River Rapids Conference Proceedings of the Society for Experimental Mechanics Series Optical Measurements, Modeling, and Metrology, Volume 5 Tom Proulx Proceedings of the 2011 Annual Conference on Experimental and Applied Mechanics River Publishers
Conference Proceedings of the Society for Experimental Mechanics Series
River Publishers Tom Proulx Editor and Applied Mechanics Proceedings of the 2011 Annual Conference on Experimental Optical Measurements, Volume 5 Modeling, and Metrology,
Published, sold and distributed by: River Publishers Broagervej 10 9260 Gistrup Denmark www.riverpublishers.com ISBN 978-87-7004-857-6 (eBook) Conference Proceedings of the Society for Experimental Mechanics An imprint of River Publishers © The Society for Experimental Mechanics, Inc. 2011 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 Optical Measurements, Modeling, and Metrology represents one of eight volumes of technical papers presented at the Society for Experimental Mechanics Annual Conference & Exposition on Experimental and Applied Mechanics, held at Uncasville, Connecticut, June 13-16, 2011. The full set of proceedings also includes volumes on Dynamic Behavior of Materials, Mechanics of Biological Systems and Materials, Mechanics of Time-Dependent Materials and Processes in Conventional and Multifunctional Materials; MEMS and Nanotechnology; Experimental and Applied Mechanics, Thermomechanics and Infra-Red Imaging, and Engineering Applications of Residual Stress. Each collection presents early findings from experimental and computational investigations on an important area within Experimental Mechanics. The papers comprising Optical Measurements, Modeling and, Metrology were taken from the general call for papers as well as sessions organized by: E. Maire, MATEIS-INSA, S. Yoshida, Southeastern Louisiana University and C.A. Sciammarella, Illinois Institute of Technology/Northern Illinois University; R. Rodriguez-Vera, Centro de Investigaciones en Optica A.C. Among the topics included in this volume are: 3D Imaging Applied to Experimental Mechanics Modeling and Numerical Analysis in Optical Methods Identification from Full-field Measurements Recent Advances in Displacement-Metrology Methods Phase Unwrapping, Phase Stepping, and High Speed Camera Calibration Dynamic and Quasi Dynamic Measurements Digital Image Correlation The Society thanks the authors, presenters, organizers and session chairs for their participation and contribution to this volume. The opinions expressed herein are those of the individual authors and not necessarily those of the Society for Experimental Mechanics, Inc. Bethel, Connecticut Dr. Thomas Proulx Society for Experimental Mechanics, Inc
Contents 1 3D Structures of Alloys and Nanoparticles Observed by Electron Tomography 1 K. Sato, K. Aoyagi, T.J. Konno, Tohoku University 2 Damage Characterization in Dual-phase Steels Using X-ray Tomography 11 C. Landron, E. Maire, J. Adrien, INSA-Lyon, MATEIS; O. Bouaziz, ArcelorMittal Research 3 19 T.F. Morgeneyer, Mines ParisTech; L. Helfen, ANKA/Institute for Synchrotron Radiation/European 4 Understanding the Mechanical Behaviour of a High Manganese TWIP Steel by the Means of in Situ 3D X ray Tomography 27 D. Fabrègue, C. Landron, Université de Lyon, CNRS/INSA-Lyon; C. Béal, Université de Lyon, CNRS/INSA-Lyon/ArcelorMittal Research; X. Kleber, E. Maire, Université de Lyon, CNRS/INSA-Lyon; M. Bouzekri, ArcelorMittal Research 5 Mechanical Properties of Monofilament Entangled Materials 33 L. Courtois, E. Maire, M. Perez, MATEIS UMR 5510 - INSA Lyon; Y. Brechet, D. Rodney, Domaine Universitaire 6 Computed Tomography 39 O. Caty, F. Gaubert, Laboratoire des Composites Thermostructuraux/LCTS; G. Hauss, Institut de Chimie et de la Matière Condensée de Bordeaux; G. Chollon, Laboratoire des Composites Thermostructuraux/LCTS 7 Multiaxial Stress State Assessed by 3D X-ray Tomography on Semi-crystalline Polymers 47 8 Effect of Porosity on the Fatigue Life of a Cast al Alloy 55 N. Vanderesse, J.-Y. Buffiere, E. Maire, Université de Lyon – INSA; A. Chabod, Centre Technique des Industries de la Fonderie 9 Fatigue Mechanisms of Brazed Al-Mn Alloys Used in Heat Exchangers 63 A. Buteri, Université de Lyon/Alcan CRV; J. Réthoré, J-Y. Buffière, D. Fabrègue, Université de Lyon; E. Perrin, S. Henry, Alcan CRV In-situ Synchrotron-radiation Computed Laminography Observation of Ductile Fracture J. Besson, Mines Paris Tech L. Laiarinandrasana, T.F. Morgeneyer, H. Proudhon, Mines Paris Tech H. Proudhon, Mines ParisTech; F. Xu, T. Baumbach, ANKA/Institute for Synchrotron Radiation; Synchrotron Radiation Facility; I. Sinclair, University of Southampton; F. Hild, LMT-Cachan; vii Characterisation of Mechanical Properties of Cellular Ceramic Materials Using X-ray
