The Application of the Extended Isogeometric Analysis (XIGA) with K-Refinement Approach for the Prediction of Fatigue Life in Linear Elastic Fracture Mechanic

This study investigates the fatigue life of a cracked plate subjected to cyclic load under linear elastic fracture mechanics, using a numerical method of extended isogeometric analysis (XIGA) with a K-refinement approach. XIGA is applied to simulate discontinuity problems without meshing and without the necessity for element boundaries to be aligned to crack faces. In this method, the crack faces are simulated by discontinuous Heaviside functions, whereas the singularity in the stress field at the crack tip is simulated by crack tip enrichment functions. The stress intensity factors for the cracks are numerically calculated using the interaction integral method. Paris law of fatigue crack growth is utilized for predicting the fatigue life of a cracked plate. In the standard finite element analysis, there is no refinement method similar to k-refinement. The effect of the k-refinement on the accuracy of the values stress intensity factor and fatigue life is investigated. To achieve this, the order of Non-uniform rational B-Splines (NURBS) basic function is considered as linear, quadratic, and cubic. It is observed that as NURBS orders are increased in k-refinement, results are improved, and the error is lower compared with the analytical solution. The results show that values of stress intensity factor and fatigue life obtained using XIGA are more accurate compared to those obtained by the finite element method. In addition, and they are closer to the results of the analytical solution, and the XIGA method is more efficient.