NONDESTRUCTIVE EVALUATION TECHNIQUES FOR FATIGUE AND DAMAGE
DETECTION

By

Bharath Basti Shenoy

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

Electrical and Computer Engineering—Doctor of Philosophy

2024

ABSTRACT

The first part of this doctoral thesis explores the application of Magnetic Barkhausen Noise and Non-

Linear Eddy Current techniques for the early-stage detection of fatigue in ferromagnetic materials,

with a specific focus on Martensitic Stainless-steel samples. Due to its exceptional mechanical

properties at elevated temperatures, stainless steel finds extensive use in various applications.

However, material fatigue poses a significant challenge in steel structures, leading to potential

catastrophic damage and substantial economic consequences. While conventional nondestructive

evaluation techniques excel at detecting macro defects, they often fall short in identifying material

degradation at the microstructure level, particularly arising from fatigue.

The Magnetic Barkhausen Noise technique involves capturing signals generated by the move-

ment of domain walls after applying a time-varying magnetic field. Different fatigue stages yield

unique Magnetic Barkhausen Noise signatures, facilitating effective classification.

In the Non-

Linear Eddy Current technique, a robust external magnetic field induces non-linear behavior in

the material’s magnetization characteristic. The harmonics extracted from the Non-Linear Eddy

Current signal provide insights into the material’s microstructure, aiding in the classification of

samples at various fatigue stages. The research work systematically investigates the feasibility of

Magnetic Barkhausen Noise and Non-Linear Eddy Current techniques by employing customized

sensor assemblies to capture and analyze signals in both time and frequency domains. Extracted

features are further processed using k-medoids clustering algorithm, and Genetic algorithm for

robust classification into distinct fatigue stages. The comparative performance of the two magnetic

non-destructive evaluation techniques is thoroughly examined.

The research findings indicate that both Magnetic Barkhausen Noise and Non-Linear Eddy

Current techniques present promising capabilities for detecting early-stage fatigue in Martensitic

Stainless-steel samples and contributes to advancing the fatigue detection in ferromagnetic struc-

tures using magnetic non-destructive evaluation techniques.

In the second part of this doctoral thesis, the focus is on addressing critical challenges of monitoring

the structural health of engineering structures, which are susceptible to damage from both stress and

environmental factors. Traditional ultrasonic nondestructive evaluation techniques typically involve

contact-based procedures that necessitate the use of a couplant. However, this thesis explores the

use of Electromagnetic Acoustic Transducers, which offer a compelling non-contact alternative.

Electromagnetic Acoustic Transducers utilize the Lorentz force, acting on induced currents, to excite

elastic waves in a sample, eliminating the need for direct contact. The drawback of conventional

Electromagnetic Acoustic Transducers being limited to conductive or ferromagnetic samples is

addressed through the introduction of a novel Electromagnetic Acoustic Transducer, specifically

designed for non-conductive samples.

This novel Electromagnetic Acoustic Transducer presents two distinct configurations: (a) Di-

rect excitation and (b) Non-contact induced excitation, both utilizing the Lorentz force transduction

mechanism. A thorough investigation into the metal patch geometry employed in both configura-

tions is detailed, providing valuable design insights. The numerical model of these Electromagnetic

Acoustic Transducer configurations is developed using COMSOL, and simulation results robustly

affirm the feasibility of the proposed approach. By successfully extending the applicability of

Electromagnetic Acoustic Transducers to non-conductive samples and introducing the innovative

embedded Electromagnetic Acoustic Transducer, this research significantly contributes to advanc-

ing the field of structural health monitoring and presents a viable nondestructive evaluation approach

for the effective detection of damage in engineering structures.

ACKNOWLEDGEMENTS

I would like to express my heartfelt gratitude to my parents, wife and family. Their unwavering

support has been the cornerstone of my journey, and without them, this thesis would not have been

possible.

I am deeply grateful to my major advisor, Professor Lalita Udpa, for her unwavering guidance,

support, and mentorship throughout my doctoral journey. Her expertise, encouragement, and

constructive feedback have been invaluable in shaping this research and my academic growth. I

also extend my sincere appreciation to Professor Sunil Chakrapani for his mentorship, assistance in

understanding acoustics, and for instilling confidence in my capabilities. Their collective wisdom

has significantly enriched my doctoral experience.

I also extend my sincere appreciation to Professor Satish Udpa for providing me with the op-

portunity to join the NDEL family and for his insightful contributions to my academic and research

development. His words of encouragement were instrumental in propelling the advancement of my

research.

I would like to express my gratitude to Professor Yiming Deng, who was like a supportive co-

advisor throughout this journey. Collaborating with him was a valuable and enriching experience. I

extend my gratitude to the members of the NDEL research group for fostering an intellectually and

stimulating research environment. Our mutual support has been instrumental throughout the years,

and I look forward to sustaining these friendships in the years ahead. I extend my thanks to Zebadiah

Miles, a PhD student at Michigan State University, for his collaboration and valuable contributions

to the experimental aspects of the research work on electromagnetic acoustic transducers.

Lastly, my sincere thanks to all my friends in Michigan for their encouragement and support,

making this academic pursuit a memorable and fulfilling experience. My time in East Lansing was

made truly enjoyable by their incredible camaraderie.

iv

TABLE OF CONTENTS

LIST OF TABLES .

. .

LIST OF FIGURES .

. .

.

.

.

.

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii

CHAPTER 1

INTRODUCTION TO FATIGUE . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1 Material fatigue .
1.2 Microstructural phenomenon in steel . . . . . . . . . . . . . . . . . . . . . . .
1.3 Existing NDE methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.

.

1
1
4
7

CHAPTER 2

PHYSICAL PRINCIPLES OF MBN AND NLEC . . . . . . . . . . . . . 10
2.1 Magnetic Barkhausen Noise Technique . . . . . . . . . . . . . . . . . . . . . . 10
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 NLEC Technique .

.

CHAPTER 3

RESEARCH PROBLEM . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.1 Research problem representation . . . . . . . . . . . . . . . . . . . . . . . . . 18
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2 Sample database . .

.

CHAPTER 4

RESULTS AND DISCUSSION . . . . . . . . . . . . . . . . . . . . . . 20
4.1 Results and discussion on MBN . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.2 Results and discussion on NLEC . . . . . . . . . . . . . . . . . . . . . . . . . 28

CHAPTER 5

CONCLUSIONS AND FUTURE WORK . . . . . . . . . . . . . . . .

. 36

CHAPTER 6

INTRODUCTION TO EMAT . . . . . . . . . . . . . . . . . . . . . . . 38
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
6.1 Literature review .
6.2 Transduction mechanisms in EMAT . . . . . . . . . . . . . . . . . . . . . . . 41
6.3 Typical EMAT designs in Literature . . . . . . . . . . . . . . . . . . . . . . . 42

.

CHAPTER 7

LORENTZ FORCE EMAT . . . . . . . . . . . . . . . . . . . . . . . . 46
7.1 Theory . .
. 46
7.2 Numerical model in COMSOL . . . . . . . . . . . . . . . . . . . . . . . . . . 47
. . . . . . . . . . . . 51
7.3 Novel EMAT configurations for non-conductive samples

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. .

. .

.

.

.

CHAPTER 8

DIRECT EXCITATION . . . . . . . . . . . . . . . . . . . . . . . . . . 53
8.1 EMAT model in COMSOL . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
8.2 Effect of input current on Lorentz force and displacement in sample
. . . . . . 65
8.3 Effect of Aluminum strip geometry on displacement in sample . . . . . . . . . 67
8.4
Impact of skin effect in Aluminum strip on displacement in sample . . . . . . . 78
8.5 Experimental validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

CHAPTER 9

NON-CONTACT INDUCED EXCITATION: EMBEDDED EMAT . .

. 84
9.1 EMAT model in COMSOL . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
9.2 Effect of Aluminum strip geometry on displacement in sample . . . . . . . . . 93
9.3 Effect of line source on acoustic modes in sample . . . . . . . . . . . . . . . . 97
9.4 Effect of plastic cover height on displacement in sample . . . . . . . . . . . . . 101

v

9.5 A Comparative Analysis: Gaussian vs. Uniform Distribution of Lorentz

force in space .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
9.6 Experimental validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

. .

CHAPTER 10

10.1 Vertical slot defect
10.2 Horizontal crack defect
10.3 A-scans on sample back-wall

DAMAGE DETECTION IN SAMPLE . . . . . . . . . . . . . . . . . . 114
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
. . . . . . . . . . . . . . . . . . . . . . . . . . . 121

.

CHAPTER 11

CONCLUSIONS AND FUTURE WORK . . . . . . . . . . . . . . . .

. 125

BIBLIOGRAPHY . .

. .

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

vi

LIST OF TABLES

Table 2.1 MBN system details

.

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Table 2.2 NLEC experimental parameters

. . . . . . . . . . . . . . . . . . . . . . . . . . 17

Table 3.1 EPRI MSS sample database . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Table 4.1 Fatigue thresholds obtained on applying KCA and GA on MBN features . . . . . 25

Table 4.2 Comparison of other MBN feature combinations

. . . . . . . . . . . . . . . . . 26

Table 4.3 Sample database with fatigue classification . . . . . . . . . . . . . . . . . . . . 27

Table 4.4 NLEC signal features .

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Table 4.5 Fatigue thresholds obtained on applying KCA and GA on NLEC features

. . . . 33

Table 4.6 Sample database with fatigue classification . . . . . . . . . . . . . . . . . . . . 35

Table 8.1 Model parameters for Direct excitation EMAT . . . . . . . . . . . . . . . . . . . 55

Table 8.2 Time at which modes peak in Hilbert magnitude plot for Direct Excitation

EMAT model . .

. .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

Table 8.3 Mode velocities for Direct excitation EMAT model

. . . . . . . . . . . . . . . . 63

Table 9.1 Model parameters for Induced excitation EMAT model . . . . . . . . . . . . . . 86

Table 9.2 Time at which modes peak in Hilbert magnitude plot for Induced Excitation

EMAT .

.

.

.

. .

. .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

Table 9.3 Mode velocities for Induced Excitation EMAT . . . . . . . . . . . . . . . . . . 90

Table 10.1 Model parameters with defect dimensions . . . . . . . . . . . . . . . . . . . . . 121

vii

LIST OF FIGURES

Figure 1.1 Stages of fatigue failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.

Figure 1.2 SN curve . .

.

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.

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Figure 1.3 Domains with magnetic moments in steel . . . . . . . . . . . . . . . . . . . . .

2

3

6

Figure 2.1 Magnetic flux density changes due to Barkhausen effect

. . . . . . . . . . . . . 11

Figure 2.2 Time domain MBN signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Figure 2.3 Block diagram of MBN experimental set-up . . . . . . . . . . . . . . . . . .

. 12

Figure 2.4 Eddy Current in material with and without surface defect

. . . . . . . . . . . . 13

Figure 2.5 B-H curve with linear and non-linear eddy current response plots . . . . . . .

. 14

Figure 2.6 Block diagram of NLEC experimental set-up . . . . . . . . . . . . . . . . . . . 16

Figure 2.7 NLEC sensor mounted on the EPRI sample . . . . . . . . . . . . . . . . . . .

. 16

Figure 3.1 Overview of the research problem . . . . . . . . . . . . . . . . . . . . . . . . . 18

Figure 3.2 Snapshot of a MSS sample provided by EPRI

. . . . . . . . . . . . . . . . . . 19

Figure 4.1 Schematic of EPRI stainless-steel sample showing scanning point locations . . . 20

Figure 4.2 Gaussian fitting of MBN signal showing time domain features . . . . . . . . .

. 21

Figure 4.3 Frequency spectrum of MBN signal showing frequency domain features

. . . . 22

Figure 4.4 Flowchart of the algorithm used to classify MSS samples based on RUL . . . . 23

Figure 4.5 Clustering of MSS samples into fatigue categories . . . . . . . . . . . . . . . . 24

Figure 4.6 Classification results based on ground-truth . . . . . . . . . . . . . . . . . . . 26

Figure 4.7 Schematic of EPRI sample showing scanning points . . . . . . . . . . . . . . . 29

Figure 4.8 Time domain NLEC signal obtained from NLEC sensor . . . . . . . . . . . . . 29

Figure 4.9 Frequency spectrum of the time domain NLEC signal

. . . . . . . . . . . . . . 30

Figure 4.10 Flowchart of the algorithm used to classify MSS samples based on RUL . . . . 32

Figure 4.11 Clustering of MSS samples into fatigue categories . . . . . . . . . . . . . . . . 33

Figure 4.12 Classification results based on ground-truth NLEC . . . . . . . . . . . . . . .

. 34

viii

Figure 6.1 Schematic representation of an EMAT . . . . . . . . . . . . . . . . . . . . . . 40

Figure 6.2 Lorentz force representation on a metal plate . . . . . . . . . . . . . . . . . .

. 40

Figure 6.3 Schematic diagram of a Bulk-wave EMAT . . . . . . . . . . . . . . . . . . . . 43

Figure 6.4 Schematic diagram of a Meander line EMAT . . . . . . . . . . . . . . . . . . . 44

Figure 6.5 Schematic diagram of a PPM EMAT . . . . . . . . . . . . . . . . . . . . . . . 45

Figure 8.1 Direct Excitation model for an EMAT in COMSOL . . . . . . . . . . . . . . . 54

Figure 8.2 Zoomed version of the EMAT model shown in Figure 8.1 . . . . . . . . . . . . 54

Figure 8.3 Representation of input current provided to the Aluminum strip . . . . . . . . . 55

Figure 8.4

Input current density provided to Aluminum strip . . . . . . . . . . . . . . . . 56

Figure 8.5

z-component of current density at measurement point in Aluminum strip . . . . 57

Figure 8.6

y-component of Lorentz force at measurement point in Aluminum strip . . . . . 58

Figure 8.7 Surface plot of z-component of current density in Aluminum strip at 5 (cid:181)s . . . . 58

Figure 8.8 Surface plot of y-component of Lorentz force in Aluminum strip at 5 (cid:181)s

. . . . 59

Figure 8.9 Surface plot of x-component of Lorentz force in Aluminum strip at 5 (cid:181)s

. . . . 59

Figure 8.10 Arrow surface plot of y-component of Lorentz force (𝑁/𝑚3) in Aluminum

strip at 5 (cid:181)s

.

.

.

.

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

Figure 8.11 Zoomed version of Figure 8.10 . . . . . . . . . . . . . . . . . . . . . . . . . . 60

Figure 8.12 Arrow surface plot of x-component of Lorentz force (𝑁/𝑚3) in Aluminum

strip at 5 (cid:181)s

.

.

.

.

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 61

Figure 8.13 A-scan of displacement at measurement point on plastic back-wall

. . . . . . . 61

Figure 8.14 Hilbert magnitude of A-scan signal showed in Figure 8.13 . . . . . . . . . . . . 62

Figure 8.15 Surface plot of full-field displacement in plastic at 12 (cid:181)s . . . . . . . . . . . . . 64

Figure 8.16 Surface plot of y-component of displacement in plastic at 12 (cid:181)s . . . . . . . . . 64

Figure 8.17 Surface plot of x-component of displacement in plastic at 12 (cid:181)s . . . . . . . . . 65

Figure 8.18 Comparison of Lorentz force at measurement point in Aluminum strip for

varying coil current magnitudes . . . . . . . . . . . . . . . . . . . . . . . . . . 66

ix

Figure 8.19 Comparison of A-scans of displacement at measurement point on plastic

back-wall for varying coil current magnitudes

. . . . . . . . . . . . . . . . . . 66

Figure 8.20 A-scan of displacement for Aluminum strip width = 5mm . . . . . . . . . . . . 67

Figure 8.21 Comparison of displacement A-scans for varying Aluminum strip widths . . . . 68

Figure 8.22 Surface plot of full-field displacement in plastic at 12 (cid:181)s for Aluminum strip

width = 5mm .

.

.

.

.

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

Figure 8.23 Surface plot of y-component of displacement in plastic at 12 (cid:181)s for Aluminum

strip width = 5mm .

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

Figure 8.24 Surface plot of x-component of displacement in plastic at 12 (cid:181)s for Aluminum

strip width = 5mm .

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

Figure 8.25 Surface plot of z-component of current density in Aluminum strip for strip

width = 5mm .

.

.

.

.

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

Figure 8.26 Surface plot of y-component of Lorentz force in Aluminum strip at 5 (cid:181)s for

strip width = 5mm .

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

Figure 8.27 Surface plot of x-component of Lorentz force in Aluminum strip at 5 (cid:181)s for

strip width = 5mm .

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

Figure 8.28 Arrow surface plot of y-component of Lorentz force in Aluminum strip at 5

(cid:181)s for strip width = 5mm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

Figure 8.29 Arrow surface plot of x-component of Lorentz force in Aluminum strip at 5

(cid:181)s for strip width = 5mm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

Figure 8.30 A-scan of displacement at measurement point on plastic back-wall for Alu-

minum strip height = 0.1mm . . . . . . . . . . . . . . . . . . . . . . . . . .

. 74

Figure 8.31 Comparison of displacement A-scans for varying Aluminum strip heights . . . . 74

Figure 8.32 Surface plot of full-field displacement in plastic at 12 (cid:181)s for Aluminum strip

height = 0.1mm . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

Figure 8.33 Surface plot of y-component of displacement in plastic at 12 (cid:181)s for Aluminum

strip height = 0.1mm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

Figure 8.34 Surface plot of x-component of displacement in plastic at 12 (cid:181)s for Aluminum

strip height = 0.1mm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

Figure 8.35 Surface plot of z-component of current density in Aluminum strip for strip

height = 0.1mm . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

x

Figure 8.36 Arrow surface plot of y-component of Lorentz force in Aluminum strip at 5(cid:181)s

for strip height = 0.1mm . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 77

Figure 8.37 Arrow surface plot of x-component of Lorentz force in Aluminum strip at

5(cid:181)s for strip height = 0.1mm . . . . . . . . . . . . . . . . . . . . . . . . . .

