Table Of ContentMECHANICS OF CREEP BRITTLE MATERIALS
2
Proceedings of the International Colloquium 'Mechanics of Creep Brittle
Materials 2' held at the University of Leicester, UK, 2-4 September
1991.
MECHANICS OF CREEP
BRITTLE MATERIALS
2
Edited by
A. C. F. COCKS
Department of Engineering, Cambridge University, UK
and
A. R. S. PONTER
Department of Engineering, Leicester University, UK
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British Library Cataloguing in Publication Data
European Mechanics Colloquium 'Mechanics of Creep
Brittle Materials 2' (1991 : University of Leicester)
Mechanics of creep brittle materials.
I. Title II. Cocks, A. C. F.
III. Ponter, A. R. S.
620.11233
ISBN 1-85166-701-6
Library of Congress CIP data applied for
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v
Preface
Mechanics of Creep Brittle Materials-l was published in 1989 as the
proceedings of a Colloquium held in Leicester in the summer of 1988.
The Colloquium examined the creep response of a wide range of
materials, including metals, engineering ceramics and ice, with the aim of
determining similarities in the response of these materials and the way in
which their behaviour is modelled. The proceedings were structured so as
to reflect the interdisciplinary nature of the Colloquium, with papers
grouped together largely on the basis of the phenomena being examined,
rather than by class of material.
Mechanics of Creep Brittle Materials-2 was held in Leicester in Septem-
ber 1991 to discuss advances made in our understanding of the response
of creep brittle materials since the first Colloquium. The scope of the
Colloquium was extended to include mineral salts, concrete and com-
posite systems. These proceedings are once more structured so that the
reader can readily compare the response of different material systems and
evaluate the suitability of the range of models presented to the materials
he is interested in. In fact a number of papers directly compare the
behaviour of a range of different materials with the aim of identifying
general strategies for the testing and modelling of creeping materials.
The proceedings are divided into two main sections. The first considers
the propagation of cracks in creeping materials, with papers concerned
with crack stability, transient and steady state crack growth and crack
growth under cyclic loading conditions. The second section is largely
concerned with continuum processes, with papers describing micromech-
ani cal and phenomenological models of creep deformation and failure
and the application of these models in the design of high temperature
components. It is often difficult to determine the continuum response of
creep brittle materials, and this section concludes with a series of papers
which investigate the use of indentation techniques to obtain appropriate
properties.
We would like to take this opportunity to thank all the people involved
in Mechanics of Creep Brittle Materials-2. We are grateful to Leicester
University for allowing us to hold the Colloquium in Beaumont Hall and
VI
the University Conference Office and Beaumont Hall staff for providing a
welcoming and relaxed environment. We are once more indebted to Jo
Denning for all the time and effort she has put into making the
arrangements for the Colloquium and into the preparation of these
proceedings.
A. C. F. COCKS
University of Cambridge, UK
A. R. S. PONTER
University of Leicester, UK
VII
Contents
Priface ............................................................................................... v
1. Crack Propagation in Creeping Bodies
A study of creep crack growth in engineering materials
A. C. F. Cocks and]. D.]. De Vqy
Transition effects in creep-brittle materials 14
K. M. Nikbin
Crack growth stability in saline ice 25
S.]. DeFranco and]. P. Dempsey
Finite element prediction of creep damage and creep crack growth.. 37
Y. Duan,].]. Webster and T. H. Hyde
Influence of continuum damage on stress distribution near a tip of a
growing crack under creep conditions ............................................... 49
V. l. Astafjev, T. V. Grigorova and V. A. Pastukhov
Dislocation movement at crack tip of single crystals of ice 62
Y. Wei and]. P. Dempsey
A theoretical study on the effect of residual stress on creep brittle
crack growth ..................................................................................... 74
D.]. Smith and A. C. F. Cocks
Creep crack growth prior to stress redistribution 90
P.]. Budden, D. W. Dean and G. E. Turner
Vlll
Creep-fatigue crack growth in welded fusion boundaries .................. 100
R. H. Priest, D. N. Gladwin and D. A. Miller
2. Continuum Mechanics-Deformation and Damage Growth
Microscopic models and macroscopic constitutive laws for high
temperature creep and creep fracture of metallic and ceramic
