Fatigue crack propagation modeling in 2D structures using the CPCN-FEM node-based approach

Introduction/purpose: The study aims to model fatigue-related crack propagation by introducing a numerical method, CPCN-FEM (Crack Propagation by Coordinates of Nodes - Finite Element Method), which predicts crack trajectories through the systematic generation of nodal coordinates around the crack front. Methods: The approach defines four principal nodes to control the propagation direction and computes the stress intensity factors (K I) and (KII), along with the crack inclination angle (β). The method was implemented in FORTRAN to automate node tracking, coordinate updating, and stepwise crack advance in a two-dimensional elastic isotropic model. Simulations were conducted and compared with analytical crack-path solutions, using the Richard criterion to determine crack orientation. Results: The numerical model reproduced expected crack trajectories with high agreement with analytical predictions and demonstrated stable displacement behavior across multiple propagation cases. Mesh integrity was preserved during all propagation steps, and no remeshing was required. Conclusion: The findings show that CPCN-FEM provides an accurate, efficient, and mesh-preserving technique for modeling crack growth under fatigue, offering reliable predictions of crack path evolution in fracture mechanics.