Study of hardness and deformation of brittle materials with a density functional theory

Abstract

We investigated controlling parameters of hardness in brittle materials by exploring the correlation between hardness and shear mode cracking. Density functional theory was used to calculate the unstable stacking energies (shear resistance to irreversible deformation) and the surface energies (tension resistance to fracture) for comparison. We found that both the unstable stacking energies and the surface energies had a monotonic relationship with hardness in Ge, Si, 3C-SiC, cBN, and diamond. In particular, both the relationship between hardness and the unstable stacking energy and the relationship between hardness and surface energy are better characterized as power law than linear relationships. Moreover, the surface energy has a better correlation with hardness than the unstable stacking energy. Both the theoretical stress for a crack to form and the stress intensity factor for a crack to propagate, which depend on surface energies, have better correlation with hardness than the stress intensity factor for a crack to emit a dislocation, which depends on unstable stacking energies. The implication of these results for fracture and deformation mechanism during hardness measurement is also discussed.