On the use of power series solution method in the crack analysis of brittle materials by indirect boundary element method

A hybridized boundary element/power series solution method is proposed for evaluating displacements and stresses near the crack tips. In the indirect boundary element method, the special crack tip elements can be used to increase the accuracy of the stress and displacement fields near the crack ends. The special crack tip elements are usually used by assuming the crack mouth opening and crack mouth displacement variations in form of an infinite power series which can end up with the special singular integrals. The aim of this paper is to solve these singular integrals by using an infinite power series. The power series solution method has been used to solve some example problems in fracture mechanics and the corresponding semi-analytical results are compared with those obtained by using the system of partial differential integral equations. This comparison demonstrates the high accuracy of the proposed method.

► The power series solution is used to model the crack tip elements.
► A hybridized boundary element/power series solution method is proposed.
► The special singular integrals are solved using the first two or four terms of an infinite power series.
► Displacements and stresses near the crack tips are accurately evaluated.
► The mixed mode stress intensity factors (Modes I and II) are numerically computed.