Table Of ContentMicromechanics
and
Inhomogeneity
The Toshio Mura
65 th Anniversary Volume
Toshio Mura
G. 1. Weng M. Taya H. Abe
Editors
Micromechanics
and
Inhomogeneity
The Toshio M ura 65 th Anniversary Volume
With 211 Illustrations
Springer-Verlag
New York Berlin Heidelberg
London Paris Tokyo Hong Kong
G.J. Weng M. Taya H.Are
Department of Mechanics Department of Department of
and Materials Science Mechanical Engineering Mechanical Engineering
Rutgers University University of Washington Tohoku University
Piscataway, NJ 08903 Seattle, WA 98195 Sendai980
U.S.A. U.S.A. Japan
Library of Congress Cataloging in Publication Data
Micromechanics and inhomogeneity, the Toshio Mura 65th anniversary
volume / GJ. Weng, M. Taya, H. Abe, editors.
p. cm.
Selected papers from the Symposium on Micromechanics and
Inhomogeneity held during the 1989 Winter Annual Meeting of the
American Society of Mechanical Engineers in San Francisco. The
symposium was co-sponsored by the Constitutive Equations Committee
et al.
ISBN-13:978-1-4613-8921-7
1. Micromechanics-Congresses. 2. Dislocations in metals
-Congresses. 3. Mura, Toshio, 1925- . I. Mura, Toshio, 1925-
II. Weng, GJ. III. Taya, Minoru. IV. Abe, H. (Hiroyuki),
1936- . V. Symposium on Micromechanics and Inhomogeneity (1989:
San Francisco, Calif.) VI. American Society of Mechanical
Engineers. Winter Meeting (1989: San Francisco, Calif.)
VII. American Society of Mechanical Engineers. Constitutive
Equations Committee.
QCI76.8.M5M53 1989 89-21898
620.1 '63-dc20
Printed on acid-free paper.
© 1990 by Springer-Verlag New York Inc.
Softcover reprint of the hardcover 1st edition 1990
All rights reserved. This work may not be translated or copied in whole or in part without
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10010, U.S.A.), 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 hereafter 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.
Typeset by Asco Trade Typesetting Ltd., Hong Kong.
9 8 7 654 3 2 1
ISBN-13:978-1-4613-8921-7 e-ISBN-13:978-1-4613-8919-4
DOl: 10.1007/978-1-4613-8919-4
Editors' Preface
Toshio Mura has written extensively on micromechanics over the years, and
in part due to his writings and many others in the field, micromechanics has
gradually emerged as a recognized discipline in the study of mechanics of
materials. The idea is to bring both the mechanics and physics on the micro
scopic level to the macroscopic scale, so that the deformation and fracture
processes of materials can be better understood. While much apparently
remains to be done, this approach has already shed new light on certain
selected topics and has proved to be fruitful. It is indeed a happy occasion to
celebrate both Toshio's upcoming 65th birthday and the emergence of this
young science at the same time.
The volume contains thirty-seven original articles on the related topics of
micromechanics and inhomogeneity; it is presented to Toshio by his friends,
colleagues, and admirers as a wish for his good health and continuing pro
ductivity. The contributors belong to both the applied mechanics and the
materials communities, all with a common belief that micromechanics is an
indispensable area of research. It is hoped that this somewhat balanced
structure will make the volume more useful to a wider range of readers, and
that in the meantime it will still reflect more or less the spectrum of Toshio's
lifelong works. As Editors we have at the outset set the highest possible
standards for the book, with a keen anticipation that the volume will be widely
circulated for many years to come.
We consider it an honor to have the opportunity to edit this volume. In the
process of preparation, Toshio has been most helpful in providing all the
needed information. We are grateful to the individual authors for their ready
cooperation, and especially to Professor Mori for his efforts in writing the
Toshio Mura Biography. The planning of this publication is also accompanied
by a Symposium on Micromechanics and Inhomogeneity during the 1989
Winter Annual Meeting of the American Society of Mechanical Engineers in
San Francisco. A total of sixty papers, including these thirty-seven, will be
presented there. The other twenty-three papers, due to the constraints oftime
and other factors, regrettably could not be included here. A list of these
twenty-three papers is appended at the end of the Preliminary matter; they
vi Preface
are available directly from the authors to whom we also extend our appre
ciation. In this regard Professors M. Eisenberg, H. Kobayashi, T. Mori, and
E. Tsuchida have also served on the Organizing Committee. The symposium
was cosponsored by the Constitutive Equations Committee, the Applied
Mechanics Division and Materials Division of ASME, and the Japanese
Society of Mechanical Engineers.
Our special thanks are due to Springer-Verlag, New York, Inc., and its most
capable and professional staff for their editing and production. The financial
support of the Urakami Foundation for some overseas participants to the
Mura Symposium is also gratefully acknowledged. Finally, we would like to
express our appreciation to Mr. Shoji of Tohoku University for his help in
the indexing of this book.
