guided elastic waves in structures with an arbitrary …

The Pennsylvania State University

The Graduate School

Department of Engineering Science and Mechanics

GUIDED ELASTIC WAVES IN STRUCTURES

WITH AN ARBITRARY CROSS-SECTION

A Thesis in

Engineering Science and Mechanics

by

Chong Myoung Lee

© 2006 Chong Myoung Lee

Submitted in Partial Fulfillment of the Requirements

for the Degree of

Doctor of Philosophy

May 2006

The thesis of Chong Myoung Lee was reviewed and approved* by the following:

Joseph L. Rose Paul Morrow Professor of Engineering Science and Mechanics Thesis Advisor Chair of Committee

Bernhard R. Tittmann Schell Professor of Engineering Science and Mechanics

Eduard S. Ventsel Professor of Engineering Science and Mechanics

Albert E. Segall Associate Professor of Engineering Science and Mechanics

Sunil Sinha Assistant Professor of Civil and Environmental Engineering

Judith A. Todd Professor of Engineering Science and Mechanics P. B. Breneman Department Head Chair Department of Engineering Science and Mechanics

*Signatures are on file in the Graduate School

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ABSTRACT

A train is one of the oldest and most important transportation methods for moving

people and goods. A train accident can causes serious casualties and property damage.

Many factors could lead to a train disaster and the defects in rail are one of the major

problems. Detection of defects and proper maintenance action for a rail is therefore

essential.

There are two kinds of typical defects in a rail head. They are shelling and

transverse defects. Shelling is a horizontal plane defect generated by the sliding and/or

rolling the wheel over the rail from shear reversal and is usually located just below the

top surface of the rail. The transverse defects are usually generated and grown inside the

rail head from the shelling region down into the head. Shelling is not fatal but transverse

defects are. Conventional ultrasonic tests (the normal incident technique and the oblique

incident technique) have difficulties in detecting the transverse defects under the shelling,

because most of the ultrasonic energy is reflected from the shelling. For this reason, the

guided wave ultrasonic technique is potentially a suitable method for detecting defects

under the shelling. The cross-sectional area of the shelling is much smaller than that of

the transverse defects in the guided wave propagation direction.

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The purpose of this study is therefore to find an appropriate guided wave mode

and frequency for the detection of a transverse defect under the shelling. The phase

velocity and group velocity dispersion curves are calculated numerically using a semi-

analytical finite element method (SAFE). From the phase velocity dispersion curves, the

spacing of the elements in an electromagnetic acoustic transducer (EMAT), an important

feature in EMAT design, is determined to generate the appropriate guided waves for

reliable defect detection. Characteristics of the guided wave propagation is also explored

at various points in the phase velocity dispersion curves using ABAQUS/Explicit, a

commercially available finite element method (FEM) package with a simulation of a

Lamb type EMAT. Finally, the aspect of the wave scattering of guided waves from

several types of defects along with the shelling located in the rail head is examined.

This research provides a new modeling technique to simulate the EMAT loading

and can suggest guide lines for a new inspection technique for finding defects in the rail

head under shelling using EMATs. Furthermore, the research area can be extended to a

study of various types of defects, different location of the defects, different loading

positions, various welding zones, and overall changes in rail boundary conditions.

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TABLE OF CONTENTS

LIST OF FIGURES .....................................................................................................viii

LIST OF TABLES.......................................................................................................xviii

ACKNOWLEDGEMENTS.........................................................................................xix

Chapter 1 INTRODUCTION ……………………………………………………………. 1

1.1 THE PRACTICAL IMPORTANCE OF NDT ……………………………………… 1

1.2 PROBLEM STATEMENT ……………………………………………………….…. 3

1.3 LITERATURE SURVEY ………………………………………………………...…. 5

1.3.1 STUDIES ON GUIDED WAVES …………………………………………...….. 5

1.3.2 STUDIES ON NUMERICAL METHODS …………………………………...… 8

1.4 SUMMARY ……………………………………………………………………...… 11

Chapter 2 THE SEMI-ANALYTICAL FINITE ELEMENT TECHNIQUE ………….. 12

2.1 INTRODUCTION …………………………………………………………………. 12

2.2 THEORY …………………………………………………………………………... 13

2.2.1 GOVERNING EQUATION …………………………………………………… 13

2.2.2 PHASE VELOCITY, GROUP VELOCITY, AND WAVE STRUCTURE …... 19

2.3 NUMERICAL RESULTS AND DISCUSSION ON THE SAFE TECHNIQUE …. 22

2.3.1 NUMERICAL RESULTS OF A STEEL PLATE ……………………………... 22

2.3.2 NUMERICAL RESULTS FOR A RAIL ……………………………………… 30

2.4 SUMMARY ………………………………………………………………………... 34

Chapter 3 FINITE ELEMENT METHOD FOR GUIDED WAVES ………………….. 35

3.1 INTRODUCTION …………………………………………………………………. 35

3.2 ABAQUS/Explicit STRATEGY …………………………………………………... 36

3.3 THE BOUNDARY VALUE PROBLEM ………………………………………….. 39

3.4 NUMERICAL MODELING OF THE GUIDED WAVE PROPAGATION ……… 43

3.4.1 MODEL ACCURACY CONSIDERATION …………………………………... 43

3.4.2 GUIDED WAVE PROPAGATION …………………………………………… 52

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3.5 SUMMARY ………………………………………………………………………... 62

Chapter 4 THREE DIMENSIONAL WAVE SCATTERING ………………………… 64

4.1 INTRODUCTION …………………………………………………………………. 64

4.2 WAVE SCATTERING FROM INTERNAL NOTCHS …………………………... 66

4.3 WAVE SCATTERING FROM INTERNALLY DRILLED HOLES ……………... 79

4.4 WAVE SCATTERING FROM CONTOUR NOTCHS …………………………… 84

4.5 WAVE SCATTERING FROM INTERNAL TRANSVERSE DEFECTS ………... 88

4.6 LONG RANGE WAVE SCATTERING FROM INTERNAL TRANSVERSE

DEFECTS ……………………………………………………………………………… 92

4.7 THE EFFECT OF THE SHELLING ………………………………………………. 94

4.8 WAVE SCATTERING AT LOWER FREQUENCIES …………………………… 99

4.9 SUMMARY ………………………………………………………………………. 104

Chapter 5 EXPERIMENTAL VALIDATION ……………………………………….. 106

5.1 INTRODUCTION ………………………………………………………………... 106

5.2 ELECTROMAGNETIC ACOUSTIC TRANSDUCER (EMAT) ………………... 107

5.3 LAB TEST ………………………………………………………………………... 109

5.3.1 DISPLACEMENT PROFILES OF THE GUIDED WAVES ………………... 109

5.3.2 A HOLE IN A CLEAN RAIL HEAD SURFACE …………………………… 110

5.3.3 A NOTCH IN A CLEAN RAIL HEAD SURFACE …………………………. 116

5.3.4 A HOLE IN A ROUGH RAIL HEAD SURFACE …………………………... 120

5.3.5 SIMULATION EXPERIMENT FOR TRANSVERSE DEFECT AND HELLING

…………………………………………………………………………………………. 121

5.3.6 BOLT HOLES ………………………………………………………………... 129

5.3.7 DISPERSIVE PORPERTY …………………………………………………... 130

5.4 FIELD TEST ……………………………………………………………………… 132

5.5 SUMMARY ………………………………………………………………………. 139

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Chapter 6 CONCLUDING REMARKS ……………………………………………… 143

6.1 CONCLUDING REMARKS ……………………………………………………... 143

6.2 CONTRIBUTIONS ………………………………………………………………. 146

6.3 FUTURE WORK …………………………………………………………………. 148

REFERENCES ……………………………………………………………………….. 149

Appendix A Nontechnical Abstract …………………………………………………... 160

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LIST OF FIGURES

Figure 2-1 Rectangular coordinate system .................................................................14

Figure 2-2 Dimensional meshes of a steel plate (1mm x 10mm) ...............................24

Figure 2-3 Dispersion curves using Navier’s equation...............................................25 (a) Phase velocity dispersion curves (b) Group velocity dispersion curves

Figure 2-4 Dispersion curves using SAFE technique .................................................26 (a) Phase velocity dispersion curves (b) Group velocity dispersion curves

Figure 2-5 Displacement of S0 mode at fd=2.0 MHz mm .........................................27 (a) Displacement of S0 mode for a steel plate using Navier’s equation (b) Displacement of S0 mode for a steel plate using SAFE technique

Figure 2-6 Displacement of A1 mode at fd=2.5 MHz mm.........................................28 (a) Displacement of A1 mode for a steel plate using Navier’s equation (b) Displacement of A1 mode for a steel bar using SAFE technique

Figure 2-7 Displacement of S1 mode at fd=3.5 MHz mm .........................................29 (a) Displacement of S1 mode for a steel plate using Navier’s equation (b) Displacement of S1 mode for a steel bar using SAFE technique

Figure 2-8 Meshes and nodes in a SAFE model of a rail ...........................................31

Figure 2-9 Phase velocity dispersion curves of a rail .................................................32

Figure 2-10 Group velocity dispersion curves of a rail ..............................................33

Figure 3-1 Numerical model of a rail with boundary and loading conditions............40

Figure 3-2 EMAT loading area in the numerical model.............................................40

Figure 3-3 Phase velocity dispersion curves and activation lines...............................41

Figure 3-4 Input signal for 60kHz ..............................................................................42

Figure 3-5 Wave propagation for 2 elements per wave length...................................44 (a) t = 0.05 msec (b) t = 0.1 msec (c) t = 0.15 msec (d) t = 0.2 msec


Figure 3-7 Wave propagation for 6 elements per wave..............................................46 (a) t = 0.05 msec (b) t = 0.1 msec (c) t = 0.15 msec (d) t = 0.2 msec

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Figure 3-9 Wave propagation for 10 elements per wave length.................................48 (a) t = 0.05 msec (b) t = 0.1 msec (c) t = 0.15 msec (d) t = 0.2 msec

Figure 3-10 Wave propagation for 15 elements per wave length...............................49 (a) t = 0.05 msec (b) t = 0.1 msec (c) t = 0.15 msec (d) t = 0.2 msec

Figure 3-11 Displacement of S0 mode at fd=2.0 MHz mm (analytical solution) .....50

Figure 3-12 Displacement at fd=2.0 MHz mm (FEM solution) ...............................51 (a) out of plane displacement (b) in plane displacement

Figure 3-13 Points of interest on the phase velocity dispersion curve ......................53

Figure 3-14 Wave propagation patterns at 30kHz ......................................................55 (a) 30-1, 0.300msec (1.33m) (b) 30-2, 0.826msec (3.01m) (c) 30-3, 1.275 msec (4.52m) (d)30-4, 1.275 msec (6.05m)

Figure 3-15 Wave propagation patterns at 60kHz ......................................................56 (a) 60-1, 0.225 msec (0.84m) (b) 60-2, 0.413 msec (1.61m) (c) 60-3, 0.675 msec (2.55m) (d) 60-4, 1.501 msec (3.33m)

Figure 3-16 Wave propagation patterns at 100kHz ....................................................57 (a) 100-1, 0.150 msec (0.57m) (b)100-2, 0.300 msec (1.09m) (c)100-3, 0.413 msec (1.61m) (d)100-4, 0.563 msec (2.13m)



Figure 3-19 Wave propagation patterns at 200kHz ....................................................60 (a)200-1, 0.090 msec (0.32m) (b)200-2, 0.113 msec (0.55m) (c)200-3, 0.188 msec (0.79m) (d)200-4, 0.248 msec (1.03m)

Figure 3-20 Wave structures at different frequencies.................................................61 (a) 30kHz (b)60kHz (c)100kHz (d)135kHz (e)175kHz (f)200kHz

Figure 4-1 Cross-section of the rail with vertical defects ...........................................66 (a)no defect, (b)10mm defect, (c)20mm defect, (d)30mm defect, (e)40mm defect

Figure 4-2 Finite element model of a rail for the 60kHz guided wave.......................67

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Figure 4-3 EMAT loading simulation (red arrows indicate forcing function direction)...............................................................................................................68

Figure 4-4 Meshes around the vertical defect.............................................................68

Figure 6-1 175kHz guided wave scattering from a 30mm vertical defect showing a guided wave generation, a propagation, a scattering, and a reflected wave and a transmitted wave .........................................................................................71

Figure 4-6 Energy distribution by 175kHz excitation at a cross-sectional area at 3 positions and different time (See Figure 4-5), showing the energy distribution over a cross-section of a rail..............................................................72

Figure 4-7 Vertical displacement of the reflected waves and the transmitted waves at 185mm from the defect (60kHz) showing that the reflected wave from the bigger defect has the larger displacement and the transmitted wave from the smaller defect has the larger displacement. ..........................................................74

Figure 4-8 Vertical displacement of the reflected waves and the transmitted waves at 110mm from the defect (175kHz) showing that the reflected wave from the 40mm defect seems to have the largest displacement and the transmitted wave from the 40mm defect has the smallest displacement..............75

Figure 4-9 Vertical displacement of the reflected waves and the transmitted waves at 50mm from the defect (315kHz) showing that there is big difference between the reflected waves and the no defect propagating waves. The transmitted wave from the 40mm defect has the smallest displacement.......76

Figure 4-10 Absolute value of vertical displacement of the reflected and transmitted wave through the vertical defect at several points for 60kHz guided wave showing magnitudes of transmitted waves between 150mm and 450mm are monotonically decreased with the crack depth..................................77

Figure 4-11 Absolute value of vertical displacement of the reflected and transmitted wave through the vertical defect at several points for the 175kHz guided wave showing that the magnitudes of the transmitted waves between 100mm and 200mm shows a large difference between defects and no defect .....77

Figure 4-12 Absolute value of vertical displacement of the reflected and transmitted wave through the vertical defect at several points for 315kHz guided wave showing a big difference in the magnitude of |U2| between defects and no defect ............................................................................................78

(a) Reflected wave (b)Transmitted wave

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Figure 4-13 Cross-section of the rail with hole defects ..............................................79 (a) hole 1 (b) hole 2 (c) hole 3

Figure 4-14 Meshes around the hole defect................................................................80

Figure 4-15 Absolute value of the vertical displacement of the reflected and transmitted wave across the cylindrical defect at several points for the 60kHz guided wave showing that the transmitted signal through the hole 1 has the second biggest amplitude because the hole 1 is located at the lowest position among the hole defects and also the transmitted signal through the hole 2 has the smallest amplitude because the hole 2 is the biggest defect. .........................81


Figure 4-16 Absolute value of the vertical displacement of the reflected and transmitted wave across the cylindrical defect at several points for the 100kHz guided wave showing that there is a big difference in amplitude of the transmitted wave between no defect and defects............................................82


Figure 4-17 Absolute value of the vertical displacement of the reflected and transmitted waves across the cylindrical defect at several points for the 185kHz guided wave showing the results with no sensitivity to defect size........82


Figure 4-18 Absolute value of the vertical displacement of the reflected and transmitted waves across the cylindrical defect at several points for the 280kHz guided wave showing the potential in detecting the defects. ..................83


Figure 6-2 Cross-section of the rail with contour notch .............................................85 (a) notch 1 (b) notch 2 (c) notch 3

Figure 4-20 Meshes around the hole defect................................................................85

Figure 4-21 Absolute value of the vertical displacement of the reflected and transmitted wave across the contour notch at several points for the 60kHz guided wave showing that it is difficult to classify no defect and notches...........86


Figure 4-22 Absolute value of the vertical displacement of the reflected and transmitted wave across the contour notch at several points for the 100kHz guided wave showing a potential to discern the defects between 200mm and 300mm. .................................................................................................................86


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Figure 4-23 Absolute value of the vertical displacement of the reflected and transmitted wave across the contour notch at several points for the 185kHz guided wave showing that it is difficult to find defects........................................87


Figure 4-24 Absolute value of the vertical displacement of the reflected and transmitted wave across the contour notch at several points for the 280kHz guided wave showing that there is a big difference in amplitude of displacement of the reflected waves between defects and no defect case. ...........87


Figure 6-3 Cross-section of the rail with a TD (transverse defect).............................89 (a) TD1 (b) TD2 (c) TD3

Figure 4-26 Absolute value of the vertical displacement of the reflected and transmitted waves across the transverse defect at several points for the 60kHz guided wave showing little potential to discern transverse defects. ....................89


Figure 4-27 Absolute value of the vertical displacement of the reflected and transmitted waves across the transverse defect at several points for the 100kHz guided wave showing that the reflected waves have a potential of classifing the transverse defects............................................................................90


Figure 4-28 Absolute value of the vertical displacement of the reflected and transmitted waves across the transverse defect at several points for the 185kHz guided wave showing high potential to classify defects with transmitted waves. ................................................................................................90


Figure 4-29 Absolute value of the vertical displacement of the reflected and transmitted waves across the transverse defect at several points for a 280kHz guided wave showing the potential of detecting transverse defects. ....................91


Figure 4-30 Meshes around the circular transverse defect located at the center of rail head for a symmetric half rail model..............................................................92

Figure 4-31 Amplitude ratio for a rail with a circular transverse defect located at the center of the rail head showing a monotonic decrease with distance .............93

Figure 4-32 Cross-section of the rail with shelling and various defects.....................94 (a):shelling, (b):10mm defect with shelling, (c):20mm defect with shelling, (d):30mm defect with shelling, (e):40mm defect with shelling

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Figure 4-33 Cross-section of shelling along the longitudinal direction of the rail .....95

Figure 4-34 Top view of the shelling..........................................................................95

Figure 4-35 The numerical model of the rail with transverse crack and shelling.......96

Figure 4-36 Absolute value of the vertical displacement of the reflected and transmitted wave across the vertical defect with the shelling at several points for the 60kHz guided wave showing that magnitudes of the transmitted waves between 150mm and 450mm are monotonically decreasing with the crack depth .....................................................................................................................97


Figure 4-37 Absolute value of the vertical displacement of the reflected and transmitted wave across the vertical defect with the shelling at several points for the 175kHz guided wave showing no big difference between the defects with shelling and no defect with shelling .............................................................98


