A nonlinear anisotropic elastic–inelastic constitutive model for polycrystalline ceramics and minerals with application to boron carbide

Abstract

A new continuum constitutive theory is developed and implemented for study of polycrystalline brittle solids subjected to possibly large stress and finite deformation. The general theory accounts for elastic anisotropy, nonlinear elasticity (via higher-order elastic constants), thermoelastic coupling, and various inelastic deformation mechanisms, including, but not restricted to, fracture, pore crushing, bulking, and stress-induced amorphization. The internal energy function depends on a logarithmic measure of material strain, entropy, and internal state variables accounting for defect accumulation, for example effects of micro-cracks on the tangent stiffness of the solid. The theory is applied towards a study of dynamic compression of boron carbide ceramic. Solutions to a planar impact problem are investigated for isotropic and anisotropic, i.e., textured, polycrystals. For the isotropic case, an implementation of the theory containing only two fitting parameters whereby conjugate thermodynamic forces provide evolution laws for damage and granular flow provides close agreement with Hugoniot data. Poled boron carbide polycrystals shocked along the c-axis are predicted to demonstrate higher peak shear stress, but reduced ductility, relative to isotropic polycrystals. Amorphization associated with nonlinear elastic instability is predicted to occur at smaller volumetric compression in poled boron carbide than its isotropic counterpart, which could further reduce relative ductility and strength of the former.