Piscataway, New Jersey G.J. WENG
Seattle, Washington M. TAYA
Sendai, Japan H.ABE
March 29, 1989
Contents
Editors' Preface . . . . . v
Biography of Toshio Mura
T. MORI ..... . xi
List of Publications by Toshio Mura XVll
List of Contributors . . . . . . . xxix
List of Additional Papers Presented. . xxxiii
An Inverse Problem in Nondestructive Inspection of a Crack in a
Plate with an Inhomogeneity by Means of the Electrical Potential
Method
H. ABE and Y. KANOH . . . . . . . . . . . . . . . 1
The Effective Thermoelastic Properties of Whisker-Reinforced
Composites as Functions of Material-Forming Parameters
D. H. ALLEN and J.-W. LEE . . . . . . . . . . . . . 17
On the Specific Damaging Effects of Surface and Near-Surface
Inclusions
M.-H. AMBROISE, T. BRETHEAU, and A. ZAOUI. . . . . . 41
On a Correspondence Between Mechanical and Thermal Effects in
Two-Phase Composites
Y. BENVENISTE and G. J. DVORAK. . . . . . . . . . . .. 65
On Atomic Spacing in Large Regular Cubic Lattices
B. A. BOLEY ............... . 83
Crack Tip Toughening by Inclusions with Pairs of Shear
Transformations
S.-J. CHANG and P. F. BECHER . . . . . . . . . . 89
Boundary Conditions at Interfaces
J. DUNDURS ....... . 109
viii Contents
On Viscoplasticity and Continuum Dislocation Theory
M. A. EISENBERG. . . . . . . . . . . . . . . 115
A Circular Inclusion with Slipping Interface in Plane Elastostatics
T. HONEIN and G. HERRMANN . . . . . . . . . . . . 127
Mechanical Properties of Cracked Solids: Validity of the Self
Consistent Method
H. HORII and K. SAHASAKMONTRI. . . . . . . . . . . 137
The Elastic and Diffusional Interaction of Spherical Inhomogeneities
in a Uniaxial Stress Field
W. C. JOHNSON . . . . . . . . . . . . . . . . . . . .. 161
Analysis of Cracks in Transversely Isotropic Media
L. M. KEER and W. LIN. . . . . . . . . . 187
Modified Green Functions in the Theory of Heterogeneous and/or
Anisotropic Linearly Elastic Media
E. KRONER . . . . . . . . . . . . . . . . . . . 197
Inclusion With and Without Free Surfaces in a Plane Strain
J. K. LEE . . . . . . . . . . . . . . . . . . " .. 213
Interaction of Slip Bands in High-Cycle Fatigue Crack Initiation
T. H. LIN and Q. Y. CHEN. . . . . . . . . . . . . . . . . 231
Elastic Behavior of Laminated Flexible Composites Under Finite
Deformation
S.-Y. Luo and T.-W. CHOU . . . . . . . . . . . . .. . 243
On the Basic Components of the Interaction Energy Between Two
Infinitesimal Circular Defects in an Isotropic Elastic Body
S. MINAGAWA and H. OGATA . . . . . . . . . . . . . . . 257
Successive Iteration Method in the Evaluation of Average
Fields in Elastically Inhomogeneous Materials
T. MORI and K. WAKASHIMA .......... . 269
Effects of Nonmetallic Inclusions on the Fatigue Strength of Metals
Y.MURAKAMI. . . . . . . . . . . . . . . . . . . .. 283
Elastic Solids with Microdefects
S. NEMAT-NASSER and M. HORI. 297
The Effective Moduli of Layered Media-A New Look at an Old
Problem
A. N. NORRIS . . . . . . . . . . . . . . . . . . . . 321
Thermomechanical Hysteresis and Analogous Behavior of Composites
O. B. PEDERSEN . . . . . . . . . . . . . . . . . . . . . 341
Contents
IX
The Effect of Voids and Inclusions on Wave Propagation in
Granular Materials
M. H. SADD, A. SHUKLA, H. MEl, and C. Y. ZHU. . . . 367
Crack, Dislocation Free Zone, and Dislocation Pile-Up Model for the
Behavior of the Hall-Petch Relation in the Range of Ultrafine Grain
Sizes
K. SAITO, M. IWAMOTO, Y. NOMURA, and T. NAKAMURA . .. 385
The Elastic Fields Produced by an Infinitesimal Dislocation Loop,
an Interstitial Atom, and a Vacancy Moving with Uniform Velocity
H. SEKlNE. . . . . . . . . . . . . . . . . . . . . .. 399
Energy Consideration on a Branched and Curved Crack Extension
Y. SUMI. . . . . . . . . . . . . . . . . . . . . • .• 407
Elastic/Plastic Indentation Hardness of Ceramics: The Dislocation
Punching Model
K. TANAKA and H. KOGucm. . . . . . . . . . . . 421
Some Thoughts on Inhomogeneous Distribution of Fillers in
Composites
M. TAYA . . . . . . . . . . . . . . . . . . . . 433
The Eigenvectors of the S Matrix and Their Relations with Line
Dislocations and Forces in Anisotropic Elastic Solids
T. C. T. TING . . . . . . . . . . . . . . . . . . . . 449
On the Strain Energy of Transformation Inhomogeneities in Solids
T. TSAKALAKOS . . . . . . . . . . . . . . . . . . .. 469
The Hemispherical Inhomogeneity Subjected to a Concentrated Force
E. TsucmDA, D. KOURIS, and I. JASIUK. . . . . . . . . . . . 497
Dislocation Inhomogeneity in Cyclic Deformation
D. WA LGRAEF and E. C. AIFANTIS. . . . . . 511
Equivalence of Green's Function and the Fourier Series Representation
of Composites with Periodic Microstructure
K. P. WALKER, E. H. JORDAN, and A. D. FREED . . . . . 535
Polarization, Virtual Mass, and Analogous Elastic Properties
L. 1. WALPOLE. . . . . . . . . . . . . . . . . . 559
Edge Crack Solution Through Use of Dislocation Shielding/
Antishielding
1. WEERTMAN . . . . . . . . . . . . . . . . . . 573
Variational Estimates for the Overall Behavior of a Nonlinear Matrix
Inclusion Composite
J. R. WILLIS. . . . . . . . . . . . . . . . . . . . . . . 581
x Contents
Theory of Plasticity for a Class of Inclusion and Fiber-Reinforced
Composites
Y. H. ZHAO and G. J. WENG 599
Author Index 623
Subject Index 629
