figure, except specific mention, displays four curves, one for each tested model, and one for the experimental data. For VIM and HybM, the number of cells assuming pulse testing functions for the approximation of P is given into parentheses in the caption, with the format (n x x ny x nz ). In the same manner, the number of global approximating functions [6] is given for SIM. These numbers have been optimized by a set of numerical experiments.


Figure 3. Real part of the absolute probe response.

53

Figure 4. Imaginary part of the absolute probe response - see Fig. 3.

3.1. Experimental Validations with an Absolute Probe - First Arrangement The tested specimen consists of a 1.55-mm-thick slab of conductivity σ 0 = 1.02 MS/m, which is containing a flaw 0.61 mm deep, 4 mm long, and 0.11 mm wide. The absolute probe is characterized by an inner radius of 1 mm, an outer radius of 1.6 mm, a height of 2 mm, and a number of turns of 328. The real and imaginary parts of the actual experimental absolute probe response are compared to simulated data obtained with the three models in Figure 3 and Figure 4, respectively. We can observe a good agreement between simulated data and experimental data but simulated data obtained by VIM are closer to experimental data. The value of the thickness of the flaw and its small size are not favorable factors for the approximation due to surface current density. 3.2. Experimental Validations with a T/R Probe - Second Arrangement We now carry out two sets of experimentations, each one involving the same T/R probe with two different orientations arising from the functional mode of the T/R probe. The operating coils are characterized by an inner radius of 1.15 mm, an outer radius of 1.39 mm, a number of turns of 90, a height of 1.2 mm, and a lift-off of 0.1 mm. They are separated by a distance of d = 6 mm. We perform tests on two EDM notches in a 1.55 mm-thick slab of inconel 600, with an opening of 0.1 mm, a length of 7 mm, and respective depths 1.23 mm (80%), for the so-called "N1" one, and 0.92 mm (60%) for "N2", at two frequencies, 1 MHz and 500 kHz. As experimental data obtained at 1 MHz present a higher magnitude, we prefer to present these results. For each method, the signal obtained on "N2" in the "T/R 1" orientation is normalized with a complex value coefficient which is then used for calibration. Figure 5 and Figure 6 show the real and imaginary parts of the simulated and actual probe response in the presence of notch "N1" (80%), with the "T/R 1" configuration. In Table 1 are reported in the first line, referred to as "Error", the difference in % on the maximum magnitude between the data obtained with each model and the experimental data. The second

54


and third lines feature the corresponding computational time required for the 1D scan, and for a 2D scan including 18 lines and 31 rows respectively, on the same standard PC (Pentium R, 3.20 GHz, RAM : 512 Mo). Table 1. Comparative elements on the “N1” / “T/R 1” configuration. VIM

HybM

Error [%]

5

9

11

CPU Time [minutes]

15’

2’

1’40

CPU Time (2D) [minutes]

5 × 60’

4’

2’

Figure 5. Real part of the probe response for “N1” (1.23 mm depth, 80%) and “T/R1”

SIM

Figure 6. Imaginary part of the probe response for “N1” and “T/R1” - see Fig. 5

We therefore conclude to a good agreement between the three models used and the experimental data. Let us consider now the configuration defined by the "N1" notch, with the probe in the "T/R 2" orientation. The real and imaginary parts of the results are given in Figure 7 and Figure 8. A first feature of these results is that the magnitudes of the signals are more than 10 times smaller than those obtained in the previous configuration. That is the reason

Figure 7. Real part of the probe response for “N1” (1.23 mm depth, 80%) and “T/R2”

Figure 8. Imaginary part of the probe response for “N1” and “T/R2” - see Fig. 7.


55

why actual testing is seldom performed in this way. The differences on the magnitude for the line scanning between the data computed with each model and experimental data are reported in Table 2. Table 2. Comparative elements on the “N1” / “T/R 2” configuration. VIM

HybM

Error [%]

16

4

SIM 17

CPU Time [minutes]

9’

2’

1’15

The VIM signal underestimates the other results with a cumulative magnitude of 0.1031 mV against 0.1173 and 0.1222 for HybM and experimental data, respectively. This underestimation often occurs when the number of cells is not sufficiently large. The increasing of the number of cells provides a higher computational time. However, an overestimation of SIM (0.1424 mV of magnitude) can be noticed for all tested cases with this “T/R 2” configuration. Moreover, we sometimes observe a real shape difference (see e.g. Figure 9). In all such cases, HybM enables to retrieve more suitable results, as illustrated here. Although the “T/R 2” configuration is not a favorable NDT configuration, it turns out to be a critical configuration for SIM, because of too restrictive assumptions, and it exemplifies the needed corrections brought by HybM by taking the total electrical field ET into account for the computation of the probe response. The second line of Table 2 features the computational times required to compute the 1D data set with each method. We observe the same behaviour, regarding the shape of the signals and the computational time, at a frequency of 500 kHz.

4. Conclusive Remarks and Open Questions The already existing VIM and SIM models provide two means of predicting the electromagnetic interactions with a thin flaw. VIM has been developed for general volumetric flaws, whereas SIM is based on assumptions coming from the ideal crack. These assumptions turn out to be too restrictive in some T/R configurations. However the main benefit of SIM remains its fast computation, while VIM requires a high computational time and a high memory space to simulate the thin flaw case. The new developed hybrid model gives quite good results for volumetric flaws as well as for planar defects. This model enables to join VIM and SIM. The thickness of the flaw is better taken into account by HybM rather than by SIM. Let us consider the particular arrangement when the probe is constituted by two identical coils functioning in the T/R2 configuration. One interesting question is what happens when the distance between the two coils is decreasing comparatively to the diameter of the coils. Figure 9 displays some simulated results obtained by the three methods VIM, SIM and HybM. One can observe a real shape discrepancy between these results. We do not observe such a shape discrepancy for the other T/R1 functioning mode. Now, if we consider an increasing of the distance separating the coils, denoted by d, the shape discrepancy does not come out. Figure 10 shows some results considering a distance which reaches a value of 7 mm. The results obtained with the three models are rather satisfying.

56


Therefore, we can observe that above the SIM model can not “see” the effect of the two coils as it should, if we refer to the results yielded by other models otherwise validated by experimental experiments. The HybM model that we propose takes advantage of the SIM and the VIM and it provides a suitable correction for the T/R2 configuration. HybM seems to be more reliable than the SIM model as it provides accurate results close to the experimental data, for all configurations, even for those appear to be critical for SIM. Moreover, the CPU time is almost similar than the one we obtain by SIM because a fewer number of discretization cells is required compared to VIM.

Figure 9. Magnitude of the e.m.f. yielded by the SIM for a distance of 4 mm between the coils.

Figure 10. Magnitude of the e.m.f. yielded by the SIM for a distance of 7 mm between the coils.

References [1] J. R. Bowler, “Eddy-current interaction with an ideal crack. I. The forward problem,” J. Appl. Phys., Vol. 75, no 12, pp. 8128-8137, 1994. [2] P. Beltrame and N. Burais, “Computing methods of hypersingular integral applied to eddy-current testing,” IEEE Trans. Magn., Vol. 38, no. 2, pp. 1269-1272, 2002. [3] P. Beltrame and N. Burais, “Application of regularization method of quasi-singular integrals to compute eddy-current distribution near cracks,” Int. J. Comp. Math. Engng, Vol. 21, no. 4, pp. 519–533, 2002. [4] J. Pávó and K. Miya, “Reconstruction of crack shape by optimization using eddy current field measurement,” IEEE Trans. Magn., Vol. 30, no. 5, pp. 3407-3410, 1994. [5] J. R. Bowler, Y. Yoshida and N. Harfield, ”Vector potential boundary integral evaluation of eddy current interaction with a crack,“ IEEE Trans. Magn., Vol. 33, no. 5, pp. 4287-4294, 1997. [6] J. Pávó and D. Lesselier, “Calculation of eddy current testing probe signal with global approximation,” IEEE Trans. Magn., Vol. 42, no. 4, pp. 1419-1422, 2006. [7] J. Pávó, D. Prémel, and D. Lesselier, “Application of volumetric and surface defect models for the analysis of eddy current non-destructive testing problems,” URSI International Symposium on Electromagnetic Theory, May 2004, Pisa, Italy, pp. 400-402. [8] Y. Deng, X. Liu, Z. Zeng, L. Udpa, W. Shih, and G. Fitzpatrick, “Numerical studies of magneto-optic imaging for probability of detection calculations,” Electromagnetic Nondestructive Evaluation, Vol. IX, L. Udpa and N. Bowler (eds), IOS Press, pp. 33-40, 2005. [9] P. Calmon and D. Prémel, “Integrated NDT models in CIVA,” IInd international Workshop of NDT Experts, 2003. [10] B. A. Auld and J. C. Moulder, “Review of advances in quantitative eddy current non destructive evaluation,” J. Nondestruct. Eval., Vol. 18, no. 1, pp. 3-10, 1999. [11] 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.


57

Application of Eigenfunction Expansions to Eddy Current NDE: A Model of Cup-Cored Probes a

Hossein BAYANI a,1, Theodoros THEODOULIDIS b and Ichiro SASADA a Dept. of Applied Science for Electronics and Materials, Kyushu University, Japan b Dept. of Engineering and Management of Energy Resources, University of West Macedonia, Greece

Abstract. An axisymmetric cup-cored coil placed above a layered conductive halfspace is analyzed by using the truncated region eigenfunction expansion method. Closed-form expressions are presented for the coil impedance as well as the induced eddy current density. The results are in very good agreement with results from 2D-FEM and with experimental ones. Keywords. Cup-cored Probe, Eddy current, Eigenfunction Expansion.

1. Introduction In order to decrease an eddy current probe’s magnetic reluctance one must wind it either on or inside ferrite cores. The latter reduces the leakage field from the test area too. In this case, where the Dodd model for air-cored coils [1], cannot be utilized numerical models have been used instead [2, 3]. Nevertheless, a closed-form expression can be derived by using the Truncated Region Eigenfunction Expansion (TREE) method [4] which involves a modification of the solution domain in order to replace the integral expressions with more convenient series ones. In this paper, the model is extended to the case of a cup-cored probe as shown in Figure 1. The probe consists of a circular coil of rectangular cross section confined coaxially by a cup-cored ferrite, and is located above a layered half-space of conductive material. The cup-cored probe not only gives a much higher flux density but it also shields the flux into the test area thus producing stronger signals when it comes to crack inspections. As in the classical approach, the method uses separation of variables to express the electromagnetic field in the various regions of the problem in an analytical form. It differs, however, from the classical approach in the truncation of the solution domain in order to limit the range of a coordinate that would otherwise have an infinite span. As a result, the solution dependence on the coordinate is expressed as a series form, rather than as an integral. In this case the numerical implementation is usually more efficient and the error control is easier.

1 Corresponding Author: Hossein Bayani, Dept. of Applied Science for Electronics and Materials, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga-Koen 6-1, Fukuoka, 816-8580, Japan; E-mail: [email protected]

58

H. Bayani et al. / Application of Eigenfunction Expansions to Eddy Current NDE

Figure 1. A cup-cored coil of finite cross section above a layered conductive half-space.

In this paper truncation of the problem region means that the cylindrical surface r=t has now become the outer boundary. On this boundary we impose a homogeneous Dirichlet condition for the magnetic vector potential although a homogeneous Neumann can also be used. The magnetic cup-core is treated as a homogeneous and isotropic region having relative magnetic permeability μf and together with the outer boundary these are about the only additional assumptions that have to be made for this model compared to the Dodd and Deeds models. The solution proceeds as follows: The only component of the vector potential (azimuthal) is expressed in the form of a series of orthogonal eigenfunctions involving discrete eigenvalues. These eigenvalues as well as the series coefficients are computed by imposing the continuity conditions on the various boundaries and interfaces of the solution. In the vertical boundaries the continuity is imposed in a term by term manner while in the horizontal boundaries this is done using mode matching. The whole analysis is very lengthy and will not be repeated. The reader is referred to [4] for details of the approach. Here we will provide the final expressions for the coil impedance and the induced eddy current densities together with all other expressions necessary for their computation.

2. Solution In the beginning we solve the electromagnetic field problem for a delta-function coil at (r0, h) as in Figure 2, driven by a harmonic current I exp( jZt ) . The coil is located above a nonmagnetic conductive half space comprising two layers with conductivities ı6 and ı7. The plane z = 0, coincides with the bottom of the ferrite core. Following the separation of variables, the expressions for Aĳ in the various regions of the problem have the following form which in addition is given in matrix notation: A1 ( r , z )

T

1

qz

J 1 (q r )q e C1 ;

0dr dt,

(1)


59

Figure 2. A cup-cored coil of delta-function circular current above a layered conductive half-space.

T

A2 ( r , z )

J 1 (m r ) T

1

m (e

mz

L1 (m r )

mz

C2 e B 2 ) ;

T

A3 ( r , z )

1

pz

pz

R1 (p r ) p (e C3 e B 3 ) ;

a d r d b,

T

R1c(p r )

bdrdt

T

0drda

J 1 (p r ) 1

T

A4 ( r , z )

,

pz

pz

R1 (p r ) p (e C 4 e B 4 ) ;

a d r d b,

R1c(p r )

bdrdt

T

1

T

qz

qz

A5 ( r , z )

J 1 (q r )q ( e C 5 e B 5 ) ;

A6 ( r , z )

J 1 (q r )s ( e C 6 e B 6 ) ;

A7 ( r , z )

J 1 (q r )u e B 7 ;

where si

bdrdt

1

T

T

(2)

0drda

J 1 (p r ) T

0drdb

sz

1

uz

qi2 jZP0V 6 and ui

sz

(3)

(4)

0dr dt,

(5)

0dr dt,

(6)

0dr dt,

(7)

qi2 jZP0V 7 , Jn, Yn are Bessel functions of

order n, Ln, Rn, R’n are defined next, the superscript T denotes a row vector, p-1, q-1, m-1, s-1, u-1 and exponentials are diagonal matrices and C, B are unknown vector coefficients. These unknown coefficients and the discrete eigenvalues are to be determined from the boundary and interface conditions. The eigenvalues for each region of Figure 2 are defined as follows: For regions 1, 5, 6, 7 the qi are the positive real roots of the equation:

60


J 1 ( qi t )

0.

(8)

For region 2 the mi are the positive real roots of the equation: L1 ( mi t )

0,

Ln ( mi r )

B2 F J n ( mi r ) C2 F Yn ( mi r ) ,

(9)

where

B2 F

C2 F

S mi b ª

(10)

J 0 ( mi b )Y1 ( mi b ) º

« J1 ( mi b)Y0 ( mi b) 2 ¬

Pf

S mi b ª

», ¼

J 0 ( mi b ) J 1 ( mi b ) º

« J 1 ( mi b) J 0 ( mi b) 2 ¬

». ¼

Pf

(11)

(12)

For regions 3 and 4 the pi are the positive real roots of the equation: R1c( pi t )

0,

(13)

where Rnc ( pi r )

B3ca

C3ca

B3ca J n ( pi r ) C3caYn ( pi r ) ,

S pi b ª

« R1 ( pi b)Y0 ( pi b) 2 ¬

S pi b ª

« R1 ( pi b) J 0 ( pi b) 2 ¬

C3 a

R0 ( pi b)Y1 ( mi b) º

Pf

», ¼

(15)

R0 ( pi b) J 1 ( mi b) º

Pf

», ¼

B3 a J n ( pi r ) C3 aYn ( pi r ) ,

Rn ( pi r )

B3 a

(14)

S pi a 2

S pi a 2

> J ( p a )Y ( p a) P 1

i

0

i

> J ( p a) J ( p a) P 1

i

0

i

(17)

@

f

f

(16)

J 0 ( pi a )Y1 ( pi a ) ,

(18)

@

(19)

J 0 ( pi a ) J 1 ( pi a ) .

The final expressions for the eddy current densities in regions 6, 7 as well as the impedance of the coil are:

61


jZV J1 (qT r ) s 1 (e s z C 67 e s z B67 )

J 6eddy ( r , z )

,(20)

1

ª¬ (T U )e md C 27 (T U )e md B27 º¼ ª¬ (T U )e md L2 (T U )e md L1 º¼ 1

1

1

1

jZV J1 (qT r ) u 1e u z

J 7eddy ( r , z )

1

ª¬ (T U )e md C 27 (T U )e md B27 º¼ ª¬ (T U )e md L2 (T U )e md L1 º¼ 1

jZP0S N

Z

1

2

p h1

e

p h2

, (21)

1

2

( r2 r1 ) ( h2 h1 )

^ª¬(e

1

2

F ( pT r1 , pT r2 )

)C 47 (e

p h2

e

p h1

4

) B47 ) º¼

ª¬(T U )e md C 27 (T U )e md B27 º¼ 1

p

1

,(22)

1

(T U )e md 1 e md F 1 ª ( H G )e pd (e ph e ph ) ( H G )e pd (e ph e ph ) º ½ ¬ ¼ °° °° 2 ® ¾ °(T U )e md 1 e md F 1 ª( H G )e pd (e ph e ph ) ( H G )e pd (e ph e ph ) º ° ¬ ¼ °¿ °¯ 2 1

2

1

2

2

2

2

1

2

2

1

1

2

2

1

2

`

[2( h2 h1 ) p e p h2 e p h1 e p h2 e p h1 ] D 1 p 3 F ( pr1 , pr2 ) where L1 L2

ª( H r G )e pd2 (e ph2 e ph1 )

P0 i0

e r md2 F -1 «

4

¬ ( H # G )e

³

F ( pr1 , pr2 ) B67

1

C 67

2

B57

1

C 57

2

B47

1

C 47

2

B27

1

C 27

2

e

r sy 2

e

pr2 pr1

(e

ph1

e

ph2

º 3 1 » p D F ( pr1 , pr2 ) , )¼

x J 1 ( x ) dx ,

(1 r su 1 )e

r qy1

pd 2

uy 2

(24)

,

(25)

[(1 # qs 1 )e C 67 (1 r qs 1 )e sy1

sy1

B67 ] ,

D 1 > ( H c # G c)C 57 ( H c r G c) B57 @ ,

e

# md2

F 1 ª¬ ( H # G )e

(23)

pd 2

C 47 ( H r G )e

(26)

(27)

pd 2

B47 º¼ ,

(28)

62


and all other matrices are defined in the Appendix. Many special cases can be obtained by the general expression for the impedance change (22). For example for a half-space conductor we can either set V6 =V7 or y2-y1 or y2ĺ. For an isolated cup-core probe we can set V6 =V7 = 0. For an air-core probe we can set μf =1.

3. Results We conducted a series of experiments besides applying 2D-FEM package for two cases of cup-cored and air-cored probe in order to test the validity of our solutions. In the experiments, we scanned a range of frequencies between 100 Hz to 100 kHz with an Agilent HP4284 impedance analyzer. The experimental parameters used in the calculations are given in Table 1. First, we calculated the impedance for a conductive plate to find the normalized impedance plane and then we conducted the first experiment to compare the measurements to the theoretical result with the result of the calculations. We also applied the parameters used in the calculation to a 2D-FEM package. The obtained results are shown in Figure 3. In the second experiment we calculated the impedance based on the special case of the air-cored coil, to find the normalized impedance plane as well as the Dodd model. The results are depicted in Figure 4. For the ferrite-cored coil, the inductance L0 is calculated 21.48 mH, while the measured value is 21.59 mH. For the air-cored coil, the relative values are 18.93 mH calculated and 18.78 mH measured and 19.01mH based on the Dodd and Deeds model. The calculations are carried out by selecting t to be 6 times the outer radius of the cupcored ferrite. In the case of cup-cored we used Ns=33 and for the case of air-cored we used Ns=45. In all cases the relative error between theoretical results and measurements is less than 1.22%, which shows a very good agreement. Even better agreement can be achieved by increasing t and Ns. In Figure 5 we depict the real part of the eddy current density computed by using the TREE method and a 2D-FEM package and the results are also in very good agreement.

1.0 1.0

0.9

f

X / X0

X / X0

0.9

TREE EXP FEM

Cup-cored Coil Pf == 2300 F 2300 0.01

0.02

0.03

0.04

(R-R0) / X0

Figure 3. Impedance plane diagram showing variation of normalized Z with frequency for a cup-cored coil above a conductive 5-mm-thick plate. X0 stands for coil’s isolated reactance.

TREE EXP DODD

f

0.8

Air-cored Coil Pf == 11 F

0.7 0.02

0.04

0.06

0.08

(R-R0) / X0

Figure 4. Impedance plane diagram showing variation of normalized Z with frequency for an air-cored coil above a conductive 5-mm-thick plate. X0 stands for coil’s isolated reactance.

63

0

2

Eddy -current Density ( MA/ m )


FEM LAB TREE

-1

-2

-3 0

5

10

15

20

25

R adial D istance ( m m )

Figure 5. Real part of eddy-current density amplitude at 2 mm below the conductor surface.

Table 1. Coil, cup core, and plate parameters used in calculations and experiments. Coil

Cup core

Aluminum plate

Inner radius r1

4.64 mm

Inner radius a

7 mm

Thickness (y2-y1)

5 mm

Outer radius r2

6.5 mm

Outer radius b

10 mm

Conductivity V6

35.36 MSm-1

Offset h1

0.74 mm

Rel. permeability μf

2300

Conductivity V7

0 MSm-1

Length (h2 - h1)

2.9 mm

Liftoff y1

0.82 mm

Number of turns 1240

4. Conclusion Important magnetic induction quantities such as impedance and eddy current density are derived by using the method of eigenfunction expansion for the case of an axisymmetric cup-cored coil above a layered half-space. Comparison between the results of the experiments and 2D-FEM package with the results of our solution showed a very good agreement. The proposed method is extremely fast and it can also be used to model a cup-cored coil above a half-space having an axisymmetric hole, or can be used to solve the problem of an E-cored probe.

Appendix The matrices E, T, U, F, G, H, D, G`, and H` are computed as

E

ij

iz j 0 ° , ®t °¯ J ( q t ) i j 2 2

2

0

i

(A1)

64


T

§

bqi

ij 2

qi m j

©

2

qi m j

F

· ¸, P ¹

(A3)

1

J 0 ( qi b ) J 1 ( m j b ) ¨ 1

2

(A2)

f

§

bqi

ij

U

· ¸, P ¹ 1

J 1 ( qi b ) J 0 ( m j b ) ¨ 1

2

©

f

0 iz j ° , º§ b ª J ( m b) 1 · ®t J (m b) » ¨ 1 ¸ i j ° 2 L (m t ) 2 « P ¯ ¬ ¼© P ¹

ij

2

2

2

2

2

i

0

i

0

f

G

H

D

2

©P

2

mi p j

t

2

R0c ( pi t ) 2

2

·

1¸ ,

J 0 ( mi a ) J 1 ( p j a ) ¨

©P

§ 1 ¨1 P 2 ©

a

(A5)

¹

f

§ 1

ami 2

i

·

1¸ ,

J 1 ( mi a ) J 0 ( p j a ) ¨

2

mi p j

ij

f

§ 1

ami

ij

(A6)

¹

f

· ¸ ª¬ J ( p a ) J ( p a ) P º¼ ¹

2

2

2

i

1

f

i

0

f

§ º 1 · ª R ( p b) ¨1 R ( p b) » ¸« P ¹¬ P 2 © ¼ b

Hc

ij

(A7)

2

i

0

f

ij

,

2

2

i

1

Gc

(A4)

i

1

f

§ 1 · ¨ 1 ¸ > aJ ( p a ) J ( q a ) bR ( p b ) J ( q b ) @ , P ¹ p q ©

(A8)

§ 1 · ¨ 1 ¸ > a P J ( p a ) J ( q a ) bR ( p b) J ( q b ) @ , P ¹ p q ©

(A9)

pi

2

2

i

j

i

1

0

j

1

i

0

j

f

pi

2

2

i

j

f

0

i

1

j

0

i

1

j

f

where the matrices T, U, G, H, G`, and H` are full and the matrices E, F, and D are diagonal. References [1] C.V. Dodd and W.E. Deeds, Analytical solutions to eddy-current probe-coil problems, Journal of Applied Physics 39 (1968), 2829-2838. [2] H.A. Sabbagh, A model of eddy-current probes with ferrite cores, IEEE Trans. Magn. 23 (1987), 18881904. [3] F. Buvat, G. Pichenot, D. Lesselier, M. Lambert and H. Voillaume, A fast model of eddy-current ferritecored probes for NDE, Electromagnetic Nondestructive Evaluation (VIII), IOS Press (2004), 44-51. [4] T.P. Theodoulidis, Model of ferrite-cored probes for eddy current nondestructive evaluation, Journal of Applied Physics 93 (2003), 3071-3078.

Eddy Current Testing and Technique


67


Experimental Extraction of Time-of-Flight from Eddy Current Test Data a

Antonello TAMBURRINOa,1, Naveen NAIRb, Satish UDPAb, Lalita UDPAb Associazione EURATOM/ENEA/CREATE, DAEIMI, Universita’ di Cassino, Italy b Electrical and Computer Engineering, Michigan State University, USA

Abstract. This paper presents a contribution in the framework of a novel method to extract defect location in conductive materials using data obtained from diffusive nondestructive evaluation (NDE) techniques such as eddy current testing. The method is based on the definition and extraction of the Time of Flight (TOF) for diffusive phenomena by using the Q-transform, a mapping that associates a wave propagation problem to a diffusion problem. In this work we present the method for extracting the TOF from diffusive data together with experimental and numerical tests for a simple configuration. The results clearly demonstrate the application of Q-Transform based approach in a realistic NDE setting. Keywords. Eddy current testing, time-of-flight, Q-Transform

1. Introduction The Q transform, first defined in [1]-[4] as

Q : u ( x, q ) → v ( x, t ) = ( 4π t 3 )

−1/ 2

∫

+∞

0

q exp ( −q 2 / 4t ) u ( x, q ) dq

(1)

relates the solution of a wave equation to the solution of a corresponding diffusion equation. It has been shown to be useful to properly associate the time of flight to diffusion domain data [5]. For wave problems, the TOF is a clearly defined quantity and so, in the light of the Q-Transform, it is reasonable to define the time of flight for a diffusion problem as the (usual) time of flight for the corresponding fictitious wave problem. In particular the extraction of the TOF from the diffusion data can be approached either through an inverse Q-transform [5, 6] or by a careful choice of the excitation waveforms [7-9]. The inverse Q-transform based method involves the evaluation of a Fredholm integral of the first kind and therefore requires regularization techniques. On the contrary, the freedom in the choice of the excitation waveform can be exploited to relate the TOF to an easily measurable quantity in the measured timedomain signal. Specifically, in past work we related the TOF to the peak position of the 1

Corresponding Author: Antonello Tamburrino, DAEIMI, Università degli Studi di Cassino; E-mail: [email protected]. Antonello Tamburrino is also with Electrical and Computer Engineering, Michigan State University.