. 77

Figure 8.38 Comparison of Hilbert magnitude peaks of A-scans of displacement in plastic,

for mode 1, and for different aluminum strip heights . . . . . . . . . . . . . . . 78

Figure 8.39 Experimental set-up for Direct Excitation EMAT . . . . . . . . . . . . . . . . . 79

Figure 8.40 Aluminum strip geometry used for experiments

. . . . . . . . . . . . . . . .

. 80

Figure 8.41 A-scan of displacement at measurement point on plastic back-wall - Simula-

tion result for Aluminum strip B . . . . . . . . . . . . . . . . . . . . . . . . . 81

Figure 8.42 A-scan of displacement at measurement point on plastic back-wall - Experi-

mental result for Aluminum strip B . . . . . . . . . . . . . . . . . . . . . . . . 81

Figure 8.43 A-scan of displacement at measurement point on plastic back-wall - Simula-

tion result for Aluminum strip C . . . . . . . . . . . . . . . . . . . . . . . . . 82

Figure 8.44 A-scan of displacement at measurement point on plastic back-wall - Experi-

mental result for Aluminum strip C . . . . . . . . . . . . . . . . . . . . . . . . 82

Figure 9.1

Induced Excitation model for an EMAT in COMSOL . . . . . . . . . . . . . . 85

Figure 9.2 Zoomed version of Figure 9.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

Figure 9.3 Arrow surface plot of y-component of Lorentz force in Copper patch at 5(cid:181)s . . . 87

Figure 9.4 Arrow surface plot of x-component of Lorentz force in Copper patch at 5(cid:181)s . . . 87

Figure 9.5 A-scan of displacement at measurement point on plastic back-wall for Induced

excitation EMAT .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

Figure 9.6 Hilbert magnitude of A-scan signal showed in Figure 9.5 . . . . . . . . . . . . 88

Figure 9.7 Surface plot of full-field displacement in plastic at 12 (cid:181)s for Induced excitation

EMAT .

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 90

Figure 9.8 Surface plot of y-component of displacement in plastic at 12 (cid:181)s for Induced

excitation EMAT . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

Figure 9.9 Surface plot of x-component of displacement in plastic at 12 (cid:181)s for Induced

excitation EMAT . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 91

xi

Figure 9.10 Comparison of A-scans of displacement at measurement point on plastic

back-wall for varying coil current magnitudes (Induced Excitation EMAT)

. . . 91

Figure 9.11 Comparison of A-scans of displacement at measurement point on plastic

back-wall for direct excitation and induced excitation EMAT’s . . . . . . . . . . 92

Figure 9.12 A-scan of displacement at measurement point on plastic back-wall for Alu-

minum strip width = 5mm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

Figure 9.13 Comparison of A-scans of displacement at measurement point on plastic back

wall for varying Aluminum strip widths (Induced Excitation EMAT)

. . . . . . 94

Figure 9.14 A-scan of displacement at measurement point on plastic back-wall for 0.1mm

Aluminum strip height (Induced Excitation EMAT)

. . . . . . . . . . . . . . . 95

Figure 9.15 Comparison of A-scans of displacement at measurement point on plastic back

wall for varying Aluminum strip heights (Induced Excitation EMAT) . . . . . . 96

Figure 9.16 Induced excitation EMAT model with point source (in 2D) - No aluminum . . . 97

Figure 9.17 Arrow surface plot of x-component of Lorentz force in Copper patch at 5 (cid:181)s

for Induced Excitation EMAT model shown in Figure 9.16 . . . . . . . . . . . . 98

Figure 9.18 Arrow surface plot of y-component of Lorentz force in Copper patch at 5 (cid:181)s

for Induced Excitation EMAT model shown in Figure 9.16 . . . . . . . . . . . . 98

Figure 9.19 A-scan of displacement at measurement point on plastic back-wall for Induced

Excitation EMAT model shown in Figure 9.16 . . . . . . . . . . . . . . . . . . 99

Figure 9.20 Quantitative comparison of Induced Excitation EMAT’s . . . . . . . . . . . . . 99

Figure 9.21 Surface plot of full-field displacement in plastic at 12 (cid:181)s for EMAT model

shown in Figure 9.16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

Figure 9.22 Surface plot of y-component of displacement in plastic at 12 (cid:181)s for EMAT

model shown in Figure 9.16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

Figure 9.23 Surface plot of x-component of displacement in plastic at 12 (cid:181)s for EMAT

model shown in Figure 9.16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

Figure 9.24 Comparison of displacement A-scans at measurement point on plastic back-

wall for varying plastic cover heights (Induced Excitation EMAT) . . . . . . . . 102

Figure 9.25 Comparison of displacement A-scans at measurement point on plastic back-

wall for varying aluminum strip placements (Induced Excitation EMAT)

. . . . 103

Figure 9.26 Representation of input current provided to Aluminum strip . . . . . . . . . . . 104

xii

Figure 9.27 Arrow surface plot of x-component of Lorentz force (Case 1) in Copper patch

at 5 (cid:181)s .

.

.

.

.

.

. .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

Figure 9.28 Arrow surface plot of y-component of Lorentz force (Case 1) in Copper patch

at 5 (cid:181)s .

.

.

.

.

.

. .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

Figure 9.29 Arrow surface plot of x-component of Lorentz force (Case 2) in Copper patch

at 5 (cid:181)s .

.

.

.

.

.

. .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

Figure 9.30 Arrow surface plot of y-component of Lorentz force (Case 2) in Copper patch

at 5 (cid:181)s .

.

.

.

.

.

. .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

Figure 9.31 Displacement A-scans (Mode 1) at measurement point on plastic back-wall . .

. 106

Figure 9.32 Surface plot of full-field displacement in plastic at 12 (cid:181)s - Case 1 . . . . . . . . 107

Figure 9.33 Surface plot of y-component of displacement in plastic at 12 (cid:181)s - Case 1 . . . . 107

Figure 9.34 Surface plot of x-component of displacement in plastic at 12 (cid:181)s - Case 1 . . . . 108

Figure 9.35 Surface plot of full-field displacement in plastic at 12 (cid:181)s - Case 2 . . . . . . . . 108

Figure 9.36 Surface plot of y-component of displacement in plastic at 12 (cid:181)s - Case 2 . . . . 109

Figure 9.37 Surface plot of x-component of displacement in plastic at 12 (cid:181)s - Case 2 . . . . 109

Figure 9.38 Experimental set-up for Induced Excitation EMAT . . . . . . . . . . . . . . . . 110

Figure 9.39 A-scan of displacement at measurement point on plastic back-wall - Simula-

tion result for Aluminum strip B (Induced Excitation EMAT)

. . . . . . . . . . 111

Figure 9.40 A-scan of displacement at measurement point on plastic back-wall - Experi-

mental result for Aluminum strip B (Induced Excitation EMAT) . . . . . . . . . 111

Figure 9.41 A-scan of displacement at measurement point on plastic back-wall - Simula-

tion result for Aluminum strip C (Induced Excitation EMAT)

. . . . . . . . . . 112

Figure 9.42 A-scan of displacement at measurement point on plastic back-wall - Experi-

mental result for Aluminum strip C (Induced Excitation EMAT) . . . . . . . . . 113

Figure 10.1 Embedded EMAT model with defect in COMSOL . . . . . . . . . . . . . . . . 114

Figure 10.2 Defect geometry representation . . . . . . . . . . . . . . . . . . . . . . . . .

. 115

Figure 10.3 A-scan of displacement at measurement point on plastic back wall (No defect

and With vertical slot defect)

. . . . . . . . . . . . . . . . . . . . . . . . . . . 115

Figure 10.4 Surface plot of full-field displacement in plastic at 12 (cid:181)s - No defect

. . . . . . 116

xiii

Figure 10.5 Surface plot of full-field displacement in plastic at 12 (cid:181)s - With defect

. . . . . 116

Figure 10.6 A-scan of displacement at measurement point on plastic back-wall for varying

defect widths (Defect height = 4mm) . . . . . . . . . . . . . . . . . . . . . . . 117

Figure 10.7 A-scan of displacement at measurement point on plastic back-wall for varying

defect heights (Defect width = 1mm) . . . . . . . . . . . . . . . . . . . . . . . 117

Figure 10.8 A-scans of displacement at measurement point on plastic back-wall (No defect

and with Horizontal crack defect) . . . . . . . . . . . . . . . . . . . . . . . . . 118

Figure 10.9 Surface plot of full-field displacement in plastic at 12 (cid:181)s - No defect

. . . . . . 119

Figure 10.10 Surface plot of full-field displacement in plastic at 12 (cid:181)s - With defect

. . . . . 119

Figure 10.11 A-scans of displacement at measurement point on plastic back-wall for varying

defect widths (Defect height = 1mm) . . . . . . . . . . . . . . . . . . . . . . . 120

Figure 10.12 A-scans of displacement at measurement point on plastic back-wall for varying

defect heights (Defect width = 4mm) . . . . . . . . . . . . . . . . . . . . . . . 120

Figure 10.13 A-scan results for a Horizontal crack defect . . . . . . . . . . . . . . . . . . . . 122

Figure 10.14 A-scan results for a Vertical slot defect

. . . . . . . . . . . . . . . . . . . . . . 123

xiv

CHAPTER 1

INTRODUCTION TO FATIGUE

Stainless-steel is used in many applications because of its excellent mechanical properties at elevated

temperatures. Martensitic grade stainless-steel is used to manufacture steam turbine blades in power

plants because of its mechanical strength, corrosion resistance and durability. Failure of turbine

blades can result in equipment damage contributing to expensive plant failures and safety concerns.

One of the primary factors which leads to degradation of the material and structural failure is plastic

deformation [1], caused by material fatigue.

1.1 Material fatigue

Material fatigue is defined as a process of progressive localized plastic deformation occurring

in a material subjected to cyclic stresses and strains. At high stress concentration locations

in the material, the progression of fatigue may culminate in cracks or complete fracture after

enough number of loading cycles [2]. Typically, material fatigue investigation in metals was

predominantly on monitoring of crack growth [3], because this is the stage that precedes ultimate

failure. Fatigue cracking is considered to be one of the most important damage mechanisms of

structural components. Hence, it is important to evaluate the material fatigue level prior to the

initiation of macro defects in order to ensure the viability of these components.

1.1.1 Stages of fatigue

There are three stages of fatigue failure: Initiation, propagation, and final rupture [4] as shown

in Figure 1.1.

Initiation: Irreversible changes in the material which is caused by repetitive shear stress applied

on it is the most important factor leading to fatigue crack initiation. Large number of loading

applications on the material leads to cumulative damage, in terms of micro-changes. In this fatigue

stage, dislocations (i.e., crystallographic defects) play a major part.

Propagation: In this stage, the micro-cracks formed during the crack initiation stage join together

and propagate in the direction perpendicular to the tensile stress. The growth of one or few of the

1

Figure 1.1 Stages of fatigue failure

larger cracks tend to dominate over the others and develop macro cracks. If cyclic loading is still

continued, the dominant crack keeps growing in size to the point where it reaches a critical size.

This is the point where the material can no longer support the load, i.e., fracture toughness of the

material is exceeded by the stress intensity factor. At this point, the crack tends to propagate rapidly.

Final rupture: The cross-sectional area of the material reduces with the propagation of fatigue

cracks. When the fatigue crack exceeds a particular size, the material is weakened and results in a

final rupture with additional loading cycles.

1.1.2 Fatigue life and SN-curve

The fatigue life of a component can be defined as the number of loading cycles needed to initiate

a fatigue crack and propagate it to the critical size. There are two regimes of fatigue, i.e., low cycle

and high cycle fatigue.

Low cycle fatigue is a regime of fatigue which is caused by large plastic strains with low number

of loading cycles before the occurrence of failure. Loading causes the development of high stress,

i.e., greater than the yield strength of the material. This leads to larger plastic deformation and

shorter fatigue life. In contrast, high cycle fatigue is a regime which is caused by small elastic

strains with higher number of loading cycles before the occurrence of failure. The stress level when

compared to low cycle fatigue is much lower, i.e., lower than the material’s yield strength. Also, the

macroscopic plastic deformation is much smaller when compared to the low cycle fatigue regime.

Fatigue life for any given material is found from the SN curve for that material.

A SN-Curve is a plot of magnitude of cyclic stress versus the number of loading cycles to

failure for a given material. A sample SN curve is shown in Figure 1.2. SN curves are determined

in the laboratory where test specimens are subjected to loading cycles of constant amplitudes until

2

Figure 1.2 SN curve

failure [5]. This technique was used before the microstructural understanding of fatigue process

and was based on empirical means. By keeping a safety margin of stress, the fatigue life of the

component/material can be easily found using SN curve for that component/material. The major

problem with this approach is the statistical variability. That is, we need to consider many specimens

of the material tested at different loading levels to define the SN curve with statistical confidence.

Hence a technique which can detect the level of fatigue in real-time is greatly beneficial.

1.1.3 Crack growth rate

Predicting crack growth rate during the process of cyclic loading on the material is important,

so that the material can be replaced before the crack reaches it’s critical size. Paris Law is a

mathematical relation which relates the crack growth rate to the stress intensity factor [3].

Experimental evidence shows that the growth rate of the crack has a correlation with cyclic

3

variation in the stress intensity factor and is given by Paris Law expressed in (1.1),

𝑑𝑎
𝑑𝑁

= 𝐴 Δ𝐾 m

(1.1)

Here 𝑑𝑎

𝑑𝑁 is the fatigue crack growth rate per cycle, Δ𝐾 = 𝐾 max −𝐾 min is the stress intensity factor

range during the cycle, A and m are material parameters that depend on the material, temperature,

stress ratio, environment and frequency. Hence, at the material scale, once a fatigue crack is

initiated, we can approximately calculate the number of loading cycles before which it reaches the

critical size. This gives us an estimate of the remaining fatigue life of the material. However, if the

macro defect/crack has not been developed, we cannot apply this approach and there is a need for

an alternative solution.

1.2 Microstructural phenomenon in steel

One plausible alternative to tackle the above problem is to look into changes in the material

properties, as the material is fatigued. This is where nondestructive evaluation (NDE) can play a

major role because it can be used to evaluate the properties of a material, component, or system [6].

The high sensitivity and broad capability of NDE techniques will be an added advantage in

determining the severity of material property changes caused by fatigue. The material under

consideration in this research work is martensitic grade stainless-steel, which is a ferromagnetic

material. A brief review on the phase transformation in steel, magnetization and effect of stress on

the magnetic properties of steel is discussed next.

1.2.1 Phase transformation in steel

Pure iron is extremely soft and cannot be used in structural applications. However, when a

small percentage of alloying element is added to it, the resulting mixture is a solid solution or

a compound. Carbon is a very unique alloying element in iron. The reason is that, addition of

carbon in iron produces steel which opens a diversity regarding the microstructure and mechanical

properties in an economic way. In iron-carbon solid solution, the carbon atom usually occupies the

interstitial site (the gap between the iron atoms in the crystal structure).

Phase is defined as a macroscopic homogeneous body of matter. A solid consists of a periodic

4

array of atoms which is called a crystal structure. Steel is composed of small crystalline particles

which are called grains and each grain has a periodic arrangement of atoms, i.e., the crystal

structure. If all grains have the same crystal structure and the only difference between them is their

orientation, then we regard it as a single-phase material. This means that dissimilar periodic array

of atoms change the micostructure and make a different phase. Hence, there can be several phases

with different crystal structures in steel like ferrite, austenite and martensite. The austenite phase

is non-magnetic in nature, whereas the martensite is magnetic.

Stainless steels are commonly divided into five groups, depending on the specific amounts of

alloying elements, which control the microstructure of the alloy. They are austenitic (face centered

cubic crystalline structure), ferritic (body centered cubic crystalline structure), martensitic (body

centered tetragonal crystalline structure), duplex (contains approximately equal amounts of ferritic

and austenitic phases) and precipitation hardening (contains austenitic or martensitic phases in aged

condition). In face centered cubic crystalline structure, atoms are located at each of the corners and

the centers of all the cubic faces. But in a body centered crystalline structure, one atom is located

in the center of the unit cell in addition to the corner atoms. Each group of stainless steel has its

own advantage and is used as per the requirement of a particular application.

Martensitic steel is a type of stainless steel that is known for its strength, corrosion resistance,

and durability. These qualities make martensitic steel a good choice for a variety of applications

such as fabrication of turbine parts, mechanical valves etc. When the austenite is cooled at a critical

rate (typically faster than 86 degrees F per second), the crystal structure gets distorted and strained

to form a body-centered tetragonal (BCT) crystalline structure, forming a hard microstructure

phase called martensite. Martensitic stainless steels, such as types 403, 410, 410NiMo and 420,

are similar in composition to the ferrite group, but contain a balance of Carbon and Nickel vs.

Chromium and Molybdenum.

1.2.2 Magnetic Domains and Magnetization

Steel is composed of small crystalline particles which are called grains and each grain has a

periodic arrangement of atoms. Each atom has a magnetic moment and thus contributes to the

5

overall magnetization (M) of steel. M is defined as the magnetic moment per unit volume of steel

and is given as,

𝑀 =

(cid:205) 𝑚
𝑉

(1.2)

where 𝑚 refers to the individual magnetic moment of an atom and 𝑉 refers to the total volume

of steel. The value of M is constant and does not depend on the material’s size.

The magnetic moments inside each grain are aligned in the same direction and together represent

a magnetic domain. Hence the magnetic domain is a region within the steel (or any magnetic

material) in which the magnetization is in a uniform direction. The direction of magnetic moments

may differ from one magnetic domain to the other and are usually random in nature. This results

in a net zero magnetization without the application of an external magnetic field. When an

external magnetic field is applied, the direction of domain magnetic moment aligns in the magnetic

field direction, resulting in a non-zero net magnetization of steel. Figure 1.3 shows the domains

(including direction of magnetic moments) with and without application of an external magnetic

field. Red arrow indicates the direction of external magnetic field.

