A Zener–Stroh crack in fiber-reinforced composites with generalized Irwin plastic zone correction

Abstract

Abstract Elastic–plastic stress analysis on a matrix Zener–Stroh crack interacting with nearby inclusions (the fibers) in fiber-reinforced composites has been carried out. The Zener-Stroh crack is initiated near one of the inclusions, while the effect of other inclusions in the composite is considered through simulating the composite material by the cylindrical three-phase model. Plastic zone correction is introduced the first time for such a crack-inclusion interaction problem so that the fracture behavior can be analyzed more accurately. To determine the plastic zone sizes, a generalized Irwin model is proposed for the mixed-mode loading 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 near-by fiber has great effect on the fracture behavior of the crack. In our study, the effective stress intensity factor (SIF), plastic zone size (PZS) and crack tip opening displacement (CTOD) are evaluated by solving the formulated singular integral equations. Through the numerical examples, the influence of the inclusion (fiber) shear modulus, inclusion volume fraction and the crack sharp tip position on the fracture behavior of the crack is discussed. It is found that the shear modulus ratio has great effect on the normalized values of PZS and CTOD, while the effect of fiber volume fraction depends highly on the conditions of the inclusion/matrix properties and the crack sharp tip position.