Plastic zone correction on a Zener–Stroh crack interacting with a circular inclusion in ductile materials

Elastic-plastic stress analysis on a matrix Zener-Stroh crack interacting with a circular inclusion (fibre) in fibre-reinforced composites has been carried out. The Zener-Stroh crack is initiated near the fibre in the pure matrix. Plastic zone correction is introduced the first time for such a crack-inclusion interaction problem so that the fracture behaviour can be analysed more accurately. To determine the plastic zone sizes, a generalized Irwin model is proposed for the mixed-mode problem where the Von Mises stress yielding criterion is employed. Different to a Griffith crack, a Zener-Stroh crack propagation always occurs from the sharp tip whose relative position to the inclusion has great effect on the elastic-plastic fracture behaviour of the crack. In our study, the plastic zone size (PZS), crack tip opening displacement (CTOD) and effective stress intensity factor (SIF) are evaluated by solving the formulated singular integral equations. Through the numerical examples, the influence of the inclusion (fibre) shear modulus, crack-inclusion distance and the crack sharp tip position on the fracture behaviour of the crack is discussed. It is found that the shear modulus ratio and the crack-inclusion distance have great effect on the normalized values of PZS and CTOD, but the effects highly depend on the crack sharp tip position.