Continuous model for the shear modulus as a function of pressure and temperature up to the melting point: Analysis and ultrasonic validation

Abstract

The aim of the present study is to propose a predictive model for the shear modulus versus pressure and temperature G(P,T) to complete the principal known elasto-plastic models implemented in hydrodynamic computer codes. The relevance of the proposed G(P,T) model is discussed in detail. The generic approach is to model G(T) by considering Lindemann theory at the melting point. This article focuses on analysis of the mechanical elastic behavior of a solid to confirm that the melting point and the shear component attenuation are closely connected. The drastic fall of G(T) at the melting point is discussed and compared to experimental data mainly derived from ultrasonics. The original part of this work is the experimental work concentrating on direct measurement of the shear wave velocity. The five materials of interest have melting points ranging from that of tin (505 K) to that of tantalum (3269 K). The corresponding Lindemann constant is determined, leading to an average value of 0.103 for cubic crystalline symmetry (Ta, Cu, Au, and Al) and 0.060 for tetragonal crystalline symmetry (Sn). We propose a relationship between G(P,T) and the melting temperature.