Table Of ContentThe Physics of Creep
The Physics of Creep
Creep and Creep-resistant Alloys
F. R. N. Nabarro
Division of Materials Science and Technology, CSIR,
Pretoria, South Africa
and
Condensed Matter Physics Research Unit,
University of the Witwatersrand, Johannesburg, South Africa
H. L. de Villiers
Division of Materials Science and Technology, CSIR,
Pretoria, South Africa
Taylor &Francis
•' Fiihli.slwr.s since I79.S
UK Taylor & Francis Ltd, 4 John St., London WCIN 2ET
USA Taylor & Francis Inc., 1900 Frost Road, Suite 101, Bristol, PA 19007
Copyright © Taylor & Francis Ltd 1995
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British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
ISBN 085066 852 2
Cover design by Hybert • Design & Type
Typeset by Euroset, Dover Close, Alresford, Hampshire
Printed in Great Britain by Burgess Science Press, Basingstoke,
on paper which has a specified pH value on final paper
manufacture of not less than 7-5 and is therefore ‘acid free’.
Contents
Preface ix
List of symbols xi
Chapter 1 Introduction to creep-resistant alloys 1
1.1 The significance of creep in engineering applications 1
1.2 Applications of creep-resistant alloys 2
1.3 The use of superalloys in gas turbines 3
1.4 The development of the superalloys 8
References 14
Chapter 2 The phenomenology of creep 15
2.1 The creep curve 15
2.2 The Monkman-Grant relationship 22
2.3 Creep damage parameters 22
2.4 The dependence of creep rate on stress 25
2.5 The dependence of creep rate on temperature 32
2.6 The 0-projection 34
2.7 Grain-boundary sliding 36
References 43
Chapter 3 The mechanisms of creep 47
3.1 The Ashby map 47
3.2 Analysis of the activation energies for creep 49
3.3 Diffusional creep 53
3.4 Low-temperature transient creep (logarithmic creep) 60
3.5 High-temperature transient creep 63
3.6 Primary creep in single crystals and in polycrystals 65
3.7 Steady-state power-law creep 66
3.8 The growth of grain-boundary voids 78
3.9 Creep in alloys containing more than one phase 79
References 80
Chapter 4 Dispersion strengthening 83
4.1 Introduction 83
4.2 Strengthening mechanisms in systems containing
penetrable particles 85
4.3 Strengthening mechanisms in systems containing
impenetrable particles 85
4.3.1 Yield stress 85
4.3.2 Work hardening 88
VI Contents
4.3.3 Creep in materials hardened by impenetrable
particles 89
4.4 Direct and indirect particle strengthening effects 98
References 100
Chapter 5 The plasticity of single crystals having the LI2 structure 103
5.1 Introduction and basic observations 103
5.2 Dislocations and planar faults in the LI2 structure 121
5.3 General considerations on the strength of ordered
alloys 134
5.4 Slip on {001} 143
5.5 The ‘classical’ theory of deformation in LI2 structures 150
5.6 Evidence against the ‘classical’ theory 158
5.7 New theories of the stress anomaly 164
5.8 Alloying and non-stoichiometry in the 7' phase 171
References 178
Chapter 6 The plasticity of ‘single crystals’ of two-phase 7/7' alloys 187
6.1 Introduction: 7/7' as a composite material 187
6.1.1 The activation energy 193
6.1.2 The influence of 7' particle size 194
6.2 The flow stress of 7/7' composites 195
6.2.1 Particle shearing or Orowan looping? 195
6.2.2 Estimates of the flow stress 202
6.2.3 Creep and the dependence of stress on strain
rate 208
6.2.4 The incubation period and the transition to
primary creep 209
6.2.5 Primary creep and the transition to secondary
creep 210
6.2.6 Steady-state secondary creep 212
6.2.7 Tertiary creep 217
6.2.8 Work hardening and the orientation dependence
of the creep life 217
6.3 Lattice misfit between 7 and 7' : 7' morphology 221
6.3.1 Nucléation and growth of non-interacting 7 '
particles 223
6.3.2 Elastic interactions between particles 227
6.3.3 The 7/7' misfit and its accommodation by
dislocations 233
6.3.4 The accumulation of dislocations under stress 237
6.3.5 Rafting 241
6.3.6 Effect of rafting on the mechanical properties 245
6.4 Appendix —Elastic constants of LI2 compounds 248
References 248
Contents
Vll
Chapter 7 Mechanical properties of polycrystals and the problem of
fracture 255
7.1 Introduction 255
7.2 Polycrystalline two-phase superalloys 255
7.2.1 The change of flow and fracture modes with
change in the loading conditions 255
7.2.2 Fatigue and its interaction with creep 262
7.2.3 Fracture of single crystals of LI2 alloys 264
7.3 Polycrystalline single-phase LI2 alloys 268
7.3.1 Dependence of the flow stress on the grain size 268
