Table Of ContentMECHANICS AND PHYSICS OF ENERGY DENSITY
ENGINEERING APPLICATION OF FRACTURE MECHANICS
Editor-in-ChieI George C. Sih
1. G.c. Sih and L. Faria (eds.), Fracture mechanics methodology:
Evaluation of structural components integrity. 1984.
ISBN 90-247-2941-6.
2. E.B. Gdoutos, Problems of mixed mode crack propagation. 1984.
ISBN 90-247-3055-4.
3. A. Carpinteri and A.R. Ingraffea (eds.), Fracture mechanisms of con
crete: Material characterization and testing. 1984.
ISBN 90-247-2959-9.
4. G.c. Sih and A. DiTommaso (eds.), Fracture mechanics of concrete:
Structural application and numerical calculation. 1984.
ISBN 90-247-2960-2.
5. A. Carpinteri, Mechanical damage and crack growth in concrete: Plastic
collapse to brittle fracture. 1986.
ISBN 90-247-3233-6.
6. J.W. Provan (ed.), Probabilistic fracture mechanics and reliability. 1987.
ISBN 90-247-3334-0.
7. A.A. Baker and R. Jones (eds.), Bonded repair of aircraft structures. 1987.
ISBN 90-247-3606-4.
8. J.T. Pindera and M.-J. Pindera, Isodyne stress analysis. 1989.
ISBN 0-7923-0269-9.
9. G.c. Sih and E. B. Gdoutos (eds.), Mechanics and physics of energy
density. 1992.
ISBN 0-7923-0604-X.
10. B.E. Gdoutos, Fracture mechanics criteria and applications. 1990.
ISBN 0-7923-0605-8.
11. G.c. Sih, Mechanics of fracture initiation and propagation. 1991.
ISBN 0-7923-0877-8.
Mechanics and Physics of
Energy Density
Characterization of material/structure behavior
with and without damage
George C. Sih
Institute of Fracture and Solid Mechanics
Lehigh University
Bethlehem, Pennsylvania, USA
and
Emmanuel E. Gdoutos
Department of Civil Engineering
Democritus University of 7hrace
X anthi, Greece
Kluwer Academic Publishers
Dordrecht / Boston / London
Library of Congress Cataloging-in-Publication Data
Mechanics and physIcs of energy density characterIzatIon of
material/structure behavior with and without damage / [edIted by]
George C. Sih and Emmanuel E. Gdoutos.
p. ern. -- (EngIneering applIcatIon of fracture mechanics 9)
Proceedings of a symposIum held July 17-20. 1989, at the
Democrltus University of Thrace.
Includes bIblIographIcal references
1. Fracture mechanlcs--Congresses. 2. StraIns and stresses-
-Congresses. I. Sih, G. C. (George C.) II. Gdoutos, E. E., 1948-
III. SerIes.
TA409.M399 1990
620.1' 126--dc20 90-41854
ISBN-13: 978-94-010-7373-8 e-ISBN-13: 978-94-009-1954-9
DOl: 10.1007/978-94-009-1954-9
Published by Kluwer Academic Publishers,
P.O. Box 17,3300 AA Dordrecht, The Netherlands.
Kluwer Academic Publishers incorporates the publishing programmes of
D. Reidel, Martinus Nijhoff, Dr W. Junk and MTP Press.
Sold and distributed in the U.S.A. and Canada
by Kluwer Academic Publishers,
101 Philip Drive, Norwell, MA 02061, U.S.A.
In all other countries, sold and distributed
by Kluwer Academic Publishers Group,
P.O. Box 322, 3300 AH Dordrecht, The Netherlands.
printed on acid:free paper
All Rights Reserved
© 1992 Kluwer Academic Publishers Dordrecht. The Netherlands.
Softcover reprint of the hardcover I st edition 1992
No part of the material protected by this copyright notice may be reproduced or utilized in any
fonn or by any means, electronic or mechanical, including photocopying, recording or by any
information storage and retrieval system, without written permission from the copyright owner.
