Topics in Fracture and Fatigue PDF
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Topics in Fracture and Fatigue Frank A. McClintock (ca. 1980) This book is dedicated to Frank A. McClintock, Professor of Mechanical Engineer ing at the Massachusetts Institute of Technology, in recognition of his pioneering contributions to the understanding of the mechanics and mechanisms of ductile fracture and fatigue crack propagation. A.S. Argon Editor Topics in Fracture and Fatigue With 152 Illustrations Springer-Verlag New York Berlin Heidelberg London Paris Tokyo Hong Kong Barcelona Budapest A.S. Argon Department of Mechanical Engineering Massachusetts Institute of Technology Cambridge, MA 02139-4307 USA Library of Congress Cataloging-in-Publication Data Topics in fracture and fatigue / edited by A.S. Argon. p. cm. Includes bibliographical references and index. ISBN-13:978-1-4612-7726-2 1. Fracture mechanics. 2. Materials-Fatigue. I. Argon, Ali S. TA409.T65 1992 620.1'126-dc20 92-10375 Printed on acid-free paper. © 1992 Springer-Verlag New York, Inc. Softcover reprint of the hardcover 1st edition 1992 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer-Verlag New York, Inc., 175 Fifth Avenue, New York, NY 10010, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereaf ter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. Production managed by Hal Henglein; manufacturing supervised by Robert Paella. Camera-ready copy prepared by the editor. 987654321 ISBN-13:978-1-4612-7726-2 e-ISBN-13:978-1-4612-2934-6 DOl: 10.1007/978-1-4612-2934-6 Preface The phenomenon of fracture, now widely recognized to be of central im portance in governing the useful service life of engineering structures of all types, was not always considered as such in physics and materials science. Even today the study of fracture is considered by some as a field in which no self-respecting scientist should be seen working. The principal reason for this attitude has been the widespread empiricism that has been associ ated with the field. While the practicing engineer has found this empiricism quite useful in coping with often bewildering material response characteris tics, this has discouraged the development of more fundamental and lasting approaches. A new departure occurred in the understanding of fracture with the pioneering work of Griffith in 1920 and 1924, who not only associated fracture and strength with cracks, but also stated the conditions for fracture in brittle solids in terms of crack growth criteria. Considerable awareness existed in the field in the late 40's that Griffith's conditions did not apply well to many ductile solids, and that these materials appeared to be coming apart more gradually by internal cavitation. While the effect of plastic deformation on the crack tip environment was studied by many workers in the late 50's and early 60's, the definitive mechanistic developments of dealing with these new problems on the microstructural scale began with McClintock's pioneering work of 1968 on ductile fracture by plastic cavitation. The stimulation of this work and related modeling studies of others re sulted in a series of rapid fundamental developments in both crack tip mech anics and material response characteristics on the microstructural scale that has continued very actively up to the present and is currently referred to often as "micromechanics." McClintock has contributed importantly to this field at every turn, starting with his elastic-plastic mode III crack tip field solution (1957), to local field models of growing mode III cracks (1970), material model for ductile cavitation (1968), growth of cavities in the envi ronment of a plastically blunted mode I crack (1969), fully plastic slip line field studies of crack tip environments in pure mode and mixed mode defor mation (1971), mechanics and mechanisms offatigue crack growth in mode III (1956), fatigue crack growth by quasi-homogeneous damage accumula tion (1963), and fatigue crack growth by irreversible crack tip distortions (1967). The contributions extended also to studies of fundamental material response in the form of strength of high angle grain boundaries (1965), brittle intergranular fractures among 2-D hexagonal grains (1974), and in cluded atomistic modeling studies on emission of dislocations from mode III cracks (1969, unpublished), and generalized ductile cavitation loci (1970, unpublished). A short annotated list ofthese contributions and some others can be found at the end of this book in Chapter 10. vi Preface This volume was assembled on the occasion of the retirement of McClin tock in June of 1991, and is the outcome of a mini-international sympo sium held at Endicott House, the MIT Conference Estate at that time. Its purpose is to assess some of the important developments