ENHANCED CRACK DETECTION BY COMBINATION OF LASER AND ULTRASONIC TECHNIQUES. A dissertation submitted to the

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2 ENHANCED CRACK DETECTION BY COMBINATION OF LASER AND ULTRASONIC TECHNIQUES A dissertation submitted to the Division of Research and Advanced Studies of the University of Cincinnati in partial fulfillment of the requirements for the degree of DOCTORATE OF PHILOSOPHY (Ph. D.) in the Department of Aerospace Engineering and Engineering Mechanics of the College of Engineering 2001 by Zhongyu Yan M.S., Institute of Acoustics, Chinese Academy of Sciences, 1993 B.S., Xuzhou Normal University, 1990 Committee Chair: Prof. Peter B. Nagy

3 ABSTRACT Pulsed laser irradiation of the surface of a medium can produce temporally and spatially distributed thermal stresses and deformations that can be exploited for enhanced detection of small fatigue cracks. Two such enhancement methods were investigated in this research project. First, using long-pulse laser irradiation in combination with conventional Rayleigh wave inspection, direct generation of ultrasonic Rayleigh waves can be avoided and the relatively slow laser induced crack closure can be detected as a parametric modulation effect in a manner similar to the acousto-elastic effect often used in nonlinear ultrasonic studies. This technique is particularly well suited to distinguish small fatigue cracks from nearby scattering artifacts, such as machine marks, mechanical wear, corrosion pits, etc., that could otherwise overshadow the flaw. Second, short-pulse irradiation in the thermo-elastic region, that is routinely used to generate ultrasonic Rayleigh waves, can be substantially enhanced when the irradiated area contains nearsurface discontinuities. Using an expanded laser beam, direct generation of ultrasonic surface waves from intact areas can be minimized and a significant increase in amplitude occurs when a discontinuity is present in the irradiated area. This technique is better suited to distinguish small fatigue cracks from distributed material noise caused by the surrounding inhomogeneous microstructure, such as coarse grains, grain colonies, precipitations, and anomalous phases. Numerous new experimental techniques combining laser irradiation with ultrasonic detection methods have been developed based on these two inspection principles. During the development of these techniques, in order to better understand and optimize them, several simplified models were built, numerical simulations were performed, and related optical, thermal, mechanical, and acoustical phenomena were also investigated. They include: (i) temporal and spatial distributions of temperature and thermal stress in the specimens due to repetitive long-pulse laser irradiation, (ii) photothermo-elastic crack closure behavior in 3-D, (iii) thermally induced refraction effects on ultrasonic Rayleigh wave propagation, and (iv) relations of the enhanced laser generated ultrasonic Rayleigh waves (amplitude, spectrum, directivity) to discontinuity parameters. This dissertation contributes to three aspects of laser-ultrasonic nondestructive evaluation (NDE), namely new enhanced inspection techniques, experimental database, and original and improved analytical models. ii

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5 ACKNOWLEDGMENTS I am proud and thankful to be a student of Professor Peter B. Nagy. I deeply appreciate his tremendous help from the beginning of my studies at the University of Cincinnati until the completion of my dissertation. His enthusiasm and scientific research methodology have been teaching and improving me every step of the way. His life attitude also led me to knowing how to manage and enjoy a real life in addition to being a good researcher. I also thank my friends in NDE lab who brought joy and fun at the same time as hard work. My appreciation goes to the dissertation committee members, Prof. Adnan H. Nayfeh, Prof. Stanislav I. Rokhlin, and Prof. James E. Wade, whose willing help accelerated the completion of my dissertation. This research effort was sponsored by the Defense Advanced Research Project Agency (DARPA) Multidisciplinary University Research Initiative (MURI), under Air Force Office of Scientific Research Grant No. F I would also like to express my deep gratefulness and love to my mom and dad and brothers and sisters who are living in a Chinese village. Their unconditional love is always an encouragement and source of energy for me to pass through every hard time. Lastly, but most importantly, my appreciation and love go to my dear wife, Hong, and baby daughter, Maggie. The accomplishment of my PhD study is inseparable from Hong's support and her provision of a lovely home. iv

6 TABLE OF CONTENTS ABSTRACT ACKNOWLEDGMENTS ii iv LIST OF TABLES AND FIGURES 5 LIST OF SYMBOLS 16 CHAPTER I INTRODUCTION 1.1 Statement of the Problem Literature Review Small Crack Detection Laser Induced Crack Closure Discontinuity-Enhanced Laser Generation of Ultrasonic Rayleigh Waves Achievement of the Dissertation Organization of the Dissertation 28 CHAPTER II IMPROVED FATIGUE CRACK DETECTION BY LASER-INDUCED CRACK CLOSURE 2.1 Principles Crack Closure Observation of Crack Closure Thermo-Optical Modulation Experimental Set-up 34 1

7 2.2.2 Temporal Modulation Experimental Results Comparison between Al-2024 and Ti-6Al-4V Differences in Material Properties Differences in Modulation Patterns Preparation of the Specimens with EDM Notches and Fatigue Cracks Short-Term Thermo-Optical Modulation in Ti-6Al-4V Long-Term Thermo-Optical Modulation in Ti-6Al-4V FEM Simulation and Correlation with Experimental Results Contour Display of the Temperature and Thermal Stress in a Semi-Space Due to Single Pulse Laser Irradiation Graph Display of the Temperature and Thermal Stress in a Semi-Space Due to Single Pulse and Repetitive Long Pulse Laser Irradiation Description of the Figures Two Thermo-Optical Modulation Mechanisms in the Ultrasonic Detection of Surface Cracks Crack Closure in a Simple Model Model Building Results and Discussion Detection of Small Fatigue Cracks Against Grain Noise Experimental Set-up Results and Discussion Summary 100 2

8 CHAPTER III LOCAL DIRECT TEMPERATURE MODULATION OF RAYLEIGH WAVES BY REPETITIVE LONG-PULSE LASER IRRADIATION 3.1 Abstract of the Chapter Introduction Analytical Model Numerical Results Experimental Results and the Correlation with Numerical Results Description of the Figures Comparison of the Experimental and Numerical Results Summary 138 CHAPTER IV IMPROVED SHORT-TERM MODULATION FOR FATIGUE CRACK DETECTION IN TI-6AL-4V 4.1 Introduction Thermo-Optical Modulation by Reshaped Laser Beam Description Results and Discussion Thermo-Optical Modulations at Low Frequencies Description Results and Discussion Summary 155 3

9 CHAPTER V ENHANCED LASER GENERATION OF SURFACE ACOUSTIC WAVES BY DISCONTINUITIES 5.1 Abstract of the Chapter Introduction Similarity of Elastic and Optical Discontinuities in the Laser Generation of SAW Experimental Set-up Results and Discussion Simplified Model for Discontinuity-Enhanced Laser Generation of SAW Simulated Results and Discussion Experimental Results and Correlation with the Simulated Data Additional Advantages of Discontinuity-Enhanced Laser Generation of SAWs Detection of a Small Crack Detection of Small Cracks with Low-Frequency Transducers Summary 209 CHAPTER VI CONCLUSION 6.1 Conclusion 210 BIBLIOGRAPHY 211 4

10 LIST OF TABLES AND FIGURES CHAPTER II Figure 2.1 Schematic illustration of crack closure as parametric modulation caused by changing normal stress 30 Figure 2.2 Schematic diagram of phase-locked synchronous detection of crack closure 32 Figure 2.3 The effects of asynchronous (ordinary) and synchronous (phaselocked) time-averaging on the detected signal 33 Figure 2.4 Schematic diagram of the experimental arrangement with thermooptical modulation 35 Figure 2.5 Sequential diagram of the synchronized optical and ultrasonic pulses 39 Figure 2.6 Identification of a fatigue crack by short-term laser induced crack closure 40 Figure 2.7 Scanning of the area to be inspected by the pulsed laser beam 41 Table 2.1 Material properties of Aluminum 2024 and Titanium alloy Ti-6Al- 4V 43 Figure 2.8 Optical absorption spectra for aluminum and titanium 44 Figure 2.9 Measured short-term modulation versus synchronization delay characteristics in (a) Al 2024 and (b) Ti-6Al-4V 47 Figure 2.10 Time dependence of the observed thermo-optical modulation of a small fatigue crack at 13 different axial (a) and lateral (b) irradiation positions (2024 Aluminum specimen #A1, 5 MHz, scanning over a 0.600" 0.600" area in 0.050"-steps) 48 5

11 Figure 2.11 Typical thermo-optical modulation in Ti-6Al-4V. The complex long-term modulation dominates the overall behavior (a) while the periodic dynamic modulation is detectable only during laser illumination (b) 49 Table 2.2 Fatigued and Intact Ti-6Al-4V Specimens 52 Figure 2.12 Received ultrasonic echoes from the fatigue damaged (a) and unfatigued (b) EDM notches using a 5 MHz Rayleigh wave transducer 53 Figure 2.13 Short-term modulation from the fatigue damaged and unfatigued EDM notches at 5 MHz 55 Figure 2.14 Short-term modulation versus the irradiation time when the laser spot directly irradiates the crack site 58 Figure 2.15 Short-term modulation when the laser beam scans along the axial direction over the area containing the small fatigue crack 59 Figure 2.16 Short-term modulation when the laser beam scans along the lateral direction over the area containing the small fatigue crack 60 Figure 2.17 Short-term modulation when the laser beam scans along the axial direction over the area containing the EDM notch 61 Figure 2.18 Short-term modulation versus the interval between hot and cold states 62 Figure 2.19 Short-term modulation versus the delay time 63 Figure 2.20 SAW signal amplitude measured by the ultrasonic transducers with different frequencies 64 Figure 2.21 Short-term modulation measured by the ultrasonic transducers with different frequencies 65 6

12 Figure 2.22 Time dependence of the observed thermo-optical modulation of two fatigue cracks (a and b) and two EDM notches (c and d) at 13 different axial positions 68 Figure 2.23 Time dependence of the observed thermo-optical modulation of two fatigue cracks (a and b) and two EDM notches (c and d) at 13 different lateral positions 69 Figure 2.24 Time dependence of the observed thermo-optical modulation of eight fatigue cracks and eight EDM notches at the center of the irradiated spot 71 Figure 2.25 Long-term thermo-optical modulation from eight fatigue cracks and eight EDM notches at the center of the irradiated spot before (a) and after (b) the end of laser irradiation (5 MHz) 72 Figure 2.26 Contour display of the temperature distribution in Ti-6Al-4V and Al-2024 after the laser irradiation 75 Figure 2.27 Contour display of the stress (σrr) distribution in Ti-6Al-4V and Al-2024 after the laser irradiation 76 Figure 2.28 Stress σrr versus the depth for a shorter time (a) and a longer time (b) 78 Figure 2.29 Stress σrr versus the shorter time in a thinner layer (a) and versus the longer time in a thicker layer (b) 79 Figure 2.30 Temperature versus the shorter time in a thinner layer (a) and versus the longer time in a thicker layer (b) 80 Figure 2.31 Temperature versus the depth in a shorter time (a) and versus the depth in a longer time (b) 81 Figure 2.32 Long-term temperature variations on the surface and at larger depth 82 Figure 2.33 Temperature versus the depth in a long-term status 82 7

13 Figure 2.34 A simplified model. A laser beam irradiates the surface of a specimen containing a small rectangular surface notch; the notch is located at the center of the beam 87 Figure 2.35 Crack closure along the middle line of the crack with 0.02-µm width 91 Figure 2.36 Crack closure along the middle line of the crack with 0.2-µm width 92 Table 2.3 Parameters of Ti-6Al-4V specimens (dimensions in mils) 94 Figure 2.37 The envelope of the RF signal detected from specimen c6 at 54 db gain 97 Figure 2.38 Examples of the measured thermo-optical modulations for two signals in specimen c6 when the laser beam is scanned along the axial direction 98 Figure 2.39 Variation of the amplitude ratio between the short-term and longterm modulations when the laser is scanned along the axial direction in specimen c6 (#3 signal is probably from a small fatigue crack) 99 Figure 2.40 Variation of the amplitude ratio between the short-term and longterm modulations when the laser is scanned along the axial direction in specimen c5 (#3 signal is from a misaligned fatigue crack) 99 CHAPTER III Figure 3.1 Schematic of the mechanism for laser induced modulation of SAW (a) ray refraction when SAW propagates through the laser heated area (b) directivity pattern of a transducer 105 8

14 Figure 3.2 A schematic diagram of the measurement configuration (a) and the coordinate system used in the analysis (b) 108 Figure 3.3 Ray refraction through a circular area of uniform temperature (a) and the integrated result through an area of distributed temperature (b) 110 Table 3.1 Material properties of titanium alloy Ti-6Al-4V 117 Figure 3.4 Long-term (a) and short-term (b) modulations of a 10 MHz SAW at normal incidence. The laser beam radius is 0.1 inches, and the temperature-velocity coefficient is C Figure 3.5 Long-term (a) and short-term (b) modulations of a 10 MHz SAW at 0.3 incidence. The laser beam radius is 0.1 inches, and the temperature-velocity coefficient is C Figure 3.6 Long-term (a) and short-term (b) modulations of different frequency SAWs at 0.3 incidence. The laser beam radius is 0.1 inches, and the temperature-velocity coefficient is C Figure 3.7 Long-term (a) and short-term (b) modulations of 10 MHz SAWs at 0.3 incidence. The laser beam diameter is 0.2 inches or 0.4 inches, and the temperature-velocity coefficient is C Figure 3.8 Long-term (a) and short-term (b) modulations of 10 MHz SAWs at normal incidence for three different temperature-velocity coefficient. The laser beam radius is 0.1 inches. The passing position of the acoustic ray is inches 125 Figure 3.9 Schematic diagram of the experimental arrangement for recording the thermo-optical modulation 127 Figure 3.10 Long-term (a) and short-term (b) modulations of the corner signal (5 MHz, 12 db) by lateral scan of the laser beam on the specimen 130 9

15 Figure 3.11 Long-term (a) and short-term (b) modulations of the corner signal (5 MHz, 12 db) by axial scan of the laser beam on the specimen 131 Figure 3.12 Long-term (a) and short-term (b) modulations of the corner signals measured by different frequency transducers 132 Figure 3.13 Long-term (a) and short-term (b) modulations of the corner signals by different diameter laser beam irradiation 133 Figure 3.14 Long-term (a) and short-term (b) modulations of the corner signals (10 MHz, 27 db at normal alignment) at different alignments of the beam. The passing position of the wave beam middle line is 0.2" on the lower side from the center of the laser spot 134 CHAPTER IV Figure 4.1 Schematic of the experimental set-up for reshaping the laser beam 144 Figure 4.2 Schematic of decreasing the direct temperature modulation by reshaping the laser beam 145 Figure 4.3 Long-term modulation of the signal (5 MHz, 44 db) reflected from c#4. (a) Circular laser beam with 0.2" diameter, (b) Trimmed laser beam with 0.1" width scans the position at 0.6" before the crack in the lateral direction 146 Figure 4.4 Short-term modulation of the signal (5 MHz, 44 db) reflected from c#4. (a) Circular laser beam with 0.2" diameter, (b) trimmed laser beam with 0.1" width scans the position at 0.6" before the crack in the lateral direction 147 Figure 4.5 Long-term modulation of the signal (5 MHz, 42 db) reflected from n#3 (a) and from c#5 (b). Trimmed laser beam with 0.1" width scans around the scatterers in the lateral direction

16 Figure 4.6 Long-term modulation of the signal (5 MHz, 42 db) reflected from n#3 (a) and from c#5 (b). Trimmed laser beam with 0.1" width scans around the scatterers in the axial direction 149 Figure 4.7 Short-term modulation of the signal (5 MHz, 42 db) reflected from n#3 (a) and from c#5 (b). Trimmed laser beam with 0.1" width scans around the scatterers in the lateral direction 150 Figure 4.8 Short-term modulation of the signal (5 MHz, 42 db) reflected from n#3 (a) and from c#5 (b). Trimmed laser beam with 0.1" width scans around the scatterers in the axial direction 151 Figure 4.9 Long-term (a) and short-term (b) modulations in different notches with/without fatigue cracks by reshaped laser beam irradiation 152 Figure 4.10 RF signals measured by the 2.25 MHz transducer on different specimens with fatigue cracks or EDM notches 156 Figure 4.11 Short-term modulation of the signal (2.25 MHz, 26 db) scattered from crack #8. Circular laser spot with 0.2" diameter scans around the crack in the axial (a) and lateral (b) directions 157 Figure 4.12 Long-term modulation of the signal (2.25 MHz, 26 db) scattered from crack #8. Circular laser spot with 0.2" diameter scans around the notch in the axial (a) and lateral (b) directions 158 Figure 4.13 Short-term modulation of the signal (2.25 MHz, 26 db) scattered from notch #7. Circular laser spot with 0.2" diameter scans around the notch in the axial (a) and lateral (b) directions 159 Figure 4.14 Long-term modulation of the signal (2.25 MHz, 26 db) scattered from notch #7. Circular laser spot with 0.2" diameter scans around the notch in the axial (a) and lateral (b) directions

17 Figure 4.15 Short-term (a) and long-term (b) modulations (2.25 MHz) measured from six specimens (three with fatigue cracks and three with EDM notches) 161 CHAPTER V Figure 5.1 Schematic of the measurement for comparing laser generation of SAWs by a laser beam irradiating a corner (a) and a trimmed laser beam irradiating an intact area (b) 166 Figure 5.2 Laser generated SAW by a beam irradiating the specimen corner (a) and a blade-truncated beam irradiating an intact part on the specimen (b). The specimen is made of Ti-6Al-4V. The signal is measured by a 5 MHz transducer at 30 db gain 169 Figure 5.3 Spectrum of the laser generated SAW by a beam irradiating the specimen's corner (a) and a blade-truncated beam irradiating an intact part on the specimen (b). The specimen is made of Ti-6Al- 4V. The signal is measured by a 5 MHz transducer at 30 db gain 170 Figure 5.4 Amplitude of the laser generated SAW versus the truncating position. It is measured by 1 MHz (a) and 2.25 MHz (b) transducers at 30 db gain. The specimen is made of Ti-6Al-4V 171 Figure 5.5 Amplitude of the laser generated SAW versus the truncating position. It is measured by 5 MHz (a) and 10 MHz (b) transducers at 30 db gain. The specimen is made of Ti-6Al-4V 172 Figure 5.6 Amplitude of the laser generated SAW versus the truncating position. It is measured by 1 MHz (a) and 5 MHz (b) transducers 12

18 respectively, and the gain is 30 db. The specimen is made of Al Figure 5.7 Schematics of the measurement for the laser generation of SAW by a laser beam irradiating the notch (a) and the analytical simulation by a rectangular notch with top view (b) and side view (c) 175 Figure 5.8 Geometry of the problem and coordinate system used (a) and the introduced notch model (b) 177 Figure 5.9 Temporal profile of the laser pulse (a = 5, b = and γ = 3) 185 Figure 5.10 Amplitude of the laser generated SAW versus the characteristic radius of Gaussian beam by simplified analysis 186 Figure 5.11 Amplitude of the laser generated SAW versus the cutting distance from the center of the original Gaussian laser beam by simplified analysis 187 Figure 5.12 Amplitude of the laser generated SAW versus the notch width (the notch length is 1 mm, and the depth is 100 µm) by simplified analysis 188 Figure 5.13 Amplitude of the laser generated SAW versus the notch length (the notch width is 100 µm, and the depth is 100 µm) by simplified analysis 189 Figure 5.14 The directivity of the SAW generated by laser irradiating a short notch (a) 1-mm long, 100-µm wide and 100-µm deep and a long notch (b) 10-mm long, 100-µm wide and 100-µm deep by the simplified analysis 190 Figure 5.15 Amplitude of the laser generated SAW versus the notch depth (the notch length is 1-mm, and the width is 100-µm) by simplified analysis

19 Figure 5.16 Amplitude of the laser generated SAW (10 MHz) with the truncated laser beam irradiating an intact area of the specimen by measurement and simplified analysis 194 Figure 5.17 Laser generated SAW (10 MHz, 52 db) by the Gaussian laser beam irradiating the seven EDM notches (experimental results) 195 Figure 5.18 Amplitude of the laser generated SAW versus the notch length (the notch depth is 178 µm, and the width is 76 µm) by measurement and simplified analysis 196 Figure 5.19 The magnified crack in a specimen of Ti-6Al-4V (the real size of the picture is 0.65 mm 0.5 mm) 199 Figure 5.20 Comparison of laser SAW and pulse-echo SAW by measuring the small crack in Figure Figure 5.21 Amplitude of the laser generated SAW versus frequency when a laser is irradiating a small notch (1-mm long, 10-µm wide and 100- µm deep) and intact area 201 Figure 5.22 SAW generated and measured by the pulse echo method with a 1 MHz transducer at 20 db gain (a) and generated by the laser irradiation of the specimens and measured by a 1 MHz transducer at 40 db gain (b) 204 Figure 5.23 SAW generated and measured by the pulse echo method with a 2.25 MHz transducer at 20 db gain (a) and generated by the laser irradiation of the specimens and measured by a 2.25 MHz transducer at 40 db gain (b) 205 Figure 5.24 SAW generated and measured by the pulse echo method with a 1 MHz transducer at 20 db gain (a) and generated by the laser irradiation of the specimens and measured by a 1 MHz transducer at 40 db gain (b)

20 Figure 5.25 SAW generated and measured by the pulse echo method with a 2.25 MHz transducer at 20 db gain (a) and generated by the laser irradiation of the specimens and measured by a 2.25 MHz transducer at 40 db gain (b) 207 Figure 5.26 SAW generated and measured by the pulse echo method with a 1 MHz transducer at 20 db gain (a) and generated by the laser irradiation of the specimens and measured by a 1 MHz transducer at 40 db gain (b)

21 LIST OF SYMBOLS φ ψ σ rr τ xx τ zz τ zx ε xx ε zz γ zx U 0 M E D ν Displacement scalar potential Displacement vector potential Radial thermal stress Normal stress in the propagation direction Normal stress parallel to the surface Shear stress Normal strain in the propagation direction Normal strain parallel to the surface Shear strain Strain energy density Modulation of the Rayleigh wave Energy of the Rayleigh wave Directivity function of a circular piston radiator Poisson's ratio µ Shear modulus λ ρ k c J 1 Ω θ v T r Lamé constant Density Wave number Temperature-velocity coefficient or specific heat capacity First-order Bessel function Angle between the ray input direction and the transducer direction Propagation angle Acoustic speed Temperature Radius of the laser circular spot 16

