Although continuum frameworks have been developed in the past for studying how material defects behave in solid solutions, recent studies have demonstrated that the self-stress field of the solutes which enter the chemical potential in the prevalent continuum models must be excluded, and instead the image stresses included, in a correct treatment. Here, working within the framework of Gibbs canonical ensemble of statistical mechanics, and accounting for the image stresses of the solutes arising due to the presence of the boundaries, we examine the interaction between a solute atmosphere and a crack in the presence of an external loading. Relying on a plane strain model, the solute atmosphere is treated as a distribution of misfitting solute rods, infinitely long in the direction normal to the plane of analysis. Since solutes interact through their image stress fields and can move around in the solid, Monte Carlo simulations, fully accounting for both the energy of interaction between the solute rods and their interaction with the external loading, are performed to explore various configurations of the solute rods in the host, and to compute the temperature-dependent ensemble averages of the enthalpy, equilibrium solute distribution, and the energy release rate (ERR) of crack growth. It is shown that solute redistribution induced by a tensile loading of the solid results in an increase in the ERR. Our simulations further interestingly reveal that even in the in the limit of large temperatures where a nearly uniform solute distribution prevails, the interaction between the collective image stress field of the solutes and the stress field of the loading results in an added contribution to the ERR which, at a fixed average concentration and a fixed loading-induced stress intensity factor, does not fade away with increasing solid dimensions, and further strengthens both with the solute concentration and with the external loading.

尽管过去已经开发了连续体框架来研究材料缺陷在固溶体中的表现，但最近的研究表明，必须排除进入普遍连续体模型中化学势的溶质的自应力场，取而代之的是图像压力包括在正确的治疗中。在这里，在统计力学的 Gibbs 标准集合的框架内工作，并考虑由于边界的存在而产生的溶质的图像应力，我们研究了在存在外部载荷的情况下溶质大气和裂缝之间的相互作用. 依靠平面应变模型，溶质大气被视为不匹配溶质棒的分布，在垂直于分析平面的方向上无限长。由于溶质通过它们的图像应力场相互作用并且可以在固体中移动，蒙特卡罗模拟充分考虑了溶质棒之间的相互作用能量及其与外部载荷的相互作用，以探索溶质棒的各种配置并计算裂纹扩展的焓、平衡溶质分布和能量释放率 (ERR) 的温度相关系综平均值。结果表明，由固体的拉伸载荷引起的溶质重新分布导致 ERR 增加。我们的模拟进一步有趣地表明，即使在溶质分布几乎均匀的高温极限下，