Fractal study on collective evolution of short fatigue cracks under complex stress conditions

► A Paris-type damage model is proposed based on fractal theory. ► A computational program is developed. ► The fractal dimension evolution presents “HILL” stage characteristics. ► The transition period between two stages is at 30% of fatigue life. ► The Paris-type damage model can describe fatigue collective damage process. This paper proposes a Paris-type damage model to investigate the collective evolution of short fatigue cracks based on fractal theory. On the basis of experimentally determined images, the fractal dimensions (FDs) of rounded notched specimens’ surfaces are numerically calculated by using Otsu threshold segmentation and box-counting dimension method. The results show that FDs’ evolution presents “HILL” curves’ characteristics. The transition period between FD rapid growth stage and FD constant stage takes place at about 30% of fatigue life. The good match between experimental results and FEM analyses reveals the model can describe collective damage process caused by all fatigue cracks.