IMPERIAL COLLEGE LONDON MODELLING OF ELECTROMAGNETIC ACOUSTIC TRANSDUCERS by Remo Ribichini A thesis submitted to Imperial College London for the degree of Doctor of Philosophy Department of Mechanical Engineering Imperial College London London SW7 2AZ February 2011 Ai Miei Genitori Declaration of originality The material presented in the thesis “Modelling of Electromagnetic Acoustic Trans- ducers” is entirely the result of my own independent research under the supervision of Professor Peter Cawley. All published or unpublished material used in this thesis has been given full acknowledgement. Name: Remo Ribichini 03/03/2011 Signed: ` “E bellissimo.” Manuela Arcuri commenting on the “sms-epistolary novel” “Il labirinto femminile” by Alfonso Luigi Marra. Abstract At present, the dominant technology for transducers in the field of Ultrasonic Non- Destructive Testing is piezoelectric. However, some industrially important applica- tions, like the inspection of components operating at high temperature or while in motion, are difficult tasks for standard piezoelectric probes since mechanical contact is required. In these cases, contactless NDT techniques can be an attractive alterna- tive. Among the available options, Electromagnetic Acoustic Transducers (EMATs) can generate and detect ultrasonic waves without the need for a physical contact between the probe and the test object, as their operation relies on electromagnetic, rather than mechanical coupling. Since EMATs do not require any coupling liquid, the experimental procedures for inspection set-up are simplified and a source of un- certaintyiseliminated, yieldinghighlyreproducibleteststhatmakeEMATssuitable to be used as calibration probes for other ultrasonic tests. A further advantage of EMATs is the possibility of exciting several wave-modes by appropriate design of the transducer. Unfortunately, EMATs are also characterized by a relatively low signal-to-noise ratio and by a complex operation relying on different transduction mechanisms that make their performance dependent on the material properties of the testpiece. The present work aims to develop a numerical model including the main transduc- tion mechanisms, the Lorentz force and magnetostriction, that can be employed as a prediction tool to improve the understanding of EMAT operation. Following an overview on the historical development of EMATs and their models, the theory de- scribing EMAT operation is presented. The governing equations are implemented into a commercial Finite Element package. The multi physics model includes the simulation of the static and dynamic magnetic fields coupled to the elastic field through custom constitutive equations to include magnetostriction effects. The modelisusedtoquantitativelypredicttheperformanceofamagnetostrictiveEMAT configuration for guided waves without employing arbitrary parameters. The results are compared to experimental data providing a validation of the model and insight 5 on the transduction process. The validated model, together with experimental tests, is exploited to investigate the performance of different EMAT designs for Shear Hor- izontal waves in plates. The sensitivities of each configuration are compared and the effect of key design parameters is analyzed. Finally, the model is used in the evaluation of the performance of bulk wave EMATs on a wide range of steel grades. Experimental data interpreted via numerical simulations are employed to investi- gate the relative weight of the transduction mechanisms, with implications on the applicability of EMATs on the range of steels usually encountered in inspections. 6 Acknowledgements IwouldliketoexpressmydeepestgratitudetoProf. PeterCawleyforhisimpeccable supervision and constant support. His scientific rigour and devotion to research are invaluableteachingsthatIwillcarrythroughoutmyfutureprofessionalandpersonal life. I am grateful to Dr Fredric Cegla for his valuable advice that was so needed to get started with my research. Credit goes to them and Prof. Mike Lowe and Dr Francesco Simonetti for creating a stimulating and fruitful research environment in the Non-Destructive Testing Group. I am extremely grateful to Prof. Peter B. Nagy of University of Cincinnati for his essential help in the experimental part of this work and for easing my ignorance in the field of electromagnetism. Not only have our discussions been enlightening for me, but also very enjoyable. I also would like to thank all the members of the NDT group in general for their help and cooperation. I must mention in particular Marco for (rightly) convincing me that joining this group was a great idea, Giuseppe for his patience and help, Prabhu, Ken, Jake and Tom for their encouragement and support that meant so much to me, especially during the early stages of my Ph.D. All my gratitude goes to those who made this beautiful scientific experience also a wonderful time with their friendship: Tino “il boss” for the time at our mansion in Ingelow road, Rosalba for the countless “short coffee breaks”, Bieppe for making me explore London culinary, Michela for teaching me not only English, but also Italian, Sara for managing all the events with a rock mood, Andrea for introducing me to the proper English traditions, Tim for letting me know about his “awesome” ideas. Nothing of this would have ever happened without the support and love of my family: a huge thank you to Mamma, Neno, Piggi, Teta e Nonna. Finally, my heartily grazie to Elvira, whose enthusiasm and smile fill my life with joy. 7 Contents 1 Introduction 23 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.2 Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2 EMAT background and literature review 27 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.2 Basic EMAT operation . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.3 Advantages and limitations of EMATs . . . . . . . . . . . . . . . . . 30 2.4 EMAT classification . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.5 History of EMAT development and modelling . . . . . . . . . . . . . 35 2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3 Theory 41 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.2 Lorentz and magnetization mechanisms . . . . . . . . . . . . . . . . . 42 3.2.1 Governing equations . . . . . . . . . . . . . . . . . . . . . . . 42 3.2.2 Lorentz force . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 8 CONTENTS 3.2.3 Magnetization force . . . . . . . . . . . . . . . . . . . . . . . . 45 3.2.4 Ultrasonic field . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.2.5 Reception process . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.3 Magnetostriction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4 Finite Element model 55 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.2 Model implementation . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.3 Numerical solution of the governing equations . . . . . . . . . . . . . 57 4.4 3D Finite Element model for magnetostrictive SH waves EMAT . . . 59 4.5 Simplified models: analytical-numerical approach . . . . . . . . . . . 65 4.6 2D axisymmetric model . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 5 Validation of the model 69 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5.2 Model benchmark . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5.2.1 Eddy current . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 5.2.2 Static magnetic field . . . . . . . . . . . . . . . . . . . . . . . 72 5.2.3 Ultrasonic field . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5.3 Multiphysics model validation . . . . . . . . . . . . . . . . . . . . . . 74 9 CONTENTS 5.4 Magnetostrictive Shear Horizontal wave EMAT . . . . . . . . . . . . 76 5.5 Magnetostriction measurement . . . . . . . . . . . . . . . . . . . . . . 78 5.6 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 5.6.1 Qualitative validation . . . . . . . . . . . . . . . . . . . . . . . 81 5.6.2 Quantitative validation . . . . . . . . . . . . . . . . . . . . . . 85 5.7 Mutual coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 5.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 5.8.1 Qualitative validation discussion . . . . . . . . . . . . . . . . . 88 5.8.2 Quantitative validation discussion . . . . . . . . . . . . . . . . 89 5.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 6 Assessment of SH wave EMAT performance 93 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 6.2 EMATs and guided wave inspection . . . . . . . . . . . . . . . . . . . 93 6.3 EMAT configurations for SH waves . . . . . . . . . . . . . . . . . . . 94 6.3.1 Periodic Permanent Magnet (PPM) EMAT . . . . . . . . . . . 95 6.3.2 Magnetostrictive EMATs . . . . . . . . . . . . . . . . . . . . . 95 6.4 FE simulations and experimental study . . . . . . . . . . . . . . . . . 97 6.4.1 Numerical model . . . . . . . . . . . . . . . . . . . . . . . . . 97 6.4.2 Experimental validation . . . . . . . . . . . . . . . . . . . . . 98 6.5 Analysis of performance of different configurations . . . . . . . . . . . 100 6.5.1 PPM EMAT . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 10