Formulation of Inelastic Constitutive Model for Metal Matrix Composites. 1st Report, Transversely Isotropic Model .

Abstract

A constitutive model to describe time-dependent inelastic behavior of unidirectionally fiber-reinforced metal matrix composites is developed from phenomenological and continuum mechanics points of view. The fibrous composite is treated as a homogeneous medium which hardens with inelastic deformation. The inherent anisotropy is assumed to be transversely isotropic. The constitutive modeling is based on the well-established thermodynamic formalism for internal state variable theories, where the thermodynamic potentials are defined using a transversely isotropic tensor of the fourth order. First, a kinematic hardening model is derived in the invariant form. In this model, the evolution of the internal state variable is prescribed by the Bailey-Orowan type so that both the transient and steady-state creep behavior can be described. Then, an isotropic hardening model is formulated by assuming a particular representation of the kinematic hardening variable. It is found that the isotropic hardening model can yield the power law relation for steady state responses.