Temperature-Dependent Modulus of Metals Based on Lattice Vibration Theory

Fundamentally understanding the temperature-dependent modulus is the key issue for materials serving in high temperature environments. This paper proposes a model based on lattice vibration theory to predict the temperature-dependent modulus with respect to isothermal and isentropic assumption. The thermal vibration free energy is expressed as a function of the two independent scalars from the strain tensor and temperature. By using the Einstein theory, we present the analytical expression for the temperature-dependent Young's modulus, bulk modulus, shear modulus, and Poisson's ratio. The theoretical prediction agrees well with the experimental data. The proposed model is further degenerated to Wachtman's empirical equation and provides the physical meaning to the parameters in Wachtman's equation.