68

A. Tamburrino et al. / Experimental Extraction of Time-of-Flight from Eddy Current Test Data

measured signal under proper conditions. In this work we will present a new method that is more general than the one based on the peak position, together with numerical results validating the proposed approach and moreover, an experimental setup designed to test the method on a simple canonical problem. The organization of the paper is as follows. The next section will discuss the Qtransform and the idea behind the extraction of the time of flight. The details of the numerical and experimental setup will be provided in section 3, whereas section 4 will attempt to draw some conclusions and point out directions for possible future work.

2. The Q-Transform for TOF Extraction

2.1. A Relationship between Parabolic and Hyperbolic Differential Equations Consider the following two scalar initial value problems defined in Ω⊆ℜN

∇ 2 v (x, t ) − k (x) ∂v(x, t ) / ∂t = F (x, t ) in Ω × ( 0, +∞ )

a (x)v(x, t ) + b(x) ∂v(x, t ) / ∂n = G (x, t ) on ∂Ω × ( 0, +∞ )

(2)

v(x, 0) = h(x) in Ω,t = 0 and

∇ 2 u (x, q) − k (x)∂ 2 u (x, q ) / ∂q 2 = f (x, q) in Ω × ( 0, +∞ )

a (x)u (x, q ) + b(x)∂u (x, q ) / ∂n = g (x, q ) on ∂Ω × ( 0, +∞ )

(3)

u (x, 0) = 0 in Ω ∂u (x, 0) / ∂q = h(x) in Ω

where ∂ ∂n represents the normal derivative w.r.t. the spatial co-ordinate x. Then the Q-transform relates the solutions of the two problems above in the following manner [1]-[4] F = Qf and G = Qg ⇒ v = Qu

(4)

For instance, for a scalar (magneto-quasi-static) diffusion problem in a nonmagnetic conductor (Eddy Current Testing) k (x ) = μ 0σ (x ) ( μ 0 is the magnetic permeability and σ is the electrical conductivity) and v is a magnetic flux density component. The “wave velocity” for the fictitious field u is, therefore, given by

c(x ) = 1 / k (x ) = 1 / μ 0σ (x ) . Eq. (4) provides the Q transform relationship for the scalar case. For vector electromagnetic equations, the relationship can be expressed as described in [9, 10]. Once the connection between a diffusion and a wave propagation problem has been established (see (4)), the TOF for a diffusive measurement v x= x in the time-domain is 0


[ ] corresponding

defined as the TOF for the waveform u x = x = Q −1 v x =x 0

69

to the

0

associated fictitious wave propagation problem. As discussed in the introduction, this definition of TOF is not practical to be applied to experimental data because of the noise affecting the measured and the ill-posedness of the problem of computing the inverse Q-Transform. However, the problem can be cast in an equivalent form. Let qTOF be the TOF associated to the waveform u x= x and let qi be the (known) instant when the field 0

source is turned on. Therefore, u x= x is vanishing for qq0, then

1

πt ∫

∞

q0

u '(q )e

−

q2 4t

dq ≤

M

πt ∫

∞

q0

e

−

q2 4t

⎛ q ⎞ dq = Merfc ⎜ 0 ⎟ ⎝2 t ⎠

(6)

70


where erfc(⋅) is the well known complementary error function. For large arguments the complementary error function can be approximated as

(

)

v(t ) −

u q 0+

−1

e − x ⎡⎣1 + O ( x −2 ) ⎤⎦ for x → +∞ (see [11]). Thanks to (6), it results that for small t, v(t) can be approximated by + u (q0 ) exp ( − q02 / 4t ) / π t . The error in this approximation is bounded by: erfc ( x ) = x π

( )e πt

2

−

q02 4t

⎛ q ≤ Merfc⎜⎜ 0 ⎝2 t

⎛ t ⎞⎤ ⎞ 2M t − q40t ⎡ ⎟≅ e ⎢1 + O⎜⎜ 2 ⎟⎟⎥ ⎟ ⎢⎣ ⎠ q0 π ⎝ q 0 ⎠⎦⎥ 2

(7)

therefore, the error is negligible with respect to u (q0 + ) exp ( − q02 / 4t ) / π t for t small

(

( )

)

enough t f c f a @ ca

(1)

where a, b and c refer to magnitude and/or phase value of the calibrated eddy current signal. The phase and magnitude computed from flaws in the calibration standard tube are used to construct the function f. This method is currently used in industry to generate estimates of the one-dimensional size of a defect.

K. Arunachalam et al. / Defect Profiling Using Multi-Frequency Eddy Current Data

133

(a)

(b) Fig 1 Calibration standard curves (a) Phase (b) Magnitude

4. Alternative Curve Fitting In practice, eddy current signals from calibration standard machined defects are not representative of the defect signals acquired from the in service heat exchange tubes. This is because the damage mechanisms that arise due to stress, corrosion, pitting, sludge piles are not captured completely by the machined defects with precise depths. Thus the calibration standard signals require a transformation to compensate for signal variation between defects in the calibration standard and in service heat exchange tubes. A modified magnitude calibration curve is constructed such that the error in using the calibration defect signals for profiling is minimized. This method generate estimates of depth profile of a defect using an expression of the form,

134


a 0 a1 log e ( flawmagnitude )

log e ( flawdepth )

(2)

where the coefficients a0 and a1 are obtained by fitting a polynomial for the magnitude of flaw signals in the calibration standard curve. Figure 2 shows a magnitude curve constructed using the logarithmic mapping.

Fig 2 Magnitude calibration curve using equation (2).

5. Radial Basis Neural Networks An alternate approach is to use a learning algorithm that implements function approximation using radial basis function neural network (RBFNN). Mathematically, this approach yields a highly nonlinear mapping from an input vector space on to an output vector space. The preference for this network architecture is due to the simplicity of its implementation and rapid convergence characteristics for small training data size. A typical architecture of RBFNN is shown in Figure 3. The input-output transformation equation for the RBFNN can be expressed as [3], P

y

¦w

i

f ( x t i ,V i )

(3)

i 1

where x is the input vector of dimension N , y is output vector of dimension M ,

t i is the i th basis center, w i is the weight vector of dimension M corresponding to the i

th

center and f ( x t i , V i ) is the scalar and radially

symmetric basis function with spread

V i . A total of P

centers (or nodes in hidden

layer) are used in the basis function expansion. The weights, bias and centers and spread V i are computed during the training process using a training data set.


Input Layer

Hidden Layer

ti

Output Layer

wi

1

1

Input vector x

Output vector y

1

135

N

M

P Fig 3 Architecture of RBFNN

The operation of RBFNN is typically divided into two distinct phases: (1) Training phase and (2) Testing phase. In training phase the inputs and desired outputs both are known. For defect profiling, radial basis function (RBF) of the form,

f ( x t i ,V i )

( x ti

2

1)

1

Vi

(4)

is chosen and the basis centers ( t i ) and their spreads or radii ( V i )are determined using unsupervised clustering algorithms on the input data. The weights ( w i ) are estimated with the help of input-output training data pairs and appropriate regularization methods [4]. In the test phase the output values for any given unknown input vector are predicted using the trained parameters of the RBFNN in (3).

6. Results and Discussions This section describes the implementation of the proposed RBFNN approach for depth profiling and presents a comparison of the performance of the method with that of the calibration approaches. The Examination Technique Specification Sheet (ETSS) maintains a database of tube defects and their associated depth profiles as determined by metallographic procedures. The ETSS - provided by EPRI - was used to develop algorithms for characterizing defect depth profiles that are consistent with metallographic results. 6.1. Flaw Length Estimation Flaw length estimation is an integral part of the defect characterization algorithms. The flaw length, as determined by industry, is computed by evaluating the magnitude and phase of each line signal within the region of interest (ROI) and performing a phase and magnitude thresholding of any extraneous line signal in accordance with the respective calibration curves. On the other hand, an adaptive threshold scheme that relies on the histogram of the rotating probe coil (RPC) signal magnitude has been implemented in this paper for estimating the flaw length in the neural network

136


predicted depth profile. An empirical relationship for the magnitude threshold (K) to the ratio of the signal magnitude in the histogram (J) is derived as,

K D exp{O [J J 0 ]} %

(5)

where the constants D, O and J0 are determined from the available profiling data. During defect characterization, RPC signals that lie within K% of the maximum magnitude are used for defect depth profiling. 6.2. Training the Neural Network Seven calibrated Westinghouse Laboratory outer diameter (OD) flaw samples of Tube Support Plate (TSP) extraction and non-constant depth were used for training the neural network and the algorithm for the implementation as shown in Figure 4. Using the axial scale and MET- magnitude correlation methods, the axial length of the ROI is determined. The peak magnitude and phase at multiple frequencies and phase spread (maximum difference in phase values for all frequencies) for each line scan is computed and stored in a feature matrix for training the network alongside the corresponding depths values obtained by metallographic (MET) analysis. For training the network, the feature vectors for the seven sample flaws are systematically aggregated and mapped unto the corresponding MET depths. A more robust neural network is obtained by mapping three spatially consecutive line scans/feature vectors onto the depth value at each position in the flaw.

Figure 4 Schematic of the overall approach using RBFNN

6.3. Testing with Examination Technique Specification Sheet (ETSS) Data A second data set of pulled tubes with metallographic profile information was used to evaluate the performance of the approach. The defect length was estimated and line scans along the defect region were used to calculate the feature vectors. Figure 5(a)-(c) shows the profiling results obtained for three ETSS flaws using the classical magnitude


137

calibration curve approach (CC), and the two RBF neural networks, RBF1 (one feature vector per depth) and RBF2 (three feature vector per depth).

(a)

(b)

(c) Fig. 5 Comparison of metallographic flaw profiles (MET) with profiles generated by different algorithms.

138


The initial results in Figure 5 indicate that the RBF network provides more accurate profiles than the calibration curve techniques. The performance of RBF network on the axial OD defects in the test dataset is summarized in Table 1. The neural network performance is significantly better than that obtained using conventional methods largely due to the fact that is utilizes all information available from multiple frequency inspections. Table 1 Flaw depth and length estimation on the test dataset

Flaw Length (Inches)

Maximum % Through Wall Flaw

1 2 3 4 5 6 7 8

MET*

RBF 1

RBF 2

Log Magnitude

Magnitude

MET*

Estimated

47.00 43.00 60.00 77.00 63.00 60.00 50.00 35.80

51.42 53.45 49.23 57.39 76.85 58.72 47.79 34.47

42.07 48.38 56.80 64.17 65.12 56.92 55.40 31.15

44.00 39.00 26.00 62.00 22.53 63.00 18.00 44.00

43.90 38.68 28.53 60.14 9.00 65.23 27.27 46.25

1.4 1.31 0.53 0.73 0.85 0.52 0.60 0.11

1.51 1.27 0.48 0.65 0.99 0.42 0.34 0.14

* MET - Metallographic Data

7. Conclusions Defect characterization algorithms based on calibration curves and RBF networks have been developed for estimating the depth profiles of axial outer diameter defect indications. Comparisons of different characterization algorithms reveal that the performance of the RBF networks is significantly better than the industry standard calibration curve approaches. The improvement in the performance of the RBF network is solely due to the fact that the multi-frequency features that capture the defect behavior in the impedance plane are used intelligently to map the eddy current data to the flaw depth profile.

References [1] S. S. Udpa, L. Udpa, Wiley Encyclopedia of Electrical and Electronics Engineering, edited by John G. Webster, vol. 6, 1999, pp 149-163. [2] Rotating Probe Eddy Current Data Analysis, Technical Report, EPRI, Palo Alto, CA: 2004. [3] Simon Haykin, "Neural Networks A Comprehensive Foundation", Prentice Hall, Upper Saddle River, New Jersey 07458, 1994, pp.Chapter 7, pp.236-281. [4] Tikhnov A.N and V.Y. Arsenin, "Solutions of Ill-posed Problems", Washington, DC, 1977.


139

Electromagnetic Reading of Laser Scribed Logistic Markers on Metallic Components Szabolcs GYIMÓTHY a,1, József PÁVÓ a, Imre KISS a, Antal GASPARICS b, Zoltán KALINCSÁK a, Imre SEBESTYÉN a, Gábor VÉRTESY b, János TAKÁCS a and Hajime TSUBOI c a Budapest University of Technology and Economics, Hungary b Research Institute for Technical Physics and Materials Sciences, Hungary c Fukuyama University, Japan Abstract. An application of electromagnetic nondestructive evaluation is presented in the paper: Laser scribed markers used as logistic codes on metallic components are reconstructed from the signal of an eddy current probe. The authors developed a computational model of the reading out process by which both the code specification and the probe can be optimized. The model is applied here for the optimization of marker density. The reconstruction of barcode using inverse filtering approach is also demonstrated. Keywords. eddy current testing, barcode, deconvolution, inverse filtering

1. Introduction Specific laser marking technique of the surface of metallic components has been reported in [1]. This marking was originally used for the detection of thermal induced stresses on the surface of rails. In recent times its application for bar-coding is being considered. This specific barcode can be used for the identification of metallic parts in production logistics, during the automated assembly, and also for tracing the manufactured product. The laser scribed barcode exhibits high endurance and thermal stability compared to other marking techniques. Moreover, it can be read out by using electromagnetic principles in a fast, non-destructing and contact free operation, and even from under protective coating (e.g. paint). The automotive industry is one of the main targeted utilizers of the laser marking technique. The measurable effect of the marking stems from the rapid heating and cooling process due to the laser treating, causing local phase transformations in the metal, as well as modifications in the stress field and the domain structure in the vicinity of the surface. These structural modifications affect the local electromagnetic properties like conductivity and permeability. Therefore an eddy-current sensor will produce some time varying signal while scanning above the marking. Figure 1 illustrates the process of laser scribing. Markers providing good signal/noise relation during the reading out can be achieved for example by CO2 laser irradiation with the following parameters: laser power: P 100 300 W; diameter of 1 Corresponding Author: Szabolcs Gyimóthy, Budapest University of Technology and Economics, Egry J. u. 18, 1521 Budapest, Hungary; E-mail: [email protected]

140

S. Gyimóthy et al. / Electromagnetic Reading of Laser Scribed Logistic Markers

Figure 1. Illustration of the process of laser scribing

laser spot: d 0.5 2.0 mm; movement speed: v 1200 mm/min. Figure 2 shows the photomicrograph image on the cross-section of the transformed zone due to laser-metal interaction in high carbon (0.6 C%) rail steel (left), and in low carbon (0.1 C%) cold rolled structural steel (right), respectively. The latter image contains some graphical enhancement, because the structural changes are not visual enough in this case. Although some parameters of the laser scribing process itself have already been fixed [1], there are still several unspecified parameters of the complete marking technique, which have to be optimized towards the efficient reading out and reconstruction of the code. These are among others the type and geometry of the sensor probe, the coding system used for the barcode, as well as the geometry specification of the marking (e.g. width, depth, density), which latter may depend on both the spatial resolution of the probe and the applied coding system. In order to facilitate the optimization, the authors have developed a computational model of the reading out process based on the finite element method. Using this model the optimal distance between adjacent markings has been estimated. Finally, barcode reconstruction from measured signal has been demonstrated by using an inverse filtering approach. The results associated with the three outlined topics are presented in this paper.

2. Numerical Model for the Simulation of the Reading Out Process Figure 3 provides two schematic views of the measurement configuration used for reading out the barcode. The Fluxset sensor [3] is applied for measuring the magnetic field above the conducting object. The magnetic field is induced by an exciting coil (inner diameter: 4 mm; outer diameter: 8.4 mm; height: 4.7 mm; lift-off: 0.25 mm)

Figure 2. Photomicrograph images taken on the cross section of laser marked metallic components. Left: high carbon rail steel (0.6 C%); right: low carbon cold rolled structural steel plate (0.1 C%)


141

Figure 3. Typical measurement configuration used for the reading out

above the sensor. The orientation of the sensor core coincides with the scanning direction of the probe (x-direction), which is perpendicular to the marker lines. The investigated steel plate specimen (size: 100mm×100mm; thickness: 0.6 mm) is made of low carbon steel (C < 0.1 %, Mn = 0.7 %, Si = 0.3 %, Ti = 0.06 %) having 0.01 mm iron-zinc coating on both sides. The applied frequency in the measurement is 20 kHz. 2.1. Simplified Finite Element Model A finite element model of the reading out process has been developed (Figure 4). The model applies the T-ĳ formulation combined with hexahedral edge elements [4]. Instead of modeling the complex microstructure in the laser irradiated zone, a macroscopic equivalent model has been defined. Using this approach the measured data can be reproduced with sufficient accuracy, while still describing the overall physical picture well. The geometry of the cross-section of the marker is simplified to the rectangular shape (width: 0.5 mm; depth: 0.2 mm) for the following two reasons. First, the non-uniform graded mesh around complex geometries would influence the calculated results in a way that a kind of “false signal” component appears in the output of the probe. Second, when using the mesh on Figure 4, which has uniform x-subdivision, one can easily modify the barcode without changing the mesh, by just adjusting the material properties. The length of each marker line is 30 mm. The region of the marking is considered as a homogeneous linear material in the model. 2.2. Fitting of the Model Parameters to Measured Data Electric conductivity and magnetic permeability of the marked region are parameters of the model, which have to be set towards achieving the best fit between the simulated output signal and the real measured data. Although the Fluxset sensor is intended to be used for code reading in the long run, particularly for the identification of the model parameters a classical test measurement has been chosen. The impedance change of a coil is measured above the sheet. We selected the impedance probe for this purpose because by using this, it is easier to get reliable quantitative data both in experiment and in theory. The fitting of electromagnetic parameters is carried out in two steps: first the parameters of the base material are determined, and then the parameters of the marked region are finely tuned. In the first step, the impedance of the exciting coil was measured above a nonmarked sheet, and was compared to its impedance measured in the absence of the sheet. At the same time, these impedance change values were calculated for several conductivity-permeability pairs, using the computer code Teddy [5] based on semi-

142


Figure 4. Part of the finite element model of the measurement used for reading out the barcode. The conducting plate, three markers and the half of the exciting coil are plotted. The surrounding air is discretized as well, but not shown here.

analytical method [6]. The comparison of measured and calculated results indicated that the ratio of the two parameters must be about P r / V 30 m/MS . Also it became evident from the simulation that the influence of the thin iron-zinc coating on these results is negligible. Finally we chose the conductivity value, V 4 MS/m from the literature, which results P r 120 for the permeability parameter of the base material. In the second step of the model calibration the impedance change of the exciting coil was recorded while it scanned above one single marker far from the edges of the plate. At the same time several impedance scans were simulated with systematically varied parameters of the marked zone in the above described finite element model. The best fit to the measurements has been found with slightly lower conductivity and higher permeability values ( V 2 3 MS/m , and P r 400 500 ) in the marked region than in the base material. We are well aware, that the expected behavior is opposite, as permeability usually decreases after rapid heating and cooling. In order to resolve this contradiction, further analysis of the complex microstructure in the metal, as well as the refinement of the numerical model would be required. Nevertheless, the current model can still be used as one which is reasonable from the point of view of the measurements.

3. Prediction of Optimal Marker Density Using the Numerical Model The information density in the barcode can be increased by lowering the distance between the marker lines. On the other hand, the signals generated by the markers tend to overlap for shorter distances, as it is witnessed by the measured curves presented in Figure 5, and the inflectional points or peaks originally relating to marker positions loose their meaning. Therefore finding the optimum distance between adjacent markers is an important practical problem. The fundamental question is whether or not the overlapped signals can be separated somehow, that is, whether, or to which extent, the superposition principle for marker signals holds. This “linearity” feature has been analyzed by using the above described finite element model.


143

Figure 5. Measured curves of the Fluxset sensor for double marker lines of various separation distances (marker positions are x = ±2.5 mm, x = ±1.5 mm and x = ±1 mm, respectively).

In the investigated problem, the Fluxset sensor measures the weighted average of the x-component of the magnetic flux density taken along the sensor core [7]. This weighted average is evaluated from the numerical model. Note that although the measurement principle of the Fluxset sensor is different, the model parameters obtained by the impedance measurements (as described in Section 2) can still be used, because the eddy current fields are practically the same. Figure 6 confirms the superposition principle for two marker lines located at x = ±0.5 mm. That is, if we shift the output signal measured for one standing alone marker (thin solid line) with +0.5 mm and –0.5 mm, respectively, and add them up, we get the dashed line, which is a good approximation of the signal measured for the two markers (thick solid line). Note, that for smaller distances the transformed regions tend to fuse, and superposition may not work any longer.

Figure 6. Illustration of the superposition principle for two marker lines located at x = ±0.5 mm.

144


4. Barcode Reconstruction Using Inverse Spatial Filtering The superposition of marker signals can be described by convolution, thus the reconstruction can be carried out by deconvolution. One of the simplest and most elegant methods of deconvolution is inverse filtering [8][9], a common solution in DSP, which can be summarized briefly for the current application as follows. A digital coding of the information scribed by the laser is considered. Assuming that the same laser lines (markers) are scribed or not scribed in equidistant positions depending on whether a digital 0 or 1 is supposed to be coded. It has been proved by the developed numerical model that the output signal y (x ) of the probe can be formulated as a sum of individual marker signals (see Section 3): N

y( x)

¦ a j y0 ( x x j ) ,

(1)

j 1

where y0 ( x ) stands for the output signal generated by one single marker located at the origin, and x j is the center of the j-th marker location; aj =0 or a j =1 is considered if a marker is present or not present at the location x j , respectively. Let us define the spatial Fourier transform (FT) and its inverse for the g (x ) and G (ik ) functions pairs as, G ( ik )

F ^ g ( x )`

f

³ g( x) e

f

ikx

dx ;

g( x)

F 1^G (ik )`

1 f G (ik ) e ikx dk . (2) 2S ³f

Taking the FT of (1) we get, N

Y ( ik )

¦ a j Y0 (ik ) e

ik x j

.

(3)

j 1

Now assume that y0 ( x ) is obtained as the convolution of two signals, that is in the spectral domain we are allowed to write, Y0 (ik )

H (ik ) W0 (ik ) .

(4)

Note that one of the functions H and W0 can be defined arbitrarily. Let us define the corresponding spatial function, w0 ( x )

F 1^W0 (ik ) `,

(5)

so that it allows to determine the actual values of aj in a simple way from the following type of combined function, N

u( x )

¦ a j w0 ( x x j ) .

(6)

j 1

This can be done easily if, for example, the w0 functions do not overlap. In the same time, let the bandwidth of W0 as small as possible. The transfer function of the filter to be used for the reconstruction of the barcode will benefit from this latter property of W0 . Writing (4) into (3) yields,

S. Gyimóthy et al. / Electromagnetic Reading of Laser Scribed Logistic Markers N

Y ( ik )

H (ik ) ¦ a j W0 (ik ) e

ik x j

.

145

(7)

j 1

After dividing by H and taking the inverse FT we get, ½ 1 F 1 ® Y ( ik ) ¾ ¿ ¯ H ( ik )

¦ a j F 1 ^W0 (ik ) e N

j 1

ik x j

`

N

¦ a j w0 ( x x j )

u( x ) .

(8)

j 1

This tells us that if we process the signal measured by the ECT sensor with a filter having the transfer function, 1 / H (ik ) , we will get a function u( x ) from which it is easy to decide whether a given marker line is present or not (i.e. whether aj is 1 or 0). Inverse filtering can be realized by simple and cheap FIR-filters, and may be carried out on-the-fly. Note however, that the method requires the knowledge of the output signal y0 ( x ) that is generated by one single marker. As this signal depends on both the material properties and the applied coating of the measured component, it cannot be “hard coded” into the reading out device. Rather, some isolated “leading marker” should be scribed before the barcode, from which the signal y0 ( x ) is to be obtained. One serious setback of inverse filtering is that it tends to amplify high frequency noise. This property can be improved by the proper selection of the w0 function. However, if this property would inhibit the reading out, then more sophisticated methods based on optimization must be used for the deconvolution [10]. Inverse filtering is demonstrated here for two markers at 1 mm distance from each other. The output signal of the probe was simulated on the numerical model described above. In order to suppress the unnecessary high frequency components of y ( x ) during the inverse filtering, the function w0 ( x ) was defined as a Blackman window [9] of 2 mm width, which has relatively low bandwidth. The simulated output signal together with the reconstructed signal representing the two markers are plotted in Figure 7. It is apparent that because of the overlapping of the impulses, the peaks shifted away from their expected positions, but the result can still be decoded if marker distances are limited to be multiples of some base unit (e.g. 1 mm).

5. Conclusions Methods of computational electromagnetism are used for the development of an electromagnetic reading out system for laser scribed logistic markers of metallic components. Simulation of the measured signal based on FEM calculations is successfully applied for the identification of the material parameter variation due to irradiation with the laser beam. Bar code system consisting of identical lines is proposed for the coding of information. The application of this coding requires the separation of the overlapping ECT signal due to the parallel code lines. This separation is made by inverse filtering. It is proved both numerically and experimentally that the signal of several bars can be assumed as the superposition of signals due to the individual bars. In other words there is practically no electromagnetic interaction between the individual bars. Based on this linearity, a method is outlined for the identification of the transfer function of a filter that can be used for the reconstruction of the bar code.

146


Figure 7. The result of inverse filtering applied to the signal of a double marker (c.f. Figure 6). The markers are approximately localized by the two high peaks.