22 P 0 β g α K χ w Y Λ t w a ω r k L I F H T Power of the laser Thermal expansion coefficient Light absorption ratio Light absorption coefficient Thermal conductivity Thermal diffusivity Laser beam radius Temporal profile for a train of pulses Laser repetitive period Pulse width Radius of a circular piston Angular frequency Spatial vector Wave vector Spectral component of the laser generated SAW Intensity of laser beam Temporal and spatial distribution of laser beam Unit step function Fourier transform in time and r and Laplace transform in z of the temperature function T r c Characteristic Gaussian beam radius 17

23 CHAPTER I INTRODUCTION 1.1 STATEMENT OF THE PROBLEM Positive identification of small fatigue cracks presents a challenging problem during nondestructive testing of fatigued structures. Fatigue cracks are usually initiated by small geometrical irregularities or material inhomogeneities that give rise to sharp local stress concentrations. In the early stages of fatigue, small cracks are often hidden from ultrasonic detection by stronger scattering from the very same structural imperfection that produced them in the first place. Our main goal is to distinguish fatigue cracks as early as possible after crack nucleation from primary geometrical features and irregularities as well as from intrinsic material inhomogeneities. One of the most characteristic features of fatigue cracks, which can be used to distinguish them from other types of discontinuities, is that they are partially closed by residual stresses and the opposite surfaces match fairly well with each other so that they can be easily closed or opened further by the application of modest external deformations. Laser generation of ultrasonic waves via the thermo-elastic effect is a well known non-contacting way of producing ultrasonic vibrations without requiring mechanical contact with the specimen. The same effect can be exploited to produce strong localized quasi-static stresses when a lower-intensity, but much longer laser pulse is used to irradiate the specimen. These stresses will have a modulating effect on ultrasonic wave propagation similar to the acousto-elastic effect often used in nonlinear ultrasonic studies. We have demonstrated that this method can be used to effectively distinguish fatigue cracks from other structural imperfections present in aluminum and titanium alloys. [1-5] Meanwhile, we found that there exist a variety of issues that complicate the phenomena. 18

24 These include (i) contributions from short-term and long-term modulations, (ii) material properties (e.g., aluminum 2024 versus titanium alloy Ti-6Al-4V), (iii) heat source parameters (laser beam spot size, intensity, irradiation time, interval, and delay time), (iv) discontinuity types (cracks, notches, corners), (v) relative position of the heat source with respect to the discontinuity, and (vi) frequency of the transducer. All of these need to be understood and taken into consideration in order to optimize this method and make it applicable in practical situations. In particular, an understanding of the thermal stress and deformation fields in the material is needed to set important laser parameters (pulse energy, pulse repetition rate, pulse activation time, and beam focus) and adjust ultrasonic parameters (delay time, interval, frequency). On the other hand, this understanding will also help make this new NDE technique more quantitative. Using the above technique laser modulation of ultrasonic Rayleigh waves via laser induced crack closure to distinguish small fatigue cracks from randomly distributed intrinsic material inhomogeneities such as coarse grains in Ti-6Al-4V, it was found that the whole procedure becomes rather cumbersome. Using laser generation of ultrasonic Rayleigh waves, it was observed that when the laser beam irradiates an area that includes surface-breaking discontinuities, the generated wave amplitudes are significantly enhanced and the spectra are different from those generated by irradiating the intact areas. Surprisingly, otherwise hidden small cracks can be distinguished from grain noise by this technique of laser generation of ultrasonic Rayleigh waves. In order to fully understand and better apply this technique to practical applications, some essential questions need to be answered, such as the relationships between the laser-generated ultrasonic Rayleigh waves (amplitude, spectrum, directivity) and discontinuity properties (optical, thermal and elastic), and how to improve the separation between discontinuities and intact parts. 19

25 1.2 LITERATURE REVIEW Small Crack Detection An ever increasing demand for early detection of fatigue damage is fueled by the fact that small cracks have been found to grow at unexpectedly high growth rates well below the large-crack threshold in aluminum, aluminum-lithium, and titanium alloys. [6] It is known that extensive multiple-site fatigue cracking may develop in airframe structures before it can be reliably detected by any of the currently available nondestructive evaluation techniques. [7] A number of experimental techniques have already been proved useful in some cases, such as scanning electron microscopy (SEM) used to obtain detailed measurements of crack opening and closing events, [8-10] monitoring small crack closure by acetate replicas, [11-12] AC and DC potential measurement of the growth of small cracks, [13-14] interferometric strain/displacement gage (ISDG) providing real-time crack length and closure data, [15] gel electrode, low-frequency and high frequency eddy current, thermal wave, x-ray, and acoustic microscopy, etc. However, of the various techniques that have been used to detect small fatigue cracks, only a few can provide useful information on small, partially closed cracks, and for the most part, they are quite tedious and time consuming. Surface acoustic wave (SAW), or Rayleigh wave inspection has been demonstrated as a useful method for evaluating crack size and investigating the crack closure phenomenon by many researchers. These studies tended to deduce information about crack size and shape from the reflection and transmission coefficients of Rayleigh wave by theoretical analyses, [16-18] numerical calculation [19-20] or empirical correlation. [21-23] They also demonstrated the feasibility to measure changes in depth of cracks beneath the surface (occasionally during periods of crack growth caused by fatigue 20

26 cycling in which no changes in crack dimension were evident at the surface) in T651 aluminum, [24] quenched and tempered 4340 steel, [25] quenched and tempered 4140 steel, [26] and 300-M alloy steel. [27] In order to increase the absolute amplitude of signals reflected from cracks, most of the current methods for measuring crack growth have applied external forces to make cracks open. Various signal processing techniques have been used to distinguish crack signals from inherent material noise and to extract the characteristics of the cracks. This implies that appropriate signal processing techniques and external stresses are needed in order to measure crack closure. Numerous signal processing techniques, such as split spectrum processing, [28] cut spectrum processing, [29] wavelet transform processing, [30] etc., have been used for improving signal to noise ratio (SNR). However, they are based on the assumption of a detectable difference between the incoherent, frequency dependent interference noise caused by grain scatter and the coherent, specular, frequency independent (or less frequency dependent) reflection caused by microcracks. This means that they can only be used efficiently when the grain size, or the microstructural backscatter, is orders-ofmagnitude smaller than the fatigue crack, which is not the case in many aerospace materials with relatively coarse grains like titanium alloys. Furthermore, in many practical applications involving macro-anomalies, the artifact reflector is comparable or larger than both the wavelength and grain size, therefore it is very similar to the fatigue crack reflection. The more recently introduced neural network technique provides another way for identifying fatigue cracks. [31] Actually, it is sophisticated self-learning signal processing method using flaw classification algorithms at the cost of much more intensive computations. 21

27 1.2.2 Laser Induced Crack Closure Generally, linear acoustic characteristics (attenuation, velocity, backscattering, etc.) are not sufficiently sensitive to very small fatigue cracks. This apparent insensitivity of conventional ultrasonic flaw detection to early fatigue damage following crack nucleation is due to two specific features of small fatigue cracks. One is that the absolute sensitivity of ultrasonic detection is reduced by crack-closure, another is that the relative sensitivity of ultrasonic detection is often limited by the presence of nearby scatterers that give rise to false alarms. On the other hand, it has been noticed that in a great variety of structural materials even very small fatigue damage can produce very significant excess nonlinearity, which can be orders of magnitude higher than the intrinsic nonlinearity of the intact material. [32] The excess nonlinearity is produced by the strong local nonlinearity of micro-cracks whose opening is smaller than the particle displacement. Buck and his co-workers were the first to report the nonlinear modulation of the ultrasonic Rayleigh wave reflection and transmission at surface breaking fatigue cracks during mechanical loading of the specimen as indicated by the varying generation of second, third, and higher harmonics of the fundamental ultrasonic frequency. [33-34] The modulating stress may be produced by different means such as external cyclic loading in a typical fatigue test [35] or exploiting the inherent vibration of the structure itself during operation. [36] The main disadvantage of using external mechanical loading is that usually the whole structure must be loaded, which requires very substantial forces and might cause additional damage in certain parts of the structure. More localized temporary stresses can be produced by simply cooling or warming the specimen to be tested. [35] Just like ultrasonic inspection, thermal wave detection of near-surface fatigue cracks is also severely limited by the need to distinguish real flaws from intrinsic artifacts that produce similar thermal signatures. Gusev et al. have suggested that crack-closure, 22

28 via the unique stress-dependence of the thermal resistance of hidden sub-surface cracks, could be used to positively identify them against the background of other thermal inhomogeneities. [37] They also suggested that the modulating deformation itself can be produced by laser generated thermal stresses. When the thermal wave used to detect the crack itself is strong enough to produce perceptible crack-closure, or breathing in thermal wave terminology, a nonlinear photo-thermal process results that is very similar to the generation of harmonics in ultrasonic scattering from fatigue cracks. [38-40] However, they only studied the sub-surface crack situation, and did not investigate how laser generated stresses affect fatigue crack closing or opening. A conceptually very similar thermo-optical modulation technique has been recently developed and experimentally demonstrated for enhanced ultrasonic fatigue crack detection in aluminum, [1-2,41-42] and also modified and adapted to titanium alloy Ti-6Al-4V. [2-5] During the experimental investigation, various spurious phenomena were also observed, which complicated the final results. In order to better understand, optimize and simplify this technique, a corresponding analytical study and further experimental verifications were needed. There have been numerous studies on thermoelastic response in materials subjected to pulsed laser irradiation. A substantial amount of effort in this field has been either dedicated to understanding deformation and failure mechanisms in thin films, which is important to the micro-electronics and electro-optical industry, [43-45] or laserultrasonics, using very short duration laser pulse with high intensity to generate ultrasonic waves in a material, which has been recognized as one of the most promising ways for generating ultrasonic waves for future applications due to its noncontacting and remote nature. [46-48] Laser shock peening, a novel surface treatment technique that imparts favorably oriented compressive residual stresses in materials for retarding crack growth initiation on the surface, has also attracted significant attention. [49-50] 23

29 One subject that has received minimal attention in the literature is the thermoelastic effects in a semi-infinite medium due to cyclic heat sources, such as a repetitive long-pulse laser. The protocol models of this subject semi-infinite space and concentrated optical load can be treated as a fundamental thermo-elastic problem, [51-52] which results in an apparently quite simple solution, but similar analytical formulations and calculation results indicate that this problem will be more complicated. [53-55] There are two aspects that complicate this problem. First, in the thermoelastic stress state prior to plastic flow or fracture of the material, the axial and shear stress components can not, in general, be neglected like in thin films. Second, for repetitive long-pulse laser irradiation, the temporal and spatial variations due to heat accumulation and thermal diffusion need to be considered unlike to the simpler case of single short-pulse laser irradiation. Some results have shown that the variation of the thermoelastic stress and displacement fields over a range of layer thicknesses exhibits some important differences between thin films and thick layers due to repetitively pulsed laser irradiation. [56-57] Furthermore, when there is a crack present in irradiated area, it becomes very complicated to solve the problem in 3-D rather than in 2-D Discontinuity-Enhanced Laser Generation of Ultrasonic Rayleigh Waves Laser-ultrasonics [46,58] offers many advantages over other ultrasonic techniques for characterization of materials because it is non-contact, non-intrusive, and, when used in the thermoelastic region, entirely nondestructive. The acoustic action of optical radiation on a material was investigated by Bell, Tyndall and Rontgen as early as Theoretical and experimental studies of laser acoustic effects were started almost immediately after the creation of the first lasers. [59,60] While laser generation of ultrasonic bulk waves had been investigated extensively [61,62] and used widely in scientific studies and applications, [63,64] laser generation of Rayleigh waves was not 24

30 studied in detail until the 1980's. [65-67] Those studies in the 80's showed the advantages of the thermo-optical excitation of Rayleigh waves, its contactless and wideband features, and the possibility of remote steering of wave directions. In recent years, with the advance of technology, much research [68-70] has been done to modify and improve the techniques for fully exploiting the advantages of laser generation of Rayleigh waves. Some theoretical analyses [71,72] also modeled the laser generated Rayleigh waves from point and line sources. Most of the studies mentioned above were mainly concentrated on the optimization of laser Rayleigh wave excitation, i.e., better design of a Rayleigh wave active transducer by laser excitation. The inverse problem, characterization of material properties by laser generation of Rayleigh waves, e.g., opto-acoustic SAW (Surface Acoustic Wave) spectroscopy, has been little investigated. Laser generation of ultrasonic waves is determined by the laser parameters (beam geometry, temporal profile of the intensity) and the medium parameters (thermal conductivity, light absorption ratio, thermal expansion coefficient, specific heat capacity, elastic parameters). In the previous studies, manipulation and optimization of the laser Rayleigh wave source were often realized by controlling the laser parameters (beam geometry via computer generated holography, [70] grating excitation, [68,69] etc.). The basic idea here is to truncate or move the laser beams. From a physical point of view, Rayleigh wave generation by the following two procedures are the same. One procedure generates surface waves by truncating the laser beam irradiating an intact area of the medium. The other relies on the intact laser beam irradiating the same area when the light absorption ratio is zero in part of that area (this zero-light-absorption-coefficient part is under the shadow of the truncated part in the first procedure). In other words, truncating the laser beam, or assuming that the light absorption ratio of the medium is zero, can generate the same Rayleigh wave. Therefore, although opto-acoustic SAW spectroscopy has not been specifically investigated, the methodologies of investigating the laser SAW active transducer can be adapted to solve certain problems in materials 25

31 characterization by laser generation of Rayleigh waves. The principle of opto-acoustic SAW spectroscopy is that discontinuities in the medium will affect the laser-generation of SAWs when a laser beam irradiates the area with discontinuities. Under this mechanism, a new method Laser Ultrasonic Detection of Surface-Breaking and Sub-Surface Cracks has been proposed and verified by experiments recently. [73,74] Due to the small elastic discontinuity in the otherwise homogeneous material, analytically solving the problem of laser generation of Rayleigh wave becomes very difficult. However, theoretical models are essential to help better understand and optimize this laser-saw technique. In this dissertation, a simplified model has been introduced to simulate the enhanced generation of ultrasonic surface waves by laser irradiation of discontinuities. The above review of the relevant literature indicates that the two techniques to be considered in this dissertation, namely laser induced crack-closure and discontinuityenhanced laser generation of Rayleigh waves, are new potential techniques for identifying early fatigue cracks. The various physical phenomena involved in these techniques, such as thermal stress and deformation in a semi-infinite space due to repetitive long-pulse laser irradiation, photo-thermo-elastic crack closure, thermal effects on the propagation of ultrasonic Rayleigh waves, and laser generation of ultrasonic Rayleigh waves by irradiating discontinuities, have not been investigated in sufficient depth. This dissertation provides the theoretical and experimental basis for developing these two new laser-ultrasonic methods. 1.3 ACHIEVEMENT OF THE DISSERTATION Two new NDE techniques combinations of laser and ultrasonic methods to improve detection of early fatigue cracks have been developed in this dissertation. Two important experimental tasks have been accomplished. The first task was to distinguish fatigue cracks from primary geometrical features (e.g., nearby holes, corners, and edges) 26

32 and secondary irregularities (e.g., uneven machining, mechanical wear, corrosion, etc.). The second task was to distinguish small fatigue cracks as early as possible after crack nucleation from intrinsic material inhomogeneities such as coarse grains, anomalous microstructure, second phases, precipitates, porosity, various types of reinforcement, etc. The following experimental and analytical results have been found: Experimental Results: 1. The characteristic modulation patterns of Rayleigh waves by repetitive long-pulse laser irradiation of fatigue cracks, artificial scatterers and intact parts were recorded. 2. The main characteristics of each modulation pattern were identified for different (i) frequencies of the Rayleigh wave, (ii) positions of the laser irradiation, (iii) durations of the irradiation, and (iv) shapes of the laser beam. 3. Rayleigh wave signatures were recorded for short-pulse laser irradiation of surface breaking discontinuities and intact parts. 4. The characteristics for discontinuity-enhanced laser-generated Rayleigh waves were analyzed. Analytical and Numerical Results: 1. The temporal and spatial distributions of temperature and thermal stress in a semiinfinite space of aluminum 2024 and titanium Ti-6Al-4V irradiated by repetitive longpulse laser were calculated. 2. The behavior of crack closure under repetitive long-pulse laser irradiation was studied. 3. Laser-induced heating effects on the propagation of Rayleigh wave were studied. 4. Enhanced laser generation of Rayleigh waves by discontinuities was studied. 27

33 1.4 ORGANIZATION OF THE DISSERTATION Overall, the dissertation is organized in the order of the research sequence, i.e., each following chapter is proposed and developed from the problems encountered or conclusions derived in the previous chapters. In chapter II, after briefly describing the principles of crack closure and the methods used to detect it, the basic experimental setup used in this dissertation for studying thermo-optical modulation is introduced. Then the modulation patterns measured in Al-2024 and Ti-6Al-4V specimens are shown. They indicate the effectiveness of the short-term modulation for detecting fatigue cracks in Al and of the long-term modulation for Ti-6Al-4V. At the same time, certain apparently anomalous phenomena are also observed, which indicates the necessity for better understanding of the technique. At the end of the chapter, finite element simulations that attempt to explain the phenomena observed in the experiment are presented. Chapter III provides in detail the measurements of the modulations of ultrasonic surface waves by laser irradiation of intact parts. By considering the refraction of the acoustic ray due to the local acoustic velocity change caused by the increase in temperature, a model is introduced and the numerical simulations are correlated with the experimental recordings. In chapter IV it is shown that the short-term modulation technique is also effective to identify fatigue cracks in Ti-6Al-4V if the direct temperature modulation of the surface wave is eliminated, or sufficiently reduced, by appropriate measures. In response to the difficulties of distinguishing small cracks from strong grain noise, that are indicated in chapter II, a new method discontinuity-enhanced laser generation of ultrasonic surface waves is proposed, tested, analyzed and validated in chapter V. 28

34 CHAPTER II IMPROVED FATIGUE CRACK DETECTION BY LASER-INDUCED CRACK CLOSURE 2.1 PRINCIPLES Crack Closure The most characteristic feature of fatigue cracks that can be exploited to positively identify them is that they are partially closed by residual stresses and the opposite surfaces match fairly well with each other so that they can be easily closed or opened further by the application of modest external deformations. Figure 2.1 shows the schematic diagram of a partially closed fatigue crack under varying normal stress. The center of the fatigue crack is usually open due to the plastic elongation of the ligament connecting the tips, that occurs during the nucleation and growth of the crack. At the same time, the tips of the crack are usually tightly closed by compressive residual stresses resulting from the same plastic deformation. In order to increase the detectability of small fatigue cracks, we can exploit the parametric modulation of the otherwise linear ultrasonic wave scattering, that is caused by the changing interfacial stiffness of the closing and opening crack. Regardless of whether we measure the ultrasonic velocity in a specimen having a cluster of micro-cracks or the scattering from large individual cracks, the crucial point is the changing mechanical contact between the opposite faces of the cracks. 29

35 expanded ligament compressive residual stress tension unloaded compression Interfacial Stiffness compression unloaded tension r/a Figure 2.1 Schematic illustration of crack closure as parametric modulation caused by changing normal stress. 30

36 2.1.2 Observation of Crack Closure Perhaps the simplest way to observe crack closure under laboratory conditions is to ultrasonically monitor the opening and closing of fatigue cracks when subjecting the specimen to static or quasi-static external loading. The technical realization of the acousto-elastic modulation method must incorporate two tasks. One is to find an effective way to generate crack closure in the specimen, i.e., the elastic problem. The other is to find a way to monitor the resulting parametric modulation by ultrasonic means, i.e., the acoustic problem. A schematic diagram of phase-locked synchronous detection of crack closure is shown in Figure 2.2. Figure 2.3 shows the effects of asynchronous (ordinary) and synchronous (phase-locked) time-averaging on the detected signal. [35] Ordinary time-averaging, that is routinely used in digital ultrasonic flaw detectors, eliminates only the truly incoherent electrical noise without discriminating between fatigue cracks and artifacts. In comparison, synchronous detection also eliminates timeinvariant artifacts by alternating the sign associated with the detected signal before averaging depending on whether it was taken during crack opening or closing. The retained phase-locked dynamic component is the difference between the reflected echoes from the fatigue crack in its closing and opening states. This signal is mainly caused by the nonlinear effect of tension and compression stresses on the interfacial stiffness between the opposite faces of the partially closed fatigue crack, while other scatterers, including fully open large cracks, are eliminated. The modulating stress may be produced by different means such as external cyclic loading in a typical fatigue test, or the inherent vibration of the structure itself during operation. More localized temporary stresses can be generated by simply cooling or warming the specimen to be tested. [35] The following sections will introduce the technique of using optically induced thermoelastic stresses for fatigue crack identification and present some results on aluminum 2024 and Ti-6Al-4V titanium alloy. 31

37 Physical System External Modulation crack signal incoherent (electrical) noise coherent (material) noise Synhronous Integrator Figure 2.2 Schematic diagram of phase-locked synchronous detection of crack closure. 32

38 noisy signal Ultrasonic Signal [a. u.] Fatigue Crack asynchronous averaging synchronous averaging Time [2 µs/div] Figure 2.3 The effects of asynchronous (ordinary) and synchronous (phase-locked) time-averaging on the detected signal. 33

39 2.2 THERMO-OPTICAL MODULATION Experimental Set-Up When relatively low-intensity radiation is incident on a specimen's surface, some of the light energy is absorbed via electrons in the conduction band and converted into heat, while the rest is reflected. The absorbed energy is dissipated within a few nanometers of the surface, producing a rapid rise in temperature. The thickness of the heated layer increases with time as heat is conducted into the bulk of the material. By increasing the length of the optical pulse to approximately 100 µs, direct generation of ultrasound in the 1-10 MHz frequency range can be eliminated and the resulting thermal stresses can be exploited to produce parametric modulation by dynamic crack-closure. Figure 2.4 shows the schematic diagram of the experimental arrangement with pulsed laser thermo-optical modulation. [1] The region of interest is continuously monitored by an ultrasonic flaw detector emitting a surface acoustic wave and operating in pulse-echo mode. The sharp temperature rise produced by laser irradiation is accompanied by a strong temporal compressive stress as the extending skin becomes too large for the bulk of the material. We used a long-pulse Brilliant Nd:YAG laser without Q-switching that produces about 150-µs-long pulses of 300-mJ total energy at 1.06-µm infrared wavelength and 50 Hz repetition frequency. The ultrasonic surface wave is generated by a Panametrics surface wave wedge transducer of 12.5 mm diameter. The ultrasonic transmitter/receiver is a Panametrics model PL5072. The digital lock-in amplifier is realized by using a software controlled signal processing board plugged in the computer. 34

