Fractal Dimensions of a Propagating Fatigue Crack in Metallic Materials

The application of fracture mechanics for fatigue crack propagation is hampered by the unavailability of the crack geometry factor for numerous structural designs. In this respect, an alternative approach correlating the fractal dimension of the propagating crack with the crack tip driving force is examined. The fatigue crack growth rate behavior of the AISI 410 martensitic stainless steel is established, and the fractal dimension is quantified. The Paris crack growth rate region spans between 16 < Δ K I < 36 MPam. The fractality of the fatigue crack is established, and the fractal dimension at the various crack lengths is quantified using box-counting method. A linear relationship between the stress intensity factor range, Δ K I and the fractional fractal dimension, d ff for crack lengths within the Paris crack growth region, is identified as Δ K I K IC = 0.54 + 2.9 d ff . This eliminates the necessity of the crack geometry factor in determining Δ K I , thus predicting the fatigue crack growth rate of the structure based on the Paris law.