Effects of mode II loading on the interaction of a solute atmosphere with a crack in the presence of image stresses: A statistical mechanics study

Abstract

Thermodynamics-based continuum models have been previously employed for examining how a solute atmosphere interacts with the stress field of various material defects in solids. However, recent studies suggest that the chemical potential used in prevalent continuum frameworks needs to be revised in the sense that the stress contribution to the chemical potential should arise only through the image stress field of the solutes, and the homogenized self-stress field of the solutes must hence be excluded from the chemical potential in a correct treatment. Here, adopting a statistical mechanics-based approach fully accounting for the image stress effects, we aim to present an investigation of the effect of a mode II loading on the interaction of a solute atmosphere with the stress field of a crack. Solute atmosphere is treated as a distribution of solute rods which extend indefinitely in the direction parallel to the crack front. Image stress effects both on the enthalpy of the solutes and on the stress intensity factors (SIFs) are taken into consideration. Monte Carlo simulations are utilized to find the equilibrium distribution of the solutes in the solid, and also to compute the ensemble average of the energy release rate (ERR) available for crack growth in the presence of an external loading. Effects of the system temperature, average solute concentration, and the loading intensity on the results are also examined. Simulation results suggest that the solute redistribution driven by mode II loading generates an additional mode II ERR for the crack growth. The results further indicate that the increase in the mode I ERR as caused by the solute redistribution induced by a mode I loading is weakened in the presence of a mode II loading. Since simulations are performed for a finite solid, the effects of solid dimensions and crack size on the results are also examined, and it is shown that the results remain insensitive to the geometric dimensions as long as the loading-induced SIFs at the crack tip and the solute concentration are kept unchanged. Effect of solute atmosphere on the maximum ERR for kinked crack growth is also examined.