Acknowledgments This work supported by the project GVOP -3.1.1.-2004-05-0452/3.0 of the Hungarian National Office for Research and Technology, by the “Bolyai János” Research Fellowship of the Hungarian Academy of Sciences, by the Hungarian Research and Technology Innovation Fund under grant JAP 17/02, and by the Hungarian Scientific Research Fund under grant T-049389. The authors also express their special thanks to Dr Oszkár Bíró for making available the finite element software EleFAnT-3D developed at TU-Graz, IGTE; as well as for Dr Theodoros P. Theodoulidis for offering his software Teddy for the required computations. References [1] Z. Kalincsák, J. Takács, G. Vértesy and A. Gasparics, “The optimisation of laser marking signals for eddy current detecting of marks”, Proc. Laser Assisted Net Shape Engineering 4, Erlangen (Germany), Sept. 21-24, 2004, vol. 1, pp. 535-544. [2] I. Mészáros, “Micromagnetic measurements and their applications”, Materials Science Forum, vols. 414415, 2003, pp. 275-280. [3] G. Vértesy, A. Gasparics, J. SzöllĘsy, “High sensitivity magnetic field sensor”, Sensors and actuators, vol. 85, 2000, pp.202-208. [4] O. Bíró, “Edge element formulations of eddy current problems”, Computer Methods in Applied Mechanics and Engineering, vol. 160, 1999, pp. 391-405. [5] T. P. Theodoulidis, M. K. Kotouzas, “Eddy current testing simulation on a personal computer”, Roma 2000 NDT World Conference. [6] T. P. Theodoulidis, E. E. Kriezis, “Impedance evaluation of rectangular coils for eddy current testing of planar media”, NDT & E International, 2002, vol. 35, pp.407-414. [7] J. Pávó, A. Gasparics, I. Sebestyén, G. Vértesy, “Calibration of Fluxset sensors for the measurement of spatially strongly inhomogeneous magnetic fields”, Sensors and Actuators A: Physical, vol. 110, no. 1-3, 2004, pp.105-111. [8] J. P. Wikswo, Jr, “The Magnetic Inverse Problem for NDE”, in SQUID Sensors: Fundamentals, Fabrication and Applications (ed. H. Weinstock), Kluwer Academic Publishers, The Netherlands, 1996, pp. 629-695. [9] S. W. Smith, The Scientist and Engineer’s Guide to Digital Signal Processing, California Technical Publishing, San Diego, 1999, pp. 297-310. [www.dspguide.com] [10] S. Esedoglu, “Blind deconvolution of bar code signals”, Inverse Problems, vol. 20, 2004, pp. 121-135.


147

Design of a Remote Field Eddy Current Probe Dedicated for Inspection of a Magnetic Tube from its Outer Surface Tomas MAREK a, Daniela GOMBARSKA a, Ladislav JANOUSEK a, 1, Klara CAPOVA a, Noritaka YUSA b, Kenzo MIYA b a University of Zilina, Faculty of Electrical Engineering Department of Electromagnetic and Biomedical Engineering Univerzitna 1, 010 26 Zilina, Slovak Republic b IIU, Imon Ikenohata Bldg. 7F, 2-7-17 Ikenohata, Taito-ku, Tokyo 110-0008, Japan

Abstract. The paper deals with the design of a special remote field eddy current probe dedicated for inspections of a magnetic tube from its outer surface. A simple configuration of the probe with one exciting coil and one pick-up coil is considered. The coils are shielded with magnetic material to gain the remote field effect in the given configuration. Results of numerical investigations prove the effectiveness of the probe. Keywords. Remote field eddy current testing, probe, shield, magnetic tube, inspection from the outer surface

1. Introduction Non-destructive testing (NDT) is utilized for examination of structural components that might cause malfunction of a system with high economical and/or ecological impacts. The remote field eddy current testing (RFECT) is an NDT method used especially for the inspection of magnetic tubes [1]. The RFECT assures almost equal sensitivity to the inner (ID) and the outer (OD) defects because the magnetic flux penetrating through a tube wall is detected. The RFECT has been mainly used for the inspection of a tube wall from the inner surface of the tube. However, not all tubes can be accessed from their inside; they must be inspected from the outer surface. It is reported that there is a significant difference between the inspection of a tube from the inner surface and the outer one; it is quite difficult to gain the remote field effect in the later case [2]. Several studies have proposed to use shielding to realize a remote field effect when probes are situated outside of a tube. Whereas successful results were reported [2], the studies consider only nonmagnetic tubes. In reality, many tubes that must be periodically inspected are made from magnetic materials [3]. The paper presents design of an RFECT probe dedicated for inspections of a magnetic tube from its outer surface. Numerical simulations of electromagnetic field 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; E-mail: [email protected]

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T. Marek et al. / Design of a Remote Field Eddy Current Probe

distribution using the finite element method are performed to simulate the inspection of a tubular specimen with a defect of a variable depth and width. The probe is shielded to achieve the remote field effect from the outside of the tube. Dimensions of the probe are adjusted in such a way that a distance between an exciting coil and a pick-up one is minimized to gain higher level of the signal while still keeping the RFEC effect.

2.

Probe Design

2.1. Target Definition This study considers the inspection of a magnetic tube with an outer diameter of 500mm and a wall thickness of 10 mm[3]. The electromagnetic parameters of the tube material are σ = 1 MS/m and μr = 100. Whole circumferential wall thinning is used to model a defect arising from the inner or the outer surfaces of the tube.

2.2. Layout of the Probe The main goal is to reach the RFEC effect with a probe situated from the outside of the tube. A shielded outer circumferential probe is utilized in the paper. There are many variable parameters concerning the design of a probe, i.e. arrangements of coils, dimensions of coils and distance between them, materials, configuration and dimensions of shield, and finally the exciting frequency. Numerical simulations have been carried out to find out a proper design of the probe. The considered tube as well as the probe is axis symmetrical and thus it is possible to dismiss one dimension of the problem. Accordingly, a two-dimensional finite element code has been used for the numerical simulations. Preliminary results of simulations indicated that a complex arrangement of the coils does not bring reasonable results for sake of the RFEC effect. Therefore, simple configuration with one exciting coil and one pick-up coil is chosen. Such configuration is also beneficial from the probe dimensions point of view.

Figure 1. Configuration of the RFECT probe with one merged shield

Several configurations of the probe shield have been studied, e.g. separate shields for each coil, compound shield layered from different materials, etc. As the complex shield does not bring any advantage, the probe with one merged monolithic shield covering both the coils is chosen for further investigation. In such case, the distance


149

between the coils can be shorter and the fabrication of the probe is simpler. The proposed configuration is shown in Fig. 1. Preliminary numerical simulations of the electromagnetic field distribution inside and around the tube revealed that electromagnetic parameters of shielding material (conductivity and relative permeability) and their ratio have significant influence in achievement of the RFEC effect in the concerned problem. Several materials have been used in numerical simulations to find a suitable one. Based on the findings, Cobalt is used for this purpose. The electromagnetic properties of Cobalt are: σ = 16 MS/m and μr = 68. Dimensions of the probe are adjusted by numerical means. 2.3. Dimensions of the Probe The distance between the exciting coil and the pick-up coil and the dimensions of the shield are adjusted to obtain reliable behaviour of the probe (Fig. 1). The driving frequency is set along with the probe dimensions. Three parameters are changed, i.e. the distance between the coils, a width of the defect and the exciting frequency to find the proper dimensions of the probe. Table 1 summarizes the changes of the three parameters. The ID and OD cracks with depths of 20 % and 50 % of the material thickness are considered. The gained results are evaluated in a way that there should be minimum difference in phase and in amplitude between the signals of ID and OD defects with the same depth and width. Table 1. Variables used in the probe design process Variable

Interval

Step

Coil distance L

70mm-90mm

5mm

Defect width wc

5mm-50mm

5mm

Frequency f

100Hz-400Hz

100Hz

Table 2. Dimensions of the probe Probe parameter

Dimensions

Cobalt shield

ws = 130 mm, hs = 15 mm

The coils distance

D = 80 mm

The coil dimensions

wec = wpc = 3 mm, hepc = 2 mm

Exciting frequency

f = 300 Hz

Lift-off

L = 0.5 mm

It should be noted that the dimensions of the coils (width, height) have been set in advance as they do not influence the required behavior of the probe. The increasing distance between the coils as well as the increasing exciting frequency reduce the amplitude of the pick-up signal. Thus, it is preferable to adjust both the parameters as low as possible to obtain a higher level of the detected signal. However, certain limitations have to be taken into account for the probe design. The distance between the coils influences maximum width of the crack for which the signals of ID and OD with a same depth are close. Outer dimensions of the shield, made of Cobalt, should be adjusted according to the selected distance between the coils to minimize unwanted

150


edge signals. The preliminary numerical simulations showed that a distance between the coil and the shield edge should be at least 25 mm to assure that the edge effect does not influence the detected signal. The exciting frequency influences the amplitude level of the pick-up signal as well as the phase distinction between the signals of cracks with different depths. Therefore, the value of the frequency is adjusted along with the other parameters of the probe to gain good properties of the probe. Table 2 summarizes the parameters of the proposed RFECT probe. The proposed probe is used for the inspection of the considered tube. Numerical results of the inspection are presented in the next section.

3.

Simulation Results

The magnetic tube with parameters given in section 2.1 is inspected by numerical means. The whole wall thinning of variable depth ranging from 0 % to 100 % of the tube thickness and of variable width is used to model the ID and OD defects. The RFECT probe shown in Fig. 1 is used for the inspection. The dimensions of the probe as well as the exciting frequency are given in Tab. 2. Figure 2 displays Lissajous plots of the crack signals obtained with the proposed probe for the ID and the OD cracks with a depth of 20 % of the tube thickness and with widths of 5 and 40 mm, respectively. 0.8 ID 20% OD 20%

ID 20% OD 20%

0.3

0.6 0.4 imaginary part [mV]

imaginary part [mV]

0.2

0.1

0

-0.1

0.2 0 -0.2 -0.4

-0.2 -0.6

-0.3 -0.3

-0.2

-0.1

0

0.1

0.2

0.3

-0.8 -0.8

real part [mV]

a.

-0.6

-0.4

-0.2 0 0.2 real part [mV]

0.4

0.6

0.8

b.

Figure 2. Lissajous plot of the pick-up signal, f = 300 Hz, D = 80 mm, ID&OD = 20%: a. wc = 5 mm; b. wc = 40 mm

Similar results for the ID and the OD cracks with a depth of 50 % of the tube thickness are shown in Fig. 3. It can be seen that the signals of the ID crack and the OD crack with the same depth are close to each other. Dependences of the crack signal amplitude and the phase on the crack depth for ID and OD cracks with depths ranging from 10 to 100 % of the tube thickness and with a constant width of 20 mm are shown in Fig. 4. The figure shows that ID signals are as clear as OD ones that confirms the effectiveness of proposed RFECT probe.

151


ID 50% OD 50%

ID 50% OD 50%

1

2

1

imaginary part [mV]

imaginary part [mV]

0.5

0

0

-1

-0.5

-2

-1 -1

-0.5

a.

0 real part [mV]

0.5

-2

1

-1

0

1

2

real part [mV]

b.

Figure 3. Lissajous plot of the pick-up signal, f = 300 Hz, D = 80 mm, ID&OD = 50%: a. wc = 5 mm; b. wc = 40 mm 100

40 ID amp OD amp ID phs OD phs

5.5

-30 ID amp OD amp ID phase OD phase

5

20

-35

4.5

-60 1

phase [deg]

-40

3.5

-45

3 -50

2.5 2

phase [deg]

-40

4

-20

amplitude [mV]

log amplitude [mV]

0 10

-55

-80 1.5

-100 0.1 10

20

30

40

50

60

70

80

90

-120 100

crack depth [%]

Figure 4. Amplitude of the pick-up signal (log scale) and its phase depending on the crack depth; crack width is wc = 20 mm

-60 1 0.5 0

5

10

15

20

25

30

35

40

45

-65 50

crack width [mm]

Figure 5. Amplitude of the pick-up signal and its phase depending on the crack width; crack depth is ID&OD 50%

The numerical results prove the applicability of the probe with merged Cobalt shield in the RFECT inspection of the magnetic tube. It was already mentioned that the distance between the coils along with the width of the defect affect the difference between the ID and OD signals. Figure 5 shows dependences of the crack signal amplitude and the phase on the crack width for the ID and the OD cracks with a depth of 50 % of the tube thickness and with a variable width 0 – 50 mm. It can be observed that when the crack is wider than 40 mm, the difference between the signals of the ID and the OD cracks starts to become significant. The robustness of the probe against fluctuations in the properties of the tube material and also of the shielding material has been investigated. The lift-off between the probe and the tube has also been changed to see its effect on the possibility to keep the RFECT effect. It can be stated that the proposed RFECT probe is quite robust

152


concerning the changes in the material properties of the tube and of the shield within considered ranges (change of conductivity and relative permeability ±10 %). Influence of the variations in the materials’ parameters on the calculated pick-up signals is negligible. However, larger lift-off causes the features of the probe to significantly deteriorate, because the remote field effect is lost when the lift-off exceeds 1 mm.

4.

Conclusion

The aim of the study was to enhance remote field eddy current testing performed from the outside of a magnetic tube. Design of a remote field eddy current probe was considered in the paper. In order to obtain the remote field effect, it was necessary to use the probe with appropriate shield. Among several considered configurations of the probe, the simple reflection type probe (1 exciter – 1 pickup) was chosen for the study as others do not bring any significant advantages; moreover, more complex signals are obtained when a multiple coil design is used. The configuration of the merged shield covering both the coils was proposed here. Numerical simulations were used to examine properties of several shielding materials; Cobalt was found to be a suitable one. The distance between the coils as well as the exciting frequency were adjusted by numerical means to gain good sensitivity of the probe to the inner and the outer defects in the tube. Numerical results proved the effectiveness of the proposed probe. The probe is quite robust against fluctuation in material properties of the tube as well as of the shield; however, increased lift-off causes loss of the remote field effect.

Acknowledgment This work has been partially supported by a grant VEGA No. 1/2053/05 “Design and Organization of Electromagnetic and Acoustic Methods and Tools for Material Nondestructive Testing” of the Slovak Ministry of Education.

References [1] [2] [3]

Yushi Sun, An introduction to electromagnetic nondestructive testing. Non-linear electromagnetic systems, IOS Press, 1998, pp.145-152. Young-Kil Shin, Achievement of RFECT effects in the nuclear fuel rod inspection by using shielded encircling coils. Electromagnetic nondestructive evaluation (VI), IOS Press, 2002, pp.83-90. METI press release, http://www2.jnes.go.jp/atom-db/en/trouble/individ/power/l/l048091/index.html.


153

Application of Thermoelectric Power Measurement to Nondestructive Testing Shinsuke YAMANAKA a,1, Yasuhiro KAWAGUCHI b, Toshihiro OHTANI c and Ken KUROSAKI a a Division of Sustainable Energy and Environmental Engineering, Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan b Maintenance Department, Reprocessing Plant, Reprocessing Business Division, Japan Nuclear Fuel Limited, 4-108, Aza Okitsuke, Oaza Obuchi Rokkasyo-mura, Kamikita-gun, Aomori 039-3212 Japan c Materials Laboratory, Ebara Research Co., Ltd., 4-2-1 Hon-Fujisawa, Fujisawa, Kanagawa 251-8502, Japan

Abstract. Thermal aging of cast duplex stainless steels and creep damage of a chrome steel were evaluated from thermoelectric power measurements. Relationships between the thermoelectric power and thermal aging and/or creep damage were studied. Keywords. thermoelectric power, duplex stainless steel, thermal aging, chrome steel, creep damage

1. Introduction Cast duplex stainless steel is frequently used in the main coolant pipes and reactor coolant pump casings of pressurized water reactor (PWR) type nuclear power plants because of its excellent material strength, toughness, and superior corrosion resistance. However, during long periods of operation at high temperature (285-325°C), thermal aging occurs and the toughness decreases. Therefore, it is necessary to develop a nondestructive inspection technique for evaluating degree of the deterioration. We have studied the feasibility of using thermoelectric power (TEP) measurement as a nondestructive inspection technique. Our previous studies reveal that the TEP measurement can be an excellent indicator to detect the degree of the thermal aging of cast duplex stainless steels [1, 2]. In addition, we have tried to detect the creep damage of chrome steel from the TEP measurement. In the present paper, we review the typical results concerning to the TEP measurement of the thermally aged cast duplex stainless steels as well as the creep damaged chrome steel. 1 Corresponding Author: Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan; E-mail: [email protected]

154

S. Yamanaka et al. / Application of Thermoelectric Power Measurement to Nondestructive Testing

2. TEP Measurement of Thermally Aged Cast Duplex Stainless Steels We prepared three kinds of cast duplex stainless steels with different ferrite content. The ferrite content and chemical composition of each phase in the samples are summarized in Table 1. The sample symbol implies the ferrite content. The samples were heated at around 1100 °C for more than 6 hours and then cooled in water under 426 °C within 5 minutes. The optical micrograph of F23 sample is shown in Fig. 1. In order to accelerate the thermal aging, the reference samples were aged at 400°C in air for 100, 300, 1000, 3000 and 10000 hours. Figure 2 shows the TEP measurement system used for the thermally aged cast duplex stainless steels [2]. The system can be utilized for measuring the TEP of field materials in nuclear power plants. Both the hot tip and the cold touch are made of copper. The shape of the hot tip is a truncated cone with a plane (0.6 mm in diameter). The hot tip is heated at 40 °C using a heating element. The temperature of the cold touch is not controlled, being almost equal to room temperature and maintained at the same temperature through the measurement. Therefore, the temperature deference between the hot and cold electrode is maintained at the same level through all the measurements. The TEP measurements were performed at 20 points for each specimen by moving the hot tip in 0.5 mm increments. Table 1. Chemical composition of each phase in cast duplex stainless steels determined by SEM–EDX analysis (at.%)

Symbol

F8

Ferrite content (vol.%) 7.3

F15

14.6

F23

21.3

Phase

Fe

Cr

Ni

Si

Mo

Mn

Ferrite Austenite Ferrite Austenite Ferrite Austenite

63.55 65.82 64.67 66.98 63.78 66.28

25.32 20.03 24.62 19.64 25.52 20.13

5.54 10.00 5.17 9.15 5.57 9.46

1.05 0.94 1.35 1.24 1.67 1.40

3.65 2.20 3.39 2.02 2.91 1.84

0.89 1.01 0.80 0.97 0.55 0.89

Austenite Phase

Ferrite Phase

100 Pm

Figure 1. Optical micrograph of cast duplex stainless steel (sample F23).


(a)

Portable computer Measurement cell

155

Instrumentation rack

(b)

Figure 2. Appearance (a) and schematic view (b) of the TEP measurement system used for the cast duplex stainless steels.

Figure 3 shows the TEP of the thermally aged cast duplex stainless steels as a function of the aging time. The TEP values are negative and increase with increasing aging time. Specifically, the TEP values of the starting samples (unaged samples) are 2.65 PVK-1 (sample F8), -2.49 PVK-1 (sample F15), and -2.35 PVK-1 (sample F23). The TEP values of the 10000 hours thermally aged samples are -2.39 PVK-1 (sample F8), -2.16 PVK-1 (sample F15), and -1.73 PVK-1 (sample F23). In addition, there is a clear correlation between the TEP and the ferrite content; that is a cast duplex stainless steel containing a low amount of ferrite content exhibits large absolute TEP values. From these results, it can be confirmed that the TEP is an excellent indicator of the degree of thermal aging of cast duplex stainless steels. In other words, the degree of the thermal aging can be detected by measuring the TEP of the materials. Figure 4 shows a relationship between the TEP and micro Vickers hardness of the thermally aged cast duplex stainless steels. It is observed that there is a clear relationship between the TEP and micro Vickers hardness. The large TEP values correspond to the large micro Vickers hardness. Therefore, the TEP measurement can be an effective method for evaluating degree of the thermal aging as well as degradation of the mechanical properties of cast duplex stainless steels.


-1

Thermoelectric power, TEP (PVK )

156

-1.5

Ferrite content: 7.3 % Ferrite content: 14.6 % Ferrite content: 21.3 % -2.0

-2.5

-3.0 10

100

1000

10000

Aging time (h) Figure 3. Thermoelectric power (TEP) vs. aging time of thermally aged cast duplex stainless steels.

Micro Vickers hardness (HV)

260 240

Ferrite content: 7.3 % Ferrite content: 14.6 % Ferrite content: 21.3 %

220 200 180 160 140 -2.8

-2.6

-2.4

-2.2

-2.0

-1.8

-1.6

-1

Thermoelectric power, TEP (PVK ) Figure 4. Relationship between thermoelectric power (TEP) and micro Vickers hardness.

3. TEP Measurement of a Creep Damaged Chrome Steel We provided a Cr-Mo-V steel (SNB16) for the creep test and TEP measurement. The chemical composition of the chrome steel is summarized in Table 2. The samples were heated at 1010 °C for 2 hours, followed by air-cooled and maintained at 950 °C for 2 hours. And then, the samples were oil-quenched, reheated at 690 °C for 6 hours, and air-cooled. The creep test was performed at 650 °C under the pressure of 25 MPa.


157

Figure 5 show a relationship between the creep time (hours) and creep strain (%), in which a reasonable result is confirmed; that is the creep strain increases with increase the creep time. Table 2. Chemical composition of the chrome steel, Cr-Mo-V (SNB16), (wt.%).

Sample SNB16

C 0.420

Si 0.290

Mn 0.66

P 0.016

S 0.009

Cr 1.090

Mo 0.51

V 0.28

Fe Balance

45 40

a b c d e f g h i j

㪚㫉㪼㪼㫇㩷㫊㫋㫉㪸㫀㫅㩷㩿㩼㪀

35 30 25 20 15 10 5 0 0

500

1000

1500

2000

Time (hour) 0 368.9 620.0 760.8 1001.0 1560.7 1485.3 1200.5 2129.0 1953.9

Srain (%) 0 4.14 6.66 6.46 12.03 16.06 23.29 29.43 35.29 38.57

2500

㪚㫉㪼㪼㫇㩷㫋㫀㫄㪼㩷㩿㪿㫆㫌㫉㪀 Figure 5. Relationship between creep time and creep strain of the chrome steel. The creep test was performed at 650 °C under the pressure of 25 MPa.

Electrode Sample Thermocouple

Small heater

Before sample setting

Electrode

Small heater

After sample setting

Figure 6. TEP measurement system (ZEM 1, ULVAC Ltd.) used for the creep damaged chrome steel sample.


-1


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Creep strain (%) Figure 7. Thermoelectric power (TEP) of chrome steel (Cr-Mo-V steel: SNB16) as a function of the creep conditions; (a) creep time, (b) creep strain.

Figure 6 shows an appearance of the TEP measurement system (ZEM 1, ULVAC Ltd.) used for the creep damaged chrome steel. The sample is a rectangular-shaped with the size of approximately 2 mm x 2 mm x 14 mm. The bottom of the sample is heated by a small heater and the temperature gradient ('T) is detected by the thermocouple attached to the surface of the sample. The voltage between one-side wires of the thermocouple ('V) is measured, and the thermopower (TEP) is calculated from a relation TEP='V/'T. The measurement was performed 21 times per sample. The base temperature and temperature gradient were set as approximately 50 °C and 10 °C, respectively Figure 7 shows the TEP of the chrome steel (Cr-Mo-V steel: SNB16) as a function of the creep conditions; (a) creep time, (b) creep strain. In these figures, the average TEP value and the standard deviation obtained from the 21 times measurements are


159

-1

Attenuation coefficient, D (Ps )

plotted. It is clearly observed that the TEP values are positive and increase with increasing the creep time or creep strain. Specifically, the TEP value of the starting sample (before the creep test) is 6.48±0.17 PVK-1 and that of the creep damaged sample (2129 hours) is 7.74±0.15 PVK-1. In addition, a broad peak is observed at the creep time of around 1000 h which corresponds to the creep strain of around 12 %. The lattice defects such as dislocations arising from the creep tests may affect the TEP of the chrome steel. Although the mechanism of this phenomenon is still unclear, it can be said that the TEP measurement can detect the creep damage of the chrome steel. In order to understand the relationship between the TEP and creep damage of the chrome steel, we investigated a result of the creep damage evaluation from an electromagnetic acoustic resonance (EMAR) analysis performed for the same samples [3]. EMAR is an emerging ultrasonic spectroscopy technique for nondestructive and noncontact materials characterization, relying on the use of electromagnetic-acoustic transducers (EMATs) and the superheterodyne circuitry for processing the received reverberation signals excited by long radio-frequency (RF) bursts [4,5]. Figure 8 shows the relationship between the attenuation coefficient and creep strain for the creep damaged chrome steel. The attenuation coefficient increases, showing a peak at the creep strain of around 3 %, and then decreases, showing a minimum near the creep strain of around 5 %, and finally increases. From the SEM and TEM observations, the behavior has been interpreted in terms of dislocation mobility and restructuring. A similar peak is observed in the TEP vs. creep strain plot, but the peak position and sharpness differ from those in the attenuation coefficient vs. creep strain plot. Although a theoretical discussion has not been carried out at this moment, it is supposed that there is a relationship between the TEP and attenuation coefficient viz. dislocations of the creep damaged chrome steel.

0.01

1E-3 0

10

20

30

40

Creep strain (%) Figure 8. Relationship between attenuation coefficient (D) and creep strain for the creep damaged chrome steel [3]. The measurements were performed for the same samples as those used in the TEP measurements. The attenuation discussed here is measured by exciting the test-specimen in one of its resonance frequencies, stimulating a reverberation, and measuring the exponential decay of the ring down curve.

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4. Summary Thermal aging of cast duplex stainless steels and creep damage of a chrome steel were evaluated though the thermoelectric power measurements. The TEP values of the thermally aged cast duplex stainless steels were negative and increase with increasing the aging time. In addition, there was a clear relationship between the TEP and micro Vickers hardness of the thermally aged cast duplex stainless steels. The TEP values of the creep damaged chrome steel were positive and increase with increasing the creep time or creep strain, in which a peak was observed in the TEP vs. creep conditions plot at the creep time and strain around 1000 hours and 12 %, respectively. A similar peak has been observed in the attenuation coefficient vs. creep strain plot collected through the EMAR analysis performed for the same samples, and the behavior has been interpreted in terms of dislocation mobility and restructuring. Now, we are trying to evaluate the electronic structure of iron with or without the lattice defects from first principle simulations. The relationship between the TEP and lattice defects such as dislocations will be clarified in near future. Nevertheless, the TEP measurement can detect degree of thermal aging of the cast duplex stainless steels as well as creep damage of the chrome steel. It can be concluded that the TEP measurement can be an effective nondestructive analytical technique for evaluating material degradation.