Figure 4-38 Absolute value of the vertical displacement of the reflected and transmitted wave across the vertical defect with the shelling at several points for the 315kHz guided wave showing a big difference in the magnitude of |U2| between defects with shelling and no defect with shelling ...........................98


Figure 4-39 Absolute value of vertical displacement of the reflected and transmitted wave for a vertical defect with/without the shelling at several points for 30kHz guided wave showing some difference between no defect without shelling and defects without shelling. .....................................................101

(a) Reflected wave without shelling (b) Reflected wave with shelling (c) Transmitted wave without shelling (d) Transmitted wave with shelling

Figure 4-40 Absolute value of vertical displacement of the reflected and transmitted wave for a vertical defect with/without the shelling at several points for 45kHz guided wave showing that the magnitudes are monotonically decreased with crack size. ............................................................102


Figure 4-41 Absolute value of vertical displacement of the reflected and transmitted wave for a vertical defect with/without the shelling at several points for 60kHz guided wave showing that the magnitudes are monotonically decreased with the crack size........................................................103


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Figure 5-1 Schematic of the directions of the Lorentz force ......................................108

Figure 5-2 Structure of EMATs..................................................................................108 (a) Lamb wave EMAT (b) SH wave EMAT

Figure 5-3 Displacement profile of guided waves.......................................................110

Figure 5-4 A Photograph of a hole in a clean rail........................................................112

Figure 5-5 The position of a hole and EMATs ............................................................112

Figure 5-6 RF wave form of a reflected wave from a hole in a clean rail for a 100kHz guided wave at a distance of 0.45m showing the direct signal, hole, and rail end. ..........................................................................................................113

Figure 5-7 Amplitude ratio for a rail with a clean surface of a rail head and a hole showing that at a distance less than 1m, 60kHz and 100kHz guided waves have more potential for detecting the hole ...........................................................113

Figure 5-8 Comparison of amplitude ratios of experiment and FEM results for a hole in a clean rail head surface for 60kHz showing a difference in the ratio level (Note that transmitter distance was approximately 600mm). ......................114

Figure 5-9 Comparison of amplitude ratios of experiment and FEM results for a hole in a clean rail head surface for 100kHz showing a similar amplitude ratio level, especially at shorter distances (Note that transmitter distance was approximately 600mm).........................................................................................115

Figure 5-10 Comparison of amplitude ratios of experiment and FEM results for a hole in a clean rail head surface for 185kHz showing a similar amplitude ratio level (Note that transmitter distance was approximately 600mm). ......................115

Figure 5-11 Comparison of amplitude ratios of experiment and FEM results for a hole in a clean rail head surface for 280kHz showing a similar amplitude ratio level (Note that transmitter distance was approximately 600mm). ......................116

Figure 5-12 A Photograph of a notch in a clean rail...................................................117

Figure 5-13 Amplitude ratio for a rail head with a clean surface and a notch showing that guided waves for 280kHz have an outstanding potential for detecting the notch................................................................................................117

Figure 5-14 Comparison of amplitude ratio of experiment and FEM results for a notch in a clean rail head surface for 60kHz showing a similar amplitude ratio level (Note that transmitter distance was approximately 600mm). ......................118

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Figure 5-15 Comparison of amplitude ratio of experiment and FEM results for a notch in a clean rail head surface for 100kHz showing a similar amplitude ratio level (Note that transmitter distance was approximately 600mm)...............118

Figure 5-16 Comparison of amplitude ratio of experiment and FEM results for a notch in a clean rail head surface for 185kHz showing a similar amplitude ratio level (Note that transmitter distance was approximately 600mm)...............119

Figure 5-17 Comparison of amplitude ratio of experiment and FEM results for a notch in a clean rail head surface for 280kHz a showing similar amplitude ratio level (Note that transmitter distance was approximately 600mm)...............119

Figure 5-18 A Photograph of a hole in a rough rail....................................................120

Figure 5-19 Amplitude ratio for a rail with a rough rail head surface and a hole showing that guided waves for 60kHz and 100kHz can find the hole, 185kHz is marginal, and the 280kHz guided wave cannot see the hole since a collection of small echoes from the rough surface does not allow any energy to reach the defect .................................................................................................121

Figure 5-20 A Photograph of a welded Notch .........................................................122

Figure 5-21 Amplitude ratios for a rail with a welded notch showing that guided waves for four frequencies (60, 100, 185, and 280kHz) can find the welded notch. ....................................................................................................................123

Figure 5-22 A Photograph of a “ssd (simulated surface damage or shelling)” .........123

Figure 5-23 The reflected signals from a “ssd” for four frequencies (60, 100, 185, and 280kHz) showing inability of 60kHz, 100kHz, and 185kHz at distance greater than 1.2m of detecting shelling simulation via “ssd” on top surface .......125

(a) 60kHz (b) 100kHz (c) 185kHz (d) 280kHz

Figure 5-24 A photograph of a welded notch under a “ssd” simulation surface roughness and a shelling.......................................................................................126

Figure 5-25 Amplitude ratio for a rail with a welded notch without a shelling and with a shelling for 60kHz showing no significant differences in average amplitude ratios between with a “ssd” and without “ssd”. ...................................126

Figure 5-26 Amplitude ratio for a rail with a welded notch without a shelling and with a shelling for 100kHz showing a similar sensitivity showing no significant differences in average amplitude ratios between that with a “ssd” and that without “ssd”...........................................................................................127

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Figure 5-27 Amplitude ratio for a rail with a welded notch without a shelling and with a shelling for 185kHz showing a difference in average amplitude ratio begins to appear after 1m. ............................................................................127

Figure 5-28 Amplitude ratio for a rail with a welded notch without a shelling and with a shelling for 280kHz showing a significantly different sensitivity for an entire range.................................................................................................128

Figure 5-29 A photograph of bolt holes......................................................................129

Figure 5-30 Amplitude ratio for a rail with bolt holes showing that guided waves for four frequencies (60, 100, 185, and 280kHz) cannot find bolt holes..............130

Figure 5-31 Dispersive characteristic of 185kHz and 280kHz guided waves showing that the 185kHz guided waves are more dispersive then the 280kHz guided waves. .......................................................................................................131

(a) Pulse duration ratio (b) Amplitude ratio

Figure 5-32 A Photograph of a notch ..........................................................................133

Figure 5-33 A Photograph of a “ssd (simulated surface damage or shelling)” ...........133

Figure 5-34 A Photograph of a notch under a “ssd”...................................................134

Figure 5-35 A Photograph of a shelling.......................................................................134

Figure 5-36 A photograph of a transverse defect (as an example) ..............................135

Figure 5-37 Reflected signal from notch under “ssd” showing direct signal, “ssd”, and noise ...............................................................................................................135

(a) 185kHz (b) 280kHz

Figure 5-38 Amplitude ratio for a notch showing that 185kHz guided waves are more sensitive to the notch than the 280kHz guided wave since wave structure is deeper into to rail head.......................................................................136

Figure 5-39 Amplitude ratios for “ssd” shown sensitive to both frequencies 185kHz and 280kHz, except for large distances away from the defect (a 100kHz sensor would be less sensitive to “ssd”, but unfortunately not available)...............................................................................................................136

Figure 5-40 Amplitude ratio for a notch under “ssd” showing that in this case both seem to see the notch, but both contains possible “ssd” echoes. Unfortunately, a 60 or 100kHz sensor was not available at Pueblo, which we feel would produce a much better result, since it would definitely not see the “ssd”......................................................................................................................137

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Figure 5-41 Amplitude ratio for a transverse defect showing that 185kHz guided wave might see the transverse defect (but in reality not sure since it could be seeing the shelling again pointing to the need of a lower frequency transducer). ...........................................................................................................137

Figure 5-42 Amplitude ratio for a shelling defect showing that both frequencies are sensitive to the shelling. (Probably a 100kHz sensor wouldn’t see the shelling) ................................................................................................................138

Figure 5-43 Amplitude ratio for a transverse defect under a shelling showing that the sensor might be OK. (But 100kHz would be clearer).....................................138

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LIST OF TABLES

Table 2-1 Material properties of a steel plate ............................................................24

Table 4-1 Length of the numerical modeling of a rail ................................................67

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ACKNOWLEDGEMENTS

The journey undertaken through this study was not accomplished alone.

Studying engineering mechanics at Penn State University was an excellent opportunity

and, at the same time, a kind of challenge for me. Without ceaseless support and

encouragement of many people, I would not build my own small cottage here. I would

like to express my sincere gratitude to my adviser, Dr. Joseph L. Rose for invaluable

knowledge, guidance and continual encouragement. Through the thoughtful mentorship

of Dr. Rose, I can make a wonderful journey at PSU.

I will always be grateful to Dr. Younho Cho and Dr. Kang Yong Lee in Korea

whose training in engineering mechanics was the basis of studying.

Last but not least, I am deeply indebted to my family for their unfailing love and

selfless support over the years. My spouse, Sung Hee Choi, daughter, Sunoo, and my

parents, without their ceaseless love and support, I would not exist here as what I am.

Especially, I cannot express my thanks to my parents with a few words. They have always

prayed for me as well as given their endless trust on me. Above all, my all gratitude belongs to

God. Praise be to the Lord of Jesus Christ for His rich blessings throughout my study. He

is the way, the truth and the life!

Chapter 1

INTRODUCTION

1.1 THE PRACTICAL IMPORTANCE OF NDT

Non-destructive testing methods are chosen for particular application areas

because of certain advantages and disadvantages of the techniques. Radiographic testing

uses x-ray or γ-ray to detect defects in a material; however the examined material volume

is relatively small. The acoustic emission technique is applied to locate the source of

elastic energy which is emitted when a crack propagates. Still this acoustic emission

technique is passive, so the inspection should be performed while a component is in

service. The eddy current technique using electromagnetic waves is used for the detection

of surface or sub-surface defects. The ultrasonic technique using bulk waves finds defects

by detecting the signals reflected from the defects.

These NDE techniques are relatively sensitive to defects; however, test efficiency

is also an important factor from an economic viewpoint. The eddy current technique and

the ultrasonic technique using bulk waves examine the structures on a point by point

basis. Therefore, the procedure is tedious and takes too much time for large area

2

inspection. Ultrasonic testing using guided waves is very promising because guided

waves can propagate over long distances along the structure with reasonable sensitivity.

The defects are found by detecting pulse echo reflected waves from the defects. The

sensitivity can be improved by proper guided wave mode and frequency selection.

3

1.2 PROBLEM STATEMENT

A train is one of the most important transportation means for moving people and

goods. A train accident can causes serious casualties and property damage. Many factors

could lead to a train disaster and the defects in rail are one of the major problems.

Detection of defects and proper maintenance action for a rail is therefore essential.

Of many defect possibilities in a rail, two types are considered here. They are

shelling and transverse defects. The shelling located below the top surface of the rail head

is generated by the sliding and/or rolling of the wheel via Hertzian contact loading which

leads to shelling defects just below the rail upper surface. Transverse defects are usually

generated and grown inside a rail head and often start at the shelling region. Shelling is

not fatal, but the transverse defects can be. The normal incident ultrasonic technique and

the oblique incident technique have difficulties in detecting the transverse defects located

under the shelling because most of the ultrasonic energy is reflected from the shelling.

For this reason, the guided wave ultrasonic technique is suitable for detecting this kind of

defect. Since the cross-sectional area of the shelling is much smaller then that of the

transverse defects in the guided wave propagation direction; detection becomes possible

with guided waves.

For reliable inspection of rail, the selection of an appropriate mode and frequency

is a primary requirement and this choice is based on the wave structure of the guided

4

wave in the rail. In this study, details of the wave structure of the guided waves in a rail

are studied. The propagation characteristics and the scattering aspects for various kinds of

defects are also examined. For this work, ABACUS/Explicit, a commercial finite element

method package is employed to solve the boundary value problem with a simulated

loading of an electromagnetic acoustic transducer (EMAT). For a verification of

numerical experiments, laboratory experiments are carried out. The objective of this work

is to be able to use theoretical modeling analysis to assist in the sensor design process

that would be used in a real vehicle to travel along the tracks while inspecting rail for

transverse cracks.

5

1.3 LITERATURE SURVEY

1.3.1 STUDIES ON GUIDED WAVES

The study of elastic guided waves has a history of over one century. Though long,

it was not commonly used because of its complicated wave behavior and understanding.

Rayleigh presented the surface wave in an infinite elastic media in 1885 [Rayleigh 1885]

and studied the free vibration in an infinite plate in 1889 [Rayleigh 1889]. After

introducing a new field of guided waves, Lamb extended Rayleigh's vibration study to

forced vibration in an infinite plate [Lamb 1889]. In 1916, Worlton experimentally

confirmed the existence of a Lamb wave [Worlton 1916].

Mindlin and Fox calculated the exact solution of the equations of elasticity and

defined the wave modes in a rectangular bar [Mindlin and Fox 1960] and Nigro obtained

the approximate solution and dispersion curves of longitudinal, flexural, and torsional

modes for the rectangular bar [Nigro 1966]. Hertelendy developed a variational equations

of motion for linear elastic bars of rectangular cross section [Hertelendy 1968]. Fraser

developed the method of collocation and calculated the dispersion curves for longitudinal

waves for a square bar, and subsequently verified them with experiments [Fraser 1969]

[Fraser 1970]. The dispersion curves of a cylinder were numerically obtained by

Zemanek in 1972 [Zemanek 1972]. Solie and Auld studied the characteristics the elastic

waves in an anisotropic plate [Solie and Auld 1972]. Sawaguchi and Toda examined

6

leaky Lamb wave propagation with a water loaded thin plate [Sawaguche and Toda

1993]. In 1993, Guzhev inspected the phase velocity and energy distribution of Stoneley

waves at a solid-liquid interface [Guzhev 1994]. The characteristic of many kinds of

guided waves had been developed by numerous researchers [Viktorov 1967] [Achenbach

1984] [Auld 1990] [Rose 1999].

In practical applications, structures can be divided into two major groups. One of

the groups are plates. Most plates are such multi-layer structures as composite plates and

plates with coatings. Researchers started to explore the characteristics of guided waves in

a complex structure. Guided waves in a multi-layer structure was studied by Zhang et al.

[Zhang et al 1996] and Zhang [Zhang 1998]. Pan et al. studied the guided waves in a

multi-layer plate with viscous coating layer [Pan et al. 1999] and Rokhlin and Wang

examined guided waves in a composite plate [Rokhlim and Wang 2002]. Vashishth and

Khurana defined inhomogeneous waves in anisotropic porous layered medium

[Vashishth and Khurana 2002].

The other major group beyond plates is pipes. Longitudinal guided waves in a rod

were studied by Nagy [Nagy 1995]. Guided waves in a pipe were also examined by

Towfighi et al. [Towfighi et al 2002] and Towfighi and Kundu [Towfighi and Kundu

2003]. Guided waves in a composite pipe were studied by Rattanawangcharoen and Shah

[Rattanawangcharoen and Shah 1992]. Barshinger and Rose studied the guided wave

propagation in a pipe with a viscoelastic coating [Barshinger and Rose 2004].

7

The effort to find defects in structures has been made by numerous researchers

and engineers. Yang et al. found defects in multilayered plates [Yang et al. 1998] and

Cho monitored the thickness variation for thin films on a plate by observing the guided

wave mode conversion [Cho 2002]. Rose et al. inspected steam generator tubes [Rose et

al 1992] [Rose et al. 1994] and Shin et al. detected defects in power plant tubes [Shin et

al 1996].

Conventional joining methods were used to join such devices as bolts, screws,

rivets, and welds. However, with the development of adhesive materials, the bonding

process became a major joining method. The monitoring of an adhesive interface became

a significant concern. Pilarski and Rose monitored the interfacial weakness of a bonding

layer with transverse wave and oblique incident techniques [Pilarski and Rose 1988]. Mal

studied the elastic wave propagation in multilayered isotropic solids containing

imperfectly welded interfaces [Mal 1988]. Rose et al. examined a lap splice joint and a

tear strap in aging aircraft [Rose et al. 1995]. In 1997, Rose et al. studied titanium

diffusion bonding with guided waves [Rose et al. 1997].

Defect detection in a rail is a relatively difficult task because of the rail’s complex

geometry. Rose et al. presented a technique to identify broken rail [Rose et al 2002].

Scalea and McNamara used air-coupled transducers and structural vibrations for

longitudinal and transverse defect detection [Scalea and McNamara 2003]. Wilcox et al.

performed a numerical simulation and a experiment for transverse defect detection with a

50kHz ultrasonic transducer [Wilcox et al. 2003]. McNamara et al. adapted a pattern

8

recognition algorithm to classify transverse type defects [McNamara et al. 2004]. Bartoli

et al used a commercial finite element package for a transverse type defect with low

frequency over the range of 20-45kHz [Martoli et al. 2005]. Clark and Singh inspected

the thermite welds with cracks generated [Clark and Singh 2003]. Dixon et al used

EMATs with a frequency range of 150-200kHz to detect surface cracks [Dixon et al.

2004]. Buttle et al. measured residual stress which influences rolling contact fatigue

[Buttle et al. 2004].

1.3.2 STUDIES ON NUMERICAL METHODS

Though many researchers developed guided wave theory, there is still a limitation

in the calculation of guided wave scattering because of possible complex geometries. For

this reason, numerical analysis has been used to calculate the resulting ultrasonic

scattering field from a defect in a rail. The finite element method (FEM), the boundary

element method (BEM), and the semi-analytical finite element method (SAFE) are

commonly used in guided wave propagation and scattering problems.

9

The Finite Element Method (FEM), the most popular computational technique in

the engineering field, is also applied to ultrasonic scattering problems. Talbot and

Przemieniecki analyzed the dispersive characteristics of elastic guided waves of an

arbitrary cross-section with FEM [Talbot and Przemieniecki 1975] and Koshiba et al.

solved the SH mode propagation using FEM [Koshiba et al. 1981] [Koshiba et al. 1987].

Bouden and Datta calculated the scattering from the interfacial cracks in layered media

[Bouden andDatta 1991]. The characteristics of guided wave propagation and scattering

in a laminated isotropic circular cylinder are defined by Rattanawangcharoen and Shah

[Rattanawangcharoen and Shah 1992] and Rattanawangcharoen et al.

