Dynamic Fracture Modeling of Impact Test Specimens by the Polygon Scaled Boundary Finite Element Method

Abstract

In the polygon scaled boundary finite element method, the modeling of crack can be simplified and the stress intensity factors are extracted from the semi-analytical solution directly. These salient features are applied to develop an efficient method to model the impact test specimens, one of which occurs without crack propagation, the other with crack propagation. The notched bend specimens are discretized by polygon elements with no local refinement around the crack tip. The mass and stiffness matrix of polygon elements are derived based on the SBFEM, and then the elastodynamic equations of the global system are established. The Newmark integration method is applied to obtain the dynamic responses of the specimens. For the case with crack propagation, an efficient local remeshing algorithm is used to track the crack tip and model the crack propagation. The dynamic stress intensity factors are computed directly from the instantaneous displacement field and crack velocity. The numerical results of the two specimens correspond well with the experimental data and other numerical results reported in the literature. The effects of the time step, mesh density and damping coefficient are also investigated. Moreover, the displacement and stress contours are extracted from the dynamic solution, which is helpful for the interpretation of the experimental observations.