Stress intensity factors for a semi-elliptical surface crack in a T-shaped geometry. II. Approximate solutions at the deepest point for arbitrary crack-face loading

The Petroski-Achenbach displacement formulation is applied in conjunction with the weight function method in order to determine the mode I stress intensity factor at the deepest point of a semi-elliptical surface crack in a T-shaped geometry subjected to arbitrary crack-face loadings. The T-geometry is taken to be representative of the web and flange of an I-section and was previously investigated for tensile and bending loading. Comparison between the model developed here and the finite element solutions for two different stress distributions reveals very good agreement for shallow cracks, although the differences between the results of the weight function formulation and the finite element results increase as the crack becomes deeper and more rounded. The normalized stress intensity factors, for up to fifth-degree polynomial crack-face loading, are given in tabular form.