STP 1359 Mixed-Mode Crack Behavior K J Miller and D L McDowell, Editors ASTM Stock #: STP1359 ASTM 100 Barr Harbor Drive West Conshohocken, PA 19428-2959 Printed in the U.S.A Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:52:19 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authoriz Library of Congress Cataloging-in-Publication Data Mixed-mode crack behavior / K.J Miller and D.L McDowell, editors p cm - - (STP ; 1359) Proceedings of the Symposium on Mixed-Mode Crack Behavior, held 5/6-7/98, Atlanta, Georgia "ASTM Stock #: STP1359." Includes bibliographical references and index ISBN 0-8031-2602-6 Fracture mechanics Mathematical models Congresses Materials Fatigue Mathematical models Congresses I Miller, K J (Keith John) I1 McDowell, David L., 1956III Symposium on Mixed-Mode Crack Behavior (1998 : Atlanta, Ga.) IV Series: ASTM special technical publication ; 1359) 99-37767 CIP TA409.M57 1999 620.1' 126 dc21 Copyright 1999 AMERICAN SOCIETY FOR TESTING AND MATERIALS, West Conshohocken, PA All rights reserved This material may not be reproduced or copied, in whole or in part, in any printed, mechanical, electronic, film, or other distribution and storage media, without the written consent of the publisher Photocopy Rights Authorization to photocopy items for internal, personal, or educational classroom use, or the internal, personal, or educational classroom use of specific clients, is granted by the American Society for Testing and Materials (ASTM) provided that the appropriate fee is paid to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, Tel: 508-750-8400; online: http://www.copyright.com/ Peer Review Policy Each paper published in this volume was evaluated by two peer reviewers and at least one editor The authors addressed all of the reviewers" comments to the satisfaction of both the technical editor(s) and the ASTM Committee on Publications The quality of the papers in this publication reflects not only the obvious efforts of the authors and the technical editor(s), but also the work of the peer reviewers In keeping with long standing publication practice, ASTM maintains the anonymity of the peer reviewers In keeping with longstanding publication practices, ASTM maintains the anonymity of the peer reviewers The ASTM Committee on Publications acknowledges with appreciation their dedication and contribution of time and effort on behalf of ASTM Printed in Philadelphia November 1999 Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:52:19 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized Foreword The Symposium on Mixed-Mode Crack Behavior was held 6-7 May 1998 in Atlanta, GA The symposium was sponsored by ASTM Committee E8 on Fatigue and Fracture and its Subcommittee E08.01 on Research and Education The symposium was chaired by Keith J Miller, of the University of Sheffield, and David L McDowell, of the Georgia Institute of Technology These men also served as editors for this resulting publication Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:52:19 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized Contents Overview vii C R A C K EXTENSION IN DUCTILE METALS UNDER M I X E D - M O D E LOADING Evaluation of the Effects of Mixed Mode I-II Loading to Elastic-Plastic Ductile Fracture of Metallic Materials A LAUKKANEN, K WALLIN AND R RINTIMAA The Crack Tip Displacement Vector Approach to Mixed-Mode Fracture-C DALLE DONNE A 21 Simple Theory for Describing the Transition Between Tensile and Shear Mechanisms in Mode I, II, III, and Mixed-Mode Fracture Y.-J CHAO AND X.