Finite element modelling of deformation in particulate reinforced metal matrix composites with random local microstructure variation

Abstract

Deformation in particulate reinforced metal matrix composites (PR MMCs) with locally varying reinforcement volume fraction has been modelled using a two-scale finite element approach. The responses of axisymmetric unit cell models were used to define the constitutive response of mesoscale regions possessing varying volume fractions. Macroscale response was then investigated using two- and three-dimensional “random arrays” of finite elements, in which element properties were randomly assigned in line with a Gaussian distribution. Two-dimensional random arrays developed non-uniform strain fields, severe strain localization ensuing as straining proceeded. Two-dimensional random arrays are, however, inappropriate for modelling the three-dimensional microstructure of PR MMCs. Three-dimensional random arrays also developed non-uniform strain fields, but severe strain localization did not arise. Reinforcement clustering was simulated by varying the standard deviation in element volume fraction. Yield stress, strain hardening and elastic modulus were all found to increase as the severity of clustering increased.