On the relationships between hardness and the elastic and plastic properties of transversely isotropic power-law hardening materials

Using a combination of dimensional analysis and large deformation finite element simulations of indentations of power-law hardening model materials, a framework for capturing the hardness characteristics of transversely isotropic materials is developed. By considering 4800 combinations of material properties, relationships that predict the hardness of transversely isotropic materials are formulated for both longitudinal and transverse indentations. It is found that hardness tends to be higher for materials with plastic anisotropy than those that exhibit equivalent elastic anisotropy. For perfectly plastic materials, the hardness to the yield stress ratio (R₀) can vary from 2.5 to 3.5, while for materials with strain hardening, R₀ can be as high as 10. A tighter relationship between the hardness and the Tabor’s representative stress is observed with the ratio of the hardness to the Tabor’s representative stress (R_t) ranging from 2.2 to 4, depending on the elastic and plastic properties and the degree of anisotropy.