numerical optimization by the pfemct-sif method of the crack propagation of a linear elastic material

Introduction/purpose: this study investigates the influence of contour numbers surrounding the crack tip on stress intensity factors (sifs) using the propagation finite element method crack tip stress intensity factor (pfemct-sif) approach. it also compares the maximum circumferential stress criterion (mcsc) and the richard criterion for crack propagation prediction. methods: a finite element code written in visual fortran was developed to model crack tips with 3, 5, 10, 15 and 20 contours using 4-node quadratic cpe4 elements. abaqus software was utilized to calculate sifs and crack orientation angles. horizontal and inclined cracks were analyzed in a steel plate under tensile loading. the results were validated against analytical solutions and previous numerical studies. results: the 10-contour model showed the best agreement with analytical sif values. increasing contour numbers improved sif accuracy for horizontal cracks, but excessive refinement led to divergence for inclined cracks. the mcsc and the richard criterion produced comparable crack trajectories, with the mcsc demonstrating slightly higher precision. conclusions: the pfemct-sif method effectively evaluates sifs and predicts crack propagation paths. a 10-contour crack tip model balances accuracy and computational efficiency. the study highlights the importance of optimizing crack tip mesh refinement in fracture mechanics simulations.