[Rattanawangcharoen et al. 1994]. Alleyne et al. calculated the reflection from the

circumferential notches using FEM [Alleyne et al. 1998] and Demma et al. studied the

reflection and transmission of a plate with a discontinuity [Demma et al. 2003]. Recently,

Peplow and Finnveden developed the super-spectral finite element method to calculate

the acoustical wave propagation in a nonuniform waveguide [Peplow and Finnveden

2004].

The FEM discretizes the whole domain with elements which leads to an increase

of memory capacity and computational time. For this reason, the BEM is often

considered since this technique only generates the element on the surface of the domain

and this greatly decreases of the number of elements and computational time. Wang and

Banerjee applied the BEM technique and solved the non-axisymmetric free vibration of

an axisymmetric solid [Wang and Banerjee 1989]. Cho and Rose studied the mode

conversion of guided waves at a free edge [Cho and Rose 1996]. Hirose and Yamano

10

calculated the displacements of a scattered field [Hirose and Yamano 1996]. Zhu and

Rose modeled a time-delay periodic transducer and experimentally verified the results

[Zhu and Rose 1999] and Cho estimated the thickness change by monitoring the mode

conversion [Cho 2000]. Niu and Dravinski solved the wave scattering from an arbitrary

shaped defect in 3 dimension using BEM [Niu and Dravinski 2003].

Though the Semi-Analytical Finite Element Method (SAFE) is limited to a plane

strain problem, SAFE is employed in some ultrasonic scattering problems. Talbot and

Przemieniecki analyzed the dispersive characteristics of elastic guided waves in an

arbitrary cross-section with SAFE [Talbot and Przemieniecki 1975]. Gavric calculated

the propagative and the evanescent waves in an arbitrary cross-section [Gavric 1995] and

Gry computed the dispersion curves and wave structure of a rail for 0-5kHz [Gry 1996].

Rattanawangcharoen et al. obtained the reflection and the transmission factors from the

jointed laminated cylinders [Rattanawangcharoen 1997] and Zhuang et al. calculated

wave structures of composite pipes [Zhuang et al. 1999]. The scattering field from

circumferential cracks in a steel and composite pipe is calculated by Bai et al. [Bai et al.

2001] [Bai et al. 2002]. Taweel et al. computed the dispersion curves of arbitrary cross-

section [Taweel et al. 2000]. Hayashi obtained the dispersion curves and wave structures

of a rail [Hayashi et al. 2003] [Hayashi et al. 2005].

11

1.4 SUMMARY

Because of the arbitrary shape of a rail, the characteristics of guided waves in a

rail are more complicated than in other simple wave guides such as plates and pipes. The

basic theory of the SAFE technique which is used to calculate the phase velocities, group

velocities and wave structures is introduced in chapter 2. The calculation results of simple

wave guides and a rail are presented.

In chapter 3, the simple strategy of the ABAQUS/Explicit program will be

explained. General statements of the guided wave scattering problem will also be shown.

Based on the phase velocity dispersion curves calculated in chapter 2, the

propagation characteristics of the guided waves generated in a rail will be explored in

chapter 4.

In chapter 5, by using the commercial FEM package, the scattering patterns from

planar and volumetric defects are studied. The effects of the shelling are also explored.

Finally, experimental validations and concluding remarks are presented in

chapters 6 and 7.

Chapter 2

THE SEMI-ANALYTICAL FINITE ELEMENT TECHNIQUE

2.1 INTRODUCTION

The finite element method (FEM) is one of the most well known numerical

computation techniques for solving a variety of engineering problems. The FEM

technique discretizes the entire domain with small elements and as the number of

elements is increased, longer computational times result with larger matrices to work

with. For this reason, many scientists and engineers have developed new methods to

decrease overall computational time. The Semi-Analytical Finite Element (SAFE)

technique is one of these methods.

The basic assumption of this SAFE technique is that the length of a waveguide problem

in propagation direction is much longer than the length of other directions. Once a wave

passes a vertical cross section of a bar-like structure, it propagates with time and spatial

harmonic function ( numberwaveke tkzi :,)( ω− ) along the wave guide. Therefore, it is not

necessary to discretize the entire domain with small elements. The elements are only

13

needed on the vertical cross-section of the structure. This means that a 3-dimensional

problem can be reduced to a 2-dimensional problem. By reducing the number of

elements and the dimension of the problem, the computational time can be decreased

tremendously.

The theory and its derivation, along with phase velocity, group velocity, and wave

structure aspects will be discussed. The numerical results of the SAFE technique will be

shown and compared with previous verified results using Navier’s equation and

Helmholtz decomposition [Rose 1999].

2.2 THEORY

2.2.1 GOVERNING EQUATION

To consider the theory of the SAFE technique, the following coordinate system is

used. If the wave propagates along the Z-axis, then the vertical cross-section is located in

the X-Y plane. Figure 2-1 shows the rectangular coordinate system. The governing

equation of this system employs the virtual work principle.

( ) ∫∫∫ +=Γ V

T

V

TT dVdVuudStu σεδρδδ ~~~~~ && 2.1

14

The fundamental variables in Equation 2.1 (displacements, stresses, strains, and

external tractions) can be written as; [Taweel et al. 2000], [Hayashi et al. 2003]

Where T denotes the matrix transpose.

Figure 2-1 Rectangular coordinate system

[ ]Tzyx uuuu =~ 2.2

[ ]Txyzxyzzzyyxx σσσσσσσ =~ 2.3

[ ]Txyzxyzzzyyxx γγγεεεε =~ 2.4

[ ]Tzyx tttt =~ 2.5

Meshes

Wave propagation

X

Y

Z

15

The left hand side of Equation 2.1 is the work done by the external force and the

right hand side of Equation 2.1 is the increment of the kinetic energy and the potential

energy. As the wave travels along the structure with the time and spatial harmonic

function ( )](exp[ tkzi ω− ), the displacement vector at an arbitrary point can be written as

Where, jU~ is nodal displacement at the jth node and ),(~ yxN is the interpolation

function for a four node element.

The strain can be expressed as follows using the stress-strain relation.

)](exp[~),(~~ tkziUyxNu j ω−= 2.6

4/)1)(1(

4/)1)(1(

4/)1)(1(

4/)1)(1(

4

3

2

1

ηξ

ηξ

ηξ

ηξ

+−=

++=

−+=

−−=

N

N

N

N

2.7

uz

Ly

Lx

L zyx~~⎥⎦

⎤⎢⎣

⎡∂∂

+∂∂

+∂∂

=ε 2.8

16

By substituting Equation 2.6 into Equation 2.8 we get the following

Where NLBNLNLB zyyxx =+= 21 ,,, , and xN , and yN , are the differentiation of the

interpolation function ),(~ yxN with respect to x and y.

The stress vector (σ~ ) can be written as follows by using the stress-strain relation

(Hooke’s Law).

The external traction vector can also be written as Equation 2.12 by using the

nodal external traction vector jT~ .

Where

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

000001010100000000

,

001000100000010000

,

010100000000000001

zyx LLL 2.9

( ) )(21

~~ tkzijeUBikB ωε −+= 2.10

εσ ~~ C= 2.11

)(~),(~ tkzijeTyxNt ω−=r

2.12

17

Substituting Equation 2.6, Equation 2.10, Equation 2.11, and Equation 2.12, into

Equation 2.1 yields

Expanding Equation 2.13 into the global system, then becomes

The dimension of the matrixes MandKKK 321 ,, leads to L by L matrices and

L is a dimension of three times the total number of nodes, since there are 3 displacements

in one node. The Equation 2.15 can be rewritten as follows;

( ) jjjjjjj UMUKkKikKf ~~~ 23

221 ω−++= 2.13

Where ( )

dxdyNNMdxdyBCBK

dxdyBCBBCBK

dxdyBCBKdTNNf

y x

Tj

y x

Tj

y x

TTj

y x

TjjTj

∫ ∫∫ ∫

∫ ∫

∫ ∫∫

==

−=

=Γ=Γ

ρ,

,~

223

12212

111

2.14

( ) UMUKkKikKf ~~~ 23

221 ω−++= 2.15

( ) PQBkA ~~=− 2.16

18

If there is no external force, then the vector P~ is zero. Equation 2.16 becomes an

eigenvalue problem and to solve this problem, the determinant of the matrix ( )BkA −

should be zero.

From Equation 2.18, the 2L eigenvalues of Equation 2.16 are the wave numbers

of the L guided wave modes of the structure. The L eigenvalues are the waves

propagating in the positive Z-direction, and the other L eigenvalues are the waves

propagating in the negative Z-direction. Also, the wave number k is a complex number. If

the real and imaginary parts of k are not zero, then this mode is an evanescent mode. If

the real part is not zero and the imaginary part is zero, then this mode is a propagating

mode.

Where

⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡=

⎥⎦

⎤⎢⎣

⎡

−−

=

⎥⎦

⎤⎢⎣

⎡

−−

=

fP

UkUQ

KMK

B

KiMKMK

A

~0~,~

~~

00

0

3

21

22

1

21

ω

ωω

2.17

0=− BkA 2.18

19

2.2.2 PHASE VELOCITY, GROUP VELOCITY, AND WAVE STRUCTURE

Using definitions, the phase velocity can be calculated from the angular frequency

and the wave number ( kcp ω= ) [Rose 1999]. Therefore, there are two ways to calculate

the phase velocity. One is a fixed angular frequency and a search for the wave number

and the other is a fixed wave number and then sweeping the angular frequency. The

group velocity of the mth mode can be expressed as

Hence, to calculate the group velocity at the angular frequencyω , the wave

number mm kk ∆+ at the angular frequency ωω ∆+ is needed. Suppose that the matrices

BA, in Equation 2.16 become AA ∆+ and BB ∆+ at an angular frequency ωω ∆+ .

Then the Equation 2.16 at the angular frequency ωω ∆+ will be

After eliminating the second order differential terms, Equation 2.20 can be

expressed as

mg dk

dcm

ω= 2.19

( ) ( )( )[ ]( ) 0~~=∆+∆+∆+−∆+ mmmm QQBBkkAA 2.20

20

Using the orthogonal property of the eigenvector mQ~ , mQ~∆ can be written as

By substitution Equation 2.22 into Equation 2.21

Multiply mQ~ from the left on both sides of Equation 2.23

By considering the orthogonal property, the Equation 2.24 becomes

( ) ( ) mmmmm QBkBkAQBkA ~~∆+∆+∆−=∆− 2.21

∑=

=∆M

lllmm QCQ

2

1

~~ 2.22

( ) ( ) mmm

M

lllmm QBkBkAQCBkA ~~2

1∆+∆+∆−=− ∑

=

2.23

( ) ( ) mmmmllmm

M

lm QBkBkAQQCBkAQ ~~~~2

1

∆+∆+∆−=−∑=

2.24

( ) ( ) mmmmmmmmm QBkBkAQQCBkAQ ~~~~∆+∆+∆−=− 2.25

21

After applying the Equation 2.18, the left hand side of the Equation 2.25 becomes

zero. Therefore the variation of the wave number at the angular frequency ωω ∆+ can be

expressed from Equation 2.25.

The mth mode group velocity can be obtained using Equation 2.19, and the upper

part of the eigenvectorQ~ is the wave structure.

( )mm

mmmm QBQ

QBkAQk ~~~~

∆−∆=∆ 2.26

22

2.3 NUMERICAL RESULTS AND DISCUSSION ON THE SAFE

TECHNIQUE

2.3.1 NUMERICAL RESULTS OF A STEEL PLATE

The phase velocity dispersion curves, group velocity dispersion curves, and

displacement profiles are calculated with an analytical method and the SAFE method to

illustrate accuracy. The SAFE program is coded with the FORTRAN language and a

LAPACK subroutine which provides the subroutines for the matrix calculation and for

solving the eigenvalue problems.

A steel plate will be considered initially. The model for the SAFE technique is a

steel plate and 100 elements to mesh the cross-section. The meshes on the cross-section

of the steel plate are shown in Figure 2-2 and the material properties are listed in Table 2-

1. Figure 2-3 show the dispersion curves using an analytical method and the dispersion

curves using the SAFE technique as displayed in Figure 2-4. The analytical method

makes use of Navier’s equation and the Helmholtz decomposition technique expressed as

Equation 2.27 and Equation 2.28, respectively ; [Rose 1999]

( ) iijijjji ufuu &&ρρλµµ =+++ ,, 2.27

23

Where µ and λ are Lame’s constants

This Helmholtz decomposition technique breaks down the displacement into

scalar and vector potentials. The scalar and vector potentials are related to a longitudinal

wave and a shear wave, respectively. However, in order to apply the Helmholtz

decomposition technique, the wave propagating material should be isotropic,

homogeneous, elastic, and linear. By substitute the Equation 2.28 into Equation 2.27,

Equation 2.27 is divided into two governing equations expressed as;

Where Lc and Tc are wave velocities of the longitudinal and shear waves.

By applying the boundary condition (a traction free condition at the top and

bottom surfaces of a plate), the possible guided waves in a plate can be calculated.

Figure 2-3 shows only the symmetric modes (S0, S1, S2) and the anti-symmetric modes

Hu ×∇+∇= φ 2.28

wavesallongitudingoverningtcL

,12

22

∂∂

=∇φφ 2.29

wavessheargoverningtH

cH

T

,12

22

∂∂

=∇ 2.30

24

(A0,A1,A2) because the solutions of Navier’s equation were assumed as symmetric mode

and anti-symmetric. However, the SAFE technique calculates not only symmetric and an

anti-symmetric modes but also all other possible modes such as shear horizontal modes,

bending modes, and twisting modes, even the evanescent modes. Because, the wave

numbers of these modes are the eigenvalues of Equation 2.18. The phase velocity

dispersion curves and the group velocity dispersion curves for these modes are displayed

in Figure 2-4. Reasonable agreement between the two methods is shown in Figure 2-5, 2-

6, and 2-7. More precise values of f and d could improve the results even further.

Figure 2-2 Dimensional meshes of a steel plate (1mm x 10mm)

Table 2-1 Material properties of a steel plate

Longitudinal wave velocity Shear wave velocity Density

sec/9.5 µmm sec/2.3 µmm 3/00786.0 mmg

25

0 1 2 3 4 5FREQUENCY*THICKNESS (MHz*mm)

0

2

4

6

8

10

PHA

SE V

ELO

CIT

Y(m

m/µ

sec)

STEEL PLATE(ANALYTICAL SOLUTION)

A0

S0

A1

S1 S2 A2

(a) Phase velocity dispersion curves


0

1

2

3

4

5

6

GR

OU

P V

ELO

CIT

Y(m

m/µ

sec)

A0

S0

A1

S1

S2

A2

STEEL PLATE(ANALYTICAL SOLUTION)

(b) Group velocity dispersion curves

Figure 2-3 Dispersion curves using Navier’s equation

26


0

2

4

6

8

10

PHA

SE V

ELO

CIT

Y(m

m/µ

sec)

STEEL PLATE(NUMERICAL SOLUTION)

(a) Phase velocity dispersion curves


0

1

2

3

4

5

6

GR

OU

P V

ELO

CIT

Y(m

m/µ

sec)

STEEL PLATE(NUMERICAL SOLUTION)

(b) Group velocity dispersion curves

Figure 2-4 Dispersion curves using SAFE technique

27

-1 -0.5 0 0.5 1NORMALIZED DISPLACEMENT

0

0.2

0.4

0.6

0.8

1

NO

RM

ALI

ZED

TH

ICK

NES

S

S0 MODE (fd=2.0MHzmm)(ANALYTICAL SOLUTION)

in planeout of plane

(a) Displacement of S0 mode for a steel plate using Navier’s equation


0

0.2

0.4

0.6

0.8

1

NO

RM

ALI

ZED

TH

ICK

NES

S

S0 MODE (fd=2.0MHzmm)(NUMERICAL SOLUTION)


(b) Displacement of S0 mode for a steel plate using SAFE technique

Figure 2-5 Displacement of S0 mode at fd=2.0 MHz mm

28


0

0.2

0.4

0.6

0.8

1

NO

RM

ALI

ZED

TH

ICK

NES

S

A1 MODE (fd=2.5MHzmm)(ANALYTICAL SOLUTION)


(a) Displacement of A1 mode for a steel plate using Navier’s equation


0

0.2

0.4

0.6

0.8

1

NO

RM

ALI

ZED

TH

ICK

NES

S

A1 MODE (fd=2.5MHzmm)(NUMERICAL SOLUTION)


(b) Displacement of A1 mode for a steel bar using SAFE technique

Figure 2-6 Displacement of A1 mode at fd=2.5 MHz mm

29


0

0.2

0.4

0.6

0.8

1

NO

RM

ALI

ZED

TH

ICK

NES

S



(a) Displacement of S1 mode for a steel plate using Navier’s equation


0

0.2

0.4

0.6

0.8

1

NO

RM

ALI

ZED

TH

ICK

NES

S

S1 MODE (fd=3.5MHzmm)(NUMERICAL SOLUTION)


(b) Displacement of S1 mode for a steel bar using SAFE technique

Figure 2-7 Displacement of S1 mode at fd=3.5 MHz mm

30

2.3.2 NUMERICAL RESULTS FOR A RAIL

Because of the complexity of the cross-section of a rail, there are many

difficulties associated with the calculation of the phase velocity and the group velocity

dispersion curves using Navier’s equation. For this reason, the SAFE method is therefore

used to calculate the dispersion curves of a wave guide with a complex cross-section. For

calculating the phase velocity and group velocity dispersion curves for a rail, 101 nodes

are used to generate 68 meshes on the cross-section of a rail. The nodes and elements are

shown in Figure 2-8.

The resulting phase velocity dispersion curves and group velocity dispersion

curves are illustrated in Figure 2-9 and Figure 2-10. Unlike the plate, there are hundreds

of modes in a rail and these modes are very close. Experimentally, it is impossible to

generate just one point in the phase velocity dispersion curves; because a tone burst is

used to generate the guided wave and this tone burst has a frequency bandwidth. There is

also a phase velocity spectrum associated with a source influence [Rose 1999]. Therefore,

guided waves in a small region in the phase velocity dispersion curves are generated.

