An XFEM-based numerical strategy to model three-dimensional fracture propagation regarding crack front segmentation. (April 2022) - Shi, Fang; Wang, Daobing; Yang, Quanquan
Highlights: An XFEM-based model for simulating 3D non-planar fracture propagation regarding crack front segmentation is presented. A robust and efficient local mesh refinement scheme fully integrated with the XFEM is proposed. A new crack propagation criterion based on the weighted average principal stress is introduced. The stress shadow effects between adjacent overlapped segments are observed for the mixed-mode I-III fluid-driven fractures. The XFEM is shown to be a competent method to simulate the complex phenomenon of crack front segmentation. Abstract: Under mixed I-III loading, a crack frequently segments into several echelon-shaped daughter cracks rotated towards the direction of principal stress. This phenomenon is called crack front segmentation and has been widely observed at different length scales in both laboratory and nature. In this paper, based on the extended finite element method (XFEM), a three-dimensional numerical strategy is proposed, validated, and adopted to model quasi-static fracture propagation considering crack front segmentation. A new crack propagation criterion based on the weighted average principal stress in conjunction with a cubic spline curve fitting of front vertexes is introduced to update the crack geometry. Further, to get a higher resolution of the stress field around the crack front, a robust and efficient local mesh refinement scheme fully integrated with the XFEM is proposed. Besides, a partitioning scheme of enriched elements containing segmentation points is presented to achieve an accurate numerical integration. Several examples are presented to illustrate the effectiveness and robustness of the proposed strategy. The hydraulic fracturing example indicates that ignoring fracture front segmentation for a mixed-mode I-III fluid-driven fracture will severely underestimate the injection pressure due to the stress shadow effects between adjacent overlapped segments.