Multiscale Deformation and Fracture in Materials and Structures - The James R. Rice 60th Anniversary Volume (Solid Mechanics and its Applications, Volume 84)

464 Pages·2000·8.126 MB·English

by  T-J. Chuang, J.W. Rudnicki

MULTISCALE DEFORMATION AND FRACTURE IN MATERIALS
AND STRUCTURES
SOLID MECHANICS AND ITS APPLICATIONS
Volume 84
Series Editor: G.M.L. GLADWELL
Department of Civil Engineering
University of Waterloo
Waterloo, Ontario, Canada N2L 3GI
Aims and Scope of the Series
The fundamental questions arising in mechanics are: Why?, How?, and How much?
The aim of this series is to provide lucid accounts written by authoritative researchers
giving vision and insight in answering these questions on the subject of mechanics as it
relates to solids.
The scope of the series covers the entire spectrum of solid mechanics. Thus it includes
the foundation of mechanics; variational formulations; computational mechanics;
statics, kinematics and dynamics of rigid and elastic bodies: vibrations of solids and
structures; dynamical systems and chaos; the theories of elasticity, plasticity and
viscoelasticity; composite materials; rods, beams, shells and membranes; structural
control and stability; soils, rocks and geomechanics; fracture; tribology; experimental
mechanics; biomechanics and machine design.
The median level of presentation is the first year graduate student. Some texts are mono-
graphs defining the current state of the field; others are accessible to final year under-
graduates; but essentially the emphasis is on readability and clarity.
Multiscale Deformation
and Fracture in Materials
and Structures
The James R. Rice 60th Anniversary Volume
Edited by
T.-J. Chuang
National Institute of Standards & Technology,
Gaithersburg, U.S.A.
and
J. W. Rudnicki
Northwestern University,
Evanston, Illinois, U.S.A.
KLUWER ACADEMIC PUBLISHERS
NEW YORK, B OSTON, DORDRECHT,L ONDON, MOSCOW
eBook ISBN 0-306-46952-9
Print ISBN 0-792-36718-9
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Editors’ Preface
The work of J. R. Rice has been central to developments in solid mechanics over the last
thirty years. This volume collects 21 articles on deformation and fracture in honor of J.R.
Rice on the occasion of his 60th birthday.Contributors include students (P. M. Anderson,
G. Beltz, T.-J. Chuang, W.J. Drugan, H. Gao, M. Kachanov, V. C. Li, R. M. McMeeking,
S. D. Mesarovic, J. Pan, A. Rubinstein, and J. W. Rudnicki), post-docs (L. B. Sills, Y.
Huang, J.Yu, J.-S. Wang), visiting scholars (B. Cotterell, S. Kubo, H. Riedel) and
co-authors (R. M. Thomson and Z. Suo). These articles provide a window on the diverse
applications of modern solid mechanics to problems of deformation and fracture and insight
into recent developments.
The last thirty years have seen many changes to the practice and applications of
solid mechanics. Some are due to the end of the Cold War and changes in the economy.
The drive for competitiveness has accelerated the need to develop new types of materials
without the costly and time-consuming process of trial and error. An essential element is
a better understanding of the interaction of macroscopic material behavior with microscale
processes, not only mechanical interactions, but also chemical and diffusive mass transfer.
Unprecedented growth in the power of computing has made it possible to attack increasingly
complex problems. In turn, this ability demands more sophisticated and realistic material
models. A consistent theme in modern solid mechanics, and in this volume, is the effort to
integrate information from different size scales. In particular, there is an increasing
emphasis on understanding the role of microstructural and even atomistic processes on
macroscopic material behavior. Despite the great advances in computational power, current
levels do not approach that needed to employ atomic level formulations in practical
applications. Consequently, idealized problems that link behavior at small, even atomic,
size scales to macroscopic behavior remain essential.
It would be presumptuous to hope that the articles here are as original, rigorous,
clear and as strongly connected to observations as the work of the man they are meant to
honor. Nevertheless, we hope that they do reflect the high standards that he has set. That
they do is in no small measure a consequence of the interaction, both formal and informal,
of the authors with J. R. Rice and the inspiration that his work has provided.