After a wave scatters from a defect, a mode conversion of guided waves takes place. All

of the guided waves in the dispersion curves at the same frequency with the incident

waves are the scattered guided waves. Therefore, guided waves in the reflected and

transmitted fields are the summation of all scattered guided waves. For this reason, it is

impossible to apply the normal mode expansion (NME) technique [Cho 1995].

31

Figure 2-8 Meshes and nodes in a SAFE model of a rail

32

Figure 2-9 Phase velocity dispersion curves of a rail

33

0 40 80 120 160 200FREQUENCY(kHz)

0

1

2

3

4

5

6

GR

OU

P V

ELO

CIT

Y(m

m/µ

sec)

RAIL(NUMERICAL SOLUTION)

Figure 2-10 Group velocity dispersion curves of a rail

34

2.4 SUMMARY

Though there is a plane strain limitation, the SAFE (Semi-Analytical Finite

Element) technique is widely used because this technique can calculate the phase and

group velocity dispersion curves and wave structures of a structure with an arbitrary cross

section. The basic theory to calculate the phase velocity dispersion curves, the group

velocity dispersion curves, and the wave structures was presented.

The dispersion curves and the wave structures of a steel plate using the SAFE

technique and Navier’s equation are calculated and compared. There is an excellent

agreement with these two techniques.

Finally, the phase velocity dispersion curves and the group velocity dispersion

curves for a rail are calculated by adapting the SAFE method. It is found out that the

NME technique is impossible to use for a wave scattering problem in a rail because of the

hundreds of close modes that exist in the rail.

Chapter 3

FINITE ELEMENT METHOD FOR GUIDED WAVES

3.1 INTRODUCTION

An analytical approach for guided wave problems has been developed for

relatively simple problems [Achenbach 1984] [Rose 1999]. However, analytical solutions

are no longer available for such complex problems as arbitrary shapes of wave guides,

piecewise mixed boundary conditions, and scattering from unusually shaped 3

dimensional defects. For this reason, many numerical methodologies have been

developed. By using these techniques, a better understanding of the guided wave

characteristics associated with all sorts of difficult problems becomes possible.

Though it is necessary to discretize the whole domain with elements, The Finite

Element Method (FEM) is commonly used for solving various boundary value problems

associated with wave mechanics. The strategy of the ABAQUS/Explicit program, a

commercial FEM package, and the modeling of guided wave propagation in a rail will be

introduced.

36

3.2 ABAQUS/Explicit STRATEGY

For a wave mechanics boundary value problem, the loads and boundary

conditions vary with time, then the displacement fields of the system also changes with

time. ABAQUS/Explicit, a FEM package, was developed to solve these dynamic

problems. The strategy of this program could start from a basic equation of a dynamic

finite element governing equation written as [Cook et al. 1989]

Where [ ]M is a mass matrix, [ ]C is a damping matrix, [ ]K is a stiffness matrix, { }nD is

a displacement vector, { }nD& and { }nD&& are the first and second derivatives of a time,

{ }nextR is a external force vector, and the subscript n is the nth time step. There are two

different methods for direct integration of Equation 3.1. The one method is an explicit

method and the displacement at the (n+1)th time step is determined with known variables

and can be written as

[ ]{ } [ ]{ } [ ]{ } { }next

nnn RDKDCDM =++ &&& 3.1

{ } { } { } { } { }( ).....,,,, 11 −+ = nnnnn DDDDfD &&& 3.2

37

The other method is an implicit method and the displacement at the (n+1)th time

step needs the time derivatives of the displacements at the (n+1)th time step and can be

written as

Comparing these two methods, the implicit method requires an iteration to

determine the solution because the displacement at the (n+1) step is calculated with

guessing values of { } 1+nD& and { } 1+nD&& ; this iteration may cause difficulty in convergence

because of contact or material complexities. On the contrary, the explicit method does not

need an iteration because the solution is decided with the known variables at a previous

time step. From the viewpoint of disk space and memory, implicit requires much larger

space because of the iteration.

In the ABAQUS/Explicit module, the velocity and the acceleration can be

obtained from a Taylor series expansion of { } 1+nD and { }nD over time 2t∆ expressed

as; [ABAQUS 2003]

{ } { } { } { }( ).....,,, 111 nnnn DDDfD +++ = &&& 3.3

...}{6

)2(}{2

)2(}{2

}{}{32

21 +

∆+

∆+

∆+=

+nnnnn

DtDtDtDD &&&&&& 3.4

38

Equation 3.6 can be obtained by subtracting Equation 3.5 from Equation 3.4 and

omitting 3t∆ and higher powers

Similarly, Equation 3.7 can be obtained by adding Equation 3.5 and Equation 3.4

and omitting 3t∆ and higher powers

Combining Equation 3.6 and Equation 3.7 with Equation 3.1 provides

...}{6

)2(}{2

)2(}{2

}{}{32

21 +

∆−

∆+

∆−=

−nnnnn

DtDtDtDD &&&&&& 3.5

{ } { } ⎥⎦⎤

⎢⎣⎡ −

∆= −+

21

21

1}{ nnn DDt

D& 3.6

{ } { } { } ⎥⎦⎤

⎢⎣⎡ +−

∆= −+

21

21

2 24}{ nnnn DDDt

D&& 3.7

[ ] [ ] { }

{ } [ ] [ ] { } [ ] [ ] { }21

22

21

2

148

14

−

+

⎥⎦⎤

⎢⎣⎡

∆−

∆−⎥⎦

⎤⎢⎣⎡ −∆

+=

⎥⎦⎤

⎢⎣⎡

∆+

∆

nnnext

n

DCt

Mt

DKMt

R

DCt

Mt

3.8

39

3.3 THE BOUNDARY VALUE PROBLEM

In an analysis of the guided wave scattering problem using numerical techniques,

the normal mode expansion technique (NMET) or the boundary value problem can be

employed. The NMET uses the displacements calculated analytically or numerically as

an input. The displacements of a forward scattering field and a backward scattering field

are the summation of all possible modes due to the mode conversion at the specific

frequency being considered [Rose 1999] [Cho 1995].

On the contrary, the boundary value problem models the ultrasonic transducer

with appropriate governing equation, boundary conditions, and loading conditions acting

on the structure. The governing equation for the wave mechanics is the Navier’s equation

expressed as

Figure 3-1 shows the boundary conditions and loading conditions in a rail model.

The fixed conditions were applied at four corner points of the base of a rail to prevent

rigid body motion. The guided waves generated from an EMAT propagate in both

directions; therefore the symmetric condition in the z-direction was applied at the left

cross-section located at the middle of an EMAT. Figure 3-2 shows the symmetry in the

( ) iijijjji ufuu &&ρρλµµ =+++ ,, 3.9

40

longitudinal direction for a five element EMAT and only the solid line part is adopted for

the numerical modeling.

Figure 3-1 Numerical model of a rail with boundary and loading conditions

SYMMETRY

Figure 3-2 EMAT loading area in the numerical model

λ/4 λ/4 λ/4 λ/4 λ/4λ/8 λ/4 λ/4

Rail Head

41

In the generation of guided waves, an angle beam transducer or a comb type

transducer are commonly applied on the surface of the structure. Figure 3-3 shows typical

phase velocity dispersion curves and corresponding sensor activation lines. The

horizontal line for an angle beam transducer is determined by Snell’s law as expressed in

Equation 3.10.


0

2

4

6

8

10

PHA

SE V

ELO

CIT

Y(m

m/µ

sec)

STEEL PLATE

A0

S0

A1 S1

S2

A2

COMB TYPE TRANSDUCER

ANGLE BEAM TRANSDUCER

Figure 3-3 Phase velocity dispersion curves and activation lines

2

2

1

1 sinsinccθθ

= 3.10

42

Where, 1c is a longitudinal velocity in a wedge, 2c is a phase velocity, 1θ is an incident

angle, and 2θ is 90 degree. Therefore the incident angle 1θ is

The wave length is fcp and the slope of the inclined line is fdc p . Therefore,

the slope of the line is determined by the spacing of the elements of the transducer

In modeling the transducer in ABAQUS, a sinusoidal signal is applied as the

time-dependent amplitude of the pressure on the surface of the waveguide. The use of

more cycles as an input can actuate a more precise point in the dispersion curves by using

a narrow frequency spectrum. Figure 3-4 shows an input signal for 60kHz as an example.

( )⎟⎟⎠

⎞⎜⎜⎝

⎛= −

p

wedgeL

cc

Sin 11θ 3.11

0E+000 2E-005 4E-005 6E-005 8E-005 1E-004TIME

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

AM

PLIT

UD

E

Figure 3-4 Input signal for 60kHz

43

3.4 NUMERICAL MODELING OF THE GUIDED WAVE

PROPAGATION

3.4.1 MODEL ACCURACY CONSIDERATIONS

Before studying the guided wave propagation using FEM, an accuracy test of the

numerical model is needed to be convinced that the numerical experiment results are

correct. Figure 3-5 ~ Figure 3-10 shows the wave propagation patterns for some wave

propagation problem with 2,4,6,8,10, and 15 elements per one wave length. The wave

propagation shows a similar pattern with the models using 8 and more elements in one

wave length; however, the model using 6 elements in one wave length shows different

patterns. For the model using 2 and 4 elements, the guided wave does not propagate. The

group velocity of the numerical model using 8, 10, and 15 elements per one wave length

has a consistency with the group velocity dispersion curves. From these series of

convergence tests, the minimum number of required elements in one wave length is

therefore 8.

44

(a) t = 0.05 msec (b) t = 0.1 msec

(c) t = 0.15 msec (d) t = 0.2 msec Figure 3-5 Wave propagation for 2 elements per wave length

( Note : a guided wave packet is not generated and does not propagate )

45

(a) t = 0.05 msec (b) t = 0.1 msec

(c) t = 0.15 msec (d) t = 0.2 msec

Figure 3-6 Wave propagation for 4 elements per wave length

( Note : a guided wave packet is not generated and does not propagate )

46

(a) t = 0.05 msec (b) t = 0.1 msec

(c) t = 0.15 msec (d) t = 0.2 msec

Figure 3-7 Wave propagation for 6 elements per wave

( Note : a guided wave packet is generated but scattered into web and base )

47

(a) t = 0.05 msec (b) t = 0.1 msec

(c) t = 0.15 msec (d) t = 0.2 msec


( Note : a guided wave packet is well generated and propagates )

48

(a) t = 0.05 msec (b) t = 0.1 msec

(c) t = 0.15 msec (d) t = 0.2 msec



49

(a) t = 0.05 msec (b) t = 0.1 msec

(c) t = 0.15 msec (d) t = 0.2 msec



50

After a convergence check, the wave structures of the guided waves in a plate are

compared with analytical solutions. Figure 3-11 shows displacements found from an

analytical solution and Figure 3-12 shows displacements using FEM. For the in plane

displacement, the maximum displacement is located in the middle of a plate. On the

contrary, the maximum displacement of the out of plane displacement is at the top and

bottom surface of a plate. The results of the two techniques have excellent general

agreement.


0

0.2

0.4

0.6

0.8

1

NO

RM

ALI

ZED

TH

ICK

NES

S



Figure 3-11 Displacement of S0 mode at fd=2.0 MHz mm (analytical solution)

51

(a) out of plane displacement

(b) in plane displacement

Figure 3-12 Displacement at fd=2.0 MHz mm (FEM solution)

52

3.4.2 GUIDED WAVE PROPAGATION

The phase velocity dispersion curves using the SAFE technique were used to

produce dispersion curves for a rail. Seemingly countless modes exist in a rail and they

are extremely close to each other. It is therefore impossible to generate only one mode in

an experimental situation. For this reason, the boundary value problem technique rather

than the NMET is adapted to explore the propagation characteristics of guided waves in a

rail.

The wave propagation properties of guided waves in a rail will now be explored.

Since, many modes exist in a rail, and it is impossible to check the wave structures at all

points in the phase velocity dispersion curves, several zones are chosen in the 0 ~ 200kHz

range and these points are displayed in Figure 3-13. It is hoped that the experimental

activation of one or more of these zones will prove useful in rail NDT with an initial goal

of finding transverse defects in the rail head, hence pointing to the necessity of getting

almost all of the energy in the rail head.

53

Figure 3-13 Points of interest on the phase velocity dispersion curve (Note : Note that there are thousands of modes and frequency combinations between 0 and 200kHz but only 24 were chosen for a detailed study assuming that they would provide beneficial displacement fields in the rail .)

0 40 80 120 160 200FREQUENCY(kHz)

0

2

4

6

8

10

PHA

SE V

ELO

CIT

Y(m

m/µ

sec)

30-1

30-2

30-3

30-4

60-1

60-2

60-3

60-4

100-1

100-2

100-3

100-3

135-1

135-2

135-3

135-4

175-1

175-2

175-3

175-4

200-1

200-2

200-3

200-4

54

Figure 3-14 ~ Figure 3-19 shows the wave propagation patterns at the different

points marked in Figure 3-13. In Figure 3-14 (a) and Figure 3-15 (a), there is some

energy in the web of the rail. However, most of the energy is concentrated in the head of

the rail as shown in Figure 3-16 (a), Figure 3-17 (a), Figure 3-18 (a), and Figure 3-19 (a).

This means that the waves of 30kHz and 60kHz have the potential of detecting defects in

the web of the rail with the appropriate sensor design whereas the waves of 175kHz and

200kHz would be very sensitive to surface cracks located on the rail head. The wave

propagation patterns of (b), (c), and (d) at each frequency shows that the echoes from the

bottom of the rail are those echoes that could lead to multiple reflection waves which

could be confusing with respect to determining the actual location of the defects.

Therefore, guided waves of these zones are not suitable for rail inspection. In conclusion,

the guided waves associated with the pseudo Rayleigh surface mode region (the lowest

modes in Figure 3-13) are recommended for studying transverse defect detection in the

rail head.

Figure 3-20 shows the total displacement of the pseudo Rayleigh surface waves at

different frequencies marked in Figure 3-13 (30-1, 60-1, 100-1, 135-1, 175-1, and 200-1).

In the Figure 3-20 (a) and (b), there is a dominant displacement in the entire rail head and

some minor displacement in the web. In cases of higher frequency (shown in Figure 3-20

(e) and (f)), the displacements are localized only near the top surface of the rail heal.

55

(a) 30-1, 0.300msec (1.33m) (b) 30-2, 0.826msec (3.01m)

(c) 30-3, 1.275 msec (4.52m) (d)30-4, 1.275 msec (6.05m) Figure 3-14 Wave propagation patterns at 30kHz

( Note : In Fig. (a), the energy is distributed in the head and web of the rail In Fig. (b), (c), and (d), there are also echoes from the bottom of the rail )

56

(a) 60-1, 0.225 msec (0.84m) (b) 60-2, 0.413 msec (1.61m)

(c) 60-3, 0.675 msec (2.55m) (d) 60-4, 1.501 msec (3.33m) Figure 3-15 Wave propagation patterns at 60kHz

( Note : In Fig. (a), the energy is distributed in the head and web of the rail In Fig. (b), (c), and (d), there are echoes from the bottom of the rail )

57

(a) 100-1, 0.150 msec (0.57m) (b)100-2, 0.300 msec (1.09m)

(c)100-3, 0.413 msec (1.61m) (d)100-4, 0.563 msec (2.13m) Figure 3-16 Wave propagation patterns at 100kHz

( Note : In Fig. (a), most of the energy is located in the head of the rail In Fig. (b), (c), and (d), there are also echoes from the bottom of the rail )

58

(a) 135-1, 0.113 msec (0.44m) (b)135-2, 0.188 msec (0.79m)


( Note : In Fig. (a), most of the energy is located in the head of the rail In Fig. (b), (c), and (d), there are echoes from the bottom of the rail )

59

(a) 175-1, 0.090 msec (0.35m) (b)175-2, 0.158 msec (0.64m)


( Note : In Fig. (a), most of the energy is located in the head of the rail In Fig. (b), (c), and (d), there are echos from the bottom of the rail )

60

(a)200-1, 0.090 msec (0.32m) (b)200-2, 0.113 msec (0.55m)


( Note : In Fig. (a), most of the energy is located in the head of the rail In Fig. (b), (c), and (d), there are also echoes from the bottom of the rail )

61

(a) 30kHz (b) 60kHz

(c) 100kHz (d) 135kHz

(e) 175kHz (f)200 kHz

Figure 3-20 Wave structures at different frequencies

( Note : The energy of guided waves for lower frequencies (30kHz and 60kHz) isdistributed over a rail head and the energy of guided waves for higher frequencies(175kHz and 200kHz) is concentrated on the top surface of a rail head )

62

3.5 SUMMARY

The basic theory of the direct integration method used in FEM was introduced.

Two typical methods of the direct integration method, explicit and implicit, were also

explained. ABAQUS/Explicit, a commercial FEM package, was used for the analysis of

the characteristics of the guided waves in a rail.

There are two general approaches for guided wave modeling; one is the normal

mode expansion technique (NMET) and the other is solving a boundary value problem.

For guided waves in a rail, the NMET is not practical because of the numerous modes.

For this reason, the boundary value problem approach was employed for modeling the

guided waves in a rail.

The simulation of an electromagnetic acoustic transducer (EMAT) loading is

developed in a 3 dimensional finite element model to solve the guided wave boundary

value problem. Although, the ABAQUS/Explicit is a powerful tool for solving problems,

it is necessary to fully understanding the guided wave problem to make up an appropriate

numerical model. Also, knowledge of wave mechanics is essential for a correct

interpretation of the numerical results.

After conducting a convergence test to see what mesh sizes was required for

particular frequencies and for comparing a wave structure with an analytical solution, the

63

guided wave propagation characteristics at various points in the phase velocity dispersion

curves between 0 and 200kHz were considered. The pseudo Rayleigh surface mode

region was suggested for the rail testing. Since guided waves above the pseudo Rayleigh

surface mode region in the phase velocity dispersion curve space had plentiful echoes

from the bottom of a rail, interpretation in rail inspection could occur.

The guided waves with lower frequency have the potential of detecting defects in

the rail head and web. The higher frequency guided waves are more sensitive to surface

type defects.

Chapter 4

THREE DIMENSIONAL WAVE SCATTERING

4.1 INTRODUCTION

Many train accidents are caused from transverse crack defects located in the rail

head. Rail inspection has therefore become a critical issue to avoid such accidents.