Contents
Series on engineering application of fracture mechanics IX
Foreword Xln
Editors' preface XV
Contributing authors XIX
Photographs XXI
1. Synchronization of thermal and mechanical disturbances
in uniaxial specimens / G.c. Sih 1
1.1 Introductory remarks 1
1.2 System inhomogeneity and continuity 2
1.3 Simultaneity of displacement and temperature change 6
1.4 Isoenergy density theory 9
1.5 Axisymmetric deformation 15
1.6 Nonequilibrium response of cylindrical bar specimen
in tension 16
1.7 Conclusions 33
References 33
2. Thoughts on energy density, fracture and thermal emission /
R. Jones, M. Heller and L. Molent 35
2.1 Introduction 35
2.2 The F -111 wing pivot fitting 35
2.3 Damage assessment of an F/A-18 stabilator 39
2.4 The finite element model 44
2.5 Thermoelastic evaluation of damage 47
2.6 Stress fields from temperature measurements 52
2.7 Conclusions 56
References 56
V
VI Contents
3. Effects of fillers on fracture performance of thermoplastics:
strain energy density criterion / T. Vu-Khanh, B. Fisa and
1. Denault 59
3.1 Introduction 59
3.2 Experimental consideration 60
3.3 Fracture analysis 61
3.4 Strain energy density criterion 64
3.5 Conclusions 71
References 72
4. Strain energy density criterion applied to characterize
damage in metal alloys / V.S. Ivanova 75
4.1 Introduction 75
4.2 Strain energy density criterion 75
4.3 Thermal/mechanical interaction in solids 77
4.4 Damage characterization 79
4.5 Transition of micro- to macrodamage 82
4.6 Concluding remarks 84
References 84
5. Local and global instability in fracture mechanics /
A. Carpinteri 87
5.1 Introduction 87
5.2 Strain energy density fracture criterion 88
5.3 Strain-hardening materials 89
5.4 Strain-softening materials 94
5.5 Size effects on strength and ductility 103
References 107
6. A strain-rate dependent model for crack growth /
G.E. Papakaliatakis, E.E. Gdoutos and E. Tzanaki 109
6.1 Introduction 109
6.2 Description of the method 110
6.3 Specimen geometry and material properties 112
6.4 Stress analysis 113
6.5 Crack growth initiation 118
6.6 Concluding remarks 119
References 119
7. Extrusion of metal bars through different shape die: damage
evaluation by energy density theory / J. Lovas 121
7.1 Introduction 121
7.2 Yielding/fracture initiation in plastic deformation 122
7.3 Nonlinear behavior of extruded metal 124
7.4 Analysis of failure initiation sites 129
7.5 Conclusions 135
References 136
Contents VII
8. Failure of a plate containing a partially bonded rigid fiber
inclusion / E.E. Gdoutos and M.A. Kattis 137
8.1 Introduction 137
8.2 A partially bonded rigid elliptical inclusion in an infinite
plate 138
8.3 Local stress distribution and stress intensity factors 140
8.4 Failure initiation from the crack tip or the fiber end 144
References 147
9. Crack growth in rate sensitive solids / O.A. Bukharin
and L.V. Nikitin 149
9.1 Introductory remarks 149
9.2 Sih criterion 149
9.3 Linear viscoelastic solid 150
9.4 Crack growth in uniformly applied stress field 151
9.5 Conclusions 153
References 153
10. Strain energy density criterion applied to mixed-mode
cracking dominated by in-plane shear / K.-F. Fischer 155
10.1 Preliminary remarks 155
10.2 Sih's strain energy density criterion 157
10.3 Mixed-mode cracking dominated by in-plane shear 159
10.4 Discussions 163
References 164
11. Group-averaging methods for generating constitutive
equations / M.M. Smith and G.F. Smith 167
11.1 Introduction 167
11.2 Generation of scalar-valued invariants 167
11.3 Generation of tensor-valued invariant functions 170
11.4 Applications 173
References 178
12. A dislocation theory based on volume-to-surface ratio:
fracture behavior of metals / C.W. Lung, L.Y. Xiong and
S. Liu 179
12.1 Introduction 179
12.2 Super-dislocation model 179
12.3 Plastic zone size 183
12.4 Dislocation distribution in plastic zone 184
12.5 Crack in semi-infinite medium 186
12.6 Relation of volume/surface ratio to plate ligament 187
12.7 Specimens with different volume/surface ratio 188
12.8 Conclusions 191
References 193
VIII Contents
13. The effect of microcracks on energy density / N. Laws 195
13.1 Introduction 195
13.2 Microcracked solid with given crack density 196
13.3 Microcrack nucleation 198
References 201
14. Convex energy functions for two-sided solution bounds
in elastomechanics / A.A. Liolios 203
14.1 Introduction 203
14.2 General problem in elastostatics 203
14.3 Convexity of strain energy and Hilbert space: elastic system 205
14.4 Global solution bounds 206
14.5 Local solution bounds 207
14.6 Concluding remarks 208
References 209
Series on engineering application of
fracture mechanics
Fracture mechanics technology has received considerable attention in recent
years and has advanced to the stage where it can be employed in engineering
design to prevent against the brittle fracture of high-strength materials and
highly constrained structures. While research continued in an attempt to
extend the basic concept to the lower strength and higher toughness materials,
the technology advanced rapidly to establish material specifications, design
rules, quality control and inspection standards, code requirements, and
regulations of safe operation. Among these are the fracture toughness testing
procedures of the American Society of Testing Materials (ASTM), the
American Society of Mechanical Engineers (ASME) Boiler and Pressure
Vessel Codes for the design of nuclear reactor components, etc. Step-by-step
fracture detection and prevention procedures are also being developed by the
industry, government and university to guide and regulate the design of
engineering products. This involves the interaction of individuals from the
different sectors of the society that often presents a problem in com
munication. The transfer of new research findings to the users is now becoming
a slow, tedious and costly process.
