Estimation of P-S-N curves in very-high-cycle fatigue: Statistical procedure based on a general crack growth rate model

Extensive experimental investigations show that internal defects play a key role in the very-high-cycle fatigue (VHCF) response of metallic materials and that crack growth from internal defects can take place even if the stress intensity factor associated to the initial defect is below the threshold for crack growth. By introducing a reduction term in the typical formulation of the threshold for crack growth, the authors recently proposed a general phenomenological model, which can effectively describe crack growth from internal defects in VHCF. The model is able to consider the different crack growth scenarios that may arise in VHCF and is enough general to embrace the various weakening mechanisms proposed in the literature for explaining why crack can grow below the threshold. In the present paper, the model is generalized in a statistical framework. The statistical distributions of the crack growth threshold and of the initial defect size are put into the model. The procedure for the estimation of the Probabilistic-S-N curves and of the fatigue limit distribution is illustrated and numerically applied to an experimental dataset.