References [1] Y. Kawaguchi and S. Yamanaka, J. Japan Inst. Metals 66 (2002), 377-383. [2] Y. Kawaguchi and S. Yamanaka, J. Alloys and Compd. 336 (2002), 301-314. [3] T. Ohtani, H. Ogi and M. Hirao, Acta Materialia 54 (2006), 2705-2713. [4] M. Hirao and H. Ogi, Ultrasonics 35 (1997), 413-421. [5] H. Ogi, M. Hirao and T. Honda, J. Acoust. Soc. Am., 98 (1995), 458-464.

NDE by Magnetism and Magnetics



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Accurate Detection of Material Degradation of Stainless Steel by ECT Sensor Tokuo TERAMOTO1 Graduate School of Systems and Information Engineering, University of Tsukuba, Japan

Abstract. Non-magnetic phase in austenitic stainless steel is often changed into ferromagnetic phase by stress induced martensitic transformation, which is accompanied by substantial plastic deformation. In order to detect the phase transformation and to accurately evaluate the material degradation by nondestructive method, an ECT sensor made of three tandem coils was used. The tensile test at low and room temperatures showed that the measurement by this sensor agreed well with the distributions of plastic stain, saturation magnetization and Vickers hardness. Keywords. ECT, Stress induced martensite, Magnetization, Plastic strain, Hardness

1. Introduction Although the austenitic stainless steel used as structural material is originally a semi-stable non-magnetic body, the applied stress often causes the martensitic transformation especially at very low temperature. This transformation amount of martensite, which is a ferromagnetic substance, depends upon residual plastic deformation. Recently, applying the magnetic fluxgate sensor to the austenitic stainless steel, several authors succeeded in clarifying the relationship between the leakage magnetic flux density and the behavior of fatigue crack propagation[1], the bending fatigue damage[2] and the creep behavior at high temperature[3]. Then, it was proved that the sensor output strongly correlated with the material degradation and the magnetization of residual martensite. This study aims at accurately evaluating the material degradation such as plastic strain, hardness and amount of martensite in stainless steel with the use of a simple ECT sensor.

2. Experimental 2.1. ECT Sensor As shown in Figure 1, an ECT sensor made of three tandem coils was produced such that the central coil was arranged as an excitation coil and two outside coils were used 1 Corresponding Author: Tokuo Teramoto, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan; E-mail: [email protected]

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T. Teramoto / Accurate Detection of Material Degradation of Stainless Steel by ECT Sensor

as a detection coil of which the two output voltages were electronically compensated as long as this sensor was away from any electric conductive body. The output was amplified in an appropriate degree by a lock-in amplifier. Then, the measurement by this sensor was conducted with high sensitivity. Each coil consisted of a small pan-cake type coil of 50 turns, 4.9mm in outer diameter, 2.5mm in inner diameter and 2mm in thickness. The excitation frequency was always set at 100kHz and the lift-off was set at 1mm. The size of this ECT sensor was expected to be small enough to accurately detect the distribution of material degradation such as plastic strain, hardness and martensite content. The output of the ECT sensor corresponds to the real part in terms of lock-in amplifier output. 2.2. Specimen The material used is a SUS304 stainless steel, whose chemical composition is shown in Table 1. Although a SUS304 stainless steel usually shows ductile and non-magnetic properties, it can become brittle and ferromagnetic by stress induced martensitic transformation because of unstable austenitic phase around and below room temperature[4]. Figure 2 shows the standard and the modified tensile test specimen where the center part is 2mm thick in both specimens. The top specimen was produced to realize in-situ measurement by ECT sensor when loaded to an extent and unloaded at 300K. This specimen yields uniform plastic strain in specimen center part. In-situ measurement may be appropriate even if the sensor position moves during test. In-situ measurement, however, is very unstable at 77K because the electromagnetic properties

Table 1. Chemical composition of SUS304 (wt%)

Material SUS304

C 0.04

Si 0.4

Mn 1.13

P 0.027

S 0.003

Ni 8.23

Figure 1. Schematic diagram of measurement equipment with ECT sensor

Cr 18.0


165

5

5

˓

˓

Figure 2. Tensile test specimen (top) and modified tensile test specimen (bottom) [unit in mm]

of coil changes in a great degree. Then, using standard tensile specimen, in-situ measurement was conducted only at 300K. On the other hand, the bottom specimen was produced to conduct the measurement along the longitudinal direction after loaded at 77K and 300K and to investigate the distribution of the ECT output with plastic strain. The modified tensile specimen was used to investigate the relation between the ECT output and the plastic strain after test. Since the plastic strain changes monotonically along the longitudinal direction of the specimen, it is convenient to compare the ECT output with the plastic strain.

3. Results and Discussion 3.1. Tensile Test at 300K First, the tensile test was carried out at 300K with several loading and unloading processes after the ECT sensor was mounted on the specimen center surface. The output of the sensor was measured continuously during the test. Figure 3 shows the variation of applied stress and ECT output with strain at 300K. The ECT output is almost constant until applied strain reaches 5 to 10% where the specimen is obviously yielded. Namely, the variation of the microscopic structure by yielding does not affect the electromagnetic parameter of this material in the early stage. The ECT output, however, increases with increasing strain after this stage. This behavior corresponds with stress-strain relation according to magnetism change by the increase of martensitic phase. The martensitic phase was found in the intensively strained body even at room temperature by measuring the magnetization with the use of VSM. In addition, MFM observation was made on 2% and 8% strained specimen as shown in Figure 4(a) and (b), respectively. The magnetic domain is found relatively clear at 8% strain while it is obscure at 2% strain. Although a clear evidence of martensitic transformation can not be drawn from these MFM images, the appearance of magnetic domain may be correlated with martensitic transformation. Accordingly, the martensitic transformation is possibly initiated at 5 to 10% applied strain. Next, the ECT output increases even at


700

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-350 35

Strain [%]

Figure 3. Variation of stress and pick-up voltage with strain

(a)

(b)

Figure 4. MFM images of (a) 2% and (b) 8% strained specimen, respectively

unloading process. This behavior may be attributed to variation of electric conductivity accompanied by elastic strain release due to unloading. 3.2. Modified Tensile Test at 77K Using schematically modified test specimen, the tensile load was applied at 77K until the development of martensitic transformation was anticipated to an extent. After the tensile test, the output of the sensor was measured at room temperature on the specimen surface. Figure 5 shows the distribution of ECT output and residual plastic strain along


167

d=6mm

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10

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-250 d=2mm

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5 10 15 20 Distance from center [mm]

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0 25

Figure 5. Distribution of pick-up voltage and plastic strain along the longitudinal direction

d=6mm

40

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d=2mm

20 10

-300 0

5 10 15 20 Distance from center [mm]

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50 -100

0 25

Figure 6. Distribution of pick-up voltage and magnetization along the longitudinal direction

the longitudinal direction of the specimen. The ‘d’ in this figure means the applied displacement between two loading pins of the specimen in the test. The plastic strain was numerically obtained by using a finite element analysis code. The amplitude-locus-curve of ECT output agrees well with that of plastic strain. Figure 6 shows the distribution of ECT output and the value of the saturation magnetization along the longitudinal direction of the specimen. Using VSM, the magnetization was


Volume fraction of martensite [%]

168

30 25

77K 300K

20 15 10 5 0 -400

-300 -200 -100 Pick-up voltage V x [mV]

0

Figure 7. Relation between pick-up voltage and volume fraction of martensite

Plastic strain [%]

50 40

77K 300K

30 20 10 0 -400

-300 -200 -100 Pick-up voltage V x [mV]

0

Figure 8. Relation between pick-up voltage and plastic strain

measured from small pieces cut from the modified tensile specimen in the longitudinal direction. In this case, the tendency of ECT output also agrees well with that of magnetization. Namely, the agreement means that the plastic strain quantitatively corresponds with the martensite content at 77K and that the extent of martensitic transformation can be accurately detected by this ECT sensor.


169

3.3. Prediction of Material Degradation Figure 7 shows the relations between ECT output and volume fraction of martensite at 77K and 300K, respectively. Using Slater-Pauling curve, the saturation magnetization of SUS304 was estimated to be 168 emu/g when the austenitic phase is fully transformed to martensitic phase[5]. In the present study, the volume fraction of martensite was obtained by normalizing magnetization by this value. The ECT output is almost linearly proportional to the volume fraction of martensite at both temperatures. However, there is an obvious difference in this relation at 77K and 300K. Figure 8 shows the relations between ECT output and plastic strain at 77K and 300K, respectively. It is found that the ECT output is linearly proportional to plastic strain at 77K and that the martensitic phase begins to come out just after yielding. On the other hand, the ECT output is almost constant at 300K until plastic strain reaches about 8% and then begins to linearly increase with increasing plastic strain. The plastic strain over 8% may produce martesitic transformation at 300K because the ECT output begins to change at this strain amount. Certainly, large plastic strain yields some amount of martensite but causes the reduction of electric conductivity at 300K. The sensor output is relatively small because of lower conductivity and larger skin depth at 300K. On the other hand, small plastic strain yields more martensitic transformation at 77K and then the sensor output becomes large because of higher permeability and conductivity. It is also found that the Vickers hardness is almost linearly proportional to ECT output at 77K and 300K, respectively. Especially the hardness is correlated with martensite content at 77K while it is not attributed to martensite content but to large plastic strain at 300K.

4. Conclusion At low and room temperatures, it is possible to accurately detect the material degradation of SUS304 stainless steel with the use of this nondestructive ECT sensor. Especially, a unique relationship between the ECT output and the material degradation such as martensite content, plastic strain and hardness, is obtained at low temperature. On the other hand, the ECT output is not only dependent upon martensite content but change of electromagnetic properties due to large plastic deformation at room temperature. References [1] Y. Nakasone et al., Non-destructive Detection of Damage in an Austenitic Stainless Steel SUS 304 by the Use of Martensitic Transformation, Int. J. of Applied Electromagnetics and Mechanics 15 (2001/2002), 309-313. [2] M. Oka et al., Evaluation of the Amount of Fatigue Damage in Austenitic Stainless Steel by the Leakage Magnetic Flux, Proc. of the 14th MAGDA Conf., Gifu, 2005, pp. 170-175. [3] Y. Nagae and K. Aoto, A Study on the Detection of Creep Damage in Type 304 Stainless Steel Based on Natural Magnetization, Int. J. of Applied Electromagnetics and Mechanics 15 (2001/2002), 295-300. [4] R.P. Read and C.J. Gunter, TMA-AIME 230, 1964, p.1713. [5] JSAEM-R-0005, 2001.

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Micromagnetic Characterization of Thermal Degradation in Cu-rich Alloys and Results of Neutron-Irradiation Madalina PIRLOGa,1, Iris ALTPETERa, Gerd DOBMANNa, Gerhard HÜBSCHENa, Melanie KOPPa, Klaus SZIELASKOa a

Fraunhofer-Institute for non-destructive testing (IZFP), Saarbrücken, Germany

Abstract. The Cu-rich German martensitic/bainitic structural steel WB36 (15 NiCuMoNb 5, 1.6368) is in service in fossil power plants as well as in pipes and pressurizer vessels of German nuclear power plants. That material – when exposed at elevated temperatures in between 280°C - 350°C – shows the effect of precipitation hardening by Cu-rich precipitates and a shift 'FATT = 70°C can be observed. Micromagnetic measurements based on multiple linear regression or pattern recognition algorithms and taking into account different micromagnetic quantities were applied in order to characterize the material degradation. In parallel a different approach was employed to evaluate in the same way alloys based on pure iron with different contents of Cu. Because Cu-rich precipitates play an essential role when nuclear pressure vessel material is exposed to neutron irradiation, micromagnetic measuring quantities are also of interest to characterize these materials. Therefore the paper reports experiments performed in the hot cells of AREVA NP in Germany. Keywords. Thermal ageing, neutrons embrittlement, non-destructive, micromagnetic

1. Introduction Non-destructive material characterization techniques have traditionally been employed to detect, classify and to size defects in materials. However in the last two decades a significant amount of effort has been invested, to develop NDT technique which can reliably characterize materials in terms of properties describing the fitness for use. In case of the power plants components such as pressure vessels and pipes the fitness for use under mechanical loads is characterized in term of the determination of mechanical properties like mechanical hardness, yield and tensile strength, toughness, fracture appearance transition temperature, fatigue strength or usage factor. Except hardness tests which are weakly invasive, all of these parameters can be determined by using destructive tests on special standardized samples. Such a procedure cannot be performed on components in service and is therefore restricted to quality checks during manufacturing where enough representative material is available. Procedures based on less destructive material sampling and weakly influencing the integrity of the 1

Corespondent author: Dr.-Ing. Madalina Pirlog, Fraunhofer-Institute for non-destructive testing (IZFP), University of Saarland, Saarbrücken, 66123, Germany Email: [email protected]

M. Pirlog et al. / Micromagnetic Characterization of Thermal Degradation

171

component are not yet validated or standardized and are still the objective of investigations. Therefore, there is a need for the development of such non-destructive testing techniques.

2. Characterization of the thermal degradation effects in Cu-rich alloys Smallest changes in the materials state e.g. the change of the precipitation of coherent Cu particles induced by the thermal ageing sensitively affect the magnetic domain structure. 2.1. Thermal degradation of WB 36 steel In the typical “as delivered” state of WB 36, half of the contained Cu is already precipitated, while the other half remains in solid solution. After long term service exposure above 320 °C, damage was observed due to further precipitation of Cu; an increase in yield strength 'Vy = +150 MPa and a shift of the fracture appearance transition temperature 'FATT = +70 °C can be measured. Small angle neutron scattering measurements revealed the fact that the mechanical properties changes are caused by Cu precipitates ranging from 1 to 3 nm in size [1]. The particles are coherent, have a bcc structure that induces a high level of compressive residual stress in their vicinity, balanced by tensile stresses in the environmental matrix. On a set of approximately 70 round samples (80 mm in length, diameter 6 mm) of WB 36, thermal service exposure was simulated in an accelerated manner through long-term annealing at 400 °C. A U-shaped electromagnet was used to excite an alternating magnetic field along the longitudinal axis of the sample. A disc-shaped pickup coil and a temperature stabilized hall probe were used to record Barkhausen noise events and magnetic field strength, respectively. The Barkhausen noise signal was amplified by 60 dB and bandpass-filtered to a range of 5 to 200 kHz. All signals were digitized using common data acquisition hardware. The Barkhausen noise signal was then digitally refiltered for separate analysis of its different frequency components. Characteristic scalar quantities [2] were extracted from the envelope of the Barkhausen noise signal as a function of the applied magnetic field strength. Moreover, an upper harmonics analysis [3] of the magnetic field strength signal was performed and characteristic quantities derived. As changes in conductivity may be expected due to copper precipitation, a simplified eddy current analysis procedure was performed based on the relationship between magnetic field strength and exciting voltage of the electromagnetic coil. The scalar result quantities of all three methods (Barkhausen noise, upper harmonics and eddy current analysis) are combined to a vector which characterizes the material condition. In the case of WB 36 steel, only few of the measured quantities seem to correlate well with the copper precipitation state at first, when comparing them across all samples mentioned above. Therefore, a preliminary experiment was performed in order to identify the optimum measurement parameters and most significant quantities for the detection of copper precipitation in WB 36. Instead of comparing the electromagnetic properties across several samples, the changes in the electromagnetic properties of single samples were recorded in several stages of the simulated service exposure. The annealing was therefore interrupted in regular intervals where electromagnetic tests were performed. All measurements were done using a fixed set of different

172


magnetization frequencies and magnetic field amplitudes in order to create a comprehensive database of material behaviour. A total 6 samples underwent this procedure for statistical coverage, and reference samples were kept for verification. As a result of these experiments, it was found that eddy current measurements allow the detection of copper precipitates whilst remaining insensitive to most disturbing influences. Fig. 1 shows how the coil impedance (expressed in terms of its relative magnitude and phase) performed as a function of the simulated service exposure duration for initially recovery-annealed WB 36. Changes in the eddy current impedance represent changes in the conductivity and the permeability of the material. The electrical conductivity is proportional to the concentration of the free electrons and their velocity, which decreases with rising defect density. Therefore the electrical conductivity decreases. It was also shown that the increase of the Cu precipitates density causes a decrease of the relative magnetic permeability. In the initial phase of the experiment, some scattering of the measured values was observed. Measurements on reference samples have shown that these deviations from the subsequent material behaviour relate to the polishing procedure which was required for additional Vickers hardness tests. 400

0.4 magnitude phase 0.2

0

0

-200

relative phase [°]

relative magnitude [μV]

200

-0.2

-400 0

250

500

750

-0.4 1000

duration of service simulation at 400 °C [h]

Figure 1. Eddy current quantities magnitude and phase as a function of service exposure duration for initially recovery-annealed (3h / 600 °C) WB 36 steel

Fraunhofer-IZFP uses the so-called 3MA method (“Micromagnetic Multi-Parameter Microstructure and Stress Analysis”) in order to solve the inverse problem of target quantity prediction from a limited set of calibration data [4]. In this case, a specialized pattern recognition algorithm [5] based on nearest neighbour search was used to obtain approximate values of the Vickers hardness (HV 5) from several quantities, including the eddy current quantities mentioned above. The optimum parameters which were found in the preliminary experiments were used throughout this measurement. Fig. 2 shows the resulting correlation of actual and predicted hardness values.


173

215

predicted HV 5 (3MA)

Calibration Test

195

175

155 155

175

195

215

actual HV 5

Figure 2. Predicted Vickers hardness for WB 36 versus actual Vickers hardness

2.2. Thermal degradation of Fe-Cu alloys The micromagnetic test methods have a high potential to detect change of the MRS because they sensitively react to the changes of the domain wall configuration [6]. The Cu precipitates coherently embedded in a ferritic matrix induce two different kinds of MRS: coherence tensile MRS of IIIrd order and thermally-induced compressive MRS of IInd order. The coherence MRS of the IIIrd order appear when the lattice parameter of the IInd phase particles coherently embedded in the matrix and the lattice parameter of the surrounding matrix are different. The thermally-induced MRS of IInd order arise at the interface between different material phases because of their different thermal expansion coefficient. In case of the Fe-Cu system the bigger lattice parameter and thermal expansion coefficient of Cu compared to Fe lead to coherence tensile MRS of IIIrd order and thermally-induced compressive RS of IInd order respectively. In order to detect the precipitation-induced MRS, Barkhausen noise measurements under superimposed tensile load stress were performed [7]. The samples were magnetized in the longitudinal uniaxial load stress direction. Due to that fact by means of that approach the detected residual stresses are those in the direction of external magnetization. That means that a change of the residual stress state in the perpendicular direction caused by the applied load will not be detected. The Barkhausen noise signal was recorded by using two differential air-core coils to separate the influence of the energizing magnetic field. The magnetic Barkhausen noise was triggered by an alternating magnetic field (Hmax = 5 A/cm, fE = 40 Hz) applied to the sample using an U-shape electromagnet. The noise signal was recorded as induced voltage, appropriately filtered, rectified, amplified and displayed as function of the tangential field strength. The resulting socalled Barkhausen noise profile curve was evaluated by a computer with respect to the maxima and their respective magnetic field strengths. Fig. 3 left- hand side, shows schematically the maximum of the Barkhausen noise amplitude (MMAX) obtained during one hysteresis cycle recorded as a function of the load-induced stress, V. Fe-Cu samples with a variation of Cu content from 0.65 to 2.1 wt.% have been manufactured and investigated. By means of a suitable heat treatment (solution annealing at

174


1000 °C/2h, quenching into water and thermal ageing at 550 °C variation of the amount of coherent Cu particles of 1.42 Vol.% was induced. The thermal ageing time was determined by means of hardness measurements performed during thermal ageing in 10 minutes steps. The thermal aging time for each sample must be shorter than the thermal aging time corresponding to the hardness maximum. Those results were validated by SANS-measurements. In case of the Fe-Cu alloys the MMAX(V) curves do not reach any maximum before break under load, i.e. the curve of Figure 3 right-hand side is strongly shifted to the right. Therefore the position of the local minimum (VMMIN) is evaluated (Fig. 3 right-hand side). 0.5 Fe-0.65 wt.% Cu Fe-2.1 wt.% Cu

MMAX

RS-free MMAX [V]

tensile RS

compressive RS _ VMMIN

0.4

0

+ V [MPa]

0.3

0.2 'V § 50 MPa 0.1 0

VMMIN

75 V [MPa]

150

Fig. 3b: Schematical (left-hand side) and experimentally determined (right-hand side) tensile load dependence of maximum Barkhausen noise amplitude

X-Ray measurements performed on two Fe-Cu samples containing 0.65 and 2.1 wt.% Cu in the “as-quenched” state showed that both samples contain compressive RS of Ist order with values of -210 MPa and -290 MPa respectively. X-Ray measurements performed after thermal ageing documented that both samples still contain compressive RS but with smaller values, of -120 MPa and -180 MPa, respectively. Those measurements confirmed the fact that the behaviour of the MMAX(V) curves is mainly influenced by quenching. However, the curve is a superimposition of RS induced by quenching (largest effect) with the coherent tensile RS of IIIrd order and thermally induced compressive RS of IInd order. By subtracting the compressive residual stresses induced by quenching and taking into account that the thermally-induced MRS of IInd order are negative too, values of the coherence MRS of IIIrd order higher than 90 MPa and higher than 110 MPa for the Fe-Cu samples containing 0.65 and 2.1 wt.% Cu respectively (Fig. 4) were obtained [8] by evaluating the shift in the minimum ('MRS). The minimum of the MMAX(V) curves indicates the load stress value which is required by the Bloch walls to break away from the lattice defects as pinning points. Therefore the position of that minimum is a measure for the lattice defects density. An increase of the lattice defects density and an increase of the MRS order causes a shift of the MMAX(V) curve to higher tensile load stresses because the Bloch walls need more energy to break away from the lattice defects. This means that the shift ('V) of the MMAX(V) curve (Fig. 3, right-hand side) indicates the in-crease of the precipitationinduced MRS. Because the thermally-induced RS of IInd order are expected to be very small, their influence can be neglected and it can be assumed that the shift of the MMAX(V) curve represents the change of the coherence tensile MRS of IIIrd order. It is


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well known that the coherence MRS increase with increasing density of Cu precipitates. A mathematical relation between the coherent MRS and the density of precipitates is unknown. For simplification the MRS in the others Fe-Cu samples were determined by interpolation (Fig. 4). The variation of the MRS between the both Fe-Cu alloys is bigger than 20 MPa, which confirm the value obtained by means of the micromagnetic procedure, if we consider the error band of the X-Ray measurement of about 25 MPa (Fig. 4).

Figure 4. Comparison between the MRS determined by means of the micromagnetic and by means of the X-ray methods

3. Characterization of the neutron irradiation induced embrittlement Depending on the specific design of a pressure vessel – which is different in the different countries of the world – the pressure vessel material in nuclear power plants (NPP) exposed to neutron flux is in a range between 5x1018 n/cm2 in 32 years at 288 °C in Germany and 8x1019 n/cm2 in 14 years at 254 °C, for instance, in France. The energy input of the neutrons is directly producing lattice defects like vacancies and indirectly by stimulating the precipitation of coherent Cu-rich particles. As in case of the thermally-induced embrittlement of the steel WB 36 these are also in the 3 nm diameter range and coherently embedded in the bcc lattice. Both, the vacancies and the precipitates reduce the toughness of the material, which can be characterized by a reduction of the Charpy energy and a shift in the fracture appearance transition temperature to higher temperatures. In practice the material degradation is characterized in surveillance programs by using standardized Charpy V-notch specimen and tensile test specimen made of the pressure vessel steel and its weldments. The specimens are exposed in special radiation chambers near the NPP core at a higher fluence than at the i.d. surface of the pressure vessel wall. These specimens from time to time are removed from the chambers and used for destructive tests. In order to assume a higher nuclear safety in between two subsequent destructive tests one would like to have many non-destructive tests and the nd-technology should also be developed to an in service inspection method to be applied at the pressure vessel inner surface. In order to characterize the neutron irradiation-induced embrittlement samples

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(10*10*55 mm) made of 20 MnMoNi 55 steel used in the German reactor pressure vessel in non-irradiated state as well as after irradiation of 3.78x1018 n/cm2, 7.66x1018 n/cm2 and 1.05x1019 n/cm2 neutron flux have been investigated. As in case of the thermally-induced embrittlement of the steel WB 36, it was observed that a suitable measuring quantity for the characterization the neutron irradiation-induced embrittlement is the eddy current impedance magnitude which decreases with the fluence (Fig. 5). 10

1.098

8 Vmag [V]

'T41 [°C]

1.092

6 4

1.086

2 0

1.08 0

4

8 18

0

12

3

Fluence*10 [n/cm ] Figure 5. Correlation between the eddy current impedance magnitude and the neutron flux

6

9 18

2

12

2

Fluence*10 [n/cm ] Figure 6. Dependency of the fracture appearance transition temperature on the neutron fluence

IZFP has applied 3MA-approaches to calibrate regression models. The measurements were performed in the same way like in case of the steel WB 36. One part of each specimen set was used to calibrate and the other part – independently selected – was taken to test the model. In this case, a specialized pattern recognition algorithm [5] based on nearest neighbour search was used to obtain approximate values of the shift of the fracture appearance transition temperature, which is a measure for the embrittlement from the measured quantities (Fig. 6). 10.5 Calibration Test

'T41 (3MA) [°C]

7.5

4.5

1.5

-1.5 -1.5

1.5

4.5

7.5

10.5

'T41 (Charpy-Test) [°C]

Figure 7. Prediction of the shift of the fracture appearance transition temperature by 3MA


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It was demonstrated that by means of the 3MA-procedure the prediction of the shift of the fracture appearance transition temperature is possible (Fig. 7). By using a regression analysis algorithm a correlation coefficient of 89.3% and a residual standard deviation of 0.35 °C is received. By testing the calibration with independently selected test specimens a standard error of 1.2 °C (residual standard deviation to the destructive test values) was obtained.

