Method for calculating stress intensity factors for surface cracks

This paper introduces an approximate weight function method for calculating stress intensity factors for semi-elliptical surface cracks under arbitrary loads. The crack face displacement field required for the calculation is approximated by using one or more known stress intensity factor solutions. The method is applied to surface cracks in a wide plate using published analytical solutions for tension and bending loads as reference solutions. These two known reference solutions allow the use of either two- or three-parameter displacement approximations. The calculated results were compared with other published results for several load cases, including loading with variable stress in the crack length direction. Several different displacement approximation functions were tested. The simplest two-parameter displacement approximation gave good accuracy when the tension solution was used as the reference case. The addition of the third parameter improved the results for several load cases but not for all cases. The method could be improved if the crack opening displacement for the reference solution was known, e.g. at the crack center. The accuracy of the present method is best at the deepest position of the crack. The stress intensity factor for the analyzed load case is interpolated along the crack front with only two interpolation functions. The choice of these functions is important to the accuracy of the results and it may be difficult to find these functions, especially if the analyzed load case differs considerably from the reference load case. More than two interpolation functions can be used if the weight function equation is applied to the analyzed load case several times using more than one linearly independent reference solution. This was tested with the two currently available reference solutions, but the tests were not successful owing to difficulties in approximating the displacement for the bending load case