Numerical modelling of cracking path in round bars subjected to cyclic tension and bending

• Fatigue crack growth (FCG) was calculated by using the Paris-Erdogan law.
• The crack paths for different initial crack geometries tend to a unique curve.
• Fracture risk due to local fracture criterion is higher in tension than in bending.
• Convergence of the results is faster under bending than under tension.
• The greater the m coefficient of the Paris law, the faster the convergence.

This paper shows the evolution of the surface crack front in round bars constituted of different materials (determined by the exponent m of the Paris law), subjected to fatigue tension loading (with free ends) or fatigue bending loading. To this end, a numerical modelling is developed on the basis of a discretization of the crack front (characterized by a semi-elliptical shape) and the crack advance at each point perpendicular to such a front, computed according to the Paris-Erdogan law and by using a three-parameter stress intensity factor (SIF). For each of the considered case the evolution of the semi-elliptical crack front is analysed, studying the variation of the crack aspect ratio a/b (defined as the ratio between the semi-axes of the ellipse which defines the crack front) against the relative crack depth a/D. The obtained results show that the dimensionless SIF values along the crack front are quite higher under tension loading than in the case of bending loading. Thus, the risk of catastrophic failure is higher in the case of tensile loading (in relation to the less dangerous bending situation) if a local fracture criterion (on the basis of the maximum local SIF K along the crack front) is used, considering that fracture takes place when K reaches the material fracture toughness KC.