4. Conclusions In the present research work the nd-characterization of the material degradation was discussed on the basis of experiences with: precipitation-induced embrittlement in WB 36 steel and Fe-Cu alloys and neutron-irradiation induced embrittlement in the 20 MnMoNi 55 steel used in the German reactor pressure vessel. It was shown that the 3MA approach using pattern recognition methods based on magnetic Barkhausen noise, upper harmonics analysis and eddy current analysis data allows with high accuracy a non-destructive prediction of the Vickers hardness and of the shift of the fracture appearance transition temperature, which are measures to characterize embrittlement. The present study shows also that eddy current impedance measurements represent a suitable method to characterize the thermally- as well as the neutron irradiationinduced embrittlement. The present research results show the suitability of the micro-magnetic method for the non-destructive evaluation of Cu precipitation-induced MRS. By means of a micromagnetic non destructive procedure based on the tensile stress dependency of the maximum Barkhausen noise amplitude the change of MRS caused by an increase of the coherent Cu precipitates volume fraction in Fe-Cu based alloys was measured.

References [1], D. Willer, G. Zies, D. Kuppler et al, Service-Induced Changes of the Properties of Copper-Containing Fer-ritic Pressure-Vessel and Piping Steels. GRS Reactor Safety Research – Project No 150 1087. Final Report avail-able at GRS, Cologne, (2001) [2] I. Altpeter, Spannungsmessung und Zementitgehaltsbestimmung in Eisenwerkstoffen mittels dynamischer magnetischer und magnetoelastischer Messgrößen. Dissertation at Saarland University, Saarbrücken, (1990) [3] H. Pitsch, Die Entwicklung und Erprobung der Oberwellenanalyse im Zeitsignal der magnetischen Tangentialfeldstärke als neues Modul des 3MA-Ansatzes (Mikromagnetische Multiparameter Mikrostruktur und Spannungsanalyse). Dissertation, Saarland University, Saarbrücken, Germany, (1989) [4] G. Dobmann and P. Höller, “Non-destructive determination of material properties and stresses”, 10th Int Conf NDE in the nuclear and pressure vessels industries, Glasgow, ASM International, (1990) [5] R. Tschuncky: Entwicklung eines Mustererkennungs- und Klassifikationsmoduls für die indirekte Charakterisierung von Werkstoffeigenschaften, Diploma Thesis, Saarland University, Germany, 2004 [6] E. Kneller, Ferromagnetismus, Springer Verlag, (1962) [7] I. Altpeter, R. Becking, R. Kern, M. Kröning, S. Hartmann, Mikromagnetische Ermittlung von thermisch induzierten Eigenspannungen in Stählen und weißem Gusseisen, in: Deutsche Forschungsgemeinschaft, Eigenspannungen und Verzug durch Wärmeeinwirkung, Forschungsbericht, Wiley-Vch, (1999), 407/426 [8] Pirlog, M., Szielasko, K., Altpeter, I., Dobmann, G., Kröning, M.: Micro-Magnetic Evaluation of Residual Stresses of the 2nd and 3rd Order, in VDI Berichte Nr. 1899 (2005), 355-365, ISBN 3-1809189-3 [9] Altpeter, I., Szielasko, K., Dobmann, G.: “Optimization and Assessment of electromagnetic testing methods for the detection of property changes in power plant components, caused by service-induced copper precipitation”. Final report to GRS reactor safety research project no. 150 1269, available at GRS Forschungsbetreuung, Köln, Germany or at IZFP, report no. 060119-TW (2006)

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Challenges in Quantifying Barkhausen Noise in Electrical Steels Anthony J MOSES 1, Harshad V PATEL and P I WILLIAMS Wolfson Centre for Magnetics, School of Engineering, Cardiff University, Wales UK

Abstract. The origin and interpretation of (a.c.) magnetic Barkhausen effect is still not fully understood. In this paper Barkhausen noise is measured by two methods, surface probes and enwrapping flux-sensing search coils. They are shown to follow similar trends with varying a.c. flux density and frequency in electrical steel. It is shown that the rate of Barkhausen noise data capture above 100 kHz at 50 Hz magnetizing frequency does not appreciably affect data interpretation. Various methods of signal analysis are compared and correlations of with static hysteresis loss have been demonstrated. Trends are found also in the influence of factors such as texture and microstructure under different magnetizing conditions in electrical steels although localized Barkhausen noise varies widely from point to point within grains and near grain boundaries. It is concluded that Barkhausen noise measurement can be a significant tool for analyzing physical and microstructural factors in electrical steels but there are challenges in the interpretation of results at present. Keywords. Barkhausen Noise, Electrical Steel, Hysteresis Loss

1. Introduction The magnetic Barkhausen effect was discovered at the beginning of the last century but its origin and interpretation is still not fully understood. It is generally accepted to be due to microscopic discontinuities in domain wall motion due to the presence of defects [1]. Various methods of measurement based on detecting induced voltages caused by Barkhausen jumps within a material have been developed. Definite trends are found in the influence of factors such as texture and microstructure on Barkhausen noise (BN) under different magnetizing conditions in electrical steels and some direct connection with hysteresis loss appears to exist [2]. However, quantitative correlation of methods of BN signal analysis is not well documented.

1 Corresponding Author: Anthony J Moses, Wolfson Centre for Magnetics, School of Engineering, Cardiff University, Wales, UK, CF24 4AA; E-mail: [email protected]

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2. Measurement Techniques and Analysis Epstein strip samples of electrical steels were tested at frequencies up to 100 Hz and sinusoidal peak flux density up to 1.5 T using the magnetization method described previously [3]. Figure 1 schematically shows two types of sensor arrangement, which have been compared, namely enwrapping coils and surface probes. In both methods, the output voltage must be filtered to remove unwanted noise and Faraday emfs of non BN origin before analyzing. A band pass filter was used so that signals in the range 3.5 kHz to 100 kHz were detected at magnetizing frequencies in the range 5 Hz to 100 Hz. The component of emf induced in coils, enwrapping the complete width of a single strip, originating from the BN has been detected and analyzed. The main challenge of this type of measurement is that the BN component is typically some 2000 times smaller than the predominate 50 Hz Faraday secondary emf in the coil. Also high order harmonics of the filtered fundamental component may still be present due to nonsinusoidal voltage components caused by grain to grain flux distortion that cannot be eliminated even using advanced flux control systems such as described in [3]. The BN detected in a single 80 turn enwrapping coil was compared with that detected from a double coil arrangement. The latter consisted of two 80 turn coils separated by 5 mm and connected in series opposition. The predominant 50 Hz Faraday emf is cancelled out by the double coil because of its differential output leaving only the BN component. The BN component is only partially cancelled out since each coil picks up a different Barkhausen contribution. The second method involved the use of a 1000 turn and 500 turn ferrite core detection coil 8 mm in length placed on the surface of the strip. Sensors supplied by Stresstech Oy with cores of length 9.5 mm, 13 mm and 24 mm were tested. The core diameter was 3 mm and the coil position relative to the sample surface remained unchanged as shown in figure 1(c). Because of the stochastic nature of BN, a variety of statistical methods can be used to analyse the signals using both detection methods. The sum of the amplitudes of BN peaks is convenient but does not count simultaneously occurring peaks or take account of the contribution of peaks of different magnitudes whereas measurement of the power spectrum does contain such information. Kurtosis is a parameter that describes the peakedness of a BN distribution relative to a normal distribution. In this investigation we focussed our attention on correlating RMS BN noise with hysteresis loss. RMS BN was chosen because its value is fairly stable from cycle to cycle. The RMS value is also very useful for determining amplitude as a function of time particularly for cyclic phenomena such as BN which has both positive and negatives amplitudes per cycle. It also allows better comparison with the work of other investigators that in the main have also measured RMS BN. However we would expect to draw similar conclusions if the BN signal were to be analysed in terms of the other parameters. The BN evaluated from the outputs of single and double coils as well as the three sizes of ferrite cored sensors were measured with dummy cardboard and aluminium samples in an attempt to quantify and compare the inherent measurement error. As the

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magnetizing field at the sensor position was increased from zero to 1200 A/m at 50 Hz the output of all sensors apart from the double enwrapping coil initially increased rapidly and then levelled out. The output from the enwrapping coils was lowest and the 24 mm ferrite cored sensor had the highest induced noise but its RMS value was 93 % less than that of the typical measured BN output of a steel sample at 1.5 T, 50 Hz. There was no obvious difference between noise outputs when the aluminium and cardboard samples were present. The random variation of BN measurements is partly due to non repeatability of domain wall motion from cycle to cycle [4].

Sample

Search Coil Outputs

PC with DAQ card and LabVIEW software package

Search Coil Outputs Sample

Search Coil Carrier


Search Coil Carrier

(a)

(b) Ferrite Search Coil Outputs

Sample

Search Coil Carrier


Pick up Coil

(c)

Fig. 1. Schematic diagrams of sensors. (a) Single enwrapping search coil (b) Double enwrapping search coil wound in series opposition (c) Ferrite cored induction coil

Figure 2 compares the outputs of a single search coil, double search coils wound in series opposition and ferrite cored surface sensor with 500 & 1000 turn pick up coils with 13 mm ferrite core length for a sample of commercial 0.27 mm thick grain oriented 3 % silicon steel magnetized from 0.1 T to 1.8 T at 50 Hz. Obviously the magnitude of the output signal depends on the sensor characteristics as well as the BN events so the results are normalized as shown. It is interesting that the trends with the ferrite cored surface probe are very similar to those of the enwrapping coils although they are oriented perpendicular to each other. However, it can be seen that the change of BN RMS value with flux density detected by the ferrite cored sensor with 1000 turn pick up coil is highest and that of the double search coil is the lowest. The ferrite cored sensor outputs increase rapidly at high flux density indicating that the different sensors are effectively picking up different BN events. It is important to note that increasing the number of turns in the ferrite cored sensor from 500 to 1000 turns does not simply double the BN measurement. In fact it can be seen that the increase is more than twice approximately 3.3 times more, this contribution maybe due to the area enclosed by the coil is larger, and signals are amplified with more turns hence data acquisition card can

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measure more BN jump signals. There maybe other factors that increase the BN signal, further investigation is needed. In the case of the double coil, some events will be lost in the subtraction process but even here, it is interesting to note that as the separation between the coils is changed the magnitude of the output changes. For a coil separation distance of 5 mm to 40 mm the BN RMS signal increases around 140 %.

1.6E-3 Ferrite Core 1000 turn coil

1.4E-3

BN RMS [V]

1.2E-3 1.0E-3 800.0E-6 600.0E-6 Ferrite Core 500 turn coil

400.0E-6 Single Coil

200.0E-6

Double Coil

000.0E+0 0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

B [T]

Fig. 2. Variation of normalized BN RMS outputs of the sensors with flux density at 50 Hz in grain oriented 3 % silicon steel (ferrite length 13 mm in both ferrite sensors) Based mainly on early d.c. measurements Barkhausen jumps were thought to occur very rapidly and therefore be largely independent of magnetizing frequency [5]. Our measurements however indicate that there is a degree of dependency on magnetizing frequency. This may be in part confirmation of the formation of microscopic eddy currents due to domain wall dynamics at the scale of microstructural features. To investigate the effect of the data acquisition rate on the BN output the number of sampling points per cycle was varied from 128 to 2048 for magnetizing frequency of 50 Hz. Figure 3 shows that as the sampling frequency increases the BN RMS value increases but eventually levels out showing that, at 50 Hz magnetizing frequency, sampling at 2048 points per cycle is sufficient for picking up most BN events.

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160.0E-6 140.0E-6

1.4 T

120.0E-6

BN RMS [V]

1.0 T 100.0E-6 0.5 T

80.0E-6 60.0E-6 40.0E-6 20.0E-6 000.0E+0 0

20

40

60

80

100

Sampling Frequency [kHz]

Fig. 3. Variation of RMS BN signal at 50 Hz magnetization with sampling frequency at peak flux densities of 0.5 T, 1 T and 1.4 T (Double coil sensor)

3. BN and Hysteresis The coating applied to the surface of grain oriented electrical steel not only provides interlaminar insulation in assembled cores but it induces a beneficial stress into the steel, which reduces losses and stress sensitivity of the steel [6]. The BN before and after chemical removal of the coating was measured using the ferrite cored sensor at 4 points on the surface of commercial 0.27 mm thick grain oriented 3 % silicon steel at 50 Hz in the range 0.3 T to 1.4 T (The sample was annealed after coating removal). The measurement points were chosen with the aid of a surface magnetic domain viewer. Points were chosen over grain boundaries or in the centre of well oriented grains. The uncertainty of RMS BN signals was up to 5 % over the measurement range. Coating removal caused domains to become wider and the power loss increased by 4 % at 1.4 T. No correlation was found between sensor position and BN output. However, the average RMS BN increased by up to 25 % as can be seen in figure 4. Removal of the coating and the subsequent annealing has resulted in 180o domain refinement leading to the observed widening of domain wall spacing. This is well known for causing increases in losses. Since changes in BN under applied stress are primarily attributable to changes in 180o domain wall population it is not unexpected to also see an increase in RMS BN. However, the relatively large change in BN (25 %) compared with power loss (4%) is not so easily explained and other factors need to be investigated further before definitive conclusions can be made.

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700E-6

600E-6

Decoated

BN RMS [V]

500E-6

400E-6

Coated 300E-6

200E-6

100E-6

000E+0 0.4

0.6

0.8

1.0

1.2

1.4

1.6

B [T]

Fig. 4. Variation of RMS BN with flux density in grain oriented 3 % Silicon steel before and after coating removal (ferrite sensor of 13 mm length) Some correlation has previously been found between BN under AC magnetization and the static hysteresis component of power loss [2]. In the present investigation, the static hysteresis loss of non-oriented electrical steels with silicon contents between 0.2 % and 6.5 % was estimated. This was achieved by measuring (using the double coil sensor) the total loss over the frequency range 5 Hz to 200 Hz at 1.5 T and extrapolating the loss per cycle curve to zero frequency in the conventional way. In all the materials tested the RMS BN at 50 Hz rises with static hysteresis as shown in figure 5 confirming the general trend found previously occurs in a wider range of materials . It is recognized today that loss separation in this way is artificial, however the result does indicate that a close relationship between BN and hysteresis under a.c. magnetization does exist.

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100E-6 90E-6 80E-6

BN RMS (V)

70E-6 60E-6 50E-6 0.23% 0.3% 1.3% 1.8% 3% 6.5% 5.5%

40E-6 30E-6 20E-6 10E-6 000E+0 0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

3

PH (W/m )

Fig. 5. Variation of RMS BN with calculated static hysteresis loss in non-oriented electrical steels with different silicon contents at 50 Hz (Double coil sensor) Interesting variations in BN were observed using a ferrite cored sensor placed on the surface of individual grains of grain oriented 3% silicon iron. Close agreement was found between BN measured at different points within a single grain at 50 Hz magnetization, however a comparison between different grains of similar size and orientation showed a variation of up to 50% in the BN signal. The RMS BN detected close to grain boundaries in the same material was 40 % lower than that seen in some of the well oriented grains. Problems in interpreting such results arise because the BN noise sensing region is not sufficiently localized. Also the BN is probably strongly related to the domain wall activity at a particular location which itself is known to vary significantly from grain to grain. Therefore, future work should attempt to correlate the two phenomena.

4. Conclusion

Similar trends in the variation of BN with flux density and magnetization frequency in electrical steels can be detected using enwrapping coils or surface probes as detectors. The method of analysis of a.c. BN signals does not require more than 2048 data capture points per cycle at 50 Hz. Correlation can be found between changes in the state of electrical steel such as that brought about by coating removal. Localized variation in BN has not been definitively quantitatively attributed to structural variation such as grain boundaries or resulting domain activity and improved sensor design is necessary to investigate such phenomena.


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Acknowledgment This work was supported by EPSRC Grant EP/C518616. The authors would also like to thank Stresstech Oy for providing the ferrite cored sensor.

References [1] [2]

[3]

[4] [5] [6]

D. Jiles, Introduction to Magnetism and Magnetic Materials, Chapman and Hall, NY, 1991 A. J. Moses, F. J. G. Landgraf, K. Hartmann and T. Yonamine, Correlation between angular dependence of A.C. Barkhausen noise and hysteresis loss in a non-oriented electrical steel, Stahleisen (2004) 215 – 219 H. V. Patel, S. Zurek, T. Meydan, D. C. Jiles, L. Li, A new adaptive automated feedback system for Barkhausen signal measurement, Journal of Sensors and Actuators A: Physical, Volume 129, Issues 1-2, Pages 112-117, 24 May 2006 A. J. Moses, P.I. Williams and O. Hoshtanar, A novel instrument for real time dynamic domain observation in bulk and micromagnetic materials, IEEE Trans. Mag. 41 (10), (2005) 3736-3738 G. Bertotti, Hysteresis in magnetism: for physicists, materials scientists and engineers, London: Academic, 1998 A. J. Moses, Electrical Steels – Past, present and future developments, IEE Proc. 137 Pt.A (5) (1990) 2333-2345

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Magnetic Adaptive Testing: Influence of Experimental Conditions Gábor VÉRTESY a,1, Tetsuya UCHIMOTO b, Toshiyuki TAKAGI b and Ivan TOMÁŠ c a Research Institute for Technical Physics and Materials Science, Budapest, Hungary b Institute of Fluid Science, Tohoku University, Sendai, Japan c Institute of Physics, Academy of Sciences of the Czech Republic, Praha, Czech Republic

Abstract. Influence of the magnetizing yoke on the calculated magnetic descriptors of Magnetic Adaptive Testing was studied by measuring gray cast iron samples. It was found that the material and shape of the yoke has no influence on the relative values of the descriptors. Keywords. Magnetic Adaptive Testing, Magnetic hysteresis measurements

1. Introduction Magnetic measurements are frequently used for characterization of changes in the structure of ferromagnetic materials, because magnetization processes are closely related to the microstructure of the materials. This fact also makes magnetic measurements an obvious candidate for non-destructive testing, for detection and characterization of any defects in materials and manufactured products made of such materials [1,2,3]. Structural non-magnetic properties of ferromagnetic materials have been non-destructively tested using traditional magnetic hysteresis measurement methods for a long time with fair success. A number of techniques have been suggested, developed and currently used in industry, see e.g. [4,5]. They are mostly based on detection of structural variations via the classical macroscopic parameters of hysteresis loops. An alternative, more sensitive and more experimentally friendly approach to this topic was considered recently in [6] and [7], based on magnetic minor loops measurement. In [6] the method of Magnetic Adaptive Testing (MAT) was presented, which introduced general magnetic descriptors to diverse variations in non-magnetic properties of ferromagnetic materials, optimally adapted to the just investigated property and material. In [7] the sets of minor hysteresis loops were scrutinized, and sensitive descriptors of plastic deformation of the material (independent on the minor loops amplitudes) were identified. In this work MAT is applied on gray cast iron samples. Influence of the experimental conditions, mainly the application of different magnetizing yokes on the 1 Corresponding Author: Gábor Vértesy, Hungarian Academy of Sciences, Research Institute for Technical Physics and Materials Science, H-1525 Budapest, P.O.Box 49, Hungary, E-mail: [email protected]

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evaluated magnetic descriptors is studied.

2. Experiments Three series (FC150, FC200 and FC250) of gray cast iron specimens were investigated. Chemical compositions of the series were different. Table 1 shows the chemical composition of the samples. In each series one sample was in as-cast condition, one sample was heated up again and cooled in air and one was heated up and cooled in a furnace. Hardness of the samples (HB) was measured by the Rockwell hardness test method. Results can be seen in Table 2. Table 1 Chemical composition of the investigated specimens Sample FC150 FC200 FC250

C% 3.77 3.36 3.13

Si% 2.78 2.15 1.66

Mn% 0.78 0.69 0.72

P% 0.025 0.018 0.017

S% 0.015 0.010 0.002

Cr% 0.029 0.014 0.038

Ti% 0.015 0.011 0.010

Table 2 Hardness of the investigated specimens

FC150 FC200 FC250

as Cast 89 178 206

Hardness HB furnace cooling 89 101 126

air cooling 135 206 212

A specially designed Permeameter [8] with a magnetizing yoke was used for measurement of families of minor loops differential permeability of the magnetic circuit. The block-scheme of the device and the sketch of the yoke with a sample can be seen in Figure 1. Two different yokes were used for the measurements. The ferrite yoke, made of M2TN-B type soft ferrite material, was 16 mm long, 11 mm high, and the cross section of its legs was 5x6 mm. The iron yoke was made of a C-shaped laminated Fe-Si core and the corresponding size was 27, 26 and 8x10 mm, respectively. The magnetizing coil wound on the ferrite yoke gets a triangular waveform current with step-wise increasing amplitudes and with a fixed slope magnitude in all the triangles. This produces time-variation of the effective field, ha(t), in the magnetizing circuit and a signal is induced in the pick-up coil. As long as ha(t) sweeps linearly with time, the voltage signal U(ha,hb), in the pick-up coil is proportional to the differential permeability, P(ha,hb), of the magnetic circuit P (ha , hb ) const * U (ha , hb ) const * wB(ha , hb ) / wha * wha / wt

The Permeameter works under full control of a PC computer, which sends appropriate control information to the function generator, and collects the measured data. An input-

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output data acquisition card accomplishes the measurement. The computer registers data-files for each measured family of the minor “permeability” loops, corresponding to each measured sample. They contain detailed information about all the pre-selected parameters of the voltage signal induced in the pick-up coil. The step of the magnetic circuit effective field amplitudes was 'hb=36 A/m, and the magnetizing current rate of change was r5 A/s.

Figure 1. Block-scheme of the Permeameter and sketch of the yoke

0,2

(a)

Ferrite yoke 0,1

0,0

-0,1

-0,2 -0,75

-0,50

-0,25

0,00

0,25

0,50

Magnetizing current, I [A]

0,75

Pick-up coil signal [arb.units]

Pick-up coil signal [arb.units]

The described regime of the Permeameter yields a characteristic signal in the pickup coil; typical examples of its shape are shown in Figure 2. The signal values start at the origin of the plot (the magnetic circuit was demagnetized before the measurement), then increases into positive values (up to the positive starting field amplitude, +1*'hb). Then it drops down into negative values as the applied field changes the direction of its rate, then proceeds in the negative values until the negative starting field amplitude 1*'hb is reached, changes its rate direction and polarity again, raises up to +2*'hb, etc.

0,2

(b)

Iron yoke 0,1

0,0

-0,1

-0,2 -0,75

-0,50

-0,25

0,00

0,25

0,50

0,75

Magnetizing current, I [A]

Figure 2. The typical signal registered for one family of the triangular variations of the magnetizing current, obtained on the same sample by using ferrite(a) and iron (b) yokes


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The experimental raw data are processed by a data-evaluation program, which divides the originally continuous data of each measured sample into a family of individual permeability half-loops. Then the family, either of the top half-loops or the bottom half-loops or their average is chosen for the next processing stage. The program filters experimental noise and interpolates the experimental data into a regular square grid of elements, Pij { P(hai,hbj), of a P-matrix with a pre-selected field-step. The consecutive series of P-matrices, each taken for one sample with a value of the strain, H, of the consecutive series of the more-and-more deformed material, describes the magnetic reflection of the material plastic deformation. The matrices are processed by a matrix-evaluation program, which normalizes them by a chosen reference matrix, and arranges all the mutually corresponding elements Pij of all the evaluated P-matrices into a Pij(HB) table. Each Pij(HB)-column of the table numerically represents one Pij(HB) matrix element. These matrix elements are used for high sensitive characterization of the investigated material. The scheme used for optimization of parameters obtained from the evaluated matrices is discussed detailed in [9]. This reference describes how the most sensitive and at the same time the most reliable descriptor (matrix element) can be picked up from the big data pool. The optimal Pij(HB)-descriptor of the investigated samples were determined according to this procedure.

3. Results The signals induced in the pick-up coils, measured on one of samples (the same piece; sample FC200, air cooled) are shown in Figure 2, for the ferrite and for the iron yoke. It is clearly seen that the recorded signals are very different. This reflects the different behaviour of the whole magnetic circuit (yoke, air gap, sample).

P m atrix elements

1,8 ferrite yoke iron yoke 1,6 1,4 furnace cooling 1,2 as cast

1,0

air cooling 0,8 80

100

120

140

160

180

200

220

Hardness

Figure 3. Calculated optimal Pij(HB) -matrix elements for the ferrite and for the iron yokes as functions of hardness (sample FC200)

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The above detailed calculation was carried out on all the investigated samples. The obtained optimal Pij(HB)-descriptors (P-matrix elements) are shown for the sample series FC200 in Figure 3, for sample series FC250 in Figure 4 and for sample series FC150 in Figure 5, respectively. In all cases the measurement and the corresponding evaluation were made for both types of yokes.

1,7 ferrite yoke iron yoke

P matrix elements

1,6 1,5

furnace cooling

1,4 1,3 as cast

1,2 1,1 1,0

air cooling

0,9 120

140

160

180

200

220

Hardness

Figure 4. Calculated optimal Pij(HB) -matrix elements for the ferrite and for the iron yokes as functions of hardness (sample FC250)

1,7

P matrix elements

1,6

furnace cooling

ferrite yoke iron yoke

1,5 1,4 1,3 1,2

as cast

1,1

air cooling

1,0 90

100

110

120

130

140

Hardness Figure 5. Calculated optimal Pij(HB) -matrix elements for the ferrite and for the iron yokes as functions of hardness (sample FC150)

4. Discussion Magnetic measurements were carried out with the aid of magnetic yokes. The consecutive series of P-matrices describe the magnetic reflection of the material modification very well. As it was proved in previous works [6,8,9], by applying the


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Magnetic Adaptive Testing method, the relatively small difference between the magnetic characteristics of the investigated sample series can be determined much more sensitively, than by the conventional methods. Another advantageous and independent outcome of the tested method is the confirmation, that without magnetic saturation of the samples, measuring a series of minor loops and performing MAT method on the obtained data-pool, reliable and sensitive parameters can be determined. Moreover, the relative measurement can be done with a ferromagnetic yoke attached to the sample, and the yoke does not even have to be large and very special. The method does not give absolute values of the traditional magnetic quantities, because of the non-uniform magnetic circuit and of the not-reached magnetic saturation, but evidently it is able to serve as a powerful tool for comparative measurements, and for detection of changes, which occur in structure of the inspected samples during their lifetime or during a period of their heavy-duty service. Even if quality of the magnetic contact between the samples and the yoke was assumed to be stable, the magnetic circuits were certainly non-uniform and the magnetic values obtained from each measurement were rather effective magnetic parameters of the circuit than real magnetic parameters of the samples. As can be seen in Figures 3-5, independently of the applied yoke very similar dependences were found between hardness and the magnetic descriptors. This fact shows that by application of MAT, the samples’ characteristics are determined, and the remaining part of the magnetic circuit – if kept constant at each measurement – has no basic influence on the relative value of the calculated quantities. The feature of the magnetic circuit has an influence on the absolute value of the measured signal, but considering that the whole measurement is relative, and only the results, measured at the same conditions are compared, this fact has no influence on applicability of the method. In certain cases the measurements, performed by the ferrite yoke give better sensitivity, in other case iron yoke does the same. This feature of the measurements is not understood yet, further study is necessary in this field. However, the difference is not significant, so it can be concluded that any of the investigated yoke is suitable for sensitive and reliable measurements. In case of sample FC150 the as cast and furnace cooled samples have the same value of hardness, in spite of the fact that – according to our measurements – they are different magnetically. This fact needs further study, the possible error of hardness measurements cannot be excluded, too. But it has no influence for the main message of the present work. The most important difference between ferrite and iron yokes is the saturation magnetization of their material. Ferrite yoke is saturated at about 300 mT, while the saturation magnetization of iron yoke is much higher. It means that the observed virtual saturation, which is suggested by Figure 2/a is the magnetic saturation of the yoke, and not the whole magnetic circuit. It should be emphasized that these descriptors show the relative modification of the material behaviour within the same series of the measured samples. These

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modifications in the present series of samples are connected with the different way of sample preparation. Due to different cooling rate, magnetic parameters became different, as seen clearly in the figures. The interpretation of the changes of magnetic parameters as a function of sample preparation (structure variation of the cast iron) is not the subject of the present paper, it will be discussed elsewhere. From the same calculated data pool the inverse values of matrix elements can be picked up, as well, which results just the opposite relationship between the independent parameter (hardness) and P-matrix elements, but the influence (or better to say the lack of influence) of the experimental condition on the MAT parameters remain the same.