viii 10 Three Dimensional Confocal Microscopy Study of Boundaries between Colloidal Crystals 69 E. Maire, INSA-Lyon; M. Persson Gulda, N. Nakamura, K. Jensen, E. Margolis, C. Friedsam F. Spaepen, Harvard University 11 Scale Independent Fracture Mechanics 75 S. Yoshida, D. Bhattarai, T. Okiyama, K. Ichinose, Southeastern Louisiana University 12 Consistent Embedding: A Theoretical Framework for Multiscale Modelling 83 K. Runge, University of Florida 13 Analysis of Crystal Rotation by Taylor Theory 91 M. Morita, O. Umezawa, Yokohama National University 14 97 J. Pontes, Federal University of Rio de Janeiro; D. Walgraef, Université Libre de Bruxelles; C.I. Christov, University of Louisiana at Lafayette 15 Photoelastic Determination of Boundary Condition for Finite Element Analysis 109 S. Yoneyama, S. Arikawa, Y. Kobayashi, Aoyama Gakuin University 16 Discussion on Hybrid Approach to Determination of Cell Elastic Properties 119 M.C. Frassanito, L. Lamberti, A. Boccaccio, C. Pappalettere, Politecnico di Bari 17 125 A.H. Huhtala, S. Bossuyt, Aalto University 18 Assessment of Inverse Procedures for the Identification of Hyperelastic Material Parameters 131 M. Sasso, G. Chiappini, Università Politecnica delle Marche; M. Rossi, Arts et Métiers ParisTech; G. Palmieri, Università degli Studi e-Campus 19 Digital Image Correlation Through a Rigid Borescope 141 P.L. Reu, Sandia National Laboratories 20 Scale Independent Approach to Strength Physics and Optical Interferometry 147 S. Yoshida, Southeastern Louisiana University 21 Optical Techniques That Measure Displacements: A Review of the Basic Principles 155 C.A. Sciammarella, Northern Illinois University 22 Techniques 181 23 Machined Silicon Nitride 187 F.M. Sciammarella, M.J. Matusky, Northern Illinois University 24 Analysis of Speckle Photographs by Subtracting Phase Functions of Digital Fourier Transforms 199 K.A. Stetson, Karl Stetson Associates, LLC Numerical Solution of the Walgraef-aifantis Model for Simulation of Dislocation Dynamics in Materials Subjected to Cyclic Loading Mesh Refinement for Inverse Problems with Finite Element Models Studying Phase Transformations in a Shape Memory Alloy with Full-field Measurement D. Delpueyo, M. Grédiac, X. Balandraud, C. Badulescu, Clermont Université Correlation Between Mechanical Strength and Surface Conditions of Laser Assisted
ix 25 Measurement of Residual Stresses in Diamond Coated Substrates Utilizing Coherent Light Projection Moiré Interferometry 209 C.A. Sciammarella, Northern Illinois University; A. Boccaccio, M.C. Frassanito, L. Lamberti, C. Pappalettere, Politecnico di Bari 26 Automatic Acquisition and Processing of Large Sets of Holographic Measurements in Medical Research 219 E. Harrington, Worcester Polytechnic Institute; C. Furlong, Worcester Polytechnic Institute/Massachusetts Eye and Ear Infirmary/Harvard Medical School; J.J. Rosowski, 27 Adaptative Reconstruction Distance in a Lensless Digital Holographic Otoscope 229 J.M. Flores-Moreno, Worcester Polytechnic Institute/Centro de Investigaciones en Optica A. C.; C. Furlong, Worcester Polytechnic Institute/Massachusetts Eye and Ear Infirmary/MIT-Harvard Division of Health Sciences and Technology; J.J. Rosowski, Massachusetts Eye and Ear Infirmary 28 3D Shape Measurements With High-speed Fringe Projection and Temporal Phase Unwrapping 235 M. Zervas, C. Furlong, E. Harrington, I. Dobrev, Worcester Polytechnic Institute 29 Measuring Local Mechanical Properties of Membranes Applying Coherent Light Projection Moiré Interferometry 243 F.M. Sciammarella, C.A. Sciammarella, Northern Illinois University; L. Lamberti, Politecnico di Bari 30 Experimental Analysis of Foam Sandwich Panels With Projection Moiré 249 A. Boccaccio, C. Casavola, L. Lamberti, C. Pappalettere, Politecnico di Bari 31 Panoramic Stereo DIC-based Strain Measurement on Submerged Objects 257 K. Genovese, L. Casaletto, Università degli Studi della Basilicata; Y.-U. Lee, J.D. Humphrey, Yale University 32 Advances in the Measurement of Surfaces Properties Utilizing Illumination at Angles Beyond Total Reflection 265 C.A. Sciammarella, F.M. Sciammarella, Northern Illinois University; L. Lamberti, Politecnico di Bari 33 Filters with Noise/Phase Jump Detection Scheme for Image Reconstruction 273 J.-F. Weng, Y.-L. Lo, National Cheng Kung University 34 An Instantaneous Phase Shifting ESPI System for Dynamic Deformation Measurement 279 T.Y. Chen, C.H. Chen, National Cheng Kung University 35 Development of Linear LED Device for Shape Measurement by Light Source Stepping Method 285 Y. Oura, M. Fujigaki, A. Masaya, Wakayama University; Y. Morimoto, Moire Institute Inc. 36 Calibration Method for Strain Measurement Using Multiple Cameras in Digital Holography 293 M. Fujigaki, R. Nishitani, Wakayama University 37 Performance Assessment of Strain Measurement With an Ultra High Speed Camera 299 M. Rossi, Arts et Métiers ParisTech; R. Cheriguene, Université Paul Verlaine de Metz; F. Pierron, Arts et Métiers ParisTech; P. Forquin, Université Paul Verlaine de Metz dical School Massachusetts Eye and Ear Infirmary/Harvard Medical School/MIT-Harvard Division of Health Sciences and Technology; J.T. Cheng, Massachusetts Eye and Ear Infirmary/Harvard Me
x 38 Rigid Body Correction Using 3D Digital Photogrammetry for Rotating Structures 307 T. Lundstrom,, C. Niezrecki, P. Avitabile, University of Massachusetts Lowell 39 Development of Sampling Moire Camera for Landslide Prediction by Small Displacement Measurement 323 M. Nakabo, M. Fujigaki, Wakayama University; Y. Morimoto, Moire Institute Inc.; Y. Sasatani, H. Kondo, T. Hara, Wakayama University 40 Energy Dissipation in Impact Absorber 331 S. Ekwaro-Osire, I. Durukan, F.M. Alemayehu, Texas Tech University; 41 Mechanics Behind 4D Interferometric Measurement of Biofilm Mediated Tooth Decay 337 M.S. Waters, National Institute of Standards and Technology; B. Yang, American Denal Association Foundation; N.J. Lin, S. Lin-Gibson, National Institute of Standards and Technology 42 Validating Road Profile Reconstruction Methodology Using ANN Simulation on Experimental Data 345 H.M. Ngwangwa, University of South Africa; P.S. Heyns, H.G.A. Breytenbach, P.S. Els, University of Pretoria 43 Electro-optical Property of Sol-gel-derived PLZT7/30/70 Thin Films 359 J.