The articles in this volume are grouped into sections on Deformation and Fracture
although, obviously, there is some overlap in these topics. As is evident by reading the
titles, the scope and subjects of the articles are diverse. This reflects not only the extensive
impact of Rice’s work but also the broad applicability of certain fundamental tools of solid
mechanics.
vi EDITORS’ PREFACE
FRACTURE: Arguably, Rice’s most well-known contribution is the
introduction of the J-integral in 1968 and its application to problems of fracture. Because
of its path-independent property, the integral has become a standard tool of fracture
mechanics that makes it possible to link processes at the crack-tip to applied loads. Three
of the papers in the Fracture section discuss this J-integral (and several others use it). Kubo
gives a concise catalog of various versions of the integral and related extensions. Li
discusses applications of the J-integral to characterization and tailoring of cementitious
materials. A special feature of these materials is the presence of fibers or aggregate
particles that transmit tractions across the crack-faces behind the tip. In his 1968 paper,
Rice showed that the J-integral is equal to the energy released per unit area of crack advance
for elastic materials. Consequently, this energy or the value of J could be used as criterion
for fracture. Haug and McMeeking use the J-integral to study the effect of an extrinsic
surface charge on the energy release rate for a piezoelectric compact tension specimen.
They find that the presence of the free charge diminishes the effect of the electric field and
suggest that this will complicate attempts to infer the portions of the crack tip singularity
that are due to stress and to the electric field. A related path-independent integral, the
M-integral, is used by Banks-Sills and Boniface to determine the stress intensity factors for
a crack on the interface between two transversely isotropic materials. A finite element
analysis is used to determine the asymptotic near-field displacements needed to evaluate the
M-integral.
Interpretation of the J-integral as an energy release is rigorous only for nonlinear
elastic materials. But much of its usefulness arises from applications to elastic-plastic
materials whose response, for proportional loading paths, is indistinguishable from a
hypothetical nonlinear elastic one. For significant deviations from proportional loading, the
interpretation of J in terms of fracture energy is approximate. Cotterell et al. present a
method for accounting for the extra work arising from deviations from proportional loading
due to significant crack growth in elastic plastic materials.
Crack growth is affected not only by mechanical loading (or coupled piezoelectric
loading as considered by Haug and McMeeking) but also by chemical processes. Numerical
simulations by Tang et al. show that the presence of chemical activity at the crack tip can
lead to blunting, stable steady crack growth or unstable sharpening of the crack tip. In the
steady state regime, the computed crack velocity as a function of applied load agrees
qualitatively with experiments but uncertainties in material parameters make quantitative
comparison difficult. Consistent with previous studies, Tang et al. find the existence of a
threshold stress level that leads to sharpening and fracture, but, contrary to previous studies,
this threshold depends not only on the mechanical driving force, but also on the chemical
kinetics.
A classic problem of material behavior is to delineate the conditions for which
materials fail ductilely or brittlely. Rice and Thomson addressed this problem by
considering the interaction of a dislocation with a sharp crack-tip and arguing that ductile
behavior occurred when the energetics of the interaction favored emission of a dislocation.
In a concise analysis, Beltz and Fischer extend this formulation to consider the effect of the
T-stress, that is , the non-singular portion of the crack-tip stress field. They show that the
EDITORS’ PREFACE vii
effect of this stress can be significant for small cracks, with lengths on the order of 100
atomic spacings.
Klein and Gao present an innovative approach to the problem of dynamic fracture
instability. They suggest that the discrepancy between predictions and observations could
be resolved by including non-linear deformations near the crack-tip. They do this by a
cohesive potential model that bridges the gap between continuum scale and atomistic scale
calculations. Using as a measure of failure the loss of strong ellipticity, they suggest that
crack branching may be associated with a loss of stiffness in biaxial stretching near the
crack-tip.
Several pioneering papers by Rice have considered the problem of determining the
stress and deformation fields near the tip of a crack in a ductile material. The chapter by
Drugan extends consideration to the case of a crack propagating along the interface of two
ductile (elastic-ideally plastic) materials. An interesting by-product of the analysis for
anti-plane deformation of bimaterials is a family of admissible solutions for homogeneous
materials (including the well-known Chitaley -McClintock solution). Analysis reveals that
beyond a certain level of material mismatch (ratio of yield stresses) a single term of the
asymptotic expansion is not sufficient to characterize accurately the near-tip field. This
suggests that the number of terms required will depend on some microstructural distance.
Yu and Cho present detailed observations of the crack-tip fields in plastically
deforming copper single crystals and compare them with fields predicted by Rice
(Mechanics of Materials, 1987). They suggest that discrepancies could be due to absence
of latent hardening in the elastic ideally plastic model analyzed by Rice.
Rubinstein presents the results of numerical calculations based on a complex
variable formulation for a variety of micromechanical models of composites. Though the
calculations are elastic, they take explicit account of various reinforcing fibers, particles,
etc. and, as a result the solutions depend on the ratio of fiber size to spacing, an important
design variable.