40 Pulsed Nd:YAG Laser Digital Lock-in Amplifier Trigger RF Signal Wedge SAW Transducer Crack Ultrasonic Transmitter/Receiver Specimen ultrasonic surface wave Figure 2.4 Schematic diagram of the experimental arrangement with thermo-optical modulation. 35

41 2.2.2 Temporal Modulation In order to detect and quantitatively measure the resulting parametric modulation, the detected ultrasonic wave form can be processed and analyzed by different methods depending on the nature of the modulation. Based on the repetition frequency of the pulsed laser and the thermal diffusion time in the material we can distinguish between two types of modulation. First, there is an essentially instantaneous dynamic modulation which is in synchronism with the repetition frequency of the pulsing laser, therefore, can be most easily detected by synchronous demodulation of the received ultrasonic amplitude [1]. This type of modulation is characteristic of materials of high thermal diffusivity, such as aluminum, in which the temperature gradients and the resulting thermoelastic stresses quickly disappear after the termination of the laser pulse. We will call this type of modulation short-term modulation. Second, there is a much slower quasi-static modulation which is an integrated effect of many individual pulses when the laser is turned on for a few seconds or longer and therefore can be most easily detected by asynchronous demodulation of the received ultrasonic amplitude. This type of modulation is characteristic of materials of low thermal diffusivity, such as titanium, in which the temperature gradients and the resulting thermoelastic stresses linger long after the termination of the individual laser pulses and the modulation is greatly amplified by the cumulative effect of subsequent pulses. We will call this type of modulation longterm modulation. The schematic diagram of the experimental arrangement for short-term thermooptical modulation was previously shown in Figure 2.4. Figure 2.5 shows the sequential diagram of the synchronized optical and ultrasonic pulses. In order to measure the shortterm modulation in phase with the 50 Hz repetition frequency of the pulsing laser, the ultrasonic transmitter is synchronized to the laser so that it produces two pulses for each irradiation; one is directly following the laser pulse with an adjustable delay of up to

42 µs and the other is further delayed by a fixed amount of 10 ms. Only the hot ultrasonic pulse is shown which reaches the location of inspection when the compressive thermal stress is at a maximum. The cold ultrasonic pulse is launched 10 ms later when the compressive stress is assumed to have completely diminished (it is not shown in Figure 2.5). It should be mentioned that the actual delay between the start of the laser irradiation and the arrival of the ultrasonic pulse at the location of inspection includes not only the adjustable synchronization delay between the laser and the ultrasonic transmitter but also the approximately 20 µs propagation delay from the transducer to the crack. The detected ultrasonic signal is analyzed by a programmable digital peak detector that assures excellent accuracy and repeatability. The short-term modulation of the measured signal is caused by the alternating variation of the detected ultrasonic echo between cold and hot states. This modulation is partly caused by direct thermal modulation of the sound velocity in the material and partly by thermal stresses via crack closure. It has been demonstrated before that in 2024 aluminum the modulation is mainly due to the latter; therefore it can be exploited for discriminating fatigue cracks against other artifacts which are much less affected by thermal stresses. [1] Figure 2.6 demonstrates how the short-term thermo-optical crackclosure technique can unequivocally distinguish real fatigue cracks from comparable artifacts in aluminum. In this example, the backscattered ultrasonic echo contains a fairly large signal from a starter notch that is hiding a small fatigue crack and an additional large signal from a surface scratch made after fatigue cycling. The measurement was taken at 5 MHz, when both the real and artifact signals were approximately 18 db above the grain noise, i.e., the echo reflected from the surface scratch has almost the same amplitude as that from the fatigue crack and thus may cause false alarm in conventional inspection. Furthermore, the fatigue crack is partially hidden by the EDM (electron discharge machined) starter notch itself that was used to initiate the crack. It is rather typical that the geometrical feature or material imperfection that produces the stress 37

43 concentration, which will ultimately start the fatigue crack, itself produces an ultrasonic echo that should be distinguished from the initially weaker scattering of the fatigue crack. Figure 2.6 clearly shows the different short-term modulation levels produced by pulsed laser irradiation for the surface scratch and the fatigue crack. The two traces on the top show that every second ultrasonic signal reaches the inspected area just after laser irradiation, i.e., when the area is hot and any possible fatigue crack is slightly closed or opened by the resulting thermal stress. The lower two traces show the output of the digital sample-hold unit that measures the peak of the ultrasonic backreflection for every ultrasonic transmission. Clearly, in this situation the reflections from the hot fatigue crack are lower than those from the cold one. This strong dynamic thermo-optical modulation of the ultrasonic signal is uniquely characteristic to partially closed fatigue cracks. In comparison, the modulation associated with the surface scratch is negligible since it lacks those characteristic features that render a real fatigue crack particularly sensitive to dynamic stress closure. One obvious disadvantage of the suggested thermo-optical modulation method is that either the whole inspected area must be irradiated by sufficiently high intensity laser light in one shot, or, when this is not feasible because of limited available laser power, a smaller irradiated spot has to be scanned over the interrogated area as shown in Figure

44 laser pulse Amplitude [a. u.] ultrasonic transmitter ultrasonic receiver trigger delay propagation delay Time [20 µs/div] Figure 2.5 Sequential diagram of the synchronized optical and ultrasonic pulses. 39

45 laser pulse Amplitude [a.u.] ultrasonic pulse fatigue crack surface scratch Time [10 ms/div] Figure 2.6 Identification of a fatigue crack by short-term laser induced crack closure. 40

46 Transducer Laser Beam lateral scan axial scan Ultrasonic Surface Wave Figure 2.7 Scanning of the area to be inspected by the pulsed laser beam. 41

47 2.3 EXPERIMENTAL RESULTS Comparison between Aluminum 2024 and Titanium Alloy Ti-6Al-4V Differences in Material Properties In theory, the short-term thermo-optical technique should provide increased sensitivity over the conventional ultrasonic flaw detection approach in titanium alloys just as well as in aluminum. The actual sensitivity of the technique, however, depends on a great variety of material parameters, which should all be considered carefully and incorporated into the optimization of the procedure. Table 2.1 lists the relevant material properties of Aluminum 2024 and Titanium alloy Ti-6Al-4V. Due to its low thermal conductivity, the thermal diffusivity is more than one order of magnitude lower in Ti-6Al-4V than in Aluminum 2024, which increases the optically induced temperature gradients since the heat cannot spread out in the short time of illumination in titanium as it does in aluminum. Other parameters, however, favor aluminum. For example, the thermal expansion coefficient is higher and the stiffness is lower in aluminum. In addition to the significant differences in mechanical and thermal properties, there is a substantial difference between aluminum and titanium in optical absorption as shown in Figure 2.8. In the near infrared region, where the Nd:YAG pulsed laser operates ( 106. µm), the optical absorption ratio (absorptance) in titanium is higher than 40% versus the meager 5% in aluminum, i.e., the same irradiating power produces one order of magnitude stronger heating in the specimen. Unfortunately, the most crucial parameter, namely the interfacial stiffness of typical fatigue cracks, is the most difficult to quantify. Generally, the tips of small fatigue cracks in ductile aluminum alloys are tightly closed and consequently significant crack closure can be achieved at modest compressive stress levels. In comparison, the tips of even relatively small fatigue cracks in less ductile 42

48 titanium alloys can be fairly open and consequently significant crack closure requires very high compressive stress levels. In conclusion, a direct comparison between Al 2024 and Ti-6Al-4V is all but impossible and additional experiments are necessary to establish the feasibility of the thermo-optical modulation technique in Ti-6Al-4V and other titanium alloys. Table 2.1 Material properties of Aluminum 2024 and Titanium alloy Ti-6Al-4V. Aluminum 2024 Ti-6Al-4V thermal expansion coefficient [10-6 o o C C ] thermal conductivity [W m ] o C specific heat [J kg ] density [kg / m 3 ] 2,710 4, thermal diffusivity [10 m s ] Young's modulus [10 N / m ] Poisson's ratio

49 1 0.8 Absorption Ratio titanium 0.2 aluminum Wavelength [µm] Figure 2.8 Optical absorption spectra for aluminum and titanium. 44

50 Differences in Modulation Patterns Figure 2.9 compares the measured short-term modulation as a function of synchronization delay in Al 2024 and Ti-6Al-4V. In aluminum, strong crack-closure occurs between 40 and 160 µs after the beginning of the laser irradiation and the effect essentially disappears before the arrival of the next laser pulse 20 ms later. In titanium, the strongest crackclosure occurs between 100 and 200 µs after the beginning of the laser irradiation, i.e., slightly later than in aluminum, and the effect decays much more slowly. Figure 2.10 shows the time dependence of the observed thermo-optical modulation of a small fatigue crack at 13 different axial (a) and lateral (b) irradiation positions in aluminum The specimen (#A1) contained a 0.025"-long fatigue crack, the Rayleigh wave inspection was made at 5 MHz, the laser beam diameter was approximately 0.2", and the 0.600" 0.600" area was scanned in 0.050"-steps. The previously described short-term thermo-optical modulation becomes strong only (i) when the laser is on (pulsing) and (ii) when the irradiated spot lies directly over the crack to be detected. Although the fine structure of the modulation cannot be seen at this scale, the periodicity of this so-called short-term modulation is 50 Hz, i.e., it is synchronous with the pulsing laser. Figure 2.11 shows a typical thermo-optical modulation pattern observed in Ti-6Al-4V. The laser is turned on for approximately 8 seconds and then the specimen is left to cool for as long as 2 minutes to eliminate all thermal stresses. The repetition frequency of the ultrasonic pulse was increased to 500 Hz in order to better resolve the details of the modulation pattern. The overall pattern can be separated into a slow long-term and a synchronous short-term modulation. However, the superposition of the two effects is highly nonlinear as indicated by the continuously changing amplitude of the short-term modulation during laser irradiation. The rather complex long-term modulation dominates the observed overall (Figure 2.11a) behavior and it lingers long after the termination of the laser irradiation. During laser illumination (Figure 2.11b), the 45

51 periodic short-term modulation is also detectable but it disappears immediately when the laser is turned off. These comparisons indicate that in titanium the modulation does not entirely disappear by the beginning of the next laser pulse therefore a very significant cumulative long-term modulation occurs, while in the case of aluminum the modulation is mainly due to synchronous dynamic crack-closure. The role of different physical mechanisms in the evolution of the rather complex thermo-optical modulation pattern shown in Figure 2.11 will have to be investigated in detail by theoretical analyses, numerical simulations, and experimental measurements. 46

52 (a) Al-2024 Amplitude Modulation [db] Total Time Delay [µs] Amplitude Modulation [db] (b) Ti-6Al-4V Total Time Delay [µs] Figure 2.9 Measured short-term modulation versus synchronization delay characteristics in (a) Al 2024 and (b) Ti-6Al-4V. 47

53 a) axial scan Modulation [0.1 db/div] Time [s] b) lateral scan Modulation [0.1 db/div] Time [s] Figure 2.10 Time dependence of the observed thermo-optical modulation of a small fatigue crack at 13 different axial (a) and lateral (b) irradiation positions (2024 Aluminum specimen #A1, 5 MHz, scanning over a 0.600" 0.600" area in 0.050"-steps). 48

54 (a) Long-term modulation Amplitude [1 db/div] laser on Time [5 s/div] (b) Short-term modulation Amplitude [0.5dB/div] laser pulse signal amplitude Time [0.1 s/div] Figure 2.11 Typical thermo-optical modulation in Ti-6Al-4V. The complex long-term modulation dominates the overall behavior (a) while the periodic shortterm modulation is detectable only during laser illumination (b). 49

55 2.3.1 Preparation of the Specimens with EDM notches and Fatigue Cracks In aluminum, the thermo-optical modulation was found to be dominated by the synchronous dynamic effect caused by the thermoelastic stress via crack-closure and the modulation was simply defined as the difference between the magnitudes of the ultrasonic echoes detected in hot and cold states. [1] Based solely on the short-term modulation, it was possible to distinguish fatigue cracks, which are susceptible to crackclosure, from other artifacts, which are not. Fatigue crack discrimination based on shortterm thermo-optical modulation was found to be much less effective in titanium alloys where sometimes there exists a strong long-term modulation comparable to or larger than the synchronous short-term modulation. In order to reduce the variation of the short-term modulation caused by the quasi-static opening or closing of the fatigue crack during longterm laser irradiation, we have to use extensive averaging. However, the measured results indicated that even this average modulation is insufficient to reliably distinguish fatigue cracks from artifacts. In order to study the thermo-optical modulation in Ti-6Al- 4V alloy we prepared a total of 16 specimens (see Table 2.2). Eight of them ( c1 through c8 ) contained starter notches and fatigue cracks while the other eight ( n1 through n8 ) contained only starter notches. The length of the starter notches varied form 0.010" to 0.030", while their width and depth was kept more or less constant at approximately 0.003" and 0.007", respectively. The eight fatigue damaged specimens contained fatigue cracks of varying length between 0.025" and 0.045". In the following experimental results, unless otherwise indicated, the center frequency of the Rayleigh wave transducer is 5 MHz, the total time delay between the start of the laser pulse and the arrival of the surface wave at the notch is 130 µs, and the repetition rate of the ultrasonic pulses is 100 Hz (twice the repetition rate of the laser pulses). Figure 2.12 shows the received ultrasonic echoes from the fatigue damaged (a) and unfatigued (b) EDM notches using a 5 MHz Rayleigh wave transducer. The digital demodulator measured the peak 50

56 amplitude within the 1.6-µs-long highlighted part of the RF signal, which corresponds to the echo coming from the EDM notch and its immediate vicinity. It should be mentioned that, in a rather unexpected way, the echoes from the fatigued notches were approximately 5 db lower than those from the unfatigued specimens. It was verified that this apparent discrepancy was caused by the somewhat higher ultrasonic attenuation due to coarser grain structure in the batch of titanium specimens that was fatigue cycled and, after normalization, there was no significant difference between the echo amplitudes from the fatigued and unfatigued EDM notches. 51

57 Table 2.2 Fatigued and Intact Ti-6Al-4V Specimens dimensions in mils Specimen ID notch length notch width notch depth crack length c c c c c c c c n n. a. n n. a. n n. a. n n. a. n n. a. n n. a. n n. a. n n. a. 52

58 a) fatigued EDM notches, 35 db gain c1 Amplitude [2 V/div]. c2 c3 c4 c5 c6 c7 c8 Time [2 µs/div] b) unfatigued EDM notches, 30 db gain Amplitude [2 V/div]. n1 n2 n3 n4 n5 n6 n7 n8 Time [2 µs/div] Figure 2.12 Received ultrasonic echoes from the fatigue damaged (a) and unfatigued (b) EDM notches using a 5 MHz Rayleigh wave transducer. 53

59 2.3.2 Short-Term Thermo-Optical Modulation in Ti-6Al-4V Figure 2.13 shows the measured short-term modulation from the fatigue damaged and unfatigued EDM notches at 5 MHz. On the average, the magnitude of the short-term thermo-optical modulation is 2.5 times larger from fatigue damaged EDM notches than from unfatigued ones. However, considering the large scatter in the data, it is clear that the short-term modulation itself cannot be used to positively distinguish fatigue cracks from artifact signals as it could be done in aluminum. The main reason for this is not the large scatter observed in the modulation from fatigue damaged specimens but rather the relatively large modulation exhibited by unfatigued specimens. The thermoelastic deformation itself is clearly insufficient to produce closure in 3-mil-wide open EDM notches therefore the observed modulation must be directly related to the temperature variation in the specimen. Figure 2.13 well illustrates the relative ineffectiveness of short-term modulation for distinguishing fatigue cracks from the EDM notches. For the specimens containing apparently similar cracks with ~0.035 length, the biggest short-term modulation for each specimen varies in a large range. The biggest modulation in each specimen was obtained when the laser spot is near the scatterer. The results show that some short-term modulations from the cracks are comparable with those from the EDM notches. In this section, we will further demonstrate that the short-term thermo-optical modulation is insufficient to distinguish fatigue cracks from other unfatigued artifacts in titanium alloy Ti-6Al-4V. We are going to describe numerous phenomena observed in the experiments which further decrease the feasibility of this technique in Ti-6Al-4V. Our desire to enhance our understanding of these phenomena motivates our further research in this area. 54

60 1.0 fatigued Short-Term Modulation [db] unfatigued -1.0 c1 c2 c3 c4 c5 c6 c7 c8 n1 n2 n3 n4 n5 n6 n7 n8 Figure 2.13 Short-term modulation from the fatigue damaged and unfatigued EDM notches at 5 MHz. 55

61 1. The short-term modulations change a lot during the time the laser is irradiating the specimens with 50 Hz repetition frequency (Figure 2.14). Different trends have been found in different specimens. The results indicate that the short-term modulation is affected by the quasi-static condition of the scatterer, which is affected by the temperature, the heat distribution in the specimen, and the induced thermo-elastic deformation. Therefore, the time when the data is acquired should be carefully considered during the experimental process. 2. Each specimen exhibits a different short-term modulation profile when the laser beam scans along the axial (Figure 2.15) and lateral directions (Figure 2.16) with respect to the crack. This indicates that for quantitative assessment of the length of a fatigue crack, the data needs to be taken in the area around the crack as shown in Figure 2.7. In practical situations, it is difficult to find the exact site of a crack. 3. Even near the unfatigued notches or corners in the specimens, there still exist short-term modulations (Figure 2.17). According to our original expectation, crack closure is the primary source of short-term thermo-optical modulation, therefore there must be other physical phenomena contributing to short-term modulation. It is assumed that the direct temperature effect on ultrasonic velocity, as mentioned before, causes the complexities for distinguishing fatigue cracks from other artificial scatterers. 4. There exists a large variation in the dependence of the short-term modulation on both interval time (Figure 2.18) and delay time (Figure 2.19) in different specimens. The delay time here refers to the total delay between the time when the ultrasonic pulse reaches the scatterer site (notch, crack) and the beginning of the laser irradiation. The interval is the duration between the two ultrasonic pulses after each start of the laser irradiation. So in the experiment, some effort should be taken for choosing the optimum delay and interval, and in the measured results these two parameters should be given. 5. Ultrasonic frequency affects the modulation significantly. Figure 2.20 shows that the SAW RF signal amplitude becomes weaker when a higher frequency transducer 56

62 is used (probably because of lower transducer sensitivity and higher attenuation in the specimen) but the short-term modulation of the ultrasonic echoes from the notches (n1- n8) and the corner (n0) becomes stronger as shown in Figure This implies that for different depths of cracks, choosing a Rayleigh wave transducer with a suitable frequency is an important step because the majority of the surface wave energy propagates in a surface layer of the medium less deeper than one wave length. Also, the observed ultrasonic echo is the result of a complicated interference between the notch and the fatigue crack and this interference is very sensitive to phase cancellations at high frequencies. Apparently, these complex phenomena greatly complicate the short-pulse technique and make quantitative measurements much more difficult. However, by better accounting for the physical properties and behavior of the material, the underlying phenomena causing these complexities can be also better understood. Our goal is to further study these apparent anomalies in the observed behavior of thermo-optical modulation so that we can optimize the inspection procedure. 57

63 c1 c2 c3 c4 c5 0.3 Short-Term Modulation [db] Laser Irradiation Time [s] Figure 2.14 Short-term modulation versus the irradiation time when the laser spot directly irradiates the crack site. 58

64 c1 c2 c3 c4 c5 0.3 Short-Term Modulation [db] Axial Position [inches] Figure 2.15 Short-term modulation when the laser beam scans along the axial direction over the area containing the small fatigue crack. 59

65 c1 c2 c3 c4 c5 0.3 Short-Term Modulation [db] Lateral Position [inches] Figure 2.16 Short-term modulation when the laser beam scans along the lateral direction over the area containing the small fatigue crack. 60

66 n1 n2 n3 n4 n5 0.3 Short-Term Modulation [db] Axial Position [inches] Figure 2.17 Short-term modulation when the laser beam scans along the axial direction over the area containing the EDM notch. 61

67 c1 c2 c3 c4 c5 0.3 Short-Term Modulation [db] Interval between "Hot" and "Cold" Status [ms] Figure 2.18 Short-term modulation versus the interval between hot and cold status. 62

68 c1 c2 c3 c4 c5 0.3 Short-Term Modulation [db] Total Delay Time [µs] Figure 2.19 Short-term modulation versus the delay time. 63

69 2.5 MHz 5 MHz 10 MHz Signal Amplitude [db] n1 n2 n3 n4 n5 n6 n7 n8 n0 ID# of the Specimens with Notches Figure 2.20 SAW signal amplitude measured by ultrasonic transducers with different frequencies. 64

70 2.25 MHz 5 MHz 10 MHz 0.3 Short-Term Modulation [db] n1 n2 n3 n4 n5 n6 n7 n8 n0 ID# of the Specimens with Notches Figure 2.21 Short-term modulation measured by ultrasonic transducers with different frequencies. 65

71 2.3.3 Long-Term Thermo-Optical Modulation in Ti-6Al-4V Based on our previous results we can conclude that the overall thermo-optical modulation in titanium is partly due to direct temperature effects on the intact specimen, and partly due to thermoelastic effects on the fatigue crack itself. Only the latter can be exploited for enhanced fatigue crack detection, therefore we have to consider possible differences between the two contributions so that they can be distinguished from each other. Such differences should include variations in time-dependence and spatial distribution. In order to further investigate this issue, we studied the effect of the relative position of the heated spot with respect to the damage site. The schematic diagram of how the area to be inspected can be scanned by the pulsed laser beam was previously shown in Figure 2.7. It is expected that in the axial direction the direct temperature effect is asymmetric with respect to the scatterer; it occurs only when the irradiated spot is between the transducer and the scatterer, but not when it is on the other side of the scatterer. In comparison, the thermal deformation induced modulation of partially closed fatigue cracks is expected to be symmetric to the scatterer since the resulting closure is essentially the same regardless whether the thermal expansion occurs on one side of the scatterer or on the other. There is also a substantial difference between the direct temperature and thermoelastic effects when the scatterer is scanned over in the lateral direction, i.e., normal to the sound propagation and parallel to the potential crack. In most cases the direct temperature effect is expected to exhibit odd symmetry with respect to the scatterer since bending the wave in opposite directions usually produces opposite changes in the echo amplitude, unless the beam is perfectly aligned. In comparison, the thermal deformation induced modulation of partially closed fatigue cracks exhibits even symmetry with respect to the scatterer since the resulting closure is essentially the same regardless whether the thermal expansion occurs at one end of the crack or at the other. 66