materials........................................................................................... 112
B. Wilshire
Characteristic temperature of deformation of materials and cold
brittleness of BCC metals and ceramics ............................................ 124
Yu V. Milman
On the linking-up of microcracks in creeping polycrystals with grain
boundary cavitation and sliding........................................................ 134
E. Van der Giessen and V. Tvergaard
Long term creep ductility minima in 12% CrMoV steel.................. 146
R. Timmins and P. F. Aplin
Failure criteria on creep rupture of mineral salt based on
micromechanical mechanisms ........................................................... 160
E. Stein and U. Heemann
Volume change and energy dissipation in rock salt during triaxial
failure tests ........ ........... ...................................... .... ... .................. ..... 172
U. Hunsche
Non-stationary cavity nucleation-a limiting process for high-
temperature strength and superplasticity in ceramics ....................... 183
H. Balke, H-A. Bahr and W. Pompe
Superplastic phenomena in some structural oxide ceramics .............. 192
]. Luyten, W. Hendrix,]. Sleurs and W. Vandermeulen
Creep of powder metallurgical chromium 202
R. Eck, W. Kock and G. Kneringer
Effective properties in power-law creep ............................................ 218
P. Ponte Castaneda
IX
Deformation and creep of silicon nitride-matrix composites ..... ........ 230
Y. Gogotsi, D. Ostrovoj and V. Traskovsky
Localization and development of damage under high temperature
loading conditions .. ......... ........ ........... ...................................... ......... 242
V. Sklenicka, I. Saxl and]. Cadek
Non-linear models of creep damage accumulation ........................... 254
V. P. Golub
Calculation offailure probability for brittle materials .................... ... 268
]. Smart and S. L. Fok
On the applicability of the superposition principle in concrete creep 282
]. C. Walraven and]. H. Shen
Creep failure of weldments in thin plates .............. ........... ........ ......... 296
M. G. Newman and R. E. Craine
Stress calculation the ceramic thermal barrier coatings for the cooled
turbine blades ................................................................................... 308
Y. A. Tamarin, V. G. Soundyrin and V. Yu. Kanayev
Modelling the mechanisms and mechanics of indentation creep with
application to zirconia ceramics ........................................................ 313
]. L. Henshall, G. M. Carter, K. E. Easterling, R. M. Hooper and
W. B. Li
Indentation creep ............................. .......... ..... ................. ................. 326
P. M. Sargent and M. F. Ashby
The use of the soft indenter technique to investigate impression
creep in ceramic crystals ................................................................... 345
C. A. Brookes, E.]. Brookes and G. Xing
Relationship between creep and fracture of ice ................................. 355
M. A. Rist and S. A. F. Murrell
A STUDY OF CREEP CRACK GROWTH IN ENGINEERING MATERIALS
ALAN C.F. COCKS· & JULIAN D.l. DE VOy+
•
Department of Engineering, Cambridge University,
Trumpington Street, Cambridge CB2 IPZ, UK.
+ Department of Engineering, Leicester University,
University Road, Leicester LEI 7RH, UK.
ABSTRACT
From an examination of the different types of stress and strain-rate
fields that can develop ahead of a growing crack in an elastic / creeping
material a simple map is developed for presenting creep crack growth data.
The map can also be used to determine the most suitable, if any, crack tip
parameter to correlate a particular set of data and to assess the range of
applicability of theoretical models describing the process of crack growth.
INTRODUCTION
structural components operating at high temperatures can often fail as
the result of the time dependent propagation of flaws which have either
been introduced into the component during manufacture or nucleate early in
the life of the component. Assessment procedures are currently being
developed for metallic components used in the power generating industry
which addresses this particular problem [1]. This type of failure is not,
however, limited to metallic components. Ceramic components invariably
contain flaws which are introduced into the component during cooling from
the sintering temperature as a result of variations in the elastic and
thermal properties along different crystallographic planes or due to the
presence of inhomogeneities in the compact. There are broad similarities
between the response of these two classes of materials and the theoretical
models that have been developed to describe their behaviour [2,3].
If a crack grows sufficiently quickly then the stress and strain-rate
