Subcritical growth of a crack interacting with the stress field of mobile solutes in an elastic solid in the presence of image effects: A kinetic Monte Carlo study

Abstract

It is well known that the presence of foreign solutes could critically affect fracture properties of the solid solutions of critical importance to many technological advances. It has been shown recently that a prevalent continuum theory widely applied to such systems is inconsistent with classical elasticity which predicts that two point defects in an isotropic unbounded solid do not interact, and interact only in a finite solid through image stresses arising due to the presence of the boundaries. Previous studies have shown that the image stresses resulting from an external boundary of a finite solid also generally raise the stress intensity factors (SIFs) induced by the solutes at a crack tip. Here, we examine the possibility that the increase in the SIFs by image stress effects together with variations in the configuration of mobile solutes around a crack tip could from time to time push the crack tip SIFs beyond the critical value required for crack growth, and hence cause subcritical crack growth over time. Incorporating crack growth criterion in kinetic Monte Carlo (KMC) simulations and fully accounting for the image stress effects, we investigate this possibility by examining how temperature, solute concentration, and the difference between the loading-induced SIF and the critical SIF could affect crack growth. In agreement with an analysis based on the central limit theorem presented for the limit of high temperatures, our simulations indicate that the probability of the Griffith-Irwin criterion being met among various solute configurations generally increases with increasing solute concentration. The model shows that, within a certain range of the loading-induced SIF below the critical SIF, the crack growth rate increases with solute concentration, and this effect becomes particularly more evident at larger temperatures.