Weight Functions for an External Longitudinal Semi-Elliptical Surface Crack in a Thick-Walled Cylinder

Abstract

Mode I weight functions were derived for the deepest and surface points of an external radial-longitudinal semi-elliptical surface crack in a thick-walled cylinder with the ratio of the internal radius to wall thickness, Ri /t = 1.0. Coefficients of a general weight function were found using the method of two reference stress intensity factors for two independent stress distributions, and from properties of weight functions. Stress intensity factors calculated using the weight functions were compared to the finite element data for several different stress distributions and to the boundary element method results for the Lamé hoop stress in an internally pressurized cylinder. A comparison to the ASME Pressure Vessel Code method for deriving stress intensity factors was also made. The derived weight functions enable simple calculations of stress intensity factors for complex stress distributions.