Physically Intuitive Anisotropic Model of Hardness

TL;DR

This paper presents a physically intuitive model linking elastic properties to material hardness, enabling anisotropic and temperature-dependent hardness predictions from first-principles calculations or experiments.

Contribution

It introduces a novel hardness model based on elastic moduli and their derivatives, allowing for anisotropic and temperature-dependent hardness predictions.

Findings

Predicts hardness anisotropy using shear modulus variation

Determines temperature dependence of hardness via pressure derivative of bulk modulus

Applicable with data from first-principles calculations or experiments

Abstract

The hardness of materials plays an important role in material design. There are numerous experimental methods to measure the hardness of materials, but theoretical prediction of hardness is challenging. By investigating the correlation between hardness and the elastic properties of materials, namely shear and bulk moduli, the pressure derivative of bulk modulus, we have constructed a simple and physically intuitive hardness model. By introducing the spatial variation of the shear modulus, it is possible to predict the hardness anisotropy of materials to define the minimum and maximum values of hardness possessed by a particular material. Furthermore, by using the equation of states to define the pressure derivative of the bulk modulus, it is possible to determine the temperature dependencies of hardness for given materials. All quantities in the model can be obtained directly from accurate first-principles calculations or from experiments, making it suitable for practical applications.