Advancement of Optical Methods in Experimental Mechanics, Volume 3

River Rapids Conference Proceedings of the Society for Experimental Mechanics Series Advancement of Optical Methods in Experimental Mechanics, Volume 3 Luciano Lamberti Ming-Tzer Lin Cosme Furlong Cesar Sciammarella Proceedings of the 2017 Annual Conference on Experimental and Applied Mechanics River Publishers

Conference Proceedings of the Society for Experimental Mechanics Series Series Editor Kristin B. Zimmerman, Ph.D. Society for Experimental Mechanics, Inc., Bethel, CT, USA

River Publishers Luciano Lamberti • Ming-Tzer Lin • Cosme Furlong • Cesar Sciammarella Editors Advancement of Optical Methods in Experimental Mechanics, Volume 3 Proceedings of the 2017 Annual Conference on Experimental and Applied Mechanics

Published, sold and distributed by: River Publishers Broagervej 10 9260 Gistrup Denmark www.riverpublishers.com ISBN 978-87-7004-958-0 (eBook) Conference Proceedings of the Society for Experimental Mechanics An imprint of River Publishers © The Society for Experimental Mechanics, Inc. 2018 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, or reproduction in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Preface Advancement of Optical Methods in Experimental Mechanics represents one of nine volumes of technical papers presented at the SEM 2017 SEM Annual Conference & Exposition on Experimental and Applied Mechanics organized by the Society for Experimental Mechanics and held in Indianapolis, IN, June 12–15, 2017. The complete Proceedings also includes volumes on: Dynamic Behavior of Materials; Challenges In Mechanics of Time-Dependent Materials; Mechanics of Biological Systems, Materials and Other Topics in Experimental and Applied Mechanics; Micro-and Nanomechanics; Mechanics of Composite, Hybrid & Multifunctional Materials; Fracture, Fatigue, Failure and Damage Evolution; Residual Stress, Thermomechanics & Infrared Imaging, Hybrid Techniques and Inverse Problems; and Mechanics of Additive and Advanced Manufacturing. Each collection presents early findings from experimental and computational investigations on an important area within experimental mechanics, optical methods being one of these areas. With the advancement in imaging instrumentation, lighting resources, computational power, and data storage, optical methods have gained wide applications across the experimental mechanics society during the past decades. These methods have been applied for measurements over a wide range of spatial domain and temporal resolution. Optical methods have utilized a full range of wavelengths from X-ray to visible lights and infrared. They have been developed not only to make twodimensional and three-dimensional deformation measurements on the surface, but also to make volumetric measurements throughout the interior of a material body. Bari, Italy Luciano Lamberti Taichung, Taiwan Ming-Tzer Lin Worcester, MA, USA Cosme Furlong Chicago, IL, USA Cesar Sciammarella v

Contents 1 A New Method for Improving Measurement Accuracy of Digital Image Correlation........................... 1 Li Bang-Jian, Wang Quan-Bao, and Duan Deng-Ping 2 Fatigue Analysis of 7075 Aluminum Alloy by Optoacoustic Method.............................................. 7 Tomohiro Sasaki, Hiroshi Ono, Sanichiro Yoshida, and Shuich Sakamoto 3 Early Strain Localization in Strong Work Hardening Aluminum Alloy (2198 T3): 3D Laminography and DVC Measurement ................................................................................................. 15 Ante Buljac, Lukas Helfen, François Hild, and Thilo F. Morgeneyer 4 On the In-Plane Displacement Measurement by 3D Digital Image Correlation Method........................ 19 Chi-Hung Hwang, Shou Hsueh Wang, and Wei-Chung Wang 5 Noise Reduction in Amplitude-Fluctuation Electronic Speckle-Pattern Interferometry........................ 27 Sanichiro Yoshida, David Didie, Jong-Sung Kim, and Ik-Keun Park 6 Evaluating Path of Stress Triaxiality to Fracture of Thin Steel Sheet Using Stereovision ...................... 37 D. Kanazawa, S. Chinzei, Y. Zhang, K. Ushijima, J. Naito, and S. Yoneyama 7 Studying with a Full-Field Measurement Technique the Local Response of Asphalt Specimens Subjected to Freeze-Thaw Cycles...................................................................................... 43 M.C. Teguedi, B. Blaysat, E. Toussaint, S. Moreira, S. Liandrat, and M. Grédiac 8 Mechanical Shape Correlation: A Novel Integrated Digital Image Correlation Approach..................... 47 S.M. Kleinendorst, J.P.M. Hoefnagels, and M.G.D. Geers 9 On the Boundary Conditions and Optimization Methods in Integrated Digital Image Correlation........... 55 S.M. Kleinendorst, B.J. Verhaegh, J.P.M. Hoefnagels, A. Ruybalid, O. van der Sluis, and M.G.D. Geers 10 Extension of the Monogenic Phasor Method to Extract Displacements and Their Derivatives from 3-D Fringe Patterns .......................................................................................................... 63 C.A. Sciammarella and L. Lamberti 11 Deformation Measurement within a Volume of Translucent Yield Stress Material Using Digital Image Correlation ............................................................................................................... 77 A. McGhee and P. Ifju 12 Surface Deformation with Simultaneous Contact Area Measurement for Soft Transparent Media due to Spherical Contact..................................................................................................... 81 A. McGhee, D. Nguyen, and P. Ifju 13 Towards Measuring Intergranular Force Transmission Using Confocal Microscopy and Digital Volume Correlation...................................................................................................... 85 Kimberley Mac Donald and Guruswami Ravichandran 14 Using Anti-aliasing Camera Filters for DIC: Does It Make a Difference?........................................ 89 PL. Reu vii

viii Contents 15 Investigation of Electronic Speckle Pattern Interferometry with Line Laser Scanning for Large Area Deformation Measurement ............................................................................................. 93 Shuichi Arikawa and Yuta Ando 16 Internal Heat Generation in Tension Tests of AISI 316 Using Full-Field Temperature and Strain Measurements............................................................................................................ 97 Jarrod L. Smith, Veli-Tapani Kuokkala, Jeremy D. Seidt, and Amos Gilat 17 A Short Survey on Residual Stress Measurements by HDM and ESPI ........................................... 105 C. Pappalettere 18 Feasibility of Using Fringe Projection System for Corrosion Monitoring in Metals of Interest in Cultural Heritage..................................................................................................... 111 C. Casavola, P. Pappalardi, G. Pappalettera, and G. Renna

