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MECHANICS 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 ELSEVIER APPLIED SCIENCE LONDON and NEW YORK ELSEVIER SCIENCE PUBLISHERS LTD Crown House, Linton Road, Barking, Essex IGII 8jU, England Sole Distributor in the USA and Canada ELSEVIER SCIENCE PUBLISHING CO., INC. 655 Avenue of the Americas, New York, NY 10010, USA WITH 19 TABLES AND 186 ILLUSTRATIONS © 1991 ELSEVIER SCIENCE PUBLISHERS LTD © 1991 NUCLEAR ELECTRIC PLC-pp. 90-99 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 No responsibility is assumed by the Publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. Special regulations for readers in the USA This publication has been registered with the Copyright Clearance Centre Inc. (CCC) , Salem, Massachusetts. Information can be obtained from the CCC about conditions under which photocopies of parts of this publication may be made in the USA. All other copyright questions, including photocopying outside the USA, should be referred to the publisher. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photo- copying, recording, or otherwise, without the prior written permission of the publisher. 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
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