72 These expectations were qualitatively verified by our experimental results. Figure 2.22 shows the time dependence of the observed thermo-optical modulation of two fatigue cracks (a and b) and two EDM notches (c and d) at 13 different axial positions. For simplicity, only the low-frequency long-term modulation is shown while the highfrequency short-term modulation was suppressed by low-pass filtering. The measurements were made at 5 MHz in 0.050"-steps over a scanning range of ± 0.300" relative to the position of the scatterer. In each case the center waveform recorded almost directly above the scatterer is shown by a thicker line for convenience. It is clear that the substantially stronger modulation observed from fatigue cracks is more-or-less symmetric to the scatterer, although it does not completely disappear when the irradiated spot is in front of the crack. On the other hand, in the case of EDM notches the modulation becomes negligible when the irradiated spot is behind the scatterer, which demonstrates that the modulation observed when the irradiated spot is in front of the scatterer, i.e., in the line of the interrogating surface wave, is entirely due to the direct temperature effect. Figure 2.23 shows the time dependence of the observed thermo-optical modulation of two fatigue cracks (a and b) and two EDM notches (c and d) at 13 different lateral positions. It is clear that the modulation observed from fatigue cracks is not only substantially stronger than the modulation exhibited by undamaged EDM notches, but it also reveals different symmetry with respect to the scatterer's position. In the case of fatigue cracks the modulation is mainly due to thermal stresses therefore it possesses even symmetry since both ends of the crack exhibit roughly the same closure behavior. In contrast, the modulation produced by an EDM notch is mainly due to the direct temperature effect therefore it exhibits dominantly odd symmetry. This is because in cases when perceptible modulation occurs the alignment between the scatterer and the interrogating beam is less than perfect, consequently the bending of the beam in opposite directions results in opposite changes in the scattered amplitude. 67

73 a) c6 b) c8 Amplitude [0.5 db/div] Amplitude [0.5 db/div] Time [5 s/div] Time [5 s/div] c) n1 d) n2 Amplitude [0.5 db/div] Amplitude [0.5 db/div] Time [5 s/div] Time [5 s/div] Figure 2.22 Time dependence of the observed thermo-optical modulation of two fatigue cracks (a and b) and two EDM notches (c and d) at 13 different axial positions. 68

74 a) c6 b) c8 Amplitude [0.5 db/div] Amplitude [0.5 db/div] Time [5 s/div] Time [5 s/div] c) n1 d) n2 Amplitude [0.5 db/div] Amplitude [0.5 db/div] Time 5 [s/div] Time 5 [s/div] Figure 2.23 Time dependence of the observed thermo-optical modulation of two fatigue cracks (a and b) and two EDM notches (c and d) at 13 different lateral positions. 69

75 Figures 2.22 and 2.23 suggest that the symmetry of the observed thermo-optical modulation with respect to the position of the scatterer is strongly dependent on whether the modulation is caused by thermal deformation via crack-closure or directly by the temperature variation via the inherent temperature dependence of the intact material. However, discrimination between small fatigue cracks and other artifacts based on this difference is rendered rather cumbersome by the need to scan the area by the laser beam after a suspected area has been identified. A simpler approach can be based on the also significant differences between the temporal modulations caused by crack-closure and direct temperature variations. Figure 2.24 shows the time dependence of the observed thermo-optical modulation of eight fatigue cracks and eight EDM notches at the center of the irradiated spot. On the average, the magnitude of the modulation is significantly higher from the fatigue cracks than from the unfatigued EDM notches. Besides the difference in magnitude, the most obvious difference between the measured modulations from fatigue cracks and intact EDM notches is the much slower decay of the modulation from fatigue cracks after terminating the laser irradiation. In order to establish the most effective strategy for fatigue crack identification, Figure 2.25 shows the measured longterm thermo-optical modulation from eight fatigue cracks and eight EDM notches at the center of the irradiated spot before (a) and after (b) the end of the 10-s-long laser irradiation at 5 MHz. 2 seconds before the end of the laser irradiation the weakest modulation from a fatigue crack (c1) is approximately 2.5 times larger than the strongest modulation from an intact EDM notch (n6). Much better discrimination can be achieved by comparing the thermo-optical modulations shortly after the laser irradiation is terminated. 2 seconds after the end of the irradiation the weakest modulation from a fatigue crack (c7) is approximately 12.5 times larger than the strongest modulation from an intact EDM notch (n2). 70

76 laser on Amplitude [1 db/div] c1 c2 c3 c4 c5 c6 c7 c8 n1 n2 n3 n4 n5 n6 n7 n8 Time [2 s/div] Figure 2.24 Time dependence of the observed thermo-optical modulation of eight fatigue cracks and eight EDM notches at the center of the irradiated spot. 71

77 Amplitude change [db] a) 2 s before the end of 10-s-long irradiation 1 fatigued 0.8 unfatigued c1 c2 c3 c4 c5 c6 c7 c8 n1 n2 n3 n4 n5 n6 n7 n8 Specimen Amplitude change [db] b) 2 s after the end of 10-s-long irradiation fatigued unfatigued c1 c2 c3 c4 c5 c6 c7 c8 n1 n2 n3 n4 n5 n6 n7 n8 Specimen Figure 2.25 Long-term thermo-optical modulation from eight fatigue cracks and eight EDM notches at the center of the irradiated spot before (a) and after (b) the end of laser irradiation (5 MHz). 72

78 2.4 FEM SIMULATION AND CORRELATION WITH EXPERIMENTAL RESULTS In order to use finite element method (FEM) simulation to explain the phenomena that occurred in the experiments and to optimize this new technique, some simple calculations were carried out using ANSYS 5.4 (university version). The limited results can qualitatively explain some of the complicated phenomena observed in the experiments, which positively indicates that more complete FEM simulations may present further guidance on how to design improved experiments Contour Display of the Temperature and Thermal Stress in a Semi-Space Due to Single Pulse Laser Irradiation Before introducing a crack into a specimen, an intact specimen is analyzed first. Because the laser beam irradiation on a specimen is a circular spot, considering the finite radiation time, the problem can be simplified as a laser spot irradiating the surface of a semi-space medium. So an axisymmetric model with an axisymmetric heat flux load can be applied to solve this problem. The parameters used for simulation are chosen from the experimental conditions. A 10 mm 10 mm square area is modeled in the axial plane, the size of the finite element within a 1-mm-thick surface layer is 25 µm 5 µm. The determination of the mesh size is based on the comparison between the FEM simulation results and the theoretical solutions in a simple case. The largest temperature error in the simulation is kept less than 2 C. The heat flux is a 150-µs-long pulse with 300-mJ of total energy at 50 Hz frequency, the laser spot on the surface of the specimen is of Gaussian profile with a 2-mm characteristic radius. The simulated materials are aluminum 2024 and Ti-6Al-4V. The light absorption ratios of these two materials are 5% 73

79 and 40% respectively. The relevant material properties were previously shown in Table 2.1. Figure 2.26 shows the spatial temperature distributions in aluminum 2024 and Ti- 6Al-4V at 150 µs and 10 ms after the start of laser irradiation. In aluminum 2024 the temperature distribution at 10 ms is almost uniform around the original temperature so the cumulative thermal effect during repetitive laser irradiation can be neglected; significant temperature variation occurs only during one laser pulse. In comparison, the temperature is still fairly high in a surface layer within a certain thickness in Ti-6Al-4V after 10 ms, which means the cumulative temperature increase needs to be considered during repetitive laser irradiation. Figure 2.27 indicates a similar situation for thermal stress distributions. For aluminum 2024, the thermoelastic effects mainly occur in each individual laser pulse so the cumulative effects due to repetitive laser pulses can be neglected, which has been proved by previous experimental results (e.g., Figure 2.10). For titanium alloy Ti-6Al-4V, the thermoelastic results at a given time include cumulative effects from previous multiple laser pulses. The temperature and thermoelastic variations due to this multiple-pulse accumulation effect have also been observed in the experiment (e.g., Figure 2.11). 74

80 Ti-6Al-4V Al-2024 (absorption 40%) (absorption 5%) after 150µs after 10 ms 1mm Temperature [ oc] Figure 2.26 Contour display of the temperature distribution in Ti-6Al-4V and Al-2024 after the laser irradiation. 75

81 Ti-6Al-4V Al-2024 (absorption 40%) (absorption 5%) after 150µs after 10 ms 1mm Stress [MPa] Figure 2.27 Contour display of the stress (σrr ) distribution in Ti-6Al-4V and Al-2024 after the laser irradiation. 76

82 2.4.2 Graph Display of the Temperature and Thermal Stress in a Semi- Space Due to Single Pulse and Repetitive Pulse Laser Irradiation Description of the Figures The simulation conditions were as follows: Gaussian profile laser beam, the laser pulse energy is 300-mJ in 150-µs duration, the repetition rate is 50 Hz, the material is Ti-6Al- 4V. In Figures , the size of the calculated specimen is 3 mm 3 mm. In Figures 2.32 and 33, the temperature distributions are shown in the long-term status. Repetitive laser irradiation is during 0-8 seconds. The temperature in each pulse duration is taken at the 20th millisecond, i.e., at the end of the duration. A 30 mm 30 mm specimen is calculated to simulate the semi-space situation. In Figures 2.29, 30 and 32, the legends are the depths starting from the surface of the specimen under the center of the laser spot. In Figures 2.28, 31 and 33, the legends are the delay times starting from laser irradiation of the specimen's surface. In Figures 2.28 and 29, the stresses are σrr., i.e., normal stresses parallel to the surface in the radial direction. Negative numbers indicate compression and positive ones refer to tension. 77

83 Stress [MPa] (a) 50 µs 300 µs 150 µs Depth [µm] Stress [MPa] (b) 10 ms 5 ms 1 ms Depth [µm] Figure 2.28 Stress σ rr versus the depth for a shorter time (a) and a longer time (b). 78

84 Stress [MPa] µm (a) 30 µm Time [µs] (b) Stress [MPa] µm 600 µm Time [ms] Figure 2.29 Stress σrr versus the shorter time in a thinner layer (a) and versus the longer time in a thicker layer(b) 79

85 (a) 250 Temperature [C] mm 60mm Time [µs] (b) Temperature [C] µm 600 µm Time [ms] Figure 2.30 Temperature versus the shorter time in a thinner layer (a) and versus the longer time in a thicker layer (b). 80

86 Temperature [C] (a) 150 µs 300 µs 50 µs Depth [µm] (b) Temperature [C] ms 5ms 10ms Depth [µm] Figure 2.31 Temperature versus the depth in a shorter time (a) and in a longer time (b). 81

87 Temperature [C] mm 2 mm Time [s] Figure 2.32 Long-term temperature variations on the surface and at larger depth. Temperature [C] s 5 s 1 s Depth [mm] Figure 2.33 Temperature versus the depth in a long-term status. 82

88 Two Thermo-Optical Modulation Mechanisms in the Ultrasonic Detection of Surface Cracks The method of laser enhanced ultrasonic detection of fatigue cracks has been successfully applied in Aluminum 2024 and Ti-6Al-4V, two typical materials with different thermal properties. The respective light absorption ratios are 5% and 40% for the wavelength (~1.06 µm) of the IR laser and the respective thermal diffusivity factors are 78 and 2.9 [10-6 m 2 /s]. The different thermoelastic properties of these two materials cause very different photo-thermo-elastic phenomena in the measurements. While short-term thermo-optical modulation can be used effectively to distinguish fatigue cracks from other scattering artifacts in aluminum 2024, long-term modulation is much more effective than short-term for distinguishing cracks in Ti-6Al-4V. What are the underlying mechanisms that cause these different phenomena? We will attempt to interpret them based on the simulated results. As it was mentioned before, there are two different photo-thermal modulation mechanisms that can affect the received ultrasonic signal in the experiment. One is the result of crack closure due to thermal stresses created by the laser induced temperature gradient. The other is the result of ultrasonic surface wave refraction caused by the laser induced local temperature increase in a certain depth under the surface. Which one of these two effects will dominate the modulation of the ultrasonic surface wave depends on several factors: the dimension of the scatterers, the material properties, the laser intensity and repetition rate, etc. Usually, in a short time (~laser pulse duration), the effects of the thermal stress penetrate much deeper in a specimen (Figure 2.27) than the pure temperature effects do (Figure 2.26). Under our experimental conditions, the aluminum specimens only absorb a small part (~5%) of the laser energy (~300 mj) in each laser pulse duration (~150 µs), and the heat penetrates in a thin layer (~50 µm), so the pure temperature increase (~1 C) is 83

89 very small for short-term modulation. Before the next laser pulse arrives after 20 ms (50 Hz), the temperature in the specimen almost uniformly equals to the initial temperature of the specimen, which is indirectly verified by the experimental results of short-term amplitude modulation vs. synchronization delay in Al 2024 as shown in Figure 2.9a. Therefore, in aluminum the long-term modulation can not be observed and the short-term modulation plays a dominant role. However, if the crack depth is beyond the range (~200 µm) of the effects of the thermal stress in the duration of a laser pulse (~150 µs), shortterm modulation can not be observed clearly, either. In order to detect a deeper crack, several steps could be taken; increasing the laser intensity and laser pulse duration, increasing the delay of the ultrasonic surface wave reaching the crack after laser irradiation, and choosing a lower frequency transducer. When the same experimental conditions are applied in Ti-6Al-4V specimens, due to the higher absorption ratio (~40%) and lower thermal diffusivity, the temperature is not uniformly equal to the initial temperature at the end of the repetition period (20 ms) of laser irradiation. Instead, the specimen can reach a certain temperature at a certain depth (~10 C at 200 µm depth, Figure 2.31), which is also indirectly verified by the experimental results of short-term modulation vs. synchronization delay in Ti-6Al-4V as shown in Figure 2.9b. With an increase of the laser irradiation duration to 8 seconds, the temperature increases and penetrates in a deeper range (~40 C during 1-8 s, at 1 mm depth, see Figures 2.32 and 33) and a significant long-term modulation can be observed. Since the temperature changes rather slowly around a certain value at a certain depth, crack tips are quasi-statically opened or closed. The presented results are typical for Ti- 6Al-4V specimens, where the crack signals are about 20 db higher than the grain noise and long-term modulation is used to distinguish starter notches containing fatigue cracks from undamaged ones. During the laser pulse duration (~150 µs), the maximum photothermal stress may not reach the crack tips, therefore the short-term modulation is not very effective. 84

90 When the crack signal is comparable with the grain noise (S/N < 6 db) and the crack tip is very close to the surface of the specimen, the effects of photo-thermal stress and the direct effects of temperature variation appear simultaneously. Both short-term and long-term modulations resulting from these two effects can be observed. It is difficult to distinguish a crack signal from grain noise relying only on the short-term or long-term modulation. However, one fact that should be noticed is that if the short-term modulation is due to pure temperature effects, the long-term modulation will be stronger due to the increased thermal diffusion at deeper positions. A crack tip is much more easily modulated by thermal stresses induced by the temperature gradient. The ratio between short-term and long-term modulations is different for crack signals and grain noise, which is verified by the experimental results. 85

91 2.4.3 Crack Closure in a Simple Model Model building The simplified model is shown in Figure The crack is in a rectangular shape with 1000-µm length, 320-µm depth. Two cases of width (0.2 µm and 0.02 µm) are considered. The specimen and the excitation are assumed to be symmetric with respect to the middle planes parallel and normal to the crack surface. So, the calculations are only applied to a quarter of the specimen as shown in Figure The quarter used in the calculation is a 6 mm 6 mm 6 mm Ti-6Al-4V block. The heat flux area (laser spot) is of a Gaussian profile with a radius of 2 mm, and the heat input is a 150-µs pulse with a total energy of 300 mj 0.4 = 120 mj at 50 Hz frequency. In order to simulate the crack closure, a simple crack model is assumed. In the undeformed state, the two surfaces of the crack are traction free and have a certain width between them. During laser irradiation, the crack closes or opens but the two surfaces are still traction free until they are in partial contact with each other. After the two surfaces are in partial contact due to thermal deformation, the displacement of the contacting parts is constrained to be zero. In the FEM model, many spring elements are used to simulate this type of crack model. One end of each spring is connected to a node in the crack surface and the other end is clamped. Each spring element has only compressional stiffness without tensional one, and one initial tension strain can be given at the start of calculations. Within the limits of this initial strain, the spring has no compressional stiffness either, which can be used to simulate the width of the crack. 86

92 laser spot crack Ti-6Al-4V Figure 2.34 A simplified model. A laser beam irradiates the surface of a specimen containing a small rectangular surface notch; the notch is located at the center of the beam. 87

93 Results and Discussion The crack closure due to the laser irradiation was calculated based on the above model. The deformation of one of the crack surfaces along the middle line (highlighted line in Figure 2.34) are shown in Figures 2.35 and 36 for crack widths of 0.02 µm and 0.2 µm, respectively. The positive and negative values in the figures indicate opening and closing of the crack, respectively. The legends without the symbol "+" represent the transient time during repetitive laser irradiation and the ones with the "+" represent the additional transient time after turning off the repetitive laser irradiation following a relatively long exposure (8 s). At first glance, the figures show the complicated crack closure behavior which has been observed in the experiment. Different crack closure phenomena result both during and after the laser irradiation. Several phenomena can be predicted from these simulated results: 1. Thermo-optical modulations change with time. During the quasi-static process (long-term repetitive laser irradiation), the crack contact state changes with time, so in the case of long-term exposure, both short-term and long-term modulations will change with time. 2. Positive and negative short-term modulations will occur in different crack contact states. If the mouth of a crack (top part of a crack) closes fairly well, i.e., the crack width is very narrow (Figure 2.35), the value of short-term modulation between hot and cold states will be positive, because the two surfaces of the crack are closer in the cold state (e.g., 10 ms) than in the hot state (e.g., 150 µs). On the other hand, if the mouth of a crack is widely open (the width is larger than 0.1 µm, as in Figure 2.36), the short-term modulation will be negative because the two surfaces of the crack are closer in the hot state. 3. The short-term modulation changes with the delay time (between the ultrasonic wave reaching the crack site and the start of the laser radiation) and the interval (between 88

94 the hot and cold states). At different times, the closure states are different, so the amplitude and sign of short-term modulation depend on the delay and interval times. 4. There is no fixed relationship between short-term and long-term modulations. As mentioned above, the amplitude and sign of the short-term modulation depend on the contact state as well as on the delay and interval times. This maybe a criteria to qualitatively distinguish pure thermal and thermo-elastic effects, because thermal effects are expected to have simple relationship between short-term and long-term modulations. 5. During the quasi-static observation of a crack, the crack is always closed during laser irradiation compared with the original contact state, and always quickly (~500 ms) changes to open after turning off the repetitive laser irradiation. This prediction appears to be inconsistent with the experimental results, because the measured long-term modulations show that the ultrasonic echoes from most cracks increase during repetitive laser irradiation on the crack sites. In this respect it is important to recognize that the detected notch/crack signal is the result of a complex interference phenomenon and it is not necessarily a monotonic function of crack opening. 6. Combining variations of the crack closure with time, delay, interval, and laser parameters such as intensity and repetition rate, the crack contact state can be semiquantitatively predicted. Several levels of crack width categories ranging from widely open to tightly closed can be identified in the same material: (i) A crack is wide open. Such a crack will have no obvious dynamic crack closure even with high intensity laser irradiation on the crack site. (ii) The crack width is large but short-term modulation can still be observed after laser irradiation for a certain time (~5 s), because of quasi-static crack closure during long-term laser irradiation. (iii) The crack width is large, short-term modulation can be observed immediately after the laser irradiation but it is not obvious in a short delay (<30 µs). In this case, the surfaces of the crack are closer after a longer delay (>100 µs, <400 µs) than in the cold state (~10 ms); there is no obvious change in the short-term modulation though by changing the interval; the long-term modulation 89

95 does not decay so slowly after turning off the repetitive laser irradiation. (iv) The crack width is large. In this case, the sign of short-term modulation changes from positive (more open in hot state) to negative as the delay increases. (v) The crack width is small. The sign of the short-term modulation changes from positive (more open in hot state) to negative when the interval is increased. (vi) The crack width is small. The short-term modulation is always positive, and there is no apparent change in short-term modulation the interval is changed. 90

96 Crack Closure [µm] Crack Depth [µm] µs 100 µs 50 µs 300 µs 2 s ms 20 ms ms 3 s+ 2 s+ 1 s+ 500 ms+ 100 ms+ 5 s Time Figure 2.35 Crack closure along the middle line of the crack with 0.02-µm-width. 91

97 Crack Closure [µm] Crack Depth [µm] µs 100 µs 50 µs 300 µs 2 s ms 20 ms ms 3 s+ 2 s+ 1 s+ 500 ms+ 100 ms+ 5 s Time Figure 2.36 Crack closure along the middle line of the crack with 0.2-µm-width. 92

98 2.5 DETECTION OF SMALL FATIGUE CRACKS AGAINST GRAIN NOISE Experimental Set-up Our previous experiments have verified that long-pulse laser irradiation of the surface of a specimen can be used to increase the detectability of fatigue cracks via thermo-optical crack closure when the crack signals are stronger than the grain noise (S/N db) and the cracks must be distinguished from artifacts. In many situations of practical importance, very small cracks must be detected as early as possible after initialization when they are still submerged in grain noise and conventional ultrasonic flaw detection methods based on the amplitude of the scattered signal cannot distinguish them from material inhomogeneities. Conceptually, the previously introduced method might be also used to distinguish crack signals from grain noise, which is not affected by crack closure. However, the thermo-optical stress modulation exhibited by small fatigue cracks might be overshadowed by the direct temperature modulation of grain scattering, therefore further experiments are needed. The basic experimental set up is similar to our previous one. An oscilloscope with reduced sampling frequency (500 samples/s) and long scanning time (20 s) is used to record both the long-term and short-term modulations. As we described before, this type of signal contains a large amount of detailed information, from which the whole procedure of signal modulation can be evaluated. A 5 MHz ultrasonic transducer is used to generate and detect the surface wave. The ultrasonic wave is still synchronized to the laser, so when the modulation is very weak, the synchronous time average can be used for eliminating electrical noise. In order to study the feasibility of discriminating small fatigue cracks from grain noise, we prepared five Ti-6Al-4V specimens with small fatigue cracks ranging from 0.020" to 0.040". The starter notch was kept in one specimen (c5), 93

99 but those in the other four specimens were removed by grinding. The parameters of the cracks are shown in Table 2.3. Table 2.3 Parameters of Ti-6Al-4V specimens (dimensions in mils) Specimen ID notch length notch width notch depth crack length crack length after notch removed c c c c c n.a. 94