Chapter 1 A New Method for Improving Measurement Accuracy of Digital Image Correlation Li Bang-Jian, Wang Quan-Bao, and Duan Deng-Ping Abstract Digital image correlation (DIC) method has been applied in wide fields including experimental mechanics. The displacement measurement accuracy plays an important role in these situations. The direct method to improve the measurement accuracy is to reduce the measurement error in DIC. In the paper, a new method has been developed to improve the DIC accuracy using the feature of DIC system error. The feature of DIC system error is analyzed. And the reduction of the DIC system error has been verified by experiment. Keywords Digital image correlation • System error • Translation measurement • Error reduction • Measurement accuracy 1.1 Introduction Digital image correlation (DIC) is an optical measurement method and DIC is popular in motion measurement, dimension measurement and experimental mechanics for its countless and full-field features [1–5]. In 2D DIC, a digital camera is used to capture the reference image before the specimen deformation and capture the deformed image when the loading is imposed by drawing machine. In motion measurement, the reference and deformed images are captured before and after the specimen or object movement respectively. In dimension measurement, the same speckle images in different positions are regarded as the reference and deformed images respectively. And in subset based DIC, the displacement of sampled point can be obtained by matching the selected subset. Subsequently the dynamic variables including velocity and acceleration can be calculated by post-processing with the displacement data. That is to say that displacement or translation measurement is the basic for other variables’ calculation. So the translation measurement of DIC has been studied by many researchers [6–8]. And the measurement accuracy of DIC has been one main research point recently [9, 10]. In addition, the DIC calculation speed has been another main research point. For calculation speed, many techniques are proposed. Pan [11] proposed that reliability guided searching method combined with interpolation coefficient pre-computed technique can make the calculation speed about 160 times faster than the classical DIC method. Jiang et al. [12] presented that path-independent searching method combined with graphics processing unit (GPU) based parallel calculation, inverse compositional Gauss Newton (IC-GN) [13] and Fast Fourier transform (FFT) can make about 66 times faster than non-path-independent method. For measurement accuracy, many researchers have studied it by theory, simulation and experiments. Generally measurement accuracy can be quantified with measurement error which contains system error and random error by theoretical and experimental analysis. For instance, Wang et al. [14] investigated the shape function induced random error theoretically and experimentally. Schreier et al. [15] studied the interpolation induced system error by simulation. Pan et al. [8] investigated lens distortion induced system error by theory and experiments. Ma et al. [7] researched the camera self-heating induced system error by experiments. Su and Xu et al. [16–18] derived the system error theoretically. Hu et al. [19] developed a method to evaluate 3D DIC error. Pan et al. [20, 21] used bilateral telecentric lens to improve the 2D DIC measurement accuracy. Considering the limitation of field of view of bilateral telecentric lens, Pan et al. [22] used a non-deformable sample to compensate the DIC measurement accuracy. Pan [23] and Zhou et al. [24] proposed that image pre-filtering in DIC can enhance measurement accuracy by smoothing the image noise but the pre-filtering parameters had to be selected and the random error increased due to the pre-filtering smoothing function. Zhou et al. [25] developed an adaptive subset offset method in incremental DIC to improve the measurement accuracy by avoiding interpolation of the sample points. L. Bang-Jian • W. Quan-Bao ( ) • D. Deng-Ping School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai, People’s Republic of China e-mail: quanbaowang@sjtu.edu.cn © The Society for Experimental Mechanics, Inc. 2018 L. Lamberti et al. (eds.), Advancement of Optical Methods in Experimental Mechanics, Volume 3, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-63028-1_1 1

2 L. Bang-Jian et al. In this paper, a novel method to reduce error will be proposed which is different from existing solutions which focus on random error and based on image pre-filtering. The new strategy is developed from the system error reduction perspective to improve the measurement accuracy. Due to the fact that systematic error is related with interpolation, noise, shape function, correlation criterion and so on, a few effective methods to reduce the systematic error are studied. In this paper, a strategy will be put forward based on the shape feature of systematic errors in translation measurement using DIC. To sum up, the improvement of the translation or displacement measurement accuracy plays an important role in practical applications, especially in motion and dimension measurement. The quasi odd function feature of the system error in DIC will be exhibited by simulation experiments. Subsequently the strategy will be proposed based on the quasi odd function feature. And the system error reduction will be derived mathematically in detail. Finally, the open access speckle image data will be applied to verify the effectiveness of the developed strategy. 1.2 Algorithm 1.2.1 Quasi Odd Function Feature of DIC System Error In this part, the open access speckle images from DIC Challenge Datasets (https://sem.org/dic-challenge/) are applied to implement the experiment which can show the quasi odd function feature of the system error. In detail, the reference speckle image is selected from the DIC Challenge 2D Datasets. Subsequently by translating, one deformed speckle image set is built. The Fourier Shift theorem [1, 15] is used to translate the reference speckle image to form the deformed set. The displacements are from 0.5 to 0.5 pixels and the displacement interval is 0.1 pixels. The subset based local DIC algorithm with first order shape function and bi-cubic interpolation is used to calculate the displacements. And the subset size is set as 25 25 pixels and the area of interest (AOI) is 100 100 pixels. And the mean bias error is used to quantify the system error. In addition, 2 2, 4 4, 6 6, 8 8 and 10 10 kernel based bi-cubic interpolations are used to demonstrate the quasi odd function feature too. As showed in Fig. 1.1, the quasi odd function feature of DIC system error for different interpolations is evident. 1.2.2 Strategy On the basis of the quasi odd function feature of DIC system error, a system error reduction strategy is developed. As displayed in Fig. 1.1, the system errors of the symmetric displacements are opposite numbers to each other. So the system error of the displacement can be reduced or removed by the system error of the symmetric displacement. In the proposed Fig. 1.1 The quasi odd function feature of system error induced by different bi-cubic interpolation methods in digital image correlation (DIC)