-F. Lin, J.-S. Jeng, W.-R. Chen, Far East University 44 Polarimetry 365 T.-T.-H. Pham, Y.-L. Lo, National Cheng Kung University 45 Measurement of Creep Deformation in Stainless Steel Welded Joints 371 46 Thermal Deformation Measurement in Thermoelectric Coolers by ESPI and DIC Method 379 W.-C. Wang, T.-Y. Wu, National Tsing Hua University 47 Structural Health Monitoring Using Digital Speckle Photography 393 F.-P. Chiang, J.-D. Yu, Stony Brook University 48 Determining the Strain Distribution in Bonded and Bolted/Bonded Composite Butt Joints Using the Digital Image Correlation Technique and Finite Element Methods 401 D. Backman, G. Li, T. Sears, National Research Council Canada 49 Improved Spectral Approach for Continuous Displacement Measurements From Digital Images 407 F. Mortazavi, M. Lévesque, École Polytechnique de Montréal; I. Villemure, École Polytechnique de Montréal/Sainte-Justine University Hospital Center 50 Experimental Testing (2D DIC) and FE Modelling of T-stub Model 415 J.F. Cardenas-García, United States Patent and Trademark Office Decoupling Six Effective Parameters of Anisotropic Optical Materials Using Stokes Y. Sakanashi, S. Gungor, P.J. Bouchard, The Open University D. Carazo Alvarez, University of Jaén; M. Haq, Michigan State University; J.D. Carazo Alvarez, University of Jaén; E. Patterson, Michigan State University
3D structures of alloys and nanoparticles observed by electron tomography Kazuhisa Sato*, Kenta Aoyagi, and Toyohiko J. Konno Institute for Materials Research, Tohoku University 2-1-1 Katahira, Aoba, Sendai, Miyagi 980-8577, Japan *E-mail address: ksato@imr.tohoku.ac.jp ABSTRACT 3D structures of bulk alloys and nanoparticles have been studied by means of electron tomography using scanning transmission electron microscopy (STEM). In the case of nanoparticles of Fe-Pd alloy, particle size, shape, and locations were reconstructed by weighted backprojection (WBP), as well as by simultaneous iterative reconstruction technique (SIRT). We have also estimated the particle size by simple extrapolation of tilt-series original data sets, which proved to be quite powerful. We demonstrate that WBP yields a better estimation of the particle size in the z direction than SIRT does, while the latter algorithm is superior to the former from the viewpoints of surface roughness and dot-like artifacts. In contrast, SIRT gives a better result than WBP for the reconstruction of plate-like precipitates in Mg-Dy-Nd alloys, in respect of the plate thickness perpendicular to the z direction. We also show our recent results on the 3D-tomographic observations of microstructures in Ti-V-Al, Ti-Nb, Cu-Ag, and Co-Ni-Cr-Mo alloys obtained by STEM tomography. 1. Introduction Our understanding on the microstructure in metals and alloys has been advanced with the progress of transmission electron microscopy (TEM) and electron diffraction. Thus, for example in the fifties, dislocation theories were directly confirmed by electron imaging based on the diffraction contrasts [1]. This technique immediately found enormous areas of applications in materials science, and utilized for instance to clarify the phase transformation behavior in a number of alloy systems. Other applications of TEM include of course high-resolution transmission electron microscopy (HRTEM) and scanning transmission electron microscopy (STEM) [2]. The images obtained by these techniques are projections of three dimensional (3D) objects; and in order to better understand the nature of phase transformation behavior, for example, a direct 3D observation is much needed. In this respect, recent advance in 3D-tomography (x-ray, electron, and atom probe tomography) has opened a new prospect. Electron tomography, especially its applications to materials science, is a novel technique, which can retrieve 3D structural information usually missing in TEM and STEM. A 3D structure different imaging techniques: bright-field (BF) TEM [3], dark-field (DF) TEM [4, 5], atomic number (Z) contrast of STEM [6], energy-filtered TEM [6] and electron holography [7]. The recent progress in this field has been summarized in essential for subsequent 3D reconstruction. Some model simulations on the accuracy of reconstruction have been fundamental interests in the electron tomography [10-13]. Here, we report some of our recent studies on magnetic can be reconstructed by processing a tilt-series of electron micrographs with mass-thickness contrasts, formed by several 1 review articles [8, 9]. In all the techniques, acquisition of clear contrast images and accurate alignments of the tilt axis are T. Proulx (ed.), Optical Measurements, Modeling, and Metrology, Volume 5, Conference Proceedings of the Society for Experimental presented in detail [6]. An investigation for a novel method to quantify 3D reconstructed structures is one of the Mechanics Series 9999999, DOI 10.1007/978-1-4614-0228-2_1, © The Society for Experimental Mechanics, Inc. 2011
