A Modified Interaction Integral for 3D Extended Finite Element based Crack Growth Prediction

Abstract

This study is focused on the development and demonstration of a single element based interaction integral within a 3D extended finite element (XFA3D) framework for extraction of mixed mode stress intensity factors along an arbitrary crack front. Unlike a conventional interaction integral approach where is spider mesh has to be developed based a local crack orientation, the single element that is cut by a crack front segment does not have to be in conformation to the local spider mesh. Driven by the nature of a much coarser mesh in the near crack front region and the use of a large number of integration points within a cracked element for the associated sub-domain integration, a well-positioned sub-cell is constructed based on the local level set values associated with an examination point on the crack front. This sub-cell forms the single element based domain for computing the interaction integral. Numerical interpolation is used to map the nodal field variables to the corresponding field variables defined within the sub-cell along with the calculation of their spatial derivatives. Example problems for an elliptical and a rectangular crack are used to examine the validity and accuracy of the modified interaction integral approach and parametric study is also performed to study the accuracy of the extraction the stress intensity factors for the different relative positions between the crack front and the boundary of the element that has been cut by the front.