Conventional ultrasonic inspection techniques consider normal and oblique incident

waves. These incident waves are reflected from shelling and other surface imperfections

which are not critical to rail failure and hence cannot detect the transverse defects under

the shelling. Also, this technique examines the specimen on a point by point basis.

Therefore, the conventional ultrasonic inspection technique use for a rail is limited in

reliability and efficiency. The guided wave technique could overcome this limitation

because it can propagate along the rail and see defects regardless of any surface defects in

the rail.

The defect detection ability of guided waves will now be demonstrated

numerically. Modeling aspects of the guided wave scattering phenomena from various

defects using ABAQUS/Explicit is developed. The effect of shelling which often exists in

65

the rail head, a non-critical defect by itself, is also investigated. This result will provide

guidelines for rail inspection. Advanced wave scattering studies can be extended from

this result.

66

4.2 WAVE SCATTERING FROM INTERNAL NOTCHS

The characteristics of wave scattering from various sizes of vertical defects

located in the rail head is studied. Figure 4-1 shows the location and size of the vertical

defects located in the rail head. The shapes of the defects are approximately rectangular

with 0.1mm crack widths. These defects are started at 4mm below the top surface of the

rail head. The pseudo Rayleigh surface waves at three frequencies (60kHz, 175kHz, and

315kHz) are considered. Figure 4-2 shows the finite element model of the rail for the

60kHz guided wave. The sizes of the elements for these three frequencies are different.

There is a limit in the total number of elements in ABAQUS because of a memory

limitation during the time of those computer runs. For this reason, the rail lengths are

different. The length of these rails is shown in Table 4-1 .

(a) (b) (c) (d) (e)

Figure 4-1 Cross-section of the rail with vertical defects

((a):no defect, (b):10mm defect, (c):20mm defect, (d):30mm defect, (e):40mm defect)

67

Figure 4-2 Finite element model of a rail for the 60kHz guided wave

Table 4-1 Length of the numerical modeling of a rail

Frequency Length

60kHz 1020mm

100kHz 820mm

175kHz 550mm

315kHz 220mm

68

Figure 4-3 EMAT loading simulation (red arrows indicate forcing function direction)

Figure 4-4 Meshes around the vertical defect

69

For a simulation of the EMAT loading, 5 cycles of a tone burst signal was used.

Figure 4-3 shows the numerical simulation of the EMAT loading by applying a pressure

on the elements with an EMAT coil. A symmetric boundary condition is applied on the

left side of a rail model since guided waves generated by an EMAT propagates in both

directions. Figure 4-4 illustrates the meshes around the 20mm vertical defect as an

example. Since the Lamb type EMAT transducer loading was modeled, this transducer

detects and converts the vertical displacements into a signal. Therefore, the vertical

displacement is an important feature.

Figure 4-5 shows the vertical displacement of a 175kHz guided wave scattering

from a 30mm vertical defect and Figure 4-6 shows an energy distribution at the cross-

section ((i), (ii), and (iii)) marked in Figure 4-5. Figure 4-5 (a) shows the generation of

the guided waves by an EMAT loading simulation at the beginning. These generated

guided waves do not arrive at the position (i), (ii), and (iii), therefore, Figure 4-6 (a), (b),

and (c) do not show any energy distributions. Figure 4-5 (b) shows the impinging wave

propagating from the left side to the right side and Figure 4-6 (d) shows the energy

distribution of the incident wave at the cross section of a position (i). Figure 4-5 (c)

shows the scattering phenomenon at a vertical defect located in the rail head. The

incident guided waves pass the position (i) and reflected waves do not arrive at the

position (i), therefore, Figure 4-6 (g) shows the energy distribution after incident waves

pass by. Figure 4-6 (h) show scattering characteristics of a vertical defect inside a rail.

Figure 4-5 (d) shows the reflected and transmitted waves and Figure 4-6 (j) and (l) shows

70

the energy of the reflected and transmitted waves. After scattering from a vertical defect,

the energy of the reflected waves is concentrated inside the rail head and a relatively

small amount of energy is distributed over the surface of the rail head. Because of this

scattering pattern, Figure 4-5 (d) shows a small displacement for the reflected waves.

After running FEM with ABAQUS/Explicit, image animation can be obtained by a post

processing of data from ABAQUS. Lots of useful information can be obtained by

observing the movies on a frame by frame basis.

Figure 4-7 shows the vertical displacements of the reflected and transmitted

waves at the top surface of the rail head at a distance of 185mm from the defect for

60kHz. As shown in Figure 4-7, as expected, the reflected wave from the bigger defect

has the larger displacement and the transmitted wave from the smaller defect has the

larger displacement. It is difficult to distinguish a defect size smaller than 40mm with the

amplitude of the reflected waves. Though, the amplitude of the transmitted waves can

discriminate the size of the defect. Figure 4-8 shows the vertical displacement of the

reflected and transmitted waves at the top surface of the rail head at a distance of 110mm

from the defect for 175kHz. The reflected wave from the 40mm defect seems to have the

largest displacement, but resolution seems to point to a two class problem of greater than

30 mm or less than 30 mm. The transmitted wave from the 40mm defect has the smallest

displacement, but is close to the 30 mm result. Figure 4-9 shows the vertical

displacement of the reflected and transmitted waves at the top surface of the rail head at

the distance of 50mm from the defect for 315kHz. There is a big difference between the

71

reflected waves and the no defect propagating waves. The transmitted wave from the

40mm defect has the smallest displacement.

(a) t = 10 µsec (b) t = 64 µsec

(c) t = 120 µsec (d) t = 160 µsec Figure 4-5 175kHz guided wave scattering from a 30mm vertical defect showing aguided wave generation, a propagation, a scattering, and a reflected wave and a transmitted wave

Guided wave generation

Impinging wave

Scattering Reflected wave

Transmitted wave

(i)

(ii)

(iii)

(i)

(ii)

(iii)

(i)

(ii)

(iii)

(i)

(ii)

(iii)

72

Position (i) Position (ii) Position (iii)

t=10µsec

(a) (b)

(c)

t=64µsec

(d) (e)

(f)

t=120µsec

(g) (h)

(i)

t=160µsec

(j) (k)

(l) Figure 4-6 Energy distribution by 175kHz excitation at a cross-sectional area at 3 positions and different time (See Figure 4-5), showing the energy distribution over a cross-section of a rail

73

Figure 4-10 shows the maximum value of the absolute value of the vertical

displacement of a reflected and a transmitted wave for 60kHz. Comparing Figure 4-10 (a)

and (b), curves in Figure 4-10 (a) are more complex than those in Figure 4-10 (b).

Because of the hardware and software memory limitation in a computer, a relatively short

model is considered. Therefore, it is difficult to separate reflected waves from incident

waves at a close area to a defect. This leads to the more complex curves shown in

Figure 4-10 (a). Overall, the reflected waves from the biggest defect has the largest

amplitude; however this trend is not true for the other defects (0mm, 10mm, 20mm, and

30mm) in Figure 4-10 (a) because of the interference between the incident and reflected

waves. In Figure 4-10 (b), the magnitudes of |U2| between 150mm and 450mm are

monotonically decreased with the crack depth. Figure 4-11 shows the maximum value of

the absolute value of the vertical displacement of a reflected and a transmitted wave for

175kHz. As shown in Figure 4-11, there is no trend in the reflected waves and the

magnitude of the transmitted waves between 100mm and 200mm in showing any large

difference between defects and no defect. For the 315kHz case, (Figure 4-12), there is a

big difference in the magnitude of |U2| between the defect and no defect case. Similar to

175kHz, the magnitudes of |U2| of the defects are relatively close.

74

0 0.0001 0.0002 0.0003 0.0004TIME

-2E-008

-1E-008

0

1E-008

2E-008

DIS

PLA

CEM

ENT(

U2)

REFLECTIONZ=-185mm (60kHz)

(no shelling)0mm10mm20mm30mm40mm

(a) Reflected wave

0 0.0001 0.0002 0.0003 0.0004TIME

-3E-008

-2E-008

-1E-008

0

1E-008

2E-008

DIS

PLA

CEM

ENT(

U2)

TRANSMISSIONZ=+185mm (60kHz)


(b) Transmitted wave

Figure 4-7 Vertical displacement of the reflected waves and the transmitted waves at185mm from the defect (60kHz) showing that the reflected wave from the bigger defect has the larger displacement and the transmitted wave from the smaller defect has thelarger displacement.

Reflected wave

Incident wave

Transmitted wave

75

0 4E-005 8E-005 0.00012 0.00016 0.0002TIME

-3E-009

-2E-009

-1E-009

0

1E-009

2E-009

3E-009

DIS

PLA

CEM

ENT(

U2)



(a) Reflected wave

0 4E-005 8E-005 0.00012 0.00016 0.0002TIME

-2E-009

-1E-009

0

1E-009

2E-009

DIS

PLA

CEM

ENT(

U2)




Figure 4-8 Vertical displacement of the reflected waves and the transmitted waves at110mm from the defect (175kHz) showing that the reflected wave from the 40mm defect seems to have the largest displacement and the transmitted wave from the 40mm defect has the smallest displacement.

Reflected wave

Incident wave

Transmitted wave

76

0.00000 0.00002 0.00004 0.00006 0.00008 0.00010TIME

-2E-008

-1E-008

0E+000

1E-008

2E-008

DIS

PLA

CEM

ENT(

U2)


(no shelling)0mm 10mm20mm30mm40mm

(a) Reflected wave


Figure 4-9 Vertical displacement of the reflected waves and the transmitted waves at 50mm from the defect (315kHz) showing that there is big difference between the reflected waves and the no defect propagating waves. The transmitted wave from the40mm defect has the smallest displacement.

0.00000 0.00002 0.00004 0.00006 0.00008 0.00010TIME

-2E-008

-1E-008

-5E-009

0E+000

5E-009

1E-008

2E-008

DIS

PLA

CEM

ENT(

U2)


(no shelling)0mm 10mm20mm30mm40mm

Reflected wave

Incident wave

Transmitted wave

77

0 100 200 300 400 500DISTANCE (mm)

0.0E+000

4.0E-009

8.0E-009

1.2E-008

MA

X(A

BS(

U2)

)

Internal Notch (60kHz)Reflected wave

0mm10mm20mm30mm40mm

0 100 200 300 400 500DISTANCE (mm)

0.0E+000

1.0E-008

2.0E-008

3.0E-008

4.0E-008

MA

X(A

BS(

U2)

)

Internal Notch (60kHz)Transmitted wave

0mm10mm20mm30mm40mm


Figure 4-10 Absolute value of vertical displacement of the reflected and transmitted wave through the vertical defect at several points for 60kHz guided wave showing magnitudes of transmitted waves between 150mm and 450mm are monotonicallydecreased with the crack depth.

0 100 200 300DISTANCE (mm)

0.0E+000

2.0E-010

4.0E-010

6.0E-010

8.0E-010

1.0E-009

1.2E-009

MA

X(A

BS(

U2)

)

Internal Notch (175kHz)Reflection wave

0mm10mm20mm30mm40mm

0 100 200 300DISTANCE (mm)

0.0E+000

1.0E-009

2.0E-009

3.0E-009

MA

X(A

BS(

U2)

)


0mm10mm20mm30mm40mm


Figure 4-11 Absolute value of vertical displacement of the reflected and transmitted wave through the vertical defect at several points for the 175kHz guided wave showingthat the magnitudes of the transmitted waves between 100mm and 200mm shows a largedifference between defects and no defect

78

0 20 40 60 80 100DISTANCE (mm)

0.0E+000

2.0E-009

4.0E-009

6.0E-009

MA

X(A

BS(

U2)

)

Internal Notch (315kHz)Reflection wave

0mm10mm20mm30mm40mm

0 20 40 60 80 100DISTANCE (mm)

4.0E-009

8.0E-009

1.2E-008

1.6E-008

2.0E-008

MA

X(A

BS(

U2)

)


0mm10mm20mm30mm40mm


Figure 4-12 Absolute value of vertical displacement of the reflected and transmitted wave through the vertical defect at several points for 315kHz guided wave showing a big difference in the magnitude of |U2| between defects and no defect

79

4.3 WAVE SCATTERING FROM INTERNALLY DRILLED HOLES

Features of the guided wave scattering from hole defects located in the rail head is

also explored. All hole defects considered have the same diameter (6.35mm), but the

depth of the hole is different (12.7mm and 20mm). The location of the hole defect is also

different as is shown in Figure 4-13. Figure 4-14 shows the meshes around the hole

defect. The same EMAT loading simulation was used for four different frequencies

(60kHz, 100kHz, 185kHz, and 280kHz).

(a) hole 1 (b) hole 2 (c) hole 3 Figure 4-13 Cross-section of the rail with hole defects

( (a) : 6.35mm diameter, 12.7mm deep, 0.75% depth of rail head (b) : 6.35mm diameter, 20.0mm deep, 0.50% depth of rail head

(c) : 6.35mm diameter, 12.7mm deep, 0.25% depth of rail head )

80

The absolute value of the vertical displacement of the reflected and transmitted

wave at several points for 60kHz, 100kHz, 185kHz, and 280kHz are plotted in Figure 4-

15, Figure 4-16, Figure 4-17, and Figure 4-18, respectively. As shown in Figure 4-15,

there is no clear trend in magnitude from the reflected waves; however, the transmitted

signal of no defect has the biggest amplitude. The transmitted signal through the hole 1

has the second biggest amplitude because the hole 1 is located at the lowest position

Figure 4-14 Meshes around the hole defect

81

among the hole defects. The transmitted signal through the hole 3 has the third biggest

amplitude. The hole 3 has the same size as the hole 1 but the hole 3 is located closer to

the top surface of a rail head than the hole 1. The closer position produces more reflection.

The amplitude of the transmitted signal across the hole 2 is the smallest. Comparing the

holes 2 and the 3, the diameter of these two holes is the same but the length of the hole 2

is bigger than that of the hole 3. However, the hole 3 is located closer to the top surface

of the rail head than hole 2. This means that the location of the defects is a much more

important factor than the size of the defects for rail inspection using 60kHz guided waves.

0 100 200 300 400 500DISTANCE (mm)

2.5E-009

3.0E-009

3.5E-009

4.0E-009

4.5E-009

5.0E-009

5.5E-009

MA

X(A

BS(

U2)

)

Drilled Hole (60kHz)Reflected wave

NO DEFECTHOLE 1HOLE 2HOLE 3

0 100 200 300 400 500

DISTANCE (mm)

8.0E-009

1.2E-008

1.6E-008

2.0E-008

2.4E-008

2.8E-008

MA

X(A

BS(

U2)

)

Drilled Hole (60kHz)Transmitted wave



Figure 4-15 Absolute value of the vertical displacement of the reflected and transmitted wave across the cylindrical defect at several points for the 60kHz guided wave showing that the transmitted signal through the hole 1 has the second biggest amplitude becausethe hole 1 is located at the lowest position among the hole defects and also the transmitted signal through the hole 2 has the smallest amplitude because the hole 2 is thebiggest defect.

82

0 100 200 300 400DISTANCE (mm)

1.0E-009

2.0E-009

3.0E-009

4.0E-009

5.0E-009

6.0E-009

MA

X(A

BS(

U2)

)



0 100 200 300 400DISTANCE (mm)

4.0E-009

8.0E-009

1.2E-008

1.6E-008

2.0E-008

2.4E-008

2.8E-008

MA

X(A

BS(

U2)

)




Figure 4-16 Absolute value of the vertical displacement of the reflected and transmitted wave across the cylindrical defect at several points for the 100kHz guided wave showing that there is a big difference in amplitude of the transmitted wave between no defect anddefects.

0 40 80 120 160 200DISTANCE (mm)

0.0E+000

1.0E-009

2.0E-009

3.0E-009

4.0E-009

MA

X(A

BS(

U2)

)



0 40 80 120 160 200DISTANCE (mm)

1.0E-008

1.2E-008

1.4E-008

1.6E-008

MA

X(A

BS(

U2)

)




Figure 4-17 Absolute value of the vertical displacement of the reflected and transmitted waves across the cylindrical defect at several points for the 185kHz guided wave showing the results with no sensitivity to defect size.

83

As shown in Figure 4-16, it is difficult to find a magnitude trend in the reflected

waves; however, there is a big difference in amplitude of the transmitted wave between

the no defect and defect case. However, the amplitudes of the transmitted waves from the

defects are almost the same. Therefore, the 100kHz guided wave can distinguish the no

defect and hole defects, but cannot discern the length or location of hole defects. The

reflected and transmitted waves of 185kHz and 280kHz depicted in Figure 4-17 and

Figure 4-18 shows the result with no sensitivity to defect size. However, the 280kHz

guided wave can be used for the detection of the hole defects without discrimination

because the amplitude difference of the transmitted wave shows huge differences

between the no defect and hole defects.

20 40 60 80 100DISTANCE (mm)

0.0E+000

4.0E-010

8.0E-010

1.2E-009

1.6E-009

2.0E-009

MA

X(A

BS(

U2)

)



0 20 40 60 80 100DISTANCE (mm)

6.0E-009

8.0E-009

1.0E-008

1.2E-008

MA

X(A

BS(

U2)

)




Figure 4-18 Absolute value of the vertical displacement of the reflected and transmitted waves across the cylindrical defect at several points for the 280kHz guided wave showing the potential in detecting the defects.

84

4.4 WAVE SCATTERING FROM CONTOUR NOTCHS

The characteristics of guided wave scattering from an arc-shaped contour notch

were also studied. The arc-shaped notch is relatively easy to make in producing a rough

simulation a dangerous transverse defect. The thickness of the contour notches is 2mm

and the radius of the notches are 5mm, 10mm, and 15mm. Figure 4-19 shows the shape

of the contour notches and the location of the contour notches. The area ratios of each

defect area to rail head area are 0.6%, 2.5%, and 5.6%, respectively. 60kHz, 100kHz,

185kHz, and 280kHz were used to simulate the EMAT loading. Figure 4-20 illustrates

the meshes near the contour notches.

