Modeling of Planar Embedded Cracks of Arbitrary Shape under Non Uniform Mode I Loadings

Abstract

A numerical method using the weight function technique is proposed in order to evaluate the stress intensity factors for planar cracks of an arbitrary shape under non uniform mode I loadings. In accordance with the crack front perturbation theory of Rice, the SIFs are calculated in an incremental way, from a known initial crack shape (circle) which we make evolve until the final form is reached. Due to the non uniform character of the loading a surface integral term reappears during the calculation of the SIF which disappeared in the uniform case. This surface integral contribution to the calculation of the SIF depends on a kernel function which we propose to approximate by an empirical weight function that was developed by Oore and Burns (OB) for embedded cracks of any shape. The OB weight function introduces new singularities in the SIF evaluation that we propose to treat numerically. Several tests of validation are proposed to appreciate the predictive capacity of the proposed model.