International Journal of Fracture 106: 259–276, 2000. © 2000 Kluwer Academic Publishers. Printed in the Netherlands. Void growth and coalescence in metals deformed at elevated temperature HELMUT KLÖCKER 1 and VIGGO TVERGAARD Department of Solid Mechanics, Technical University of Denmark, DK-2800 Lyngby, Denmark Received 5 October 1999; accepted in revised form 19 May 2000 Abstract. For metals deformed at elevated temperatures the growth of voids to coalescence is studied numerically. The voids are assumed to be present from the beginning of deformation, and the rate of deformation considered is so high that void growth is dominated by power law creep of the material, without any noticeable effect of surface diffusion. Axisymmetric unit cell model computations are used to study void growth in a material containing a periodic array of voids, and the onset of the coalescence process is defined as the stage where plastic flow localizes in the ligaments between neighbouring voids. The focus of the study is on various relatively high stress triaxialities. In order to represent the results in terms of a porous ductile material model a set of constitutive relations are used, which have been proposed for void growth in a material undergoing power law creep. Key words: Coalescence, void growth, power law creep. 1. Introduction When metals are deformed at high temperatures the active fracture mechanism depends strongly on the rate of deformation, as has been discussed by Ashby et al. (1979). At low strain rates, where the corresponding stress levels are relatively low, failure tends to occur by intergranular creep fracture, where diffusive growth of grain boundary cavities plays an important role. However, at rather high strain rates and higher stress levels failure occurs by transgranular creep fracture or ductile fracture, where the failure mechanism is dominated by power law creep of the material around the voids. In an analysis of the rate of growth of a grain boundary cavity Needleman and Rice (1980) have shown the transition from diffusion dominated growth at low overall strain rates to growth dominated by power law creep when the strain rates are higher, and this behaviour has been implemented in a model for creep constrained cavitation of grain boundary facets by Tvergaard (1984). In the present investigation the focus is on void growth in hot working situations, i.e., cases where the strain rates are so high that the grain deformation mechanism dominates void growth. Therefore, effects of diffusion are neglected here, and the dislocation creep of the grains is represented as power law creep, allowing also for a small amount of strain hardening. Experimental studies for such void growth at elevated temperatures have been carried out by Tinet (1998). In studies of ductile fracture at room temperature, much understanding has been obtained by analyses for a characteristic volume element containing a single void. This includes the early plane strain analysis of Needleman (1972), representing a material with a square array of cylindrical voids, the analyses of Gurson (1977) for a spherical volume with a concentric 1 On leave from D´ epartement Science des Mat´ eriaux et Structures, Ecole des Mines, 42023 Saint-Etienne, France.