-K ZHU 41 Further Studies on T* Integral for Curved Crack Growth e w LAM, A S KOBAYASHI~ S N ATLURI AND P W TAN Recommendations for the Determination of Valid Mode II Fracture Toughnesses K n c - - w m n s E AND J F KnLTHOF~ 58 74 A CTOD-Based Mixed-Mode Fracture Criterion F MA, X DENG, M A SUTTON AND J C NEWMAN, JR A Software Framework for Two-Dimensional Mixed Mode-I/II Elastic-Plastic Fracture M A JAMES AND D SWENSON 86 111 M I X E D - M O D E C R A C K GROWTH IN HETEROGENEOUS M A T E R I A L SYSTEMS Mixed-Mode Fracture Behavior of Silica Particulate Filled Epoxide Resin-K KISHIMOTO, M NOTOMI~ S KADOTA, T SHIBUYA, N KAWAMURA AND T KAWAKAMI Mixed-Mode Fracture Mechanics Parameters of Elliptical Interface Cracks in Anisotropic Bimaterials Y XUE AND J QU 129 143 Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:52:19 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions auth Microtexture, Asperities and Crack Deflection in AI-Li 2090 T8E41m J D HAASE~ A GUVENILIR, J R WITT, M A LANGOY, AND S R STOCK 160 Micromechanical Modeling of Mixed-Mode Crack Growth in Ceramic Composites J ZHAI AND M ZHOU 174 FATIGUE CRACK GROWTH UNDER MIXED-MODE LOADING Polycrystal Orientation Effects on Microslip and Mixed-Mode Behavior of Microstructurally Small Cracks v BENNETTAND D L McDOWELL 203 Some Observations on Mixed-Mode Fatigue Behavior of Polycrystalline Metals K J MILLER,M W BROWN,AND J, R YATES 229 A Fractographic Study of Load-Sequence-Induced Mixed-Mode Fatigue Crack Growth in an AI-Cu Alloy N E A S H B A U G H , W J PORTER, R, V PRAKASH AND R SUNDER Mixed-Mode Static and Fatigue Crack Growth in Central Notched and Compact Tension Shear Specimens v N SHLYANNIKOV 258 279 The Propagation of a Circumferential Fatigue Crack in Medium-Carbon Steel Bars Under Combined Torsional and Axial Loadings K TANAKA, Y A K I N I W A AND H YU 295 Near-Threshold Crack Growth Behavior of a Single Crystal NilBase Superalloy Subjected to Mixed-Mode Loading R JOHN, D DELUCA, T NICHOLAS AND J PORTER Indexes 312 329 Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:52:19 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized Overview Engineering components and structures necessarily involve the introduction of defects, including holes, grooves, welds, and joints The materials from which they are made have smaller imperfections, such as surface scratches, inclusions, precipitates, and grain boundaries All of these defects range in size from sub-microns to many millimeters Engineers who design such components or structures must be fully cognizant of the level and orientation of the applied loading (whether static or dynamic, of constant or variable amplitude, or proportional or nonproportional) and the density, size, shape, and orientation of the defects Under combined loading, or even remote Mode I loading, effective strain or strain energy density approaches can lead to dangerously nonconservative predictions of fatigue life, and similarly the opening mode stress-intensity factor, K~, is seldom appropriate for describing local mixed-mode crack growth For mixed-mode conditions, the crack growth direction does not follow a universal trajectory along a path in the orthogonal mixed-mode KI-KH-KHIspace Under cyclic loading, a surface in this space can be defined as representing an envelope of constant crack growth rate that tends towards zero for the threshold state In general, this envelope depends intimately on the crack driving and resisting forces The application of linear elastic fracture mechanics (LEFM), elastic-plastic fracture mechanics (EPFM), or microstructural fracture mechanics (MFM) is dictated by the scale of plasticity or material heterogeneity relative to the crack length, component dimension, and damage process zone All of these features come into play during mixed-mode loading and mixed-mode crack growth ASTM special technical publications (STPs) have a rich history of considering complex aspects of fracture such as effects of mixed-mode loading This subject has been couched under various labels such as multiaxial fatigue, 3-D crack growth, and microstmcturally sensitive crack growth, among others From previous symposia and related STPs, we have gained understanding of the physics of these phenomena and have developed appropriate experimental techniques, yet our understanding is far from complete There is still a struggle to identify the role of material resistance in establishing the growth path for the mixed-mode propagation of