Development of higher-order displacement discontinuity method to simulate fatigue crack growth in brittle materials

The 2D displacement discontinuity method (2D. DDM) is an indirect boundary element technique in which the stresses and displacements are expressed through normal and shear displacement discontinuities. The governing equations of fatigue crack growth are mostly power equations that depend on the stress intensity factor range. Accurate calculation of displacement discontinuity has importance in fatigue analysis of DDM. Therefore, in this study, DDM is extended using cubic variations of displacement discontinuity for ordinary and crack tip elements. This method also uses an appropriate algorithm based on the linear elastic fracture mechanics (LEFM) principle to analyze crack growth under cyclic fatigue loading. This process is accomplished by assuming the homogeneity of brittle material and the small plastic zone of the crack tip compared to the crack dimension. The condition of applying constant and stationary variable amplitude loading was provided. The algorithm is designed based on an iterative process, and the new incremental elements gradually are added to the crack tip until the failure criteria are reached; The size of these elements at each step of growth depends on the crack growth rate in the previous step. Therefore, the fatigue modeling of the structures with multiple cracks and different growth rates is enabled. Virtual crack criteria were employed to improve the accuracy and speed of analysis, which involves crack tips with a slower growth rate. Moreover, the direction of crack propagation is evaluated using the maximum circumferential stress criterion. Examples of simple and multi-fractured structures under constant and variable amplitude load are considered. Comparison of results with literature data shows excellent agreement with high accuracy.