1 A New Method for Improving Measurement Accuracy of Digital Image Correlation 3 Fig. 1.2 Schematic of system error reduction strategy using quasi odd function feature strategy, the deformed speckle image with the symmetric displacement is obtained by Fourier Shift theorem. Due to the fact that the true displacement of the sampled point is unknown in practical application, the symmetric displacement is estimated by the traditional DIC calculation. Here it should be noted that the updated deformed speckle image with the symmetric displacement is generated from the original deformed image (not the reference image), since the noises of the original deformed and reference images are different. So the amplitude of the final translated displacement is double of that of the symmetric displacement estimated by DIC calculation. As displayed in Fig. 1.2, the first step of the developed strategy is implementing the traditional DIC calculation between the original reference image and original deformed image. The calculated displacement is assumed as uc. Subsequently, the updated deformed image is generated by translating the original deformed image with -2uc displacement. Then DIC calculation is carried out again between the original reference image and the updated deformed image. And the second calculated displacement is assumed as uc2. Next the updated displacement uu can be obtained by the following formula: uu D uc Cuc2 . 2uc/ 2 D 3uc Cuc2 2 : (1.1) The sampled points are judged whether calculated or not in the final step of the proposed strategy. Mathematically, the system error of the proposed strategy can be derived. The true displacement of the sampled point is assumed as u. and the corresponding system error is denoted bye(u). As displayed in Fig. 1.1, the quasi odd function feature can be written as e.u/ De. u/ : (1.2) In addition, the first calculated displacement uc can be written as uc DuCe.u/: (1.3) Similarly, the second calculated displacement uc2 can be written as uc2 Du 2uc Ce.u 2uc/ : (1.4)

4 L. Bang-Jian et al. Then the updated displacement uu can be derived by substituting formulas (1.3) and (1.4) into (1.1): uu D 2uCe.u/ CeŒ u 2e.u/ 2 : (1.5) According to the quasi odd function feature of the system error and formula (1.2), the updated displacement uu and formula (1.5) can be written as: uu DuC e.u/ eŒuC2e.u/ 2 : (1.6) From the above derivation, the system error of the updated displacement can be written as: e.uu/ D e.u/ eŒuC2e.u/ 2 : (1.7) When e(u) is small and generally this situation is tenable with suitable interpolation method, u C2e(u) will be close to u and then e(uu) will be smaller than e(u). That is to say, the system error will be reduced by the proposed strategy mathematically. 1.3 Experiments The open access speckle images (https://sem.org/dic-challenge/) will be used to verify the proposed strategy too. Measurement accuracy will be investigated in this part. The proposed strategy is tested with the open access speckle images (https://sem.org/dic-challenge/). The open access speckle image is selected as reference image. And one deformed image set is obtained by translating. The deformed image set contains 11 deformed images which are generated by Fourier shift theorem with displacement from 0.5 to 0.5 pixels and the displacement interval is 0.1 pixels. In the experiments, the area of interest (AOI) is 101 101 pixels. The subset size is 25 25 pixels. The subset based local DIC with first order shape function and bi-cubic interpolation is utilized. The system error which is calculated by the mean bias error is displayed in Fig. 1.3. As showed in Fig. 1.3, the system error is reduced for different bi-cubic interpolations by the proposed strategy. In addition, the result of 2 2 bi-cubic interpolation is worse than others, which can be explained that 2 2 bi-cubic interpolation is similar to bi-linear interpolation which is low order interpolation method [26]. Here it should be noted that the reduced system error is not equal to zero for many other factors induced system error such as shape function [27] and correlation criterion [28]. Fig. 1.3 System error reduction for different bi-cubic interpolation methods (update denotes the proposed strategy)

