A unified approach from elasticity to viscoelasticity to viscoplasticity of particle-reinforced solids

This paper presents a novel approach to determine the overall elastic-viscoplastic behavior of a particle-reinforced metal-matrix composite. It is built upon the linkage from elasticity to viscoelasticity through the correspondence principle, and then from viscoelasticity to viscoplasticity by means of the concept of secant viscosity and an energy approach. Albeit approximate, this theory is analytically tractable, and capable of delivering the stress-strain relations of the composite system under various applied strain rates. The theory embodies the nonlinear, rate-dependent, and work-hardening nature of the constitutive equations of the ductile matrix, as well as the elasticity of both matrix and inclusions. The influence of particle concentration, elastic stiffness, and applied strain rate on the overall dilatational and deviatoric stress-strain behaviors are examined in detail. The theory is finally applied to predict the response of a silicon-carbide/aluminum system and the result is found to be in accord with experimental observations.