nanoparticles and bulk alloys, where electron tomography has played an important role in identifying the 3D structures and spatial distribution of nanocrystals, dislocations, and precipitates. 2. Experimental Procedures We employed BF and high-angle annular dark-field (HAADF) imaging modes of STEM for the tilt-series acquisition using an FEI Titan 80-300 (S)TEM operating at 300 kV with a field emission gun. We set the beam convergence to be 10-14mrad in half-angle, taking into account the spherical aberration coefficient (1.2 mm) of the pre-field of objective lens. The Xplore3D software (FEI Co. Ltd) was used for data sets acquisition taking the dynamic focus into consideration. A single-tilt holder (Fischione model 2020) and a triple-axes holder (Mel-Build model HATA-8075) were used for the tilt series acquisition with the maximum tilt angle of 70º. Alignment of the tilt axis for the obtained data set by an iterative cross-correlation technique and subsequent 3D reconstruction were performed by using the Inspect3D software package (FEI Co. Ltd). As for the algorithm for 3D reconstruction, we employed weighted back-projection (WBP) [14], as well as simultaneous iterative reconstruction technique (SIRT) [15]. The reconstructed 3D density data were then visualized using the AMIRA 4.1 software (VISAGE IMAGING). 3. Results and Discussion 3.1 Shapes and distribution of FePd nanoparticles Figure 1a shows a series of STEM-HAADF images taken at different tilt angles with the detector inner half angle of 60mrad. The tilt-series was observed sequentially from 0 to -70º and then 0 to +70 º. The tilt angle increments were set 2º for angle ranges of 0 to |50|º, and 1º for |50| to |70|º. Out of this data set, we employed, by careful inspection of contrasts, images taken at tilt angles between -66 and +64º for later 3D reconstruction. As seen, the apparent particle length in the y-direction becomes shorter as the tilting angle increases. A nanoparticle enclosed by the circle in the figure is one of the examples to demonstrate the reduction of the particle image in the y-direction. To examine an accuracy of a reconstructed particle height in the z-direction, we therefore measured projected particle length in the y-direction as a function of tilt-angle, and deduced the particle height by extrapolating the projected length to the value expected at the tilt-angle of 90º. The results are plotted in Fig.1b. The projected length clearly decreases with tilting, which indicates that the particle height is actually shorter than the in-plane diameter. Here, the extrapolation was performed by fitting the data points at angles higher than 40º using cosine of the tilt angle (α), because of the fact that the projected y-length is proportional to cosα at high angles when the particle height is shorter than the diameter. Using the aforementioned procedure, here termed “tilt-series extrapolation (TSE) method”, we obtained a relation, which summarizes the relation between particle diameter and thickness estimated by using several different techniques (Fig.2a). Solid triangles and solid squares indicate the results obtained from the reconstructed images based on SIRT and WBP, respectively. In the present study, 20 iterations were carried out in SIRT to minimize the differences between the original projected series and the calculated ones. The large error bar for WBP indicates a possible elongation of dz = 4.1 nm [13]. Therefore, we divided the apparent particle thickness (tz), which was deduced from the 3D volumes based on WBP, by the elongation factor (eyz=1.42) [12] for the present experimental condition. The results, tz / eyz, are indicated by open squares. Solid circles denote the deduced particle thickness measured from the TSE method. A solid curve indicates the previous result based on the electron holography [16]. Note that the deduced thicknesses obtained by the TSE agree well 2
with those obtained by WBP (tz / eyz) as well as those by electron holography. On the other hand, the thicknesses suggested by SIRT are much larger than the values deduced by the TSE method or electron holography. The apparent thickness predicted by WBP (tz) is close to the deduced values with an error of about 1-4 nm in thickness, without taking the elongation factor into consideration. Therefore, within a framework of single-axis tilt geometry, it is demonstrated in a semi-quantitative manner that the WBP gives a better result in terms of the accuracy of the particle length in the z-direction than that predicted by SIRT, despite the fact that the latter algorithm is superior to the former from the viewpoints of artifacts. Fig. 1 (a) A series of Z-contrast images taken at different tilt angles. (b) The analyzed particle length in the y-direction as a function of the tilt-angle. The particle length decreases as the tilt-angle increases towards 90º, indicating the fact that the particle height is shorter than the diameter. Extrapolation of particle length in the y-direction to the value expected at the tilt-angle α = 90º leads to an elucidation of the true particle height. Here, the extrapolation was performed by fitting the data points at angles higher than 40º using cosine of the tilt angle [13]. Fig. 2 (a) The relation between particle diameter and thickness (height) for the FePd nanoparticles estimated by using several different techniques. (b) Oblique-view of the reconstructed volume processed by SIRT (upper) and (c) WBP (lower). Large discrepancy in particle thickness (height) is apparent. The reconstructed volume is 75 × 75 × 36 nm3 [13]. 3
