The Application of Self-Consistent Approaches to Modeling Mechanical Behaviour of Heterogeneous Two Phase Solids

One of the key problems in understanding the mechanical response of particulate-reinforced materials is the role played by heterogeneity of microstructure. Such heterogeneity occurs on a variety of scales. At the level of individual particles, there is the distribution in particle size (and perhaps also particle shape and orientation). When the particles are small (submicron), the yield stress (essentially the stress for dislocation bypass) is a function of particles size and spacing [1]. For larger particles, the yield strength becomes size-independent. However, the fracture strength of the particles (i.e. the stress required to either break a particle of to decohere its interface with the matrix) is size-dependent at all scales. Therefore, in a material containing a distribution of particle sizes there will be a distribution of both the local flow and fracture stress.