1 A New Method for Improving Measurement Accuracy of Digital Image Correlation 5 1.4 Conclusion The quasi odd function feature of system error in DIC is displayed for different interpolations. An effective system error reduction strategy is proposed using the quasi odd function feature. Open access speckle images (https://sem.org/dicchallenge/) are used to test the proposed strategy. The measurement accuracy of the proposed strategy is investigated. And the results indicate that the system error can be reduced by the proposed strategy. In addition, the developed strategy is suitable for the situations including motion measurement and dimension measurement which can employ the DIC technique. And the simulated speckle pattern can be pasted on the moving target or the same speckle patterns can be pasted on different positions of the specimen whose dimension needs to be measured. References 1. Sutton, M.A., Orteu, J.J., Schreier, H.: Image Correlation for Shape, Motion and Deformation Measurements: Basic Concepts, Theory and Applications. Springer Science & Business Media, New York (2009) 2. Pan, B., et al.: Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review. Meas. Sci. Technol. 20(6), 062001 (2009) 3. Wu, R., Qian, H., Zhang, D.: Robust full-field measurement considering rotation using digital image correlation. Meas. Sci. Technol. 27(10), 105002 (2016) 4. Ashrafi, M., Tuttle, M.E.: Measurement of strain gradients using digital image correlation by applying printed-speckle patterns. Exp. Tech. 40(2), 1–7 (2016) 5. Zhao, J., Zhao, D., Zhang, Z.: A non-contact varying temperature strain measuring system based on digital image correlation. Exp. Tech. 40(1), 101–110 (2016) 6. Wang, D., et al.: Bias reduction in sub-pixel image registration based on the anti-symmetric feature. Meas. Sci. Technol. 27(3), 035206 (2016) 7. Shaopeng, M.A., Pang, J., Qinwei, M.A.: The systematic error in digital image correlation induced by self-heating of a digital camera. Meas. Sci. Technol. 23(2), 344–347 (2012) 8. Pan, B., et al.: Systematic errors in two-dimensional digital image correlation due to lens distortion. Opt. Lasers Eng. 51(2), 140–147 (2013) 9. Wang, Y., et al., Theoretical analysis on the measurement errors of local 2D DIC: part II assessment of strain errors of the local smoothing method–approaching an answer to the overlap question. Strain. 52(2):129–147, 2016 10. Li, B., Wang, Q., Duan, D.: A modified digital image correlation with enhanced speed and improved accuracy. Proc. SPIE. (2017) 11. Pan, B.: Reliability-guided digital image correlation for image deformation measurement. Appl. Opt. 48(8), 1535–1542 (2009) 12. Jiang, Z., et al.: Path-independent digital image correlation with high accuracy, speed and robustness. Opt. Lasers Eng. 65, 93–102 (2015) 13. Shao, X., et al.: Real-time 3D digital image correlation method and its application in human pulse monitoring. Appl. Opt. 55(4), 696–704 (2016) 14. Wang, B., Pan, B.: Random errors in digital image correlation due to matched or overmatched shape functions. Exp. Mech. 55(9), 1–11 (2015) 15. Schreier, H.W., Braasch, J.R., Sutton, M.A.: Systematic errors in digital image correlation caused by intensity interpolation. Opt. Eng. 39(11), 2915–2921 (2000) 16. Su, Y., et al.: Fourier-based interpolation bias prediction in digital image correlation. Opt. Express. 23(15), 19242–19260 (2015) 17. Su, Y., et al.: Noise-induced bias for convolution-based interpolation in digital image correlation. Opt. Express. 24(2), 1175 (2016) 18. Xu, X., Su, Y., Zhang, Q.: Theoretical estimation of systematic errors in local deformation measurements using digital image correlation. Opt. Lasers. Eng. 88, 265–279 (2017) 19. Hu, Z., et al.: Error evaluation technique for three-dimensional digital image correlation. Appl. Opt. 50(33), 6239–6247 (2011) 20. Pan, B., Yu, L., Wu, D.: High-accuracy 2D digital image correlation measurements with bilateral telecentric lenses: error analysis and experimental verification. Exp. Mech. 53(9), 1719–1733 (2013) 21. Pan, B., Yu, L., Wu, D.: Accurate ex situ deformation measurement using an ultra-stable two-dimensional digital image correlation system. Appl. Opt. 53(19), 4216–4227 (2014) 22. Pan, B., Yu, L., Wu, D.: High-accuracy 2D digital image correlation measurements using low-cost imaging lenses: implementation of a generalized compensation method. Meas. Sci. Technol. 25(2), 025001–025012 (2014) 23. Pan, B.: Bias error reduction of digital image correlation using Gaussian pre-filtering. Opt. Lasers. Eng. 51(10), 1161–1167 (2013) 24. Zhou, Y., et al.: Image pre-filtering for measurement error reduction in digital image correlation. Opt. Lasers. Eng. 65(1), 46–56 (2015) 25. Zhou, Y., Sun, C., Chen, J.: Adaptive subset offset for systematic error reduction in incremental digital image correlation. Opt. Lasers. Eng. 55(7), 5–11 (2014) 26. Luu, L., et al.: Accuracy enhancement of digital image correlation with B-spline interpolation. Opt. Lett. 36(16), 3070–3072 (2011) 27. Yu, L., Pan, B.: The errors in digital image correlation due to overmatched shape functions. Meas. Sci. Technol. 26(4), 045202 (2015) 28. Bing, P., et al.: Performance of sub-pixel registration algorithms in digital image correlation. Meas. Sci. Technol. 17(6), 1615 (2006) Li Bang-Jian is a PhD candidate in the School of Aeronautics and Astronautics at Shanghai Jiao Tong University. His research interests include digital image correlation and its applications in control science and engineering.