Figure 1.3 Domains with magnetic moments in steel

6

1.2.3 Effect of stress on magnetic properties of steel

When a ferromagnetic material like martensitic stainless-steel (MSS) is exposed to a magnetic

field, its dimension tends to change. The effect responsible for change in dimension is known as

magnetostriction.

The fractional change in length, also referred as magnetically induced strain is given by 𝜆

expressed in (1.3),

𝜆 =

Δ𝑙
𝑙

(1.3)

Here Δ𝑙 is the change in length due to magnetostriction and 𝑙 is the original length of MSS

material. Saturation magnetostriction (denoted as 𝜆𝑠) is the value of 𝜆 measured at magnetic

saturation. 𝜆𝑠 is typically very small and is of the order 10−5 in magnetic materials [7]. The

magnetically induced strain depends on extent of magnetization in the material and hence on the

applied magnetic field intensity 𝐻 ( 𝐴/𝑚).

Even though the magnetostrictive strain is very small in magnetic materials, the application

of mechanical stress can change the domain structure. This can have a significant effect on the

magnetic material properties like permeability and remanence. The effect of mechanical stress on

the magnetization behavior of magnetic materials is referred to as magneto-mechanical effect.

In perspective of the research work, fatigue happens because of application of stress on the

material and stress in-turn alters the magnetic material properties. Hence it can be concluded that,

fatigue ultimately changes the magnetic properties of MSS materials and magnetic NDE techniques

will be most-suitable for this application. The following section details and summarizes the existing

NDE techniques for fatigue detection.

1.3 Existing NDE methods

Existing NDE methods for fatigue detection include optical [8, 9], acoustic [10, 11], magnetic

[12, 13] and thermal [10, 14] and have been applied in metals as well as composites [15–18].

Typically, fatigue affects the electrical impedance and further alters the magnetic properties of

materials due to changes in microstructure [19, 20]. Electrical and magnetic NDT methods are

7

sensitive to the corresponding characteristics and play a major role in detecting fatigue at an early

stage, i.e., before the macro crack initiates.

In this area, Magnetic Barkhausen Noise (MBN) has shown promise in fatigue detection

and evaluation in carbon steel [21], ferrite steel [22] and martensitic stainless steel [23]. The

Barkhausen effect consists of discontinuous changes in magnetic flux density, known as Barkhausen

jumps [24]. MBN is a promising electromagnetic nondestructive technique used to characterize

ferromagnetic materials and is sensitive to changes in the material microstructure [21]. The

MBN signal features is proved to have a linear relationship with the carbon content of steel [21].

MBN technique has also been used particularly in classification of martensitic steel based on

fatigue [23]. Principal component analysis (PCA) and probabilistic neural network (PNN) classifies

the martensitic stainless-steel samples based on the percentage of remaining fatigue life with 79%

classification accuracy [23].

Since the material under consideration is ferromagnetic, a magnetic NDE technique which takes

into account local changes in the hysteresis in relation to fatigue is relevant in this scenario. In

this regard, the non-linear eddy current (NLEC) technique (i.e., a magnetic NDE technique) was

applied on steel to characterize automotive bearing assemblies with challenging geometries and

has shown a classification accuracy of approximately 95.7% [25].

Some of the other NDE methods used for material characterization are Magneto-Acoustic

Emission (MAE), the 3MA (Micromagnetic Multiparameter Microstructure and Stress Analysis)

[26] and Ultrasonic techniques (UT) [27]. A considerable amount of research has been carried out

regarding material aging at Fraunhofer Institute – IZFP [27]. The MAE technique is sensitive to

the environmental noise and has a low signal to noise ratio. But, MAE signal only responds to

domains that are at an angle to the applied stress [21].

This research work investigates the feasibility of magnetic NDE techniques, MBN and NLEC

for garnering information related to the fatigue condition in martensitic grade stainless-steel compo-

nents. The NLEC technique excites the non-linear modes in the sample and measures the amplitude

of harmonics. The ratio of harmonic amplitudes provides interesting information related to fatigue

8

in the steel sample under test. The MBN technique measures the discontinuous changes in mag-

netic flux density. The features obtained from these measurements provide interesting information

related to fatigue in the steel sample under test. The following chapter describes more information

on the physical principles for both MBN and NLEC techniques.

Some parts of this doctoral thesis are adapted from [28] ("Fatigue Detection and Estimation

in Martensitic Stainless-Steel Using Magnetic Nondestructive Evaluation Technique" by B. B.

Shenoy, Z. Li, L. Udpa, S. Udpa,Y. Deng, and T. Seuaciuc-Osorio, Quantitative Nondestructive

Evaluation, vol. 85529, p. V001T14A001, American Society of Mechanical Engineers 2021,

https://doi.org/10.1115/QNDE2021-74657. Copyright © 2021 by ASME) and [29] ("Magnetic

Barkhausen Noise Technique for Fatigue Detection and Classification in Martensitic Stainless-

Steel" by B. Basti Shenoy, Z. Li, L. Udpa, S. Udpa, Y. Deng, and T. Seuaciuc-Osorio, Journal of

Nondestructive Evaluation, Diagnostics and Prognostics of Engineering Systems, vol. 5, no. 4, p.

041010, 2022, https://doi.org/10.1115/1.4055992. Copyright © 2022 by ASME).

9

CHAPTER 2

PHYSICAL PRINCIPLES OF MBN AND NLEC

This chapter describes the physical principles of MBN and NLEC techniques in detail and also

provides information regarding the experimental set-up used for both techniques.

2.1 Magnetic Barkhausen Noise Technique

Magnetic Barkhausen Noise (MBN) is a NDE technique, which is sensitive to the changes in

material microstructure and stress state of the material. This technique has been widely used to

investigate ferromagnetic materials [30–33], due to the link between MBN signal and the material’s

mechanical properties.

The Barkhausen effect consists of discontinuous changes in magnetic flux density, known as

Barkhausen jumps [24], as shown in Figure 2.1. These are caused by sudden irreversible motion

of magnetic domain walls, when they break away from pinning sites due to changes in the applied

external magnetic field [34]. This results in a noise, which is known as the Magnetic Barkhausen

Noise (MBN) and it is correlated to the material microstructure as discussed in [21,35]. Figure 2.2.

shows a typical MBN time domain signal obtained from the experimental set-up discussed in the

next section.

In a crystalline material such as martensitic stainless-steel, whenever stress is applied, a disloca-

tion travels through the lattice [28]. The movement of dislocations results in plastic deformation of

the material. Thus, the material is fatigued. This elongates the grain size, which is a microstructure

feature of the material. Changes in grain size will result in changes in the material properties,

such as conductivity and permeability. Hence, features obtained from the MBN signal contains

information which allows the separation of samples having different levels of fatigue.

2.1.1 MBN system details

The block diagram of the experimental set-up is shown in Figure 2.3. The function generator is

used to provide the sinusoidal excitation voltage, which is then amplified using the power amplifier.

The output of power amplifier is connected to the MBN sensor. The MBN sensor consists

10

Figure 2.1 Magnetic flux density changes due to Barkhausen effect

Figure 2.2 Time domain MBN signal

of a U-shaped magnetic core, an excitation coil (which generates the AC magnetic field) and a

volumetric pick-up coil (which picks up the generated MBN signal from the stainless-steel sample).

11

Figure 2.3 Block diagram of MBN experimental set-up

Table 2.1 MBN system details

Function generator output voltage

Sinusoidal signal

4 V (peak to peak)

Frequency of function generator output (Hz)

Power amplifier gain (V/V)

Excitation coil turns

Pick-up coil turns

5

10

80

400

Sampling rate (samples per second)

200,000

The pick-up coil is housed in a holder attached to the magnetic core. DAQ Card and PC are used

to acquire and then process the generated MBN signal from the stainless-steel sample. The system

details are outlined in Table 2.1.

12

2.2 NLEC Technique

This section provides a basic introduction to the physical principles of linear and non-linear

eddy current techniques.

2.2.1 Conventional ECT

Eddy current testing (ECT) is widely used in NDT of metal components, due to its non-contact

operation, rapid inspection capability and sensitivity to defect detection [36].

Conventional (linear) ECT uses electromagnetic induction to detect and characterize surface

and sub-surface defects in conductive materials [37]. Here, the eddy current probe is excited using

time harmonic excitation. The time harmonic magnetic field induces eddy currents in the sample.

In the presence of a defect (i.e., a surface crack), the induced currents are redistributed, as shown in

Figure 2.4., resulting in a change in the eddy currents which alters the induced magnetic field and

hence the impedance of the probe coil. Hence, by monitoring the impedance changes in the coil,

we can detect defects in the material of interest. ECT works only on non-ferromagnetic conducting

materials and the operation is largely linear. Ferromagnetic materials can be inspected using the

non-linear operation of the ECT technique.

Figure 2.4 Eddy Current in material with and without surface defect

2.2.2 Non-linear eddy current technique

In non-linear eddy current (NLEC) technique, a strong periodic excitation magnetic field is

applied forcing the material to operate in the non-linear region of its magnetization characteristic,

as shown in Figure 2.5. This results in response signals that contain higher order harmonic

frequencies.

13

Figure 2.5 B-H curve with linear and non-linear eddy current response plots

14

Typical excitation and response signals for linear eddy current and NLEC techniques are also

shown in Figure 2.5. It can be observed that the linear eddy current output response (the waveform

in orange) is sinusoidal and of the same frequency as that of the excitation current, but with a

different amplitude and phase.

On the other hand, NLEC output response has higher order harmonic frequencies when com-

pared to the excitation signal. The non-linear eddy current technique was successfully applied to

evaluate the case hardening profile of automotive bearing assemblies, in nondestructive evaluation

laboratory (NDEL) at Michigan State University [25]. Bruchwald. O et al. [38] designed a cus-

tomized high temperature resistant eddy current sensor at Institut für Werkstoffkunde (IW), Leibniz

University Hannover and studied the higher order harmonics to quantify the material transformation

and microstructure evolution in steel. Also, L. V. Fricke et al. performed a higher order harmonic

analysis on the eddy current signal to differentiate between the microstructural constituents formed

in steel [39].

In a crystalline material (like the Martensitic stainless-steel (MSS)), when stress is applied, a

dislocation travels through the lattice. The movement of dislocations result in plastic deformation

of the material. This elongates the grain and increases its size, which is a microstructure feature

of the material. Changes in grain size will result in changes in the material properties, such as

conductivity and permeability. Hence features of the NLEC response signals contain information

that allows us to separate the MSS samples at different levels of fatigue.

2.2.3 NLEC system details

Figure 2.6. shows the block diagram of NLEC experimental set-up along with schematic of

connections of the NLEC sensor [40]. The function generator is used to generate a low frequency

sinusoidal signal which is further amplified using a power amplifier and given to the NLEC sensor.

The NLEC sensor consists of a measurement probe (MP) and a reference probe (RP), as shown

in Figure 2.6. Each probe consists of one excitation coil and one pick-up coil. The two excitation

coils (E1 and E2) are connected in series and the two pick-up coils (P1 and P2) are connected

in a differential configuration.

In each of the probes (MP or RP), the excitation coil is wound

15

Figure 2.6 Block diagram of NLEC experimental set-up

Figure 2.7 NLEC sensor mounted on the EPRI sample

around the pick-up coil with the help of a 3-D printed bobbin and a custom designed metal pot

core. The pick-up coils collect the NLEC signal from MSS sample under test and gives it to the

data acquisition (DAQ) set-up, i.e., using the NI DAC board and then to the computer for further

data processing. The measurement probe is placed on the gage section of the MSS sample and

16

the reference probe is placed as shown in Figure 2.7. The experimental parameters are outlined in

Table 2.2. American wire gauge is abbreviated as AWG.

Table 2.2 NLEC experimental parameters

Function generator output

Sinusoidal signal of 14 V (peak-peak) at 17 Hz

Power amplifier gain

10

Excitation coil turns & AWG

600 & 32 AWG

Pick-up coil turns & AWG

1200 & 26 AWG

Sampling rate (samples per second)

10,000

17

CHAPTER 3

RESEARCH PROBLEM

3.1 Research problem representation

Overview of the research problem is summarized in Figure 3.1. In the funded research project,

martensitic stainless-steel samples (un-cracked) with different loading cycles were first provided by

Electric Power Research Institute (EPRI). NDE measurements were then performed. The number

Figure 3.1 Overview of the research problem

of loading cycles were known at the time of NDE measurements. Following this, the samples were

loaded further till they developed a crack. The data on additional loading cycles to failure was then

provided by EPRI. Details regarding the stainless-steel samples is given in this chapter. Goal of

the research work is to classify the stainless-steel samples (having different levels of fatigue) into

broad fatigue categories, i.e., low fatigue, mid fatigue, and high fatigue. The contribution of the

research work is mainly in developing techniques to classify the samples based on levels of fatigue.

The following section describes the database of martensitic stainless-steel samples.

3.2 Sample database

The geometry of a typical martensitic stainless-steel (MSS) sample is shown in Figure 3.2. A

set of 16 samples were stressed by applying varying number of loading cycles (0, 150K, 300K,

450K, 600K, 750K, and 900K) and sent to MSU for data collection. These samples were then sent

back to EPRI for destructively estimating the remaining useful life, by subjecting them to additional

loading cycles till failure or cracking.

18

Table 3.1 presents two columns for each sample showing number of loading cycles at NDE test

and additional cycles to failure which is a measure of remaining useful life (RUL).

RUL of a sample is calculated as,

𝑅𝑈 𝐿 = 𝐿𝑜𝑎𝑑𝑖𝑛𝑔 𝑐𝑦𝑐𝑙𝑒𝑠 𝑎𝑡

𝑓 𝑎𝑖𝑙𝑢𝑟𝑒 − 𝐿𝑜𝑎𝑑𝑖𝑛𝑔 𝑐𝑦𝑐𝑙𝑒𝑠 𝑎𝑡 𝑁 𝐷𝐸 𝑡𝑒𝑠𝑡

(3.1)

Figure 3.2 Snapshot of a MSS sample provided by EPRI

Table 3.1 EPRI MSS sample database

MSS sample ID Loading cycles
(at NDE Test)
0
0
450,000
0
900,000
150,000
900,000
300,000
450,000
450,000
150,000
150,000
450,000
750,000
600,000
300,000

41C
44C
30C
43C
42C
7C
37C
9C
19C
46C
8C
35C
32C
27C
21C
10C

Additional
cycles to failure
2,889,703
1,318,034
1,103,303
690,512
603,724
551,901
514,878
493,803
464,392
447,380
352,928
309,868
306,142
297,627
200,007
127,204

19

CHAPTER 4

RESULTS AND DISCUSSION

This chapter provides a detailed discussion on the results of both MBN and NLEC techniques.

4.1 Results and discussion on MBN

This section describes the data collection and feature extraction procedure for MBN technique

along with a detailed discussion on results.

4.1.1 Data collection and feature extraction

The MBN time-domain data is collected at 19 (18 scanning and 1 reference) points on the EPRI

stainless-steel sample, the schematic of which along with the dimensions are shown in Figure 4.1.

The MBN sensor is placed on the sample in such a way that, the center of the pick-up coil (which

is volumetric) is placed on a particular scanning point (say 1, which is shown in Figure 4.1). The

MBN data (voltage signal) is recorded using LabView and then a similar procedure is carried out

for the remaining 17 scanning points. The 18 scanning points are chosen on the gage section of

the sample (fatigued region) and the reference point is chosen at the center of non-fatigued region.

The pick-up coil captures the localized effect of fatigue at a particular scanning point.

Figure 4.1 Schematic of EPRI stainless-steel sample showing scanning point locations

The MBN data obtained at each scanning point (1 to 18) provides useful information related

to the change in permeability due to stress (loading) applied on the sample, which is linked to

20

the microstructure and fatigue condition of the sample. Many scanning points are chosen and the

extracted features are averaged to obtain a better representation for a particular sample, in-terms of

fatigue. The goal of the research work (as previously mentioned) is to classify the 16 samples (in

Table 3.1) into broad fatigue categories, i.e., low fatigue, mid fatigue, and high fatigue based on

MBN signal features and RUL.

The upper profile of the MBN signal shown in Figure 4.2.

is fitted by using a mixture of

two Gaussian distributions. This provides a way to obtain the time domain MBN signal features

shown in Figure 4.2. The time domain features such as MBN signal peak (MP), Full width at half

maximum (FWHM) and Difference between peaks of Gaussian fitted curve 1 and 2 (DBP) are

related to the microstructure of the material [23].

Figure 4.2 Gaussian fitting of MBN signal showing time domain features

The frequency spectrum of the MBN signal provides two more features, i.e., Maximum fre-

21

Figure 4.3 Frequency spectrum of MBN signal showing frequency domain features

quency spectrum amplitude (MFA) and Frequency for maximum frequency spectrum amplitude

(FMFA) as shown in Figure 4.3. Another MBN signal feature, i.e., MBN signal energy is related

to grain boundary misorientation angle that influences the arrangement of magnetic domains along

the boundary [34]. Each feature shows a variation across the entire EPRI sample database.

The normalized feature (NR) for each sample is given as,
(cid:205)18
𝐴𝑖 𝑗 𝑘
𝑖=1
18 ∗ 𝑅 𝑗 𝑘

𝑁 𝑅 𝑗 𝑘 =

where 𝑖 refers to a particular scan position, ranges from 1 to 18.

𝑗 refers to the sample number, ranges from 1 to 16.

𝑘 refers to the corresponding feature, ranges from 1 to 6.

𝐴𝑖 𝑗 𝑘 refers to the feature value at a particular scanning point.

𝑅 𝑗 𝑘 is the feature value at reference point for a particular sample.

22

(4.1)

NR will be used as a representation for each sample while applying the KCA and GA on the MBN

features.

4.1.2 Results

The flowchart of the approach used to classify the martensitic stainless-steel (MSS) samples

(provided by EPRI) into broad fatigue categories is given in Figure 4.4.