cracks Consequently, industrial practice, codes, and standards have not been updated in the face of this uncertainty The ASTM E08-sponsored Symposium on Mixed-Mode Crack Behavior was held in Atlanta, GA on May 6-7, 1998, and gave rise to this STR The conference was international and balanced in scope, as witnessed by the presentation of over 20 papers addressing the following topics: 9 9 9 Elastic-Plastic Fracture Three-Dimensional Cracks Anisotropic Fracture and Applications Fracture of Composite Materials Mixed-Mode Fracture Toughness Mixed-Mode Fatigue Crack Growth Experimental Studies in Mixed-Mode Fatigue and Fracture In practice, cracks that are confined to follow weak paths of material resistance along weld fusion lines or relatively weak material orientations due to process history, composite Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:52:19 EST 2015 vii Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized viii MIXED-MODE CRACK BEHAVIOR reinforcement, or interfaces will often be subject to local mixed-mode crack driving forces One of the more difficult challenges facing treatment of mixed-mode effects is the difference between global (apparent) mode-mixity and local (crack tip) mode-mixity due to microstructure heterogeneity, for example, at the tip of small fatigue cracks or within damage process zones at the tips of longer cracks Although a number of technologies have already benefitted from an enhanced understanding of mixed-mode fatigue and fracture, much design today is performed assuming local Mode I conditions even when this assumption is not applicable Briefly stated, too much focus is placed on the crack driving force and too little on micromechanisms of damage that lead to crack advance This STP is intended to contribute to a deeper understanding of these issues Among the authors of this volume are some of the leaders in the disparate and far-reaching field of mixed-mode fracture Consequently the papers contained herein span the range of experimental, computational/theoretical, and physical approaches to advance our understanding of the various aspects of mixed-mode fracture problems, and are organized into several categories The first set of papers deals with experimental observations and modeling of crack extension in ductile metals under mixed-mode loading conditions The paper by Laukkanen and colleagues is selected to lead off this STP because it offers a fairly comprehensive evaluation of the effects of mixed Mode I-II loading on elastic-plastic fracture of metals and provides experimental data for a range of alloys as well as taking an, in-depth look at failure mechanisms ahead of the crack This paper was recognized as the outstanding presentation at the symposium The paper by Dalle Donne approaches the same class of problems using the crack tip opening displacementapproach Ma and colleagues apply computational methods to predict the crack growth path for mixed Mode I-II behavior of 2024-T3 A1 Chao and Zhu develop an engineering approach to problems of mixed-mode growth to consider experimental observations of crack path in terms of a plastic fracture criterion based on crack tip fields Lam et al employ the T* integral to model crack growth by computational means along curved paths Hiese and Kalthoff present a study that considers the determination of valid mode II fracture toughness, an essential parameter in any practical mixed-mode law The work of Deng et al suggests that a critical level of the generalized crack tip opening displacement (CTOD) at a fixed distance behind the crack tip dictates the onset of crack extension, while the direction of the crack path is determined by maximizing either the opening or shearing component of the CTOD Since the crack path is a prior unknown in complex components, computational fracture approaches must be flexible and adaptive, permitting re-meshing to account for the evolution of the crack; James and Swenson discuss recent developments in two-dimensional modeling of mixed Mode I-II