Chapter 2 Fatigue Analysis of 7075 Aluminum Alloy by Optoacoustic Method Tomohiro Sasaki, Hiroshi Ono, Sanichiro Yoshida, and Shuich Sakamoto Abstract The influence of fatigue damage on the elastic response of AA7075 aluminum alloy was investigated through a combination of optical and acoustical experiments. Specimens were previously subjected to fatigue cyclic loads at various fatigue levels within the fatigue life. Macroscopic deformation process under a certain load below the yield point (elastic region) for the pre-fatigued specimen was visualized by electronic speckle pattern interferometry (ESPI). At the same time, the acoustic velocities of vertical and shear waves propagating in the fatigued specimen were measured using an ultrasonic probe. The acoustic analysis showed the following change in residual stress by the fatigue cyclic load; an increase in compressive residual stress with the number of pre-fatigue cycles (NP) below 10 3, and relaxation of the residual stress NP over 10 3. The visualization using ESPI demonstrated that the strain heterogeneity in the macroscopic elastic regime was enhanced with increase of the pre-fatigue cycle. The correlation between the optical and the acoustical measurement results is discussed based on the change in the residual stress, localized plastic deformation, and the crack initiation. Keywords Fatigue • Optical method • Acoustic method • Speckle patter interferometry • Aluminum alloy 2.1 Introduction Fatigue of metals is generally interpreted as a process of crack initiation by localized deformation, and crack propagation, leading to final fracture under cyclic loading. A number of fatigue inspection methods such as those use X-ray, ultrasonic wave, and acoustic emission have been established [1–4]. These methods mainly aim at detection of the presence of fatigue crack, and fatigue life is predicted by monitoring the crack length based on fracture mechanical parameters. On the other hand, the stage of localized plastic deformation prior to the crack initiation is a complex phenomenon and not fully understood. Thus, it is generally difficult to detect the fatigue damage at the earlier fatigue stage particularly in ductile metals, because most of the fatigue life is spent by the stage before the crack initiation. The localized plastic deformation occurs not only in “Low cycle fatigue”, but also in “High cycle fatigue” that is characterized by lower stress condition below the macroscopic yield stress. This study focuses on the influence of the localized plastic deformation on macroscopic deformation behavior of metals. Our previous works using a full field optical method [5, 6] demonstrated that the strain concentration, which is observed in the macroscopic elastic regime, is enhanced depending on the degree of fatigue cycles. On the other hand, a similar effect of fatigue damage on the elastic behavior of metals was also confirmed through acoustical methods by several researchers [7–10]. These methods are based on stress dependence of elastic wave velocity that propagates through the material, termed as “acousto-elasticity”. The fatigue damage was detected as a change in the elastic wave velocity or attenuation attributed to residual stress induced by the localized plastic deformation. Both the results obtained from the optical and the acoustical methods are associated with the elastic response of metals, and indicate the possibility of analyzing the elastic response as a mean of fatigue diagnosis. T. Sasaki ( ) • H. Ono • S. Sakamoto Graduate school of Niigata University, 8050 Ikarashi-ninocho, Nishi-ku, Niigata-shi, Niigata, Japan e-mail: tomodx@eng.niigata-u.ac.jp S. Yoshida Department of Chemistry and Physics, Southeastern Louisiana University, SLU 10878, Hammond, LA, 70402, USA e-mail: syoshida@selu.edu © The Society for Experimental Mechanics, Inc. 2018 L. Lamberti et al. (eds.), Advancement of Optical Methods in Experimental Mechanics, Volume 3, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-63028-1_2 7

8 T. Sasaki et al. In the present study, in order to establish the correlation of the elasticity of metals and the fatigue damage, the deformation behavior of aluminum alloys previously subjected to cyclic loading are visualized with electronic speckle pattern interferometry (ESPI). At the same time, the change of elasticity due to the fatigue damage is evaluated by the acoustic measurement. We demonstrate the influence of microscopic factors including the localized plastic deformation, the presence of micro-cracks, on strain heterogeneity, and discuss the change in elastic response of the material. 2.2 Experimental Procedure 2.2.1 Fatigue Test An AA7075-T1 aluminum alloy sheet with thickness of 3.0 mm was used for experiments. Necked shape specimens as shown in Fig. 2.1 were cut from the sheet for fatigue tests by electronic discharge machining. The yield strength of specimen measured by a static tensile test was approximately 8.0 kN. The fatigue test was conducted for the specimen under load control condition with a sinusoidal waveform of 5 Hz. The maximum tensile load ranged from 5.0 kN to 7.0 kN, and the minimum load was a constant at 0.1kN. Figure 2.2 shows the maximum load – number of cycle curve obtained from the fatigue test. From this curve, the maximum load in the pre-fatigue test was determined to 5.0 kN which was approximately the fatigue limit. The numbers of cycles used in the pre-fatigue test, NP, were 10, 10 2, 103, 104, and 105, respectively. 2.2.2 Acoustic Measurement Acoustic wave velocity in the specimen was measured using an ultrasonic transducer driven by a square wave pulserreciever with 35 MHz bandwidth (Olympus 5077PR). As shown in Fig. 2.3, the measurement was conducted for the necked center of specimen. Velocities of vertical wave propagating in the thickness direction (Vzz), and shear vertical waves in the displacement directions of x and y (Vzx, Vzy) were respectively measured. Coupling media used was distilled water for the vertical wave measurement, and glycerin paste for the shear wave measurement. 2.2.3 Dynamic Observation of Deformation Behavior of Pre-fatigued specimen Deformation behavior during tensile tests was visualized with a two-dimensional ESPI in the same manner described in a previous work [6]. Figure 2.4 shows the optical setup in this study. Two optical interferometers were arranged to horizontal Fig. 2.1 Specimen used in this study

2 Fatigue Analysis of 7075 Aluminum Alloy by Optoacoustic Method 9 Prefatigue load Fig. 2.2 Maximum load vs. number of cycle plot in the fatigue test Fig. 2.3 Acoustic measurement Vzz Vzy Vzx x y z Mirror Beam splitter Laser (Interferometer x) Laser (Interferometer y) Specimen Beam expander Illuminated area Tensile load Stationary end CCD camera Stepping motor Glass window Fig. 2.4 Experimental arrangement of 2D-ESPI [6] direction (x) and vertical direction (y) to the tensile machine (interferometer x, and interferometer y). Each interferometer was sensitive to in-plane displacement along its horizontal direction. Semiconductor laser with the wave length of 660 nm and the power of 50 mW was used for light source. The individual displacement fields in each sensitive direction were obtained by switching light sources of the two interferometers. The laser beam was expanded by a beam expander and split into two paths by a beam splitter and converged to the surface of specimen via two mirrors. The incident angels to the surface were 36.3ı for the interferometer x, and 48.0ı for the interferometer y. The speckle pattern was captured with a CCD camera with a frame rate of 15 frames per a second. The speckle intensity received by each pixel changes depending on the displacement in the sensitive direction due to optical path difference between the two interferometric arms. Thus, the displacement field on the measured surface can be obtained by computing the intensity difference as fringe contours.

