On the Crack-Tip Blunting Model for Fatigue Crack Propagation in Ductile Materials

Abstract

The conventional geometric crack-tip blunting model for fatigue crack growth based on the crack-tip opening displacement (CTOD) is examined numerically with the objective of modeling crack advance solely in terms of the effect of local plastic deformation, without introducing any specific failure criterion or presumed slip behavior. In the absence of an analytical solution for cyclic plastic deformation at the crack tip, computational solutions are used to check the validity of the description of fatigue crack growth rates as a nonlinear function of a linear stress intensity factor, K. A finite element analysis is performed in plane strain for a crack tip, blunted from an initial tip radius of submicron to micron size; the crack is considered for a wide range of lengths and is subjected to zero-to-tension cycling with both tension and bending loads. The calculated results are compared with experimental fatigue crack growth data on aluminum alloy 7075-T6, where it is found that with the tip radius of 0.5 μm, results are in reasonable agreement with experiment. By examining the crack-tip plastic deformation for the first and subsequent cycles, crack extension is seen to result from the dissimilarity in the loading and unloading deformation. Reverse yielding brings about a crack tip “shrink”, with a full recovery of cyclic CTOD and a partial recovery of crack advance. In the limit of a sharp crack, this model predicts that the maximum growth rate per cycle will be 0.35 of the cyclic CTOD. Such aspects are deemed critical in the future development of analytical solutions to this problem.