7.3.2 Grain-boundary fracture 269
7.3.3 The nature of grain boundaries in the LI2
structure 272
7.3.4 The influence of boron on grain-boundary
fracture 277
7.3.5 The influence of antiphase boundaries on the
ductility 286
7.3.6 The effect of boron doping on environmental
embrittlement 287
References 289
Chapter 8 Possible new high-temperature creep-resistant materials 295
8.1 The demands and the prospects 295
8.1.1 The underlying physical principles 296
8.1.2 Other underlying principles 305
8.2 Ordered alloys with the LI2 structure 306
8.3 Ordered alloys with the B2 structure 310
8.4 Ordered alloys with other structures 325
8.4.1 The Llo structure (CuAu, TiAl) and Llj (CuPt) 326
8.4.2 The DO22 structure (Al3Ti, Al3Nb), DO23 and
the devil’s staircase 331
8.4.3 The L'l2 or E2| perovskite structure of
Fe3AlC, Ti3AlC and Fc3NiN 334
8.4.4 The DO3 structure of Fe3Al 335
8.4.5 The L2i (Heusler) structure of Ni2AlTi 341
8.4.6 The DO19 ordered hexagonal structureo f Ti3Al 342
8.4.7 Exotic structures 348
8.5 Polyphase materials 357
8.5.1 Mechanical properties of polyphase materials 357
8.5.2 Plastic anisotropy of lamellar structures 361
8.5.3 Semi-coherent two-phase structures not based
on 7/18 Ti-Al or TiAl/Ti3Al 362
8.5.4 The systems 7//? Ti-Al and TiAl/Ti3Al 364
8.5.5 Three-phase systems 367
8.5.6 Materials of very fine grain size 368
Vlll Contents
8.6 Alloy design by computation 371
8.6.1 PHACOMP and its extensions 371
8.6.2 Pettifor maps 373
8.6.3 Electron-theoretical calculations for ordered
structures 374
8.6.4 Electron-theoretical calculations for disordered
structures 375
References 378
Subject index 391
Author index 403
Preface
This book arose from a series of lectures given by Frank Nabarro at the Division
of Materials Science and Technology of the South African CSIR (Council for
Scientific and Industrial Research) in 1988. It was suggested that the material
should be amplified and published in book form, and Heidi de Villiers, who
had taken careful notes and was acquainted with creep more from a materials
engineering perspective, agreed to join Frank Nabarro as a co-author. The
audience at the lectures consisted mostly of young materials engineers, mechanical
engineers, physicists and chemists, all of whom were then working on creep-
resistant alloys. The lecturer, a physicist, tried to convey his approach to the
subject to this diverse audience, and the present book has the same aim. No
attempt is made to treat topics such as corrosion, which are best approached
by the methods of the chemist or metallurgist, or fatigue and the initiation and
propagation of cracks, which involve the special considerations of fracture
mechanics.
Chapter 1 briefly introduces the nature of the engineering problems involved
to those who are not already acquainted with the field. Chapters 2, 3 and 4,
which deal largely with well-established facts and theories, analyse the
observations made on creep and discuss the physical considerations underlying
them. Chapters 5, 6 and 7 deal mainly with that important class of superalloys
in which coherent precipitates of a Ni3Al-based alloy having the ordered cubic
LI2 structure are formed in a cubic (but not ordered) matrix having roughly
the same composition. The ordered phase has remarkable properties, including
the so-called ‘temperature anomaly’ in which the mechanical strength increases
with increasing temperature over a wide temperature range. Understanding of
the anomalous behaviour has increased greatly between the time the lectures
were given and date of completion of the book.
Finally, Chapter 8 treats possible new high-temperature creep-resistant
materials. These are numerous, and while some general principles are discussed,
present understanding of the behaviour of these materials does not approach the
depth of available knowledge of the superalloys.
It would not have been possible to survey this wide field without the help of
many colleagues, who are too numerous to name individually here, but our thanks
are due especially to R. W. Cahn, P. B. Hirsch, P. M. Hazzledine and D. G.
Pettifor. We would also like to thank R. Smith of the University of the
Witwatersrand who re-drew most of the figures, Christelle Steam of the CSIR
who uncomplainingly typed the first draft from a tortuous manuscript and the
Division of Materials Science and Technology of the CSIR for their continued
support through the programme of N. R. Comins.
F. R. N. Nabarro
H. L de Villiers-Filmer
