~ Pergamon lnt. J. Solids Structures Vol.34, No. 6, pp. 703-726, 1997 Copyright © 1997 Elsevier Science Ltd Printedin Great Britain.All rightsreserved 002~7683/97 $17.00 + .00 PII: S0020-7683(96)00051-0 INFLUENCE OF MICROSTRUCTURAL VARIATIONS ON STEADY STATE CREEP AND FACET STRESSES IN 2-D FREELY SLIDING POLYCRYSTALS PATRICK ONCK and ERIK VAN DER GIESSEN Delft University of Technology, Laboratory for Engineering Mechanics, P.O. Box 5033, 2600 GA Delft, The Netherlands (Received 31 October 1995; in revised form 13 March 1996) Abstract--At elevated temperatures, creep in polycrystalline aggregates is often accompanied by free grain boundary sliding, which tends to enhance the macroscopic creep rate and the transverse facet stresses. This paper deals with the influence on these phenomena of variations in the micro- structure, in terms of variations in the size and shape of grains in an aggregate. Numerical results for two-dimensional cell analyses involving many grains are presented which demonstrate that random rnicrostructural variations relative to an array of regular hexagonal grains invariably lead to an increase of the creep rate enhancement due to sliding. For power-law creeping grains and for the variations considered here, the effects amount to up to a 60% increase. Moreover, it is shown that microstructural variations lead to a wider distribution of transverse facet stress levels with a considerably higher average than for regular hexagonal grains. Both effects are of significance for creep rupture life time estimates. Copyright © 1997 Elsevier Science Ltd. 1. INTRODUCTION At elevated temperatures and typical creep loading conditions, creep in polycrystalline engineering metals is often accompanied by grain boundary sliding. This is due to the fact that the resistance of grain boundaries against sliding of the adjacent grains relative to each other is low compared to the creep resistance of the grains themselves. Even though irregularities of the grain boundaries, such as ledges, and second-phase particles act as barriers for grain boundary sliding, the sliding resistance in many materials is frequently considered to be negligible all together (see, e.g., Ashby, 1972). In such cases of completely free grain boundary sliding, the overall creep rate of the polycrystalline material is increased appreciably compared to that in the absence of grain boundary sliding. There has been substantial interest in linking the overall (macroscopic) creep response to that of the (microscopic) response of the constituting grains for over two decades. Assuming simple isotropic creep models for the behavior of the grain material, various simple theoretical models were considered initially, such as the slip line approach of Brunner and Grant (1959), while shortly after, the phenomenon was studied more accurately by using numerical methods, first by Crossman and Ashby (1975) and cul- minating in Ghahremani's (1980) paper. The cited studies were all concerned with 2-D arrays of hexagonal grains. They have been complemented more recently by the 3-D works of Anderson and Rice (1985) and Dib and Rodin (1993). In addition to creep rate enhancement, free sliding leads to an enhancement of the average normal stress transmitted by grain boundaries that are normal to the macroscopic maximum principal tensile stress direction. This has been discussed in a 2-D context by, e.g., Rice (1981) and for 3-D by Anderson and Rice (1985) and by Dib and Rodin (1993). As this so-called principal facet stress is an important driving force for the development of grain boundary cavitation, there is an obvious interest in adequate descriptions of this phenomena because of the implications for creep fracture (see, e.g., Nix et al., 1989). All 2-D studies mentioned above have used periodic arrangements of completely regular hexagonal grains. Similarly, the cited 3-D studies used regular truncated octa- hedrons as space-filling model grains. It is clear that grains in real materials vary in size 703