Temperature dependence of the ideal fracture strength of a b.c.c. crystal

Abstract

The temperature dependence of ideal strength is studied for a b.c.c. crystal in [001] and [001] loadings. Born's criterion, with Milstein's variables, is employed to determine the strength. The Helmholtz free energy is calculated under the self-consistent Einstein model devised by Matsubara. For mathematical convenience, a Gaussian type pair-wise central potential is employed to represent atomic interactions. We attempt to fit both elastic constants at 0 K and the thermal expansion for α-Fe, but both cannot be fitted simultaneously. Three different potentials are used for calculation and the results are compared. The calculated value of the strength is closely related to the predicted value of C ₁₁ – C ₁₂ or Young's modulus. With a potential which is approximately fitted to the experimental Young's modulus at 0 K, the calculated strength and the fracture strain are found to be in fair agreement with the experimental results for the α-Fe whiskers. Tensile strength in [011] loading is about five times larger than that in [001] loading for all the potentials studied, which is consistent with the experimentally observed {100} cleavage plane for b.c.c. metals. The percentage decrease in strength with temperature is in close agreement with that in C ₁₁ – C ₁₂ or Young's modulus. The change at fracture in the spring constant for the Einstein oscillator is almost independent of temperature, which implies only a weak coupling between the anharmonicity effects due to temperature and strain.