Natural Crack Growth of Nozzle Corner Crack Using Extended Finite Element Method (XFEM)

The nozzle corner region in a pressure vessel experiences stress concentration under various loading such as internal pressure and thermal transients. There are many situations in which a postulated or detected flaw at the nozzle corner needs to be addressed for life assessment and fitness-for-service determinations which require stress intensity factor (KI) solutions. To assess the remaining life, the crack growth calculation of nozzle corner crack is typically performed with KI assuming a semi-circular or semi-elliptical crack shape which are limited to KI values at the deepest and surface points of the crack. However, due to the complex geometry of the nozzle corner crack, it is desired to compute KI along the entire crack front. To that end, the extended finite element method (XFEM) which can simulate cracks without the need for modeling the crack-tip can be used to calculate KI along the entire crack front for arbitrary crack shapes. Using the KI values calculated from XFEM, ‘natural’ crack growth can be simulated. The objective of this paper is to perform a feasibility study in evaluating the fatigue crack growth behavior of a nozzle corner crack using XFEM. For this purpose, an initial circular nozzle corner crack was used for benchmarking the KI values from XFEM against those from a traditional 3-D finite element model. In the next step, the XFEM model was subjected to cyclic internal pressure to grow the crack where the ‘natural’ crack behavior was studied. Using the fatigue crack growth equation (i.e., Paris Law), the succeeding crack profile was calculated for a given number of cycles using the K values from the previous step and the updated crack profile was then used as an initial crack in the next step. This iterative procedure is automated using Python Script in ABAQUS® and the final crack shape is determined for total number of cycles. Finally, the XFEM based fatigue crack growth results were validated using existing experimental data and were also compared against the crack growth results using an existing KI solution.