A least squares procedure for the evaluation of multiple generalized stress intensity factors at 2D multimaterial corners by BEM

Abstract

Detailed characterization of linear elastic stress states at corners and crack tips requires knowledge of the stress singularity orders, the characteristic angular functions and the generalized stress intensity factors (GSIF). Typically a high accuracy is found in the literature for the evaluation of the stress singularity orders and characteristic angular functions (numerically computed from analytical expressions in most cases). Nevertheless, GSIF values, evaluated by means of a numerical model using FEM or BEM and usually by postprocessing the results, are often reported with a lower level of confidence. A robust procedure is presented in this work for the evaluation of the GSIF at multimaterial corners. The procedure is based on a simple least squares technique involving stresses and/or displacements, computed by BEM, at the neighborhood of the corner tip. A careful verification of the robustness and accuracy of the procedure using a few benchmark problems in the literature has been carried out. Applications of the procedure developed to the evaluation of GSIFs appearing at corners in metal-composite adhesive lap joints are presented.