A secant-viscosity approach to the time-dependent creep of an elastic viscoplastic composite

Abstract

At present no homogenization theory seems to exist to estimate the time-dependent creep behavior of a two-phase viscoplastic composite. In this paper an approach introducing a linear viscoelastic comparison composite in conjunction with the secant viscosity is proposed for this purpose. The method makes use of a Maxwell matrix in the viscoelastic composite, and sets its shear viscosity equal to the secant viscosity of the viscoplastic matrix at every stage of deformation. The property of the viscoelastic composite is in turn determined from its elastic comparison composite, and the results are cast in the rate forms to reflect the continuously changing secant viscosity of the viscoplastic matrix. This new approach is neither restricted to rigid particles nor to a viscoplastic matrix with rigid elasticity, and it is capable of accounting for the strain-hardening of the matrix phase. The theory is developed fully for the particle-reinforced composite and, when applied to a TiC/Al system, it leads to a satisfactory agreement with available experimental data. Both concepts of viscoelastic comparison composite and secant viscosity are believed to be new in a homogenization scheme, and, as the secant moduli in the rate-independent plasticity, the secant viscosity now can play a useful role in the determination of the effective behaviour of an elastic-viscoplastic composite.