(a) notch 1 (b) notch 2 (c) notch 3 Figure 4-19 Cross-section of the rail with contour notch

( (a) 5mm radius (0.6%), (b) 10mm radius (2.5%), (c) 15mm radius (5.6%) )

85

The absolute value of the vertical displacements of the reflected and transmitted

waves at several points for 60kHz, 100kHz, 185kHz, and 280kHz are graphed in

Figure 4-21, Figure 4-22, Figure 4-23, and Figure 4-24 respectively. Unlike the result of

previous sections, Figure 4-21 shows that the 60kHz guided wave has some difficulty in

classifying the no defect case and notches. On the contrary, the 100kHz guided wave has

the potential to discern the no defect and notches between 200mm and 300mm as shown

in Figure 4-22. The 185kHz and the transmitted waves for 280kHz shows the worse

results, however, the reflected waves for 280kHz shows a big difference in the amplitude

of the displacement between the defect case and no defect.

(a) meshes around a contour notch (b) meshes at the cross section of a contour notch

Figure 4-20 Meshes around the hole defect

86

0 100 200 300 400 500DISTANCE (mm)

4.0E-009

6.0E-009

8.0E-009

1.0E-008

1.2E-008

1.4E-008

MA

X(A

BS(

U2)

)Contour Notch (60kHz)

Reflected waveNO DEFECTNOTCH 1NOTCH 2NOTCH 3

0 100 200 300 400 500DISTANCE (mm)

8.0E-009

1.2E-008

1.6E-008

2.0E-008

2.4E-008

2.8E-008

3.2E-008

MA

X(A

BS(

U2)

)

Contour Notch (60kHz)Transmitted wave

NO DEFECTNOTCH 1NOTCH 2NOTCH 3


Figure 4-21 Absolute value of the vertical displacement of the reflected and transmitted wave across the contour notch at several points for the 60kHz guided wave showing that it is difficult to classify no defect and notches.

0 100 200 300 400DISTANCE (mm)

0.0E+000

2.0E-009

4.0E-009

6.0E-009

8.0E-009

1.0E-008

MA

X(A

BS(

U2)

)

Contour Notch (100kHz)Reflected wave


0 100 200 300 400DISTANCE (mm)

4.0E-009

8.0E-009

1.2E-008

1.6E-008

2.0E-008

2.4E-008

2.8E-008

MA

X(A

BS(

U2)

)




Figure 4-22 Absolute value of the vertical displacement of the reflected and transmitted wave across the contour notch at several points for the 100kHz guided wave showing a potential to discern the defects between 200mm and 300mm.

87

0 40 80 120 160 200DISTANCE (mm)

0.0E+000

5.0E-010

1.0E-009

1.5E-009

2.0E-009

2.5E-009

3.0E-009

MA

X(A

BS(

U2)

)Contour Notch (185kHz)

Reflected waveNO DEFECTNOTCH 1NOTCH 2NOTCH 3

0 40 80 120 160 200DISTANCE (mm)

8.0E-009

1.0E-008

1.2E-008

1.4E-008

1.6E-008

1.8E-008

MA

X(A

BS(

U2)

)




Figure 4-23 Absolute value of the vertical displacement of the reflected and transmitted wave across the contour notch at several points for the 185kHz guided wave showing that it is difficult to find defects.

20 40 60 80 100DISTANCE (mm)

0.0E+000

1.0E-009

2.0E-009

3.0E-009

MA

X(A

BS(

U2)

)

Contour Notch (280kHz)Reflected wave


0 20 40 60 80 100DISTANCE (mm)

1.0E-008

1.2E-008

1.4E-008

1.6E-008

1.8E-008

MA

X(A

BS(

U2)

)




Figure 4-24 Absolute value of the vertical displacement of the reflected and transmitted wave across the contour notch at several points for the 280kHz guided wave showing that there is a big difference in amplitude of displacement of the reflected waves between defects and no defect case.

88

4.5 WAVE SCATTERING FROM INTERNAL TRANSVERSE

DEFECTS

The characteristics of guided wave scattering from internal transverse defects

were studied. The thickness of the transverse defect is 1mm and the radius of the

transverse defects are 5mm, 10mm, and 15mm. Figure 4-25 shows the shapes and

locations of the transverse defects. The area ratios of each defect area to rail head area are

2%, 9%, and 20%, respectively. Frequencies of 60kHz, 100kHz, 185kHz, and 280kHz

were used to simulate the EMAT loading.

The absolute value of the vertical displacement of the transmitted wave at several

points for 60kHz, 100kHz, 175kHz, and 280kHz are graphed in Figure 4-26, Figure 4-27,

Figure 4-28, and Figure 4-29 respectively. As shown in Figure 4-26, the reflected and

transmitted waves have little potential to discern transverse defects. For 100kHz

(Figure 4-27), the reflected waves have a potential to classify the defects. The transmitted

guided waves for 185kHz has a high potential as shown in Figure 4-28. The guided wave

for 280kHz (Figure 4-29) has the potential of detecting transverse defects.

89

(a) TD1 (b) TD2 (c) TD3

Figure 4-25 Cross-section of the rail with a TD (transverse defect)

( (a):5mm radius (2%), (b):10mm radius (9%), (c):15mm radius (20%) )

0 100 200 300 400 500 600DISTANCE (mm)

0.0E+000

2.0E-009

4.0E-009

6.0E-009

8.0E-009

1.0E-008

MA

X(A

BS(

U2)

)

Internal TD (60kHz)Reflected wave

NO DEFECTTD 1TD 2TD 3

0 100 200 300 400 500 600

DISTANCE (mm)

1.0E-008

2.0E-008

3.0E-008

4.0E-008

5.0E-008

MA

X(A

BS(

U2)

)

Internal TD (60kHz)Transmitted wave



Figure 4-26 Absolute value of the vertical displacement of the reflected and transmitted waves across the transverse defect at several points for the 60kHz guided wave showing little potential to discern transverse defects.

90

0 100 200 300 400DISTANCE (mm)

0.0E+000

2.0E-009

4.0E-009

6.0E-009

8.0E-009

MA

X(A

BS(

U2)

)



0 100 200 300 400

DISTANCE (mm)

1.0E-009

1.5E-009

2.0E-009

2.5E-009

3.0E-009

3.5E-009

4.0E-009

MA

X(A

BS(

U2)

)




Figure 4-27 Absolute value of the vertical displacement of the reflected and transmitted waves across the transverse defect at several points for the 100kHz guided wave showing that the reflected waves have a potential of classifing the transverse defects.

40 80 120 160 200DISTANCE (mm)

0.0E+000

2.0E-008

4.0E-008

6.0E-008

MA

X(A

BS(

U2)

)



0 40 80 120 160 200DISTANCE (mm)

8.0E-009

1.2E-008

1.6E-008

2.0E-008

2.4E-008

MA

X(A

BS(

U2)

)




Figure 4-28 Absolute value of the vertical displacement of the reflected and transmitted waves across the transverse defect at several points for the 185kHz guided wave showing high potential to classify defects with transmitted waves.

91

20 40 60 80 100DISTANCE (mm)

0.0E+000

1.0E-008

2.0E-008

3.0E-008M

AX(

AB

S(U

2))



0 20 40 60 80 100DISTANCE (mm)

1.2E-008

1.4E-008

1.6E-008

1.8E-008

2.0E-008

2.2E-008

MA

X(A

BS(

U2)

)




Figure 4-29 Absolute value of the vertical displacement of the reflected and transmitted waves across the transverse defect at several points for a 280kHz guided wave showing the potential of detecting transverse defects.

92

4.6 LONG RANGE WAVE SCATTERING FROM INTERNAL

TRANSVERSE DEFECTS

The numerical experiments for previous scattering problems were performed

within relatively short distances (0.5m for 60kHz, 0.4m for 100kHz, 0.2m for 185kHz,

and 0.1m for 280kHz) because of an element number limitation. To extend the analytical

result on scattering from various kinds of defects, a numerical experiment for long range

is needed. Assuming symmetry in the lateral direction is one way to extend the length of

the rail model. Figure 4-30 shows a half rail model and the meshes around the circular

transverse defect located at the center of the rail head. Using the symmetry condition, the

rail can be modeled as a half of a whole rail by applying a symmetry boundary condition

on the left surface in shown Figure 4-30.

Figure 4-30 Meshes around the circular transverse defect located at the center of rail headfor a symmetric half rail model

93

Figure 4-31 shows the amplitude ratio of the reflected wave for a 280kHz guided

wave from a circular transverse defect located at the center of the rail head. Without a

defect, the amplitude ratio is almost same with a small value. On the contrary, the

amplitude ratio of the reflected signal from a defect has a large value at close distance

from a defect and then rapidly decreased. The reason for this rapid decrease is that the

scattered waves propagate not only along the top surface of a rail head but also into the

rail. However, this monotonic decrease trend without an oscillation along the distance can

be extended the previous scattering analysis to long range scattering.

0 100 200 300DISTANCE FROM DEFECT (mm)

0

0.1

0.2

0.3

0.4

AM

PLIT

UD

E R

ATI

O O

F R

EFLE

CTE

D S

IGN

AL

(AIN

CID

ENT

WA

VE/A

REF

LEC

TED

WA

VE)

280 kHzWITH CIRCULAR DEFECT

Figure 4-31 Amplitude ratio for a rail with a circular transverse defect located at thecenter of the rail head showing a monotonic decrease with distance

94

4.7 THE EFFECT OF THE SHELLING

The characteristic of wave scattering from shelling located beneath the top surface

of the rail head is studied. The shelling is combined here with the transverse vertical

defects. Figure 4-32 shows the location and size of the defects and the shelling

considered. Figure 4-33 shows the shape of the shelling that lies above the defect 1mm

below the top surface of the rail head.

Figure 4-34 and Figure 4-35 shows the top view of the shelling and the meshes

near the vertical defect and the shelling. Guided waves for 60kHz, 175kHz, and 315kHz

are employed for this study.

(a) (b) (c) (d) (e)

Figure 4-32 Cross-section of the rail with shelling and various defects

( (a):shelling, (b):10mm defect with shelling, (c):20mm defect with shelling,

(d):30mm defect with shelling, (e):40mm defect with shelling)

95

Figure 4-33 Cross-section of shelling along the longitudinal direction of the rail

Figure 4-34 Top view of the shelling

3

1 10 mm

20 mm

20 mm

0.1 mm Incident wave

1 mm

Top surface of the rail head

3

2

96

The maximum values of the absolute value of the vertical displacements of the

reflected and transmitted waves at several points for 60kHz, 175kHz, and 315kHz are

plotted in Figure 4-36, Figure 4-37, and Figure 4-38 respectively. In Figure 4-36 (a), the

reflected waves show no trend. On the contrary, the magnitudes of transmitted waves

between 150mm and 450mm are monotonically decreasing with the crack depth as shown

in Figure 4-36 (b). However, the amplitudes of shelling and the 10mm defect with

shelling are almost the same, because the size of the crack is relatively small. As shown

Figure 4-35 The numerical model of the rail with transverse crack and shelling

97

in Figure 4-37, the magnitude of |U2| shows no big difference between defects with

shelling and no defect with shelling. Because the wave with higher frequency is closer to

a surface wave, the shelling looks like a defect. In Figure 4-38, there is a big difference in

the magnitude of |U2| between defects with shelling and no defect with shelling. Similar

to 175kHz, the magnitudes of |U2| of the defects with shelling are relatively close.

0 100 200 300 400 500DISTANCE (mm)

0.0E+000

4.0E-009

8.0E-009

1.2E-008

MA

X(A

BS(

U2)

)

Internal Notch (60kHz)with shelling

Reflected wave0mm10mm20mm30mm40mm

0 100 200 300 400 500DISTANCE (mm)

0.0E+000

4.0E-009

8.0E-009

1.2E-008

1.6E-008

MA

X(A

BS(

U2)

)


Transmitted wave0mm10mm20mm30mm40mm


Figure 4-36 Absolute value of the vertical displacement of the reflected and transmitted wave across the vertical defect with the shelling at several points for the 60kHz guided wave showing that magnitudes of the transmitted waves between 150mm and 450mm are monotonically decreasing with the crack depth

98

0 100 200 300DISTANCE (mm)

0.0E+000

2.0E-010

4.0E-010

6.0E-010

8.0E-010

1.0E-009

MA

X(A

BS(

U2)

)Internal Notch (175kHz)

with shellingReflected wave

0mm10mm20mm30mm40mm

0 100 200 300DISTANCE (mm)

0.0E+000

4.0E-010

8.0E-010

1.2E-009

1.6E-009

MA

X(A

BS(

U2)

)




Figure 4-37 Absolute value of the vertical displacement of the reflected and transmitted wave across the vertical defect with the shelling at several points for the 175kHz guided wave showing no big difference between the defects with shelling and no defect with shelling

20 40 60 80 100DISTANCE (mm)

0.0E+000

2.0E-009

4.0E-009

6.0E-009

MA

X(A

BS(

U2)

)


Reflected wave0mm10mm20mm30mm40mm

0 20 40 60 80 100DISTANCE (mm)

4.0E-009

6.0E-009

8.0E-009

1.0E-008

1.2E-008

MA

X(A

BS(

U2)

)




Figure 4-38 Absolute value of the vertical displacement of the reflected and transmitted wave across the vertical defect with the shelling at several points for the 315kHz guided wave showing a big difference in the magnitude of |U2| between defects with shelling and no defect with shelling

99

4.8 WAVE SCATTERING AT LOWER FREQUENCIES

From the numerical experiments of the wave scattering patterns from various

kinds of defects for several frequencies, guided waves at lower frequency shows reliable

results in detecting and sizing the defects. Also, these guided waves of lower frequency

are less sensitive to the shelling and possible surface roughness. In other words, the lower

frequency wave (60kHz) seems more suitable for the rail inspection than the higher

frequency wave (175kHz and higher). Therefore, more studies on the wave scattering

patterns at lower frequencies is needed. Three frequencies, 30kHz, 45kHz, and 60kHz,

are therefore chosen to study the wave scattering patterns further from the same defects

(Figure 4-1 and Figure 4-32).

As shown in Figure 4-39, there is some difference between the no defect without

shelling case and the defects without shelling, but the magnitudes of the displacement of

the 10mm and 20mm defect with/without shelling are close. The average displacement of

no defect without shelling and no defect with shelling are almost the same. For the 45kHz

case (Figure 4-40), the magnitudes are monotonically decreased with crack size. Still, the

magnitude of no defect with shelling and the 10mm defect with shelling are close. The

average displacement of no defect without shelling and no defect with shelling is also

almost the same.

100

Shown in Figure 4-41, the magnitudes are monotonically decreased with the

crack size and the magnitudes of no defect with shelling and 10mm defect with shelling

are close. The average displacement of 0mm with shelling is almost half of the 0mm

without shelling.)

In conclusion, as shown in Figure 4-39 (a), Figure 4-40 (a), and Figure 4-41 (a),

there is a big difference between a no defect case without shelling and defects without

shelling. Therefore, these three frequencies are all suitable for detecting defects without

shelling in the rail head. However at 60kHz waves, the average displacement of the no

defect case without shelling is 2X10-8m and the average displacement of no defect with

shelling is about 1.0X10-8m. There is a big difference in the average displacement

between no defect without shelling and no defects with shelling for 60kHz. On the

contrary, the average displacements between no defect without shelling and no defects

with shelling for 30kHz and 45kHz are almost the same. Hence, the 60kHz wave is still

sensitive to the shelling thus making 45kHz a better frequency for the rail inspection,

neglecting the dispersiveness issue for long lengths. (Unfortunately, laboratory

equipment available to us cannot input a narrow frequency bandwidth to evaluation this

theoretical conclusion, nor can it input anything under 50kHz. When considering

dispersive issues, however, our recommendation moves to a 100 to 185kH Pseudo-

Rayleigh surface wave mode position anyway.)

101

0 100 200 300 400 500DISTANCE(mm)

4E-009

8E-009

1.2E-008

1.6E-008

2E-008

2.4E-008

MA

X(A

BS(

U2)

)

REFLECTED WAVEWITHOUT SHELLING(30kHz)

0mm10mm20mm30mm40mm

0 100 200 300 400 500

DISTANCE(mm)

8E-009

1.2E-008

1.6E-008

2E-008

2.4E-008

MA

X(A

BS(

U2)

)

REFLECTED WAVEWITH SHELLING(30kHz)

0mm10mm20mm30mm40mm

(a) Reflected wave without shelling (b) Reflected wave with shelling

0 100 200 300 400 500DISTANCE(mm)

1E-008

2E-008

3E-008

4E-008

MA

X(A

BS(

U2)

)

TRANSMITTED WAVEWITHOUT SHELLING(30kHz)

0mm10mm20mm30mm40mm

0 100 200 300 400 500DISTANCE(mm)

1.2E-008

1.6E-008

2E-008

2.4E-008

2.8E-008

3.2E-008

MA

X(A

BS(

U2)

)

TRANSMITTED WAVEWITH SHELLING(30kHz)

0mm10mm20mm30mm40mm

(c) Transmitted wave without shelling (d) Transmitted wave with shelling

Figure 4-39 Absolute value of vertical displacement of the reflected and transmitted wave for a vertical defect with/without the shelling at several points for 30kHz guided wave showing some difference between no defect without shelling and defects without shelling.

102

0 100 200 300 400 500DISTANCE(mm)

0

4E-009

8E-009

1.2E-008

1.6E-008

MA

X(A

BS(

U2)

)


0mm10mm20mm30mm40mm

0 100 200 300 400 500

DISTANCE(mm)

0

4E-009

8E-009

1.2E-008

1.6E-008

MA

X(A

BS(

U2)

)


0mm10mm20mm30mm40mm


0 100 200 300 400 500DISTANCE(mm)

5E-009

1E-008

1.5E-008

2E-008

2.5E-008

MA

X(A

BS(

U2)

)


0mm10mm20mm30mm40mm

0 100 200 300 400 500

DISTANCE(mm)

5E-009

1E-008

1.5E-008

2E-008

2.5E-008M

AX(

AB

S(U

2))


0mm10mm20mm30mm40mm


Figure 4-40 Absolute value of vertical displacement of the reflected and transmitted wave for a vertical defect with/without the shelling at several points for 45kHz guided wave showing that the magnitudes are monotonically decreased with crack size.