elastic-plastic crack growth using boundary element and re-meshing techniques The next set of papers considers the growth of cracks in materials with a strongly defined mesostructure that controls mixed-mode fracture Kishimoto and colleagues provide a detailed experimental study of the mixed-mode fracture behavior of silica particulate-filled epoxide resin that is used in electronic packaging applications The driving force for cracks between layers of material in composites or lying within bimaterial interfaces between anisotropic materials is of fundamental importance to fracture analysis; in this volume Xue and Qu present the first analytical solution ever obtained for the mixed-mode stress intensity factors and crack opening displacement fields for an arbitrary elliptical interface crack between two distinct, anisotropic, linear-elastic half spaces In an experimental study employing computed microtomography to quantify closure of deflected fatigue cracks in highly anisotropic A1-Li 2090, Stock presents a means to study highly complex crack opening and sliding fields in anisotropic materials having, in this case, mesostructure and mesotexture Zhai and Zhou employ a novel local mixed-mode interface separation law for all interfaces (and elements) within a finite element mesh to predict crack paths in ceramic composites under Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:52:19 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized OVERVIEW ix dynamic loading conditions as a function of interface strength and phase properties; this approach is not of the classical singularity type, but rather can be categorized as a cohesive zone approach The final set of papers deals primarily with various aspects of fatigue crack growth under mixed-mode loading conditions Bennett and McDowell conduct computational studies using two-dimensional crystal plasticity to shed light on the influence of intergranular interactions on driving forces for the formation and early growth of fatigue cracks in polycrystals, as well as discrete orientation effects of neighboring grains and free surface influences on the crack tip displacements for microstructurally small surface cracks in polycrystals The paper by Miller and colleagues raises a number of stimulating issues for further consideration, it also highlights the classification of crack growth behavior as belonging principally to either normal stress- or shear stress-dominated categories Ashbaugh et al report on a detailed fractographic study of crack growth behavior under variable amplitude, mixed-mode loading conditions Shlyannikov provides experimental data regarding mixed crack growth in cdnter cracked and compact tension shear specimens Tanaka and associates report on their axialtorsional studies of propagating and nonpropagating fatigue cracks in notched steel bars, with emphasis on the dependence of the fatigue limit on notch root radius and mixity of applied loading John and colleagues consider the fatigue threshold for a single crystal NiBase superalloy under mixed-mode loading, a problem of great relevance to fatigue limits in the design of gas turbine engine components, for example One of the important points of convergence of this Symposium was the realization that, for a large number of mixed-mode crack growth problems of which we are aware, there are two fundamentally distinct classes of growth: maximum principal stress-dominated and shear-dominated This is true regardless of whether we consider static or cyclic loading conditions This observation is likely to enable the development of certain very robust, simplified, material-dependent design approaches for cracks in components and structures Another point, emphasized in several papers, is the intimate connection of the crack tip displacement concept to mixed-mode elastic-plastic fracture mad fatigue processes As coeditors of this publication, we are greatly indebted to the host of international reviewers who are essential when bringing a publication of this nature