A Simple Model for Fatigue Crack Growth Near Stress Concentrations

Fatigue crack growth rates are often difficult to predict for short cracks growing near stress concentrations. This paper presents a simple model to predict those growth rates which incorporates the phenomenon of crack closure. Crack opening stresses are shown to change significantly as cracks grow away from notches, and the simple model is designed to describe those changes. The effective stress range ratio, U, is assumed to be dependent on the local stress at the crack tip location in a corresponding uncracked body. The value of U changes with the normalized maximum stress in unnotched bodies, and this dependence can be quantified with elastic-plastic finite element models or simpler modified-Dugdale crack analyses. The local stress distribution is estimated with a Neuber analysis. A semi-empirical stress intensity factor solution is constructed and calibrated with known exact solutions. The crack growth rate is then calculated with the modified Paris law, taking crack growth constants from long crack data. The model is illustrated with a specific case study, the growth of cracks from center notches in an SAE 1026 steel. Experimental crack growth data for notches of different sizes and shapes compare favorably with the calculations. The scheme is contrasted with previous models for notch fatigue cracks. The implications of the simple model for other fatigue design problems are explored, highlighting the simplicity and generality of the model.