Molecular-dynamics simulation of stress relaxation on a triangular lattice

Abstract

Simulations were performed using the method of molecular dynamics for ideal lattices and for lattices with defects generated by three different procedures. Curves of relaxation of stress \ensuremath{\sigma} vs logarithmic time t were obtained. In agreement with experimental results, the simulated curves exhibit three regions: initial, nearly horizontal, starting at ${\mathrm{\ensuremath{\sigma}}}_{0}$; central, descending approximately linearly; and final, corresponding to the internal stress ${\mathrm{\ensuremath{\sigma}}}_{\mathit{i}}$ as defined by Li. The existence of the central linear part has been predicted by a cooperative theory. In agreement with the theory, the slope of the simulated central part is proportional to the initial effective stress ${\mathrm{\ensuremath{\sigma}}}_{0}^{\mathrm{*}}$=${\mathrm{\ensuremath{\sigma}}}_{0}$-${\mathrm{\ensuremath{\sigma}}}_{\mathit{i}}$. The central part extends over approximately one decade of ${\mathrm{log}}_{10}$t for ideal lattices but over several decades for lattices with defects. High values of the imposed strain \ensuremath{\varepsilon} correspond to low internal stresses ${\mathrm{\ensuremath{\sigma}}}_{\mathit{i}}$, and vice versa. Stress relaxation is mainly due to deformations that occur in the vicinity of the defects, hence the process is related to the defect concentration and the amount of free volume ${\mathit{v}}^{\mathit{f}}$. Collective response of atoms in groups is observed. The origin of the defects does not seem to influence the relaxation.