On the crack-tip stress field due to the presence of isotropic dilatational inclusion: theoretical and numerical analysis

Abstract

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.