10 T. Sasaki et al. In addition, a glass window with 5.2 mm thick and the refraction index of 1.53 was placed after the beam splitter for one interferometric arm of each interferometer, in order to introduce “a carrier fringe system” [11]. The optical distance of the laser beam which passes through the glass window varies depending on its incident angle. Since the beam is expanded by the expander, optical distance on the irradiated surface has a gradient. By rotating the window with a stepping motor, the carrier fringes orthogonal to the sensitive direction appear. The resultant fringe contours represents the superimposing displacement obtained from the carrier and the displacement, thus actual displacement can be obtained by subtracting the carrier from the measured fringe. The number of carrier fringes introduced to the measurement surface was 6 for the horizontal direction, x, and 3 for the tensile direction, y. Tensile load was applied up to 800 N (5% of the yield load), and the dynamic deformation behavior was measured. 2.3 Result and Discussion 2.3.1 Effect of Fatigue Cycle on Acoustic Wave Velocity Figure 2.5 shows acoustic velocity plotted against logarithm of the number pre-fatigued cycles. The value of non-fatigued specimen (NP D0) pis plotted to the pre-fatigue cycles, NP D10 0 for convenience. The vertical wave propagating in the thickness direction, Vzz, decreased as NP increased up to 10 3, then it increased again (Fig. 2.5a). In acousto-elastic theory, the elastic modulus depends on applied stress due to the non-linearity between the interatomic force and the interatomic distance [11]. In particular, tensile stress leads to a decrease in the sound velocity. Thus, the initial decrease in the Vzz at NP <10 3 is indicative of an increase of the tensile internal stress in the thickness direction, z. On the other hand, in the results of shear waves (Fig. 2.5b), although the change was relatively small, both Vzx andVzy exhibited a slight increase at lower NP, followed by a decrease in contrast to the change of Vzz. Toda et al. [12] proposed “R-value acoustoelastic method” that uses the ratio of vertical wave velocity and averaged value of shear wave velocity. According to this method, the ratio of Vzz. and (Vzx CVzy)/2 is proportional to the sum of in-plane principle stress as shown below. RD Vzz Vzx CVzy =2 DR0 CCR x C y (2.1) where R0 is microstructural factor, CR is stress-acoustic constant, ¢x, and ¢y are components of plane stress. Figure 2.6 shows the R value plotted against the pre-fatigue cycle. Since the R-value generally has a positive value, a decrease at (a) (b) Fig. 2.5 Acoustic wave velocity for (a) vertical wave Vzz, and (b) shear vertical waves Vzx andVzy

2 Fatigue Analysis of 7075 Aluminum Alloy by Optoacoustic Method 11 Fig. 2.6 The ratio of vertical and averaged shear wave velocity u – 0 u – 200 u – 400 u – 600 u – 800 v –0 v –200 v –400 v –600 v –800 x y Fig. 2.7 Load-elongation curve and fringe pattern observed at various tensile loads of a non-fatigued specimen. The tensile load is indicated in the load – elongation curve by arrows NP < 10 3 implies an increase of compressive stress in the x-y plane. Cyclic tensile load during the pre-fatigue causes the localized plastic deformation in the necked area. This fact might result in the increase of compressive residual stress, because the deformed area is restrained by the surrounding area. Therefore, the earlier pre-fatigue stage of NP < 10 3 can be interpreted as an increasing process of the residual stress in the necked part. Furthermore, the latter increase in the R-value at NP >10 3 indicates a relaxation of the residual stress. This relaxation behavior agrees with the result of surface acoustic wave velocity measurement by a scanning acoustic microscope in our previous work [6]. In the previous work, crack initiation was confirmed at the latter fatigue stage when the acoustic wave velocity decreased. It can be understood that the residual stress induced by the localized plastic deformation was relaxed with the crack initiation. 2.3.2 Deformation Behavior in Tensile Test Figure 2.7 shows a load-elongation curve and optical fringe patterns observed in a tensile test of the non-fatigued specimen (NP D0). These fringe patterns represent displacement contours along x, and y resulting from subtracting captured images at various tensile load levels by a base image before the tensile test (tensile load D0 N). Fringe pattern at 0 N (v-0 N or u-0 N) means the carrier fringes initially introduced. The fringe in the tensile direction y (v-fringe) concentrated to the neck

12 T. Sasaki et al. u – 0 u – 200 u – 400 u – 600 u – 800 v –0 v –200 v –400 v –600 v –800 x y Fig. 2.8 Load-displacement curve and fringe pattern observed of a pre-fatigued specimen of NP D10 5 26.0mm 485 pixel 5.7mm (110 pixel) Analyzed area x y Np = 10^5 a b Fig. 2.9 Displacement vector field showing the deformation of necked part obtained from fringe analysis. The analyzed area is indicated in the image on the right part of specimen with increase of tensile load, showing the strain concentration. In the horizontal direction, x (u-fringe), the initial carrier fringes gradually became a bent shape. Difference between the non-fatigue and pre-fatigued specimen was observed in this strain concentration behavior. Figure 2.8 shows an example of the fringe patterns in a tensile test for the pre-fatigued specimen (NP D10 5). In all the pre-fatigued condition, the pre-fatigued specimens basically exhibited a similar concentration behavior of the v-fringe, whereas the curvature of u-fringe tended to be higher than that in the non-fatigued specimen. Figure 2.9 shows displacement vector field of the necked part obtained from phase analysis of the u, and v fringe contours. The analysis was conducted for an area of 110 485 pixel (5.7 mm 26.0 mm) around the necked part indicated by dashed line. The quiver plot on the left indicates that the strain concentrates at one side of the neck, implying strain heterogeneity. To discuss this strain concentration behavior in detail, the mean value of strain in the measured area was computed. Normal strain along the tensile axis "yy, and shear strain xy were obtained from the displacement components v and u as follows.