in the field of ductile fracture and fatigue to which McClintock contributed significantly. The select group of contributors to this volume include a number of active practitioners in this important field, who individually have made contri butions as pioneering and lasting as those of McClintock himself. They discuss developments varying from atomistic level responses of crack tips, to elastic-plastic crack tip fields, to cavitation models for ductile fracture and intergranular creep fracture, and include models of fracture in com posites, and mechanisms of fatigue fracture. While the coverage of these topics is not at all complete or uniform, they all incorporate unique mech anistic perspectives that collectively furnish examples of the best thinking in this field and in both style and approach point out the future directions in further development. I gratefully acknowledge the financial support of the National Science Foundation, Mechanics and Materials Program in the Engineering Direc torate, under Grant 9108983-MSS, that has made this book possible. I am also grateful to Ms. Mary Toscano for her expert help, not only in the preparation of the basic manuscript, but also for her perseverance in ex tracting manuscripts from some of the illustrious contributors and for the preparation of the index. A.S. Argon Cambridge, MA December, 1991 Contents Preface ............................................................. v List of Contributors ................................................ IX 1. Peierls Framework for Analysis of Dislocation Nucleation from a Crack Tip ............................................... 1 J. R. Rice, G. E. Beltz, and Y. Sun 2. Advances in Characterization of Elastic-Plastic Crack-Tip Fields . 59 D. M. Parks 3. Constraint and Stress State Effects in Ductile Fracture ........... 99 J. W. Hancock 4. Void Growth in Plastic Solids ........ '" ........................ 145 A. Needleman, V. Tvergaard and J. W. Hutchinson 5. Crack Blunting and Void Growth Models for Ductile Fracture ... 179 R. M. McMeeking 6. Global and Local Approaches of Fracture - Thansferability of Laboratory Test Results to Components ...................... 197 A. Pineau 7. Growth of Cracks By Intergranular Cavitation in Creep ......... 235 A. S. Argon, K. J. Hsia and D. M. Parks 8. Cracking and Fatigue in Fiber-Reinforced Metal and Ceramic Matrix Composites .................................. 271 A. G. Evans and F. W. Zok 9. Metal Fatigue - A New Perspective ............................. 309 K. J. Miller 10. Reflections on Contributions to Deformation and Fracture ..... 331 F. A. McClintock Index ............................................................. 343 List of Contributors A. S. Argon K. J. Miller Dept. of Mechanical Eng. Dept. of Mechanical Eng. Mass. Institute of Technology University of Sheffield Cambridge, MA 02139-4307 Sheffield, England USA G. E. Beltz A. Needleman Div. of Applied Sciences Div. of Engineering Harvard University Brown University Cambridge, MA 02138 Providence, RI02912 USA USA A. G. Evans D. M. Parks College of Engineering Dept. of Mechanical Eng. University of California Mass. Institute of Technology Santa Barbara, CA 93106 Cambridge, MA 02139-4307 USA USA J. W. Hancock A. Pineau Dept. of Mechanical Eng. Centre des Materiaux University of Glasgow Ecole des Mines Glasgow, Scotland Paris, France K. J. Hsia J. R. Rice Dept. of Theo. &, Applied Mech. Div. of Applied Sciences University of Dlinois Harvard University Urbana, IL 61801 Cambridge, MA 02138 USA USA J. W. Hutchinson Y. Sun Div. of Applied Sciences Div. of Applied Sciences Harvard University Harvard University Cambridge, MA 02138 Cambridge, MA 02138 USA USA F. A. McClintock V. Tvergaard Dept. of Mechanical Eng. Department of Solid Mechanics Mass. Institute of Technology The Tech. University of Denmark Cambridge, MA 02139-4307 Lyngby, Denmark USA R. M. McMeeking F. Zok College of Engineering College of Engineering University of California University of California Santa Barbara, CA 93106 Santa Barbara, CA 93106 USA USA 1 Peierls Framework for Dislocation Nucleation from a Crack Tip J. R. Rice, G. E. Beltz, and Y. Sun ABSTRACT Dislocation nucleation from a stressed crack tip is analyzed based on the Peierls concept, in which a periodic relation between shear stress and atomic shear displacement is assumed to hold along a slip plane emanating from a crack tip. This approach allows some small slip displace ment to occur near the tip in response to small applied loading and, with increase in loading, the incipient dislocation configuration becomes unsta ble and leads to a fully formed dislocation which is driven away from the crack. An exact solution for the loading at that nucleation instability was developed using the J-integral for the case when the crack and slip