The difference in the particle height of the reconstructed results is pronounced when viewed from an oblique direction as shown in Fig.2b. Indeed SIRT gave particle heights, which are almost comparable to or even longer than the particle diameter (Fig.2b), while rather flat 3D shapes can be seen in the result by WBP (Fig.2c). Nanoparticles in the upper image (SIRT) show prolate 3D-shapes, i.e., elongated in the z-direction. The reason for this artifact is not clear at this moment. To reduce the artifacts, a minimization of the missing wedge will be most effective, which can be attained by increasing the maximum tilt-angle together with number of 2D-slice images as possible. Using the same experimental setup, recently we succeeded in reconstructing double-layer of 2nm-sized CoPt nanoparticles separated by a thin amorphous carbon film [18]. 3.2 Phase separation in Ti-V-Al alloy We have examined 3D morphology of α (hcp) and β (bcc) dual phase structure of a Ti-12mass%V-2mass%Al alloy after aging for 24 h at 500oC by means of STEM-HAADF tomography. In the present study, we set the inner half angle of the HAADF detector to be 30mrad to ensure a clear contrast during the tilt-series acquisition. This setting of a rather low angle may break the simple Z2 dependence of the HAADF-STEM images to some extent due to possible diffraction contrasts during the tilting. The tilt-series was obtained sequentially from 0 to -70° and then 0 to +70°. The angular tilt angle increments were set 2°. Out of this data set, we employed images taken at tilt angles between -62 and +62° for subsequent 3D reconstruction. Figure 3 shows one of the original images (Fig.3a) and corresponding reconstructed images processed by WBP (Fig.3b). Here, the x-axis is the tilt-axis, about which the specimen film is sequentially tilted towards the y-direction; while the primary beam incidence direction is parallel to the z-axis. Bright contrast region corresponds to the precipitated V-rich β phase (<40mass%V). A bird-view of the reconstructed volume is shown in Fig. 3c. The plate-like 3D shapes of β phase, precipitated by decomposition of hexagonal α’ martensites, has been successfully reconstructed. As seen in these images, general features projected onto the x-y plane, such as plate-like shape, size, and the location of precipitates, are clearly reconstructed. However, it is noted that floating dot-like artifacts are seen in the reconstructed volume, which can be attributed to a low signal to noise ratio and diffraction effects of the original tilt series STEM images. Fig.3 3D distribution of the β phase in Ti-12mass%V-2mass%Al after annealing for 24 h at 500oC [19]. (a) An original STEM-HAADF image. Bright regions correspond to the V-rich β phase. (b) Reconstructed images processed by WBP. (c) A bird-view of the reconstructed volume (690 × 720 × 375nm3). Plate-like structures correspond to the β precipitates. 4
3.3 Dislocations in a Ti-Nb alloy Figure 4 shows STEM-BF images of an as-quenched Ti-35mass%Nb alloy acquired during a tilt-series observation. The alloy composed of acicular orthorhombic α” martensites and bcc β phase [20]. In this observation, hh0 systematic reflections of the β phase (bcc) was set parallel to the tilt-axis of the triple-axes holder. As seen in the corresponding diffraction patterns, 110 reflection of the β phase is always excited during the tilt-series observation. The tilt-series was obtained sequentially from 0 to -70° and then 0 to +70° with the angular tilt angle increments of 2°. The reconstruction was carried out by WBP using 71 images. Figure 5 shows a snapshot of reconstructed image of dislocations observed in the β phase region. It is presumed that origin of these dislocations in the β phase can be attributed to the β−α” martensitic transformation at quenching. Detailed characterization of these dislocation structures is now in progress. Fig.4 STEM-BF images of an as-quenched Ti-35mass%Nb alloy acquired during a tilt-series observation (after tilt-axis correction). Corresponding diffraction patterns are shown in the inset, showing excitation of hh0 systematic row. Fig.5 Reconstructed 3D image of dislocations in an as-quenched Ti-35mass%Nb alloy processed by WBP from the tilt series of STEM-BF images in Fig.4. 5
3.4 Precipitates in Cu-Ag, Mg-Dy-Nd, and Co-Ni-Cr-Mo alloys Figure 6a and 6b show STEM-BF and HAADF images of a Cu-4at%Ag alloy aged at 450oC for 20min, respectively [21]. Discontinuous precipitation of Ag at grain boundary regions is clearly seen. Figure 6c and 6d are snapshots of reconstructed images of Ag precipitates processed by SIRT. The reconstruction was carried out using 70 individual images. As can be seen in these snapshots, the precipitates possess a “flat” rod shape, i.e., the cross-section of the rods are not circular but elliptic. We found that the aspect ratio or the ellipticity is more than two, the origin of which is still under question. Fig.6 STEM-BF (a) and HAADF (b) images of a Cu-4at%Ag alloy aged at 450oC for 20min, showing discontinuous precipitation of Ag at grain boundary regions. (c, d) Reconstructed volumes of the Ag precipitates processed by SIRT. Fig.7 Reconstructed images of β’ precipitates in a Mg-7mass%Dy-3mass%Nd alloy aged at 200oC for 30h. 6
