Anisotropy in the scratch hardness of cubic crystals

Abstract

A smooth parallel-sided groove can be formed in all single crystals, by a harder slider, when the experimental conditions are adjusted to facilitate extensive plastic flow. Under these conditions scratch hardness measurements can be based on the width of the groove and expressed in terms of a mean pressure. The hardness values depend on crystal face and sliding direction and results obtained for a range of metallic and non-metallic crystals indicate that the observed anisotropy is determined by the relevant slip systems. For example, the nature of anisotropy in the scratch hardness of diamond cubic crystals is directly analogous to that of face-centred cubic crystals. While there is generally a significant difference in the hardness of materials in these two categories, plastic flow occurs on $\{111\}\langle 1\overline{1}0\rangle $ slip systems in both types of crystal structure. The deformation and displacement of material beneath, and in front of, a moving slider has been considered on the basis of resolved shear stress criteria. An analysis of the scratch hardness process is presented in which the relative magnitude of the 'effective resolved shear stress $(\tau _{\text{e}}^{\prime})$', as a function of sliding direction, can be determined. Sliding in crystallographic directions which correspond to the minimum values of $\tau _{\text{e}}^{\prime}$, on specific crystallographic surfaces, are those of maximum hardness and conversely. The nature of anisotropy predicted by this analysis, and based on the relevant slip systems, is shown to be consistent with the results for cubic crystals.