Two general equations for deriving SIF expressions of some axisymmetric finite domain problems

Abstract

Using the previous analytical method (Wang QZ, The crack-line (plane) stress field method for estimating SIFs—a review. Engineering Fracture Mechanics 1996; 55(4): 593–603.) and Green's function approach, two general equations are formulated for deriving approximate stress intensity factor (SIF) expressions for two categories of finite domain problems: (1) a finite-width strip with a center crack; (2) a circular cylinder with a concentric penny-shaped crack, both under various axisymmetric tensile loading at the crack faces. Examples with concentrated and distributed (up to quadratic variation) loading conditions are given to show the efficiency of these two general equations. As compared with the previous method, now the necessity of finding out the exact crack-line (plane) stress solution for the counterpart infinite problem is eventually waived. Another merit is that some SIF results for concentrated loading cases derived by using the general equations may have better accuracy than those given by the previous method. These two general equations are almost identical in form except for a small difference. Examples also show that the dimensionless SIF expressions for some problems in category (1) are identical with those in category (2), and there exists a regular correspondence between their loading conditions. Such identities in the dimensionless SIF expressions are useful in applications. Several example solutions given in this paper fill in the vacancy of missing solutions in present SIF handbooks, while other solutions are much simpler than the corresponding solutions in SIF handbooks.