Effect of a Microdefect ahead of a Main Crack on Strength of Solids : Exact Solution to the Main Crack-Microdefect Interaction Model

Abstract

In our previous paper, an approximate solution to the main crack-microdefect interaction model was derived using a main crack stress field, and the effect of a microdefect ahead of a main crack on the strength of solids was discussed in terms of the model. In the present paper, in order to investigate more precisely the above effect, the main crack-microdefect interaction model is formulated more specifically based on the method of continuously distributed theory of dislocations, and the distribution functions for both a main crack and a microdefect are obtained. As a result, we obtain stress intensity factors K both at the tip of a main crack and a microdefect in the closed form. Using these K values, we elucidate the effective range of the above model and the crack shielding effect by a microdefect. Furthermore, the crack length dependence of the fracture strength and fracture toughness of engineering ceramics can be explained well theoretically using the present model.