A new macroscopically anisotropic pressure dependent yield function for metal matrix composite based on strain gradient plasticity for the microstructure

Abstract

Metal matrix composites with long aligned elastic fibers are studied using an energetic rate independent strain gradient plasticity theory with an isotropic pressure independent yield function at the microscale. The material response is homogenized to obtain a conventional macroscopic model that exhibits anisotropic yield properties with a pressure dependence. At the microscale free energy includes both elastic strains and plastic strain gradients, and the theory demands higher order boundary conditions in terms of plastic strain or work conjugate higher order tractions. The mechanical response is investigated numerically using a unit cell model with periodic boundary conditions containing a single fiber deformed under generalized plane strain conditions. The homogenized response can be modeled by conventional plasticity with an anisotropic yield surface and a free energy depending on plastic strain in addition to the elastic strain. Hill's classical anisotropic yield criterion is extended to cover the composite such that hydrostatic pressure dependency, Bauschinger stress and size-effects are considered. It is found that depending on the fiber volume fraction, the anisotropic yield surface of the composite is inclined compared to a standard pressure independent yield surfaces. The evolution of the macroscopic yield surface is investigated by quantifying both anisotropic hardening (expansion) and kinematic hardening (translation), where the coefficients of anisotropy and the Bauschinger stress are extracted.