An adaptively refined XFEM for the dynamic fracture problems with micro-defects

•A new adaptively refined extended finite element method (VP-XFEM) is presented.•A multi-level, adaptively mesh refinement method is proposed.•The effectiveness and accuracy of the proposed method are verified.•The influences of micro-defects on the macro-crack propagating are analyzed. Micro-defects near the macro-crack might produce a significant role in triggering the long crack propagation. Well understanding the crack shielding and amplification is thus critical to simulate the crack growth and predict structural total lifetime. However, the modeling of macro-crack growth involving multiple micro-defects is inconvenient due to spatial scales in terms of crack extension. A multi-level, adaptively refined mesh approaching the macro-crack with micro-defects is formulated by the combination of virtual node polygonal element shape function and quadtree meshes. Within the framework of extended finite element method (XFEM), the crack growth under different scales is unified and predicted only by one set of meshes. The effect of different micro-defects on the macro-crack propagation was thus investigated numerically. The validation and accuracy of the proposed method are verified by a typical cracking problem, and the influence of micro-defect position and size on fracture parameters and running path are examined. Results show that the proposed method can obtain accurate SIFs at the crack tips of both macro-crack and micro-crack. The influence of the micro-defects on the macro-crack propagation path varies with their locations and sizes.