The linked crack solved by Mellin transform
The problem of the evaluation of the stress intensity factors (SIF) at a kinked crack-tip is treated by the use of the most appropriate tool for this problem, the Mellin transform technique. The advantage of this technique lies on the validity of the solution everywhere in the stress field and for every length of the branched crack. Since in the limiting case of the kinked crack, numerical difficulties appear in the evaluation of the kernel functions of the corresponding Fredholm integral-equation system, an asymptotic development, with respect to the length of the kinked crack, is constructed for these functions and therefore for the SIFs at the kinked tip. This analysis yields the interesting result that the SIFs at the crack tip tend to vanish as the kinked crack reduces in length, a result which is similar to the already established behavior of the SIFs at an interfacial tip.
reduction to system of four coupled Fredholm integral equations of the second kind
reduction of line integrals to real integrals
scientific article; zbMATH DE number 3972384