Effective elastic-plastic response of particulate two-phase composite materials under multi-axial loading

Abstract

In recent papers (Teng, 2014, 2018), an incremental elastic-plastic double-inclusion model was developed to determine the effective elastic-plastic response of two-phase composites of spherical or aligned spheroidal particles. For composites of purely elastic particles and elastic-plastic matrix of von Mises yield criterion with isotropic strain hardening, the double-inclusion model was formulated through the use of an isotropic matrix tangent stiffness tensor. The use of the isotropic tangent stiffness tensor, however, is only suitable for uniaxial loading or pure shear, but not for multi-axial loading. For in general the elastic-plastic tangent stiffness tensor of the matrix is inherently anisotropic, and during plastic deformation normal stress (strain) increment and shear strain (stress) increment are coupled, as a result of the anisotropy of the tangent stiffness tensor. In this paper, the original incremental elastic-plastic double-inclusion formulation presented in the previous papers (Teng, 2014, 2018) for composites of elastic spherical or aligned spheroidal particles and elastic-plastic matrix is modified by adding anisotropic corrections of stress increment defined in terms of the difference between the anisotropic and isotropic tangent stiffness tensors of the matrix. The resulting improved incremental double-inclusion model can be applied to multi-axial loading. Comparison of the model predictions to the results of the direct approach using representative volume elements containing many particles shows that the improved incremental elastic-plastic double-inclusion formulation is capable of predicting the effective elastic-plastic response of two-phase composites of spherical or aligned spheroidal particles under multi-axial loading.