100 2.5.2 Results and Discussion As an example, Figure 2.37 shows the envelope of the RF signal detected from specimen c6. Clearly, from this figure the crack signal can not be identified since it is totally hidden by grain noise. Before the starter notch had been removed, similar signal amplitudes were measured from the same specimen at 39 db, i.e., 15 db lower gain, which indicates that those previously measured strong signals were mainly due to the starter notches. In order to identify the different behavior of crack signals and grain noise under thermo-optical modulation, five potential flaw signals close to the expected time of arrival from the original location of the EDM notch (marked by #1 through #5) were identified, gated, and their modulation profiles were measured. Figure 2.38a and b show two examples of the obtained modulation curves for signals #2 and #3. The line marked with 0" represents the measured modulation when the laser beam irradiates the estimated position of the crack. The lines with positive numbers represent the modulation when the laser beam scans between the suspected crack site and the transducer. Figure 2.38 confirms our earlier conclusion that direct temperature modulation occurs when the laser irradiates the propagating path of the ultrasonic wave. This phenomenon is indicated by the strong modulation shown on the lines with positive numbers regardless of whether the signal is due to reflection from a small crack or grain scattering. In certain situations, e.g., when the transducer is misaligned, the temperature induced deflection of the ultrasonic wave may be substantial and perceptible short-term modulation can also appear. Therefore, it is difficult to distinguish a crack signal from grain noise based solely on either the short-term or long-term modulation. However, if the short-term modulation is due to the direct temperature effect, the long-term modulation will be also stronger. In contrast, the thermo-optical modulation due to crack closure is higher when the laser beam directly hits the crack region. With the time increasing, although the temperature increases everywhere, the temperature gradient changes little 95

101 near the surface, so that crack-closure due to thermal stresses does not change much with time. This means that the modulation produced by fatigue cracks has a relatively strong short-term component with respect to the long-term modulation, therefore the amplitude ratio between the dynamic and long-term modulations will be greater. Figure 2.39 shows this modulation ratio for different signals identified in Figure The modulation ratio is calculated from the magnitudes of the average short-term and long-term modulations within 8 and 14 s. Figure 2.39 clearly shows that there is only one signal (#3) whose ratio at certain positions (0.0" and -0.1") is obviously greater than those of all the other signals. With the same strategy, the other four specimens were also measured, and the same phenomenon was found, i.e., there exists one signal in each specimen, which exhibits a 4-8 times higher modulation ratio at certain points than all the other signals from the same specimen. In order to verify that this particular signal exhibiting the very high modulation ratio is indeed the signal scattered from a crack, we intentionally misaligned the transducer in specimen c5, in which the starter notch was not removed, so that the crack signal is of roughly the same amplitude as the grain noise. As expected, the known fatigue crack signal (#3) was the one which exhibited the very high modulation ratio. Although the modulation ratio seems to be the most characteristic feature that distinguishes fatigue cracks from false alarms caused by local maxima in the grain noise, the absolute value for this ratio seems to vary significantly from specimen to specimen. The underlying cause for this variance should be further investigated in the future and, for the time being, a suspicious backscattered signal of high modulation ratio (above 0.2) should be treated as a potential flaw indication. 96

102 #1 #2 #3 #4 #5 Amplitude [mv] Time [µs] Figure 2.37 The envelope of the RF signal detected from specimen c6 at 54 db gain. 97

103 a) signal #2-0.2" Modulation [1dB/div] -0.1" 0.0" +0.1" +0.2" +0.3" +0.4" Time [5 s/div] b) signal #3-0.3" Modulation [1dB/div] -0.2" -0.1" 0.0" +0.1" +0.2" +0.3" Time [5 s/div] Figure 2.38 Examples of the measured thermo-optical modulations for two signals in specimen c6 when the laser beam is scanned along the axial direction. 98

104 Modulation Ratio #1 #2 #3 (probable crack) #4 # Axial Position [inch] Figure 2.39 Variation of the amplitude ratio between the short-term and long-term modulations when the laser is scanned along the axial direction in specimen c6 (#3 signal is probably from a small fatigue crack). Modulation Ratio #1 #2 #3 (known crack) # Axial Position [inch] Figure 2.40 Variation of the amplitude ratio between the short-term and long-term modulations when the laser is scanned along the axial direction in specimen c5 (#3 signal is from a misaligned fatigue crack). 99

105 2.6 SUMMARY We have investigated the feasibility of the unequivocal discrimination of real fatigue cracks from spurious artifact signals produced by other scattering objects unrelated to fatigue damage. The suggested method is based on the susceptibility of partially closed fatigue cracks to modulation by normal stresses acting on the opposite surfaces. Direct mechanical deformation of the whole structure is usually not practical except during realtime monitoring of fatigue cycling. Even then, the overall mechanical deformation and vibration of the specimen causes instability and artifacts might be mistakenly identified as fatigue cracks. Alternatively, localized dynamic thermal stresses produced by laser irradiation can be used to produce crack closure without adverse deformations and vibrations in the specimen as a whole. Infrared laser excitation offers an attractive way to produce the necessary compressive stresses as the suspected area can be optically scanned while the ultrasonic scattering is monitored by either conventional contact or more sophisticated laser-ultrasonic means. The resulting transient thermoelastic deformation perceptibly changes the opening of partially closed surface cracks without affecting other scatterers, such as surface grooves, corrosion pits, coarse grains, etc., that might hide the fatigue crack from ultrasonic detection. The magnitude, spatial extent, and temporal variation of the thermo-optically induced compressive stress depends on a number of material properties including optical absorption, thermal conductivity, specific heat, thermal expansion coefficient, etc. Generally, the affected spot size where crack closure can be expected is slightly larger than the size of the area actually irradiated. This localized nature of the induced stress is an important advantage of the thermo-optical modulation by pulsed laser irradiation over the previously described mechanical loading and cooling methods. Maximum modulation level can be achieved by focusing the laser beam to the smallest spot size that can be maintained on the surface without causing permanent damage. However, a larger 100

106 diameter laser beam allows us to detect cracks in a large area without having to focus the laser exactly to the tip of the crack. The received ultrasonic signal contains backscattering information from a long range along the propagation path of the acoustic beam, but only a fraction of this path is actually irradiated by the pulsed laser light. Unless the approximate location of the suspected crack is already known, full coverage of the acoustic path necessitates the axial scanning of the laser beam. Furthermore, the ultrasonic beam is usually significantly wider than the modulating laser beam, therefore some lateral scanning of the laser beam might be also necessary. The thermo-optical modulation method has been previously shown to be capable of identifying small fatigue cracks in aluminum alloys, where the high thermal diffusivity of the material results in a uniquely strong high-frequency short-term modulation. [1,2,41,42] Unfortunately, the same technique was found to be much less effective in titanium alloys because of their much lower thermal diffusivity. The high temperature coefficient of the sound velocity in titanium further complicated the problem by introducing a direct temperature modulation even in the case of scatterers that would not exhibit stress induced crack closure at all. This spurious modulation is caused by direct thermal modulation of the sound velocity in the material rather than thermal stresses via crack closure. These difficulties prompted us to modify the thermo-optical method and rely on low-frequency long-term modulation for fatigue crack detection instead of the previously used high-frequency short-term modulation. With this modification we have successfully demonstrated the feasibility of thermo-optical fatigue crack identification in Ti-6Al-4V. Different methods have been developed to distinguish direct thermal modulation from crack closure modulation due to thermoelastic stresses. It was found that the suggested thermo-optical modulation method can increase the detectability of hidden fatigue cracks in Ti-6Al-4V specimens by approximately one order of magnitude. By this technique, otherwise dubious flaw indications that are partially or fully immersed in grain and structural noise could be recovered and positively identified 101

107 without necessarily raising the number of false alarms. It is also possible to distinguish crack signals from grain noise based on the amplitude ratio between the short-term and long-term thermo-optical modulations. 102

108 CHAPTER III LOCAL DIRECT TEMPERATURE MODULATION OF RAYLEIGH WAVES BY REPETITIVE LONG-PULSE LASER IRRADIATION 3.1 ABSTRACT OF THE CHAPTER On the basis of the previous chapter, we know that pulsed infrared laser irradiation can be used to positively identify small fatigue cracks on the surface of fatigue damaged specimens. The resulting transient thermoelastic deformation perceptibly changes the opening of partially closed surface cracks without affecting other scatterers, such as surface grooves, corrosion pits, coarse grains, etc., that might hide the fatigue crack from ultrasonic detection. We found that this method is relatively less efficient in Ti-6Al-4V, where significant thermo-optical modulation occurs even from straight corners or widely open notches. This spurious modulation is caused by direct thermal modulation of the sound velocity in the intact material rather than thermal stresses via crack closure. When an ultrasonic beam propagates through the affected area, refraction occurs and a spurious modulation results. We have developed a theoretical method to analyze this phenomenon. [75] Local perturbation of the transmitted ultrasonic signal is modeled by assuming repetitive irradiation by a long-pulse infrared Gaussian laser beam. Numerical results are presented to illustrate the dependence of the modulation on a number of parameters, such as ultrasonic frequency, laser power, and the temperature coefficient of the surface wave velocity. These predictions are in good agreement with the experimental observations and might be used to further improve the detectability of small fatigue cracks by the thermo-optical modulation technique. 103

109 3.2 INTRODUCTION Generally, nonlinear measurements are more sensitive to distributed microcracking commonly found in fatigue damaged materials than conventional linear techniques measuring the ultrasonic velocity or attenuation in the specimen. [32] Two basic nonlinear effects of practical importance can be exploited for material evaluation. The first is the dependence of the ultrasonic velocity on an external stress (or strain) applied to the specimen, the so-called acousto-elastic effect. The second effect is harmonic generation as an acoustic wave of finite amplitude propagates through the medium. The disadvantage of these measurements is that they either need external stresses or strong acoustic waves, and usually the measurements need to be carried out on the whole structure, which can easily cause unstable measurements and even damage the whole system. The previously described laser enhanced ultrasonic detection method offers the advantage of thermoelastically inducing crack-closure by laser heating the specimen locally. During the investigation of the above method, some unexpected modulations were also observed when the laser irradiated intact parts on the surface of the specimen. This effect was qualitatively explained by the temperature dependence of the surface acoustic wave velocity. [4] When a laser beam with smooth (e.g., Gaussian) profile irradiates the surface of a specimen, the material absorbs the energy and generates an axisymmetrically distributed temperature distribution. The temperature in the affected volume is higher than in other parts of the specimen and the increased temperature lowers the ultrasonic surface wave velocity in this volume. According to the ray refraction theory, an ultrasonic surface wave is refracted when it passes through a boundary between two parts with different wave velocities. A schematic diagram of the refraction is shown in Figure 3.1a. Of course a transducer always has its own directivity pattern, as schematically shown in Figure 3.1b. 104

110 (a) incident ray refracted ray C A B laser heated area corner of the specimen (b) 0 90 Figure 3.1 Schematic of the mechanism for laser induced modulation of SAW (a) ray refraction when SAW propagates through the laser heated area (b) directivity pattern of a transducer. 105

111 Let us consider the slightly misaligned beam shown in Figure 3.1a. Without laser heating, the original ray should hit the corner of the specimen (which is used as a reference reflector that cannot produce crack closure) at point A. During laser irradiation, the ray will be refracted to point B provided that the ray passes through the upper side of the circular heated spot, so the ray will be refracted farther away from the normal direction resulting in a received signal that will be smaller than a signal without laser irradiation. On the other hand, if the ray passes through the lower side of the circular heated spot, it will be refracted to point C and becomes closer to the normal direction, so the received signal will be greater. Therefore, the refraction of the beam induced by the laser irradiation will cause an asymmetric variation or modulation of the received signal with respect to the lateral position of the laser spot. In the rare case of perfectly normal alignment the modulation will be symmetric, but also very small, therefore negligible. Based on the theory of transient laser heat conduction, the empirical temperature dependence of acoustic velocity, the directivity of the transducer, and the theory of Rayleigh waves, a new theoretical model for this modulation is proposed in the following. Using the actual parameters from the experimental arrangement a repetitive long-pulse circular Gaussian laser beam, a surface wave wedge transducer working in pulse-echo mode, a Ti-6Al-4V specimen a series of numerical results are calculated for different parameter values. Experimental measurements were carried out and the results are shown to be in good qualitative agreement with the theoretical predictions. Both the theoretical and experimental results suggest ways for distinguishing, minimizing and even exploiting these local laser induced modulations of Rayleigh waves via the direct laser heating effect. 106

112 3.3 ANALYTICAL MODEL The problem to be solved is schematically shown in Figure 3.2a. A transducer working in pulse-echo mode is used to detect the Rayleigh wave reflected from one corner of the specimen. A repetitive long-pulse laser is applied to irradiate the surface area between the transducer and the corner. The laser heating will locally increase the temperature in the medium, and the increased temperature will cause the Rayleigh wave velocity to change in the heated area. When a Rayleigh ray passes through the boundary between two parts with different acoustic impedance, part of the ray will be reflected and part will be refracted. In this analysis, because the irradiating laser is a long-pulse one, the temperature distribution in the medium can be considered as continuous, so the temperature induced velocity change is also continuous. According to the theory of acoustics, this continuous change between the two parts produces a good matching and the reflection of the ultrasonic wave due to this laser heating spot is negligible. 107

113 (a) Laser Beam lateral direction Transducer axial direction Corner SAW (b) x r y z Figure 3.2 A schematic diagram of the measurement configuration (a) and the coordinate system used in the analysis (b). 108

114 The modeling of this problem needs to consider the temperature distribution in the medium in 3-D coordinates, the Rayleigh wave distribution along the depth, and the directivity pattern of the transducer. In order to simplify the problem, the medium here is assumed to be an isotropic, homogeneous material, and the laser heated area is axisymmetric. The coordinate system is shown in Figure 3.2b. The origin is chosen to be at the center of the irradiating laser spot. The Rayleigh wave is assumed to propagate in a semi-infinite solid along the x direction. The z axis is directed into the medium. In a simple 2-D model shown in Figure 3.3a, an ultrasonic ray passes through a circular area with uniform temperature with an acoustic speed v which is different from the acoustic speed of the surrounding area v 0. The incident angle at the boundary of the circular area is θ 0. The refracted angle inside the circular area is θ, and the output angle exiting the circular area is θ' 0. According to Snell s Law: sin θ sin = v v. (3.1) θ 0 0 In the analysis of this problem, the acoustic velocity is assumed to be the function of temperature v(t). The temperature distribution in the medium determines the velocity distribution. Based on the experimental results in some solids, the temperature dependence of the acoustic velocity is assumed to be a linear relationship: v= v001 + c( T T0) 5, (3.2) where T and T 0 are the temperatures in the circular area and the surrounding material, respectively, and c is the temperature coefficient of the velocity, that is determined by the material. 109

115 (a) θ v 0 0 v θ r 0 θ r θ' 0 (b) θ R r 0 Figure 3.3 Ray refraction through a circular area of uniform temperature (a) and the integrated result through an area of distributed temperature (b). 110

116 For non-uniformly distributed temperatures, the elementary refraction angles should be integrated through each refraction between each tiny neighboring area with a temperature difference (Figure 3.3b). Therefore, it is necessary to find the derivative of the angle with respect to the temperature. Substituting equation (3.2) into (3.1), and taking the derivative of both sides yields: cosθ sin θ 0 dθ= cdt. (3.3) For each small temperature difference, θ θ 0, so equation (3.3) can be written as: cosθ sin θ dθ = cdt. (3.4) Considering sin θ= r r 0, the above equation (3.4) can be expressed as: dθ= c r0 dt r2 r0 2. (3.5) This is an infinitesimal angle due to refraction at the hypothetical boundary between two circular rings of slightly different temperature that depends on the temperature gradient. Considering a pulse-echo measurement, the ray will pass the boundary twice both forward and backward directions, therefore the overall change in propagation angle will be approximately four times larger, i.e., 4 dθ. The total angle change in this 2-D model can be obtained by integrating (3.5) along the whole wave path through the laser heated circular area (figure 3b). Therefore, the next step is to obtain the temperature as a function of spatial coordinates and time. For a semi-infinite solid, the temperature distribution due to a continuous Gaussian laser beam irradiating the surface is: [76] 111

117 2 Hκ t 2 2 dβ β w P0 r z Tc ( r, z, t) = exp exp 32 / 2 2 K π β + w β! #"! #" +, (3.6) where the symbols represent: r, z - spatial coordinates, t - time, P 0 - power of the laser, K - thermal conductivity, κ - thermal diffusivity, w - laser beam radius. The temporal profile for a pulse train emitted by a repetitively pulsed laser is adopted as: [56] N 1 j= 0 :? Yt () = Ht [ jλ] Ht [ ( jλ+ t w )]. (3.7) Here, H(t) is the unit step function, Ht [] = 0 if t< 0 and Ht [] = 1 if 0 t, (3.8) so that the difference term in equation (3.7) represents a switch that activates each pulse, j, at t = jλ, and then deactivates the pulse at t = jλ + t w. t w is the pulse width or activation time. The number of pulses in the pulse train is designated by N, and Λ is the repetition time period between two successive pulses. The temperature field due to the temporal profile given by equation (3.7) can be expressed in the following format using Duhamel's theorem: [77] t H dy( τ) Trzt (,,) = Tc (,, rzt τ) dτ. (3.9) dτ τ= 0 Substitutions of equation (3.7) and (3.8) into equation (3.9) gives / N 1 ; c c w j= 0 T( r, z, t) = T r, z, t jλ T r, z, t ( jλ+ t ) H t ( jλ+ t ). (3.10) 112

118 Combinations of equations (3.5), (3.6) and (3.10) give dθ as a function of r, z and t, i.e., dθ( r,,). z t If the transit time of the acoustic ray passing through the heated area is short enough so that the temperature variation in this time is negligible, then at a known depth z and time t, by integrating 4dθ along the ray path through the heated area, the total refracted angle can be obtained as follows R H c r θ( zt,) = 4 0 T (,,) r z t dr. (3.11) v r2 r r= r The directivity function of a (3-D) circular piston radiator is chosen as a qualitative (2-D) approximation of the surface wave wedge transducer, which is: J ( aksin Ω) D( Ω) = 2 1, (3.12) ak sin Ω where J1 is the first-order Bessel function of the first kind. Ω is the angle between the ray direction and the transducer orientation on the surface. From equations (3.11) and (3.12), the variation of the measured signal at a known depth can be calculated. However, the stresses and strains produced by the Rayleigh wave change with depth under the surface of the medium. Clearly, the measured result will be affected by this distribution. For Rayleigh waves, the displacement potentials (without the common exp[ iω t] term) are: [78] ϕ = F exp[ κ z]exp[ ik x]. (3.13a) 0 d R ψ = G exp[ κ z]exp[ ik x]. (3.13b) 0 s R 113

119 G F 0 0 i2κ k = κ + k d R 2 2 s R. (3.13c) where κ d = k 2 R k 2 and κ d s = k 2 R k 2 s, k R =ω/ c R, kd =ω/ cd, and ks =ω/ c are the wave numbers of the Rayleigh surface wave, longitudinal bulk wave and shear bulk wave, respectively. Here, ω is the angular frequency, c R, c d and c s are the speeds of the Rayleigh wave, longitudinal wave and shear wave, respectively. s λ + cd = 2 µ µ + cs = cr ν,, ρ ρ 1+ ν, where λ is the Lamé constant, µ is the shear modulus, ν is Poisson's ratio, and ρ is the density of the medium. Through the well-known mathematical formulas for acoustic wave propagation, the following stresses and strains can be obtained: normal stress in the propagation direction: τ λ ϕ ϕ µ ϕ ψ xx= + 2 (3.14a) x2 z2 x2 x z 2 normal stress parallel to the surface: shear stress: τ λ ϕ ϕ µ ϕ ψ zz = (3.14b) x2 z2 z2 x z 2 2 ϕ ψ ψ τ zx= τ xz= µ 2 + x z x2 z2 2 2 (3.14c) the corresponding strains: 114

120 ε xx 2 2 ϕ ψ = x2 x z (3.15a) ε zz 2 2 ϕ ψ = + z2 x z (3.15b) γ zx 2 2 ϕ ψ ψ = γ xz= 2 + x z x2 z2 2 (3.15c) The strain energy density is 0 = H τ δε + τ δε + γ δγ. (3.16) U xx xx zz zz xz xz Because only the relative change before and after laser irradiation will be considered and measured, the term with x, i.e., exp[ i2 k R x] in the extended expression of equation (3.16), can be omitted. The Rayleigh wave energy received by the transducer having a unit width in the y direction is proportional to 2 E( Ω) = HU0( z) D ( Ω) dz. (3.17) 0 Combining equations (3.11), (3.12) and (3.17), the modulation of the Rayleigh wave due to laser irradiation can be expressed as Mt ()[ db] = 10 log! #" E( Ω+ θ). (3.18) E( Ω) 115

121 3.4 NUMERICAL RESULTS On the basis of the above analysis, if the parameters of the laser, the surface wave transducer, and the medium are given, the modulation can be obtained by numerical computation. Two types of modulation are computed in the numerical results. One is the long-term modulation which is the accumulated result due to repetitive long-pulse laser irradiation. The long-term modulation has about a 20 second period with the laser pulses turned on for half of that time. The first laser pulse is started at the 5th second, and the laser pulse train is turned off at 14.8 seconds. The short-term modulation is calculated only during one laser repetition period, i.e., for 20 milliseconds. The laser pulse starts at 0 seconds. In order to see the modulation clearly during the 150-µs laser pulse, we only show the result until about the 10 milliseconds. In the analysis, the parameters are chosen to match as closely as possible with the experimental conditions. The laser beam is of Gaussian profile with 0.1 inches radius, the laser pulse is a square one with 150 µs duration, and the repetition frequency is 50 Hz. The laser energy is 300 mj/pulse MHz, 5 MHz and 10 MHz SAW transducers with 0.5 inches diameter are used for the calculation of the directivity pattern. The medium is Ti-6Al-4V with the properties as shown in Table 3.1. Using these parameters, the following results are obtained. 116

122 Table 3.1 Material properties of titanium alloy Ti-6Al-4V. thermal expansion coefficient [10-6 o o C C] 9.5 thermal conductivity [W m ] 7.3 specific heat [J kg o C] 565 density [kg / m 3 ] 4,430 thermal diffusivity [10-6 m2 s] 2.9 Young's modulus [109 N / m2] 114 Poisson's ratio 0.33 longitudinal wave velocity [103 m / s] 6.1 transverse wave velocity [103 m / s] 3.1 Rayleigh wave velocity [103 m / s]

