An abaqus implementation of the regularized extended finite element method with novel mixed mode cohesive fatigue model

The Regularized eXtended Finite Element Method (Rx-FEM) is a fracture mechanics based technique for progressive failure simulation in which multiple damage events, such as matrix cracks and delaminations, are introduced into the finite element model via mesh-independent displacement discontinuities. In the Rx-FEM, the Heaviside step function used in the eXtended Finite Element Method (x-FEM) is replaced by a continuous function approximated by the FE shape functions. This regularization lends itself to a natural implementation in commercial finite element software as a superposition of native elements. The advantages of Rx-FEM implementation lie in its ability to utilize built-in capabilities from the host software, including contact, variety of native elements, geometric nonlinearity, as well as the standard post-processing, and visualization tools. This capability of Rx-FEM to insert mesh-independent cohesive interfaces also makes the method particularly well suited for the analysis of fatigue damage propagation in composites. A recently-developed cohesive fatigue model was implemented into the Rx-FEM framework for the Abaqus software suite. This fatigue model assumes that the cohesive law that describes quasi-static tearing is the envelope of the fatigue damage. Fatigue damage accumulates within the envelope at a rate that satisfies the S-N diagram and Miner’s rule. The parameters of the model are obtained from idealizations of S-N diagrams used in engineering design. The fatigue model relies on intrinsic relationships between S-N curves and their corresponding Paris law curves to predict the rates of crack propagation. The implementation of the new fatigue model is demonstrated by comparing the experimental and predicted response and failure of a mixed-mode bending (MMB) test, as well as a Clamped Tapered Beam (CTB) sub-element. The CTB is a test designed to study matrix crack and delamination initiation and subsequent propagation and migration from one ply interface to another.