Abstract
The 2D stress intensity factor at the tip of a crack plays an essential role in the models of brittle fracture to predict the growth of a pre-existing crack. The coupled criterion, based on a twofold condition in energy and stress, extends the results to the initiation of a new crack at any 2D singular points. The generalized stress intensity factor, sometimes baptized notch stress intensity factor, is the relevant parameter for failure predictions. This criterion has been recently extended to the 3D case. In order to be able to implement it, it is necessary to have a means of calculating the 3D stress intensity factors. To this aim, a method based on a path independent integral is developed. It is an extension of the 2D approach relying on the so-called dual displacement field, also called complementary field. An algorithm is proposed to calculate the 3D singular field as well as its dual counterpart and the post-processing procedure to implement the path independent integral in a FE code is described. Examples of 3D corner singularities are chosen to check the independence of the integral with respect to the chosen paths. The ability of the method is tested through an analysis of the way the generalized stress intensity factors vary along the edge of a slanted V-notch in a 3-point bending specimen as a function of the orientation of the wedge. Finally, the method is applied to a bi-material corner and compared to experimental results from the literature.
Published Version
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