Evolution of crack paths and compliance in round bars under cyclic tension and bending

• General method for evaluating fatigue crack paths and compliance in round bars.
• Different initial crack shapes tend to a preferential crack path during fatigue.
• Dimensionless compliance is higher for tension loading than for bending moment.
• Convergence of the results is faster under bending than under tension.
• The greater the m coefficient of the Paris law, the quicker the convergence.

The aim of this paper is to calculate how the surface crack front and the dimensionless compliance evolve in cylindrical bars containing a transverse edge crack subjected to cyclic tension or bending with different initial crack geometries (crack depths and aspect ratios). A Java computer program was developed and implemented to obtain the crack path evolution (changes of crack depth and aspect ratio), as well as the progress of mechanical compliance, by discretizing the crack front (characterized with elliptical shape) and calculating the crack front changes on the basis of the Paris law, and using a three-parameter stress intensity factor (SIF). The results show that in fatigue crack propagation, relative crack depth influences more on dimensionless compliance than the aspect ratio, because the crack front tends to converge when the crack propagates from different initial geometries, showing greater values of dimensionless compliance for tension than for bending. Furthermore, during fatigue crack growth, materials with higher values of the exponent of the Paris law produce slightly greater dimensionless compliance and a better convergence between the results for straight-fronted and circular initial cracks.