123 Figure 3.4 shows the calculated modulations assuming that the initial acoustic ray is normal to the reflector. The radius of the laser beam is 0.1 inches, and the temperaturevelocity coefficient is set to /C. The labels in the figures represent the positions of the acoustic ray passing through the circular heated area. Each number indicates the distance between the ray and the center of the laser spot on the surface of the medium. The "+" and "-" signs refer to the two different sides in the lateral direction. Figure 3.4a is the long-term modulation, which shows that at normal incidence, the long-term modulation is very small. Figure 3.4b is the short-term modulation, which results from the changing of the SAW signal during one laser repetition period (20 ms) which includes one laser pulse (150 µs) at the beginning. When the ray passes near (<0.01") to or far (>0.10") from the center of the heated spot, the modulation is smaller than when the ray is in an intermediate range (around +0.05" or -0.05") of the spot. The modulations are symmetric to the center of the laser spot. The modulations show that the received SAW always decreases during the laser pulse. This is understandable because the laser induced refraction always tilts the ray from the normal incidence where the received SAW is the biggest. In real measurements, it is difficult to adjust the transducer direction exactly normal to the straight corner, so it is important to study the modulations when the acoustic ray is incident to the scatterer with a small angle. Figure 3.5 shows the results when the ray is incident at a 0.3 angle to the lateral side corresponding to the "+" label. The other conditions are the same as those for Figure 3.4. Figure 3.5a indicates that the long-term modulation is significantly increased compared with that in Figure 3.4 at normal incidence. The long-term modulations are opposite when the ray passes in different lateral sides of the laser spot, which means that when the ray passes the "+" side of the laser spot, the received SAW increases, and it decreases when the ray passes the " " side of the spot. This also shows that when the passing ray is near to or far from the center of the spot, the modulation is smaller than when the ray is in an intermediate range 118

124 (around +0.05" or 0.05") of the spot. The farther the passing ray is from the spot center, the smoother the modulation slope. Figure 3.5b shows the short-term modulations. It is obvious that the short-term modulations are not perfectly symmetric about the center of the laser spot, though the main trends are still opposite on the two lateral sides they increase on the "+" side and decrease on the " " side. It also shows that when the passing ray is in the intermediate position, the modulation is bigger. One thing that needs to be noticed is that when the passing ray is in the +0.05" position of the laser spot, the modulation indicates that the received SAW increases first (< 30 µs), then decreases (30 µs µs), and then increases again (> 150 µs). This can be explained by the strong refraction of the acoustic ray. After the start of the laser irradiation, the ray tilts to normal incidence, so the received SAW increases; during the period 30 µs µs the temperature is so high that the refracted ray passes the normal incidence position (where the received SAW reaches a maximum) and continuously tilts to the other lateral direction, so the SAW decreases. The above figures only show the results for the 10 MHz SAW. Figure 3.6 shows the combined long-term (a) and short-term (b) modulations for 2.25 MHz, 5 MHz and 10 MHz SAWs. The modulations are shown at +0.1" and 0.1" positions. The modulations for the 2.25 MHz and 5 MHz SAWs also show the opposite trends when the ray passes on different lateral sides. Both long-term and short-term modulations indicate that the lower the SAW frequency, the smaller the modulation. Figure 3.7 compares the modulations when the laser beam is enlarged. In this figure, each label indicates the diameter of the laser spot and the passing position of the acoustic ray. For example, the label D 0.4", +0.01" indicates that the diameter of the laser spot is 0.4 inches and the passing position of the ray is 0.01 inches from the center of the spot. As in the previous figures, the signs "+" and " " distinguish the two lateral sides around the center. The modulations in Figure 3.7 show that after enlarging the laser spot, 119

125 both long-term and short-term modulations decrease, most significantly when the passing position of the ray is close (<0.01") to the center of the laser spot. In the above examples, all of the modulations were computed on the basis of assuming the temperature-velocity coefficient to be C -1. Figure 3.8 shows the dependence of the modulation on the temperature-velocity coefficient. The acoustic ray is at normal incidence, and the passing position of the ray is 0.10 inches from the center of a laser spot of 0.2 inches in diameter. The modulations corresponding to the three temperature-velocity coefficients C -1, C -1 and C -1 indicate that the modulations increase significantly with the increase in the temperature-velocity coefficient. 120

126 (a) Modulation [1 db/div] +0.20" +0.15" +0.10" +0.05" +0.01" -0.01" -0.05" -0.10" -0.15" -0.20" Time [s] (b) Modulation [0.2 db/div] Time [ms] +0.20" +0.15" +0.10" +0.05" +0.01" -0.01" -0.05" -0.10" -0.15" -0.20" Figure 3.4 Long-term (a) and short-term (b) modulations of a 10 MHz SAW at normal incidence. The laser beam radius is 0.1 inches, and the temperature-velocity coefficient is C

127 (a) Modulation [1 db/div] +0.20" +0.15" +0.10" +0.05" +0.01" -0.01" -0.05" -0.10" -0.15" -0.20" Time [s] (b) Modulation [0.2 db/div] Time [ms] +0.20" +0.15" +0.10" +0.05" +0.01" -0.01" -0.05" -0.10" -0.15" -0.20" Figure 3.5 Long-term (a) and short-term (b) modulations of a 10 MHz SAW at 0.3 incidence. The laser beam radius is 0.1 inches, and the temperaturevelocity coefficient is C

128 (a) Modulation [1 db/div] 10 MHz, +0.1" 5 MHz, +0.1" 2.25MHz, +0.1" 2.25 MHz, -0.1" 5 MHz, -0.1" 10 MHz, -0.1" Time [s] (b) Modulation [0.2 db/div] 10 MHz, 0.1" 5 MHz, 0.1" 2.25 MHz, 0.1" 2.25 MHz, -0.1" 5 MHz, -0.1" 10 MHz, -0.1" Time [s] Figure 3.6 Long-term (a) and short-term (b) modulations of different frequency SAWs at 0.3 incidence. The laser beam radius is 0.1 inches, and the temperature-velocity coefficient is C

129 (a) Modulation [1 db/div] D-0.2", +0.10" D-0.4", +0.10" D-0.2", +0.01" D-0.4", +0.01" D-0.4", -0.01" D-0.2", -0.01" D-0.4", -0.10" D-0.2", -0.10" Time [s] (b) Modulation [0.2 db/div] D-0.2", +0.10" D-0.4", +0.10" D-0.2", +0.01" D-0.4", +0.01" D-0.4", -0.01" D-0.2", -0.01" D-0.4", -0.10" D-0.2", -0.10" Time [ms] Figure 3.7 Long-term (a) and short-term (b) modulations of 10 MHz SAWs at 0.3 incidence. The laser beam diameter is 0.2 inches or 0.4 inches, and the temperature-velocity coefficient is C

130 (a) Modulation [db] C C C Time [s] 0 (b) Modulation [db] C C C Time [s] Figure 3.8 Long-term (a) and short-term (b) modulations of 10 MHz SAWs at normal incidence for three different temperature-velocity coefficient. The laser beam radius is 0.1 inches. The passing position of the acoustic ray is inches. 125

131 3.5 EXPERIMENTAL RESULTS AND THE CORRELATION WITH NUMERICAL RESULTS Figure 3.9 shows the schematic diagram of the experimental arrangement with pulsed laser thermo-optical modulation. All of the signals measured here are surface acoustic waves reflected from one corner of the Ti-6Al-4V specimen and detected by the pulseecho method. We used a long-pulse Brilliant Nd:YAG laser without Q-switching that produces 150-µs-long pulses of 300-mJ total energy at 1.06-µs infrared wavelength and 50 Hz repetition frequency. The laser beam exhibits a Gaussian profile of 0.2 inch diameter MHz, 5 MHz and 10 MHz SAW transducers of 0.5 inch diameter were used in pulse-echo mode of operation. The modulation of the SAW during the laser irradiation is recorded by the Digital Recorder. In the recordings, the laser is turned on for about 10 seconds from the 5th second to the 15th second, which is similar to the simulation conditions. By extending a 0.5-seconds period around the 10th second in the long-term recording, the short-term modulation can be also observed. It needs to be noticed that the short-term modulations shown here include 25 laser pulses (0.5 seconds at 50 Hz) rather than a single laser pulse as in the previous numerical examples. By lowpass filtering, the long-term modulations are shown in the figures without the highfrequency short-term modulation components. Upward modulation means that the received SAW signal is increasing, and downward modulation means that the SAW signal is decreasing. 126

132 2WNUGF Nd:YAG Laser Trigger &KIKVCN 4GEQTFGT /GCP XCNWG &KIKVCN )CVGF &GVGEVQT RF Signal %QTPGT Transducer Specimen 7NVTCUQPKE Transmitter/Receiver 5#9 Figure 3.9 Schematic diagram of the experimental arrangement for recording the thermo-optical modulation. 127

133 3.5.1 Description of the Figures Figures 3.10 and 3.11 show the modulations of the corner signals measured by a 5 MHz transducer when the laser beam scans the surface of the specimen along the lateral and axial directions. The lines labeled with 0 correspond to the middle position between the transducer and the corner and close to the lateral center. In the lateral scans, the positive labels represent the laser beam irradiating the upper side of the specimen relative to the 0 position; the negative ones represent the laser beam irradiating the lower side. In the axial scans, the positive labels represent the laser beam irradiating the side of the specimen, which is closer to the transducer than the 0 position is; the negative ones represent the laser beam irradiating the other side of the specimen, which is farther from the transducer than the 0 position is. The 12 db refers to the gain of the Ultrasonic Receiver. Figure 3.12 shows the strongest modulation of the corner signals measured by each transducer (10 MHz, 5 MHz and 2.25 MHz). Figure 3.13 shows the strongest modulation of the corner signals with the irradiation of the original (0.2" diameter) and extended (0.4" diameter) laser beam. Figure 3.14 shows the modulations of the corner signals when the 10 MHz transducer is deliberately misaligned. The line labeled with "0 db" represents the modulation of the SAW when the beam is in the "normal" alignment, which means that the wave propagation direction is normal to the corner. Normal alignment in the experiment is achieved by adjusting the transducer to receive the maximum ultrasonic surface wave signal (Gain: 27 db). The other labels represent the modulations of the misaligned SAWs that are directed to the upper side or lower side of the specimen compared with the "normal" alignment. For example "-1 db upper" means that the SAW signal is 1 db smaller (Gain: 28 db) than the signal in the normal alignment while the transducer is aligned to the upper side direction. Here, the laser beam always irradiates 128

134 the same position at 0.2" upper side in the lateral direction, i.e., the passing position of the middle line of the wave beam is at 0.2" on the lower side of the laser spot. 129

135 (a) Modulation [1dB/div] -0.3" -0.2" -0.1" 0 0.1" 0.2" 0.3" Time [s] (b) Modulation [0.2 db/div] laser trig laser off -0.3" -0.2" -0.1" 0 0.1" 0.2" 0.3" Time [100 ms/div] Figure 3.10 Long-term (a) and short-term (b) modulations of the corner signal (5 MHz, 12 db) by lateral scan of the laser beam on the specimen. 130

136 (a) -0.3" Modulation [1dB/div] -0.2" -0.1" 0 0.1" 0.2" 0.3" Time [s] (b) Modulation [0.2 db/div] laser trig laser off -0.3" -0.2" -0.1" 0 0.1" 0.2" 0.3" Time [100 ms/div] Figure 3.11 Long-term (a) and short-term (b) modulations of the corner signal (5 MHz, 12 db) by axial scan of the laser beam on the specimen. 131

137 (a) Modulation [1 db/div] laser trig 10 MHz 5 MHz 2.25 MHz Time [s] (b) Modulation [0.2 db/div] laser trig 10 MHz 5 MHz 2.25 MHz Time [100 ms/div] Figure 3.12 Long-term (a) and short-term (b) modulations of the corner signals measured by different frequency transducers. 132

138 (a) Modulation [1 db/div] laser trig 10 MHz, D-0.2" 10 MHz, D-0.4" 5 MHz, D-0.2" 5 MHz, D-0.4" Time [s] (b) Modulation [0.2 db/div] laser trig 10 MHz, D-0.2" 10 MHz, D-0.4" 5 MHz, D-0.2" 5 MHz, D-0.4" Time [100 ms/div] Figure 3.13 Long-term (a) and short-term (b) modulations of the corner signals by different diameter laser beam irradiation. 133

139 (a) Modulation [1 db/div] -4 db upper -2 db upper -1 db upper 0 db -1 db lower -2 db lower -4 db lower Time [s] (b) -4 db upper Modulation [0.2 db/div] -2 db upper -1 db upper 0 db -1 db lower -2 db lower -4 db lower Time [100 ms/div] Figure 3.14 Long-term (a) and short-term (b) modulations of the corner signals (10 MHz, 27 db at normal alignment) at different alignments of the beam. The passing position of the wave beam middle line is 0.2" on the lower side from the center of the laser spot. 134

140 3.5.2 Comparison of the Experimental and Numerical Results These experimental results themselves are very interesting and present a good argument for the application of laser enhanced ultrasonic materials characterization. They may also provide guidance for designing tests to obtain certain thermoelastic material properties. In addition, and most importantly, they reveal the underlying physical mechanism that is responsible for the observed phenomena. This understanding allows us to improve the accuracy of the current measurements and stimulate new applications. In the following, we present the correlation between the experimental phenomena and the numerical results we obtained earlier. 1. Laser generated local temperature changes affect the ultrasonic surface wave propagation. In Figure 3.10b, the short-term modulation appears to be significant only when the laser beam scans within a certain lateral range (<0.2") of the ultrasonic beam. This can be explained by the limited heat diffusion area between two laser pulses. When the laser beam hits outside of the main part of the acoustic beam, during the short period (~20 ms) between two subsequent pulses the temperature effect does not reach the path of the wave propagation, so the short-term modulation is not significant. This observation correlates well with the theoretical predictions shown in Figures 3.4b and 3.5b. This explanation is further supported by the long-term modulation shown in Figure 3.10a and correlates with the theoretical predictions of Figures 3.4a and 3.5a. When the laser beam scans in the lateral direction far (>0.2") from the middle, the amplitude of the long-term modulation changes slowly, which means the heat slowly propagates into the path of the acoustic beam. The relatively stable modulations at the different axial positions in Figure 3.11 during the axial scan also indicate that the temperature effects are mainly on the propagation path of the ultrasonic surface wave. Figure 3.12 indicates that the amplitudes of long-term and short-term modulations are smaller for lower frequency ultrasonic surface waves. Because an ultrasonic surface wave with lower frequency propagates 135

141 within a deeper layer (~ 1 wavelength), the laser induced temperature, that decreases rapidly with the depth, affects a lower frequency surface wave less than it affects a higher frequency surface wave. This correlates with the theoretical predictions of Figure 3.6. Figure 3.13 indicates that the amplitude of the modulation decreases with increasing laser beam diameter. For a larger laser beam the temperature in the center of the beam (Gaussian profile) is lower than for a smaller one and the temperature effects become smaller. This is also predicated by the theoretical results of Figure When an ultrasonic surface wave propagates through the laser heated volume with a circular boundary, it is refracted. This mechanism explains how the temperature affects ultrasonic surface wave propagation which was shown in the schematic diagram of Figure 3.1. If the incident ray is close to the normal direction when it passes through the circular heated spot, regardless whether it is passing through the upper side or the lower side, the ray will be refracted farther away from the normal direction, so the received signal tends to be smaller than that without laser irradiation. This situation is similar to the theoretical results shown in Figure 3.4. In the experiment, it is difficult to align the ultrasonic beam perfectly normal to the corner. In the case of long-term observation, there is a smaller temperature increase over a larger area. This refracts a larger fraction of the acoustic beam, but the refraction angle itself is smaller so the long-term modulation usually shows inverse signs when the laser irradiates different sides of the lateral direction as shown in Figure 3.10a. However, in the experiment the transducer is usually aligned as closely as possible to the normal direction, which reduces the direct temperature modulation effect. In the case of short-term observation, there is a larger temperature increase over a smaller area. It refracts a smaller fraction of the acoustic beam but the refraction angle is larger, so that the small refracted part is farther away from the normal direction on both lateral sides. Therefore, short-term modulations are frequently observed with a negative sign, i.e., the ultrasonic signal decreases after the laser pulse starts, as it is shown in Figure 3.10b. Figure 3.11 is also evidence for the 136

142 above explanation. Figures 3.10 and 3.11 were obtained using a 5 MHz transducer to detect the ultrasonic surface wave in pulse-echo mode. When the laser scans in the lateral direction, inverse long-term modulations are observed, and the obviously negative shortterm modulations are also detected. When the laser scans in the axial direction, the refraction angles are almost the same at different axial positions, so the modulations are relatively stable. Figure 3.12 shows that the amplitudes of the modulations decrease with decreasing frequency. The main reason for this is the directivity pattern of the transducers. For any transducer with a certain radius, the lower the frequency, the wider the directivity pattern. Therefore, for the same refraction effects the modulation of the received signal will be smaller at lower frequencies. This is also predicted by the theoretical results shown in Figure 3.6. Figure 3.13 shows that the amplitudes of the modulations are smaller for the larger diameter laser beam. One of the reasons is the larger radius of the heated area. For a larger circular area, the acoustic beam passes mainly through the center part of it, where the refraction effect is weak according to the refraction theory. This is well predicted by the theoretical results of Figure 3.7. In order to further verify the refraction mechanism of the laser modulation of SAW, the measurements were also performed by intentionally misaligning the acoustic beam direction. In Figure 3.14, 0.2" upper side indicates that the laser beam impinges at the same position of the upper side (0.2") of the specimen. This implies that the acoustic beam passes mainly through the lower part of the circular heated area. When the acoustic beam is aligned to the upper side, the modulation decreases; when the acoustic beam is aligned to the lower side, the modulation increases. This is also predicted by the above theoretical model as illustrated by Figure 3.5. In Figure 3.14, the inverted short-term modulations are also observed and consistent with the theoretical prediction shown in Figure 3.5b. 137

143 3.6 SUMMARY Laser irradiation can be exploited for enhanced ultrasonic crack detection because of perceivable crack closure under the resulting transient thermal stresses. However, laser irradiation also causes some direct modulation of the ultrasonic signals even in intact specimens because of the slight change in velocity. This lower-velocity area refracts the transmitted acoustic beam thereby affecting the amplitude of the detected signal depending on the transducer's directivity pattern and the conditions of alignment. We developed a simple analytical model that well describes the resulting spatial and temporal modulations. We have shown that the numerical results are qualitatively consistent with the experimental measurements. The presented results suggest different ways to minimize the modulations due to laser induced refraction. The modulations are smaller when the laser spot is larger, the acoustic frequency is lower, the directivity pattern is wider, the acoustic beam is closer to the center of the laser spot, and the alignment is closer to normal incidence. These predictions will be used for further optimization of the method of laser enhanced ultrasonic detection of fatigue cracks. 138

144 CHAPTER IV IMPROVED SHORT-TERM MODULATION FOR FATIGUE CRACK DETECTION IN TI-6AL-4V 4.1 INTRODUCTION From the measurements in Chapter II, we know that there are other physical mechanisms of thermo-optical modulation besides laser-induced crack closure. This brings to light the complexities of using laser enhanced differentiation of fatigue cracks from other artificial scatterers, particularly by short-term modulation. In Chapter III, we confirmed the direct temperature effect as a source of spurious modulation through the dependence of the acoustic velocity on temperature. We also suggested ways for decreasing this effect, such as making the acoustic ray pass through the center of the circular laser spot, extending the laser spot, reshaping the laser spot, widening the directivity pattern of the transducer, etc. In this chapter, two easily realizable methods are used to verify the suggestions presented in Chapter III. One way is to reshape the laser spot so that its edges become straight instead of circular. The other way is to use a lower frequency (2.25 MHz) transducer, so the directivity pattern of the transducer is wider than that of higher frequency (5 MHz, 10 MHz) transducers of similar diameter. The results obtained by using these two methods indicate a great improvement compared to the measurements we did in Chapter II so that fatigue cracks can be easily distinguished from EDM notches by short-term modulation. 139

145 4.2 THERMO-OPTICAL MODULATION BY RESHAPED LASER BEAM Description A circular laser beam irradiating the surface of a specimen generates a circular spot of increased temperature, where the ultrasonic velocity changes from the rest of the specimen due to the temperature dependence of the ultrasonic velocity. This area of slower velocity with its circular boundary will cause wave refraction when an ultrasonic surface wave propagates through it, except those rare cases when the ray passes through the boundary at normal incidence. This refraction mechanism increases the difficulty of distinguishing fatigue cracks from intact notches by the previously proposed method because of the unpredictable addition (or subtraction) of the effect of wave refraction to that of crack closure. By trimming the circular laser beam, a special laser spot with two straight edges can be created. Compared to the original circular spot, this special one will not significantly change the local stress near to the center of the spot in a short time (~ 20 ms). When the ultrasonic surface wave goes through the straight edges at normal incidence, there will be no wave refraction. First, a comparison of the short-term and long-term modulations between the original circular and trimmed laser beam irradiation will be given. Then, the measured modulations will be presented for trimmed laser beam irradiation in the case of lateral and axial scanning around a couple of EDM notches with or without fatigue cracks. The results indicate that when the trimmed laser beam hits close (~0.5 inch) to the notches, the short-term modulation from the notches with cracks are obviously stronger than from the ones without cracks. Therefore, it is convenient to distinguish fatigued notches from intact ones only by measuring the short-term modulation using trimmed laser beam irradiation of the suspicious part. 140

146 4.2.2 Results and Discussion Figures 4.1 and 4.2 show a schematic diagram of the experiment and the resulting laser beam, respectively. The lateral and axial directions are normal and parallel to the transducer orientation, respectively. In the experiment, the characteristic diameter of the Gaussian laser beam is 0.2 inch ± 0.02 inch. The width of the trimmed laser beam is 0.1 inch ± 0.01 inch. The transducer used here is a 5 MHz surface wave transducer working in pulse-echo mode. The distance between the notch and the transducer is kept approximately the same (~ 1.2 inches) during all the measurements. A pair of blades is used to trim the laser beam so that two straight edges can be created. During the measurement, the transducer direction is adjusted to be normal to the straight edge as close as possible. The frequency of the laser trigger is 50 Hz, and the repetition frequency of the ultrasonic pulser is 500 Hz. Figures 4.3 and 4.4 show the long-term and short-term modulations of the signal from a fatigued notch, respectively, when the laser beam scans the surface area along the lateral direction. In this case, the irradiated surface area is not around the notch, but between the transducer and the notch, and the label 0 represents the fact that the laser irradiation area is in the middle of the effective beam (the part that will be reflected by the notch) and 0.6 inches before the notch, so it can be assumed that the modulations in the figures are mainly due to the laser induced wave refraction. Figures 4.3a and b are the long-term modulations corresponding to the irradiation of circular and trimmed beams, respectively. Figures 4.4a and b are the corresponding short-term modulations. Each short-term modulation shown in the figures is the average of 10 subsequent modulations. A comparison of the four figures shows that both long-term and short-term modulations are reduced to about half after trimming the laser beam. The modulation is significantly reduced especially when the laser beam irradiates near to the middle (<0.05 inches) in the lateral direction. It is also noticed that when the laser beam irradiates in the middle 141