Features MP, FWHM,

Figure 4.4 Flowchart of the algorithm used to classify MSS samples based on RUL

DBP, MFA, FMFA and ME are extracted from the MBN time domain data. They are utilized

to obtain the fifteen combinations (e.g., MP vs FWHM, MFA vs FMFA etc.) in the 2D feature

space and then fed as inputs to K-medoids clustering algorithm (KCA) and Genetic algorithm (GA)

blocks. The idea here is to investigate the signal features which are most-sensitive to the material’s

fatigue state. KCA helps to cluster the samples and GA helps to obtain fatigue thresholds with

23

optimum system performance. The combined output of KCA and GA is the sample classification

based on remaining useful life (RUL).

The system performance (SP) proposed to evaluate the sample classification accuracy is quantita-

tively expressed as,

𝑆𝑦𝑠𝑡𝑒𝑚 𝑃𝑒𝑟 𝑓 𝑜𝑟𝑚𝑎𝑛𝑐𝑒 =

𝐶
𝑇

(4.2)

where, C is the number of correctly classified samples and T is the total number of samples.

The feature combination which leads to optimum system performance (i.e., highest number of

correctly classified samples) is obtained as FWHM vs DBP and the clustering results are shown in

Figure 4.5.

Figure 4.5 Clustering of MSS samples into fatigue categories

The Barkhausen effect is caused by sudden irreversible motion of magnetic domain walls, when

they break away from pinning sites due to changes in the applied external magnetic field [34].

FWHM is a common qualifier that changes significantly with distribution of the phase boundary

domain wall pinning strength [41]. Also, the DBP extracted from among the gaussian fitting curves

24

varies linearly with the carbon content on various types of mild steels and is linked with the material

microstructure [21]. For comparison, few other feature combinations and their system performance

are given in table 4.2. The fatigue thresholds for these combinations are same as obtained in

Table 4.1.

The green, blue, and red dots (Figure 4.5.) are the representations for all MSS samples which

are categorized as low fatigue, mid fatigue, and high fatigue respectively. After applying KCA

and GA on the MBN features, the obtained thresholds for the broad fatigue categories are given in

Table 4.1.

Table 4.1 Fatigue thresholds obtained on applying KCA and GA on MBN features

Fatigue category Fatigue threshold (based on RUL)

Low fatigue

≥ 690 K

Mid fatigue

> 310 K to < 690 K

High fatigue

≤ 310 K

Hence, samples having a RUL lesser than or equal to 310 K are classified as high fatigue,

between 310 K to 690 K as mid fatigue and above or equal to 690 K as low fatigue.

The classification results based on ground-truth (i.e., after applying the fatigue thresholds in

table 4.1 to categorize the samples in table 3.1) is shown in Figure 4.6. Comparing Figure 4.5., and

Figure 4.6., it can be observed that there is one mid fatigue sample (42C) which is misclassified

as high fatigue and one low fatigue sample (30C) which is also misclassified as high fatigue. The

KCA and GA classified fourteen samples (all high fatigue samples, six mid fatigue samples and

three low fatigue samples) in different stages of fatigue (i.e., having different RUL) correctly. The

system performance is calculated as 87.5% using (4.2).

Discussion on low fatigue threshold selection:

The KCA and GA were applied to MBN features to determine the fatigue thresholds. As

discussed earlier, KCA helps to cluster the samples and GA helps to obtain fatigue thresholds with

25

optimum system performance (i.e., obtain maximum number of correct classifications). Table 4.3

shows the sample database with ground-truth and fatigue classification results.

Figure 4.6 Classification results based on ground-truth

Table 4.2 Comparison of other MBN feature combinations

Feature Combination System Performance

FWHM vs DBP

FWHM vs MFA

FWHM vs ME

DBP vs ME

87.50

81.25

81.25

75.00

RUL greater than a fatigue threshold of 690,511 (additional loading cycles to failure) for

low fatigue category would result in maximum number of correct classifications as observed from

26

Table 4.3 Sample database with fatigue classification

Sample ID

RUL

Ground-truth Classification Results

41C

2,889,703

Low fatigue

Low fatigue

44C

1,318,034

Low fatigue

Low fatigue

30C

1,103,303

Low fatigue

High fatigue

43C

42C

690,512

Low fatigue

Low fatigue

603,724

Mid fatigue

High fatigue

7C

551,901

Mid fatigue

Mid fatigue

37C

514,878

Mid fatigue

Mid fatigue

9C

493,803

Mid fatigue

Mid fatigue

19C

46C

464,392

Mid fatigue

Mid fatigue

447,380

Mid fatigue

Mid fatigue

8C

352,928

Mid fatigue

Mid fatigue

35C

32C

27C

21C

10C

309,868

High fatigue

High fatigue

306,142

High fatigue

High fatigue

297,627

High fatigue

High fatigue

200,007

High fatigue

High fatigue

127,204

High fatigue

High fatigue

27

table 4.3. The nearest thousand (floor) which satisfies the above criterion, is used while determining

the fatigue threshold value (after obtaining fatigue thresholds using KCA and GA).

Alternatively, since 42C is misclassified, RUL greater than 551,902 for low fatigue threshold

would also provide a system performance of 87.5%. This would result in a low fatigue threshold

of RUL greater than 552,000. The maximum of 552,000 and 690,000 is chosen as the final low

fatigue threshold.

In addition to the above discussion, if we observe table 4.3, there is a lack of data (additional

cycles to failure) in the range of 690,000 to 1 million RUL. If there were additional samples in the

range, it would be possible to obtain more accurate fatigue thresholds.

In this research work, feasibility of the approach based on available data is presented. Hence,

the same approach when applied to a larger data set (i.e., a greater number of samples with varying

additional cycles to failure) can provide more accurate fatigue thresholds and classifications.

4.2 Results and discussion on NLEC

This section describes the data collection and feature extraction procedure for NLEC technique

along with a detailed discussion on results.

4.2.1 Data collection and feature extraction

NLEC signal is collected at three different positions, on the gage section of the sample (S1-S3

shown in Figure 4.7.).

R denotes the position for reference probe at all times during the data

collection stage. The measurement probe is moved from S1 to S3 to collect the NLEC signals. The

measured NLEC signal (from the NLEC sensor) is given to LabView and MATLAB for further

processing. Typical NLEC response signals, obtained from the NLEC sensor, in time domain is

shown in Figure 4.8. The waveform in blue is the input signal (function generator output), which is

then amplified and given to the excitation coils. The typical NLEC signal (orange), i.e., obtained

from differentially connected pick-up coils is shown in Figure 4.8.

The NLEC waveform is an odd signal having a half-wave symmetry. Hence it contains odd

harmonic components and zero even harmonic components. The frequency spectrum of the

obtained NLEC signal is shown in Figure 4.9. The odd harmonic peaks, i.e., the first, third, fifth

28

Figure 4.7 Schematic of EPRI sample showing scanning points

Figure 4.8 Time domain NLEC signal obtained from NLEC sensor

29

Figure 4.9 Frequency spectrum of the time domain NLEC signal

and seventh odd harmonic peaks can be observed at 17 Hz (fundamental frequency), 51 Hz, 85 Hz

and 119 Hz respectively. It can also be observed that, odd harmonic peaks show significantly higher

amplitudes and variations, when compared to even harmonic peaks. Features computed from the

harmonics are listed in Table 4.4.

The normalized feature value for each sample is obtained by averaging the feature values

extracted from each of the three probe positions and is represented as,

𝑁 𝑅𝑖 𝑗 𝑘 =

(cid:205)3

𝐷𝑖 𝑗 𝑘
𝑖=1
3

(4.3)

where 𝑖 refers to a particular scan position, ranges from 1 to 3.

𝑗 refers to the sample number, ranges from 1 to 16.

𝑘 refers to the corresponding feature, ranges from 1 to 6.

𝐷𝑖 𝑗 𝑘 refers to the feature value at a particular scanning point.

30

Table 4.4 NLEC signal features

Feature Set 1

Feature Set 2

(Odd harmonic peaks)

(Odd harmonic peak ratios)

First harmonic peak

Third harmonic peak / Fifth harmonic peak

Third harmonic peak

Fifth harmonic peak

Fifth harmonic peak / Seventh harmonic peak

Seventh harmonic peak

4.2.2 Results

The flowchart of the algorithm used to classify MSS samples, based on the remaining useful life

of the sample, is given in Figure 4.10. NLEC data in time domain is analyzed in frequency domain

to extract features, i.e., the odd harmonic peaks (1, 3, 5 & 7, i.e., the first, third, fifth and seventh odd

harmonic peaks). Odd harmonic peaks are then used to obtain the possible combinations (1st/3rd,

1st/5th, 1st/7st, 3rd/5th, 3rd/7th and 5th/7th) of odd harmonic peak ratios. The odd harmonic peak

ratios obtained are then analyzed in the two dimensional feature space using K-medoids clustering

algorithm (KCA) [42] and genetic algorithm (GA) [43] to cluster the samples into broad fatigue

categories. The six odd harmonic peak ratios are combined, two at a time (i.e., 2D feature space),

to obtain fifteen combinations and clustering is done on each of them. KCA and GA then together

help to classify the samples into fatigue categories with optimum system performance.

From the physical principles of NLEC operation, the values of the odd harmonics in the received

signal are related to local changes in the hysteresis and incremental permeability of the test sample,

which in turn relate to fatigue state of the material and associated microstructural changes. The

ratios of odd harmonic peaks consider the rate of change of the harmonics, which are sensitive to

small changes in the hysteresis curves at different fatigue levels. A six-dimensional clustering in

6D feature space was tried, but the results were not as encouraging as the one obtained using 2D

feature space.

The feature combination which leads to optimum system performance (i.e., highest number of

31

Figure 4.10 Flowchart of the algorithm used to classify MSS samples based on RUL

correctly classified samples) are the odd harmonic peak ratios 35 & 57, i.e., 3rd/5rd and 5th/7th odd

harmonic peak ratios.

The system performance to evaluate the sample classification accuracy is quantitatively expressed

as,

𝑆𝑦𝑠𝑡𝑒𝑚 𝑃𝑒𝑟 𝑓 𝑜𝑟𝑚𝑎𝑛𝑐𝑒 =

𝐶
𝑇

(4.4)

where C is the number of correctly classified samples and T is the total number of samples.

After applying KCA and GA on the frequency domain NLEC features (35 and 57), the thresholds

in the feature space for the broad fatigue categories obtained are given in Table 4.5. Hence, samples

32

Table 4.5 Fatigue thresholds obtained on applying KCA and GA on NLEC features

Fatigue category Fatigue threshold (based on RUL)

Low fatigue

≥ 1.2 M

Mid fatigue

> 310 K to < 1.2 M

High fatigue

≤ 310 K

Figure 4.11 Clustering of MSS samples into fatigue categories

having a RUL lesser than or equal to 310 K are classified as high fatigue, between 310 K to 1.2 M

as mid fatigue and above or equal to 1.2 M as low fatigue.

The clustering and classification results, after applying KCA and GA on NLEC signal features

33

Figure 4.12 Classification results based on ground-truth NLEC

are shown in Figure 4.11. The green, blue, and red dots are the representations for all samples

which are categorized as low fatigue, mid fatigue, and high fatigue respectively. Figure 4.12. shows

the classification results based on the ground-truth data.

Comparing Figure 4.11., Figure 4.12., and RUL data in Table 3.1, it is observed that, there is

one high fatigue sample (32C) which is misclassified as low fatigue. Table 4.6 shows the sample

database with ground-truth and fatigue classification results.

The system performance for EPRI MSS sample database shown in Table 4.6 is calculated as

93.75%. The approach should be tested more extensively with additional samples data.

34

Table 4.6 Sample database with fatigue classification

Sample ID

RUL

Ground-truth Classification Results

41C

2,889,703

Low fatigue

Low fatigue

44C

1,318,034

Low fatigue

Low fatigue

30C

1,103,303 Mid fatigue

Mid fatigue

43C

42C

690,512

Mid fatigue

Mid fatigue

603,724

Mid fatigue

Mid fatigue

7C

551,901

Mid fatigue

Mid fatigue

37C

514,878

Mid fatigue

Mid fatigue

9C

493,803

Mid fatigue

Mid fatigue

19C

46C

464,392

Mid fatigue

Mid fatigue

447,380

Mid fatigue

Mid fatigue

8C

352,928

Mid fatigue

Mid fatigue

35C

32C

27C

21C

10C

309,868

High fatigue

High fatigue

306,142

High fatigue

Low fatigue

297,627

High fatigue

High fatigue

200,007

High fatigue

High fatigue

127,204

High fatigue

High fatigue

35

CHAPTER 5

CONCLUSIONS AND FUTURE WORK

Both magnetic NDE techniques show promise in classifying the martensitic stainless-steel samples

into broad fatigue categories. The conclusions for both techniques are presented in this section.

Non-linear eddy current technique is developed and investigated to check the feasibility of

detecting fatigue damage in martensitic grade stainless-steel materials. Odd harmonic peaks and

their ratios are identified as non-linear eddy current signal features. A methodology is proposed

to classify the stainless-steel samples based on the remaining useful life. K-medoids clustering

algorithm and genetic algorithm are applied on the non-linear eddy current signal features, which are

computed from the harmonics obtained from the frequency domain representation of the acquired

non-linear eddy current data. Results, based on the available data set, indicate that the martensitic

grade stainless-steel samples in different stages of fatigue can be classified into broad categories of

low, mid and high levels of fatigue based on the remaining useful life with a system performance

of 93.75%.

Magnetic Barkhausen Noise technique is developed and investigated to estimate the fatigue

damage in martensitic grade stainless-steel samples. Time and frequency domain features of

the magnetic Barkhausen noise signal, along with K-medoids clustering algorithm and genetic

algorithm are used to classify the samples into broad fatigue categories. The results, based on

the available data set, indicate that the martensitic stainless-steel samples having different levels

of fatigue damage can be classified into broad fatigue categories, i.e., low fatigue, mid fatigue and

high fatigue based on the remaining useful life of the sample. The system performance is obtained

as 87.5%.

The lower fatigue threshold obtained for MBN technique is different when compared to NLEC

technique. The reason for this is that, there is a lack of data (additional cycles to failure) in the

range of 690,000 to 1 million loading cycles.

If there were additional samples in the range, it

would be possible to obtain more accurate fatigue thresholds and an agreement between the fatigue

thresholds for MBN and NLEC techniques will be possible. In this research work, feasibility of

36

the approach based on the available data set is presented. Hence, the same approach when applied

to a larger data set (i.e., a greater number of samples with varying additional cycles to failure) can

provide more accurate fatigue thresholds and classifications.

As part of the future work, imaging of the micro-structure (for samples with different loading

cycles) can be performed to investigate the changes in grain size, which is a microstructure property

of the material. This will give an idea about the correlation of NLEC and MBN signal features

with changes in material micro-structure due to fatigue.

37

CHAPTER 6

INTRODUCTION TO EMAT

Engineering structures are prone to damages from stress and environmental factors. This is a

well-known problem in manufacturing industries. Over time, these damages progressively worsen,

eventually resulting in the fracturing of vital systems and imposing significant economic losses.

Regular inspections are crucial in ensuring the integrity of these structures. One effective way of

monitoring the structural health of mechanical structures is by monitoring the properties of the

materials used in their construction. Nondestructive evaluation (NDE) techniques are particularly

useful in this regard. These techniques rely on changes in material properties to detect potential

issues and can be used to identify defects without causing further damage. By utilizing NDE,

manufacturing industries can identify problems early on and take corrective action to prevent

further damage or fracturing. This can help prevent significant economic losses and ensure the

longevity of structures, by retiring only the severely damaged parts. NDE is therefore an invaluable

tool for reporting the structural health of mechanical structures and is a critical aspect of modern

manufacturing practices.

To detect defect locations in engineering structures, ultrasonic and eddy current NDE inspection

techniques are commonly used. Eddy current technique is a simple and effective NDE technique

that can be easily applied on structures, but it only works on conductive materials [44]. Another

drawback with this technique is that, it can primarily identify only surface and sub-surface defects.

When detecting defects inside the material, ultrasonic techniques (typically piezoelectric transducer-

based) are commonly used [45]. However, this method is contact-based and requires a couplant [46]

to facilitate the transmission of ultrasonic energy from transducer into the sample under test.

Impurities or curvature on the material surface can cause problems and require additional effort

to set up this NDE technique.

In order to address these issues, the Electromagnetic Acoustic

Transducer (EMAT) technique has been proposed in this research work. EMAT’s have found

practical applications and are very effective in evaluation of damage using NDE [47]. With its non-

contact, non-destructive testing capabilities, EMAT technology has the potential to revolutionize

38

quality control in industries [48] that rely on welded structures (such as construction, petroleum,

aerospace, and automotive industries).

6.1 Literature review

EMAT is a non-contact ultrasonic NDE technique that can generate elastic waves without a

couplant [49]. This makes it a convenient and efficient method for detecting defects. This technique

does not require surface preparation [50], which significantly reduces the inspection time. These

unique features make EMAT’s suitable for a variety of applications, including:

1. Material Characterization: EMAT’s can be used to determine the elastic and magnetic

properties of materials, which is useful for research and development in fields such as

materials science, metallurgy, and magnetic materials.

2. Process Monitoring: EMAT’s are used for NDT in industries such as automotive, and power

generation to inspect defects, cracks, and corrosion in materials like metals, composites, and

ceramics. Also, EMAT’s are used to monitor the quality of industrial processes, such as

welding, casting, and rolling, by detecting defects or changes in the material properties.

In general terms, EMATs are devices composed of a coil designed to induce dynamic electro-

magnetic fields at the surface of a conductive material, accompanied by a magnet or a series of

magnets to provide a DC biasing magnetic field, as depicted in Figure 6.1. This contrasts with a

typical piezoelectric device, as illustrated in the figure, which necessitates a couplant for coupling

with the sample surface.