5. Conclusions The influence of the applied magnetizing yoke was investigated on the nondestructive magnetic characterization of gray cast iron samples when Magnetic Adaptive Testing method was used. It was found that exactly the same relationship with very similar sensitivity was obtained, regardless of the actual type of yoke. The results obtained are considered to be very important, because if different relative dependencies within the same sample series would have been experienced by application of different yokes, the reliability and applicability of the whole MAT became questionable. In other words: the obtained relationship is not influenced by the experimental conditions (how the samples are magnetized), it reflects only nature of the measured samples.

Acknowledgments The financial support by the Hungarian Scientific Research Fund (K-62466), by the Research and Technology Innovation Fund of the Hungarian Government in the frame of the Japanese-Hungarian Bilateral Intergovernmental S&T Cooperation (JAP 17/02), by the Academy of Science of the Czech Republic (project No.1QS100100508) and by the Grant Agency of the Czech Republic (project No.102/06/0866) is appreciated.

References [1] [2] [3] [4] [5] [6] [7] [8] [9]

M.J. Johnson, C.C.H.Lo, B.Zhu, H.Cao, D.C.Jiles, J. Nondestruct. Eval. 20 (2000), 11. D.C. Jiles, Magnetic methods in nondestructive testing, K.H.J.Buschow et al., Ed., Encyclopedia of Materials Science and Technology, Elsevier Press, Oxford, (2001), 6021. I. Mészáros, Materials Science Forum, 473-474 (2005), 231-236. D.C. Jiles, NDT International, 21 (1988), 311-319. J. Blitz, Electrical and magnetic methods of nondestructive testing, Adam Hilger IOP Publishing, Ltd., Bristol, 1991. I.Tomáš, J.Magn.Magn. Mat., 268 (2004), 178-185. S.Takahashi, L.Zhang, T.Ueda, J.Phys.: Condens.Matter, 15 (2003), 7997-8002. I. Tomáš, O.Perevertov., in: JSAEM Studies in Applied Electromagnetics and Mechanics 9, ed. T. Takagi and M. Ueasaka, (IOS Press, Amsterdam, 2001), 5-15. G. Vértesy, I. Tomáš, I. Mészáros, J. Magn. Magn. Mat., 310 (2007), 76-82.


193

Magnetic and Acoustic Barkhausen Noise for the Characterisation of Tensile Deformation and Stresses in Steel Gui Yun TIAN a, 1, John WILSON a, Jiri KEPRT b a

b

Newcastle University, UK Brno University of Technology, Kolejni 2906, Brno 612 00, Czech Republic

Abstract. This paper introduces a new method of pulsed acoustic Barkhausen noise for stress detection and material characterisation. Pulsed excitation can provide wide spectral components and time information for non-destructive evaluation and material characterisation. After introducing the system set-up, several experiments including stress variation and residual stress orientation are outlined, in comparison with magnetic field intensity measurement. Different Barkhausen noise and magnetic acoustic emission characterisation methods such as Root Mean Square (RMS), absolute energy and event count are discussed and a new quantitative method for pulsed acoustic Barkausen noise and magnetic flux leakage is investigated for stress detection and material characterisation. Keywords. Acoustic emission, permeability, Acoustic Barkhausen noise (ABN), Magnetic Barkhausen noise (MBN), NDT&E, pulsed excitation

1. Introduction Non-Destructive Evaluation (NDE) is used to assess the integrity of a system or component without compromising its performance. Detailed defect sizing and characterisation has become the major objective of much NDE work underway today. To address this challenge, the NDE community has turned to novel techniques and a combination of multiple mode inspections and computer-aided data analyses. In many of the non-destructive techniques used for material evaluation, such as acoustics, magnetic particle, eddy current, magnetic flux leakage methods or their integration [13], surface and sub-surface flaws in the material are detected by measuring the induced or leakage fields as a result of the interaction of an excitation electromagnetic/magnetic field with the flaws. An electromagnetic pulse contains many frequency components, so pulse sources typically produce significantly more peak power than single frequency sources using a simple control circuit. The advantage of a pulsed excitation source is that it can provide time information along with rich frequency components, which can deliver depth information for defects and materials based on skin effects. Pulse techniques have been used for pulsed eddy current and pulsed magnetic flux leakage for non-destructive 1 Corresponding Author: G Y Tian, School of Electrical, Electronic and Computer Engineering, Newcastle University, UK, NE1 7RU Email: [email protected]

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G.Y. Tian et al. / Magnetic and Acoustic Barkhausen Noise

testing and evaluation [2, 3] with the help of advanced signal processing. In a ferromagnetic material, Barkhausen noise is generated by the discontinuous movement of irreversible domains walls. This movement can be induced by applying a time varying magnetic field across the sample. This noise can be detected in the form of acoustic noise (electrical energy) known as acoustic Barkhausen noise (ABN) or magneto-acoustic emission (MAE) and in the form of voltage pulses which are induced in a coil placed near the surface of the material, called magnetic Barkhausen noise (MBN). MBN results from the reversible and irreversible displacement of 180o and non-180o domain walls, or by abrupt rotation of domain magnetisation vectors at higher magnetic fields; ABN is only caused by the discontinuous motion of non-180o walls, or the irreversible rotation of domains through angles other than 180o. ABN and MBN are highly correlated [4]. Therefore, MBN is a useful NDE technique and many researchers have studied MBN for iron-based materials [4,5]. The mechanism of MBN, however, has not been clearly understood, especially the relationship between MBN and micromagnetic states such as grain size, residual stress, dislocations, voids, etc.

2.

Probe Design and Characterisation of Signals

Figure 1 shows the design of the dual acoustic emission / magnetic permeability probe. The probe consists of a ferrite core wound with a 200 turn excitation coil supplied with current by a power amplifier supplied with a 10Hz waveform, wound onto one leg of the ferrite core is a 100 turn pick-up coil. 45mm to the left of the core is a piezoelectric ABN sensor; this has a 1kg weight applied to it during the tests and petroleum jelly is used to insure effective acoustic coupling between the sensor and the material surface.

Figure 1. System design and associated signals

The ABN sensor and the pickup coil are interfaced to a data acquisition card via signal processing electronics. The ABN sensor used in the tests is a R15I-AST from Physical Acoustics Corporation (PAC); the sensor is a resonant type with a frequency range of 50 kHz – 200 kHz. This frequency range was deemed acceptable by previous testing with a broadband sensor. Data acquisition was via an Adlink 2010 4-channel data acquisition card, using a sampling frequency of 2MHz. Data recording was performed in LabView and data processing in Matlab.


(a)

195

(b)

Figure 2. Pulsed excitation current and ABN signal (a) and excitation current and integrated pickup coil voltage (b)

Figure 2 shows some typical signals from the ABN sensor and the pickup coil, along with the current applied to the excitation coil using pulsed excitation. Figure 2a shows the excitation current along with the signal from the ABN sensor. It can be seen from the plot that the ABN sensor output is greatest where the excitation current is exhibiting its greatest rate of change and the minimum ABN amplitude comes where the gradient of the excitation signal is at a minimum. The voltage drop over the pickup coil indicates the rate of change of the field through the coil with respect to time, and is given by:

VCOIL

§ dB · kn¨ ¸ © dt ¹

(1)

Where VCOIL is the potential drop over the pickup coil, B is the magnetic field through the coil, n is the number of turns in the coil and k is a constant associated with the coil characteristics. So integration of the coil voltage gives a signal proportional to the field through the coil. The coil voltage integral is shown in figure 2b, where the difference in the form of the two curves shows the effect of the hysteresis of the material and the high level of magnetism where the excitation reaches zero indicates the remnant magnetisation of the material. As the coil voltage indicates the field intensity round magnetic circuit formed by the core and the material under test, measurement of the coil voltage can be used to indicate variations in the magnetic permeability of the material. It has been shown previously that variations in magnetic permeability can be used to indicate both applied and residual stresses in ferromagnetic materials [6]. Once the ABN signal exceeds a certain level (the threshold), it is classed as an acoustic event. Each repetition of the excitation waveform evokes hundreds of these events, each of which corresponds to “noise” picked up by the transducer. Several parameters can be used to quantify each of these events, including area – this is a measurement of the area contained between the peaks of the event and the threshold and is also referred to as signal energy and the event count – the number of times that the signal rises and crosses the threshold during each event. The overall RMS amplitude is also used to quantify the signal. A single Matlab program was developed for the work to process the signals acquired during the tests and output several

196


parameters, including peak to peak and RMS values of the coil voltage, pickup coil integral and RMS voltage and signal energy and event count for the ABN signal.

3. Active Stress Measurement 3.1. Barkhausen Acoustic Emission Analysis The test shown in figure 3a was set up to study the effect on the acoustic emission signal and coil voltage of the application of stress. A steel sample measuring 230mm x 30mm x 2mm was placed in a Hounsfield material test machine with the test system shown in figure 1 attached. The force applied to the sample was increased from 0kN to 16kN in 1kN steps, corresponding to a maximum stress of 267MPa and a maximum nominal strain of 8.5%, well into the plastic region for the material. After each 1kN step, both sine wave and pulsed excitation were applied to the sample and the corresponding ABN signals and coil voltages recorded.

(a)

(b)

Figure 3. Active stress test set-up (a) and stress/strain plot for the material (b)

Before the test was carried out, the stress / strain curve for the material (figure 3b) was calculated using an identical test sample, cut from the same piece of steel. The stress / strain curve shows that the yield point for the material is around 150MPa of stress at 0.8% strain. So stresses below this point will be referred to as elastic and stresses above this point will be referred to as plastic. Figures 4a and 4b shows plots of the event count (the number of times the ABN signal crosses a particular threshold) using sine and pulsed excitation for applied stress. It can be seen from the plots that the event count is most sensitive to stresses in the elastic region, below 150MPa. As applied stress approaches the yield point, the event count for both sine and pulsed excitation starts to level out, but the pulsed excitation exhibits the most linear correlation with applied stress up the 100 MPa point. Figures 4c and 4d show plots of the integral of the pickup coil voltage in volts x seconds (VS) for sine and pulsed excitation divided by the RMS excitation power (watts) for the two excitation waveforms to show the sensitivity of the two methods with respect to excitation power. It can be seen from the plots that the permeability of the material is most sensitive to stresses in the plastic region, giving a fairly linear correlation with measured strain, especially above the yield point of 0.8%.


(a)

(b)

(c)

(d)

197

Figure 4. Event count for applied stress for sine excitation (a) and pulsed excitation (b), Peak to peak integral of coil voltage / excitation power (watts) plotted against % nominal strain for pulsed (a) and sine (b) excitation

The sensitivity of the integral pick-up coil signal (VS) with respect to the extension of the material under test (%strain) and the power supplied to the excitation coil (Watts) was calculated, for pulsed and sine excitation signals. The result of the for pulsed excitation and calculation yielded 494 u 10 6 VS / Watt / % Strain 6 for sine excitation; three times greater sensitivity for pulsed 164 u 10 VS / Watt / % Strain excitation, giving a considerable power saving for the pulsed excitation for comparable results. 3.2. Barkhausen Noise The test outlined in section 3.1 was repeated using an identical sample cut from the same sheet of steel. The ABN sensor was replaced by a GMR sensor positioned equidistant between the feet of the ferrite core (figure 3a). The signal from the sensor was sampled at a frequency 2MHz and 0.3 kHz – 38 kHz band-pass filtered using a Matlab program to extract the Barkhausen noise from the sensor signal. The RMS value for each reading was then computed. Figure 5a shows a typical filtered signal from the GMR sensor. It can be seen from the plot that, as with the acoustic emission signal, the greatest amplitude of Barkhausen noise comes where the excitation signal is exhibiting its greatest rate of change. Figure 5b shows the RMS amplitude of the Barkhausen noise signal using sine excitation. Examination of figure shows that after an initial increase in amplitude, the MBN signal decreases all the way to the end of the test, rapidly in the elastic region and then less steeply in the plastic region.

198


(a)

(b)

Figure 5. a) Barkhausen noise signal with excitation current, b) RMS Barkhausen noise amplitude for applied nominal strain

3.3. Discussion Stress dependence of domain wall activity is complex and heavily influenced by microstructural factors such as material phases and grain size. This is especially true for MBN measurement which has been shown to increase or decrease in response to applied tensile stress dependant the microstructure of the material under inspection, with MBN activity increasing with applied tensile stress for martensitic structures and decreasing with applied tensile stress in cementite structures [7]. In contrast ABN is in general less sensitive to microstructure, with the application of tensile stress to steel almost always causing a decrease in ABN activity. The results from both the magneto-acoustic emission and the Barkhausen noise tests confirm that for this particular material under these test conditions, Barkhausen noise testing for active stress detection is most suited to the measurement of stresses in the elastic region, with both ABN and MBN showing greater variation in response to elastic stresses. The differences in sensitivity in the elastic and plastic regions are due to the fact that the mechanisms which give rise to domain wall activity are different in each region. So changes due to elastic and plastic stresses must be considered as separate phenomena. In the elastic region, deformation causes changes in the inter-atomic spacing in the material and corresponding changes in domain configuration. This has a direct effect on magneto-elastic energy and thus the Barkhausen activity [8]. Once the plastic region is reached, the macroscopic elastic strain remains fairly constant and other mechanisms take over, the most significant of these being the introduction of dislocations to the material acting as pinning sites to domain wall motion. In the plastic deformation region, at each stain value, the substructure changes in addition to the change in stress. The influence of substructure dominates, which reduces the mean free path and hence the overall emission is reduced and the correlation is not held. In the elastic region, the easy magnetisation direction rotates towards the tensile axis without any structural changes and hence a good correlation with applied stress is maintained. Another factor which influences domain wall motion is the intensity of the applied magnetic field. An increase in the maximum applied magnetic field has been shown to invoke greater ABN and MBN activity as well as a shift of the maximum ABN and MBN activity to a higher stress level [5], thus changing the sensitivities of the techniques to different sections of the stress strain curve. In this case maximum


199

sensitivity is apparent in the elastic region. This effect is thought to be due in some part to the application of fixed maximum excitation amplitude in the tests [4]. Although the applied field is initially sufficient to drive the material into saturation, as pinning sites increase in number the mean free path for pinning sites reduces [9] and the energy required to overcome these barriers to domain wall movement increases, thus modifying the hysteresis curve for the material and increasing the level of applied magnetic field required to drive the material into saturation. So although the potential Barkhausen energy and therefore the sensitivity of Barkhausen techniques to applied stress is higher in the plastic region, through greater release of energy from domains overcoming pinning sites, the actual measured Barkhausen noise reduces because not as many domains are able to overcome pinning sites with the supplied excitation field. 4.

Determination of Residual Stress Orientation in Pre-stressed Steel Sample

The test shown in figure 6a was set up to investigate the correlation between residual stress orientation, permeability and ABN in a steel sample previously exposed to plastic tensile stress. A steel sample which had been exposed to 8.5% nominal strain in the tests outlined in the previous section was used, along with a miniature version of the developed probe. After the load had been removed, readings from the ABN sensor and the signal from the pickup coil were taken at 22.5° increments as the ferrite core was rotated by 360°.

(a)

(b)

(c)

Figure 6. a) Pre-stressed steel test set up, b) Change in peak to peak coil voltage, c) Change in ABN event count in 22.5° increments around a 360° scan for pre-stressed steel sample.

Figures 6b and 6c show the change in peak to peak coil voltage and ABN event count around the full 360° scan of the material, with the residual stress orientated horizontally. It can be seen from figure 6b that the coil voltage is at a maximum at 90° with respect to residual stress and from figure 6c that the event count is greatest parallel to residual stress.

200


Plastic deformation causes dislocations, leading to a complete reorganisation of the material domain structure and increased magnetic anisotropy, with the easy magnetic direction of domain walls rotating towards the tensile stress direction leading to increased permeability parallel to tensile stress and at 90° to compressive stress. It has been shown in previous studies that the application of plastic tensile stress to a material usually results in the generation of compressive residual stress on release of applied stress [1]. This corresponds to figure 6c, where the signal from the pickup coil indicates increased permeability at 90° to the previously applied stress, thus indicating the presence of compressive residual stress. The two sets of results are complementary, in that the maximum displacement of non-180° domain walls will take place at 90° to the easy magnetisation direction. 5.

Conclusions

The work shows that the pulsed ABN system can offer substantial improvements to traditional single frequency ABN systems where depth information is of primary concern. The nature of the pulsed signal also means that magnetic saturation can be achieved with a much lower RMS current than with single frequency excitation, so the system could offer improvement where power consumption is of importance, i.e. portable test devices. Fusion of the signals from the ABN sensor and the pickup coil could provide data for stress measurement from the elastic region right up to fracture, with the ABN sensor providing data in the elastic region and the pickup coil in the plastic region. Acknowledgments - The authors would like to thank EPSRC for funding the research and Dr T. Jayakumar at IGCAR, India for some useful comments and suggestion. References [1] [2] [3] [4] [5] [6] [7]

[8] [9]

A. Dhar, L. Clapham and D. L. Atherton, Influence of uniaxial plastic deformation on magnetic Barkhausen noise in steel, NDT and E Int., 34(8), Dec. 2001, pp. 507-514. A Sophian, G Y Tian, S Zairi, Pulsed Magnetic Flux Leakage probe for crack detection and characterisation, Sens. Actuators, A, 125(2), 10 Jan. 2006, pp. 186-191. A Sophian, R S Edwards, G Y Tian and S Dixon, Dual-probe methods using pulsed eddy currents and electromagnetic acoustic transducers for NDT inspection, INSIGHT, 47(6), Jun. 2005, pp. 341-345. D O'Sullivan, M Cotterell, D A Tanner and I Mészáros, Characterisation of ferritic stainless steel by Barkhausen techniques, NDT and E Int., 37(6), Sep. 2004, pp. 489-496. B Augustyniak, Correlation between acoustic emission and magnetic and mechanical Barkhausen effects, J. Magn. Magn. Mater., 196-197, 1999, pp. 799-801. J M Makar and B K Tanner, The effect of plastic deformation and residual stress on the permeability and magnetostriction of steels, J. Magn. Magn. Mater., 222(3), Dec. 2000, pp. 291-304. D J Buttle, C B Scruby, G A D Briggs, J P Jakubovics, The Measurement of Stress in Steels of Varying Microstructure by Magnetoacoustic and Barkhausen Emission, Proc. R. Soc. London, Ser. A, 414(1847), Dec. 1987, pp. 469-497. C G Stefanita, D L Atherton and L Clapham, Plastic versus elastic deformation effects on magnetic Barkhausen noise in steel, Acta Mater., 48(13), Aug. 2000, pp. 3545-3551. S Vaidyanathan, V Moorthy, P Kalyanasundaram, T Jayakumar, and B Raj , Effect of Different Stages of Tensile Deformation on Micromagnetic Parameters in High-Strength, Low-Alloy Steel, Metall. Mater. Trans. A, 30A, Aug. 1999, pp. 2067-2072.


201

Electromagnetic Acoustic Resonance to Assess Creep Damage in a Martensitic Stainless Steel Toshihiro OHTANI Materials Lab., Ebara Research Co. LTD., Japan

Abstract. The microstructure evolution of a martensitic stainless steel, JISSUS403, subjected to tensile creep at 873K has been studies by monitoring of shear-wave attenuation and velocity using electromagnetic acoustic resonance (EMAR). The study revealed an attenuation peak at around 20 % of and a minimum value at 50 % of the creep life, independent of the applied stress. This novel phenomenon is interpreted as a result of microstructural changes, especially dislocation structure. This interpretation is supported by TEM observations of dislocation structure. The relationship between attenuation change and microstructure evolution can be explained with the string model. The study results have suggested that EMAR possesses the potential to assess the progress of creep damage and predict the remaining creep life of metals. Keywords. Creep damage, Ultrasonic attenuation, Martensitic stainless steel, Noncontacting evaluation, dislocation.

1. Introduction Structural metals are subject to aging from fatigue, creep, corrosion, and their combination. Exposure to elevated temperatures promotes creep. Aged metals lose toughness, or the ability to absorb energy for stresses above the yield point. They can not endure the occasional high load without fracturing. In-service degradation by creep is one of the most critical factors determining the structural integrity of the elevatedtemperature components in power plants, chemical plants and oil refineries the world over [1]. For instance, fossil-plants have been in operation for such long durations that the critical components have exceeded the design life of 30 to 40 years. They have undergone progressive damage as time has proceeded. In order to save energy and meet recent regulatory standards for CO2 emission, as well as to improve thermal efficiency, the steam pressures and operating temperatures in the components have been increased. As a consequence, material degradation has been accelerating. Economic and environmental concerns that prohibit the construction of new plants increase the severity of this problem. Therefore, in-service assessment of the state of damage is important for ensuring safe operation, predicting remaining life, and promoting lifeextension programs [2, 3]. For this assessment, a non-destructive technology enabling the evaluation of the current state of materials and the prediction of their remaining life Corresponding Author: Toshihiro Ohtani, Ebara Research Co. LTD., 4-2-1 Hon-Fujisawa, Fujisawa, 2518502, Japan; E-mail:[email protected]

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T. Ohtani / Electromagnetic Acoustic Resonance to Assess Creep Damage

has long been sought [1]. It is essential that the technique should provide simple and quick measurement to cope with a large number of objects and give accurate information about microstructural change. This study describes the changes in ultrasonic attenuation and velocity and microstructural evolution during creep tests on a martensitic stainless steel (JISSUS403) as observed using EMAR (electromagnetic acoustic resonance) [4]. This steel is widely used as a high temperature material in power plants and chemical plants. It has high strength at elevated temperatures (up to 923 K) and also provides thermal expansion and good resistance to corrosion [5]. EMAR is a combination of the resonant technique and a non-contacting electromagnetic acoustic transducer (EMAT) [4]. Incorporation of EMATs in resonant measurement greatly contributes to the improvement of the weak coupling efficiency of EMATs. The attenuation measurement is inherently free from the energy loss associated with contact transduction, thus providing a pure measurement of attenuation in a metal sample.

2. Sample and EMAT The material was from a commercial plate of martensitic stainless steel, JIS-SUS403. It was heated at 1253 K for 2 h, water-quenched, heated at 1023 K for 2 h, and tempered. A specimen for the creep test was machined; the gauge sections appeared as plate shapes of 5 mm thickness, 18 mm width and 35 mm length [6]. The mechanical properties of the plates at room temperature were as follows: 0.2% proof stress at 562 MPa, an ultimate tensile strength at 720 MPa and elongation of 25 %. The chemical composition is given in Table 1. A shear-wave EMAT with a 10 mm x 10 mm active area was used. It was comprised of an elongated spiral coil and a pair of permanent magnets in directions opposite to the specimen surface. It generated and received the shear waves with the magnetostrictive effect of ferromagnetic materials in a non-contacting manner [4]. The polarized shear waves traveled back and forth in the thickness direction. For more details, see Refs [7, 8]. Resonant frequencies and attenuation coefficients for thickness resonant modes were measured with a superheterodyne spectrometer [4]. The resonant peaks appear at equal frequency intervals and at each resonant frequency the attenuation coefficient was measured by the free-decay method, leading to the frequency dependence of attenuation [4].

3. Experiments Creep tests were carried out at 873 K in air for three stresses of 120, 140 and 160 MPa with lever-type equipment. During the creep test, creep loading was interrupted and the samples were cooled in the furnace. After measuring ultrasonic properties (the attenuation coefficients and velocity), the creep test was restarted. This procedure was repeated every 20, or 50 h until rupture. A series of crept samples with different strains was obtained. To distinguish the effects of thermal history alone, the unstressed samples along side the stressed samples was examined.

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T. Ohtani / Electromagnetic Acoustic Resonance to Assess Creep Damage Table 1. Chemical composition of SUS403 (wt. %).

C 0.120

Si 0.300

Mn 0.40

P 0.033

S 0.018

Ni 0.200

Cr 11.67

Fe Bal

To investigate the relationship between the microstructure and ultrasonic responses through the creep life, the microstructures of specimens were observed with an optical microscope (OM), a scanning electron microscope (SEM) and a transmission electron microscope (TEM). To obtain the microstructure observation samples, the modified Tҏҏ projection [9] and a rupture parameter, PD [10] were applied. The sample preparation procedure is shown in detail elsewhere [6].These micrographs were scanned into the computer for further analysis.

