Creep of a composite with dual viscoplastic phases

Abstract

A homogenization theory is developed to predict the time-dependent creep strain of a two-phase composite whose constituent phases are both elastic–viscoplastic. To address this non-linear, time-dependent problem, a unified approach from elasticity to viscoelasticity, and then from viscoelasticity to viscoplasticity, is suggested, with the first step involving the correspondence principle and the second adopting a secant-viscosity approach. Albeit approximate, this approach is simple and capable of delivering the essential features of the time-dependent creep process for the elastic-viscoplastic composite. As the Laplace inversion needs to be cast in an explicit form, the theory at present can be applied only to the simple microgeometry involving randomly dispersed spherical inclusions. However, the theory developed is versatile enough to allow either phase to be viscoplastically stiffer than the other, including the limiting case that one phase is purely elastic. Application of the theory indicates that the viscoplasticity of the inclusion phase plays a very important role in determining the time-dependent creep of the composite. As its property changes from purely elastic to viscoplastic, the overall creep strain is visibly enhanced; this becomes even more evident when its property changes from being viscoplastically stiffer to being viscoplastically softer than the matrix.