A model for damage in a clustered particulate composite

Previous models for the deformation of two-phase materials containing hard, brittle particles have been extended to allow the simultaneous treatment of damage and particle clustering. The model is based on a self-consistent analysis and uses an incremental, tangent modulus approach. Two problems are tackled. In the first we treat the effect of a distribution of particle sizes on damage development. We show that once the effect of the size distribution on the overall level of damage has been calculated a single damage parameter can be used to determine the stress–strain behavior with good precision. This validates the approach taken in our previous work. In the second problem we incorporate damage (in the form of particle cracking) into an elastic–plastic deformation model for a material containing a heterogeneous distribution of particles. The level of damage, as well as the local stress and strain, is allowed to vary between regions with different particle densities. The results indicate that clustering has a small but significant weakening effect on two-phase materials. This is in contrast with the effect of clustering in the absence of damage when a strong strengthening effect results. The results can be rationalized in terms of load redistribution between regions during the course of deformation.