The interaction between induced eddy currents and the static magnetic field leads to the gener-

ation of elastic waves within the conductive sample. The ability to generate distinct wave modes

is dependent upon the coil’s geometry and the arrangement of the magnets. The magnitude of the

eddy current depends on several factors, such as magnitude of the coil current, distance between the

coil and the sample (known as lift-off), and frequency of the coil current. The interaction between

the static magnetic field and eddy current generates a force on the sample surface, known as the

Lorentz force. The Lorentz force represents the coupling between electromagnetic and acoustic

39

domains, and is illustrated in Figure 6.2. Here 𝐹 refers to the Lorentz force, 𝐵𝑆 is the static magnetic

flux density and 𝐼 is the coil current. The generated elastic waves then penetrate into the sample

and carries information about the defects present inside.

Figure 6.1 Schematic representation of an EMAT

Figure 6.2 Lorentz force representation on a metal plate

While conventional EMAT techniques are used for generating elastic waves in conductive

and ferromagnetic materials [51], non-conductive structures pose a challenge. This is because the

dynamic magnetic field generated by the EMAT coil cannot induce eddy currents in non-conductive

structures. This thesis explores and proposes methods to inspect non-conductive samples using

EMAT’s, which is the major and interesting contribution of this research work on EMAT’s.

40

6.2 Transduction mechanisms in EMAT

Transduction mechanism refers to the process by which a device or system converts one form

of energy or signal into another form that can be used for a specific purpose. In simpler terms, it is

how a device turns one type of input into another type of output. Understanding the transduction

mechanism is crucial in designing and optimizing the performance of many devices and systems,

including sensors, actuators, and communication systems.

There are two transduction mechanisms in a EMAT [52]. They are:

1. Lorentz force transduction mechanism, which works on conductive and ferromagnetic mate-

rials.

2. Magnetostriction transduction mechanism, which works only on ferromagnetic materials.

The Lorentz force transduction mechanism used in EMAT’s convert electromagnetic waves

into elastic waves. When an alternating current is passed through the EMAT coil, eddy currents

are induced in the sample under test. The interaction between the static magnetic field and eddy

current generates a force on the sample surface, known as the Lorentz force.

The Lorentz force represents the coupling between electromagnetic and acoustic domains, and

is given by the equation:

𝐹 = 𝐽 × 𝐵

(6.1)

where F is the force vector, J is the current density vector, and B is the magnetic flux density

vector.

The frequency of elastic waves is determined by the frequency of the alternating current

provided to the EMAT coil. The amplitude of elastic waves depends on the strength of Lorentz

force and the properties of the sample (such as conductivity, density etc.) being tested. To detect the

generated elastic wave, an EMAT receiver should be used. As the elastic wave propagates through a

conducting sample, the atoms in the lattice move normal to the direction of wave propagation [53].

The interaction between the particle displacement and static magnetic field (generated by permanent

41

magnet) induces eddy currents at the sample surface (region of skin-depth), which are then detected

by the EMAT coil.

The Lorentz force transduction mechanism in EMAT’s is a powerful and versatile technique

for generating elastic waves in conductive and ferromagnetic materials, and it has a wide range of

applications in non-destructive testing and material characterization.

Magnetostriction is a transduction mechanism used in EMAT’s for generating elastic waves in

ferromagnetic samples. It is based on the principle that when a ferromagnetic sample is subjected

to a magnetic field, it undergoes a change in shape or size. This change in shape or size is

called magnetostriction. Magnetostriction takes place as a result of the tendency of ferromagnetic

domains to align in the direction of an external magnetic field, causing a net mechanical strain [54].

If the magnetic field has a time-varying component, this strain can be harnessed to generate elastic

waves [55].

In a EMAT using magnetostriction as the transduction mechanism, a dynamic magnetic field

is generated by the EMAT coil carrying alternating current, which interacts with the ferromagnetic

sample being tested. This dynamic magnetic field, along with the bias static magnetic field

(generated by the permanent magnet) causes the material to undergo a change in shape or size,

which generates elastic waves that propagate through the sample. The amplitude of elastic waves

generated by magnetostriction is dependent upon the magnetostriction coefficient, elastic constants

of the ferromagnetic sample, and the strength of the applied magnetic field. Frequency of the

generated elastic wave is determined by frequency of the alternating current provided to the EMAT

coil. Further, to detect the generated elastic waves, an EMAT receiver can be used.

6.3 Typical EMAT designs in Literature

The typical EMAT design available in literature are discussed in this section.

6.3.1 Bulk-wave EMAT

The bulk-wave EMAT shown in Figure 6.3 is capable of generating both longitudinal waves

(direction of wave propagation is parallel to the direction of particle displacement) and shear

waves (direction of wave propagation is perpendicular to direction of particle displacement). The

42

unidirectional coil elements are positioned under a static magnetic field generated by the permanent

magnet. The magnetic field is oriented normally to the surface beneath the coil elements and

tangentially at the center of the coil elements [53]. The dynamic magnetic fields generated by the

coil elements induces eddy currents on the sample surface. The resulting force (Lorentz force) is

parallel to the sample surface. Hence the direction of particle particle displacement is parallel to

the sample surface and is perpendicular to the direction of wave propagation as shown in Figure 6.3.

This configuration is termed as a shear wave EMAT [53].

Figure 6.3 Schematic diagram of a Bulk-wave EMAT

6.3.2 Meander line EMAT

The meander line EMAT shown in Figure 6.4 is capable of generating Rayleigh (surface waves

having a particle motion that is counterclockwise with respect to the direction of travel), angled

shear and longitudinal waves, i.e., traveling obliquely into the sample.

The drawback of this EMAT lies in the challenge of identifying the modes in received echoes.

The combination of a normal biasing field and the EMAT coil results in Lorentz force parallel to

the surface. These forces alternate in direction according to the meander-line coil. The generation

frequency is determined by the period of the meander-line, which can be adjusted through man-

43

ufacturing the coil using a printed circuit technique. Consequently, it is possible to modify the

generation frequency by altering the coil’s periodicity.

Figure 6.4 Schematic diagram of a Meander line EMAT

6.3.3 Periodic Permanent Magnet (PPM) EMAT

PPM-EMATs are devices designed to generate shear waves polarized parallel to the specimen’s

surface [56]. The EMAT configuration is commonly utilized for measurements involving Shear

Horizontal (SH) waves in a plate. These waves are particularly advantageous for nondestruc-

tive testing (NDT) purposes and are generally challenging to excite with traditional piezoelectric

transducers [53]. The classical configuration of this EMAT type is depicted in Figure 6.5.

PPM EMATs typically feature a racetrack-shaped coil positioned in front of the PPM array,

where the north and south poles alternate periodically, as shown in Figure 6.5. The Lorentz force

in the tangential direction vary due to the alternating polarity of the permanent magnets within the

array [57]. The optimal transfer efficiency is achieved when the device is driven by a current selected

in accordance with the spacing of magnets. The periodically alternating polarity establishes the

wavelength of the generated ultrasound. Therefore, to excite higher frequency SH waves, the width

44

Figure 6.5 Schematic diagram of a PPM EMAT

of the magnets needs to be reduced, thereby decreasing the wavelength. However, it is essential

to note that the efficiency significantly decreases with reduced magnet thickness, leading to a

limitation on the operational frequency of this EMAT.

45

CHAPTER 7

LORENTZ FORCE EMAT

The Lorentz force transduction mechanism used in EMAT’s, as discussed in previous chapter,

converts electromagnetic waves into elastic waves. This chapter describes more details on the

associated theory and modeling aspects of electromagnetic and acoustic phenomenon.

7.1 Theory

As discussed earlier, the current density in EMAT coil generates eddy currents in the conducting

material. This current is opposite in direction (compared to current in EMAT coil) according to

Faradays law given in (7.1). Eddy currents are loops of electric currents induced within a conductor

due to the application of a time-varying magnetic field.

∇ × 𝐸 = −

𝜕𝐵
𝜕𝑡

(7.1)

Here 𝐸 is the electric field (V/m) vector and 𝐵 is the magnetic flux density (T) vector. Eddy

currents are generated when there is a changing magnetic field (as can be deduced from (7.1)).

The eddy currents generated in the material are confined to a small region at the sample surface.

The depth of this region is quantified by a parameter called skin depth (𝛿) and represented as given

in (7.2).

𝛿 =

1
√︁𝜋 𝑓 𝜎𝜇

(7.2)

Here, 𝑓 is the frequency of coil current, 𝜎 is the conductivity of the conductor (S/m) and 𝜇 is

the permeability of the material.

𝜇 = 𝜇0𝜇𝑟

(7.3)

where 𝜇0 is the permeability of free space (≈ 4𝜋 × 10−7 H/m) and 𝜇𝑟 is the relative permeability

of the material.

When we have a charged particle (static or moving) in a magnetic field, it will experience a

force known as the Lorentz force. In an EMAT, the Lorentz force generated is given in (7.4).

46

𝐹 = 𝑞𝑉 × 𝐵

= 𝐽 × 𝐵

(7.4)

Here 𝑞 is the charge (𝐶), 𝑉 is the velocity vector (m/s), 𝐵 is the magnetic flux density vector

(𝑇) and J is the induced current density vector (A/m2).

In the following sections of this chapter, electromagnetic modeling, and elastic wave modeling

details will be discussed.

7.2 Numerical model in COMSOL

The Finite Element Analysis (FEA) tool employed for the design and simulation of Electromag-

netic Acoustic Transducers (EMATs) in this research is COMSOL. Renowned for its versatility,

COMSOL serves as a robust FEA tool capable of modeling a diverse array of physical systems,

encompassing domains such as electrical circuits, electromagnetics, fluid dynamics, heat transfer,

and structural mechanics. This tool empowers engineers, scientists, and researchers to construct

computer models mirroring real-world systems, enabling the simulation of their behavior under

varied conditions.

The application of COMSOL proves instrumental in predicting real-world system performance,

testing diverse designs and configurations, and optimizing overall system functionality. Its utility

extends to gaining insights into the behavior of intricate physical systems, thereby facilitating

informed engineering decisions.

The software tool is based on the concept of finite element analysis, which breaks down a

complex system into smaller, simpler elements. Each element is then analyzed separately, taking

into account the interactions between neighboring elements. This allows for a more detailed and

accurate analysis of the system’s behavior.

The subsequent subsections will delve deeper into the modeling intricacies of EMAT, elucidating

the associated governing equations.

47

7.2.1 Electromagnetic modeling

The module used to simulate the electromagnetic phenomenon in this research work is the

magnetic field (mf) interface, available within the AC/DC module. This is a specialized tool

that allows users to model and simulate electromagnetic fields and their interactions with electric

currents. It can be used to simulate a wide range of electromagnetic phenomena, such as magnetic

fields, electric fields, and electromagnetic waves.

The magnetic field (mf) physics interface within the AC/DC module specifically focuses on

the behavior of magnetic fields in various physical systems. It allows users to model the behavior

of magnetic fields generated by electric currents or magnetic materials, and to analyze how these

fields interact with other physical phenomena such as heat transfer or structural mechanics. The

dependent variable in mf interface is the magnetic vector potential. One of the main advantages of

the magnetic field interface in COMSOL is its ability to simulate both steady-state and time-varying

magnetic fields. This can be useful for predicting the behavior of electromagnetic systems under

various conditions, such as changes in electric currents or magnetic materials.

As discussed earlier, in an EMAT, we have the coil carrying an AC current which generates

a time-varying magnetic field inducing eddy currents in a conducting material. Also, there is a

permanent magnet which provides the static magnetic field. To obtain the Lorentz force (7.4), we

will need both the eddy current density and magnetic flux density.

The governing equations for eddy current simulation in COMSOL can be described by Maxwell’s

equations given below:

1) (7.5) is also the Faraday’s law of electromagnetic induction, which relates a changing

magnetic field to an induced electric field. Here 𝐸 is the electric field vector (V/m) and 𝐵 is the

magnetic flux density vector (𝑇).

∇ × 𝐸 = −

𝜕𝐵
𝜕𝑡

(7.5)

2) (7.6) is from Ampere’s law, which relates the magnetic field to conduction current density and

rate of change of electric displacement. Here 𝐻 is the applied magnetic field strength vector (A/m),

48

𝐽 is the conduction current density vector (A/m2) and the term 𝜕D
𝜕𝑡

is negligible for frequencies

lesser than 100 MHz (i.e., quasi-static approximation).

∇ × 𝐻 = 𝐽 +

𝜕𝐷
𝜕𝑡

(7.6)

3) (7.7) states that the magnetic flux through any closed surface is zero, indicating that magnetic

monopoles do not exist.

∇ · 𝐵 = 0

(7.7)

4) (7.8) relates the electric flux through a closed surface to the electric charge enclosed within

the surface. Here 𝜌 is the electric charge density vector in (C/m2)

∇ · 𝐷 = 𝜌

The constitutive relations are given in (7.9), (7.10) and (7.11)

𝐽 = 𝜎𝐸

where 𝜎 is the conductivity of the conductor (S/m)

𝐷 = 𝜖0𝜖𝑟 𝐸

(7.8)

(7.9)

(7.10)

where 𝜖0 is the permittivity of free space (8.854 × 10−12 F/m) and 𝜖𝑟 is the relative permittivity

of the conductor.

𝐵 = 𝜇0𝜇𝑟 𝐻

(7.11)

where 𝜇0 is the permeability of free space (≈ 4𝜋 × 10−7 H/m) and 𝜇𝑟 is the relative permeability

of the conductor.

The dependent variable in magnetic field physics interface in COMSOL (i.e., the magnetic

vector potential which is a vector field) is linked to magnetic flux density as given in (7.12). The

units of magnetic vector potential is 𝑇 𝑚 or 𝑊 𝑏/𝑚. Also, electric field can be written in terms of

magnetic vector potential as given in (7.13).

49

∇ × 𝐴 = 𝐵

𝐸 = −

𝜕 𝐴
𝜕𝑡

(7.12)

(7.13)

The permanent magnet is modeled using the Maxwell’s equations and constitutive relations

described earlier (7.5 - 7.13). The magnetization model describes the direction of static magnetic

field. The constitutive relation used in COMSOL to specify magnetization (𝑀) is given in (7.14).

𝐵 = 𝜇0 (𝐻 + 𝑀)

(7.14)

From the results obtained using Maxwell’s equations and constitutive relations (7.5 - 7.14),

the electromagnetic FEM in COMSOL helps to calculate the Lorentz force given in (7.4). This

concludes the electromagnetic modeling of EMAT in COMSOL. The next step is to describe the

elastic wave modeling.

7.2.2 Elastic wave and Multiphysics modeling

To model the interaction between electromagnetic field and elastic waves, equations for elastic

wave propagation needs to be considered. The solid mechanics interface within the structural

mechanics module is utilized for simulating the acoustic phenomenon. The meshing in non-

conducting sample is set to ensure a minimum of 10 elements per elastic wave wavelength (in

all COMSOL models discussed in the thesis), and utilized free triangular meshing. A Courant-

Friedrichs-Lewy (CFL) number of 0.1 will be used for simulating EMAT models in COMSOL.

The equations for elastic wave modeling in COMSOL can be written as follows:

1) Equation of Motion (Newton’s second law):

𝜌

𝜕2𝑈
𝜕𝑡2

= ∇ · 𝜎 + 𝐹

2) Stress-Strain Relationship (Constitutive Equation):

In (7.15) and (7.16),:

𝜎 = C : 𝜀

50

(7.15)

(7.16)

𝑈 is the displacement vector,

𝑡 is time,

𝜌 is density of the sample,

𝝈 is the stress tensor,

𝐹 is force vector acting on the structure,

∇ is the nabla operator (vector differential operator),

C is the fourth-order elasticity tensor, and

𝜺 is the strain tensor.

Combining the electromagnetic and elastic models, the acoustic displacement vector for a

continuous elastic isotropic medium can be computed using,

𝜇∇ × ∇ × 𝑈 − (𝜆 + 2𝜇)∇(∇ · 𝑈) + 𝜌

𝜕2𝑈
𝜕𝑡2

= 𝐹

(7.17)

𝑈 is the displacement vector,

𝑡 is time,

𝜇, 𝜆 are Lame’s constants,

𝜌 is density of the material,

𝐹 is force vector acting on the structure,

∇ is the nabla operator (vector differential operator),

7.3 Novel EMAT configurations for non-conductive samples

Conventional EMATs are primarily employed for generating elastic waves in conductive or fer-

romagnetic samples, as highlighted in [51]. However, the application of EMATs to non-conductive

structures presents a challenge due to the inability to induce eddy currents, rendering the Lorentz

force transduction mechanism ineffective. Additionally, if the material lacks ferromagnetic prop-

erties, the magnetostriction phenomenon is absent, resulting in the failure of the magnetostriction

transduction mechanism.

51

The initial concept of applying EMATs to insulating samples was introduced in [58], where

the proposed method involved directly bonding a current-carrying coil to the sample’s surface.

Subsequent research, as seen in [59] and [53], explored the application of a metal foil onto

non-conductive samples for elastic wave generation using EMAT. In both cases, the induced

configuration was utilized, with an adhesive layer beneath the metal foil serving as a couplant.

Notably, these studies did not explore the direct application of current to the metal foil/strip

and generation of longitudinal waves in through transmission mode for non-conductive sample

inspection using EMAT.

This thesis addresses the gap by introducing novel EMAT configurations, specifically designed

for non-conductive samples. Two approaches are proposed, (a) Direct excitation and (b) Non-contact

induced excitation in an embedded metal patch, both relying on the Lorentz force transduction

mechanism. The subsequent chapters will delve into a comprehensive investigation of these

approaches, presenting numerical results that offer valuable insights into the design considerations

for effective non-destructive evaluation of non-conductive materials.

52

CHAPTER 8

DIRECT EXCITATION

This chapter presents the outcomes derived from numerical simulations of EMATs applied to a non-

conducting sample. The initial section introduces the direct excitation model, offering results that

substantiate the propagation of an acoustic wave within the non-conducting sample. Subsequently,

an exploration of acoustic velocity is presented for comparison. Moving forward, the subsequent

sections delve into an examination of the impact of varying metal strip width and height on both

Lorentz force and displacement, impact of skin effect in Aluminum strip with accompanying

presentation of numerical findings and the chapter concludes with experimental validation.

