Part-through cracks in pipes under cyclic bending

The propagation of a circumferential external surface crack in a metallic round pipe under cyclic bending loading is examined through a two-parameter theoretical model. A finite element analysis is carried out to determine the stress-intensity factor distribution along the front of the flaw, which is assumed to present an elliptical-arc shape with aspect ratio α=ael/bel (ael, bel=ellipse semi-axes). The relative depth ξ of the deepest point on the front is equal to the ratio between the maximum crack depth, a, and the pipe wall thickness, t. The parameter R/t, with R=internal radius of the pipe, is made to vary from 1 to 10. The fatigue growth of the surface flaw occurs according to preferred paths in the diagram of α against ξ