Fatigue crack growth simulations of 3-D problems using XFEM

• A simple and efficient XFEM approach is presented to simulate 3-D fatigue crack growth simulations.
• Auxiliary fields are approximated using higher order interpolation functions for the ease in calculation of gradient and derivatives.
• Level set functions are approximated using the concept of hanging nodes using quadratic finite element shape functions.
• Various 3-D crack growth problems are solved to reveal the sturdiness and versatility of the XFEM approach.
• The division of crack front into several piecewise curve segments makes the computations easier as compared to iterative schemes.

In this work, a simple and efficient approach based on extended finite element method (XFEM) has been presented to simulate three-dimensional fatigue crack growth simulations. In XFEM, standard displacement based approximation is enriched by additional functions using partition of unity concept. These enrichment functions are derived from the theoretical background of the problem under consideration. In the proposed approach, a crack front has been divided into many piecewise curve crack segments to avoid an iterative solution. Three-dimensional triangulation scheme is adopted for the calculation of level set functions on the crack surface. At the crack front, the level set functions are approximated using the concept of hanging nodes using quadratic finite element shape functions. These level sets are used to accurately define the crack geometry. The fatigue crack growth simulations have been performed using Paris law of fatigue crack growth. Various 3-D planar, non-planar and arbitrary shape crack growth problems are solved to reveal the sturdiness and versatility of the proposed XFEM approach.