LAUSR

In order to gain insight into the effect of elevated temperature on the mechanical performance of zirconium carbide (ZrC) and hafnium carbide (HfC), their temperature-dependent elastic constants have been systematically studied. For both ZrC and HfC, isoentropic C11\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_{11}$$\end{document} gradually decreases with the increase in temperature, while the values of C44\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_{44}$$\end{document} and C12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_{12}$$\end{document} of both are nearly temperature-independent. Temperature effects on modulus of elasticity, Poisson’s ratio, elastic anisotropy, hardness, and fracture toughness are further explored and discussed. A good agreement is observed between the predicted isoentropic Young’s modulus E and the available experiments for ZrC. Using quasistatic approximation can underestimate the decline rate of C11\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_{11}$$\end{document}, bulk modulus B, shear modulus G, and Young’s modulus E at high temperatures, especially above 298 K. This suggests the importance of the vibrational component of the free energy to calculate mechanical properties.