8.1 EMAT model in COMSOL

The direct excitation model (two-dimensional) for an EMAT involves supplying current directly

to the metal strip applied on a non-conducting sample. Figure 8.1 illustrates the schematic of the

direct excitation model geometry in COMSOL, while Figure 8.2 provides a zoomed-in version to

elucidate the metal strip and measurement point on the sample’s back wall. The magnetic field

interface within the AC/DC module is employed to simulate the electromagnetic phenomenon, and

the structural mechanics module is utilized for simulating the acoustic phenomenon.

The model consists of a permanent magnet, a metal strip, a steel core, and the non-conducting

sample (plastic). The permanent magnet generates the static magnetic field, and the metal strip

produces a changing (dynamic) magnetic field. Perfectly matched layers, located at the left and

right corners of the sample, are implemented to prevent reflections and eliminate high-frequency

noise. The entire model is enclosed in air. The static magnetic field of the permanent magnet is

specified in the x-direction.

A surface current density (A/m) is applied to the Aluminum strip in the z-direction, as depicted

in Figure 8.3. Accordingly, following the right-hand rule, the Lorentz force generated should be in

the y-direction. The resulting displacement and wave propagation (longitudinal wave) occur in the

y-direction, along the thickness of the plastic (acrylic). Detailed model parameters are provided in

Table 8.1.

53

Figure 8.1 Direct Excitation model for an EMAT in COMSOL

Figure 8.2 Zoomed version of the EMAT model shown in Figure 8.1

54

Figure 8.3 Representation of input current provided to the Aluminum strip

Table 8.1 Model parameters for Direct excitation EMAT

Parameter

Plastic (Sample) Width

Plastic (Sample) Height

Magnet Width

Magnet Height

Value

150 mm

12.7 mm

12.7 mm

25.4 mm

Longitudinal velocity in plastic

2077.45 m/s

Wavelength in plastic

Aluminum strip Width

4.15 mm

10 mm

Aluminum strip Height

0.254 mm

Conductivity of plastic

62.5 X 10-18 S/m

Poisson’s ratio (Plastic)

0.35

Young’s Modulus (Plastic)

3.2 G Pa

Density (Plastic)

1190 kg/m3

Frequency of coil current

500 kHz

Conductivity of Aluminum strip

36 MS/m

55

The coil current, as shown in Figure 8.4, is a Gaussian modulated pulse with a carrier frequency

of 500 kHz as given in (8.1).

𝑔(𝑡) = 𝐴 · exp

(cid:18)

−

(cid:19)

(𝑡 − 𝑡0)2
2𝜎2

· cos(2𝜋 𝑓𝑐 (𝑡 − 𝑡0) + 𝜙)

(8.1)

where:

𝑔(𝑡) is the Gaussian modulated pulse as a function of time, 𝑡,

𝐴 is the amplitude of the pulse,

𝑡0 is the center time of the pulse,

𝜎 is the standard deviation of the Gaussian envelope,

𝑓𝑐 is the carrier frequency of the pulse,

𝜙 is the phase of the pulse.

Figure 8.4 Input current density provided to Aluminum strip

56

Figure 8.5 depicts the current density at a measurement point on aluminum strip, specifically

situated at center of the highlighted red line in Figure 8.3. Simultaneously, Figure 8.6 illustrates

the y-component of the Lorentz force at this measurement point on aluminum strip. Notably, both

the current density and Lorentz force exhibit analogous Gaussian-shaped temporal profiles.

In

accordance with equation (6.1), the Lorentz force is obtained by multiplying current density with

magnetic flux density.

Figure 8.5 z-component of current density at measurement point in Aluminum strip

Figure 8.7, Figure 8.8, and Figure 8.9 present surface plots of current density and Lorentz force

within the Aluminum strip at 5 (cid:181)s. The selection of 5 (cid:181)s is based on the expectation that the current

density will peak at this time. The observed decrease in current density along the aluminum height

is attributed to the skin effect of aluminum, as evident in Figure,8.7. The corresponding Lorentz

force plots exhibit a similar trend, in accordance with equation (6.1). It is also noteworthy that there

is a non-zero x-component of Lorentz force, attributed to the non-zero y-component of magnetic

flux density.

57

Figure 8.6 y-component of Lorentz force at measurement point in Aluminum strip

Figure 8.7 Surface plot of z-component of current density in Aluminum strip at 5 (cid:181)s

58

Figure 8.8 Surface plot of y-component of Lorentz force in Aluminum strip at 5 (cid:181)s

Figure 8.9 Surface plot of x-component of Lorentz force in Aluminum strip at 5 (cid:181)s

Figure 8.10, Figure 8.11, and Figure 8.12 depict arrow surface plots of Lorentz force within the

Aluminum strip at 5 (cid:181)s. The arrow surface plots visually represent the skin effect, as previously

discussed. Notably, the intriguing observation is the presence of the x-component of Lorentz force.

This pattern in the x-component is a consequence of the variation in the y-component of magnetic

59

flux density. Such variations could give rise to coupled modes in the propagation of acoustic waves,

adding complexity to the wave dynamics.

Figure 8.10 Arrow surface plot of y-component of Lorentz force (𝑁/𝑚3) in Aluminum strip at 5 (cid:181)s

Figure 8.11 Zoomed version of Figure 8.10

60

Figure 8.12 Arrow surface plot of x-component of Lorentz force (𝑁/𝑚3) in Aluminum strip at 5
(cid:181)s

Figure 8.13 A-scan of displacement at measurement point on plastic back-wall

61

Figure 8.14 Hilbert magnitude of A-scan signal showed in Figure 8.13

Figure 8.13 shows the displacement at a measurement point on plastic back-wall (A-scan).

Figure 8.14 shows the Hilbert magnitude plot for the A-scan of displacement. Few observations

can be made from these plots:

1. The mode 1 (longitudinal wave) and the reflection of this wave can clearly be observed.

2. Mode 1 is expected to appear at 8.11 us from theoretical wave velocity calculation and can

also be seen in the plot.

3. The interesting part to note here is the mode 2.

Wave velocity calculations

The longitudinal wave velocity for a solid sample can be calculated using (8.2),

√︄

𝑉 =

𝐸 (1 − 𝑣)
𝜌(1 + 𝑣) (1 − 2𝑣)

62

(8.2)

where:

𝑉 is the velocity of longitudinal wave,

𝐸 is the Young’s modulus of the sample,

𝜌 is density of the sample,

𝑣 is the Poisson’s ratio.

The theoretical value of longitudinal wave velocity for the non-conducting sample (acrylic

plastic) using material properties (Table 8.1) can be calculated as 2077.45 𝑚/𝑠.

The Hilbert magnitude plot (Figure 8.14) is used to find the time at which mode 1, mode 2

and mode 3 peak. These values are given in Table 8.2. The wave velocities for mode 1 and mode

2 are calculated using the Hilbert magnitude data and sample thickness. These are presented in

Table 8.3. The wave velocity of Mode 1 is comparable to the theoretical value of 2077.45 𝑚/𝑠.

But, mode 2 has a velocity which is slightly greater than that of shear wave (half of longitudinal

wave velocity) and much lesser than the longitudinal wave velocity. Hence, mode 2 can possibly

be considered as a coupled mode.

Table 8.2 Time at which modes peak in Hilbert magnitude plot for Direct Excitation EMAT model

Mode

Mode 1

Mode 2

Mode 1 (reflected)

Time (us)

11.38

18.67

23.93

Table 8.3 Mode velocities for Direct excitation EMAT model

Mode Velocity (m/s)

Mode 1

2023.9

Mode 2

1280.23

63

Figure 8.15 Surface plot of full-field displacement in plastic at 12 (cid:181)s

Figure 8.16 Surface plot of y-component of displacement in plastic at 12 (cid:181)s

Figure 8.15, Figure 8.16 and Figure 8.17 shows the full-field displacement plots in the sample

at 12 (cid:181)s. 12 (cid:181)s is chosen for a good representation of the wave modes. These plots validate the

propagation of an acoustic wave in the non-conducting sample and provides a visual representation

64

of wave propagation in plastic. The mode 1 and mode 2 can be clearly observed in these plots.

Figure 8.17 Surface plot of x-component of displacement in plastic at 12 (cid:181)s

8.2 Effect of input current on Lorentz force and displacement in sample

This study aims to provide further validation for the EMAT direct excitation model by in-

vestigating the impact of two different input current magnitudes applied to the aluminum strip.

Notably, all model parameters are maintained with precision throughout this investigation to ensure

consistency.

Figure 8.18 and Figure 8.19 showcase the Lorentz force (in Aluminum strip at measurement

point described earlier) and displacement A-scan (in plastic at measurement point on the back-wall)

plots corresponding to input current magnitudes of 1A and 2A. It’s essential to emphasize that the

preceding results were presented for the current magnitude (peak) of 1A. This study serves as a

validation step for the direct excitation model, confirming the expected doubling effect in both the

Lorentz force within the aluminum strip and the resulting displacement in the plastic material with

the increased input current magnitude.

65

Figure 8.18 Comparison of Lorentz force at measurement point in Aluminum strip for varying coil
current magnitudes

Figure 8.19 Comparison of A-scans of displacement at measurement point on plastic back-wall for
varying coil current magnitudes

66

8.3 Effect of Aluminum strip geometry on displacement in sample

This section delves into an exploration of the influence of Aluminum strip width and height

on the displacement within the sample (plastic). The objective is to study and analyze the effects

of varying dimensions of the Aluminum strip on the observed acoustic modes within the EMAT

model. This investigation contributes to an understanding of how geometric parameters impact the

displacement characteristics, thereby providing valuable insights for optimizing EMAT design and

performance.

8.3.1 Aluminum strip width variation

In this study, all model parameters remain constant, with the exception of the width of aluminum

strip. The chosen widths for the aluminum strip in this study are 10mm and 5mm.

Figure 8.20 A-scan of displacement for Aluminum strip width = 5mm

67

Figure 8.20 illustrates the displacement A-scan at the plastic back-wall (measurement point) for

an aluminum strip width of 5mm. Mode 1 is clearly observable, and it appears at the expected time

of 8.11 us. Additionally, Mode 2 remains present.

Figure 8.21 Comparison of displacement A-scans for varying Aluminum strip widths

Figure 8.21 provides a comparison of displacement A-scans for varying aluminum strip widths,

specifically 10mm and 5mm. The observed increase in displacement amplitude for the 10mm

aluminum width is attributed to the larger source width. Furthermore, maintaining a consistent

input current leads to an increase in the effective line current for the 10mm Aluminum strip width,

contributing to the amplified displacement amplitude. Acoustically, the larger source width narrows

the beam spread, concentrating more acoustic energy at the center of the beam. This phenomenon

is reflected in the displacement A-scan, clearly showcasing the increased displacement amplitude

68

for the 10mm aluminum strip width. This analysis offers valuable insights into the intricate

interplay between geometric parameters (of Aluminum strip) and the electromagnetic and acoustic

characteristics within the context of EMAT design.

Figure 8.22, Figure 8.23 and Figure 8.24 shows the full-field displacement plots in the sample

at 12 (cid:181)s for aluminum strip width of 5mm. These plots validate the propagation of an acoustic

wave in the non-conducting sample, as in the previous case (aluminum strip width = 10mm). Also,

the mode 1 and mode 2 can clearly be observed in these plots. The amplitude of displacements

(in plastic) are reduced when compared to the previous set of results (Figure 8.15, Figure 8.16 and

Figure 8.17, i.e., for Aluminum strip width = 10mm).

Figure 8.22 Surface plot of full-field displacement in plastic at 12 (cid:181)s for Aluminum strip width =
5mm

Current density and Lorentz force plots are presented in Figure 8.25, Figure 8.26, Figure 8.27,

Figure 8.28 and Figure 8.29 for aluminum strip width of 5mm. The presence of non-zero x-

component of Lorentz force, attributed to the y-component of magnetic flux density, is still evident

in these plots. The overall pattern remains similar when compared to the plots with an aluminum

strip width of 10mm, as anticipated.

Units of Lorentz force in Figure 8.28 and Figure 8.29 are 𝑁/𝑚3. This concludes the study of

69

Figure 8.23 Surface plot of y-component of displacement in plastic at 12 (cid:181)s for Aluminum strip
width = 5mm

Figure 8.24 Surface plot of x-component of displacement in plastic at 12 (cid:181)s for Aluminum strip
width = 5mm

variation in aluminum strip width. The following subsection explores the impact of aluminum strip

height on the displacement in plastic.

70

Figure 8.25 Surface plot of z-component of current density in Aluminum strip for strip width =
5mm

Figure 8.26 Surface plot of y-component of Lorentz force in Aluminum strip at 5 (cid:181)s for strip width
= 5mm

8.3.2 Aluminum strip height variation

In this investigation, the study maintains uniformity in all model parameters, except for the

height of the aluminum strip. The objective is to assess the influence of varying aluminum strip

71

Figure 8.27 Surface plot of x-component of Lorentz force in Aluminum strip at 5 (cid:181)s for strip width
= 5mm

Figure 8.28 Arrow surface plot of y-component of Lorentz force in Aluminum strip at 5 (cid:181)s for strip
width = 5mm

heights on the displacement observed in the sample. The selected heights for the aluminum strip

in this particular study are 0.25 mm and 0.1 mm.

72

Figure 8.29 Arrow surface plot of x-component of Lorentz force in Aluminum strip at 5 (cid:181)s for strip
width = 5mm

Figure 8.30 represents the displacement A-scan at the plastic back-wall, precisely at the mea-

surement point, for an aluminum strip height of 0.1mm. Notably, both modes are still present, as

seen from the plot.

Figure 8.31 provides a comparative analysis of displacement A-scans for aluminum heights of

0.25 mm and 0.1 mm. Notably, the displacement amplitude for the 0.1mm aluminum strip height

surpasses that of the 0.25mm aluminum strip height. This observed difference is attributed to the

skin effect of the aluminum strip. It is essential to consider that the skin depth of the aluminum

strip at 500 kHz is approximately 116 (cid:181)m. As the aluminum height decreases, the Lorentz force

increases, consequently resulting in an enhanced displacement at the sample back-wall.

Figure 8.32, Figure 8.33 and Figure 8.34 shows the full-field displacement plots in the sample

at 12 (cid:181)s. These plots validate the propagation of an acoustic wave in the non-conducting sample,

as in the previous case (aluminum strip height = 0.25mm). Also, the mode 1 and mode 2 can

clearly be observed in these plots. The amplitude of displacements are increased when compared

to Figure 8.15, Figure 8.16 and Figure 8.17 (aluminum strip height = 0.25mm).

Current density and Lorentz force plots are presented in Figure 8.35, Figure 8.36 and Figure 8.37.

73

Figure 8.30 A-scan of displacement at measurement point on plastic back-wall for Aluminum strip
height = 0.1mm

Figure 8.31 Comparison of displacement A-scans for varying Aluminum strip heights

74

Figure 8.32 Surface plot of full-field displacement in plastic at 12 (cid:181)s for Aluminum strip height =
0.1mm

Figure 8.33 Surface plot of y-component of displacement in plastic at 12 (cid:181)s for Aluminum strip
height = 0.1mm

The pattern is similar when compared to plots with Aluminum strip width of 10mm, as expected.

Units of Lorentz force in Figure 8.36 and Figure 8.37 are 𝑁/𝑚3.

The interesting thing to observe is the variation of current density and Lorentz force inside

75

Figure 8.34 Surface plot of x-component of displacement in plastic at 12 (cid:181)s for Aluminum strip
height = 0.1mm

Figure 8.35 Surface plot of z-component of current density in Aluminum strip for strip height =
0.1mm

Aluminum strip. The variation is much lesser in the case where aluminum strip height is 0.1mm

compared to when the aluminum strip height is 0.25mm (Figure 8.7, Figure 8.8, Figure 8.9, Fig-

76

Figure 8.36 Arrow surface plot of y-component of Lorentz force in Aluminum strip at 5(cid:181)s for strip
height = 0.1mm

Figure 8.37 Arrow surface plot of x-component of Lorentz force in Aluminum strip at 5(cid:181)s for strip
height = 0.1mm

ure 8.10, Figure 8.11 and Figure 8.12). The decrease in Lorentz force variation is attributed to the

skin effect. In the subsequent section, the numerical outcomes of a parametric study are presented

77

to delve deeper into comprehending the skin effect of aluminum on the displacement within the

sample.

8.4

Impact of skin effect in Aluminum strip on displacement in sample

This section delves into the skin effect of the aluminum strip and its effect on the displacement

within the plastic sample.

Figure 8.38 offers a quantitative evaluation of displacement at the

Figure 8.38 Comparison of Hilbert magnitude peaks of A-scans of displacement in plastic, for
mode 1, and for different aluminum strip heights

plastic back-wall, shedding light on the influence of the skin effect in the aluminum strip. The

skin depth of Aluminum at 500 kHz is calculated to be approximately 116 (cid:181)m (as determined by

equation (7.2)). The analysis encompasses four distinct aluminum strip heights (0.05mm, 0.1mm,

0.2mm, and 0.25mm). The Hilbert magnitudes of mode 1 (representing the longitudinal wave) are

normalized relative to the Hilbert magnitude peak observed in the case of approximately 100% skin

depth (i.e., aluminum strip height = 0.1mm).

The response exhibits an exponential trend, aligning with theoretical expectations. Additionally,

78

the findings highlight that optimal displacement in plastic occurs at half skin depth, a result of the

heightened Lorentz force in the aluminum strip as the height decreases from 0.25mm to 0.05mm.

In practical applications, setting the aluminum strip height to one skin depth, rather than half skin

depth (i.e., 0.05mm), proves advantageous, facilitating a higher current input that can be provided

to the aluminum strip. The following section is dedicated to the experimental validation of the

induced EMAT configuration.

8.5 Experimental validation

This section focuses on the experimental validation of the EMAT model, providing a comparison

between experimental and simulation results.

The experimental validation in this chapter is

Figure 8.39 Experimental set-up for Direct Excitation EMAT

a collaborative effort with Zebadiah Miles, a PhD student at Michigan State University, and I

acknowledge his valuable contribution to this work.