planes coincide (Rice, 1992). Solutions are discussed here for cases when they do not. The results were initially derived for isotropic materials and some generalizations to take into account anisotropic elasticity are noted here. Solutions are also given for emission of dissociated dislocations, especially partial dislocation pairs in fcc crystals. The level of applied stress intensity factors required for dislocation nucleation is shown to be proportional to ..;;y;;; where 'rus, the unstable stacking energy, is a new solid state param eter identified by the analysis. It is the maximum energy encountered in the block-like sliding along a slip plane, in the Burgers vector direction, of one half of a crystal relative to the other. Approximate estimates of 'rua are summarized, and the results are used to evaluate brittle versus ductile response in fcc and bcc metals in terms of the competition between dis location nucleation and Griffith cleavage at a crack tip. The analysis also reveals features of the near-tip slip distribution corresponding to the saddle point energy configuration for cracks that are loaded below the nucleation threshold, and some implications for thermal activation are summarized. Additionally, the analysis of dislocation nucleation is discussed in connec tion with the emission from cracks along bimaterial interfaces, in order to understand recent experiments on copper bicrystals and copper/sapphire interfaces, and we discuss the coupled effects of tension and shear stresses along slip planes at a crack tip, leading to shear softening and eased nucle ation. 2 1. Peierls Framework for Dislocation Nucleation from a Crack Tip 1.1 Introduction Armstrong (1966) and Kellyet al. (1967) advanced the viewpoint of brittle versus ductile response as the competition between Griffith cleavage and plastic shear at a crack tip. The latter proposed that the response of a crystal or grain boundary should be treated by comparing the ratio of the largest tensile stress to the largest shear stress close to a crack tip with the ratio of the ideal cleavage stress to the ideal shear stress. Armstrong compared the applied stress necessary to meet the Griffith condition with the stress to shear apart a dislocation dipole near a crack tip, and there by b, noted the importance of the dimensionless combination ''/J .Lb = surface = = energy, J.L shear modulus, b magnitude of the Burgers vector) as an index of how relatively easy it was for the shear process to occur before cleavage. Subsequently Rice and Thomson (1974) specifically modeled the shear process as the nucleation of a dislocation from a stressed crack tip. The Rice and Thomson approach made use of elasticity solutions for a fully formed dislocation (i.e., a dislocation with slip equal to the Burgers vector b of some complete or partial lattice dislocation) and a core cut off parameter had to be introduced to derive a nucleation criterion. Their 18/ analysis showed, likewise, the importance of large J.Lb and also of low core energy (large rc/b, where rc is the core cut-off radius in their analysis) for ductile response. Recent treatments of the Rice-Thomson model have evolved to charac terizing the crack-tip competition in terms of the parameters Gcleave, the energy release rate for cleavage and Gdis), the energy release rate associ ated with the emission of a single dislocation on a slip plane emanating from the crack tip. In its original form, the Rice-Thomson model treated dislocation emission by considering the stability of a straight dislocation line or a semicircular dislocation loop; both proceeded by assuming the existence of a freshly generated dislocation at a relatively small distance (turning out to be less than a few atomic spacings) away from the crack tip, on a slip plane which intersects the crack front. A drawback to this procedure, as well as the Peierls-type model to be discussed shortly, is that the analysis may be straightforwardly applied only to cases in which the slip plane(s) intersect the crack front. Following Mason (1979), however, we may envision a scenario in which dislocations are emitted when a moving crack front undergoes local deviations which bring it into line with a poten tially active slip plane. Another drawback to the Rice-Thomson treatment is that it involves the core cutoff radius, an uncertain parameter. Here, following a suggestion by Argon (1987), the Peierls (1940) concept is used in an analysis of dislocation formation at a crack tip. That is, a periodic relation is assumed to hold between shear stress and sliding displacement along a crystal slip plane emanating from a crack tip, and a solution is then derived for the critical external loading which corresponds to dislocation nucleation.
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