Methodology for simulating the elastoplastic behavior in crack propagation problems using dual formulations of the boundary element method

Abstract

Due to the application of cyclic loads, the existing crack length in a structure increases with time, resulting in greater stress concentration around the crack tip and therefore causing an increase in propagation velocity and a decrease in residual strength of the structure which, at a given time, becomes so low that the structure can no longer support the service loads. This paper presents a new approach to evaluate two-dimensional elastoplastic models in a crack propagation scenario, based on the boundary element method and its dual formulations. The methodology adopted consists of two stages: firstly, the simulation of the elastoplastic behavior, which considers the process of initial stresses and allows the treatment of several flow criteria, without taking into account the incompressibility of inelastic deformations. In this step, the domain integral due to non-homogeneous terms in the plastification region is transformed into a boundary integral by the Dual Reciprocity Method (DRM) using the polyharmonic splines functions due to its local behavior and, from the plastic calculus, the J-Integral is used to compute the SIF's. The second stage aims to simulate, in an incremental way, the crack propagation path using homemade software for crack modeling and analysis based on ElastoPlastic Fracture Mechanics (EPFM) and the Dual Boundary Element Method (DBEM). To validate the adopted methodology, as well as correctly simulate the mechanical behavior of cracks in the plastic regime of the material, three 2D models with straight and inclined cracks are used. Initially, the von Mises criterion for perfectly plastic materials is used and the numerical results compared with classic models from the literature, showing the effectiveness of the program in crack treatment and in the prediction of the propagation path, as well as the non-linear algorithm in the region plastification using the DRM.