Anisotropy affects brittleness and stress-strain in ZrC

Abstract

The topology structures are investigated for Zener and Every anisotropy, universal elastic anisotropy, stress-strain, and brittleness in ZrC based on Bond matrix model and tensor theory. Although the mathematical expressions of these three kinds of anisotropy are different, they give the same results, that is, the anisotropy is along the directions of [100], [110] and [111] respectively. The study of the brittleness of ZrC shows that there is a one-to-one relationship between anisotropy and brittleness. The cause of this phenomenon can be explained from the 3-D spatial structure of its negative Cauchy pressure. The investigations mainly focus on the topological structures of stress - strain in ZrC induced by point force. The results indicate that the orientation of stress-strain is not only consistent with the direction of the anisotropy of the crystal, but also with the symmetry of the crystal.