to press We can claim that this volume follows in the proud tradition of the thorough peer-review system that is characteristic of ASTM STPs in fracture and fatigue We trust that this STP will give valuable insight into various aspects of mixed-mode fracture, as well as provide substantial inroads to resolving some characteristic, yet fundamental mixed-mode behavioral problems frequently observed in engineering materials, components, and structures Keith J Miller SIRIUS The University of Sheffield Sheffield, UK Symposium cochairman and coeditor David L McDowell Georgia Institute of Technology Atlanta, GA Symposium cochairman and coeditor Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:52:19 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized Crack Extension in Ductile Metals Under Mixed-Mode Loading Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:52:19 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further repr 320 MIXED-MODECRACK BEHAVIOR Mode Mixity Effects on Crack Growth Rate Behavior The crack growth behavior of PWAI422 with the standard microstructure under three types of mixed mode loading conditions is discussed next The variation of the applied KI and K~I with increasing crack length for these tests is shown in Fig = 16~ corresponded to an initial K~IK~ ~ 2.0 and = 27 ~ to an initial K~ = The main features of these tests are" (a) = 16 ~ and constant maximum load: In this case, AK~ was maintained near-constant (~6.4 MPa~,/-m) and AKH increased with increasing crack length (b) = 16~ and decreasing maximum load: In this case, 5K~ was maintained near-constant (-~10 MPaV/-m) and AK~ decreased with increasing crack length 2xK~ as > during about 80% of the crack growth and < towards the end of the test This implies that crack surface contact most likely occurred during the final stages of the test (c) = 27 ~ and decreasing maximum load: In this case, 2xKH was maintained near-constant (~11 M P a V ~ ) and ~K~ decreased with increasing crack length AK~ is close to that used for the previous test but 2xKt was < throughout the test This implies that crack surface contact should have occurred during the entire test in contrast to the previous test (b), in which contact was expected only during the last part of the test The = 16 ~ tests correspond to AK~I2~K~ - when 5K~ > in contrast to 5Kz~IAK~ 0 10-8 o (-9 z 10-9 0=27~ O -o 10 -~~ 10-11 ~ Kl can produce crack growth rates 10 to 50 times faster than that under Mode I loading Mixed-mode loading with K~ < can produce threshold type crack growth behavior implying an apparent arrest Data obtained with Kj > 0, show that the bimodal microstructure is significantly more damage tolerant than the standard microstructure under mixed mode loading In the birnodal microstructure, mixed-mode loading at 593~ did not produce planar crystallographic crack extension as did the tests at room temperature Acknowledgments This research was conducted at Air Force Research Laboratory (AFRL/MLLN), Materials and Manufacturing Directorate, Wright-Patterson Air Force Base, OH 45433-7817, USA Reji John and John Porter were supported under on-site contract number F33615-94-5200 The damage tolerant material described in this publication is the property of United Technologies and is covered under U.S Patents 5605584 and 5725692 The authors gratefully acknowledge the extensive testing support provided by Andrew Lackey from the University of Dayton Research Institute References [l] Cowles, B A., "High Cycle Fatigue in Aircraft Gas Turbines An Industry Perspective," International Journal of Fracture, Vol 80, 1996, pp 147-163 [2] McDowell, D L., "Basic Issues in the Mechanics of High Cycle Fatigue," International Journal of Fracture, Vol 80, 1996, pp 103-145 [3] Nicholas, T and Zuiker, J R., "On the Use of the Goodman Diagram for High Cycle Fatigue Design," International Journal oft;'racture, Vol 80, 1996, pp 219-235 [4] Multiaxial Fatigue, ASTM STP 853, K J Miller and M W Brown, Eds., American Society for Testing and Materials, West