Theoretical and numerical prediction of crack path in the material with anisotropic fracture toughness

The crack path in the anisotropic medium is studied theoretically and numerically in this paper, with focusing on the effects of the anisotropic fracture toughness. A weak plane model is adopted to characterize the anisotropic fracture toughness and the maximum energy release rate criterion (MERR) is chosen to predict the crack path. We prove that the crack deflecting direction in a weak plane material, theoretically, only relates to the weak plane direction, the weakness of the plane, and the ratio of stress intensity factors before crack extending. Two critical weakness ratios are found: one is for that the weak plane captures all cracks for any loading state; the other is for that the weak plane traps the crack once it is deflected to the plane. To further numerically study the complex crack path in an anisotropic medium, the extended finite element method (XFEM) embedded MERR criterion and weak plane model is developed, in which a mesh independent piecewise linear crack formulation is proposed to capture the curved crack path. By modeling the three point bending loading test, the influences of the weak plane angles and the weaknesses on crack path deflection are studied, and periodically oscillatory crack path behaviors are found as observed in experiments. Further more, the crack extending through multiple layers of weak plane material and isotropic material is numerically studied, which shows that the crack diffracts at the material interface, and the crack path in the anisotropic toughness material is rougher than in the isotropic material. The presented work in this paper will be helpful to understand and control the crack path in the rocks as well as other anisotropic materials.