The experimental configuration includes a steel core, permanent magnet, metal strip (alu-

minum), and the sample (acrylic plastic), as depicted in Figure 8.39. This setup mirrors the

simulation configuration. The magnet, yoke, and sample geometries adhere to the specifications

outlined in Table 8.1. A 2-cycle tone-burst signal (at a frequency of 500 kHz) is generated using a

function generator and subsequently amplified using a high-power RITEC GA-2500A Gated Am-

79

plifier. The output of the power amplifier is provided as input to the aluminum strip (EMAT coil).

The resulting elastic waves were detected by a piezoelectric transducer (as shown in Figure 8.39),

coupled to the sample with a liquid couplant. Conditioning and amplification of the received signals

were performed using an ultrasonic pulser/receiver with +60 dB gain. Subsequently, the amplified

signals were digitized through an 8-bit oscilloscope operating at a 1 GHz sampling rate.

The geometries of aluminum strips used in the experiments are provided in Figure 8.40.

Figure 8.40 Aluminum strip geometry used for experiments

The simulation and experimental A-scan results for aluminum strip B are shown in Figure 8.41

and Figure 8.42. The simulation and experimental A-scan results for aluminum strip C are shown

in Figure 8.43 and Figure 8.44. The simulation and experimental outcomes exhibit indications of

a second mode (mode 2) alongside the mode 1 (longitudinal wave). However, the mode 2 wave is

less distinct in experimental results, in comparison to the simulation results. Mode 2 can be seen

occurring between mode 1 and the first reflection of mode 1 in both simulation and experimental

results. Following the application of Hilbert transforms to the A-scan results (simulation and

experiment), the velocity of mode 1 is calculated as 2707.88 m/s (experiment) and 2027.13 m/s

(simulation). The difference between the experimental and simulation values for the longitudinal

wave velocity (mode 1) arises from differences in material properties such as Young’s modulus and

Poisson’s ratio for the acrylic samples used in experiments as compared to the simulation. The

80

Figure 8.41 A-scan of displacement at measurement point on plastic back-wall - Simulation result
for Aluminum strip B

Figure 8.42 A-scan of displacement at measurement point on plastic back-wall - Experimental result
for Aluminum strip B

81

Figure 8.43 A-scan of displacement at measurement point on plastic back-wall - Simulation result
for Aluminum strip C

Figure 8.44 A-scan of displacement at measurement point on plastic back-wall - Experimental result
for Aluminum strip C

82

experimentally obtained A-scan results validate the direct excitation EMAT model.

This concludes the discussion on direct excitation configuration of the EMAT for non-conductive

materials. The direct excitation configuration’s reliance on contact contradicts the fundamental

non-contact nature of EMATs. To address this limitation, the proposed approach holds promise

for an extension toward developing a non-contact-based approach. Further details on this potential

solution will be elaborated upon in the following chapter.

83

CHAPTER 9

NON-CONTACT INDUCED EXCITATION: EMBEDDED EMAT

This chapter presents the findings obtained from extensive numerical simulations conducted on

EMATs applied to a non-conductive sample using the non-contact induced excitation approach.

The initial section introduces the induced excitation model specifically tailored for an embedded

EMAT configuration, providing substantial results that validate the successful propagation of an

acoustic wave within the non-conductive sample. It’s crucial to note that this model serves as an

extension of the previously discussed direct excitation model. Subsequently, the chapter includes a

comparative analysis of acoustic velocity, enabling a comprehensive comparison with theoretically

derived values. As the narrative progresses, the subsequent sections meticulously explore the impact

of varying aluminum strip width and height on both Lorentz force and displacement, accompanied

by the presentation of corresponding numerical results. Moreover, the chapter delves into a detailed

examination of the implications of employing a line source in lieu of the aluminum strip, shedding

light on the associated acoustic modes. The discussion also extends to the experimental validation,

offering insights into the observed acoustic behavior and further contributing to the understanding

of the induced excitation approach in EMATs applied to non-conductive samples.

9.1 EMAT model in COMSOL

The induced excitation model (two-dimensional) for the EMAT involves inducing current in

the metal patch embedded inside the non-conducting sample. Figure 9.1 shows schematic of the

non-contact induced excitation model geometry in COMSOL and Figure 9.2 shows the zoomed in

version to illustrate the metal patch (copper patch) and measurement point on the sample back-

wall. The magnetic field interface (in AC/DC module) is used to simulate the electromagnetic

phenomenon and structural mechanics module is used to simulate the acoustic phenomenon.

The model comprises of a permanent magnet, aluminum strip, embedded copper patch, steel

core and the non-conducting sample (plastic). The permanent magnet is used to generate the static

magnetic field and the aluminum strip induces current in the copper patch to generate a changing

(dynamic) magnetic field. The entire model is enclosed in air. The static magnetic field of the

84

Figure 9.1 Induced Excitation model for an EMAT in COMSOL

Figure 9.2 Zoomed version of Figure 9.1

permanent magnet is specified in x direction. A surface current density (A/m) is applied to the

Aluminum strip as shown in Figure 8.3, in z direction. Hence according to right hand rule, the

Lorentz force generated should be in the y-direction. And the displacement and wave propagation

85

(longitudinal wave) will also be in the y-direction, i.e., along the thickness of sample (plastic). The

model parameters are given in Table 9.1.

Table 9.1 Model parameters for Induced excitation EMAT model

Parameter

Plastic (Sample) Width

Plastic (Sample) Height

Magnet Width

Magnet Height

Value

150 mm

12.7 mm

12.7 mm

25.4 mm

Longitudinal velocity in plastic

2077.45 m/s

Wavelength in plastic

Aluminum strip Width

4.15 mm

10 mm

Aluminum strip Height

0.254 mm

Conductivity of plastic

62.5 X 10-18 S/m

Poisson’s ratio (Plastic)

0.35

Young’s Modulus (Plastic)

3.2 G Pa

Density (Plastic)

1190 kg/m3

Frequency of coil current

500 kHz

Conductivity of Aluminum strip

36 MS/m

Copper patch Height

Copper patch Width

Conductivity of Copper

Plastic cover Height

Plastic cover Width

0.05 mm

150 mm

60 MS/m

1.5 mm

150 mm

The coil current, as shown in Figure 8.4, is a Gaussian modulated pulse with a carrier frequency

of 500 kHz as given in (8.1).

Figure 9.3 and Figure 9.4 shows the arrow surface plots of Lorentz force in copper patch (y

and x components) at 5 (cid:181)s. The y component shows a uniform current density distribution, due to

86

application of a surface current density, as shown in Figure 8.3. The x component shows a pattern

similar to the results obtained for direct excitation. As observed from the direct excitation model,

this pattern of Lorentz force led to a coupled acoustic mode in the sample.

Figure 9.3 Arrow surface plot of y-component of Lorentz force in Copper patch at 5(cid:181)s

Figure 9.4 Arrow surface plot of x-component of Lorentz force in Copper patch at 5(cid:181)s

87

Figure 9.5 A-scan of displacement at measurement point on plastic back-wall for Induced excitation
EMAT

Figure 9.6 Hilbert magnitude of A-scan signal showed in Figure 9.5

88

Figure 9.5 shows the A-scan of displacement at the measurement point on plastic back-wall.

Figure 9.6 shows the Hilbert magnitude plot for the displacement A-scan. Few observations can be

made from these plots:

1. The mode 1 (longitudinal wave) and the reflection of this wave can clearly be observed

(similar to the results obtained for direct excitation model).

2. Mode 1 is expected to appear at 8.11 us from theoretical wave velocity calculation and can

also be seen in the plot.

3. Mode 2 can also be distinctly observed, similar to the direct excitation model results.

Wave velocity calculations

The longitudinal wave velocity for the acrylic sample can be calculated using (8.2). The theo-

retical value of longitudinal wave velocity for the non-conducting sample using material properties

(Table 9.1) can be calculated as 2077.45 𝑚/𝑠.

The Hilbert magnitude plot (Figure 8.14) is used to find the time at which mode 1, mode 2 and

mode 3 peak. These values are given in Table 9.2. The wave velocities for mode 1 and mode 2 are

calculated using the Hilbert magnitude data and sample thickness. These are presented in Table

9.3. The wave velocity of Mode 1 is comparable to the theoretical value of 2077.45 𝑚/𝑠. But,

mode 2 has a velocity which is a slightly greater than that of shear wave (half of longitudinal wave

velocity) and much lesser than the longitudinal wave velocity. Hence, mode 2 can be considered as

a coupled mode.

Table 9.2 Time at which modes peak in Hilbert magnitude plot for Induced Excitation EMAT

Mode

Mode 1

Mode 2

Mode 1 (reflected)

Time (us)

11.79

18.99

24.17

89

Table 9.3 Mode velocities for Induced Excitation EMAT

Mode Velocity (m/s)

Mode 1

2051.69

Mode 2

1297.23

Figure 9.7 Surface plot of full-field displacement in plastic at 12 (cid:181)s for Induced excitation EMAT

Figure 9.8 Surface plot of y-component of displacement in plastic at 12 (cid:181)s for Induced excitation
EMAT

90

Figure 9.9 Surface plot of x-component of displacement in plastic at 12 (cid:181)s for Induced excitation
EMAT

Figure 9.10 Comparison of A-scans of displacement at measurement point on plastic back-wall for
varying coil current magnitudes (Induced Excitation EMAT)

91

Figure 9.7, Figure 9.8 and Figure 9.9 shows the full-field displacement plots in the sample at 12

(cid:181)s. These plots validate the propagation of an acoustic wave in the non-conducting sample. The

mode 1 and mode 2 can be clearly observed in these plots and the results are similar to that obtained

for direct excitation configuration.

Figure 9.10 shows the displacement A-scan plots for input current magnitudes of 1A and 2A.

The results presented so far for the induced configuration are for the current magnitude (peak) of

1A. This additional investigation serves to validate the induced excitation model, revealing that

displacement in plastic has doubled, as anticipated, with the increase in input current magnitude.

Additionally, it is important to note that all model parameters are maintained precisely the same for

this study.

Figure 9.11 Comparison of A-scans of displacement at measurement point on plastic back-wall for
direct excitation and induced excitation EMAT’s

92

Figure 9.11 depicts the displacement A-scan plots for both direct and induced configurations,

utilizing the model parameters described in Table 8.1 and Table 9.1, respectively. The aluminum

strip width is set at 10mm. It is important to note that the data for induced displacement is

multiplied by 10. This adjustment is made to enhance clarity for observation on the same plot.

The reduction in displacement amplitude for the induced configuration can be attributed to lift-off

between the aluminum strip and copper patch. Additionally, an intriguing observation is the phase

shift between the direct and induced displacement A-scans. This is attributed to the phase difference

between the applied current to the aluminum strip and induced eddy current in the copper patch.

9.2 Effect of Aluminum strip geometry on displacement in sample

This section delves into an exploration of the influence of Aluminum strip width and height

on the displacement within the sample (plastic). The objective is to study and analyze the effects

of varying dimensions of the Aluminum strip on the observed acoustic modes within the EMAT

model. This investigation contributes to an understanding of how geometric parameters impact the

displacement characteristics, thereby providing valuable insights for optimizing EMAT design and

performance.

9.2.1 Aluminum strip width variation

In this study, all model parameters remain constant, with the exception of the width of aluminum

strip. The chosen widths for the aluminum strip in this study are 10mm and 5mm.

Figure 9.12 illustrates the displacement A-scan at the plastic back-wall (measurement point) for

an aluminum strip width of 5mm. Mode 1 is clearly observable, and it appears at the expected time

of 8.11 us. The two modes can still be observed in this plot, similar to the direct excitation and

induced excitation with 10mm aluminum strip width results.

Figure 9.13 provides a comparison of displacement A-scans for varying aluminum strip widths,

specifically 10mm and 5mm. The observed increase in displacement amplitude for the 10mm

aluminum width is attributed to the larger source width. Furthermore, maintaining a consistent

input current leads to an increase in the effective line current for the 10mm Aluminum strip width,

contributing to the amplified displacement amplitude. Acoustically, the larger source width narrows

93

Figure 9.12 A-scan of displacement at measurement point on plastic back-wall for Aluminum strip
width = 5mm

Figure 9.13 Comparison of A-scans of displacement at measurement point on plastic back wall for
varying Aluminum strip widths (Induced Excitation EMAT)

94

the beam spread, concentrating more acoustic energy at the center of the beam. This phenomenon

is reflected in the displacement A-scan, clearly showcasing the increased displacement amplitude

for the 10mm aluminum strip width. This analysis offers valuable insights into the intricate

interplay between geometric parameters (of Aluminum strip) and the electromagnetic and acoustic

characteristics within the context of EMAT design. The results are in-line with the direct excitation

configuration, as expected.

9.2.2 Aluminum strip height variation

In this study, all model parameters remain constant, with the exception of the height of aluminum

strip. The chosen heights for the aluminum strip in this study are 0.25 mm and 0.1 mm. Figure 9.14

Figure 9.14 A-scan of displacement at measurement point on plastic back-wall for 0.1mm Aluminum
strip height (Induced Excitation EMAT)

95

shows the displacement A-scan at plastic back-wall (at the measurement point) for aluminum strip

height of 0.1mm. The two modes can still be observed in this plot, similar to the direct excitation

results and induced excitation with aluminum strip heights of 0.25mm.

Figure 9.15 Comparison of A-scans of displacement at measurement point on plastic back wall for
varying Aluminum strip heights (Induced Excitation EMAT)

Figure 9.15 provides a comparative analysis of displacement A-scans for aluminum heights of

0.25 mm and 0.1 mm. The displacement amplitude for the 0.1mm aluminum strip height surpasses

that of the 0.25mm aluminum strip height, attributed to the lift-off between Aluminum strip and

copper patch. A lower lift-off results in a higher Lorentz force in copper patch, consequently leading

to an increased displacement in plastic.

96

9.3 Effect of line source on acoustic modes in sample

This section investigates the impact of a line source (modeled as a point source in 2D) on

the acoustic modes. The objective of these simulations is to observe the potential emergence of

a second mode in the absence of the aluminum strip.

In the induced configuration model, the

aluminum strip is substituted with the point source (2D), as depicted in Figure9.16.

Figure 9.16 Induced excitation EMAT model with point source (in 2D) - No aluminum

Figure 9.17 and Figure 9.18 shows the arrow surface plots of Lorentz force in copper patch (x

and y components) at 5 (cid:181)s. The x component shows a pattern similar to the results obtained for

direct excitation and induced excitation with aluminum strip. But, the interesting thing to note

here is that y component of Lorentz force is much higher than the x component of Lorentz force.

Figure 9.19 displays the A-scan of displacement at the plastic back-wall, revealing the presence of

two distinct acoustic modes in the displacement plot. This simulation provides confirmation of the

existence of the second mode, even in the absence of the aluminum strip. But, the peak of mode 2

is seen to be much lesser than peak of mode 1.

97

Figure 9.17 Arrow surface plot of x-component of Lorentz force in Copper patch at 5 (cid:181)s for Induced
Excitation EMAT model shown in Figure 9.16

Figure 9.18 Arrow surface plot of y-component of Lorentz force in Copper patch at 5 (cid:181)s for Induced
Excitation EMAT model shown in Figure 9.16

Figure 9.20 presents a comparative analysis of induced configurations with aluminum strip

widths of 5mm, 10mm, and a point source. All other parameters in the model are kept constant.

The plots specifically illustrate the ratio of mode 2 Hilbert magnitude (HM) peak to mode 1

98

Figure 9.19 A-scan of displacement at measurement point on plastic back-wall for Induced Excita-
tion EMAT model shown in Figure 9.16

Figure 9.20 Quantitative comparison of Induced Excitation EMAT’s

99

HM peak for the three induced excitation configurations. This study aims to observe the trend

in amplitude reduction for mode 2 in comparison with mode 1, as the source width decreases,

providing valuable insights into the acoustic behavior under varying source widths. The outcomes

indicate that a decrease in source width leads to a reduction in the HM peak for mode 2, when

compared with mode 1. This reduction is associated with the decrease in x-component of Lorentz

force relative to the y-component of Lorentz force in the Aluminum strip.

Figure 9.21 Surface plot of full-field displacement in plastic at 12 (cid:181)s for EMAT model shown in
Figure 9.16

Figure 9.22 Surface plot of y-component of displacement in plastic at 12 (cid:181)s for EMAT model
shown in Figure 9.16

100

Figure 9.23 Surface plot of x-component of displacement in plastic at 12 (cid:181)s for EMAT model
shown in Figure 9.16

Figure 9.21, Figure 9.22 and Figure 9.23 shows the full-field displacement plots in the sample at

12 (cid:181)s. These plots provide a visual representation and validate the propagation of an acoustic wave

in the non-conducting sample. The mode 1 and mode 2 can clearly be observed in these plots.

9.4 Effect of plastic cover height on displacement in sample

In this section, the impact of plastic cover height on the induced excitation configuration EMAT

is explored. The plastic presents as a lift-off for the source (Aluminum strip), and the copper patch

is embedded within the sample (plastic), characterizing it as an embedded EMAT. The investigation

involves a comparison of displacements at the sample back-wall, considering variations in plastic

cover heights. Additionally, a scenario where aluminum is positioned at a specific height above the

plastic cover is examined. The primary goal is to validate the induced excitation model further and

ensure consistency in the generation of acoustic wave modes.

In the first study, all model parameters (Figure 9.1) remain constant, with the exception of

the plastic cover height. Figure 9.24 presents a comparative analysis of displacement A-scans for

plastic cover heights of 0.5 mm and 1.5 mm. The displacement amplitude for the 0.5 mm plastic

cover height exceeds that of the 1.5 mm plastic cover height, attributed to the lift-off between

101

Aluminum strip and copper patch. A lower lift-off results in a higher Lorentz force in copper patch,

consequently leading to an increased displacement in the sample. Therefore, having a thin layer of

plastic above the copper patch is certainly desirable for this application.

