COMPUTATIONAL MATERIALS SCIENCE Computational Materials Science 5 (1996) 177-186 Modelling void nucleation and growth processes in a particle-reinforced metal matrix composite material L.G. Lim, F.P.E. Dunne zyxwvutsrqponmlkjihgfedcbaZYXWVUTS Department of Mechanical Engineering, University of Manchester Institute of Science and Technology, P.O. Box 88, Sackville Street, Manchester M60 IQD, UK Received 15 July 1995; accepted 31 August 1995 zyxwvutsrqponmlkjihgfedcbaZYXWVUTS Abstract The nucleation and growth of voids in a particle-reinforced metal matrix composite (MMC) material have been modelled using internal state variable equations implemented in a unit-cell finite element model. The coupled elastic-viscoplastic damage constitutive equations enable a good representation of the dependence of the stress-strain behaviour on particle volume fraction, the influence of the damage process on the stress-strain behaviour, and the nature of the damage evolution over a range of volume fraction of particles. In particular, the volume fraction of reinforcement in the MMC material is found to influence the nature of the damage evolution process, and a volume fraction of approximately 20% has been identified as separating two different modes of damage evolution. 1. Introduction Modelling the deformation behaviour of struc- tures constructed from metal matrix composite (MMC) materials, as well as the modelling of the processing of such a material, by extrusion or forging for example, require continuum-level con- stitutive equations that account for the various effects of the reinforcement on the deformation behaviour of the MMC material. Parameters such as shape, size, volume fraction and distribution of the reinforcing phase are important. One impor- tant requirement of such a constitutive equation set is the ability to capture the effect of material damage, which leads to the progressive degrada- tion of the load-bearing capacity of the material. The finite element (FE) method is useful in the development of such constitutive equations, as it allows the detailed stress, strain and damage dis- tributions within the MMC material to be mod- elled. It is thought that the failure of MMC materials results from the nucleation, growth, and subse- quent coalescence of micro-voids within the ma- terial. Since the early’work of McClintock [l] and Rice and Tracey [2], it has been well established that the growth of voids is strongly dependent on the tensile hydrostatic stresses developed during the deformation process. Experimental studies conducted by Vasudevan et al. [3] and the FE modelling conducted by Christman et al. [4], on the effect of superimposed hydrostatic stresses on the deformation behaviour of MMC materials, have all revealed the strong dependence of the ductility on the hydrostatic stress. Tensile hydro- static stresses tend to hasten the growth of exist- 0927-0256/96/$15.00 0 1996 Elsevier Science B.V. All rights reserved SSDZ 0927-0256(95)00069-O