Conshohocken, PA 1985 [5] Hua, G., Brown, M W., and Miller, K J., "Mixed-Mode Fatigue Thresholds," Fatigue of Engineering Materials and Structures, Vol 5, 1982, pp 1-17 [6] Tong, J., Yates, J R., and Brown, M W., "The Formation and Propagation of Mode I Branch Cracks in Mixed Mode Fatigue Failure," Engineering Fracture Mechanics, Vol 56, No 2, 1997, pp 213-231 [7] Qian, J and Fatemi, A., "Mixed Mode Fatigue Crack Growth: A Literature Survey," Engineering Fracture Mechanics, Vol 55, No 6, 1996, pp 969-990 [8] Tong, J., Yates, J R., and Brown, M W., "Significance of Mean Stress on the Fatigue Crack Growth Threshold for Mixed Mode l+II Loading," Fatigue and Fracture of Engineering Materials, Vol 17, No 7, 1994, pp 829-838 [9] Reed, E A S and King, J E., "Mixed Mode Effects in Ni-Base Single Crystals Preliminary Results," Scripta Metallurgica, Vol 26, 1992, pp 1829-1834 [10] Reed, E A S and King, J E., "Orientation Effects on Fatigue Crack Growth in Udimet 720 Single Crystals," Fatigue 93, J -E Bailon and J I Dickson, Eds., Engineering Materials Advisory Services Ltd., West Midlands, U.K., 1993, pp 841-846 [11] Wu, X D and Reed, E A S., "Mode I and Mixed Mode I/I1 Fatigue of Ni-Base Single Crystal Udimet 720 in Air and in Vacuum," Fatigue 96, G Liitjering and H Nowack, Eds., Elsevier Science Ltd., Oxford, U.K., 1996, pp 855-860 [12] Telesman, J and Ghosn, L J., "The Unusual Near-Threshold FCG Behavior of a Single Crystal Superalloy and the Resolved Shear Stress as the Crack Driving Force," Engineering Fracture Mechanics, Vol 34, No 5/6, 1989, pp 1183-1196 [13] Telesman, J and Ghosn, L J., "Effect of Crystal Orientation Effects on the Fatigue Crack Growth Behavior of a Single Crystal Alloy," Fatigue 93, J -P Bailon and J I Diekson, Eds., Engineering Materials Advisory Services Ltd., West Midlands, U.K., 1993, pp 835-840 Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:52:19 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized 328 MIXED-MODE CRACK BEHAVIOR [14] Telesman, J and Ghosn, L J., "Fatigue Crack Growth Behavior of PWA 1484 Single Crystal Superalloy at Elevated Temperatures," ASME, 95-GT-452, 1994, pp 1-11 [15] John, R., Nicholas, T., Lackey, A E, and Porter, W J., "Mixed Mode Crack Growth in a Single Crystal Ni-Base Superalloy," Fatigue '96, G Lutjering and H Nowack, Eds., Elsevier Science Ltd., Oxford, U.K., May 1996, pp 399-404 [16] John, R Nicholas, T., Lackey, A E, and Johansen, K., "Mixed-Mode Fracture Behavior of Ti-6AI4V," to be published, 1998 [17] Cunningham, S E., DeLuca, D E, and Haake, E K., "Crack Growth and Life Prediction in Single Crystal Nickel Superalloys," WL-TR-94-4089, Vol I, Materials and Manufacturing Directorate, Air Force Research Laboratory (AFRL), Wright-Patterson Air Force Base, OH, February 1996 [18] Atkinson, C., Smelser, R E., and Sanchez, J., "Combined Mode Fracture Via the Cracked Brazilian Disk Test," International Journal of Fracture, Vol 18, 1982, pp 279-291 [19] Awaji, H and Sato, S., "Combined Mode Fracture Toughness Measurement by the Disk Test," Journal of Engineering Materials and Technology, Vol 100, April 1978, pp 175-182 [20] Yarema, S Ya., Ivanitskaya, G S., Maistrenko, A L., and Zboromirskii, A I., "Crack Development in a Sintered Carbide in Combined Deformation of Types I and II," Problemy Prochnosti, No 8, August 1984, pp 51-56 [21] Louah, M., Pluvinage, G., and, Bia, A., "Mixed Mode Crack Growth Using the Brasilian Disk," Fatigue 87, R O Ritchie and E A Starke, Jr., Eds., Engineering Materials Advisory Services, Ltd., West Midlands, U.K., 1987, pp 969-977 [22] John, R and Johnson, D A., "K~ and K~ Solutions for a Centrally Notched Disk," to be published, 1998 [23] Erdogan and Sih, G., "On the Crack Extension in Plates Under Plane Loading and Transverse Shear," Journal of Basic Engineering, ASME, Vol 85, 1963, pp 519-527 [24] Hussain, M A., Pu, S L., and Underwood, J H., "Strain Energy Release Rate for a Crack Under Combined Mode I and Mode II," Fracture Analysis, ASTM STP 560, American Society