DEFORMATION: Another major contribution of Rice has been the
development of shear localization theory as a model of failure in ductile materials. In
contrast to fracture, where the stress intensification caused by acute geometry plays a
dominant role, the approach of shear localization is based on the constitutive description of
homogeneous deformation. The constitutive relation developed by Gurson, under Rice’s
direction, has seen much application in this context because it includes softening due to the
nucleation and growth of micro-voids, an important microscale feature of ductile metal
deformation. Chen et al. discuss modifications of the Gurson model that are necessary to
describe the anisotropy of aluminum sheets. A related chapter by Chien et al. uses a three
dimensional finite element analysis of a unit cell to confirm the accuracy of a
phenomenological anisotropic yield condition for porous metal and apply the
phenomenological condition to analyze failure in a fender forming operation. The chapter
by Rudnicki discusses shear localization of porous materials in a quite different context: the
effects of coupling between pore fluid diffusion and deformation on the development of
shear localization in geomaterials.
viii EDITORS’ PREFACE
Although the constitutive model developed by Gurson and those used by Chien et
al., Chen et al. and Rudnicki are more complex than classic elastic-plastic relations, they
include microstructural information simply by means of the void volume fraction or
porosity. The paper by Riedel and Blug presents an example of the type of sophisticated
constitutive model needed for implementation in a finite element code to model a complex
technology, solid state sintering. Application of the model to silicon carbide demonstrates
the level of detail and accuracy this kind of material modelling combined with finite element
analysis can bring to technological processes.
Elastic-plastic contact is an example of the fruitful application of continuum
mechanics to microscale processes. Applications include indentation hardness testing,
atomic force microscopy, powder compaction, friction and wear. Mesarovic reviews and
summarizes the current understanding in this area and identifies a number of problems in
need of further work. Recent computational advances have improved understanding but
further work is needed in several areas.
Hydrogen is an element whose presence on an interface or at a crack-tip can lead
to embrittlement. In an elegant analysis that combined thermodynamics and fracture
mechanics and extended the introduction of surface energy into fracture analysis by Griffith,
Rice showed how the presence and mobility of segregants can alter the surface energy.Wang
reviews the analysis of Rice and co-workers and shows that the predictions are consistent
with observations of hydrogen embrittlement in iron single crystals.
Anderson and Xin address the classic problem of the stress needed to drive a
dislocation. In particular, they examine how this stress is affected by a welded interface
using a model that allows them to vary independently the unstable stacking fault energy gus,
the peak shear strength and the slip at peak shear. Using a numerical solution, they find that
the critical resolved shear stress increases with gus, but is relatively insensitive to the
maximum shear strength.
Suo and Lu present a model for the growth of a two-phase epilayer on an elastic
substrate. By means of a linear perturbation analysis and numerical computations, they
show that the competition between phase coarsening, due to phase boundary energy, and
phase refining, due to concentration dependent surface stress, can lead to a variety of growth
patterns, including a stable periodic structure.
The chapter by Kachanov et al. gives a complete solution for the problem of
translation and rotation of ellipsoidal inclusions in an elastic space. Although they do not
pursue applications of the solution, the solution is relevant to deformation around hard
particles in a matrix, motion of embedded anchors, etc.
Thomson et al. present a percolation theory approach to addressing the inevitable
inhomogeneous deformation on the microscale. They show how it can be used to construct
stress/ strain response and give insight into processes of microlocalization.
We consider it an honor and privilege to have had the opportunity to edit this
volume. In the preparation of the biography, H. Gao, W. Drugan and Y. Ben-Zion provided
extra needed information. Jim himself provided autobiographical source material and
helped proofread it to assure its correctness and completeness. We are grateful to the
individual authors for their contributions and timely cooperation, and to the technical review
EDITORS’ PREFACE ix
board members who enhanced the quality of the volume by providing critical reviews on the
articles.
Our special thanks are due to Kluwer Academic Publishers, Dordrecht Office and
its professional staff for their editing and production, and for their agreement to publish the
Volume given even when it was still unwritten, but existed simply as a proposal in the form
of a list of authors and titles. Financial support and encouragement from NIST management
team, S. Freiman, G. White and E. R. Fuller, Jr. are gratefully acknowledged. Finally, we
would like to express our appreciation to Drs. W. Luecke, X. Gu and J. Guyer for their help
in the editing of this book.
T-J. CHUANG, Gaithersburg, MD J. W. RUDNICKI, Evanston, IL
25 August 2000