Modeling hardness of polycrystalline materials and bulk metallic glasses

Though extensively studied, hardness, defined as the resistance of a material to deformation, still remains a challenging issue for a formal theoretical description due to its inherent mechanical complexity. The widely applied Teter’s empirical correlation between hardness and shear modulus has been considered to be not always valid for a large variety of materials. The main reason is that shear modulus only responses to elastic deformation whereas the hardness links both elastic and permanent plastic properties. We found that the intrinsic correlation between hardness and elasticity of materials correctly predicts Vickers hardness for a wide variety of crystalline materials as well as bulk metallic glasses (BMGs). Our results suggest that, if a material is intrinsically brittle (such as BMGs that fail in the elastic regime), its Vickers hardness linearly correlates with the shear modulus (Hv = 0.151G  ). This correlation also provides a robust theoretical evidence on the famous empirical correlation observed by Teter in 1998. On the other hand, our results demonstrate that the hardness of polycrystalline materials can be correlated with the product of the squared Pugh’s modulus ratio and the shear modulus (Hv=2(k2G)0.585−3Hv=2(k2G)0.585−3 where k = G/B is Pugh’s modulus ratio). Our work combines those aspects that were previously argued strongly, and, most importantly, is capable to correctly predict the hardness of all hard compounds known included in several pervious models.

Graphical abstractOne sentence for highlighted figure: Vickers hardness has been theoretically evidenced to correlate successfully with shear modulus for various bulk metallic glasses (BMGs, left panel) and with a product of the squared Pugh’s modulus ratio and shear modulus for a wide variety of polycrystalline materials (including all superhard materials known, right panel).Figure optionsDownload full-size imageDownload as PowerPoint slideHighlights► This work derived a theoretical formula of Vickers hardness linearly correlated with shear modulus for various bulk metallic glasses. ► This work derived a theoretical formula to predict Vickers hardness of a wide variety of polycrystalline materials. ► This work generalized the hardness formula through a thorough comparison for BMGs and polycrystalline materials. ► This work validated the powerful prediction of the proposed hardness formula. ► This work highlighted a comparison of several semi-empirical hardness models with the currently proposed formula.