Keywords

discontinuous two-phase media, inelastic, isotropic, phase distribution, Statistical continuum, velocity gradient

Abstract

This work was supported in part (B.L. Adams) by the MRSEC Program of the National Science Foundation under Award no. DMR-9632556. Further support was provided by the Center for Materials Research and Technology (MARTECH at FSU) and Center for Nonlinear and Nonequilibrium Sciences (CENNAS at FAMU). A statistical contiuum mechanics formulation is presented to predict the inelastic behavior of a medium consisting of two isotropic phases. The phase distribution and morphology are represented by a two-point probability function. The isotropic behavior of the single phase medium is represented by a power law relationship between the strain rate and the resolved local shear stress. It is assumed that the elastic contribution to deformation is negligible. A Green's function solution to the equations of stress equilibrium is used to obtain the constitutive law for the heterogeneous medium. This realtionship links the local velocity gradient to the macroscopic velocity gradient and local viscoplastic modulus. The statistical continuum theory is introduced into the localization relation to obtain a closed form solution. Using a Taylor series expanision an approximate solution is obtained and compared to the Taylor's upper-bound for the inelastic effective modulus. The model is applied for the two classical cases of spherical and unidirectional discontinuous fiber-reinforced two-phase media with varying size and orientation.

Original Publication Citation

Int. J. Plasticity 14: (8) 719-731 (1998)