Fracture analysis of semi-circular and semi-circular-bend geometries

A fracture mechanics analysis of the semi-circular (SC) and semi-circular-bend (SCB) fracture geometries is presented. The weight function method is implemented to obtain wide ranging stress intensity factor (SIF) and crack opening displacement (COD) expressions. This study has as its basis a finite element analysis of the semi-circular disk (SC) subjected to a reference loading case. The latter is required to determine both the associated reference stress intensity factor and the weight function for the base-edge-cracked semi-circular geometry. With this information, SIF and COD expressions for the full range of crack lengths are obtained. The special cases of the SC subject to a concentrated crack mouth loading and the SCB are analyzed in detail. The weight function for the SCB is fully developed, with an accurate expression for the SIF and and a numerical result for the crack mouth opening displacement (CMOD). The latter wide ranging expressions can, in turn, be applied as a reference solution. From this weight function approach, SIF's and COD's for the SC and SCB subject to any other loading can be obtained.