Effect of temperature and small-scale defects on the strength of solids

Abstract

Using a statistical-thermodynamic formulation, we investigate the failure of ideal and almost-ideal solids at finite temperature. We propose that the onset of failure in a defect-free crystal is associated with the loss of a metastable minimum in the free energy at a critical value of the applied tensile force. Using a mean-field approximation, we estimate the free energy of the two-dimensional Lennard-Jones crystal under stress and derive the temperature dependence of its ideal strength and other properties. These results are compared to Monte Carlo simulations of this system, and the mean-field estimate of the ideal strength is shown to be an upper bound to the values observed via simulation. We also show that atomic-scale defects such as vacancies and substitutional impurities significantly reduce the crystal’s strength as a result of stress enhancement effects. While the overall strength of a defective crystal depends strongly on both temperature and the nature of the defects, the maximum local stress that the crystal can sustain without failure is essentially independent of these factors.