One of the practical objectives of this series on Engineering Application of
Fracture Mechanics is to provide a vehicle for presenting the experience of real
situations by those who have been involved in applying the basic knowledge of
fracture mechanics in practice. It is time that the subject should be presented in
a systematic way to the practising engineers as well as to the students in
universities at least to all those who are likely to bear a responsibility for safe
and economic design. Even though the current theory of linear elastic fracture
mechanics (LEFM) is limited to brittle fracture behavior, it has already
provided a remarkable improvement over the conventional methods not
accounting for initial defects that are inevitably present in all materials and
G. C. Sih and E. E. Gdoutos (eds): Mechanics and Physics afEnergy Density, IX-XI.
© 1992 KIUI'veI' Academic Publishers.
x
Series on engineering application of fracture mechanics
structures. The potential of the fracture mechanics technology, however, has
not been fully recognized. There remains much to be done in constructing
a quantitative theory of material damage that can reliably translate small
specimen data to the design of large size structural components. The work of
the physical metallurgists and the fracture mechanicians should also be
brought together by reconciling the details of the material microstructure with
the assumed continua of the computational methods. It is with the aim of
developing a wider appreciation of the fracture mechanics technology applied
to the design of engineering structures such as aircrafts, ships, bridges,
pavements, pressure vessels, off-shore structures, pipelines, etc. that this series
is being developed.
Undoubtedly, the successful application of any technology must rely on the
soundness of the underlying basic concepts and mathematical models and
how they reconcile with each other. This goal has been accomplished to a large
extent by the book series on Mechanics of Fracture started in 1972. The seven
published volumes offer a wealth of information on the effects of defects or
cracks in cylindrical bars, thin and thick plates, shells, composites and solids in
three dimensions. Both static and dynamic loads are considered. Each volume
contains an introductory chapter that illustrates how the strain energy
criterion can be used to analyze the combined influence of defect size,
component geometry and size, loading, material properties, etc. The
criterion is particularly effective for treating mixed mode fracture where the
crack propagates in a nonself similar fashion. One of the major difficulties
that continuously perplex the practitioners in fracture mechanics is the
selection of an appropriate fracture criterion without which no reliable
prediction of failure could be made. This requires much discernment,
judgement and experience. General conclusion based on the agreement of
theory and experiment for a limited number of physical phenomena should
be avoided.
Looking into the future the rapid advancement of modern technology will
require more sophisticated concepts in design. The micro-chips used widely in
electronics and advanced composites developed for aerospace applications are
just some of the more well-known examples. The more efficient use of
materials in previously unexperienced environments is no doubt needed.
Fracture mechanics should be extended beyond the range of LEFM. To be
better understood is the entire process of material damage that includes crack
initiation, slow growth and eventual termination by fast crack propagation.
Material behavior characterized from the uniaxial tensile tests must be related
to more complicated stress states. These difficulties should be overcome by
unifying metallurgical and fracture mechanics studies, particularly in assessing
the results with consistency.
This series is therefore offered to emphasize the applications of fracture
mechanics technology that could be employed to assure the safe behavior of
