Probabilistic model of early fatigue crack growth

A model is developed in this paper to describe the nucleation and early growth of fatigue cracks. Polycrystalline materials are modelled as a set of elements (grains) with random properties. It is assumed that the resistance to damage of neighboring elements is mutually independent and follows the same probability distribution, except for the elements situated near the surface whose resistance is lower and which are subjected to higher scattering. Damage accumulation in each element due to cyclic loading is considered, and an element is treated as ruptured when a critical damage level is attained; then the ruptured element is included in the cracked domain. The finite element technique is applied to realize the modelling. Numerical results exhibit all the principal features of early fatigue crack growth such as nonmonotonous change of crack growth rates, statistical scatter of crack dimensions and growth rates, and stabilization of the process when a considerable number of grains enter the cracked domain.