Towards a nonlinear elastic representation of finite compression and instability of boron carbide ceramic

A nonlinear constitutive model invoking third-order anisotropic elasticity is developed for boron carbide single crystals subjected to potentially large compressive stresses. The model makes use of limited available published data from various experimental and theoretical (i.e., quantum or ab initio) studies. The model captures variations in second-order tangent elastic moduli and loss of elastic mechanical stability with increasing compression. In particular, reduced stability of boron carbide single crystals compressed normal to the c-axis (i.e., [0001]-direction) relative to higher stability in spherical compression is represented. Different stability criteria proposed in the literature are examined for boron carbide under spherical and uniaxial compression; model predictions show that the most critical criterion corresponds to a vanishing eigenvalue of a particular tangent stiffness matrix (i.e., incremental modulus) derived exactly in the present work. Model constants are proposed for CCC (less elastically stable) and polar CBC (more elastically stable) polytypes of boron carbide. Application of the model to a homogeneously strained polycrystal provides support for the hypothesis that failure (e.g., amorphization) follows a loss of elastic stability of favorably oriented grains at shock pressures on the order of 18-20 GPa. Additional experiments or atomic simulations are suggested that would resolve currently indeterminate features of the nonlinear elastic model.