103

0 100 200 300 400 500DISTANCE(mm)

0

2E-009

4E-009

6E-009

8E-009

1E-008

MA

X(A

BS(

U2)

)


0mm10mm20mm30mm40mm

0 100 200 300 400 500

DISTANCE(mm)

2E-009

4E-009

6E-009

8E-009

1E-008

1.2E-008

1.4E-008

MA

X(A

BS(

U2)

)


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Figure 4-41 Absolute value of vertical displacement of the reflected and transmitted wave for a vertical defect with/without the shelling at several points for 60kHz guided wave showing that the magnitudes are monotonically decreased with the crack size

104

4.9 SUMMARY

The characteristics of guided waves scattering from defects located in a rail head

were studied. The internal notches, internal holes, arc-shaped contour notches, and interal

transverse defects are chosen for the defects and 60kHz, 100kHz, 175kH, 280kHz, and

315kHz are selected for the frequencies. The effect of the shelling was also explored.

From a practical point of view, focus is on the vertical displacement at the top surface of

the rail head.

Because of a computational efficiency limitation in hardware and software of the

computation, there is a limitation in the length of the numerical rail model used in the

study. For this reason, the length of the model used in this study is relatively short thus

leading to difficulties in separating the reflected waves from the incident waves.

Therefore, the transmitted waves are more suitable for an analysis in the numerical

models. However, the length of the model can be extended for symmetric problems

except in the case of a non-symmetric defect. In order to use longer lengths, an additional

cut was made across the midsection of the web thinking that since most of the energy was

in the head that little would leak into the web, hence leading to almost no energy

reflection back into the head, but this was not the case. The numerical experiment of the

long range scattering for circular transverse defect located at the center of the rail head

can be extended the short range scattering analysis to long range scattering.

105

The guided waves at lower frequency (60kHz) have more potential for detecting

defects located in a rail head and minimizing the effect of shelling than the guided waves

for higher frequency (185kHz or higher). The higher frequency guided waves see the

shelling as a defect. Therefore, lower frequency guided waves are more highly

recommended for rail inspection for the detection of a transverse defect under the

shelling.

Chapter 5

EXPERIMENTAL VALIDATION

5.1 INTRODUCTION

The characteristics of the propagation and scattering of guided waves in rail are

studied using ABAQUS/Explicit. From the results, the guided waves in the pseudo

Rayleigh surface wave region seem practically useful when the goal is to have energy

concentration in the rail head. Guided waves at lower frequency are less sensitive to the

shelling near the surface, yet still with a reasonable potential for detecting the defects in

the rail head. Some basic experiments are now presented that validate some of the

theoretical predictions.

107

5.2 ELECTROMAGNETIC ACOUSTIC TRANSDUCER (EMAT)

Of many possibilities of generating ultrasonic energy into a rail via piezoelectric

devices, laser beams, or air coupled transducers an Electromagnetic Acoustic Transducer

(EMAT) was selected. Principal reasons include couplant not needed, ability to generate

via a rough surface, non-contact lift off possibilities, sufficient energy, possibility of

mode and frequency control. The basic principle of the EMAT is associated with the

Lorentz force expressed as

Where F is Lorentz force, J is an eddy current, and B is a magnetic field. The direction of

the Lorentz force is shown in Figure 5-1 [Rose 1999]

BJF ×= 5.1

(a) Shear horizontal (SH) wave (b) Longitudinal wave

F F

B

BJJ

108

With a combination of the magnet stacking and coil directions, various guided

waves can be generated. Figure 5-2 shows the structures of the Lamb wave EMAT and

the SH wave EMAT. The spacing is an important parameter in EMAT design since twice

the spacing is the slope of the activation line reported earlier in Figure 3-3. The distance

between coils is the spacing in the Lamb wave EMAT and the thickness of the magnets is

the spacing in the SH wave EMAT.

Though the EMAT requires complex coil design and strong magnets, it is widely

used because of its couplant-free advantage. This couplant-free EMAT can be applied at

reasonable lift off distance of up to 5mm at high or low temperature, with specimens in

motion, and also to rough surfaces.

Figure 5-1 Schematic of the directions of the Lorentz force

(a) Lamb wave EMAT (b) SH wave EMAT

Figure 5-2 Structure of EMATs

S

N

S

N S

N S

N S

N S

N S

N S

N

109

5.3 LAB TEST

5.3.1 DISPLACEMENT PROFILES OF THE GUIDED WAVES

Before performing any of the scattering experiments, the displacement profiles

around the rail for four different frequencies (60kHz, 100kHz, 185kHz, and 280kHz)

were studied. The guided waves were generated with an EMAT at the top surface of a rail

head. The displacement profiles was measured about 2m from the EMAT loading with a

piezoelectric transducer. The displacements for each frequency were normalized with the

maximum displacement at that frequency.

Figure 5-3 shows the displacement profile around a rail for four frequencies. As

expected from the numerical experiments reported in Chapter 3, the most of the energy is

concentrated in the rail head. The displacements at the side of head are smaller than the

displacement at under the head. Since the piezoelectric transducer detects the normal

displacement of a surface, at the side of head, the normal displacement is small because

of the pseudo Rayleigh wave. Also the guided wave for higher frequency has a smaller

displacement at side of the head, under the head, and on the web and base. These results

are also expected from the numerical experiments.

110

5.3.2 A HOLE IN A CLEAN RAIL HEAD SURFACE

The experiments for various types of artificial defects were performed in the

Laboratory. To generate guided waves and to receive reflected waves from the defects,

the Lamb type EMATs with four different frequencies (60kHz, 100kHz, 185kHz, and

280kHz) were used in a pulse-echo mode. The first specimen is a rail with a 0.25"

diameter hole and a clean rail head surface. Figure 5-4 shows the location of a hole in the

rail. Figure 5-5 shows the position of the hole and the EMAT locations. The guided

0

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60kHz100kHz185kHz280kHz

UNDER OFHEAD

UNDER OFHEAD

BASE WEB SIDE OFHEAD

TOP OF HEAD

SIDE OFHEAD

WEB BASE

BASE

WEB

SIDE OFHEAD

TOP OF HEAD

SIDE OFHEAD

WEB

BASE

UNDER OFHEAD

UNDER OFHEAD

Figure 5-3 Displacement profile of guided waves

111

waves are generated from the transmitter, passing the receiver directly, propagating along

the rail, and then reflected from a hole or a rail end, and then arriving at the receiver

again. Signals were obtained at different distances from a hole by moving the transmitter

and the receiver. Figure 5-6 shows the RF waveform at 18" from a hole as an example.

Unlike the numerical experiments, a received signal can be affected by many

factors such as filtering, alignment of the EMATs, liftoff of the magnet of the EMAT,

and the number of cycles used for input. Among them, the alignment of the EMATs is

different when moved to new position. If the EMATs are misaligned, then both the direct

signal and the reflected signal have small amplitudes. Therefore, the reflected signal from

a defect is normalized with the direct signal. Figure 5-7 shows the amplitude ratio of a

reflected signal from a hole and a direct signal for a rail with a clean rail head surface

with a hole at different positions. At a distance less than 1m, 60kHz and 100kHz guided

waves have more potential for detecting the hole and after 1m, guided waves for four

frequencies have a similar ability for detecting the hole.

112

Figure 5-4 A Photograph of a hole in a clean rail

Figure 5-5 The position of a hole and EMATs

Rail EndRail Head Hole

T R

EMATs

113

Direct signal

Hole Rail end

0 1 2 3DISTANCE

(a hole in a clean rail, 100kHz )

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Figure 5-6 RF wave form of a reflected wave from a hole in a clean rail for a 100kHz guided wave at a distance of 0.45m showing the direct signal, hole, and rail end.

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a holein a clean rail


Figure 5-7 Amplitude ratio for a rail with a clean surface of a rail head and a hole showing that at a distance less than 1m, 60kHz and 100kHz guided waves have morepotential for detecting the hole

114

Figure 5-8 ~ Figure 5-11 shows the comparisons of amplitude ratios of a reflected

signal from a hole in a clean rail head surface for 60, 100, 185, and 280kHz. Though the

ratio curves of experiment and FEM results show a different trend at each frequency, the

levels of the amplitude ratios are similar, because the shapes of a rail cross section and a

hole defect are not exactly same.

0 100 200 300 400 500RECEIVER DISTANCE FROM DEFECT(mm)

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(HOLE 60kHz)EXPFEM

Figure 5-8 Comparison of amplitude ratios of experiment and FEM results for a hole in a clean rail head surface for 60kHz showing a difference in the ratio level (Note thattransmitter distance was approximately 600mm).

115


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(HOLE 100kHz)EXPFEM

Figure 5-9 Comparison of amplitude ratios of experiment and FEM results for a hole ina clean rail head surface for 100kHz showing a similar amplitude ratio level, especially atshorter distances (Note that transmitter distance was approximately 600mm).

0 100 200 300 400RECEIVER DISTANCE FROM DEFECT(mm)

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(HOLE 185kHz)EXPFEM

Figure 5-10 Comparison of amplitude ratios of experiment and FEM results for a hole ina clean rail head surface for 185kHz showing a similar amplitude ratio level (Note thattransmitter distance was approximately 600mm).

116

5.3.3 A NOTCH IN A CLEAN RAIL HEAD SURFACE

The second specimen is a rail with a clean rail head surface and a notch. It is

shown in Figure 5-12. Figure 5-13 shows the amplitude ratio for a rail with a clean rail

head surface and a notch at different positions. Guided waves for 280kHz have an

outstanding potential for detecting the notch because the notch is not only an internal

defect but is also an open to the surface defect. The notch edge around the rail head

therefore receives sufficient surface wave energy.


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(HOLE 280kHz)EXPFEM

Figure 5-11 Comparison of amplitude ratios of experiment and FEM results for a hole in a clean rail head surface for 280kHz showing a similar amplitude ratio level (Note thattransmitter distance was approximately 600mm).

117

Figure 5-14 ~ Figure 5-17 show a comparison of amplitude ratio of a reflected

signal from a notch in a clean rail head surface for four different frequencies. Similar to

Figure 5-12 A Photograph of a notch in a clean rail

0 1 2 3DISTANCE (m)

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a notch in a clean rail


Figure 5-13 Amplitude ratio for a rail head with a clean surface and a notch showing thatguided waves for 280kHz have an outstanding potential for detecting the notch

118

the hole defect, the trend of the amplitude ratios of the experiment and FEM result are

different, however, the level is similar.


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(NOTCH 60kHz)EXPFEM

Figure 5-14 Comparison of amplitude ratio of experiment and FEM results for a notch in a clean rail head surface for 60kHz showing a similar amplitude ratio level (Note thattransmitter distance was approximately 600mm).


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(NOTCH 100kHz)EXPFEM

Figure 5-15 Comparison of amplitude ratio of experiment and FEM results for a notchin a clean rail head surface for 100kHz showing a similar amplitude ratio level (Note thattransmitter distance was approximately 600mm).

119


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Figure 5-16 Comparison of amplitude ratio of experiment and FEM results for a notchin a clean rail head surface for 185kHz showing a similar amplitude ratio level (Note thattransmitter distance was approximately 600mm).


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Figure 5-17 Comparison of amplitude ratio of experiment and FEM results for a notchin a clean rail head surface for 280kHz a showing similar amplitude ratio level (Note thattransmitter distance was approximately 600mm).

120

5.3.4 A HOLE IN A ROUGH RAIL HEAD SURFACE

The third specimen is a rail with a rough rail head surface and a 0.25" diameter

hole. It is shown in Figure 5-18. Figure 5-19 shows the amplitude ratio for a rail with a

rail head rough surface and a hole at different positions. In this case, the guided waves for

280kHz cannot detect a hole over the entire distance since a collection of small echoes

from the rough surface does not allow any energy to reach the defect. On the contrary,

guided waves for lower frequencies (60kHz and 100kHz) can find the hole.

Figure 5-18 A Photograph of a hole in a rough rail

121

5.3.5 SIMULATION EXPERIMENT FOR TRANSVERSE DEFECT AND

SHELLING

Figure 5-20 shows a welded notch (the edge of a notch is welded which simulates

a transverse defect). A cut was initially put into the rail, then welded closed. Figure 5-21

shows the amplitude ratios of a welded notch for waves of 60kHz, 100kHz, 185kHz, and

0 0.4 0.8 1.2 1.6DISTANCE (m)

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a holein a rough rail


Figure 5-19 Amplitude ratio for a rail with a rough rail head surface and a hole showingthat guided waves for 60kHz and 100kHz can find the hole, 185kHz is marginal, and the280kHz guided wave cannot see the hole since a collection of small echoes from the rough surface does not allow any energy to reach the defect

122

280kHz. As seen in Figure 5-21, Lamb waves for all frequencies show similar

sensitivities for the welded notch.

Figure 5-22 shows a “ssd (simulated surface damage or shelling)” with an average

0.8mm depth. Figure 5-23 shows the reflected signal from a “ssd”. In Figure 5-23, the

reflected waves from a “ssd” should be located in the red circles. The guided waves for

280kHz detect the “ssd” for entire distance and the 185kHz guided waves find the “ssd”

at close distance (less than 1m). On the contrary, the guided waves for 60kHz and

100kHz cannot detect the “ssd”, therefore the guided waves for lower frequency is more

suitable for the rail inspection with minimizing the interference of the shelling.

Figure 5-20 A Photograph of a welded Notch

123

-3 -2 -1 0 1 2 3DISTANCE (m)

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Figure 5-21 Amplitude ratios for a rail with a welded notch showing that guided wavesfor four frequencies (60, 100, 185, and 280kHz) can find the welded notch.

Figure 5-22 A Photograph of a “ssd (simulated surface damage or shelling)”

124

0 1 2 3

DISTANCE (m)

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ssd (60kHz)

0.3m

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ssd (100kHz)

0.3m

0.6m

0.9m

1.2m

1.5m

1.8m

(a) 60kHz (b) 100kHz

125

Figure 5-24 shows a photograph of a welded notch under a “ssd” and Figure 5-25

~ Figure 5-28 displays differences of the amplitude ratios for a rail with a welded notch

without a “ssd” and with a “ssd”. As seen in Figure 5-25 and Figure 5-26, there are no

significant differences in average amplitude ratios between that with a “ssd” and that

without a “ssd”. However, for the 185kHz (Figure 5-27), a difference in average

amplitude ratio begins to appear after 1m. The 280kHz Lamb wave shows a significant

difference in amplitude ratio for an entire range, because the “ssd” scatters the incident

wave before a welded notch, and Lamb waves for higher frequency have a more

concentrated energy near the top surface of a rail head.

0 1 2 3

DISTANCE (m)

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ssd (185kHz)

0.3m

0.6m

0.9m

1.2m

1.5m

1.8m

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ssd (280kHz)

0.3m

0.6m

0.9m

1.2m

1.5m

1.8m

(c) 185kHz (d) 280kHz

Figure 5-23 The reflected signals from a “ssd” for four frequencies (60, 100, 185, and 280kHz) showing inability of 60kHz, 100kHz, and 185kHz at distance greater than 1.2m of detecting shelling simulation via “ssd” on top surface

126

Figure 5-24 A photograph of a welded notch under a “ssd” simulation surface roughness and a shelling

0 1 2 3DISTANCE (m)

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welded notch(60kHz)"ssd" : simulated surface damage or shelling

without “ssd”with “ssd”

Figure 5-25 Amplitude ratio for a rail with a welded notch without a shelling and with ashelling for 60kHz showing no significant differences in average amplitude ratios between with a “ssd” and without “ssd”.

127

0 1 2 3DISTANCE (m)

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Figure 5-26 Amplitude ratio for a rail with a welded notch without a shelling and with ashelling for 100kHz showing a similar sensitivity showing no significant differences inaverage amplitude ratios between that with a “ssd” and that without “ssd”.

0 1 2 3DISTANCE (m)

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Figure 5-27 Amplitude ratio for a rail with a welded notch without a shelling and with ashelling for 185kHz showing a difference in average amplitude ratio begins to appearafter 1m.

128

0 1 2 3DISTANCE (m)

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"ssd" : simulated surface damage or shellingwithout “ssd”with “ssd”

Figure 5-28 Amplitude ratio for a rail with a welded notch without a shelling and with ashelling for 280kHz showing a significantly different sensitivity for an entire range.

129

5.3.6 BOLT HOLES

In this experiment, the reflected signals from bolt holes will be compared with

reflected signals from a transverse defect simulation to see if an error could be made in

calling a defect. Figure 5-29 shows a photograph of some bolt holes and Figure 5-30

displays an amplitude ratio for a rail with bolt holes. Because most of the energy of the

pseudo Rayleigh surface wave is concentrated in the rail head, the waves of four

frequencies (60kHz, 100kHz, 185kHz, and 280kHz) cannot find the bolt holes. This is

good! Therefore the guided waves at these frequencies are suitable for rail inspection

without a reflected wave from the bolt holes.

Figure 5-29 A photograph of bolt holes

130

5.3.7 DISPERSIVE PROPERTY

For long range rail inspection, according to the theoretical results, the dispersive

guided waves decrease in amplitude and also lead to increase in pulse duration, hence

reduced longitudinal resolution. For these reasons, the dispersive characteristic is an

important factor. The reflected waves from a rail end have huge amplitudes; therefore a

wave reflected from a rail end is used to calculate a dispersive characteristic. Figure 5-31

0 0.5 1 1.5 2 2.5DISTANCE (m)

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Figure 5-30 Amplitude ratio for a rail with bolt holes showing that guided waves for four frequencies (60, 100, 185, and 280kHz) cannot find bolt holes.

131

shows an amplitude ratio of a direct signal and a reflected signal from a rail end. The

pulse width ratio for 280kHz is about 1, this means that the pulse width of the reflected

waves are the same as the pulse width of the direct waves. However, the pulse width of

the 185kHz guided waves is 4 times wider than the pulse width of the direct waves. For

pseudo Rayleigh surface waves, the waves at lower frequency are more dispersive then

the higher frequency waves. Therefore, the higher frequency guided waves are more

suitable for a longer range inspection if dispersiveness is a critical issue.