4. Results

0.008

(b)

:D :'V/Vi

14 th mode

0.05 0.00

0.006 0.004

0

500

0

500

873 K, 0 MPa -0.05 1000

Time [h]

'V/Vi [%]

Attenuation -1 coefficient, D [Ps ]

The resonant frequencies in the 1 to 8 MHz range and their attenuations during the creep test were measured. Figure 1(a) shows the typical relationship between the attenuation coefficientҏ D, velocity change, 'V/Vi (Vi: initial velocity), creep strain, and life fraction t/tr (creep time/rupture life) as creep advances. The rupture life was 990.6 h. The attenuation coefficient increases, showing a peak at t/tr =0.2, then decreases, showing a minimum near t/tr =0.5, and finally increases until rupture. The velocity gradually decreased and showed a local minimum at the attenuation peak, then slightly increased until the attenuation minimum, and finally quickly decreased to the rupture. The total decrease in velocity was about 0.3 %. The creep strain, however, monotonously increased until the rupture.

1000 20

0.03 0.0 0.02

:D :'V/Vi

0.01

:Strain

15 10

Strain [%]

14 th mode 873 K, 120 MPa

'V/Vi [%]

Attenuation -1 coefficient,D [Ps ]

25 (a)

5

-0.5 0

0.00 0.0

0.2

0.4

0.6

0.8

1.0

Life fraction, t/tr Figure 1. Relationship between attenuation coefficient, D, velocity change, 'V/Vi, creep strain and life fraction, t/tr, at the 14th resonant mode (around 4.5 MHz) [(a) 120 MPa, 873 K] and reference sample [(b) stress free, 873 K, until 1000 h]. The rupture life of crept sample was 990.6 h. The shear wave polarization was parallel to the stress direction.

204

Attenuation -1 coefficient, D [Ps ]


0.05

14th mode

0.04

873 K

:120 MPa :120 MPa :140 MPa :160 MPa

0.03 0.02 0.01 0.00 0.0

0.2

0.4

0.6

0.8

1.0

Life fraction, t/tr Figure 2. Relationship between D at the 14th resonant modes and life fraction (120, 140 and 160 MPa, 873 K). The shear wave polarization is parallel to the stress direction. Rupture life tr= 990.6 h and 1077.3 h for 120 MPa, tr =1040.4 h for 140 MPa and tr =356.5 h for 160 MPa.

These trends were commonly observed in the other resonant modes and the other direction of polarization. Attenuation always showed a peak at around t/tr = 0.2 and a minimum near t/tr = 0.5, independent of the stress for creep as shown in Fig. 2. The heat treatment only caused insignificant changes in the attenuation and velocity as shown in Fig. 1(b), indicating that the changes in the ultrasonic properties were caused solely by creep.

5. Discussion Possible factors contributing to the attenuation coefficient change in a MHz frequency range [11] are as follows: 1) Grain scattering, 2) Scatterings caused by precipitation, and 3) Dislocation damping Effects of 1) and 2) were examined with the scattering theory in the Rayleigh region [11]. It has been reported that they cause only negligible change in the attenuation coefficient [6]. Therefore, only dislocation damping can explain the observed acoustic response. 5.1 Dislocation Damping Dislocations vibrate in response to ultrasonic stress with a phase lag because of viscosity and dissipate the energy of the ultrasonic waves. This anelastic mechanism also lowers the ultrasonic velocity. Dislocation lines are pinned by point defects, precipitates, and other dislocations. These pinning points act as nodes of vibration of elastic strings. From the string model by Granato and Lücke [12] for dislocation damping, the following equation for a lower frequency range than the dislocationsegment resonant frequency has been derived: D = A1 /̓L 4 f 2

(1),


205

where A1 is a positive constant that depends on the shear modulus, Poisson’s ratio, specific damping constant, and Burger’s vector. / is the dislocation density, and L is the dislocation length. According to this model, D is proportional to the density / multiplied by the fourth power of the segment length of the “effective” dislocations, which are mobile and can vibrate with the low-stress ultrasonic waves. Not all dislocations interact with ultrasonic waves. These interacting dislocations were defined as mobile dislocations, which cause ultrasonic attenuation. Dislocations piling up against grain boundaries or sub-boundaries cannot vibrate and contribute to D.

Dislocation Cell structure

Lath

1Pm

(a) t/tr=0

1Pm

(b) t/tr=0.20

Re-crystallization

Sub-grain

1Pm

(c) t/tr=0.52

1Pm

(d) t/tr=0.71

Figure 3. Transmission electron micrographs of crept specimens at t/tr = 0, 0.20, 0.52, and 0.71 (120 MPa, 873 K).

206


0.0 -1

10

0.2

㩷 Life fraction, t/tr

0.4

0.6

0.8

(b)

1.0

14th mode

-2

10

-3

10

2

:Calculated D :Measured D

㩷

:Density :Length

(a)

0.6 0.4

1

0.2 0 0.0

0.2

0.4

0.6

0.8

Dislocation length, L1[Pm]

Dislocation density, Attenuation -1 14 -2 /1[x10 m ] coefficient, D[Ps ]

To demonstrate the possibility of dislocation damping, the dislocation structure of specimens was observed with TEM. Figure 3 shows the TEM micrographs of a crept sample at 120 MPa. Figure 3 (a) shows the dislocation structure before creep (t/tr = 0), and Fig.3 (b) through (d), at t/tr = 0.20, 0.52, and 0.71. The direction of stress was in the longitudinal direction of the photograph. In Fig. 3 (a), the lath structure covered the entire area. Many dislocations were observed within the lath. Figure 3 (b) shows the microstructure at t/tr = 0.20, when D shows a peak (Fig. 1). The lath structures still accounted for the majority of the whole area. The width of the lath structure was larger than that in Fig. 3 (a). The dislocation density within the lath structure increased. In a small fraction of the area, cells and sub-grains were observed. Their boundaries were not clear. Figure 3 (c) shows the microstructure at t/tr = 0.52, when D was at its minimum. Numerous sub-grains were observed. They were larger in size and their boundaries were clearer than in Fig. 3 (b). The dislocation density within the sub-grains was low. Figure 3 (d) shows the microstructure at t/tr = 0.71, when D increased again. The entire area was covered by the sub-grain structure. The boundaries of the subgrains were clearer than those in Fig. 3 (c). The size was larger than in Fig. 3 (c), and the density was about the same as in Fig. 3 (c). Figure 4 shows the results obtained by analyzing the TEM microstructures stored in the computer. For the following determination, at least five TEM micrographs from different locations on the thin foil were used. Figure 4 (a) shows the dislocation density /1 and the average dislocation length L1. The density of dislocations was measured with a method proposed by Keh and Weissmann [13]. Only the dislocations pinned by carbides in grains and other dislocations, as well as movable dislocations, were considered. As shown in Fig. 4(a), /1 increased until t/tr = 0.2 and then decreased until rupture. On the other hand, L1 increased until t/tr = 0.2, and it remained almost constant within the range of t/tr = 0.2 to 0.5. Afterward, L1 increased with an increase in t/tr. The change of the dislocation structure in Fig. 3 and the change in free dislocation density in Fig. 4(a) can be found in past reports. [13-16].

1.0

Life fraction, t/tr

Figure 4. (a): Change of dislocation density and length as creep progresses (120 MPa, 873K), (b): Comparison between calculated and measured attenuation coefficient in the 14th resonant mode (120 MPa, 873 K).

207


The attenuation coefficient was given by substituting L1 and /1 for L and / of Equation (1). Shown in Fig. 4 (b) was the comparison with the calculated and measured attenuation coefficients of the 14th resonant mode at 120 MPa, based on an assumption that /1 v / and, L1 v L as shown in Fig. 4 (b). The constant A1 was determined so that the measured and calculated Ds were consistent with each other before creep. Theoretically, / and L are the density and length of dislocations that vibrate with ultrasonic waves (on the order of 0.1 nm or less amplitude), and they are not exactly equal to L1 and /1. It is impossible to identify which dislocations in the TEM image actually oscillated with the ultrasonic waves. In general, point defects were absorbed and pinned on dislocation lines. The distance between the point defects corresponded to L, which means that L1 exceeded L. The interaction of the point defects pinning dislocations was considered. It was assumed that longer dislocation lines would provide longer distances between the point defects. In Fig. 4(b), the calculated and measured Ds show similar behavior. Similar to the case of austenite stainless steels, 2.25% Cr-1% Mo and Cr-Mo-V steels and Ni-based super-alloy [6, 17-19], it is proved that this assumption is valid, and the attenuation change results from energy absorption caused by dislocations. Figure 4(b) shows, however, that the absolute value of the calculated attenuation coefficient is different from that of the measured one. This difference arises from the difference between L1 and L since L affects D, as shown in Equation (1). Thus, the attenuation mainly changes from dislocation restructuring. In addition, Granato and Lücke [12] derived the following equation for velocity: 'V/V0 = -A2 / L2

(2),

where A2 is a positive constant and V0 =(G/U)1/2 which is the dislocation-independent velocity, which would ideally be determined at such a high frequency that the dislocation cannot oscillate in response to the elastic waves. G is the shear modulus and Uis the density of the material. Velocity is proportional to the dislocation density / multiplied by the square of the dislocation length L. The increases in / and L lead to the decrease in velocity. At the point showing the peak of the attenuation coefficient in Fig. 1, the velocity is altered from a decrease to a slight increase. The velocity rapidly decreases while D quickly increases (t/tr > 0.5). It appears to be the strongest proof that the velocity change is caused by dislocation vibration. The attenuation peak was observed in the creep progression on austenite stainless steels, 2.25%Cr-1%Mo, CrMo-V steels and Ni-based super-alloy [6, 17-19]. Shown in Table 2 is t/tr, where the attenuation shows the peak in these materials. These data show the universality of the EMAR method. In addition, the method is capable of detecting the microstructural evolution, dislocation mobility, and transition of the dislocation structure during creep progression.

Table 2. Life fraction at attenuation peak for various materials. Material

SUS 403

Type 304

Type 316L

Life fraction, t/t r , 20-30 % 30-40% 60-70% at attenuation peak 䇭 Stress (MPa) 120, 140 and 160 100, 110 and 120 100,110 and 120 Temperature (K) 873 973 973

2.25Cr-1Mo steel 50-60% 45 and 65 923

Cr-Mo-V steel

Waspaloy

25-30%

35-40%

25,35,45 and 55 140, 150 and 160 923 1073

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6. Conclusion Creep damage in a martensitic stainless steel (JIS-SUS403) at 873 K in air was evaluated through ultrasonic attenuation measured with the EMAR method. Attenuation showed a peak at around 20% and a minimum value at 50 % of the creep life, independent of the applied stress, which is interpreted as resulting from microstructural changes, especially, dislocation mobility and restructuring. This result is supported by TEM observations. The relationship between the changes in ultrasonic attenuation and velocity and the microstructural change can be explained with the Granato-Lücke string model. This technique has the potential to assess the damage advance and to predict the creep life of metals. The EMAT which is most suitable for a real component will be studied as a future work

References [1] [2]

[3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19]

R. Viswanathan, Damage mechanism and life assessment of high temperature components, ASM International, Ohio, 1989. G. Dobmann, M. Kroning, W. Theiner, H. Willems and U. Fiedler, Nondestructive characterization of materials (ultrasonic and micromagnetic techniques) for strength and toughness prediction and detection of early creep damage, Nucl. Eng. Design 157 (1995), 137-158. P. Auerkari, J. Salonen, Accuracy requirement for life assessment, Int. J. Pressure Vessel Piping 39 (1989), 135-144. M. Hirao, and H. Ogi, EMATs for Science and Industry: Nondestructive Ultrasonic Measurements, Kluwar Academic Publishers, Boston, 2003. J. Pesicka, R. Kuzel, A. Dronhofer and G. Eggler, The evolution of dislocation density during heat treatment and creep of tempered martensitic ferritic steels, Acta Materialia 51 (2003), 4847-4862. T. Ohtani, H. Ogi and M. Hirao, Creep-induced microstructural changes in 304-type austenitic stainless steel, Trans. ASME J. Eng. Mat. Tech. 128 (2006), 234-242. B. W. Maxfield and C. M. Fortuko, The design and use of electromagnetic acoustic wave transducers (EMATs), Mater. Eval. 11 (1983), 1399-1408. R. B. Thompson, In: R. N. Thurston and A. D. Pierce A D, eds. Physical Acoustics, XIX. Academic Press, New York, 1990. K. Maruyama, C. Harada and H. Oikawa, A strain-time equation applicable up to tertiary creep stage, J. Soc. Mater. Sci. Jpn. 34 (1985), 1289-1295. K. Maruyama and H. Oikawa, An extrapolation procedure of creep data for St Determination: with special reference to Cr-Mo-V steel, Trans. ASME. J. Pressure Vessel Tech. 109 (1987), 142-146. R. C. Truell, C. Elbaum, B. B. Chick, Ultrasonic methods in Solid State Physics, Academic Press, New York, 1969. A. Granato and K. Lücke, Theory of mechanical damping due to dislocations, J. Appl. Phys. 27 (1956), 583-593. A. S. Keh and S. Weissmann, In: G. Thomas, J. Washburn, eds. Electron Microscopy and Strength of Crystals, Interscience, New York, 1963. C. R. Barrett, W. D. Nix and O. D. Sherby, The influence of strain and grain size on the creep substructure of Fe-3Si, Trans. ASM. 59 (1966), 3-15. A. Orlova and J. Cadek, Some substructure aspects of high-temperature creep in metals, Phil. Mag. 28 (1973), 891-899. T. Hasegawa, Y. Ikeuchi and S. Karashima, Internal stress and dislocation structure during sigmoidal transient creep of a copper-16 at.-% Aluminum alloy, Metal. Sci. J. 6 (1972), 78-82. T. Ohtani, H. Ogi and M. Hirao, Change of ultrasonic attenuation and microstructure evolution during creep of 2.25%Cr-1%Mo steels, Metall. Mater. Trans. A 36A (2005), 2967-2977. T. Ohtani, H. Ogi and M. Hirao, Evolution of microstructure and acoustic damping during creep of a Cr-Mo-V ferritic steel, Acta Materialia 54 (2006), 2705-2713. T. Ohtani, H. Ogi and M. Hirao, Acoustic damping characterization and microstructure evolution of Nibased super-alloy during creep, Int. J. Solids Struct. 42 (2005), 2911-2928.


209

NDE Method Using Minor Hysteresis Loops in Ferromagnetic Materials Seiki TAKAHASHI 1, Satoru KOBAYASHI, Yasuhiro KAMADA, Hiroaki KIKUCHI, and Katsuyuki ARA NDE and Science Research Center, Faculty of Engineering, Iwate University, Morioka 020-8551, Japan Abstract. Minor hysteresis loops of plastically deformed Fe single crystals, polycrystals and low carbon steel have been analyzed. We propose an analysis method of minor loops where coefficients sensitive to lattice defects are obtained from relations between field-dependent minor-loop parameters. The coefficients are independent of magnetic field amplitude of minor loops and magnetic field, and can be obtained with low magnetic fields less than a 1 kA/m. These characters are useful for nondestructive evaluation of material degradation in ferromagnetic materials. Keywords. Minor hysteresis loops, dislocations, nondestructive testing, Fe, low carbon steel

1. Introduction Nondestructive evaluation (NDE) of material degradation of the pressure vessel in nuclear reactor is one of the most urgent priorities for the safe operation of such plants. The deterioration of the pressure vessel determines the lifetime of the nuclear reactor and is currently evaluated by impact tests of Charpy test pieces which are made of the individual vessel base and weld material and preinstalled in the reactor. However, Charpy tests need a large number of test pieces and the shortage of test samples becomes problematic especially when liftime extension is planned. The structure-sensitive magnetic properties are useful physical quantities to obtain information on lattice defects.[1,2] It was revealed that coercive force of the major loop increases in proportion to the square root of dislocation density. However, magnetic fields larger than 10 kA/m are necessary to measure the major loop in general. On the other hand, minor hysteresis loops, which can be obtained with lower magnetic field, offer several advantages compared with the major loop. By measuring minor loops with various magnetic field amplitudes, it would be possible to obtain much information on lattice defects in ferromagnetic materials with high sensitivity.[3] However, the analysis of minor loops has not been exploited as a NDE technique so far, because minor-loop properties strongly 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]

210

S. Takahashi et al. / NDE Method Using Minor Hysteresis Loops in Ferromagnetic Materials

depend on external parameters and it is difficult to relate magnetic properties with lattice defects quantitatively. In this paper, we present a method for analyzing minor hysteresis loops by using results of Fe single crystals, Fe polycrystals and low carbon steel, where the above disadvantages are drastically reduced and field-independent structure-sensitive properties can be obtained.[4-6]

2. Experiment The Fe single crystals, Fe polycrystals, and A533B steel were plastically deformed in tension. Sheets of Fe single crystals with 1 mm in thickness have surface plane of (001) and were deformed along [100]. A533B, a low carbon steel (0.18 wt% C, 0.15 wt% Si, 1.50 wt% Mn, 0.03 wt% Cu, 0.66 wt% Ni, 0.56 wt% Mo, balance Fe) is used in nuclear reactor pressure vessels. The grain size of A533B steel, determined using metallurgical microscopy, is about 10 Pm. After unloading, the samples were shaped into picture frames for Fe single crystals or rings for Fe polycrystals and A533B steel for minor-loop measurements. The exciting and detecting coils were wound on these samples. Minor hysteresis loops with various magnetic field amplitude Ha up to 1.6 kA/m for Fe single crystals and polycrystals and up to 8 kA/m for A533B steel, were measured at room temperature using a flux meter. Before measuring each minor loop, the samples were demagnetized. Magnetic properties of the major loops for Fe single crystals and polycrystals, and for A533B steel were obtained with Ha = 1.6 kA/m and Ha = 8 kA/m, respectively.

3. Experimental Results

Figure 1. Set of minor loops for Fe single crystals with true stress of (a) 0 MPa, (b) 95 MPa, and (c) 142 MPa. For clarity, only representative loops are shown.

211


As representative data, we will show results of minor loops for Fe single crystals. Figure 1 shows a set of minor hysteresis loops for Fe single crystals with and without tensile deformation. It is clearly seen that tensile stress drastically changes the shape of minor loops. For analysis of minor loops, several magnetic properties of minor loops are introduced as shown in Fig. 2: minor-loop coercive force Hc*, minor-loop magnetization Ma*, minor-loop hysteresis loss WF*, minor-loop remanence MR*, minor-loop remanence work WR*, and three minor-loop susceptibilities FH*, FR*, and Fa* at magnetic field H =

M

Fa*

Ma*

FR*

+MR*

WR*

-Hc*

FH* +Hc* +Ha H

0

WF* MR* Figure 2. Magnetic parameters of a minor loop.

㪈㪅㪍

㪐㪇

(a)

㪈㪅㪋 True stress 0 MPa 95 MPa 142 MPa

㪈㪅㪉㪈㪅㪇

0.5

㪇㪅㪏

0.4

54 MPa 135 MPa

0.3

㪇㪅㪍

0.2

㪇㪅㪋

0.1

㪇㪅㪉

0.0

㪇㪅㪇㪇㪅㪇

㪇㪅㪉

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0

20

㪇㪅㪏

40

60

Ha (A/m)

㪈㪅㪇

80 100

㪈㪅㪉

㪈㪅㪋

㪈㪅㪍

㪤㪸㪾㫅㪼㫋㫀㪺㩷㪽㫀㪼㫃㪻㩷㪸㫄㫇㫃㫀㫋㫌㪻㪼㩷㪟㪸㩷㩷㩿㪈㪇㪊㩷㪘㪆㫄㪀

㪤㫀㫅㫆㫉㪄㫃㫆㫆㫇㩷㪺㫆㪼㫉㪺㫀㫍㪼㩷㪽㫆㫉㪺㪼㩷㪟㪺㪁㩷㩷㩿㪘㪆㫄㪀

㪤㫀㫅㫆㫉㪄㫃㫆㫆㫇㩷㫄㪸㪾㫅㪼㫋㫀㫑㪸㫋㫀㫆㫅㩷P㪇㪤㪸㪁㩷㩿㪫㪀

㪈㪅㪏

㪏㪇

(b)

㪎㪇㪍㪇㪌㪇㪋㪇㪊㪇㪉㪇㪈㪇㪇㪇㪅㪇

True stress 0 MPa 95 MPa

㪇㪅㪉

㪇㪅㪋

㪇㪅㪍

54 MPa 135 MPa

㪇㪅㪏

㪈㪅㪇

142 MPa

㪈㪅㪉

㪈㪅㪋

㪈㪅㪍

㪤㪸㪾㫅㪼㫋㫀㪺㩷㪽㫀㪼㫃㪻㩷㪸㫄㫇㫃㫀㫋㫌㪻㪼㩷㪟㪸㩷㩷㩿㪈㪇㪊㩷㪘㪆㫄㪀

Figure 3. (a) Minor-loop magnetization Ma* and (b) minor-loop coercive force Hc*, as a function of magnetic field amplitude Ha for Fe single crystals with and without tensile deformation.

212


Hc*, 0, and Ha, respectively. WR* is the area enclosed by a minor loop in the second quadrant. These parameters correspond to those of the major loop when Ha is large enough to saturate the samples. Figures 3(a) and 3(b) show Ma* and Hc* as a function of Ha, respectively, for Fe single crystals with and without tensile deformation. It is clearly seen that Ma* decreases with increasing true stress while Hc* drastically increases. The curves of Fig. 3(a) correspond to the virgin magnetization curves and can be divided conveniently into four stages as follows. In the first stage, the Bloch wall moves reversibly and the slope at low fields gives the initial susceptibility. The irreversible displacement of the Bloch wall contributes mainly to the magnetization in the second stage and the magnetization shows the steepest slope. The gentle slope following the steepest section corresponds to the third stage. Finally, in the fourth stage, the magnetic domain walls sweep out of the sample and the magnetization proceeds only by the rotation of magnetic moments. For the present analysis of minor loops, magnetization process both in first and second stages is very important. For all deformed Fe single crystals, minor loops have a similar figure in the second stage. This can be confirmed by comparing WR* and MR* with WF* and Ma*, respectively. As shown in Fig. 4, both WF*-WR* and Ma*-MR* curves can be plotted on a straight line for all samples except for the large values; WR*/WF* a 1/6 and MR*/Ma*a 3/4. The former relation means that the area of hysteresis work is one-third of the total area of a minor loop in the second stage. These results show that the shape of minor loops is independent of Ha as well as true stress, being indicative of the shape similarity of the Bloch wall potential in the second stage. Such similarity was observed also in Fe polycrystals and A533B steel after tensile deformation, whereas a slope of the relations is slightly different from that of Fe single crystals; WR*/WF* a 1/8 and MR*/Ma*a 2/3 for Fe polycrystals and WR*/WF* a

㪤㫀㫅㫆㫉㪄㫃㫆㫆㫇㩷㪿㫐㫊㫋㪼㫉㪼㫊㫀㫊㩷㫃㫆㫊㫊㩷㪮㪝㪁㩷㩷㩿㪡㪆㫄㪊㪀

True stress 0 MPa 54 MPa 95 MPa 135 MPa 142 MPa

㪍㪇㪇㪌㪇㪇㪋㪇㪇㪊㪇㪇㪉㪇㪇

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㪉㪇

㪊㪇

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㪍㪇

㪤㫀㫅㫆㫉㪄㫃㫆㫆㫇㩷㫉㪼㫄㪸㫅㪼㫅㪺㪼㩷㫎㫆㫉㫂㩷㪮㪩㪁㩷㩷㩿㪡㪆㫄㪊㪀


㪈㪅㪏

㪎㪇㪇

㪈㪅㪍㪈㪅㪋


㪈㪅㪉㪈㪅㪇㪇㪅㪏㪇㪅㪍

㪤㪩㪁㪆㪤㪸㪁㪔㪊㪆㪋

㪇㪅㪋㪇㪅㪉㪇㪅㪇㪇㪅㪇

㩿㪹㪀㪇㪅㪉

㪇㪅㪋

㪇㪅㪍

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㪈㪅㪉

㪤㫀㫅㫆㫉㪄㫃㫆㫆㫇㩷㫉㪼㫄㪸㫅㪼㫅㪺㪼㩷P㪇㪤㪩㪁㩷㩿㪫㪀

Figure 4. Relations (a) between WF* and WR* and (b) between Ma* and MR* for Fe single crystals with and without tensile deformation.


213

㪤㫀㫅㫆㫉㪄㫃㫆㫆㫇㩷㪿㫐㫊㫋㪼㫉㪼㫊㫀㫊㩷㫃㫆㫊㫊㩷㪮㪝㪁㩷㩷㩿㪡㪆㫄㪊㪀

㪈㪇㪊


㪈㪇㪉

㪈㪇㪈

㪈㪇

㪇

㪈㪇㪄㪈

㩿㪸㪀㪈㪇㪄㪉㪈㪇㪄㪊

㪈㪇㪄㪉

㪈㪇㪄㪈

㪤㫀㫅㫆㫉㪄㫃㫆㫆㫇㩷㫉㪼㫄㪸㫅㪼㫅㪺㪼㩷㫎㫆㫉㫂㩷㪮㪩㪁㩷㩷㩿㪡㪆㫄㪊㪀

1/8 and MR*/Ma*a 3/5 for A533B steel. All minor-loop parameters depend on the external parameter Ha as shown in Fig. 3 and it is difficult to extract the intrinsic physical properties from the Ha dependence of

㪈㪇㪉㪈㪇㪈㪈㪇㪇


㪈㪇㪄㪈㪈㪇㪄㪉㪈㪇㪄㪊

㩿㪹㪀

㪈㪇㪄㪋㪈㪇㪄㪋

㪈㪇㪇


㪈㪇㪄㪊

㪈㪇㪄㪉

㪈㪇㪄㪈

㪈㪇㪇


Figure 5. The relations (a) between WF* and Ma* and (b) between WR* and MR* for Fe single crystals with and without tensile deformation. The solid lines through the data show least-squares fits.


㪤㫀㫅㫆㫉㪄㫃㫆㫆㫇㩷㫊㫌㫊㪺㪼㫇㫋㫀㪹㫀㫃㫀㫋㫐㩷F㪩㪁㩷

㪤㫀㫅㫆㫉㪄㫃㫆㫆㫇㩷㪺㫆㪼㫉㪺㫀㫍㪼㩷㪽㫆㫉㪺㪼㩷㪟㪺㪁㩷㩷㩿㪘㪆㫄㪀

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㪈㪇㪄㪈

㪈㪇㪇


Figure 6. The relations (a) between Hc* and MR* and (b) between FR* and MR* for Fe single crystals with and without tensile deformation. The solid lines through the data show least-squares fits.

