INVESTIGATION OF MIXED-MODE CRACK TRAJECTORY USING IMPLICIT SCHEME

Abstract

This paper presents a study of crack trajectory determination for an inclined crack in a planar structural element using an implicit investigation scheme optimized for the accuracy of mixed mode fracture analysis. The developed scheme ensures that the condition that the shear stress intensity factor (SIF) is zero at each algorithmic step holds strictly, enabling accurate tracking of crack propagation direction. For this purpose, an adaptive algorithm was developed to generate a regular mesh in the circular zone around the crack tip, modeled as a piecewise linear curve. This meshing approach improves the accuracy of SIF computation, which is validated through comparison with established mode I solutions in the literature. In addition, the dependence of the shear SIF on the rotation angle of the second crack segment under critical state conditions is analyzed to simplify the implementation of the implicit algorithm. For further validation, a parallel study using an irregular mesh generated by MATLAB’s built-in meshing functions was conducted, which demonstrated comparable accuracy of SIF determination in different types of meshes. Finally, this paper shows the calculated crack trajectory and the von Mises stress field distribution around the crack tip for the first four propagation steps, which provides a comprehensive understanding of the stress behavior and the effect of mesh refinement on the trajectory prediction.