A particular implementation of the Modified Secant Homogenization Method for particle reinforced metal matrix composites

The stress–strain relationship for Particle Reinforced Metal Matrix Composites (PMMCs) in the nonlinear regime has been frequently assessed by means of the Modified Secant Homogenization Method. This nonlinear Homogenization uses a Linear Elastic Homogenization scheme to calculate the Secant Compliance tensor of the composite in terms of the known Secant Compliance tensors of the composites’ constituent phases. The subject of the present work is the development of a particular implementation of the Modified Secant Homogenization Method for the case of PMMCs using, as the required underlying Linear Elastic Homogenization scheme, the Halpin–Tsai equation. The developed implementation, valid for PMMCs of geometrically isotropic microstructure, results in a relatively simple iterative procedure for the estimation of the nonlinear macroscopic stress–strain response. It has only two explicit parameters: the reinforcement volume fraction F and the ‘s’ parameter of the Halpin–Tsai equation, which carries implicitly information about particle aspect ratio and orientation. The proposed scheme is applied to the prediction of the uniaxial hardening curve and to the study of the influence of macroscopic hydrostatic stress on composite’s yield.