214


minor-loop parameters. Therefore, it is important to find new magnetic properties that are represented by the internal physical properties. Figures 5(a) and 5(b) show WF*-Ma* and WR*-MR* curves, respectively, for Fe single crystals with and without tensile deformation. In the second stage, these curves show nearly straight lines in double logarithmic scale and can be represented by a simple equation given by

WF

*

nF

§ M* W ¨ a ¨ Ms ©

· ¸ , ¸ ¹

§ M* W ¨ R ¨ MR ©

· ¸ , ¸ ¹

0 F

(1)

and

WR

*

0 R

nR

(2)

where WF0 and WR0 are minor-loop coefficients independent of Ha and sensitive to lattice defects. Ms and MR are the saturation magnetization and remanence of the major loop, respectively. nF a 3/2 and nR a 3/2, being independent of true stress and ferromagnetic materials. Note that the relation of Eq. (1) was discovered by Steinmetz about a century ago and is known as Steinmetz law where nF a 1.6.[7] As shown in Fig. 6(a), we also found that Hc* shows a relation with MR* in the second stage, expressed as

Hc

§ M* H ¨ R ¨ MR ©

*

0 c

nc

· ¸ , ¸ ¹

(3)

where Hc0 is a coefficient and nc a0.45. Similarly, as is seen in the relation between FR* and MR* in Fig. 6(b), three simple relations about minor-loop susceptibilities were found as below; Rc*

1

F H*

Rc0 exp(b

H c* , ) Hc

(4)

nT

§ M R* · , ¸ © MR ¹

F R*

F T0 ¨

F a*

Fs0 ¨

(5)

ns

§ M a* · , ¸ © Ms ¹

(6)

215


Fe polycrystal A533B steel

4

Fe single crystal

10

3

10

2

10

(b)

Coefficient WF0

14 12

Coercive force HC

8

6

10 8 6 4 2

4

A533B steel

100 200 300 400 500 600 700 800

True stress(MPa)

2

0

0

0

WF0(103 J/m3)

Coefficient F

10

Coefficient HC0

Fe single crystal

10

F6F5FK

0 S

Initial susceptibility Fi

5

16

Coefficient FT0

Hc0, Hc(102 A/m)

(a)

Fe polycrystal

6

10

0

100 200 300 400 500 600 700 800

True stress(MPa)

Figure 7. The true stress dependence (a) of Fi, FT0 and FS0, and (b) Hc, WF0 and Hc0, for Fe single crystals, polycrystals and A533B steel. The solid lines through the data are guide to eyes.

where Rc0, FT0 and Fs0 are coefficients which are related with lattice defects. b, nT and ns are constants which depend on the kind of materials, and have a value of 2-6, 0.1-0.5 and 0.5-1.0, respectively. The six simple relations between field-dependent minor-loop parameters, Eqs. (1)-(6), were found to be valid also for Fe polycrystals and A533B steel, and the dependence of minor-loop coefficients on true stress was obtained for all samples investigated. Figures 7(a) and 7(b) show the true stress dependence of minor-loop coefficients FT0, 0 FS , WF0 and Hc0. To compare with traditional structure-sensitive properties of the major loop, initial susceptibility Fi and coercive force Hc are also shown. As shown in Fig. 7(a), FT0, Fs0 and Fi decrease with the increase of true stress for all deformed samples, though the sensitivity of these coefficients is low in A533B steel. This is due to the fact that A533B steel contains many lattice defects even at zero true stress and the increase of dislocation density by tensile deformation does not influence the Bloch wall mobility significantly. The minor-loop coefficients WF0 and Hc0, and Hc increase with increasing true stress for all samples as shown in Fig. 7(b).

4. Discussion The six minor-loop coefficients, WF0, WR0, Hc0, Rc0, FT0, and Fs0 were obtained from simple relations between field-dependent minor-loop parameters. They are intrinsic physical quantities that are independent of magnetic field amplitude as well as the magnetic field, and are sensitive to lattice defects such as dislocations. The present method using set of

216


minor hysteresis loops has several advantages of nondestructive evaluation of degradation compared with the traditional method using major loop. One of them is the very small magnetic field required for minor-loop measurements. For instance, a maximum field amplitude used for minor-loop analysis is typically less than 20% of that for major-loop analysis. This small measurement field is an important characteristic for the design of the equipment. The minor loops were measured with increasing Ha, step by step, and the smaller step may bring about higher reliability of minor-loop coefficients. Nevertheless, using a similarity rule of minor loops, the amount of time for measurements and analysis can be drastically reduced without loss of reliability. In the present study, the picture frame samples cut from deformed tensile test pieces were used for the detailed analysis of minor loops. For NDE of pressure vessel in nuclear reactor, however, we need to measure magnetic properties of Charpy impact test pieces nondestructively. It has been shown by recent magnetic measurements using magnetic yokes that our analysis method can be applied for NDE of such test pieces and the detailed results will appear elsewhere. We need further investigation of lattice defects due to neutron irradiation using present minor-loop analysis. The relation between Cu precipitates and minor-loop coefficients are under investigation for samples irradiated by neutrons.

Acknowledgments This research was supported by a Grant-in-Aid for Scientific Research (S), No. 141020345, from the Ministry of Education, Culture, Sports, Science and Technology of Japan.

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

H. Kronmüller and M. Fähnle, Micromagnetism and the microstructure of ferromagnetic solids, Cambridge University press, 2003. H. Träuble: Magnetism and Metallurgy. Edited by Berkowitz A E and Kneller. E (Academic, New York 1969) Chap XIII 621. I. Tomás, J. Magn. Magn. Mater. 268 (2004) 178-185. S. Takahashi, T. Ueda and L. Zhang, J. Phys. Soc. Jpn. 73 (2004) 239-244. S. Takahashi and L. Zhang, J. Phys. Soc. Jpn. 73 (2004) 1567-1575. S. Takahashi, L. Zhang, S. Kobayashi, Y. Kamada, H. Kikuchi, and K. Ara, J. Appl. Phys. 98 (2005) 033909/1-8. C. P. Steinmetz, Trans. A. I. E. E. 9 (1892) 3-51.


217

Investigation of Neutron Radiation Effects on Fe Model Alloys by Minor-loop Analysis Satoru KOBAYASHI1 , Hiroaki KIKUCHI, Seiki TAKAHASHI, Katsuyuki ARA, and Yasuhiro KAMADA NDE and Science Research Center, Faculty of Engineering, Iwate University, Morioka 020-8551, Japan

Abstract. We have measured minor hysteresis loops of neutron-irradiated Fe model alloys. The change of minor-loop properties with neutron fluence, which depends on the copper content was detected. The results were explained as a compensation of internal stress in dislocations by copper precipitates around the dislocations. Keywords. Neutron irradiation, minor hysteresis loop, steel, Fe alloy, copper precipitates

1. Introduction The nondestructive evaluation of irradiation embrittlement of pressure vessels in nuclear-power plants has became an urgent matter of study because deterioration of the pressure vessels determines the lifetime of the nuclear reactors. At present, the irradiation embrittlement of pressure vessels is evaluated using the Charpy impact test. This destructive testing technique exploits the increase in ductile-brittle transition temperature (DBTT). The diminishing stock of Charpy impact test samples preinstalled in the reactors is an urgent issue. The change of mechanical properties due to neutron irradiation has been studied for reactor pressure vessel materials and Fe model alloys.[1] The neutron irradiation induces several kinds of lattice defects such as vacancies, interstitial atoms, voids, dislocation loops and copper precipitates. Some of the lattice defects make the ductility of materials low and make the brittleness increase. The structure of copper precipitates has been studied by the atom-probe field ion microscope,[2] positron annihilation,[3] and small-angle neutron scattering[4] because copper precipitation is the primary cause of brittleness in nuclear reactor pressure vessels (NRPVs). It has been shown that copper precipitates of 2 - 3 nm in size, which nucleate and grow due to irradiation, make materials brittle.[5,6] However, the nucleation mechanism which takes into effect of dislocations has not been studied in detail, although the NRPVs have high dislocation density even in the initial state. Dislocations 1

Corresponding Author: 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]

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would exert a great influence on the nucleation of lattice defects, because there exists elastic interaction between copper precipitates and dislocations. The magnetic method using minor hysteresis loops offers several advantages to get information on lattice defects.[7-9] It has been shown for cold rolled low carbon steel that minor-loop properties exhibit good correlation with mechanical properties such as Vickers hardness and DBTT.[10] In addition, the magnetic method is nondestructive and can be used with low magnetic fields (less than a 1 kA/m). However, reports on magnetic properties of irradiated materials are very few and irradiation effects on magnetic properties are not fully understood yet. In this paper, we have systematically investigated minor-loop properties of neutron irradiated Fe model alloys and tried to explain the results in view of copper precipitation in the presence of dislocations.

2. Experiment Neutron-irradiated tensile test samples were prepared by Professor Odette’s group at the University of California, Santa Barbara (UCSB). The samples have dimensions of 24 u 5 u 0.5 mm3 and their chemical compositions are listed in Table I, where the samples are labeled as OV15-20. Before neutron irradiation, the samples were solution treated for 17 h at 775 qC and then quenched at room temperature by forced helium gas. Table I. Chemical compositions of measuring samples. (wt %) Sample

Cu

Ni

Mn

OV15

0.9

1.6

1.0

OV16

0.5

1.6

1.0

OV17

0.2

Mo

Si

1.6

1.6

OV18

1.6

1.6

0.25

OV19

1.6

1.6

0.5

1.6

OV20

0.5

0.5

Table II. Conditions of neutron irradiation. Capsule

Fluence ) 19

t

-2

Flux I 12

Flux regime -2

-1

t

Effective Fluence ) eff 19

(10 n·cm )

(10 n·cm ·s )

T29

0.44

0.89

high

0.44

T30

0.02

0.07

low

0.07

T31

0.06

0.72

high

0.07

T32

0.02

0.26

Medium

0.04

-2

(10 n·cm )


219

We examined four irradiation conditions with various neutron fluence )t up to 0.44 × 10 n cm-2, and with neutron flux in the three different regimes as listed in Table II; 0.07 × 1012 n cm-2s-1 (low), 0.26 × 1012 n cm-2s-1 (medium), and 0.72 - 0.89 × 1012 n cm-2s-1 (high). The irradiation temperature was 290 qC. Minor hysteresis loops with various magnetic field amplitude Ha up to 6 kA/m were measured at room temperature using an apparatus for neutron-irradiated small tensile test samples. The apparatus includes a closed magnetic circuit with a sample sandwiched between two magnetic yokes made of Fe-3wt% Si steel. The magnetic field with the frequency of 1 Hz was applied along the long axis of the sample. The magnetic properties were typically averaged over 5 and 2 samples for unirradiated and irradiated cases, respectively. To analyze minor loops, we introduce several minor-loop parameters as shown in Fig. 1: minor-loop coercive force Hc*, minor-loop magnetization Ma*, minor-loop hysteresis loss WF*, minor-loop remanence MR*, minor-loop remanence work WR*, and three minor-loop susceptibilities FH*, FR*, and Fa* at magnetic field H = Hc*, 0, and Ha, respectively. WR* is the area enclosed by a minor loop in the second quadrant. These minor-loop parameters strongly depend on Ha and it is difficult to extract intrinsic physical properties from minor loops. Recently, however, we found six simple relations between the field-dependent minor-loop parameters, where minor-loop coefficients independent of Ha and sensitive to lattice defects were obtained[7-9]. In this study, we will pay attention to three relations given by 19

WF

*

§ M* W ¨ a ¨ Ms © 0 F

M Ma*

FR*

-Hc*

nF

· ¸¸ , ¹

(1)

Fa*

+MR*

FH*

WR*

+Hc* +Ha H

0

WF* MR* Figure 1. Magnetic parameters of a minor loop.

220


WR

H c*

*

§ M* W ¨ R ¨ MR © 0 R

§ M* H c0 ¨ R ¨ MR ©

· ¸ ¸ ¹

nR

,

(2)

nc

· ¸ . ¸ ¹

(3)

Here, WF0, WR0, and Hc0 are minor-loop coefficients, and Ms and MR are the saturation magnetization and remanence of the major loop, respectively. The exponents of the power laws, nF, nR, and nC are a 3/2, a 3/2, and a0.45, respectively, which are independent of kinds of lattice defects and ferromagnetic materials. The relation of Eq. (1) with nF a 1.6 is known as Steinmetz law.[11] These minor-loop coefficients were usually obtained with low magnetic fields (less than 1 kA/m) and are proportional to coercive force of the major loop. In this study, these coefficients were used to obtain intrinsic physical properties reflecting lattice defects in irradiated materials.

3. Experimental Results Figures 2(a)-2(d) show hysteresis loops for OV15, OV16, OV17, and OV19 samples, respectively, before and after neutron irradiation, obtained with the maximum magnetic field amplitude of Ha = 6 kA/m. For clarity, only the results obtained for high flux conditions are shown. Note that although the amplitude of Ha = 6 kA/m is not enough to saturate the samples, Hc* is almost saturated and equals to coercive force. For all measuring samples, changes in the shape due to neutron irradiation are not so large. However, we found that for OV15, OV16, and OV17 samples, Hc* becomes small at a sufficiently high neutron fluence and its behavior with fluence strongly depends on the chemical composition. On the other hand, no significant change in Hc* was detected for OV18, OV19 and OV20 samples within limit of experimental accuracy. Figure 3(a) shows minor-loop coefficients WF0 and WR0, as a function of neutron fluence for OV15 sample with various neutron flux. Note that since Hc0 obtained from Eq. (3) shows a similar fluence dependence to WF0 and WR0, the data for Hc0 are not shown. Both coefficients for medium and low flux have different from each other despite the same neutron fluence of )t = 0.02 × 1019 n cm-2. Such difference was also seen for OV16 and OV17 samples. To compare the minor-loop coefficients obtained for different neutron flux, an effective neutron fluence )teff is introduced [12]:

) teff

§I )t ¨ r Ï ©

1/ 2

· ¸¸ ¹

,

(4)


221

where I is a neutron flux and Ir is a reference flux and 0.89 × 1012 n cm-2s-1 in this study. This equation is based on a vacancy plus self-interstitial-atom recombination rate controlling mechanism and is used to explain the dependence of irradiation hardening on neutron flux; pre-plateau region of irradiation hardening is shifted to higher )t with increasing neutron flux.

Figure 2. M-H loops for (a) OV15, (b) OV16, (c) OV17, and (d) OV19 samples with various neutron fluence, measured with Ha = 6 kA/m. Only the data for high flux are shown.

222


Figures 3(b)-3(d) show the dependence of WF0 and WR0 on )teff for OV15, OV16, and OV17 samples, respectively. One can see that both WF0 and WR0 show smooth curves in this case. This implies that both magnetic and mechanical properties have the underlying mechanism of irradiation effects. Both WF0 and WR0 sharply increase at low fluence and show a maximum around )teff = 0.05 × 1019 n cm-2, followed by a gradual decrease for 300

4200

(a)

4200

300

(b)

OV15

OV15

4000

3800

260

3800

260

3600

240

3600

240

3400

220

3400

220

3200

200

3200

200

0

0.1

0.2

0.3

0.4

180 0.6

0.5 19

WF0 (J/m3)

WR0 (J/m3)

WF0 (J/m3)

3000 -0.1

260

(c) 3700

0.1

0.2

0.4

180 0.6

0.5

t

19

OV17

250

400 380

5000

WF0 (J/m3)

WR0 (J/m3)

240

230

3400 3300

220

3200

360

WF0 (J/m3)

3600 3500

-2

420

5500

(d)

OV16

0.3

Effective neutron fluence ) eff (10 cm )

-2

Neutron fluence )t(10 cm ) 3800

0

WR0 (J/m3)

3000 -0.1

280

WR0 (J/m3)

280

4000

340

4500

320 300

4000 280

210 3100

260 3000 -0.1

0

0.1

0.2

0.3

Effective neutron fluence

0.4 t ) eff

0.5

200 0.6 19

-2

(10 cm )

3500 -0.1

0

0.1

0.2

0.3

Effective neutron fluence

0.4 t ) eff

0.5

0.6 19

-2

(10 cm )

Figure 3. WF0 and WR0 as functions of neutron fluence )t for (a) OV15 sample, and of effective neutron fluence )teff for (b) OV15, (c) OV16, and (d) OV17 samples. The solid circles, open circles, and triangles denote the data for high, medium, and low flux, respectively.


223

OV15 and OV16 samples, while WF0 and WR0 monotonically decrease with fluence for OV17 sample. In contrast, for OV18, OV19, and OV20 samples, no significant change in minor-loop coefficients was detected within an experimental accuracy.(not shown) These results indicate that the copper content influences the behavior of minor-loop coefficients at low neutron fluence.

4. Discussion For OV15, OV16, and OV17 samples including copper, minor-loop coefficients become smaller at a sufficiently high neutron fluence. This indicates that internal stress decreases during neutron irradiation. This result is in contrast to our expectation that the coefficients will increase with neutron fluence because irradiation defects act as obstacles to the movement of Bloch wall. To explain this, we introduce an idea that copper precipitates grow up in the vicinity of dislocations during neutron irradiation. Copper precipitates have stress field in themselves and will make minor-loop coefficients increase if copper precipitates form in the matrix. However, the stress field is reduced and minor-loop coefficients will decrease when copper precipitates exist in the vicinity of dislocations. Edge dislocations include the compressive and repulsive stress field and copper precipitates will gather around the dislocations in order to reduce the elastic energy. Consequently, the copper precipitates compensate the stress field of dislocations, resulting in a decrease in minor-loop coefficients as was observed experimentally. The radiation defects fixed around dislocations strongly disturb the dislocation movement and will make mechanical properties increase. Direct observation using transmission electron microscopy is planned to confirm this explanation.

5. Conclusions Minor hysteresis loops of neutron-irradiated Fe model alloys have been measured to investigate the influence of radiation defects on minor-loop properties. It was revealed that the behavior of minor-loop coefficients at low neutron fluence depends on copper content and the coefficients become small at a sufficiently high neutron fluence, whereas no significant change was detected for alloys with no copper content. This indicates that copper precipitates induce the changes in magnetic properties. The decrease of the coefficients with neutron fluence may be explained as due to compensation of internal stress of dislocations by copper precipitates grown around the dislocations.

Acknowledgments This research project has been conducted under the research contract with the Japan

224


Nuclear Safety Organization (JNES). We thank Professor G. R. Odette of UCSB for allowing us to measure neutron irradiated samples, and Dr. T. Yamamoto, J. Smith, and Dr. D. Klingensmith of UCSB for their technical supports for treating irradiated samples.

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

J. Koutský and J. Koík, in Radiation Damage of Structural Materials, (Elsevier Science Publishers, 1994). P. Othen, M. Jenkins, G. Smith, and W. Phythian, Phil. Mag. Lett. 64 (1991) 383. S. Pizzini, K. Roberts, W. Phythian, C. English, and G. Greaves, Phil. Mag. Lett. 61 (1990) 223. M. K. Miller, B. D. Wirth and G. R. Odette, Mater. Sci. Eng. A 353 (2003) 133. A.Youle and B. Ralph, J. Met. Sci. 6 (1972) 149. S. Goodman, S. Brenner, and J. R. Low, Jr., Metall. Trans. 4 (1973) 2371. S. Takahashi, L. Zhang, S. Kobayashi, Y. Kamada, H. Kikuchi, K. Ara, J. Appl. Phys. 98 (2005) 033909. S. Takahashi, T. Ueda and L. Zhang, J. Phys. Soc. Jpn. 73 (2004) 239. S. Takahashi and L. Zhang, J. Phys. Soc. Jpn. 73 (2004) 1567. S. Takahashi, S. Kobayashi, H. Kikuchi, Y. Kamada, J. Appl. Phys. 100(2006) 113908. C. P. Steinmetz, Trans. A. I. E. E. 9 (1892) 3. G. R. Odette, T. Yamamoto, D. Klingensmith, Philos. Mag. 85 (2005) 779.


225

Numerical Analysis for Non-Destructive Evaluation of Hardening Steel Taking into Account Measured Magnetic Properties Depending on Depth a

Yuichiro KAI a,1, Yuji TSUCHIDA b and Masato ENOKIZONO b JSPS Research Fellow, Oita University, 700 Dannoharu, Oita, 870-1192, JAPAN b Faculty of Engineering , 700 Dannoharu, Oita, 870-1192, JAPAN

Abstract. We will examine a non-destructive evaluation method of hardening depth and hardness using numerical analysis. In our numerical analysis, the magnetic properties of carbon steel at different hardening depth are assumed by using the measured results from the cut-out ring type specimens. We try to evaluate the hardening depth and the hardness by calculating the magnetic flux density and the magnetic field strength by the two-dimensional finite-element method taking into account the measured magnetic properties. Keywords. Carbon steel, Hardening depth, Magnetic property, Numerical analysis

1. Introduction Parts of machines and structures are hardened by using induction heating. The case hardening can increase the hardness of steel. The different strength for the parts is required by controlling the hardening depth and the hardness. However, it is difficult to control the hardening depth and the hardness. If the case hardening is applied effectively to the steels, it is very important to evaluate the hardening depth and the hardness. We have proposed a non-destructive evaluation system of the hardening depth and the hardness by using an electromagnetic method. In previous works, the difference of the magnetic property depending on depth is clarified by measuring the magnetic properties of cut-out ring specimens [1, 2]. And we suggest to evaluate the hardening depth and the hardness by measuring the change of the magnetic properties depending on the depth. At first, we try to detect the change of the eddy current inside the hardening carbon steel by using a pick-up coil. In this case, we proposed to employ a multi-frequency excitation and spectrogram (MFES) method [3, 4]. Seen from the results, it was clear that the pick-up voltage changes as a function of the different hardening conditions. However, we suppose that it is important to obtain not only the change of the pick-up voltage but also the plenty of information inside the hardening steel since the several magnetic properties and mechanical properties change by using 1

Corresponding Author: JSPS Research Fellow, Materials Science and Production Engineering, Graduate School of Engineering, Oita University, 700 Dannoharu, Oita 870-1192, Japan; E-mail: [email protected]

226

Y. Kai et al. / Numerical Analysis for Non-Destructive Evaluation of Hardening Steel

the case hardening. Therefore, We suggest to evaluate the hardening depth and the hardness by measuring magnetic flux density B and the magnetic field strength H from outside instead of measuring the pick-up voltage. It is possible to obtain the plenty of information inside the hardening steel, which mean the permeability, the coercive force and the residual magnetic flux density. Therefore, we suppose that the measurement of the B and the H is an effective method to evaluate the hardening depth and the hardness. In the other institution, the non-destructive evaluation method for measuring the change of the material has been reported by measuring the B and the H [5]. We try to develop magnetic sensor to measure the B and the H and we obtain the magnetic properties depending on the depth by changing the frequency to control the penetration depth of the magnetic flux. We have examined the hardening depth and the hardness by measuring the B and the H for the steels of the different hardening temperature. It is clear that the measured B and the measured H change by the different hardening temperature. However, we could not clarify the relationship between the measured magnetic properties and the depth. Because it is difficult to estimate the magnetic properties depending on depth. In the numerical analysis, it is possible to take into account the magnetic properties depending on depth. Therefore, we propose the hardening model, which takes into account the measured magnetic properties depending on depth. In this paper, we will examine the non-destructive evaluation method of the hardening depth and the hardness by using the numerical hardening model. First, the definition of the hardening model is given by considering the measured magnetic properties. Then, the B and the H at the surface of the hardening steel are examined by using the proposed hardening model and the two-dimensional finite-element method.

2. Magnetic Property of Hardening Carbon Steel depending on Depth

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Figure 1 shows the measured magnetic properties of the hardening carbon steel depending on depth. The measured hysteresis loops change as shown in Figure 1. In particular, the measured hysteresis loops at the surface and the boundary change very much in comparison with the interior. So, the changes of the measured magnetic properties have to be clarified depending on the depth by measuring cut-out ring type specimens. We try to evaluate the hardening depth and the hardness by measuring the B and the H from the surface. Additionally we propose to obtain information depending on the depth by changing the frequency. In the numerical analysis, we try to examine whether the changes of the magnetic

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Figure 1. Magnetic properties of hardening carbon steel depending on depth (Hardening depth : 2 mm).

Y. Kai et al. / Numerical Analysis for Non-Destructive Evaluation of Hardening Steel

227

properties depending the hardening depth and the hardness are obtained by measuring the B and H from the surface.

3. Expression Method of Measured Magnetic Property The approximation method of Potter and Schmulian is employed to consider the measured magnetic properties [6]. The relationships between magnetization M and field H are approximated by using the hyperbolic curve function. As an advantage of this method, the hysteresis loop is expressed by giving the coercive force, the residual magnetization and the saturation magnetization in the measured magnetic property. The relationship between H and M is given by the following equation, M

ª ° § H H sgn D · ½°º M S «sgn D D ®1 tanh ¨ C tanh 1 S ¸ ¾» , HC °¯ «¬ © ¹ °¿»¼

(1)

where Ms is the saturation magnetization of the major loop, Hc is the coercive force of the major loop, S is the squareness ratio, D is the curve parameter, respectively. The range of Dis -1

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Advances in applied mechanics

Advances in Applied Mechanics

Advances in applied mechanics,

Advances in applied mechanics,

Advances in applied mechanics,

Advances in applied mechanics

Advances in applied mechanics,

Analytical and Computational Methods in Electromagnetics (Artech House Electromagnetic Analysis)

Asymptotic and Hybrid Methods in Electromagnetics (IEE Electromagnetic Waves Series)

Ill-Posed Problems for Integrodifferential Equations in Mechanics and Electromagnetic Theory (SIAM Studies in Applied and Numerical Methematics) (Studies in Applied and Numerical Mathematics)

Ill-Posed Problems for Integrodifferential Equations in Mechanics and Electromagnetic Theory (SIAM Studies in Applied and Numerical Methematics) (Studies in Applied and Numerical Mathematics)

Advanced Methods in Materials Processing Defects (Studies in Applied Mechanics)

Nondestructive Evaluation of Food Quality: Theory and Practice

Classical Mechanics: Applied Mechanics and Mechatronics

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