147 (position 0 here) of the effective part of the acoustic beam, the modulations are smaller regardless of whether the circular or trimmed beam was used. This can be explained by the fact that the effective beam goes through the boundary of the laser spot normally. This phenomenon can be used to check whether a scatterer is in the line connecting the laser spot and the transducer. It is useful to locate the position of a scatterer when the scatterer signal is hidden by coherent noise, which might provide an advantage in distinguishing fatigue cracks from grain noise. Recognizing that the spurious wave refraction effect can be reduced by more than two times using trimmed laser beam irradiation near the middle part of the effective wave beam, a trimmed beam is used to irradiate the surface areas around the notches in the following measurement. Figures 4.5 and 4.6 show the modulations when the trimmed laser beam scans around two notches with and without fatigue crack. Figures 4.5 and 4.6 are the long-term modulations in the lateral and axial directions, respectively. The label 0 in each figure represents the approximate position of the notch. A comparison of the figures reveals that there is no significant difference in the long-term modulations between fatigued and intact notches. However, a comparison of the corresponding shortterm modulations shown in Figures 4.7 and 4.8 clearly indicates that the amplitude of the short-term modulation of the fatigued notch is bigger than that of the intact one when the trimmed laser beam irradiates the notches. In order to verify that this difference occurs consistently and is not just an occasional phenomenon, the same measurement is repeated on several other notches with and without fatigue cracks. The combined results are shown in Figure 4.9. The same conclusion is obtained, i.e., the trimmed laser beam can generate a significantly larger short-term modulation in notches with fatigue cracks, which means that crack closure plays a dominant role in the short-term modulation. Due to the thermo-elastic deformation, the slight change of the notch shape itself could also affect the ultrasonic 142

148 surface wave reflection a little, which might be the reason for the slight modulation occurring in the signal from the intact notches when the laser irradiates them. In the experiment, one aspect that needs to be paid close attention to is the cleanliness of the irradiated surface because the ultrasonic surface wave is very sensitive to the load on the surface. Any dust or liquid on the surface can be affected by the laser heating and the effect may change the received ultrasonic signal and cause some modulations. Experimental observations showed that filling the fatigued notches with couplant oil increases the long-term modulation and decreases the short-term modulation. Intentionally filling a notch with liquid may create different behaviors between fatigued and intact notches during laser irradiation, which may be used to verify the presence of small cracks. 143

149 Laser Beam lateral direction Transducer axial direction Blades Corner Notch Ultrasonic Surface Wave Figure 4.1 Schematic of the experimental set-up for reshaping the laser beam. 144

150 Input wave Non-refracted wave Diameter 0.2" Notch Refracted wave Circular beam Non-refracted wave Input wave Width 0.1" Notch Trimmed beam Figure 4.2 Schematic of decreasing the direct temperature modulation by reshaping the laser beam. 145

151 (a) Modulation [ 1dB/div] -0.15" -0.10" -0.05" " 0.10" 0.15" Time [s] (b) Modulation [ 1dB/div] -0.15" -0.10" -0.05" " 0.10" 0.15" Time [s] Figure 4.3 Long-term modulation of the signal (5 MHz, 44 db) reflected from c#4. (a) Circular laser beam with 0.2" diameter, (b) Trimmed laser beam with 0.1" width scans the position at 0.6" before the crack in the lateral direction. 146

152 (a) Modulation [0.2 db/div] laser trigger radiation off -0.15" -0.10" -0.05" " 0.10" 0.15" Time [100 ms/div] (b) Modulation [0.2 db/div] laser trigger radiation off -0.15" -0.10" -0.05" " 0.10" 0.15" Time [100 ms/div] Figure 4.4 Short-term modulation of the signal (5 MHz, 44 db) reflected from c#4. (a) Circular laser beam with 0.2" diameter, (b) trimmed laser beam with 0.1" width scans the position at 0.6" before the crack in the lateral direction. 147

153 (a) Modulation [ 1dB/div] -0.15" -0.10" -0.05" " 0.10" 0.15" Time [s] (b) Modulation [ 1dB/div] -0.15" -0.10" -0.05" " 0.10" 0.15" Time [s] Figure 4.5 Long-term modulation of the signal (5 MHz, 42 db) reflected from n#3 (a) and from c#5 (b). Trimmed laser beam with 0.1" width scans around the scatterers in the lateral direction. 148

154 (a) Modulation [ 1dB/div] -0.15" -0.10" -0.05" " 0.10" 0.15" Time [s] (b) Modulation [ 1dB/div] -0.15" -0.10" -0.05" " 0.10" 0.15" Time [s] Figure 4.6 Long-term modulation of the signal (5 MHz, 42 db) reflected from n#3 (a) and from c#5 (b). Trimmed laser beam with 0.1" width scans around the scatterers in the axial direction. 149

155 (a) Modulation [0.2 db/div] laser trigger radiation off -0.15" -0.10" -0.05" " 0.10" 0.15" Time [100 ms/div] (b) Modulation [0.2 db/div] laser trigger radiation off -0.15" -0.10" -0.05" " 0.10" 0.15" Time [100 ms/div] Figure 4.7 Short-term modulation of the signal (5 MHz, 42 db) reflected from n#3 (a) and from c#5 (b). Trimmed laser beam with 0.1" width scans around the scatterers in the lateral direction. 150

156 (a) Modulation [0.2 db/div] laser trigger radiation off -0.15" -0.10" -0.05" " 0.10" 0.15" Time [100 ms/div] (b) Modulation [0.2 db/div] laser trigger radiation off -0.15" -0.10" -0.05" " 0.10" 0.15" Time [100 ms/div] Figure 4.8 Short-term modulation of the signal (5 MHz, 42 db) reflected from n#3 (a) and from c#5 (b). Trimmed laser beam with 0.1" width scans around the scatterers in the axial direction. 151

157 (a) Modulation [1 db/div] c4 c5 n1 n3 n5 n Time [s] (b) Modulation [0.2 db/div] laser trigger c4 c5 n1 n3 n5 n7 Time [100 ms/div] Figure 4.9 Long-term (a) and short-term (b) modulations of different notches with/without fatigue cracks by reshaped laser beam irradiation. 152

158 4.3 THERMO-OPTICAL MODULATION AT LOW FREQUENCIES Description From the theoretical and experimental results presented earlier in Chapter 3, we know that the effect of direct temperature modulation is greater on a higher frequency surface wave than on a low frequency surface wave. By using a higher frequency transducer to generate and receive an ultrasonic surface wave, a stronger modulation can be observed even if the specimen has no fatigue cracks. This increased direct modulation can be attributed to two effects. One is the narrower directivity pattern of a higher frequency transducer, and the other is the thinner penetration depth of higher frequency surface waves. Strong direct modulation can hide the modulation caused by crack closure, so it makes it difficult to distinguish fatigue cracks from other artifacts using higher frequency transducers, particularly when using short-term modulation. The previous results also predicted that the direct modulation of lower frequency signals is weaker. It has been shown earlier in the literature that reducing the inspection frequency can actually increase the crack closure induced modulation. [35] How low of a frequency can be used to significantly decrease the spurious direct modulation without adversely affecting the sought crack closure induced modulation? In the previous measurements, we used laser irradiation to modulate the signals generated by the 5 MHz and 10 MHz surface wave transducers, and found strong direct temperature modulations. In the following measurements, lower frequency 2.25 MHz transducers are used to generate and detect ultrasonic surface waves. It will be shown that reducing the frequency can significantly improve the detectability of fatigue cracks by the thermo-optical modulation technique. 153

159 4.3.2 Results and Discussion Figure 4.10 shows the RF signals measured by a 2.25 MHz ultrasonic surface wave transducer working in pulse-echo mode. The labels with c indicate signals scattered by fatigue cracks, and the labels with n refer to the signals scattered by unfatigued EDM notches. Comparing these signals with the previous ones (Figure 2.12) measured by the high frequency transducer, we found the S/N ratios are much smaller here due to the lower frequency detection. Like before at higher frequencies, we can not distinguish fatigue cracks from the unfatigued EDM notches based on the raw RF signals. Using the laser to irradiate the area around the scatterers (cracks and EDM notches) during surface wave monitoring, modulations are observed in the following figures. Figure 4.11 shows the short-term modulations when the laser spot scans the area around crack #8 along the axial (a) and lateral (b) directions. This figure clearly indicates that when the laser spot is close to the crack, the short-term modulation is fairly strong, while when the spot is far away from the crack, the modulation disappears. We also observed the long-term modulations shown in Figure 4.12 and found that the modulation is bigger when the laser spot is closer to the crack. Figures 4.13 and 4.14 indicate the real reason why we are using the lower frequency transducer; they show the disappearance of the modulations when the laser spot irradiates the area around the unfatigued EDM notch #7. Figure 4.13 shows the short-term modulation when the laser spot scans the EDM notch along the axial (a) and lateral (b) directions, and Figure 4.14 is the corresponding longterm modulation. Comparing Figures 4.11 and 4.13 on one side and Figures 4.11 and 4.13 on the other side, fatigue crack #8 can be clearly distinguished from unfatigued EDM notch #7. The same measurements were carried out on specimens crack #2, crack #6, EDM notch #4, and EDM notch #8. The short-term and long-term modulations are shown in Figure 4.15a and b, respectively. It should be particularly emphasized that by 154

160 using short-term modulation the fatigue cracks can be easily distinguished from the unfatigued EDM notches, which can not be done by using higher frequency transducers. 4.4 SUMMARY By reshaping the laser spot and lowering the transducer frequency, fatigue cracks can be distinguished from other artifacts even using short-term modulation, which was not feasible in the previous measurements using a circular Gaussian beam to modulate a highfrequency ultrasonic surface wave. The cause of this improvement was shown to be the decrease of the direct temperature modulation by weakening the refraction of the wave when it passes through the laser spot. Based on the presented model predictions and experimental results, we can conclude that, under the condition of detectable individual RF signals (flaw versus artifact problem), using lower frequency transducers and straighter edges for the laser spot, the identification of fatigue cracks by short-term modulation becomes much more effective. 155

161 RF Signal [500 mv/div] c2 (32dB) c6 (22 db) c8 (26 db) n4 (32 db) n7 (26 db) n8 (28 db) Time [5 µs/div] Figure 4.10 RF signals measured by the 2.25 MHz transducer on different specimens with fatigue cracks or EDM notches. 156

162 (a) laser trigger Modulation [0.2 db/div] radiation off -0.15" -0.10" -0.05" " 0.10" 0.15" Time [100 ms/div] (b) Modulation [0.2 db/div] laser trigger radiation off -0.15" -0.10" -0.05" " 0.10" 0.15" Time [100 ms/div] Figure 4.11 Short-term modulation of the signal (2.25 MHz, 26 db) scattered from crack #8. Circular laser spot with 0.2" diameter scans around the crack in the axial (a) and lateral (b) directions 157

163 (a) -0.15" Modulation [1 db/div] -0.10" -0.05" " 0.10" Time [s] 0.15" (b) -0.15" Modulation [1 db/div] -0.10" -0.05" " 0.10" 0.15" Time [s] Figure 4.12 Long-term modulation of the signal (2.25 MHz, 26 db) scattered from crack #8. Circular laser spot with 0.2" diameter scans around the notch in the axial (a) and lateral (b) directions. 158

164 (a) laser trigger Modulation [0.2 db/div] radiation off -0.15" -0.10" -0.05" " 0.10" 0.15" Time [100 ms/div] (b) laser trigger Modulation [0.2 db/div] radiation off -0.15" -0.10" -0.05" " 0.10" 0.15" Time [100 ms/div] Figure 4.13 Short-term modulation of the signal (2.25 MHz, 26 db) scattered from notch #7. Circular laser spot with 0.2" diameter scans around the notch in the axial (a) and lateral (b) directions. 159

165 (a) -0.15" Modulation [1 db/div] -0.10" -0.05" " 0.10" Time [s] 0.15" (b) -0.15" Modulation [1 db/div] -0.10" -0.05" " 0.10" 0.15" Time [s] Figure 4.14 Long-term modulation of the signal (2.25 MHz, 26 db) scattered from notch #7. Circular laser spot with 0.2" diameter scans around the notch in the axial (a) and lateral (b) directions. 160

166 (a) Modulation [0.2 db/div] laser trigger c2 c6 c8 n4 n7 n8 Time [100 ms/div] (b) c2 Modulation [1 db/div] c6 c8 n4 n Time [s] n8 Figure 4.15 Short-term (a) and long-term (b) modulations (2.25 MHz) measured from six specimens (three with fatigue cracks and three with EDM notches). 161

167 CHAPTER V ENHANCED LASER GENERATION OF SURFACE ACOUSTIC WAVES BY DISCONTINUITIES 5.1 ABSTRACT OF THE CHAPTER Laser generation of Rayleigh waves or surface acoustic waves (SAW) can be enhanced by discontinuities that include optical, thermal and elastic discontinuities. Most real material discontinuities such as cracks, notches and corners in a medium cause all of these three types of discontinuities. Optical discontinuities include geometrical discontinuities of the laser beam on the surface of the medium and discontinuities of the light absorption ratio in the medium. Thermal discontinuities refer to discontinuities of the thermal properties of the medium, such as the thermal expansion coefficient, specific heat capacity and heat conductivity. Elastic discontinuities include stiffness and density discontinuities. In laser generation of Rayleigh waves, the thermal diffusion distance during an acoustic period is typically much less than the depth of the crack. Elastic discontinuities should be included in the analysis, which would of course greatly complicate the calculations. In order to derive at least qualitatively valid relationships, we have developed a simple model which neglects the elastic discontinuities so that only the optical and thermal types are considered. [79] In the simplest realization of this approximation, the real discontinuities are analytically simulated by using only the discontinuity of the light absorption ratio. The results to be presented illustrate the dependence of laser generated SAW (amplitude, directivity and spectrum) on the discontinuity size. The experimental results are selfconsistent and in fairly good agreement with the theoretical data. Both analytical and experimental results indicate that the enhancement of laser generation of SAW by material discontinuities is very promising for the detection of tiny cracks that are difficult to identify by conventional ultrasonic or laser-ultrasonic nondestructive evaluation (NDE) 162

168 methods. The results also show the possibility for sizing of small discontinuities by laser generation of SAWs. 5.2 INTRODUCTION Laser generation of ultrasonic SAWs have been studied in detail since the 1980's. [65-72] Most of these studies were concentrated on the optimization of Rayleigh wave generation by laser excitation. Laser generation of ultrasonic waves is determined by laser parameters (spatial and temporal profile of the intensity distribution) and material properties (thermal conductivity, light absorption ratio, thermal expansion coefficient, specific heat capacity, elastic parameters). In previous studies, the laser-generated SAWs were often optimized by controlling the laser parameters (e.g., beam geometry). It is well known that laser generation of SAWs can be enhanced by truncating the laser beam over an intact area of the medium. The same effect can be achieved by using an intact laser beam to irradiate the specimen containing surface or near-surface discontinuities. Based on this mechanism, a new method Laser Ultrasonic Detection of Surface-Breaking and Sub-Surface Cracks has been proposed and verified by experiments recently by Kromine et al. [73,74] Due to the existence of small elastic discontinuities in the otherwise homogeneous material, analytically solving the problem of laser generation of SAW in the presence of an elastic discontinuity becomes very difficult. However, there are obvious similarities in the laser generation of SAW due to general material discontinuities to the simpler case when there are only thermal and optical discontinuities. By omitting the elastic discontinuity and modifying the light absorption ratio in a volume of the medium to approximate material discontinuities such as notches and corners, some aspects of enhanced laser generation of SAWs by more general material discontinuities can be studied. For example, the results can be used to investigate the dependence of the laser 163

169 generation of SAW on the size of small discontinuities. We are going to present simple theoretical predictions and correlate them with experimental data. The analytical and experimental results obtained in this section are helpful for better understanding and optimizing surface and near-surface crack detection techniques based on laser generation of SAWs. This method will find applications mainly in discriminating crack signals from grain noise while the previously studied thermo-optical modulation method was aimed at improving the probability of detection of fatigue cracks against artifact signals. 5.3 SIMILARITY OF THE ELASTIC AND OPTICAL DISCONTINUITIES IN THE LASER GENERATION OF SAW Experimental Set-up In order to compare the similarities of laser generation of SAWs by two types of discontinuities, namely optical discontinuities and material discontinuities, two simple measurements corresponding to these two types of discontinuities were carried out. A schematic diagram of these two situations are shown in Figure 5.1. In the experiment, a Q-switched Nd-YAG laser (pulse duration of 6.6 ns, energy of 200 mj) with Gaussian beam profile was used as a source. The specimens used here were made of Ti-6Al-4V and Al Because the intensity of the original laser beam (beam radius of 2.5 mm) is so strong that it can damage the material, a concave lens was used to extend the laser beam to a 12.5-mm beam radius. It is also very important that the profile of the expanded Gaussian beam is smoother than it would be without expansion let alone that of other laser sources often used in laser ultrasonics, such as a line source. Therefore, direct generation of SAW by the expanded laser beam is very small when it irradiates intact areas (homogeneous without discontinuities). Actually, by expanding the laser beam, this direct laser generation of SAW is reduced to the noise level so that the laser generated 164

170 SAW detected in the experiments is mainly due to the presence of discontinuities. The substantial reduction of directly generated SAW caused by the expansion of the laser beam will be also analyzed in the following theoretical section. In all of the following experiments, the laser beam is normally incident to the surface of the specimen. In the experiment depicted in Figure 5.1a, the laser beam is scanned over the area around the corner in the axial direction by moving the specimen so that the laser beam is simply truncated by the corner. In the experiment depicted in Figure 5.1b, a blade is used to cut the laser beam. This blade is located above an intact area of the specimen and it can be moved together with the specimen. By moving the blade and the specimen together in the axial direction, a different degree of truncation can be achieved, which is similar to the beam cut by the corner. The truncated laser beam is also shown magnified in Figure 5.1a, where the d represents the distance between the center of the original Gaussian beam and the truncation line. The only difference between these two situations is the boundary condition along the truncation line. It is elastically free (with air loading) in Figure 5.1a and elastically continuous (with the same material) in Figure 5.1b. The laser generated SAWs were detected by Panametrics 10 MHz, 5 MHz, 2.25 MHz and 1 MHz (central frequency) surface wave wedge transducers, and the detected signal was amplified by a Panametrics 5072PR Receiver. The trends of changing signal magnitudes and power spectra of the SAWs will be compared to establish similarity. 165

171 (a) d (b) Laser Beam Transducer axial direction Blade Corner Laser-SAW Figure 5.1 Schematic of the measurement for comparing laser generation of SAWs by a laser beam irradiating a corner (a) and a trimmed laser beam irradiating an intact area (b). 166

172 5.3.2 Results and Discussion Figure 5.2 shows the signals generated (a) by a laser beam irradiating the straight corner of a Ti-6Al-4V specimen and (b) by the blade-truncated beam irradiating an intact part of the same specimen. The signals in these figures were measured by the 5 MHz transducer and the gain of the receiver was 30 db. The labels in the figures represent the positions of the truncating line from 0.0" for negligible shadowing to 1.2" for total shadowing. In other words, the maximum truncation occurs around 0.6" (d = 0). The changing trends appear to be very similar though the corner signal is perceivably stronger (the scale in Figure 5.2b is finer). The signal increases with the truncating line moving to the center of the spot. By the same procedure, the signals (not shown here) were also measured with 1 MHz, 2.25 MHz and 10 MHz transducers on the Ti-6Al-4V specimen, and with 1 MHz and 5 MHz transducers on the specimen Al-2024 and yielded similar results. Figures 5.3a and b are the power spectra of the signals corresponding to Figures 5.2a and b. The comparison shows that the spectra of the signals generated by the corner truncated beam and the blade truncated beam are similar. Of course, the finite bandwidth of the detecting transducer makes it difficult to distinguish small differences of the spectra, but it would still show big differences if they had any. Additional spectra (not shown here) of the signals measured by other transducers and on the Al-2024 specimen also show great similarity. Figures 5.4 and 5.5 further demonstrates the changing trends in the amplitude of the laser-generated SAW versus the truncating position. These results were measured by 1 MHz, 2.25 MHz, 5 MHz and 10 MHz transducers. The specimen used here is made of Ti-6Al-4V. The truncating positions refer to the positions of the truncating line, which are relative values. With the value increasing, the truncated part increases. The 0-inch position means that the beam is cutting off but a small part. Around the 0.6-inch position, the beam is truncating off half, i.e., the truncating line crosses the center of the beam. At 167

173 the 1.2-inch position, a large part of the beam is cut off. In each figure, there are two groups of data, one (the left side scale) is measured when the laser beam irradiates the corner and the beam is truncated by the corner itself while the other (the right side scale) is measured when the blade-truncated beam irradiates an intact part of the specimen. These figures indicate that the amplitude of the laser generated SAW due to the cornertruncated irradiation is about 3 times stronger than that due to the blade-truncated irradiation, but the changing trends are similar. The truncation profiles are also very similar to the profile of the laser beam. Figures 5.6a and b are the results measured in the Al-2024 specimen by 1 MHz and 5 MHz transducers. The changing trends due to the two truncated methods are also similar. Here we need to notice the differences of the SAW amplitudes in the Al-2024 specimen compared with those measured in the Ti-6Al-4V specimen. First, the amplitudes measured in Al-2024 are smaller than the corresponding ones measured in Ti- 6Al-4V, which may be explained by the smaller light absorption rate (~5%) in Al-2024 versus the much larger value (~40%) in Ti-6Al-4V. Second, the percentage of the highfrequency content (5 MHz versus 1 MHz) of SAWs generated in Al-2024 is higher than that in Ti-6Al-4V, which is mainly due to the higher grain-scattering induced attenuation in titanium. Third, for the signals measured by transducers of different nominal frequencies, the SAW amplitude ratios between the corner-truncated irradiation and the blade-truncated irradiation are slightly different. For Al-2024 at 1 MHz, the ratio is about 3 times; for 5 MHz, it is about 4 times. For Ti-6Al-4V, the ratios are almost the same (3 times) for all different frequencies at 1, 2.25, 5 and 10 MHz. This relatively small difference of magnitude results from the different boundary conditions in the two situations as mentioned above. In conclusion, the simpler analysis of laser generation of SAW by truncated laser irradiation of a homogeneous medium, which has been well investigated, can approximately simulate enhanced laser generation of SAW by the intact beam irradiating a corner in the same material. 168

