On the plastic zone size and CTOD study for a Zener–Stroh crack interacting with a circular inclusion

An analytical solution is given for plastic yielding of a Zener–Stroh crack near a circular inclusion embedded in an infinite matrix. The crack is orientated along the radial direction of the inclusion. In the solution procedure, the crack is simulated as a continuous distribution of edge dislocations. Using the Dugdale model of small-scale yielding, plastic zones are introduced at both crack tips. Using the solution of a circular inclusion, interacting with a single dislocation as the Green’s function, the physical problem is formulated into a set of singular integral equations. With the aid of Erdogan’s method and iterative numerical procedures, the singular integral equations are solved numerically for the plastic zone sizes and crack tip opening displacement. The results obtained in the current work are verified by reduction to simpler cases of the Dugdale model. Various parameters such as the distance, shear modulus ratio, Poisson’s ratio, and loading condition are studied.