Pergamon Engineering Fracture Mechanics Vol. 57, No. 2/3, pp. 205-226, 1997 1997 Elsevier Science Ltd. All rights reserved Printed in Great Britain PII: S0013-7944(97)00009-X oo13-7944/97 $17.oo+ o.oo SOME EFFECTS OF RANDOM MICROSTRUCTURAL VARIATIONS ON CREEP RUPTURE E. VAN DER GIESSEN, P. R. ONCK and M. W. D. VAN DER BURG Laboratory for Engineering Mechanics, Delft University of Technology, Delft, The Netherlands Abstract--High-temperature creep rupture of polycrystalline materials involves a number of physical mechanisms, such as the nucleation and diffusive growth of grain boundary cavities and grain bound- ary sliding, which act at different length scales in the material. This paper uses a micromechanical model to explore how random variations in the microstructure of the material affect its lifetime. The model involves a chain of size scale transitions and two size scales are considered in particular: the size scale of individual cavities and the scale of aggregates of grains. Emphasis is put on geometrical vari- ations in the microstructure, i.e. random variations in size and shape of grains in an aggregate. The role of grain boundary sliding, and the competition between creep flow and grain boundary diffusion are highlighted. Wherever possible, regimes are indicated where such microstructural variations can be safely neglected or where they are critical in determining the lifetime. © 1997 Elsevier Science Ltd. 1. INTRODUCTION FAILURE OF metals, alloys as well as certain types of ceramics, under creep conditions at tem- peratures of 0.3-0.4 times the melting temperature commonly occurs by intergranular fracture. The main mechanisms for tertiary creep and this type of fracture have been identified to be the nucleation and growth of grain boundary cavities. Coalescence of these cavities leads to grain boundary microcracks and macroscopic failure takes place by the linking-up of these micro- cracks. Fracture surfaces show that grain boundary facets are covered with many small dimples, being the remains of cavities. Because of the evident technological importance, creep fracture has been the subject of many investigations. Comprehensive overviews of the field may be found in a number of review articles, such as refs [1-3]. Modelling of creep fracture has been explored along a number of different routes. Firstly, at the truly macroscopic scale, fracture mechanics approaches have been used to characterize the conditions for creep fracture in terms of indicators of the fields near the crack tip such as C* (see e.g. refs [3, 4]). Also, purely phenomenological descriptions of tertiary creep have been attempted, e.g. in ref. [5]. Secondly, continuum damage models have been proposed to incorporate the effect of the evolving damage in the material on the response of the material (see e.g. refs[6-8]). Generally speaking, these models are clearly motivated by the above-mentioned micromechanisms of creep fracture, but incorporate damage in a purely phe- nomenological manner without attempting to model the individual micromechanisms. Finally, micromechanical models have been developed that are directly based on descriptions of the var- ious physical mechanisms involved. This paper will be concerned exclusively with micromechanical models. To be more specific, we shall follow the multi-step modelling approach outlined in Fig. 1 involving a number of nested size scales. The starting point is the size scale of the individual grain boundary cavities (to be referred to as the microscopic level), followed by the size scale of aggregates of grains (called here the mesoscopic level) and finally the macroscopic level where the polycrystalline ma- terial can be treated as a continuum. The objective of this micromechanical modelling is to pro- vide a description of the behaviour at any level on the basis of a model of the mechanisms at the previous size scale level. Consecutive scale transitions ultimately should lead to a description of the macroscopic behaviour based on all relevant underlying micromechanisms. This kind of approach involves different material microstructures at each of the size scales considered. Making the scale transition to the next size scale necessarily implies modelling these microstructures. Often, this is done by making simplifying assumptions about the microstruc- ture, so as to replace the actual structure with a much simpler microstructure that is considered to be representative for the actual microstructure and which can be conveniently translated into 205