174 (a) corner truncation Laser Generated SAW [2 V/div] 1.2" 1.1" 1.0" 0.9" 0.8" 0.7" 0.6" 0.5" 0.4" 0.3" 0.2" 0.1" 0.0" Delay [2 µs/div] (b) blade truncation Laser Generated SAW [1 V/div] 1.2" 1.1" 1.0" 0.9" 0.8" 0.7" 0.6" 0.5" 0.4" 0.3" 0.2" 0.1" 0.0" Delay [2 µs/div] Figure 5.2 Laser generated SAW by a beam irradiating the specimen corner (a) and a blade-truncated beam irradiating an intact part on the specimen (b). The specimen is made of Ti-6Al-4V. The signal is measured by a 5 MHz transducer at 30 db gain. 169

175 (a) corner truncation Power Spectrum [20 db/div] 1.2" 1.1" 1.0" 0.9" 0.8" 0.7" 0.6" 0.5" 0.4" 0.3" 0.2" 0.1" 0.0" Frequency [MHz] (b) blade truncation Power Spectrum [20 db/div] 1.2" 1.1" 1.0" 0.9" 0.8" 0.7" 0.6" 0.5" 0.4" 0.3" 0.2" 0.1" 0.0" Frequency [MHz] Figure 5.3 Spectrum of the laser generated SAW by a beam irradiating the specimen's corner (a) and a blade-truncated beam irradiating an intact part on the specimen (b). The specimen is made of Ti-6Al-4V. The signal is measured by a 5 MHz transducer at 30 db gain. 170

176 Amplitude [mv] (corner truncation) corner blade (a) 1 MHz, Ti-6Al-4V Truncating Position [inch] Amplitude [mv] (blade truncation) (b) 2.25 MHz, Ti-6Al-4V Amplitude [mv] ( corner truncation) corner blade Amplitude [mv] (blade truncation) Truncating Position [inch] Figure 5.4 Amplitude of the laser generated SAW versus the truncating position. It is measured by 1 MHz (a) and 2.25 MHz (b) transducers at 30 db gain. The specimen is made of Ti-6Al-4V. 171

177 (a) 5 MHz, Ti-6Al-4V Amplitude [mv] (corner truncation) corner blade Amplitude [mv] (blade truncation) Truncating position [inch] (b) 10 MHz, Ti-6Al-4V Amplitude [mv] (corner truncation) corner blade Amplitude [mv] (blade truncation) Truncating position [inch] Figure 5.5 Amplitude of the laser generated SAW versus the truncating position. It is measured by 5 MHz (a) and 10 MHz (b) transducers at 30 db gain. The specimen is made of Ti-6Al-4V. 172

178 (a) 1 MHz, Al-2024 Amplitude [mv] (corner truncation) corner blade Amplitude [mv] (blade truncation) Truncating position [inch] (b) 5 MHz, Al-2024 Amplitude [mv] (corner truncation) corner blade Amplitude [mv] (blade truncation) Truncating position [inch] Figure 5.6 Amplitude of the laser generated SAW versus the truncating position. It is measured by 1 MHz (a) and 5 MHz (b) transducers respectively, and the gain is 30 db. The specimen is made of Al

179 Theoretically, the above described experimental conditions can be modeled as follows. The straight corner can be considered as an infinite (infinite length, width and depth) notch. The heat distribution in the specimen, that is generated by the cornertruncated laser beam, is equivalent to that generated by the original laser beam irradiating the surface, if we assume that there is no light absorption and thermal conduction in the missing part of the specimen. In other words, under the cut off part of the laser spot the light absorption ratio and the thermal diffusivity are both zero. In the case of flaw detection shown in Figure 5.7a, the crack (or notch) is usually smaller than the laser beam. During the period of an acoustic oscillation, the heat diffuses over a much smaller distance χ / πf (χ is the thermal diffusivity and f is the frequency of the surface acoustic wave) than the width of the crack (or notch), therefore the discontinuity can be approximated as an optical notch in which the light absorption ratio is zero. The only difference is that the medium filling this simulated optical notch is the original material itself instead of nothing (air) as in a real notch where the notch boundary is free. For the experimental situation considered here, the diffusion distance is about 1 µm in Ti-6Al- 4V, which is small enough to simulate small material cracks as optical discontinuities. The physical basis for this approximation is that the main reason for the enhanced laser generation of SAW is the thermal strain discontinuity at the edges of the notch. In order to maintain this discontinuity, several different assumptions can be made for the medium in the notch the thermal expansion coefficient is zero, the specific heat capacity is infinity and/or the light absorption ratio is zero. In this section only notches of rectangular shape are considered as it is shown in Figures 5.7b and c, where l, w and h are the length, width and depth of the notch, respectively. The notch is simulated by assuming a small block of volume (l w h) with a light absorption ratio of zero. 174

180 Laser Beam lateral direction Transducer axial direction (a) Notch Laser-SAW w w d l (b) (c) Figure 5.7 Schematics of the measurement for the laser generation of SAW by a laser beam irradiating the notch (a) and the analytical simulation by a rectangular notch with top view (b) and side view (c). 175

181 5.4 SIMPLIFIED MODEL FOR DISCONTINUITY-ENHANCED LASER GENERATION OF SAW Consider a homogeneous, isotropic and elastic half-space, whose boundary is chosen to be the xy plane, with the z-axis directed into the medium (Figure 5.8). r is the spatial coordinate vector and k is the wave vector. The spectral component L(ω, k) of the laser generated SAW can be represented as: [67] L s k k k i t = ωβ 1 t 4 ( 2 ) 3 ( 2k kt ) 4k ( k kl ) / ( k kt ) / T ( ω, k,( k2 k2 ) 12 / ) l , (5.1) where k is the absolute value of the wave vector k and β is the thermal expansion coefficient of the medium. For Rayleigh waves, k is the Rayleigh wave number. k l and k t are the longitudinal and transverse wave numbers, respectively. k = kr =ω cr, k l =ω c, and k =ω c, where c R, c l and c t are the Rayleigh, longitudinal and transverse l t t wave velocities, respectively, and s= c c. T ( ω, k, p) is obtained from the temperature t l distribution T(, tr, z) by Fourier transform in t and r ={x,y} and Laplace transform in z. The temperature field is determined by the light intensity distribution over the cross section of the laser beam and by the depth dependence of the light absorption ratio. The laser beam is assumed to be normally incident on the surface of the solid and its intensity is written as I = I 0 F(, t r ), (5.2) where F(t, r) is the temporal and spatial distribution of the laser beam. The temperature increment is then described by the following equation: [67] 176

182 (a) y θ k r x z (b) y θ k r x z Figure 5.8 Geometry of the problem and coordinate system used (a) and the introduced notch model (b). 177

183 T t χ T 0 gic ρ Ft df = (, r ), (5.3) dz where g is the light absorption ratio, i.e., the fraction of the light entering the medium, ρ is the medium density, χ is the thermal diffusivity, and c is the specific heat capacity of the medium. The function Hz f () z = exp α () z dz 0 (5.4) describes the depth dependence of the light intensity, and α(z) is the distribution of the light absorption coefficient. In order to introduce a notch in the above model, the center of the notch surface is chosen at the origin (0,0,0) of the coordinate system, and the width, length and depth of the notch are in the x, y and z directions, respectively. Then, equation (5.3) can rewritten as: T t χ T gic ρ F t x y df dz gic ρ F t x y df = 1(,, ) 2 (,, ), (5.5) dz where F(, txy, ) = Ftxy (,, ) 1 Hx ( + w/ 2) Hx ( w/ 2) Hy ( + l/ 2) Hy ( l/ 2) 1 F(, txy, ) = Ftxy (,, ) Hx ( + w/ 2) Hx ( w/ 2) Hy ( + l/ 2) Hy ( l/ 2) (5.6) where H is the unit step function. Through modifying the distribution of the light absorption coefficient α(z) in equation (5.4), the optical notch can be effectively simulated in the second term of the right side of equation (5.5). In the original material, α 178

184 (z) is assumed to be the constant α which is independent of z. In the notch part, it is assumed: α ( z) = 0, when z h, and α (z) = α, when z > h. So αz f () z = e, f () z = e α( z h) 1 2 when z > h and f2 ()= z 0 when z h. (5.7) The boundary condition of the medium in the absence of thermal flux is T = 0 (5.8) z z = 0 and considering T(z + ) 0, the solution of equations (5.5) and (5.8) can be sought as follows. For frequencies lower than 3 GHz, the thermal wavelength remains smaller 2 than the Rayleigh wavelength, i.e., ω < ω = / χ (χ is thermal diffusivity), the T c R expression for T ( ω, k, p) can be simplified as: ~ (,, ) (, ) ~ T ω i p 0 k = ( ) (, ) ( ) gic F ω k ω ρ f p + F ω k f p , (5.9) where f ( p ) = e 1 0 f ( p ) = e 2 H H 0 pz pz df1 dz dz df2 dz dz (5.10) and ~ F (, ) ei( t ) 1 ω k = H H H ω kr F1 ( t, r ) dt dr. (5.11) ~ F (, ) ei( t ) 2 ω k = H H H ω kr F2 ( t, r ) dt dr 179

185 If the laser and material parameters are known, numerical results can be obtained from the above equations for the laser generated SAW. If the laser source is assumed to be a stationary (or slowly moving) beam, the spatial and temporal distribution function can be separated as Ft (, r) = FtF () () r. For a beam of Gaussian distribution: Fr Ie r 2 ( / () r 2 c ) =, (5.12) 0 where r c is the characteristic beam radius that represents the circular boundary within the Gaussian source that contains 63% of the total power incident to the surface. A typical temporal laser pulse profile can be expressed as: [53] * t * * Ft ( ) = exp[ bt ( tr )] γ γ t*, (5.13) r a where t * a = χt / rc, tr * = ( ) bγ 4 2 γ 1, a, b and γ are temporal shape factors that affect the negative skewness of the temporal profile, the pulse activation time and the positive skewness of the temporal profile, respectively. 180

186 5.5 SIMULATED RESULTS AND DISCUSSIONS The temporal profile of the laser pulse used in the experiment is shown in Figure 5.9. Values of a, b and γ are fitted to the actual pulse as 5, and 3, respectively. The spatial distribution of the laser beam on the surface of the medium is Gaussian. The strategy for simulating elastic notches was indicated in Figures 5.7b and c, where it was assumed that within a rectangular block (l w h) the light absorption ratio is zero. The energy in each pulse of 6.6 ns duration is 380 mj. The material properties of Ti-6Al-4V were previously given in Table 3.1 on page 117. The light absorption ratio is 40% for the near-ir wavelength (1064 nm) used in the experiments. On the basis of these known parameters, the results of laser generated SAW are evaluated in the following cases. During the measurements, there are usually two types of laser generated SAWs. One is generated directly by the laser irradiating the intact part of the material and the other is by the laser irradiating the discontinuity. If these two types of signals are comparable and mixed together, it will be difficult to distinguish them and the direct signal can hide the presence of the discontinuity, so it is necessary to increase the difference between these two signals. First, let us compare the direct generation of SAWs for Gaussian laser beams of different radii but the same total energy per pulse and temporal profile. Figure 5.10 shows the amplitude of the laser generated SAW at three different frequencies (2.25 MHz, 5 MHz and 10 MHz) versus the characteristic radius of the Gaussian beam when the laser beam irradiates the intact part of the medium. The result indicates that with the beam radius increasing, the laser generated SAW decreases rapidly, and the higher the frequency, the faster the decrease. So, by extending the laser beam on the surface of the medium, the direct laser generation of SAW can be greatly decreased. Considering this effect and also trying to avoid damaging the specimen, in the following analysis and experiment, the radius of the laser beam is extended to 12.5 mm. 181

187 Figure 5.2 already showed this effect, i.e., no direct laser generated SAWs were detected and the signals were entirely due to either the corner or the truncation of the laser beam. Figure 5.11 shows the amplitude of the SAW generated by the truncated laser beam irradiating the specimen and its variation with the cutting distance. The cutting distance from the center refers to the distance d between the cutting line and the center of the original Gaussian beam as shown in Figure 5.1a. Negative distance means cutting a smaller part of the beam, and positive distance means cutting a larger part of the beam. The result indicates that the laser generated SAWs are the same when the cutting lines are symmetric about the center of the original Gaussian beam, and they have more lowfrequency (2.25 MHz) than high-frequency (10 MHz) contents. The symmetry also indicates that the laser generated SAW here is dominantly generated by the discontinuity presented by the truncation line. The SAW generated by the original intact Gaussian laser beam irradiating the intact material is very weak, which is illustrated by the zero amplitude in the far negative (smaller than -30 mm) part of Figure 5.11, where the laser beam almost keeps its original Gaussian shape. With the cutting line moving to the center, the amplitude of the laser generated SAW increases. Figure 5.12 shows the amplitude of the laser generated SAW versus the notch width w while the notch length l is 1 mm and the depth h is 100 µm. When the notch width is small enough for a certain frequency (e.g., less than 600 µm for 2.25 MHz), the amplitude of the laser generated SAW increases with the width. When the width increases to a certain value (half wavelength corresponding to the frequency), the amplitude reaches a maximum, then decreases with increasing width and reaches a minimum when the width equals the wavelength of the corresponding frequency. For each frequency, there are many amplitude maxima and minima that appear in the laser generated SAW by increasing the notch width. These maxima and minima appear because the two edges of the notch generate SAWs at the same time. Due to the phase difference, the final signal is affected by the interference of these two signals. At certain 182

188 frequencies, the phases of the two SAWs are opposite (w = nλ, λ is the Rayleigh wavelength, n is a positive integer) and a minimum will appear. At other frequencies, the phases of the two SAWs are the same (w = (n + 1/2)λ) and a maximum will appear. However, for pulsed laser generation of SAWs, when the notch width is larger than a certain distance (usually 2 or 3 wave lengths), the two generated SAWs can be separated due to the propagation delay, so the laser-saw amplitude will no longer change with the increasing width. The amplitude variation of the laser generated SAW with the notch length l is shown in Figure 5.13, where the notch width w is 100 µm and the depth h is also 100 µm. The results indicate that the amplitude of the laser generated SAW increases with the length. For this size (w h) of the notch, the high-frequency (10 MHz) content of the laser-saw is more sensitive to the changing of the length than the low-frequency (2.25 MHz) content is. Figures 5.14a and b show the directivity patterns of the SAWs generated by a laser irradiating a short and a long notch, respectively. As one would expect, a short notch (1- mm long, 10-µm wide, and 100-µm deep) produces SAWs with wider directivity patterns than a long notch (10-mm long, 10-µm wide and 100-µm deep) at all frequencies (10 MHz, 5 MHz, 2.25 MHz). These figures also show that for a shorter notch and a lower frequency the directivity pattern of the laser generated SAW is wider. Another promising feature shown by these results is the wide angular width of the SAW produced by the smaller notch. Figure 5.15 shows the amplitude of the laser generated SAW with the notch depth. The notch length and width are 1 mm and 100 µm, respectively. The results indicate that the amplitude of the laser generated SAW increases with the depth of the notch within a certain range of depth for a certain frequency. The deeper the notch, the slower the laser generated SAW increase with depth. Over a certain depth, the variation of the high-frequency components tends to be saturated (e.g., over 200 µm at 10 MHz), 183

189 but the low-frequency component can still reflect the change of the depth (e.g., up to 1 mm at 2.25 MHz). This is because the energy of the surface wave is spread over one wavelength in depth. So for a certain frequency, when the depth of the notch is deep enough (such as 1 mm to 10 MHz), it can be treated as an infinite depth for solving the laser generated SAW problem. If a deep notch needs to be quantified, the low-frequency content needs to be analyzed. 184

190 F(t) Time [ns] Figure 5.9 Temporal profile of the laser pulse (a = 5, b = and γ = 3). 185

191 0-20 Log{amplitude[a.u.]} MHz 5 MHz 2.25 MHz Radius [mm] Figure 5.10 Amplitude of the laser generated SAW versus the characteristic radius of Gaussian beam by simplified analysis. 186

192 MHz 1500 Amplitude[a.u.] MHz MHz Truncation Position [mm] Figure 5.11 Amplitude of the laser generated SAW versus the cutting distance from the center of the original Gaussian laser beam by simplified analysis. 187

193 MHz Amplitude [a.u.] MHz 2.25 MHz Notch Width [µm] Figure 5.12 Amplitude of the laser generated SAW versus the notch width (the notch length is 1 mm, and the depth is 100 µm) by simplified analysis. 188

194 MHz Amplitude [a.u.] MHz 2.25 MHz Notch Length [mm] Figure 5.13 Amplitude of the laser generated SAW versus the notch length (the notch width is 100 µm, and the depth is 100 µm) by simplified analysis. 189

195 30 (a) Amplitude [a.u.] MHz 10 MHz 2.25 MHz Angle [deg] 300 (b) Amplitude [a.u.] MHz 5 MHz 2.25 MHz Angle [deg] Figure 5.14 The directivity of the SAW generated by laser irradiating a short notch (a) 1-mm long, 100-µm wide and 100-µm deep and a long notch (b) 10-mm long, 100-µm wide and 100-µm deep by simplified analysis. 190

196 40 5 MHz MHz Amplitude [a.u.] MHz Notch Depth [µm] Figure 5.15 Amplitude of the laser generated SAW versus the notch depth (the notch length is 1-mm, and the width is 100-µm) by simplified analysis. 191

197 5.6 EXPERIMENTAL RESULTS AND CORRELATION WITH THE SIMULATED DATA In order to validate the theoretical analysis and investigate the advantages of enhanced laser generation of SAWs by surface discontinuities, a group of notches with different lengths were measured. The comparison between conventional ultrasonic inspection and the new technique of laser-generated SAW included a tiny crack that was not detectable by conventional means. The experimental arrangement was the same as the one previously presented in Figure 5.1. First, a simple baseline measurement is performed by a truncated laser beam irradiating an intact area of the specimen. By moving the blade and the specimen together as in Figure 5.1b, a different size of truncated beam can be created. A 10 MHz Panametrics surface wave wedge transducer was used for reception with orientation normal to the cutting line, i.e., at 0 in Figure The laser generated SAW signals were showed in Figure 5.2b. Through normalizing the amplitude of the measured SAW signals, the analytical and the measured results are presented together in Figure This figure shows that the theoretical data is in fair agreement with the experimental data in this situation. In this measurement, the directivity pattern is also examined by changing the cutting line direction. When the cutting line is almost parallel to the transducer direction, no laser generated SAW is detected. Seven EDM notches with different lengths from 254 µm to 750 µm were machined in different positions on a specimen, and the widths and depths of the seven notches were almost the same (~76-µm wide and ~176-µm deep). With the Gaussian laser beam irradiating these notches, the laser generated SAWs were detected by a 10 MHz Panametrics surface wave wedge transducer and amplified by a Panametrics 5072 PR receiver. The recorded signals are presented in Figure 5.17, which shows that the signals are almost the same, except that the amplitude of the laser generated SAW 192

198 increases with the length of the notch. In order to quantitatively compare the experimental results to the analytical data, the absolute amplitude of the measured laser generated SAW is normalized to fit the calculated values. The comparison shown in Figure 5.18 indicates that the changing slope with the notch length is in agreement with the theoretical prediction to a certain extent. It needs to be mentioned here again that the actual analytical data is based on the optical discontinuities to simulate the laser beam irradiation of the material notches therefore no comparison between the absolute amplitudes was attempted. 193

199 500 theory experiment 400 Amplitude[a.u.] Truncation Position [mm] Figure 5.16 Amplitude of the laser generated SAW (10 MHz) with the truncated laser beam irradiating an intact area of the specimen by measurement and simplified analysis. 194

200 n1 Laser Generated SAW [500 mv/div] n2 n3 n4 n5 n7 n8 Time [1 µs/div] Figure 5.17 Laser generated SAW (10 MHz, 52 db) by the Gaussian laser beam irradiating the seven EDM notches (experimental results). 195

201 30 25 theory experiment Amplitude [a.u.] Notch Length [µm] Figure 5.18 Amplitude of the laser generated SAW versus the notch length (the notch depth is 178 µm, and the width is 76 µm) by measurement and simplified analysis. 196

202 5.7 ADDITIONAL ADVANTAGES OF DISCONTINUITY-ENHANCED LASER GENERATION OF SAWS Detection of a Small Crack The above measurements show that laser generated SAWs can be used to detect and quantify even small discontinuities. The great advantage of this laser-based SAW detection method is that it can identify small cracks which are totally hidden in material noise when conventional ultrasonic NDE methods are used. Figure 5.19 shows the optical micrograph of a small surface-breaking crack in Ti-6Al-4V. Using surface wave wedge transducers (with central frequencies of 2.25 MHz, 5 MHz and 10 MHz) working in pulse-echo mode, conventional ultrasonic NDE could not distinguish which signal (upper part of Figure 5.20) is scattered from the crack, so this case would certainly result in a missed defect. Under the same conditions, a Gaussian laser beam was used to irradiate the crack area, and the same transducers were used to detect the laser generated SAW signals. A significant SAW signal is clearly identified (lower part of Figure 5.20) by each transducer from the fatigue crack that was previously hidden among other scatterers. Due to the limited bandwidth of the detecting transducers, the central frequencies of both types of SAWs are almost the same except that the central frequency of the laser generated SAW (2.5 MHz) detected by the 2.25 MHz transducer is higher than that of the corresponding pulse-echo SAW (1.8 MHz). In other words, the laser generated SAW from this small crack has more high frequency content. From the laser generated SAW signals in Figure 5.20, an interesting observation can be made. Even using a low frequency (2.25 MHz) detecting transducer, the laser generated SAW can be still detected because it is enhanced by the small crack. In the conventional ultrasonic NDE method, the detection of small cracks is limited by the ultrasonic frequency and the presence of incoherent inhomogeneities (such as coarse grains and large colonies in Ti- 197

203 6Al-4V). In order to theoretically examine this apparently flat frequency response of laser generated SAWs from small cracks, a small notch with 1-mm length, 100-µm depth and 10-µm width was used to simulate a crack. The analytical results are shown in Figure 5.21, where the result from the same Gaussian beam irradiating an intact area is also shown for comparison. The figure indicates that a small notch in the medium can significantly increase the laser generated SAW amplitude in a broad frequency range, while the laser generated SAW by the Gaussian laser beam irradiating the intact medium can be neglected. 198

204 Figure 5.19 The magnified crack in a specimen of Ti-6Al-4V (the real size of the picture is 0.65 mm 0.5 mm). 199