2 Fatigue Analysis of 7075 Aluminum Alloy by Optoacoustic Method 13 "yy D @v @y ; xy D @u @y C @v @x (2.2) Figure 2.8 shows the result plotted against the tensile load up to 400 N. The tensile strain, "yy monotonically increased with the increases of applied load as shown in Fig. 2.9a. The pre-fatigued specimens exhibited higher slopes than that in the non-fatigued specimen. In addition, a larger difference was seen in the shear strain xy as shown in Fig. 2.9b. The increase in xy implies strain heterogeneity that is probably due to the localized plastic deformation during the fatigue test. The slopes of "yy and xy, (compliance d"yy/dF, and d xy/dF) obtained by a least square method are shown in Fig. 2.10. Variation of normal compliance, d"yy/dF by the pre-fatigue cycle was consistent with the measurement result of shear velocity along the tensile direction (Fig. 2.5b); d"yy/dF showed an increase at NP < 10 3 and a decrease at NP > 10 3. In addition, the shear compliance, d xy/dF showed a slight increase at NP >10 3 and a rapid increase at NP <10 3. These results demonstrate that the (a) Tensile strain, eyy, (b) Shear strain, gxy Fig. 2.10 Mean value of strain plotted against the applied load. (a) Tensile strain, "yy, (b) Shear strain, xy Elastic compliance Fig. 2.11 Elastic compliance

14 T. Sasaki et al. fatigue damage due to the pre-fatigue load influenced elastic deformation behavior as well as the acoustic velocity. However, the acoustic measurement suggests the increase in the elasticity along the tensile direction by compressive residual stress (Fig. 2.6), and this is inconsistent with the increase in the elastic compliance d"yy/dF. The discrepancy between the acoustic and the optical measurement can be explained by taking into consideration the effect of internal force by residual stress field described in another work [13]. The neck part of specimen is initially compressed by the surrounding region including both grip of specimen. When the specimen is stretched, the restoring force acts on the compressed region, resulting in decreasing the external tensile force. Consequently, the value d"yy/dFin the compressed region decreases. At the same time, the heterogeneity of residual stress in both side of the neck part of specimen may cause bending deformation. In the latter fatigue stage of NP > 10 3, the residual stress is released by crack initiation, leading to the predominant shear deformation (Fig. 2.11). 2.4 Conclusion The influence of fatigue damage on the elastic response of aluminum alloy has been investigated through acoustic wave velocity measurement and visualization of macroscopic deformation behavior using ESPI. In the earlier fatigue stage of prefatigue cycle NP < 10 3, the change in the acoustic velocities suggested an increase of compressive residual stress along the tensile direction induced by the localized plastic deformation. On the other hand, the visualization of macroscopic deformation using ESPI demonstrated that strain heterogeneity in the macroscopic elastic regime was enhanced with increasing the pre-fatigue cycle, NP. We infer that the residual stress induced by the fatigue cyclic load influenced to the macroscopic deformation behavior. These results indicate that the fatigue damage at the earlier fatigue stage due to the localized plastic deformation can be detected by the macroscopic deformation behavior using ESPI. References 1. Ogura, K., Miyoshi, Y., Kayama, M.: A study of X-ray analysis of fatigue fracture surface. Eng. Fract. Mech. 22, 123 (1985) 2. Steuwer, A., Edwards, L., Pratihar, S., Ganguly, S., Peel, M., Fitzpatrick, M.E.: In situ analysis of cracks in structural materials using synchrotron X-ray tomography and diffraction. Nucl. Instrum. Methods Phys. Res. B. 246, 246 (2006) 3. Steuwer, A., Rahman, M., Shterenlikht, A., Fitzpatrick, M.E., Edwards, L., Withers, P.J.: The evolution of crack-tip stresses during a fatigue overload event. Acta Mater. 58, 4039 (2010) 4. Moorth, V., Jayakumar, T., Raj, B.: Influence of microstructure on acoustic emission behavior during stage 2 fatigue crack growth in solution annealed, thermally aged and weld specimens of AISI type 316 stainless steel. Mater. Sci. Eng. A212, 212 (1996) 5. Hasegawa, S., Sasaki, T., Yoahida, S., Hebert, S.L.: Analysis of fatigue of metals by electronic speckle pattern interferometry. Conf. Proc. Soc. Exp.Mech. 3, 127 (2014) 6. Sasaki, T., Hasegawa, S., Yoahida, S.: Fatigue Damage Analysis of Aluminum Alloy by ESPI. Conf. Proc. Soc. Exp. Mech. 9, 147 (2015) 7. Stratoudaki, T., Ellwood, R., Shrples, S., Clark, M., Somekh, M.G.: Measurement of material nonlinearity using surface acoustic wave parametric interaction and laser ultrasonics. J. Acoust. Soc. Am. 129(4), 1721 (2011) 8. Rivière, J., Remillieux, M.C., Ohara, Y., Anderson, B.E., Haupert, S., Ulrich, T.J., Johnson, P.A.: Dynamic acousto-elasticity in a fatiguecracked sample. J. Nondestruct. Eval. 33, 216–225 (2014). doi:10.1007/s10921-014-0225-0 9. Su, Z., Zhou, C., Hong, M., Cheng, L., Wang, Q., Qing, X.: Acousto-ultrasonics-based fatigue damage characterization: linear versus nonlinear signal features. Mech. Syst. Signal Process. 42, 25 (2014) 10. Eira, J.N., Vu, Q.A., Lott, M., Payá, J., Garnier, V., Payan, C.: Dynamic acousto-elastic test using continuous probe wave and transient vibration to investigate material nonlinearity. Ultrasonics. 69, 29 (2016) 11. Yoshida, S., Sasaki, T., Craft, S., Usui, M., Haase, J., Becker, T., Park, I.-K.: Stress analysis on welded specimen with multiple methods. Conf. Proc. Soc. Exp. Mech. 3, 143 (2015) 12. Toda, H., Fukuoka, H., Aoki, Y.: R-value acoustielastic analysis of residual stress in a seem plate. Jpn. J. Appl. Phys. 23, 86 (1984) 13. Yoshida, S., Miura, F., Sasaki, T., Rouhi, S.: Optical analysis of residual stress with minimum invasion. In: Conference and Exposition on Experimental and Applied Mechanics, Indianapolis, USA, #141 (2017) Tomohiro Sasaki Associate professor, The topics includes fatigue analysis, measurement of welding induced residual stress metals, using optical and acoustical techniques.