Figure 7 shows reconstructed images of β’ precipitates in a Mg-7mass%Dy-3mass%Nd alloy aged at 200oC for 30h processed by SIRT [22]. The tilt-series was observed sequentially from 0 to -70º and then 0 to +70 º. The tilt angle increments were set 2º for angles of 0 to |40|º, and 1º for |40| to |70|º. We can observe distribution of plate-like precipitates, separated by 10-50nm. Note that in the reconstruction of plate-like precipitates, it was found that SIRT gives a better result than WBP does in respect of the plate thickness perpendicular to the z direction as well as a smooth surface with little apparent dot-like artifacts. Using the same experimental setup, we also observed 3D structures of lamellar precipitates in Co-Ni based superalloys as shown in Fig.8 [23]. Fig.8 STEM-HAADF image (a) and a snapshot of reconstructed 3D image (b) of a Co-Ni-Cr-Mo superalloy. 4. Conclusion We have studied 3D structures of nanoparticles and bulk alloys by means of electron tomography using STEM. In the case of FePd nanoparticles, we demonstrate that WBP yields a better estimation of the particle size in the z direction than SIRT does, most likely due to the presence of a missing wedge in the original data set, while the latter algorithm is superior to the former from the viewpoints of surface roughness and dot-like artifacts. Dislocation network in β phase of a Ti-Nb alloy was visualized by STEM-BF tomography exciting hh0 systematic reflections using a triple-axes holder. We also observed 3D structures and spatial distribution of precipitates in Ti-V-Al, Cu-Ag, Mg-Dy-Nd, and Co-Ni-Cr-Mo alloys by means of single-axis STEM-HAADF tomography. For the reconstruction of plate-like precipitates in bulk Mg-Dy-Nd alloys, it was found that SIRT gives a better result than WBP does in respect of the plate thickness perpendicular to the z direction. Acknowledgments The authors would like to express their sincere thanks to Prof. A. Chiba, Dr. H. Matsumoto, and Dr. S. Semboshi, Tohoku University, for their kind supplying samples of Ti-V-Al and Ti-Nb alloys used in the present study, and also to Dr. K. Inoke, FEI Co. Japan Ltd., Mr. E. Aoyagi, and Mr. Y. Hayasaka, Tohoku University, for their help using TEM. This work was partially supported by a Grant-in-Aid for Young Scientists (B) (Grant No. 19760459) from the Ministry of Education, Culture, Sports, Science, and Technology, Japan, a Grant from the New Energy and Industrial Technology Development Organization (NEDO, 08E51003d), and by the Nano-Materials Functionality Creation Research Project in IMR (2008-2009). TJK appreciates supports from JFE-21 century foundation. 7
References [1] Hirsch P, Howie A, Nicholson R, Pashley DW, Whelan MJ, Electron Microscopy of Thin Crystals (Krieger, Florida, 1977). [2] Buseck P, Cowley JM, Eyring L, (ed.), High-Resolution Transmission Electron Microscopy and Associated Techniques (Oxford, New York, 1992). [3] Shirai M, Horiuchi T, Horiguchi A, Matsumura S, Yasuda K, Watanabe M, Masumoto T, Morphological change in FePt nanogranular thin films induced by irradiation with 2.4MeV Cu2+ ions: electron tomography observation, Mater. Trans. 47(1), 52-58 (2006). [4] Kimura K, Hata S, Matsumura S, Horiuchi T, Dark-field transmission electron microscopy for a tilt series of ordering alloys: toward electron tomography, J. Electron Microscopy 54(4), 373-377 (2005). [5] Barnard JS, Sharp J, Tong JR, Midgely PA, High-resolution three-dimensional imaging of dislocations, Science 313, 319 (2006). [6] Midgley PA, Weyland M, 3D electron microscopy in the physical sciences: the development of Z-contrast and EFTEM tomography, Ultramicroscopy 96, 413-431 (2003). [7] Twitchett AC, Yates TJV, Dunin-Borkowski RE, Newcomb SB, Midgley PA, Three-dimensional electrostatic potential of a Si p-n junction revealed using tomographic electron holography, J. Phys. Conf. Ser. 26, 29-32 (2006). [8] Kübel C, Voigt A, Schoenmakers R, Otten M, Su D, Lee, Carlsson A, Bradley J, Recent advances in electron tomography: TEM and HAADF-STEM tomography for materials science and semiconductor applications, Microsc. Microanal. 11, 378-400 (2005). [9] Midgley PA, Dunin-Borkowski RE, Electron tomography and holography in materials science, Nature Mater. 8, 271-280 (2009). [10] Fujita T, Qian LH, Inoke K, Erlebacher J, Chen MW, Three-dimensional morphology of nanoporous gold, Appl. Phys. Lett. 92(25), 251902-1−251902-3 (2008). [11] Benlekbir S, Epicier T, Bausach M, Aouine M, Berhault G, STEM-HAADF electron tomography of palladium nanoparticles with complex shapes, Philos. Mag. Lett. 89(2), 145-153 (2009). [12] Alloyeau D, Ricolleau C, Oikawa T, Langlois C, Le Bouar Y, Loiseau A, Comparing electron tomography and HRTEM slicing methods as tools to measure the thickness of nanoaprticles, Ultramicrosc. 109, 788-796 (2009). [13] Sato K, Aoyagi K, Konno TJ, Three-dimensional shapes and distribution of FePd nanoparticles observed by electron tomography using HAADF-STEM, J. Appl. Phys. 107(2), 024304-1−024304-7 (2010). [14] Radermacher M, Weighted Back-Projection Method, in: Frank J. (ed.), Electron Tomography: Three-dimensional Imaging with the Transmission Electron Microscope (Plenum Press, New York, London, 1992). [15] Gilbert P, Iterative methods for the three-dimensional reconstruction of an object from projections, J. Theor. Biol. 36, 105-117 (1972). [16] Sato K, Hirotsu Y, Mori H, Wang Z, Hirayama T, Long-range order parameter of single L10-FePd nanoparticle determined by nanobeam electron diffraction, J. Appl. Phys. 98(2), 024308-1−024308-8 (2005). [17] Arslan I, Tong J, Midgley PA, Reducing the missing wedge: High-resolution dual axis tomography of inorganic materials, Ultramicrosc. 106, 994-1000 (2006). [18] Epicier T, Benlekbir S, Sato K, Tournus F, Konno TJ, "STEM-HAADF tomography and generalized stereoscopy 3D studies of nano-particles in Transmission Electron Microscopy", invited talk at MicroScience 2010 (session M2.1), 8
