Modelling of stress gradient effect on fatigue life using Weibull based distribution function

In the present paper, a new approach is developed in order to take into account the stress gradient effect on fatigue life of structural components. The proposed approach is based on the weakest link concept in which the shape coefficient of the Weibull distribution becomes a function of a local damage parameter. The function simulates the experimentally observed relationship between the shape of the fatigue life distribution and the stress level. Such an approach allows one to calculate the global probability distribution of the fatigue life for notched structural components in a wide range of fatigue life regime: $ 10^4$-$10^7$ cycles typically. For comparison purposes, the approach is applied to calculate the number of cycles to crack initiation of structural elements under three probability levels: 5%, 63% and 95%. The calculated lifetimes are compared with the lifetimes obtained from experiments performed on notched cruciform specimens and notched round specimens subjected to constant amplitude loading.