Figure 9.24 Comparison of displacement A-scans at measurement point on plastic back-wall for
varying plastic cover heights (Induced Excitation EMAT)

In the second study, the objective is to verify the acoustic modes in plastic with variation in

aluminum strip placement above the plastic cover. Figure 9.25 provides a comparative analysis

of displacement A-scans for plastic cover heights of 0.5 mm, where a) The aluminum strip is

placed on the plastic cover and b) The aluminum strip is placed 0.5mm above the plastic cover.

The displacement amplitude for the case where aluminum strip is positioned on the plastic cover

shows a slightly higher displacement amplitude. This is attributed to the lift-off between aluminum

strip and the copper patch. A lower lift-off results in a higher Lorentz force in the copper patch,

consequently leading to an increased displacement in the sample. Hence, positioning the aluminum

102

strip in close proximity to the plastic cover is certainly desirable for this application.

Figure 9.25 Comparison of displacement A-scans at measurement point on plastic back-wall for
varying aluminum strip placements (Induced Excitation EMAT)

9.5 A Comparative Analysis: Gaussian vs. Uniform Distribution of Lorentz force in space

In this investigation, the input is applied to aluminum strip as outlined in Figure 9.26. Gaussian

weights are assigned to the currents provided to the designated points in Case 1, representing a

Gaussian distribution in space (along the x, i.e., direction of aluminum width). Conversely, in

Case 2 (Uniform distribution in space), all points illustrated in Figure 9.26 receive equal weights.

All other parameters in the model remain consistent with the details provided in Table 9.1. The

aluminum strip width is 10mm.

In Case 1, the simulation is designed to generate a Gaussian

distribution in the Lorentz force. The objective of this study is to validate the model for different

spatial Lorentz force distributions.

Figure 9.27 and Figure 9.28 shows the arrow surface plots of Lorentz force in copper patch

103

Figure 9.26 Representation of input current provided to Aluminum strip

Figure 9.27 Arrow surface plot of x-component of Lorentz force (Case 1) in Copper patch at 5 (cid:181)s

(x and y components) at 5 (cid:181)s for case 1. The x component shows a pattern similar to the results

obtained for direct excitation and induced excitation with aluminum strip. The y-component exhibits

a Gaussian distribution in space (along the x-axis) due to the spatial pattern in which the input

current is applied to the aluminum strip.

Figure 9.29 and Figure 9.30 shows the arrow surface plots of Lorentz force in copper patch (x

and y components) at 5 (cid:181)s for case 2. The x component shows a pattern similar to the results

obtained for direct excitation and induced excitation with aluminum strip. The y component shows

a uniform distribution in space, as discussed earlier.

104

Figure 9.28 Arrow surface plot of y-component of Lorentz force (Case 1) in Copper patch at 5 (cid:181)s

Figure 9.29 Arrow surface plot of x-component of Lorentz force (Case 2) in Copper patch at 5 (cid:181)s

Figure 9.31 presents a comparative analysis depicting displacement (mode 1) at the plastic

back-wall for Gaussian (Case 1) and uniform distributions (Case 2) in space. As expected, the

displacement amplitude is higher for the uniform distribution. Mode 2 is evident in the displacement

surface plots within the sample (plastic).

105

Figure 9.30 Arrow surface plot of y-component of Lorentz force (Case 2) in Copper patch at 5 (cid:181)s

Figure 9.31 Displacement A-scans (Mode 1) at measurement point on plastic back-wall

106

Figure 9.32 Surface plot of full-field displacement in plastic at 12 (cid:181)s - Case 1

Figure 9.33 Surface plot of y-component of displacement in plastic at 12 (cid:181)s - Case 1

Figure 9.32, Figure 9.33 and Figure 9.34 presents the full-field displacement plots in the sample

at 12 (cid:181)s for case 1 (i.e., Gaussian distribution of Lorentz force in space). These plots provides

a visual representation and validate the propagation of an acoustic wave in the non-conducting

sample. The mode 1 and mode 2 can be clearly observed in these plots.

Figure 9.35, Figure 9.36 and Figure 9.37 presents the full-field displacement plots in the sample

107

Figure 9.34 Surface plot of x-component of displacement in plastic at 12 (cid:181)s - Case 1

Figure 9.35 Surface plot of full-field displacement in plastic at 12 (cid:181)s - Case 2

at 12 (cid:181)s for case 2 (i.e., uniform distribution of Lorentz force in space). These plots provides a visual

representation and validate the propagation of an acoustic wave in the non-conducting sample. It

can be observed that the displacement amplitudes are much higher for case 2 when compared to

case 1. The mode 1 and mode 2 can be clearly observed in these plots. The following section is

dedicated to experimental validation of the induced EMAT configuration.

108

Figure 9.36 Surface plot of y-component of displacement in plastic at 12 (cid:181)s - Case 2

Figure 9.37 Surface plot of x-component of displacement in plastic at 12 (cid:181)s - Case 2

9.6 Experimental validation

This section focuses on the experimental validation of the induced EMAT model, providing

a comparison between experimental and simulation results. The experimental validation in this

chapter is a collaborative effort with Zebadiah Miles, a PhD student at Michigan State University,

109

Figure 9.38 Experimental set-up for Induced Excitation EMAT

and I acknowledge his valuable contribution to this work.

The experimental set-up consists of the steel core, permanent magnet, metal strip (aluminum),

copper patch, FR4 (plastic cover) and the sample (acrylic plastic) as shown in Figure 9.38. This

setup mirrors the simulation configuration. The magnet, yoke, and sample geometries adhere to

the specifications outlined in Table 9.1. The copper patch is available underneath the FR4 material

(a single sided copper clad PCB) and located on the acrylic plastic. The copper patch is coupled to

the sample using a liquid couplant. 3D printed structures can avoid this use of the liquid couplant.

A 2-cycle tone-burst signal (at a frequency of 500 kHz) is generated using a function generator and

subsequently amplified using a high-power RITEC GA-2500A Gated Amplifier. The output of the

power amplifier is provided as input to the aluminum strip (EMAT coil). The resulting elastic waves

were detected by a piezoelectric transducer (as shown in Figure 9.38), coupled to the sample with

a liquid couplant. Conditioning and amplification of the received signals were performed using

110

Figure 9.39 A-scan of displacement at measurement point on plastic back-wall - Simulation result
for Aluminum strip B (Induced Excitation EMAT)

Figure 9.40 A-scan of displacement at measurement point on plastic back-wall - Experimental result
for Aluminum strip B (Induced Excitation EMAT)

111

an ultrasonic pulser/receiver with +60 dB gain. Subsequently, the amplified signals were digitized

through an 8-bit oscilloscope operating at a 1 GHz sampling rate. The geometries of aluminum

strips used in the experiments are provided in Figure 8.40.

Figure 9.41 A-scan of displacement at measurement point on plastic back-wall - Simulation result
for Aluminum strip C (Induced Excitation EMAT)

The simulation and experimental A-scan results for aluminum strip B are shown in Figure 9.39

and Figure 9.40. The simulation and experimental A-scan results for aluminum strip C are shown

in Figure 9.41 and Figure 9.42. The simulation and experimental outcomes exhibit indications of

a second mode (mode 2) alongside the mode 1 (longitudinal wave). However, the mode 2 wave is

more noisy in experimental results when compared with simulation results. Mode 2 can be seen

occurring between mode 1 and the first reflection of mode 1 in both simulation and experimental

results. Following the application of Hilbert transforms to the A-scan results (simulation and

experiment), the velocity of mode 1 is calculated as 2582.35 m/s (experiment) and 2051.69 m/s

(simulation). The difference between the experimental and simulation values for the longitudinal

112

Figure 9.42 A-scan of displacement at measurement point on plastic back-wall - Experimental result
for Aluminum strip C (Induced Excitation EMAT)

wave velocity (mode 1) arises from differences in material properties such as Young’s modulus and

Poisson’s ratio for the acrylic samples used in experiments as compared to the simulation. The

experimentally obtained A-scan results validate the non-contact induced excitation EMAT model.

This concludes the discussion on induced excitation configuration of the EMAT for non-conductive

materials. The following chapter will extensively explore the application of non-contact induced

excitation EMAT, also called the Embedded EMAT.

113

CHAPTER 10

DAMAGE DETECTION IN SAMPLE

The preceding chapter offered detailed descriptions of the EMAT models and elucidated the

influence of metal strip and metal patch geometries on the displacement in plastic. This chapter

delves into the application of embedded EMAT for detecting defects within the sample under test.

The study focuses on two distinct types of defects: a) Vertical slot/crack and b) Horizontal crack.

10.1 Vertical slot defect

Figure 10.1 illustrates the model used for simulating the vertical slot type of defect. Notably,

this model is identical to the one employed for induced excitation, as depicted in Figure 9.1. The

model parameters remain consistent and are detailed in Table 9.1. The defect width considered for

this study is 1mm and defect height is chosen as 4mm and the defect geometry representation is

shown in Figure 10.2.

Figure 10.1 Embedded EMAT model with defect in COMSOL

Figure 10.3 presents the A-scans of displacement both with and without a defect in plastic at

the measurement point. The ends of the defect function as diffraction sources. The amplitude of

mode 1 is diminished due to energy absorption, scattering and reflection by the defect. Meanwhile,

mode 2 generates a Rayleigh wave along the vertical flats, leading to diffraction and a subsequent

114

Figure 10.2 Defect geometry representation

Figure 10.3 A-scan of displacement at measurement point on plastic back wall (No defect and With
vertical slot defect)

increase in amplitude, as observed. The full-field displacement plots depicted in Figure 10.4 and

Figure 10.5 provide additional visual insights into the wave propagation, scattering and reflection

occurring within the sample in the presence and absence of a vertical slot defect.

Figure 10.6 and Figure 10.7 displays the A-scans of displacement with variations in defect width

and defect height. For the study on defect width variation, defect height is kept constant at 4mm

115

Figure 10.4 Surface plot of full-field displacement in plastic at 12 (cid:181)s - No defect

Figure 10.5 Surface plot of full-field displacement in plastic at 12 (cid:181)s - With defect

and for study on defect height variation, defect width is held constant at 1 mm. As anticipated, the

amplitude of mode 1 decreases with increase in defect width. Conversely, mode 2 exhibits greater

sensitivity to changes in defect height.

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Figure 10.6 A-scan of displacement at measurement point on plastic back-wall for varying defect
widths (Defect height = 4mm)

Figure 10.7 A-scan of displacement at measurement point on plastic back-wall for varying defect
heights (Defect width = 1mm)

117

10.2 Horizontal crack defect

The model utilized for this investigation remains consistent with the one described for the

vertical slot defect (Figure 10.1). The sole distinction lies in the rotation of the vertical slot to

generate a horizontal crack defect. The defect width chosen for this study is 4mm, and the defect

height is set at 1mm.

Figure 10.8 A-scans of displacement at measurement point on plastic back-wall (No defect and with
Horizontal crack defect)

Figure 10.8 presents the A-scans of displacement both with and without a defect in plastic at the

measurement point. The ends of the defect function as diffraction sources, as discussed earlier. The

amplitude of mode 1 is diminished considerably due to energy absorption, scattering and reflection

by the defect, when compared to vertical slot defect.

Mode 1 is highly sensitive to horizontal crack defect, when compared to the vertical slot defect.

Meanwhile, mode 2 generates a Rayleigh wave along the vertical flats, leading to diffraction and a

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Figure 10.9 Surface plot of full-field displacement in plastic at 12 (cid:181)s - No defect

Figure 10.10 Surface plot of full-field displacement in plastic at 12 (cid:181)s - With defect

subsequent increase in amplitude, as observed and discussed earlier. The full-field displacement

plots depicted in Figure 10.9 and Figure 10.10 provide additional visual insights into the wave

propagation, scattering and reflection occurring within the sample in the presence and absence of

the horizontal crack defect.

119

Figure 10.11 A-scans of displacement at measurement point on plastic back-wall for varying defect
widths (Defect height = 1mm)

Figure 10.12 A-scans of displacement at measurement point on plastic back-wall for varying defect
heights (Defect width = 4mm)

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Figure 10.11 presents the A-scans of displacement with variations in defect width, maintaining

a constant defect height of 1mm. Figure 10.12 presents the A-scans of displacement with variations

in defect height, maintaining a constant defect width of 4mm. As expected, the amplitude of mode

1 diminishes for a wider defect. Conversely, mode 2 exhibits greater sensitivity to changes in defect

height (Figure 10.12).

10.3 A-scans on sample back-wall

This section presents A-scan results for various points on the plastic back-wall, considering the

horizontal crack and vertical slot defect types. Details regarding defect locations, aluminum strip

positions, and other parameters are provided in Table 10.1.

Table 10.1 Model parameters with defect dimensions

Parameter

Horizontal crack width

Horizontal crack height

Vertical slot width

Vertical slot height

Value

4 mm

1 mm

2 mm

4 mm

Horizontal crack defect location (x-coordinate)

73 to 77 mm

Vertical slot defect location (x-coordinate)

74 to 76 mm

Aluminum strip location (x-coordinate)

70 to 80 mm

Magnet location on left (x-coordinate)

53.35 to 66.05 mm

Magnet location on right (x-coordinate)

84.35 to 97.05 mm

Magnet width

Magnet height

Aluminum strip width

Aluminum strip height

12.7 mm

25.4 mm

10 mm

0.254 mm

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Figure 10.13 presents the outcomes of this investigation for the horizontal crack defect. Dis-

placement A-scans on the plastic back-wall (for with and without defect) are acquired at intervals

of 0.25 mm, ranging from 30 mm to 120 mm. Subsequently, Hilbert magnitudes are extracted from

the displacement A-scans. The earlier discussions emphasized that mode 1 is particularly sensitive

to horizontal dimension (width) of the defect. Therefore, the Hilbert magnitudes of mode 1 are the

focus of consideration in this study for the horizontal crack-type defect.

Figure 10.13 A-scan results for a Horizontal crack defect

Key observations from the results in Figure 10.13 are:

1. The beam profile in the absence of a defect exhibits a Gaussian shape, spanning from 70 to

80 mm, coinciding with the location of the source (Aluminum strip).

2. The signal amplitude is diminished in the presence of a defect when compared to the scenario

without any defect.

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3. The beam profile in the presence of a defect exhibits multiple peaks, particularly in the region

of the defect and source. The dominant one here is between 73 to 77 mm, which coincides

with the location of defect.

4. A prominent peak is observed at the center-line of both the source and the defect, precisely

at 75 mm. Additionally, peaks are evident at the edges of the defect, specifically at 73 mm

and 77 mm.

5. The next set of dominant peaks are occurring at 70 mm and 80 mm, which coincide with the

location of aluminum strip (source).

6. From all the above observations, it can be concluded the embedded EMAT is able to detect

the horizontal crack type defect (located between 73 to 77 mm as indicated in Table 10.1).

Figure 10.14 A-scan results for a Vertical slot defect

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Figure 10.14 presents the outcomes of a similar investigation for the vertical slot type defect.

Displacement A-scans on the plastic back-wall (for with and without defect) are again acquired

at intervals of 0.25 mm, ranging from 30 mm to 120 mm. Subsequently, Hilbert magnitudes are

extracted from the displacement A-scans. The earlier discussions emphasized that mode 2 is more

sensitive to vertical dimensions (height) of the defects. Therefore, the Hilbert magnitudes of mode

2 are the focus of consideration in this study for the vertical slot type defect. The dominant peak

for the signal with defect is at the center-line of the defect, i.e., at 75mm. It can observed that the

beam profile (for the signal with defect) coincides with the defect location.

Conclusively, the findings from the damage detection study indicate that mode 1 is more

sensitive to the horizontal dimension (width) of the defect, while mode 2 demonstrates greater

sensitivity to the vertical dimension (height) of the defect. Given the availability of both mode

1 and a coupled mode (mode 2), the embedded EMAT emerges as a valuable tool for advanced

nondestructive evaluation in structural health monitoring.

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CHAPTER 11

CONCLUSIONS AND FUTURE WORK

The numerical model for an Electromagnetic Acoustic Transducer (EMAT) tailored for inspecting

non-conductive samples is developed using COMSOL. Two distinct approaches, namely direct

excitation and non-contact induced excitation, are systematically explored. The simulation results

affirm the propagation of an elastic wave within the non-conductive sample for both approaches. The

numerical findings reveal the presence of two modes in the displacement A-scans: the longitudinal

mode and a coupled mode.

An in-depth analysis of the influence of aluminum strip geometry on both the Lorentz force

in aluminum strip and displacement in plastic is conducted, yielding pertinent numerical results.

Notably, a reduction in height of the aluminum strip corresponds to an increased displacement at the

back-wall of plastic, while an increase in the aluminum strip width is correlated with an enhanced

displacement at the plastic back-wall. The influence of skin effect (in copper patch and aluminum

strip) on displacement in plastic is also explored and presented as part of this research work.

The limitation of the direct excitation configuration, rooted in its reliance on contact and

contradicting the non-contact nature of EMATs, is addressed through the extension of the proposed

approach to a novel non-contact induced excitation configuration – the embedded EMAT.

Moreover, the simulations involving defects in the embedded EMAT highlight the robustness

of this non-contact NDE technique for efficient damage detection. Furthermore, the embedded

EMAT technique demonstrates potential for detecting not only horizontal defects but also vertical

slot-type defects. This capability is attributed to the coupled mode, as evident in the numerical

simulation results. In conclusion, the outcomes from the damage detection study emphasize that

mode 1 exhibits higher sensitivity to the horizontal dimension of the defect, while mode 2 displays

greater sensitivity to the vertical dimension of the defect.

As part of future work, delving into the application of 3D printing techniques for the fabrication

of embedded EMATs emerges as a promising avenue. Such an exploration extends beyond conven-

tional manufacturing approaches, offering opportunities to optimize the performance and efficiency

125

of embedded EMATs through innovative design considerations. Additionally, the investigation of

coil and magnet configurations, specifically tailored for flux focusing to enhance the x-component

of magnetic flux density within copper, holds substantial potential. This line of inquiry aims to

further enhance the efficacy of EMAT systems, contributing to advancements in non-destructive

evaluation techniques for damage detection and structural health monitoring.

126

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