London, UK, June 29 – July 1, 2010. [19] Sato K, Matsumoto H, Kodaira K, Konno TJ, Chiba A, Phase transformation and age-hardening of hexagonal α’ martensite in Ti-12%V-2%Al alloys studied by TEM, J. Alloys Compd. 506, 607-614 (2010). [20] Semboshi S, Shirai T, Konno TJ, Hanada S, In-situ transmission electron microscopy observation on the phase transformation of Ti-Nb-Sn shape memory alloys, Metall. Mater. Trans. 39A, 2820-2829 (2008). [21] Shizuya E, Konno TJ, A study on age hardening in Cu-Ag alloys by transmission electron microscopy in Frontiers in Materials Science, edited by Fujikawa Y, Nakajima K, Sakurai T (Springer-Verlag, New York, 2008). [22] Konno TJ, Aoyagi K, Shizuya E, Lee JB, Sato K, Kiguchi T, Hiraga K, Phase transformation behavior in alloys viewed by 3D-tomography, Proc. 9th Asia-Pacific Microscopy Conference (APMC9), 227-228 (2008). [23] Konno TJ, Tadano T, Matsumoto H, Chiba A, Microstructure of Co-Ni based superalloys, Proc. 14th European Microscopy Congress (EMC2008), 2, 447-448 (2008). 9
Damage characterization in Dual-Phase steels using X-ray tomography C. Landron a, E. Maire a, J. Adrien a, O. Bouaziz b a INSA-Lyon, MATEIS UMR5510, 25 av. Capelle, 69621 Villeurbanne, France b ArcelorMittal Research, Voie Romaine, 57283 Maizieres-les-Metz Cedex, France ABSTRACT In-situ tensile tests have been carried out during X-ray microtomography imaging of dual-phase steels. Void nucleation has been quantified as a function of strain and triaxiality using the obtained 3D images. The Argon's criterion of decohesion has then been used in a model for nucleation in the case where martensite plays the role of inclusions. This criterion has been modified to include the local stress field and the effect of kinematic hardening present in such an heterogeneous material. 1 Introduction Ductile damage is characterized by a three step process: cavities first nucleate, then grow, until coalescence leads to the ductile fracture. The first step of nucleation has been extensively studied and modeled. Void nucleation is usually associated to the presence of a second phase, like particles or inclusions. In the latter case, the cavities appear close to the inclusions, either inside the particle or at the interface [1-3]. Dual-Phase steels (DP steels) containing hard martensite islands embedded in a ductile ferritic matrix, are such kind of materials promoting inhomogeneous nucleation. In DP steels, the main nucleation mechanism is the interface decohesion as experimentally observed by [4, 5]. To model this interface debonding, an energy criterion [2,6,7] is necessary for the creation of new surfaces and a stress criterion [1,8] or a strain criterion [9,10] is required for breaking the bonds. To combine the two criteria, numerical models using cohesive zones have also been developed [1113]. In order to be validated, these models have to be compared with key experiments. X-ray absorption microtomography is currently one of the most reliable ways to obtain quantitative three-dimensional (3D) information on damage [14,15]. In the present paper, damage in a DP steel is studied by in-situ tensile tests during X-ray microtomography imaging. Quantitative data is then used to validate an analytical modeling of void nucleation based on the Argon's criterion [1]. 2 Experimental procedure X-ray microtomography has been used in the present study to quantify damage during in-situ tensile tests. The method can be used for the imaging and the quantification of the microstructure of materials. Applications to study damage in ductile materials can be found in Refs. [14-16]. The tomography setup used is the one located at the ID15 beam line at the European Synchrotron Radiation Facility (ESRF) in Grenoble, France (more information is given in [17]). Tomography acquisition is carried out with a voxel size of (1.6µm)3. With such a resolution, the smallest observed voids have a diameter of almost 2µm. Smaller voids, not accounted in the quantification, do exist in the sample but may not play a major role in damage. The DP steel used for this study was cut from a 3 mm thick sheet obtained by hot rolling and thermal treatment. Its mechanical properties are given in Table 1. It has been checked by image analysis of optical micrographs of polished surfaces that the steel contains about 11% martensite. Axisymetric specimens were machined from the original sheet. Two kinds of specimen's shapes inspired by [18] were cut: two smooth samples and two samples with a 1 mm notch radius. The specimen's geometry is given in Fig.1. Each shape induces a different initial triaxiality. This allows us to study the effect of this important parameter on damage. Only the central part, 1.6 mm in height, is imaged during the present study. Table 1 Mechanical properties in tension of the studied DP steel Re (MPa) Rm (MPa) Ag (%) A (%) 366 603 17.7 26.6 The fractured samples were polished after the in situ tensile test down to their central plane and etched with a 2 pct nital solution. The samples were dipped in a solution of ethanol and placed into a ultrasound cleaner for a duration of 30 minutes T. Proulx (ed.), Optical Measurements, Modeling, and Metrology, Volume 5, Conference Proceedings of the Society for Experimental Mechanics Series 9999999, DOI 10.1007/978-1-4614-0228-2_2, © The Society for Experimental Mechanics, Inc. 2011 11
