Crack morphology models for fracture toughness and fatigue strength analysis

Planar cracks represent an approximation, largely adopted in fracture mechanics and fatigue problems, of the physical reality, where cracks feature complex geometric morphologies related to material microstructure, residual stresses, material properties dispersions and so on. In the present paper, firstly a model to describe the influence of roughness and friction of the crack surfaces is reviewed in relation to the resulting near-tip stress field and the fracture resistance under monotonic loading. Such a model is based on the Distributed Dislocation Technique, and considers a periodic profile of the crack. Then, some approximate theoretical models describing periodically kinked cracks are reviewed in their application to the estimation of fatigue strength of materials. In particular, the influence of crack path meandering on fatigue propagation is analysed by modelling the crack profile as a piecewise linear periodic curve in two dimensions. The same type of model is discussed within the framework of self-similar fractal geometries. In the paper, emphasis is given to the effect of crack size on the fracture resistance and fatigue strength, where such an effect depends on the ratio between the characteristic length of the crack morphology and the nominal length of the crack itself.