Chapter 3 Early Strain Localization in Strong Work Hardening Aluminum Alloy (2198 T3): 3D Laminography and DVC Measurement Ante Buljac, Lukas Helfen, François Hild, and Thilo F. Morgeneyer Abstract The effect of strain hardening on localization in front of a notch is assessed by following the interactions between strain concentrations, damage, initial microstructure and grain orientations. A CT-like specimen made of strong work hardening 2198 T3 aluminum alloy is subjected to an in situ synchrotron laminography experiment. Kinematic fields are measured via digital volume correlation. The final results are bulk displacement and strain fields including their corresponding resolutions. The reported results refer to the portion of the specimen around 1 mm away from the notch root. With the selected spatial resolution, damage nucleation and growth is evaluated in strained bands until the very end of the loading process. Keywords Digital Volume Correlation (DVC) • Flat-to-slant transition • High work hardening material • Laminography • Plastic flow 3.1 Introduction One of the examples that summarize well the current challenges in ductile damage understanding and modeling is ductile tearing. It has been reported [1–6] that during mode I opening of Compact Tension (CT) specimens, the initial crack starts to propagate normal to the loading direction but then tilts and continues in a slant manner as a combination of modes I and III. The investigation of the origin for such behavior has its engineering relevance since it has been shown that mixed-mode I/III leads to reduced toughness when compared to pure mode I fracture [7]. The parallel use of laminography [8] and global Digital Volume Correlation (DVC) [9] enables in situdisplacement fields to be measured at the microscale. Laminography as a non-destructive imaging technique allows flat specimens to be analyzed (Fig. 3.1a) and wider stress states to be achieved when compared with tomography. Thanks to DVC, bulk displacement fields can be measured and strain fields calculated [10]. Up to now, each new portion of the results obtained by laminography and DVC reveals interesting phenomena at micrometer resolutions. This is per se a strong motivation for further analyses on other aluminium alloys. However, to be consistent it was decided to proceed in a systematic manner by selecting a specific family of alloys using different heat treatments. In particular, aluminum alloys AA2139 and AA2198 have been studied [10–14]. Representing the latest generation of aeronautical alloys, the understanding of the underlying failure mechanisms is of great interest. Extensive analyses on CT-like specimen made of AA2198 T8 [11, 13] have shown that in the zone close to the notch root, i.e. 800 m from the notch [11] and even in its immediate vicinity [13], strained bands appeared early in A. Buljac ( ) Laboratoire de Mécanique et Technologie (LMT), ENS Paris-Saclay / CNRS / Université Paris-Saclay, 61 avenue du Président Wilson, 94235, Cachan Cedex, France MINES ParisTech, PSL Research University, Centre des Matériaux, CNRS UMR 7633, BP 87, 91003, Evry, France e-mail: buljac@lmt.ens-cachan.fr L. Helfen ANKA/Institute for Photon Science and Synchrotron Radiation, Karlsruhe Institute of Technology (KIT), 76131, Karlsruhe, Germany European Synchrotron Radiation Facility (ESRF), 38043, Grenoble, France F. Hild Laboratoire de Mécanique et Technologie (LMT), ENS Paris-Saclay / CNRS / Université Paris-Saclay, 61 avenue du Président Wilson, 94235, Cachan Cedex, France T.F. Morgeneyer MINES ParisTech, PSL Research University, Centre des Matériaux, CNRS UMR 7633, BP 87, 91003, Evry, France © The Society for Experimental Mechanics, Inc. 2018 L. Lamberti et al. (eds.), Advancement of Optical Methods in Experimental Mechanics, Volume 3, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-63028-1_3 15

16 A. Buljac et al. Fig. 3.1 (a) Schematic representation of the laminography technique with the loading device and CT-like sample; (b) early strain field from slanted region shown together with the position of the final failure illustrated as height map the loading history. Plane strain conditions in the crack propagation direction predicted in numerical simulations [15] have been confirmed by kinematic measurements [13] while through thickness equivalent strain distributions varied significantly. Slant strained bands appeared well before damage, i.e. plastic flow is very heterogeneous before any significant signs of void nucleation and growth is measured at micrometer resolutions. The origin and observed behavior (i.e. activation and deactivation) of strained bands at the microscale still remains unclear. The T8 heat treatment induces relatively high yield stress followed by low work hardening. Low work hardening materials are believed to be prone to flow localization [16]. Following the same logic, strong work hardening materials should be more resistant to the flow localization. However, this was not the case for another aluminum alloy (i.e. AA2139 T3). Numerous strain bands were observed. Their intermittent activity and pattern were two key findings [14]. Further, damage set in very late during loading. Since these two alloys were different, the question remains open for AA2139 with T8 treatment and AA2198 under T3 condition. The latter is studied herein. 3.2 Kinematic Fields and Damage Micromechanisms In this work, results obtained for a CT-like specimen made of AA2198 T3 are presented. The T3 heat-treatment results in a microstructure responsible for a strong work hardening behavior, which is the key feature for conducting such analyses. Strong work hardening and high strains to failure indicate low level damage development and subsequent late softening phases. Logically, this should be promoted by homogeneous strain flow with less strain heterogeneities. Hence, the strain fields in this high work hardening material are analyzed in the work. Moreover, since similar analyses exist for the T8 heat-treatment [11], the influence of the latter is also studied. The strain fields and damage micromechanisms in the slant region 1 mm from the notch root as well as in the region closer to the notch root are presented in the work. Despite strong work hardening, the slant strained bands occur early on in the loading history before any signs of damage onset. Interestingly, void growth inside and outside the bands does not differ

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