after the polishing to eliminate the possible fragments blunting the cavities. Light optical micrographs were then acquired in order to observe the nucleation sites. Fig.1 Tensile samples used: smooth specimen (a), 1mm radius notched specimen (b), 3D view (c) 3 Results and discussion 3-1 Damage characterization X-ray microtomography imaging has already been used in order to visualize and quantify damage in DP steel in [17]. The same procedure was used in this study: raw processing were performed with the ImageJ freeware [19]. Initial volumes were median filtered and simply thresholded to differentiate material from voids. Damage can be qualitatively observed in 2D using sections inside the volume as ones presented in Fig.2 or in 3D using a global view of the sample as ones showed in Fig.3. 3D visualization softwares allow one to have a transparent view of some of the voxels (for instance those located in the solid phase) and then lead to the possibility of seeing cavities inside the sample. Tomography volumes can also be employed to quantify damage appearing during the tensile test. As in [17], only the central part of the tensile specimen is used for this damage quantification. This sub-region was chosen to be a cubic volume of (300µm)3. Fig.4. shows this studied sub-region in a notched specimen of DP steel at several steps of deformation. This qualitative figure shows clearly that the number of cavities increases (nucleation) and that the size of the nucleated cavities also increases (growth) with the increase of strain. It is noticeable in this image that nucleation is a quantitatively important part of the damage progression in these materials, as evidenced already in [17]. Each pore of the volume is then subsequently labeled using a dedicated image processing plugin implemented in the ImageJ [19] freeware. The labeling plugin uses a binary image as input. It simply detects the 3D clusters of connected voxels and gives a label to each. The void density is calculated as the number of cavities per cubic millimeter in the sub-volume. The volume of each cavity is also measured as well as its dimensions permitting to quantitatively characterize the growth and the shape change of voids during the tensile deformation. Fig.2 Sections at the center of a notched strained specimen at various steps of deformation: εloc=0 (a), εloc=0.35 (b) and εloc=0.83 (c) 12
Fig.3 3-D views of a notched strained specimen at various steps of deformation: εloc=0 (a), εloc=0.35 (b) and εloc=0.83 (c). The outline of the specimen appears in gray and the cavities in red Fig.4 3-D views of damage at the center of a notched strained specimen at various steps of deformation: εloc=0 (a), εloc=0.35 (b) and εloc=0.83 (c) Some mechanical parameters were calculated using the outside shape of the specimen. The minimal section area S was measured in order to calculate the local strain εloc at each step using equation (1): εloc =ln S0 S (1) S0 being the initial section of the sample. This equation implies that the effect of porosity in the volume change of the sample is neglected in our analysis. The curvature radius Rnotch is also measured in order to determine the stress triaxiality T using equation (2), derived from the Bridgman analysis of notched bars [20]. T = 1 3 ln 1 a 2Rnotch (2) a being the radius of the minimal section, easily tractable from the value of S. Fig.5. shows the evolution of N, the number of voids per unit volume (expressed per cubic mm) in several DP steel samples with smooth and notched geometries. A very small amount of porosity (0.03%) can be detected before the tensile test, may be due to the fabrication process. The experimental results show that the triaxiality has a straightforward impact on the nucleation kinetic: void nucleation occurs earlier in notched samples inducing higher triaxiality than in smooth samples. Optical micrographs performed on the fractured specimens and given in Fig.6. show that most cavities are localized between the ferritic matrix and martensite islands and thus nucleate by decohesion of the ferrite/martensite interface as previously observed in [4, 5]. 13
Fig.5 Evolution of N, the number of cavities per cubic mm in the four studied samples measured during the in-situ tensile tests [21] Fig.6 Micrograph of fractured specimen. Voids appear in black, ferrite in light gray and martensite in dark gray [21] 3-2 Void nucleation modeling As demonstrated by [6], the energy criterion necessary for the creation of new surfaces at the inclusion/matrix interface is satisfied at the onset of plastic deformation in materials containing inclusions bigger than about 25 nm in diameter. Only a stress criterion will therefore be used to model the interface decohesion in DP steels as the observed inclusions are about 100 times larger than this. The Argon's criterion [1] is a critical stress criterion stating that the void nucleation occurs when a critical stress state, necessary for the interface decohesion, is reached in the material. This stress state involves a contribution of the hydrostatic stress σm and the equivalent stress σeq. σeq σm=σC (3) where σC is the interface strength, e.g. the maximum shear stress that the interface can support without breaking. The interest in using the Argon's criterion lies in the fact that it accounts for the triaxiality T (T being the ratio between σeq and σm ). T = σeq σm (4) Combining Eq. (3) and Eq. (4), the criterion can be expressed as: σeq1 T =σC (5) In the original Argon's criterion, the triaxiality used is the macroscopic triaxiality. However, decohesion is a local 14
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