Plastic zone size and crack tip opening displacement of doubly periodic Dugdale cracks with diamond-shaped-interleaving arrays under longitudinal shear

Abstract

The interaction among multiple cracks plays a crucial role in the elastoplastic fracture behavior of materials. Although numerous studies have been devoted to elastic analyses of doubly periodic crack problems, the elastoplastic response of complex configurations such as doubly periodic cracks with diamond-shaped-interleaving arrays remains insufficiently explored. This paper investigates the plastic zone size (PZS) and crack tip opening displacement (CTOD) of doubly periodic cracks with diamond-shaped-interleaving arrays (DPC-DSIA) under longitudinal shear. Based on the Dugdale plastic zone model and the continuously distributed dislocation model, the mixed-boundary-value problem of elastoplastic behavior for DPC-DSIA configurations is transformed into a system of singular integral equations, where the semi-analytical solution is achieved using the Lobatto-Chebyshev numerical quadrature method. The accuracy of the proposed solution is verified against existing results for two typical periodic cracks with rectangular arrays and diamond-shaped arrays and the complex periodic cracks with diamond-shaped-interleaving small arrays. Furthermore, the influence of periodic parameters on key fracture quantities, including the PZS, CTOD, and stress intensity factor (SIF), are systematically examined. The results reveal the interaction mechanism between vertically and horizontally oriented cracks and highlight the complex effects of doubly periodic crack arrangements on the system’s elastoplastic behavior.