Fatigue fractal cracks propagating in self-balanced microstress fields

A kinked crack propagating in a periodic self-balanced multiaxial microstress field having self-similar characteristics is considered. The kinking angle of the crack is shown to depend on the properties of the microstress field. Using the Richardson’s expression for self-similar fractals, the fractal dimension of the crack is expressed as a function of the kinking angle. Crack size effect on the fatigue crack growth rate in the Paris regime can be interpreted by the present model. Further, the Kitagawa diagram can be interpreted by showing that the threshold condition of fatigue crack growth is affected by the crack kinking angle which, in turn, is a function of the ratio between crack length and microstructure characteristic length.