0 0.5 1 1.5 2DISTANCE (m)

0

1

2

3

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PULS

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(A

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DISPERSION185kHz280kHz

0 0.5 1 1.5 2

DISTANCE (m)

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DISPERSION185kHz280kHz

(a) Pulse duration ratio (b) Amplitude ratio

Figure 5-31 Dispersive characteristic of 185kHz and 280kHz guided waves showingthat the 185kHz guided waves are more dispersive then the 280kHz guided waves.

132

5.4 FIELD TESTS

A field experiment was conducted at the Transpotation Technology Center, Inc.

(TTCI) in Pueblo, Colorado. The reflected signals from numerous artificial and natural

defects were collected. Lamb type EMAT transducers of 185kHz and 280kHz were used

to collect the signals. Figure 5-32, Figure 5-33, and Figure 5-34 show artificial defects (a

notch, a “ssd”, and a notch under a “ssd”) and Figure 5-35 and Figure 5-36 shows a

natural defect (a shelling and a transverse defect; Note the photograph of the transverse

defect as an example). Figure 5-37 shows the reflected signals from the notch under the

“ssd” for 185kHz and 280kHz Lamb type guided waves as an example. Different from

the lab tests, there were unexpected difficulties in the field experiments. One typical

difficulty was some undefined noise and this noise; shown in Figure 5-37 (b).

Figure 5-38, Figure 5-39, and Figure 5-40 shows the amplitude ratios for the

artificial defects and Figure 5-41, Figure 5-42, and Figure 5-43 show the amplitude ratios

for the natural defects. Overall, the 185kHz guided waves show better results than the

280kHz guided waves. The 185kHz guided wave has more energy inside the rail head

compared to the 280kHz situation The 185kHz approach has more potential for detecting

the transverse defects.

133

Figure 5-32 A Photograph of a notch

Figure 5-33 A Photograph of a “ssd (simulated surface damage or shelling)”

134

Figure 5-34 A Photograph of a notch under a “ssd”

Figure 5-35 A Photograph of a shelling

135

Figure 5-36 A photograph of a transverse defect (as an example)

(a) 185kHz (b) 280kHz

Figure 5-37 Reflected signal from notch under “ssd” showing direct signal, “ssd”, and noise

“ssd”

“ssd”

“ssd”

“ssd” Noise

0 1 2 3DISTANCE (m)

A

M

P L

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( m )

0 1 2 3DISTANCE (m)

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P L

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( m )

2ft

4ft

6ft

2ft

4ft

6ft

185kHz 280kHz

Direct signal

136

-2 -1 0 1 2DISTANCE (m)

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185kHz280kHz

Figure 5-38 Amplitude ratio for a notch showing that 185kHz guided waves are more sensitive to the notch than the 280kHz guided wave since wave structure is deeper into torail head

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185kHz280kHz

Figure 5-39 Amplitude ratios for “ssd” shown sensitive to both frequencies 185kHz and 280kHz, except for large distances away from the defect (a 100kHz sensor would be lesssensitive to “ssd”, but unfortunately not available)

137

-2 -1 0 1 2DISTANCE (m)

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185kHz280kHz

Figure 5-40 Amplitude ratio for a notch under “ssd” showing that in this case both seem to see the notch, but both contains possible “ssd” echoes. Unfortunately, a 60 or 100kHz sensor was not available at Pueblo, which we feel would produce a much better result,since it would definitely not see the “ssd”.

-2 -1 0 1 2DISTANCE (m)

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185kHz280kHz

Figure 5-41 Amplitude ratio for a transverse defect showing that 185kHz guided wave might see the transverse defect (but in reality not sure since it could be seeing the shellingagain pointing to the need of a lower frequency transducer).

138

-2 -1 0 1 2DISTANCE (m)

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NATURAL SHELLING 1185kHz280kHz

Figure 5-42 Amplitude ratio for a shelling defect showing that both frequencies aresensitive to the shelling. (Probably a 100kHz sensor wouldn’t see the shelling)

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TRANSVERSE DEFECT 2 UNDER SHELLING 2185kHz280kHz

Figure 5-43 Amplitude ratio for a transverse defect under a shelling showing that thesensor might be OK. (But 100kHz would be clearer)

139

5.5 SUMMARY

The basic principle of an EMAT (electromagnetic acoustic transducer) used in the

experiments was introduced. Experiments for artificial defects and natural defects in a

rail were carried out both in the laboratory and in the field. The important knowledge

acquired from the experiments is summarized as follows.

(1) Do modes and frequencies along the pseudo Rayleigh surface wave line really show

that energy is only in the rail head?

The guided wave for lower frequency has more energy in the web and base,

however the magnitude is much smaller than the energy in the rail head. (See Figure 5-3)

(2) Is defect detection possible with all frequencies when there are no surface defects or

shelling?

The inspection of a defect in a rail with a clean rail head surface was studied.

From the laboratory tests of a hole in a rail with a clean rail head surface and a welded

notch, all guided waves for four frequencies (60kHz, 100kHz, 185kHz, and 280kHz)

show a considerable amplitude ratio of the reflected waves (See Figure 5-7 and Figure 5-

21). Therefore, the guided waves for these four frequencies are suitable for the detecting

a defect in a rail with a clean rail head surface.

140

(3) Is defect detection possible with all frequencies with surface defects or shelling?

The inspection of a defect in a rail with a rough rail head surface was studied. For

the experiment of a hole in a rail with a rough rail head surface, the guided waves for

280kHz cannot detect a hole. The 185kHz guided waves show a little better sensitivities

than the 280kHz guided waves but cannot find a hole over a long distance (See Figure 5-

19). For the experiment of a “ssd” and a welded notch under a “ssd”, the guided waves

for 280kHz show a significant sensitivity for a “ssd” and also the guided waves for

185kHz show a high sensitivity for a “ssd” at close distance (See Figure 5-23). Especially,

for the amplitude ratio for 280kHz guided waves is shown a significant sensitivity drop

with the presence of the “ssd” (See Figure 5-28). Therefore, guided waves for lower

frequency (60kHz and 100kHz) are recommended for the rail inspection with minimizing

the effect of a shelling and a rough surface.

(4) Is it possible to find a surface defect with all frequencies?

The inspection of a surface defect was studied. For the experiment of a notch in a

rail with a clean rail head surface, the 280kHz guided waves shows an excellent

sensitivity for a notch because the notch extended to the surface and the energy of higher

frequency (280kHz) is concentrated on the surface of the rail head (See Figure 5-13).

Therefore, guided waves of higher frequency are appropriate for the detection of a

surface defect.

141

(5) What inspection can be carried out to not see the bolt holes in the web?

The effect of the bole holes was studied. The guided waves over the frequency

range from 60kHz to 280kHz can avoid possible reflection waves from the bolt holes,

hence reducing false alarm possibilities (See Figure 5-30).

(6) From what distance should the dispersive characteristic be considered?

For pseudo Rayleigh surface waves, waves at lower frequency are more

dispersive then the higher frequency waves and these are verified with the 185kHz and

280kHz guided waves (See Figure 5-31). Therefore, the higher frequency guided waves

are more suitable for a longer range inspection if dispersiveness were the only issue.

(7) Comparison between experiments and numerical experiments.

Though the trends of the experimental and FEM results are not exactly the same,

the amplitude ratio levels of the reflected waves are close (See Figure 5-8 ~ Figure 5-11,

Figure 5-14 ~ Figure 5-17). A difference in the cross sectional shape between a real rail

and the rail model leads to some disagreement in the trends.

(8) The field tests

Though only two guided wave frequencies (185kHz and 280kHz) were used for

the field tests because of sensor availability, the 185kHz guided waves were more

suitable compared to the 280kHz guided wave for the detection of defects located in a rail

head (Figure 5-38 ~ Figure 5-43).

142

(9) The optimized condition for a rail inspection sonsidering shelling influences and

dispersiveness.

The best condition in detecting a transverse defect under a shelling is a pseudo

Rayleigh surface waves between 100kHz or 185kHz.

Chapter 6

CONCLUDING REMARKS

6.1 CONCLUDING REMARKS

Ultrasonic guided waves are well-known for long-range inspection. The waves

can travel a relatively long distance along a structure with excellent sensitivity from a

single sensor position. In this study, new rail inspection techniques using guided waves

are developed with the aid of numerical and laboratory experiments.

The theory of the Semi-analytical Finite Element (SAFE) technique was

developed to calculate the phase and group velocity dispersion curves, essential

information for the theoretically driven experiments with ultrasonic guided waves. This

SAFE technique was verified with an analytical solution for a plate problem and

associated phase and group velocity dispersion curves.

The ABAQUS/Explicit program, a commercial FEM package, was also verified

with the analytical solution for a plate before studying the rail problem. With the

assistance of the FEM technique, the propagation characteristics of guided waves in a rail

were explored at various regions in the phase velocity dispersion curve space. From this

144

calculation, the guided waves near the pseudo Rayleigh surface wave region were most

suitable for rail inspection because most of the energy was concentrated in the rail head.

The scattering characteristics of guided waves from various defects were studied

at several frequencies. The effects of the shelling were also explored. It is difficult to

distinguish the defects and the shelling with higher frequency guided waves because the

ultrasonic energy is concentrated at the top surface of the rail head. Therefore, from the

numerical experiments, guided waves for lower frequency have the potential to minimize

the effects of the shelling and to detect and size defects.

In numerical experiments to study the propagation and scattering characteristics

of the guided waves in rail, the hybrid guided wave-FEM technique was developed. In

this technique, the Lamb type EMAT (electromagnetic acoustic transducer) loading is

simulated to generate the guided waves based on the phase velocity dispersion curves and

activation lines.

Experiments for artificial defects and natural defects in a rail were carried out in

the laboratory and in the field. From the experiments for artificial defects (especially a

welded notch under a saw cut), the results of the numerical experiments pointed ot the

use of lower frequency guided waves (60kHz and 100kHz) with more potential for

detecting defects while minimizing the effects of shelling compared to the higher

frequency guided waves (185kHz and 280kHz). However, for long range inspection, the

higher frequency guided waves are recommended for a more accurate test, because

145

guided waves for higher frequency are less dispersive. Therefore, the compromising best

condition in detecting a transverse defect under a shelling is the pseudo Rayleigh surface

waves between 100kHz and 185kHz.

146

6.2 CONTRIBUTIONS

1. A robust research tool, hybrid guided wave-FEM technique is utilized in computational

aspects of guided wave propagation and scattering in a rail.

2. The 3D FEM technique was used to simulate EMAT loading.

3. Wave structures were calculated by the hybrid guided wave-FEM technique. These

wave structures are useful in selecting the frequency and mode for efficient inspection.

4. Analysis of the numerical experiments for guided wave propagation showing that, the

pseudo Rayleigh surface waves region in the dispersion curve space was a high potential

for finding transverse defects in a rail head because most of the energy is concentrated in

the rail head.

5. It is experimentally confirmed that the pseudo Rayleigh surface wave has most of the

energy in the rail head.

6. The top surface is the best position on a rail to generate and receive the guided waves

associated with transverse defect detection in the rail head.

147

7. It is proven theoretically and experimentally that the higher frequency waves along the

pseudo Rayleigh surface wave line are less dispersive compared to lower frequency

waves.

8. The potential of the pseudo Rayleigh surface wave in detecting and sizing transverse

defects in a rail head is studied

9. Shelling influences are not major for lower frequency guided waves less than 185kHz.

10. The pseudo Rayleigh surface wave for higher frequency is very sensitive to the

shelling and surface defects than lower frequency.

11. A new guided wave technique for rail inspection is developed and tested in a Lab and

field environment.

148

6.3 FUTURE WORK

1. More studies of longer distances are required say 1ft to 10ft

2. There are two types of welds in a rail; one is a shop-weld and the other is thermite-

weld. The study of the effect of these welds is needed.

3. The study of the effect of ties (sleepers) is needed.

4. The mode conversions at a defect.

5. The effect of the location and orientation of transverse defects

6. The proper frequency and mode to detect defects located in the web and base.

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Appendix A

Nontechnical Abstract

A train is one of the oldest and most important transportation methods for moving

people and goods. A train accident can causes serious casualties and property damage.

Many factors could lead to a train disaster and the defects in rail are one of the major

problems. Detection of defects and proper maintenance action for a rail is therefore

essential.

There are two kinds of typical defects in a rail head. They are shelling and

transverse defects. Shelling is a horizontal plane defect generated by the sliding and/or

rolling the wheel over the rail from shear reversal and is usually located just below the

top surface of the rail. The transverse defects are usually generated and grown inside the

rail head from the shelling region down into the head. Shelling is not fatal but transverse

defects are. Conventional ultrasonic tests (the normal incident technique and the oblique

incident technique) have difficulties in detecting the transverse defects under the shelling,

because most of the ultrasonic energy is reflected from the shelling. For this reason, the

guided wave ultrasonic technique is potentially a suitable method for detecting defects

under the shelling. The cross-sectional area of the shelling is much smaller than that of

the transverse defects in the guided wave propagation direction.

161

The basic five senses of a human are the primary tools in diagnosis. Among them,

the visual test and hearing test has quite a long history. If a patient goes to the hospital,

the doctor first sees the patient to observe the sickness. The doctor might then use the

stethoscope to hear inside the patient. A similar procedure is applying in nondestructive

evaluation. Large defects can be detected by eye-inspection and sound. However, micro

cracks cannot be detected by sound; therefore ultrasonics is used to detect defects in the

structures. Generally, two kinds of transducers are used to generate and detect defects

with ultrasonics. One uses a piezoelectric transducer and the other used an

electromagnetic acoustic transducer (EMAT). In this research, the EMAT is simulated

using ABAQUS/Explicit (a commercial three dimensional finite element method (FEM)

package).

The inspection technique using ultrasonics is well known because of its excellent

sensitivity. However, the conventional technique (normal incident and oblique incident

technique) inspects the structure point by point; therefore, becoming very tedious takeing

long time. Also, this method has a difficulties in finding defects under shelling, because

most of the ultrasonic energy is reflected from the shelling. On the other hand, the guided

ultrasonic technique is an efficient and promising inspection technique because this wave

can propagate along the structure with an excellent sensitivity.

There is still difficulty in using the guided waves because of so many modes in a

structure. Because of these modes, it is difficult to understand the behavior of the guided

162

waves, to control the modes, and to interpret the inspection results. Usually there are

several modes in plates and pipes between 0 ~ 200kHz, however there are hundreds of

modes in a rail in the same frequency range. Therefore, the right mode is an important

factor in rail inspection along with the appropriate frequency.

It is found that the surface wave (the wave localized near the surface) is the best

guided wave to keep energy in the rail head fro critical transverse crack detection. Other

modes could cause confusion in interpreting the test results. With these surface guided

waves, the scattering patterns from defects are also studied. The defects adapted in this

study are internal notches, internal holes, side notches, transverse crack simulations, and

the shelling. The lower frequency (below 60kHz) guided wave is more suitable in

detecting the defects under the shelling than the higher frequency (above 175kHz) guided

wave.

This research provides a new modeling technique to simulate EMAT loading and

can suggest guide lines for a new inspection technique for finding defects in the rail head

under shelling. Furthermore, the research area can be extended to various types of defects,

different location of the defects, different loading position, and welding areas.

VITA

Chong Myoung Lee

EDUCATION Ph.D. – Engineering Science and Mechanics, The Pennsylvania State University, 2001 – 2006 M.S. – Mechanical Engineering, Yonsei University, Seoul, Korea, 1993 – 1995; B.S. – Mechanical Engineering, Yonsei University, Seoul, Korea, 1991 – 1993; B.S. – Physics, Yonsei University, Seoul, Korea, 1987 – 1991; SELECTIVE PUBLICATIONS

Prefereed Journal 1. Chong Myoung Lee, Joseph L. Rose, Wei Luo, and Younho Cho, “A Computational

Tool for Defect Analysis in Rail with Ultrasonic Guided Waves”, Accepted for publish in Key Engineering Materials

2. Chong Myoung Lee, Joseph L. Rose, and Younho Cho, “A Characteristic of scattering patterns from defect in a rail”, Accepted for publish in Key Engineering Materials.

3. Younho Cho, Chong Myoung Lee, Joseph L. Rose and Ikkeun Park, “Health monotoring of piping weld with guided waves”, Journal of Materials Engineering and Performance, in progress Conference

1 Chong Myoung Lee, Joseph L. Rose, and Younho Cho, “A Characteristic of scattering patterns from defect in a rail”, the 1st International Conference on Advanced Nondestructive Evaluation, Jeju, Korea, November 7-9, 2005

2 Chong Myoung Lee, Joseph L. Rose, Wei Luo, and Younho Cho, “A Computational Tool for Defect Analysis in Rail with Ultrasonic Guided Waves”, the 1st International Conference on Advanced Nondestructive Evaluation, Jeju, Korea, November 7-9, 2005

3 C. He, J. K. Van Velsor, Chong Myoung Lee, and J. L. Rose, “Health Monitoring of Rock Bolts Using Ultrasonic Waves”, Presented at the 31st Review of Progress in Quantitative Nondestructive Evaluation Conference, July 31st – August 5th , Brunswick, Maine, 2005.

4 Younho Cho, Chong-Myoung Lee, Joseph L. Rose, and Ik-Keun Park, “Health Monitoring of Piping Weld”, ASME Pressure Vessels and Piping Division Conference, July 20th – 24th , 2004; San Diego, CA, 2004

5 Younho Cho, Joseph L. Rose, Chong Myoung Lee, and Gregory N. Bogan, “Elastic Guided Waves in Composite Pipes”, ASME Pressure Vessels and Piping Division Conference, July 20th – 24th , 2004; San Diego, CA, 2004

6 Chong Myoung Lee, Younho Cho, Joseph L. Rose, and Eric Hauck, “Characterization Potential of Plane Defects in a Rail”, 16th World Conference on Nondestructive Testing, August 30th – September 3rd , Montreal, Canada, 2003

7 Chong Myoung Lee, Joseph L. Rose, Younho Cho, and Ik Keun Park, “Guided Wave Focusing Feasibility in Layered Devices”, Presented at the 29th Review of Progress in Quantitative Nondestructive Evaluation Conference, July 27th – August 1st , Green Bay, Wisconsin, 2003.

guided elastic waves in structures with an arbitrary …

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