for Testing and Materials, West Conshohocken, PA, 1974, pp 2-28 [25] Sih, G C., "Strain Energy Density Factor Applied to Mixed Mode Crack Problems," International Journal of Fracture, Vol 10, No 3, 1974, pp 305-321 [26] James, M and Swenson, D., "FRANC2D/L: A Crack Propagation Simulator for Plane Layered Structures," Kansas State University, Manhattan, KS, available through the Internet at http:l/ www.mne.ksu.edu/-franc2d/, 1997 Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:52:19 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized STP 1359-EB/Nov 1999 Author Index Lava, R W., 58 Langoy, Morten A., 160 Lankkanen, Anssi, Akinawa, Yoshiaki, 295 Ashbaugh, N E., 258 Atluri, S N., 58 M B Ma, Fashang, 86 McDowell, David L., vii, 203 Miller, Keith J., vii, 229 Bennett, Valerie, 203 Brown, M W., 229 C Chao, Yuh-Jin, 41 N Newman, Jr., James C., 86 Nicholas, Ted, 312 Notomi, Misuo, 129 deLuca, Dan, 312 Deng, Xiaomin, 86 Donne, Claudio Dalle, 21 G Porter, John, 312 Porter, W J., 258 Prakkesh, R V., 258 Q Guvenilir, Abbas, 160 Qu, Jianmin, 143 It R Haase, Jake D., 160 Hiese, W., 74 Rintamaa, Rauno, James, Mark, 111 John, Reji, 312 K Kadota, Shun, 129 Kalthoff, J F., 74 Kawakami, Takashi, 129 Kawamura, Noriyasu, 129 Kishimoto, Kikuo, 129 Kobayashi, A S., 58 Shibuya, Toshikazu, 129 Shtyannikov, Valery N., 279 Stock, Stuart R., 160 Sunder, R., 258 Sutton, Michael A., 86 Swenson, Daniel, 111 T Tanaka, Keisuke, 295 Tan, R W., 58 Copyright by ASTM Int'l (all rights reserved); Wed 329 Dec 23 19:52:19 EST 2015 Downloaded/printed by © Copyright of1999 by A S T M(University International www.astm.org University Washington of Washington) pursuant to License Agreement No further reproductions autho 330 MIXED-MODECRACK BEHAVIOR W Yates, J R., 229 Yu, Huichen, 295 Wallin, Kim, Witt, Jason R., 160 X Xue, Yibin, 143 Y Zhai, J., 174 Zhou, M., 174 Zhu, Xian-Kui, 41 Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:52:19 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized STP 1359-EB/Nov 1999 Subject Index A Aluminum alloys elastic-plastic crack growth, 279 load-sequence-induced mixed-mode fatigue crack growth, 258 microtexture, asperities, and crack deflection, 160 Aluminum composites, mixed-mode crack growth, 174 Anisotropic bimaterials, elliptical interface cracks, 143 Asperities, 160 Asymmetric four-point bending, microstructurally small cracks, 203 vector approach, mixed-mode fracture, 21 Crack tip opening angle, 111 Crack-tip opening displacement, mixed-mode fracture criterion, 86 Crack tip plastic zones, 74 Crack tip sliding displacement, 21 Cross-ply laminates, 143 Crystal plasticity, 203 D Delamination, 143 Ductile fracture elastic-plastic, thin structures, 21 B Central notched specimens, 279 Ceramic composites, micromechanical modeling of crack growth, 174 Circumferential fatigue crack, 295 Cohesive force, 174 Compact tension shear specimens, 279 Crack closure, roughness-induced, 160 Crack growth CTOD critical value, 86 curved, 58 elastic-plastic, 111,279 near-threshold, 312 stable, 21, 58 thresholds, 229 Crack propagation, 174 circumferential, 295 dynamic, 174 polyrystalline metals, 229 rate, combined torsional and axial loadings, 295 Crack reorientation criterion, 279 Cracks branching, 258 deflection, 160 kinking, 58, 86 path, 279 speed, 174 three-dimensional, 143 Crack tip displacement Elasticity, 174 Elastic-plastic conditions, mixed-mode CTOD criterion, 86 Elastic-plastic ductile fracture, metallic materials, Elastic-plastic finite element analysis, 58 Elastic-plastic fracture, 279 Elliptical interface cracks, mixed-mode fracture mechanics parameters, 143 Engineering Treatment Model, 21 Epoxide resin, silica particulate filled, mixed-mode fracture behavior, 129 F Fatemi-Socie critical plane fatigue parameter, 203 Fatigue, 160 Fatigue crack growth, load-sequence-induced, fractographic study, 258 Fatigue cracks, polycrystalline metals, 229 Finite element method, I 11 temperature effect on mixed-mode fracture behavior, 129 Flaw assessment, 21 Fourier transform, 