Part-through cracks in round bars under cyclic combined axial and bending loading

Fatigue fracture mechanics concepts can usefully be applied to analyse the propagation of surface cracks in metallic round bars under cyclic combined axial and bending loading. A finite element analysis is carried out to determine the stress field in the case of an elliptical-arc part-through flaw, the aspect ratio, a = a/b, of which ranges from 0.0 to 1.2 (~ = 0.0 corresponds to the straight front, while a = 1.0 represents the circular-arc front). The fatigue crack growth is numerically examined by means of a two-parameter model based on the Paris-Erdogan law. The propagation paths for different material properties and loading conditions converge to an inclined asymptote in the diagram of a against ~:, where ~ is the relative crack depth of the deepest point on the crack front. Experimental data and theoretical fracture energy considerations reported in the literature validate the results obtained through the above model.