Deterministic and probabilistic description of fatigue short-crack growth in notched members

We suggest deterministic and probabilistic methods for the prediction of crack growth in notched members taking into account the regularities of short-crack growth and simplifying the procedure of prediction. In the proposed deterministic approach, it is assumed that the stress concentration factor exponentially decreases with the distance from the notch root in the direction of the short crack. The equations of crack propagation both on the surface and into the depth of the material are obtained on the basis of the Paris formula. The probabilistic method is based on linear fracture mechanics and the assumption that fatigue crack growth is a stochastic process. The core of this concept is formed by a difference equation reflecting the dynamics of fatigue changes and a:Paris-type formula. In both methods, we deduce the expressions allowing one to estimate the fatigue life of shea and, long cracks. The validity of the presented approaches is demonstrated by the description of the behavior of short cracks in notched specimens made of a medium-carbon steel.