Mechanics of Creep Brittle Materials 1

317 Pages·1989·9.28 MB·English

by  P. B. Hirsch, S. G. Roberts, J. Samuels, P. D. Warren (auth.), A. C. F. Cocks, A. R. S. Ponter (eds.)

MECHANICS OF CREEP BRITTLE MATERIALS
1
Proceedings of the European Mechanics Colloquium 239 'Mechanics of Creep
Brittle Materials' held at Leicester University, UK, 15-17 August 1988.
MECHANICS OF CREEP
BRITTLE MATERIALS
1
Edited by
A. C. F. COCKS
and
A. R. S. PONTER
Department oj Engineering, University oj Leicester, UK
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Softcover reprint ofthe hardcover I st edition 1989
British Library Cataloguing in Publication Data
Mechanics of creep brittle materials I.
I. Materials. Creep
I. Cocks, A.C.F. II. Ponter, A.R.S.
620.1'1233
ISBN-13: 978-94-010-6994-6 e-ISBN-13: 978-94-009-1117-8
001: 10.1007/978-94-009-1117-8
Library of Congress CIP data applied for
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v
Preface
Failure of components which operate in the creep range can result either from
the growth of a dominant crack or through the accumulation of 'damage' in the
material. Conventional and nuclear power generating plant are generally
designed on the basis of continuum failure, with assessment routes providing an
indication of the effects of flaws on component performance. Another example
where an understanding of creep failure is important is in the design of offshore
structures which operate in arctic waters. These structures can be subjected to
quite considerable forces by wind-driven ice sheets, which are limited by failure
of the ice sheet. Design codes are currently being developed which identify the
different mechanisms of failure, ranging from continuum crushing to radial
cracking and buckling of the ice sheet. Our final example concerns engineering
ceramics, which are currently being considered for use in a wide range of
high-temperature applications. A major problem preventing an early adoption of
these materials is their brittle response at high stresses, although they can behave
in a ductile manner at lower stresses.
In each of the above situations an understanding of the processes of fast
fracture, creep crack growth and continuum failure is required, and in particular
an understanding of the material and structural features that influence the
transition from brittle to ductile behaviour. The translation of this information to
component design is most advanced for metallic components. Research on ice
mechanics is largely driven by the needs of the oil industry, to provide
information on a limited class of problems. While, at the present time, ceramic
materials are still very much in the process of development. Uncertainties in the
reproducibility of physical properties and the difficulties encountered in testing
these materials at elevated temperatures are hindering the development of
suitable design procedures.
The aim of Euromech Colloquium 239 was to bring together researchers
interested in the creep behaviour of metals, engineering ceramics and ice to
examine the processes of crack growth and continuum failure. These proceedings
are divided into four sections, which examine either a particular type of failure
process, allowing comparisons to be made between the modelling of different
materials, or the behaviour of a particular class of materials. Each section
contains a selection of papers which discuss the material phenomena, the
Vl
development of material models and the application of these models to practical
situations. The first section examines the processes of crack propagation. This is
followed by two sections devoted to the behaviour of engineering ceramics and
ice, with a final section on continuum damage mechanics. This grouping of
papers is by no means exclusive and many of the papers which have been
assigned to one section could equally well have appeared in another.
It is evident from the papers presented in this volume and from the lively
discussions which accompanied each session of the Colloquium that we can learn
a great deal from the activities of researchers working on related problems in
different fields of study. We would therefore encourage the reader not only to
read the papers that relate directly to his own research interests, but also to
examine the papers which, at first sight, might appear to be outside his field of
study.
We would like to take this opportunity to thank all those people who helped to
make the Colloquium a success. We are grateful to Sue Ingle, Tim Wragg and
their staff in the University Conference Office and at Beaumont Hall for
providing a welcoming, relaxed environment and ensuring that the Colloquium
ran smoothly. Our thanks are also extended to Paul Smith for ensuring that none
of the presentations was disrupted by problems with audio-visual equipment.
We are particularly indebted to Jo Denning for all the time and effort she put
into the preparations for the Colloquium, and for looking after the needs of the
delegates, allowing us to participate fully in the proceedings.
A. C. F. COCKS
A. R. S. PaNTER
University of Leicester, UK
VB
Contents
Preface . ... V
1. Crack Propagation in Creeping Bodies
The brittle-to-ductile transition in silicon ..... .
P. B. Hirsch, S. C. Roberts,]. Samuels and P. D. Warren
Stress redistribution effects on creep crack growth 13
R. A. Ainsworth
Contour integrals for creep crack growth analysis 22
W. S. Blackburn
Modelling of creep crack growth 36
C. A. Webster
M0delling creep-crack growth processes in ceramic materials 50
M. D. Thouless
On the growth of cracks by creep in the presence of residual stresses 63
D.]. Smith
2. Deformation and Failure of Engineering Ceramics
Creep deformation of engineering ceramics 75
B. Wilshire
Statistical mapping and analysis of engineering ceramics data 99
]. D. Snedden and C. D. Sinclair
Indentation creep in zirconia ceramics between 290 K and 1073 K 117
]. L. Henshall, C. M. Carter and R. M. Hooper
YI11
Ductile creep cracking in uranium dioxide 129
T. E. Chung and T. j. Davies
Physical interpretation of creep and strain recovery of a glass ceramic near
