Simulation of the Griffith's Crack Using Own Method of Predicting the Crack Propagation

The paper presents the results of numerical simulation of brittle material fracture initiated by Griffith's crack situated at any angle with respect to the load direction. The simulations were performed with the Simulia Abaqus FEA system using the X-FEM method. The direction of the crack propagation was determined using the user's subroutine written in Fortran, implemented in the Abaqus system. The authors programmed several conditions for the direction of the fracture propagation: maximum principal stress criterion, Ottosen-Podgorski criterion, three criteria based on displacements around the crack tip, and the MTS criterion, which is based on stress intensity factors. For the purposes of this study, two shapes of the crack tip were analyzed - sharp and blunted. The relationship between the direction of the initial fracture and the direction of crack propagation was found. The simulations were carried out for the angles of the initial crack from 0 degrees to 90 degrees. every 10 degrees. A theoretical analysis of the implemented criteria was also carried out and compared to numerical results. The influence of the shape of the crack tip on the simulation result was analyzed. It was shown that the simulation results closest to the theoretical results were obtained for the own implementation of the stress-based criteria. It has also been proven that the shape of the crack tip has little effect on the result if the finite element mesh is properly densified. However, the sharp crack has a disadvantage for small initial crack angles. The Author's method of predicting the crack propagation has been proven correct and effective. This work is also the basis for the further development of the described method.