On the plastic zone sizes of cracks interacting with multiple inhomogeneous inclusions in an infinite space

Abstract

The plastic zones of crack tips play a significant role in the fracture behavior of material. This paper proposes a semi-analytic solution for the plastic zones and stress distribution of an infinite space with multiple cracks and inhomogeneous inclusions under remote stress. In this solution, cracks can be treated as a distribution of edge dislocations with unknown densities according to the distributed dislocation technique, while inhomogeneous inclusions can be modeled as homogeneous inclusions with initial eigenstrain plus the unknown equivalent eigenstrain by using the equivalent inclusion method. These unknowns can be obtained by using the conjugate gradient method. The plastic zones ahead of crack tips are one-dimensional slender strips, and their sizes can be determined by canceling the stress intensity factor (SIF) due to the closure stress and that due to the applied load based on the Dugdale model of small-scale yielding. It is found that the plastic zones of crack tips are significantly affected by Young’s modulus and the positions of inhomogeneous inclusions.