glass transition temperature .. . . . . . . . . . . . . . . . . . . 141
C. Mai, H. Satha, S. Etienne andj. Pere;:;
3. Ice Mechanisms and Mechanics
Ice loading on offshore structures: the influence of ice strength 152
M. R. Mills and S. D. Hallam
Ice forces on wide structures: field measurements at Tarsuit Island 168
A. R. S. Ponter and P. R. Brown
The double torsion test applied to fine grained freshwater columnar ice,
and sea ice. . . . . . . . . . . . . . . . . . . . . . . . . . 188
B. L. Parsons,j. B. Snellen and D. B. Muggeridge
Ice and steel: a comparison of creep and failure . . . . . . . . . . . 201
N. K. Sinha
A micromechanics based model for the creep of ice including the effects of
general microcracking . . . . . . . . . . . . . . . . . . . . . . . 213
A. C. F. Cocks
4. The Growth of Continuum Damage in Creeping Materials
Continuum damage mechanics applied to multi-axial cyclic material
behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
D. A. Lavender and D. R. Hayhurst
Multiaxial stress rupture criteria for ferritic steels . . . . . . . . . . . 245
P. F. Aplin and G. F. Eggeler
Segregation of impurities in a heat-affected and an intercritical zone in an
operated O.SCr O.SMo 0.2SV steel . . . . . . . . . . . . . . . . . . 262
P. Battaini, D. D'Angelo, A. Olchini and F. Parmigiani
Effect of creep cavitation at sliding grain boundaries ......... 277
E. van der Giessen and V. Tvergaard
Creep fracture under remote shear. . . . . . . . . . . . . . . . . . 290
N. A. Fleck
THE BRITTLE-TO-DUCTILE TRANSITION IN SILICON
P.B. HIRSCH, S.G. ROBERTS, J. SAMUELS AND P.D. WARREN
Department of Metallurgy and Science of Materials
University of Oxford, Parks Road, Oxford OXl 3PH, UK
ABSTRACT
Recent experiments on the brittle-ductile transition (BDT) of precracked
specimens of Si show that the transition is sharp, and that the strain rate
dependence of the transition temperature, Te , is controlled by dislocation
velocity. Etch pit observations show that dislocation generation from the
crack tip begins at K just below Kre , from a small number of sources around
the crack tip. The dynamics of plastic relaxation has been simulated on a
model in which a small number of crack-tip sources operate and shield the
crack. The model predicts cleavage after some plasticity, and that a sharp
transition is obtained only if crack-tip sources are nucleated at K=Ko just
below Kre , and if these sources operate at K=KN«Ko . A mechanism for the
formation of crack-tip sources by the movement of existing dislocations to
and interaction with the crack tip is proposed. The model predicts a
dependence of Te and of the shape of the BDT on the existing dislocation
distribution, and this has been confirmed by experiment.
1. INTRODUCTION
This paper presents results of recent experiments on the brittle-to-ductile
transition (BOT) in silicon. At the BDT plastic relaxation processes blunt
and shield the crack making crack propagation more difficult, leading to an
increase in fracture stress with increasing temperature. The brittle-to-
ductile transition temperature, Te , depends on strain rate, the activation
energy controlling Te being that for dislocation velocity. A computer model
simulating the dynamics of dislocation generation at crack tips has been
developed and the predictions of this model have been compared with
experiment.
2. EXPERIMENTAL APPROACH
Mechanical tests have been carried out using four-point bending of
precracked bar-shaped speCimens of float zone Si, with their long axis
(25mm) parallel to [111] and their shorter axes along [110] (lmm) and [112]
(3mm) respectively. The intended fracture plane, perpendicular to the
2
direction of applied tensile stress, was a (Ill) plane, a natural cleavage
plane in Si. The sharp precrack was introduced by Knoop indentation at room
temperature. Crack depths of l3~m and 37~m were used. This technique also
leaves a plastic zone in the region of the indentation; the residual stress
was relaxed by annealing the crystals at 800°C in vacuum.
3. EXPERIMENTAL RESULTS
Fig. 1 shows fracture stress against temperature for a given strain rate,
for intrinsic Si. The transition is extremely sharp. The range of
temperatures from the highest at which a specimen fractures in a completely
brittle manner to the lowest at which a specimen deforms plastically is
typically about 10°C.
~e
:z
CD~ 4
Brittle Ductile
b ............. .o. 0 0 0- 00 " 0 =
." ' .
o • •
20 ~50 5 0 550 6 0
Temperatu re (°0
Figure 1. Failure stress vs. temperature for intrinsic silicon specimens
tested at the minimum strain rate, 1.3xl0- 6S- 1 • Note the sharpness of the
brittle-ductile transition.
The transition temperature Tc is strongly strain-rate dependent,
varying by about 100°C when the strain-rate is changed by a factor 10. Fig.
2 shows the results of tests carried out at different strain rates, for
intrinsic (2.5 x 1013 P atoms cm- 3 ) and n-type material (2 x 1018 P atoms
cm- 3 ). The precrack depth is l3~m in all experiments except for point C,
where the crack depth is 37~m. The strain rate is expressed in terms of
rate of increase of stress intensity factor, K, using the expression of
Newman and Raju [lJ for a semicircular crack, and the relation between
stress and strain for a perfectly elastic beam in four-point bending.
Fig. 2 shows that K a exp-Ue/kTc ' where Ue is the experimental
activation energy. The values of the experimental activation energy agree
(within experimental error) with those determined by George and Champier [2J
for dislocation motion in similarly doped silicon specimens. This confirms
the original suggestion of St.John [3J that the activation energy
controlling the strain-rate dependence of Tc is that for dislocation
veloci ty. Fig. 2 also shows St. John's original data for intrinsic Si,
obtained using a tapered double cantilever technique, with specimens
containing straight through cracks. It should be noted that while the
activation energy is close to that for dislocation velocity for intrinsic
material, there is a considerable shift in Tc to higher values compared with
those from the Oxford experiments. Typically the shift is -100°C for