Comparisons between three-dimensional and two-dimensionalmulti-particle unit cell models for particle reinforced metal matrixcomposites

Abstract

Three-dimensional and two-dimensional unit cell models for describing themechanical behaviour of particle reinforced metal matrix composites (MMCs) arecompared by assessing predictions obtained from microgeometries consisting of20 randomly positioned elastic particles embedded in an elastoplastic matrix.The elastic response to uniaxial loading predicted by the three-dimensionalunit 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 berequired to resolve the regions of concentrated plastic strains that developin inhomogeneous materials. This implies that in the nonlinear range the sizeof reference volume elements depends on material behaviour. Comparisons ofresults obtained from planar and three-dimensional multi-particle unit cellsshow clear differences in terms of both the overall stiffnesses and phaseaverages as well as the standard deviations of the microscale stress andstrain fields. These differences are much more pronounced in the elastoplasticrange, where planar analyses do not adequately describe the overall strainhardening behaviour of particle reinforced MMCs and tend to markedlyunderpredict the equivalent stresses and maximum principal stresses in theparticles.