Early fatigue crack growth as the damage accumulation process

A probabilistic approach to modeling of the initial stage of fatigue crack growth is suggested based on the concepts of continuum damage mechanics. The material is presented as a set of microstructural elements with randomly distributed properties. Both the grains and intergranular boundaries are considered as the elements of microstructure. The parameters of resistance of each element to damage accumulation are considered as random variables. These parameters are distributed among the elements independently that allows to model the damage process in polycrystalline materials. The damage measure depends on the characteristic normal and tangential stresses in order to take into account the tensile and shear fracture modes for each element of microstructure. It is assumed that a nucleus of a crack is initially present near the body surface as a single completely ruptured element. The final damage of an element is considered as the crack advancement. The crack is modelled as a sequence of ruptured grains for the transgranular fracture, and as a sequence of couples of neighboring ruptured grains when the intergranular rupture is considered. Numerical simulation is performed to illustrate feasibility of the proposed model. In particular, non-planar crack propagation, blunting, kinking and branching of cracks at the early stage is demonstrated. The non-monotonous pattern of the short crack growth process is observed. Statistical scattering of the current crack size and the crack growth rate as functions of the cycle number and the crack depth is studied.