In this paper, the stress field at the crack-tip of a semi-infinite crack interacting with an isotropic dilatational inclusion is studied. The fundamental solution for a semi-infinite crack interacting with an eigenstrained point is presented first. By employing it as Green’s function, a crack enclosed by a homogenous inclusion is formulated and its Kolosov–Muskhelishvili complex potentials are obtained. Then the approximate solutions for the full-field stress in the vicinity of the crack-tip are derived. Finally, numerical method is performed, which not only reveals the distribution of the stress field, but also validates the theoretical analysis. As expected, theoretical and numerical results show that the presence of dilatational inclusion will produce a significant shielding effect on crack-tip. Importantly, it is found that a stress jump occurs at the interface between inclusion and matrix, which may unexpectedly trigger a micro-damage prior to the semi-infinite crack-tip. This mechanism is capable of leading to the crack growth fundamentally, when it is exposed to an oxidizing or corrosive environment.

本文研究了半无限裂纹与各向同性膨胀夹杂物相互作用时裂纹尖端处的应力场。首先提出了与特征应变点相互作用的半无限裂纹的基本解决方案。通过将其用作格林函数，可形成由均质夹杂物包围的裂纹，并获得其Kolosov-Muskhelishvili复杂势。然后得出裂纹尖端附近全场应力的近似解。最后采用数值方法，不仅揭示了应力场的分布，而且验证了理论分析。如预期的那样，理论和数值结果表明，膨胀夹杂物的存在将对裂纹尖端产生显着的屏蔽作用。重要的，发现在夹杂物和基体之间的界面处发生应力跃变，这可能会意外地触发半无限裂纹尖端之前的微损伤。当其暴露于氧化或腐蚀性环境中时，该机制能够从根本上导致裂纹扩展。