143 Fractography, 3, 295 load-sequence-induced mixed-mode fatigue crack growth, 258 Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:52:19 EST 2015 331 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized 332 MIXED-MODE CRACK BEHAVIOR Fracture boundary curve, 129 Fracture mechanics, 111,295 Fracture mode, 174 Fracture stress in shear, 41 Fracture stress in tension, 41 Fracture toughness determination, 74 transition between opening and in-plane shear modes, FRANC2D/L software, extension, 111 G Gurson-Tvergaard model, H High cycle fatigue, 203 High temperature, 312 Hoop stress criterion, maximum, 129 Inhomogeneous materials, 174 Interface fracture, anisotropic bimaterials, 143 J-integral, 3,295 L Lap splice joint, 58 Lane patterns, 160 Loading combined torsional and axial, 295 mixed-mode, near-threshold crack growth, 312 mixed mode I-II loading, effects on elasticplastic ductile fracture, programmed, 258 Local failure criterion, 129 Microtexture, 160 Mixed-mode crack growth, micromechanical modeling, 174 Mixed-mode crack surfaces, aluminum, 160 Mixed-mode energy release rate, 143 Mixed-mode fatigue behavior, polycrystalline metals, 229 Mixed-mode fatigue crack growth central notched and compact tension shear specimens, 279 load-sequence-induced, fractographic study, 258 Mixed-mode fracture crack tip displacement vector approach, 21 criterion, crack-tip opening displacement, 86 mechanics, parameters, elliptical interface cracks, 143 toughness, silica particulate filled epoxide resin, 129 transition between tensile and shear mechanisms, 41 Mixed mode I/II elastic-plastic fracture, twodimensional, 111 Mixed-mode FllI fatigue crack, 295 Mixed-mode static crack growth, central notched and compact tension shear specimens, 279 Mode I fracture transition between tensile and shear mechanisms, 41 toughness determination, 74 silica particulate filled epoxide resin, 129 Mode II fracture crack tip displacement vector approach, 21 toughness, determination, 74 transition between tensile and shear mechanisms, 41 Mode III fracture, transition between tensile and shear mechanisms, 41 Moire interferometry, 58 Multiaxial loading, polycrystalline metals, 229 N M Metallic materials, elastic-plastic ductile fracture, Micromechanical modeling, mixed-mode crack growth, 174 Microslip, polycrystal orientation effects, 203 Microstructure nickel superalloy, 312 polycrystalline metals, 229 small cracks, microslip and mixed mode behavior, 203 Nickel-base superalloy, near-threshold crack growth, 312 Numerical simulation, 174 P Polycrystalline metals, mixed-mode fatigue behavior, 229 Polycrystal orientation, effects on microslip and mixed mode behavior, 203 Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:52:19 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized SUBJECT INDEX Residual strength, prediction, 111 Retardation effects, 258 Richard's criterion, 129 Roughness-induced closure, 160 Semiconductor package, 129 Shear fracture, toughness, mode I[, 74 transition to tensile mechanisms, 41 Silica particulate filled epoxide resin, mixed-mode fracture behavior, 129 Single edge notched specimens biaxially loaded, fatigue precracked, 58 elastic-plastic ductile fracture, Sliding contact, 295 Small cracks, microstructure, 203 Software framework, two-dimensional mixed mode HI elastic-plastic fracture, 111 Specimen size, requirements, 74 State variable mapping, 111 Steels 333 circumferential fatigue crack, 295 elastic-plastic crack growth, 279 Stress intensity factor, combined torsional and axial loadings, 295 elliptical interface cracks, 143 Striation, 295 Stroh method, 143 Synchrotron radiation, 160 Tearing, 111 Tear straps, 58 Tensile fracture, transition to shear mechanisms, 41 Tensile stress, maximum, 111 T~ integral, curved crack growth, 58 V Validity criteria, 74 X X-ray diffraction, microbeam, 160 Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:52:19 EST 2015 Downloaded/printed by University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized ISBN 0-8031-2602-6