Comparisons between three-dimensional and two-dimensional multi-particle unit cell models for particle reinforced metal matrix composites

Three-dimensional and two-dimensional unit cell models for describing the mechanical behaviour of particle reinforced metal matrix composites (MMCs) are compared by assessing predictions obtained from microgeometries consisting of 20 randomly positioned elastic particles embedded in an elastoplastic matrix. The elastic response to uniaxial loading predicted by the three-dimensional unit cells is found to comply with the appropriate three-point bounds. Predictions for the elastoplastic regime are somewhat less satisfactory, indicating that configurations containing a higher number of particles will be required to resolve the regions of concentrated plastic strains that develop in inhomogeneous materials. This implies that in the nonlinear range the size of reference volume elements depends on material behaviour. Comparisons of results obtained from planar and three-dimensional multi-particle unit cells show clear differences in terms of both the overall stiffnesses and phase averages as well as the standard deviations of the microscale stress and strain fields. These differences are much more pronounced in the elastoplastic range, where planar analyses do not adequately describe the overall strain hardening behaviour of particle reinforced MMCs and tend to markedly underpredict the equivalent stresses and maximum principal stresses in the particles.