Fatigue crack growth in brittle rocks was numerically simulated by a modified displacement discontinuity method. Mode I and Mode II stress intensity factors and their increments due to cyclic loading of brittle rock samples were numerically estimated using linear elastic fracture mechanics. Effective methodologies were introduced for modeling the fatigue crack propagation in brittle rocks under cyclic loading. The quadratic displacement discontinuity and crack tip elements were used to predict the mixed mode stress intensity factors at crack tips in the brittle material specimens. The maximum tangential stress criterion was used to predict the crack growth paths using the incrementally increasing cracks lengths in the predicted direction. Several examples were solved to evaluate the accuracy and efficiency of the proposed algorithm. It is concluded that the fatigue crack growth in brittle rocks under mixed-mode loading conditions can be effectively analyzed by the modified higher order displacement discontinuity.
The fatigue phenomenon occurs in structures that are exposed to cyclic loads. At present, three approaches of stress, strain, and fracture mechanics are utilized to investigate fatigue (Woodford, 1993). Based on fracture mechanics concepts, all materials have inherent flaws and defects. These cracks may grow due to cyclic loading and continue to grow until reaching a critical value, this approach specifically treats fatigue crack growth behavior by the principle of fracture mechanics. Several analytical methods have been presented to study the fatigue crack growth behavior (NASCRAC, 1989). Nevertheless, these methods are available only in a limited group of geometry combinations and boundary conditions. Hence, it is suitable to use numerical methods to examine the fatigue crack growth behavior and life estimation. The classical finite element method (FEM) has been extensively employed as a numerical tool for several decades to study fatigue and fracture mechanics problems (Bittencourt et al., 1996). However, this method has several limitations in meshing and, if it is employed, the mesh around the crack tip should be small enough to model the changes of the crack tip and stress gradients appropriately. Besides, at each step of crack growth, re-meshing of an existing boundary is required. The extended finite element method (XFEM) which is based on FEM has been proposed. In this method, the complex processes related to the crack growth were resolved by enriching the nodes and virtually enhancing the degrees of freedom (Surendran et al., 2019). In recent years, using meshless methods in order to develop the numerical modeling of crack growth has been at the center of interest as well. For instance, Belytschko et al., for the first time, introduced the element-free Galerkin method (EFGM) to study the growth of cracks (Belytschko et al., 1994). Free-mesh methods were later employed to develop fatigue crack growth (Kumar et al., 2014)
