A weight function methodology for the assessment of embedded and surface irregular plane cracks

Abstract

A low cost numerical tool for the calculation of mode I stress intensity factors K in embedded and surface irregular cracks is presented in this paper. The proposed tool is an extension of the O-integral algorithm due to Oore and Burns for the assessment of embedded plane cracks using the weight function methodology. The performance of the O-integral is assessed first by comparing its K results to exact solutions for embedded elliptical and rectangular cracks. From the analysis of this data it is found that the error in the K results systematically depends on the crack aspect ratio and the local crack front curvature. Based on this evidence a corrective function is derived in order to remediate the limitations of the O-integral. Solutions due to Newman and Raju are used to account for the effects of free surfaces and finite thickness. The accuracy of the proposed procedure is assessed by solving a number of examples and by comparing the obtained results to those available in the literature.