Shear Modulus and Yield Stress Change with Pressure and Temperature

Abstract

It is well known that the shear modulus (G) and the yield stress (Y) of metals increase with pressure (P) and decrease with temperature (T). Steinberg [1], in his popular compendium of dynamic material properties, assumes for Y/Y₀(P,T)=G/G₀(P,T) linear relations based on tests at ambient conditions. But recent tests of high-pressure dynamic loading of certain metals yielded results that generally deviate from Steinberg’s equations. Here we use a different approach to estimate G/G₀(P,T). As a first approximation we let G/G₀ follow from the assumption of constant Poisson ratio (n). This leads to G/G₀=K/K₀, where K is the isentropic bulk modulus. With this assumption we compute the longitudinal sound speed of tantalum along its principal Hugoniot curve, and compare the result to recent measurements. There is a slight disagreement which we correct by assuming (second approximation) that Poisson’s ratio decreases slightly with pressure, and increases slightly with temperature. As K is always available in a hydrocode run from the equation of state, so are therefore also G/G₀ and Y/Y₀.