Energy-Based Automatic Mixed-Mode Crack-Propagation Modeling

Abstract

Based on an energy principle and a virtual crack extension technique, a practical finite-element modeling approach for the automatic mixed-mode two-dimensional (2D) linear elastic fracture mechanics (LEFM) crack-propagation analysis has been developed. By decomposing the displacement field obtained from a conventional finite-element analysis into symmetric and antisymmetric displacement fields with respect to the crack, Mode-I and Mode-II energy release rates can be determined using a generalization of the stiffness derivative method, and the corresponding stress intensity factors can then be calculated. The load at which a crack propagates and the propagation direction can be determined using one of the well-established mixed-mode crack-propagation criteria. Unlike the previously developed approaches to crack propagation, this approach does not require the use of symmetric crack-tip mesh, nor crack-tip singular elements, which greatly simplifies the subsequent remeshing process to allow for crack propagation. The automatic crack-propagation process is achieved by using a simple and efficient local 2D remeshing algorithm that can be easily programmed. Convergence studies, mesh sensitivity studies, and the practical use of the new approach are presented through various example problems.