Probabilistic model for length effect on fatigue life of longitudinal elements

This paper studies the length effect on fatigue life of longitudinal element at the macroscale. An asymptotic weakest-link Weibull phenomenological model that incorporates a statistical length effect for the fatigue life of longitudinal element is proposed in this research. In the proposed model, the weakest-link effect gradually becomes dominant and causes a decrease in fatigue life that increases along (Formula presented.), the normalized length of the longitudinal element. To this end, the fatigue life under a specified stress range is divided into 3 zones according to the normalized length (Formula presented.) : (1) (Formula presented.) is the zone where length effects can be ignored, and the fatigue life can be treated as a random variable; (2) (Formula presented.) is the zone where the fatigue life is length dependent; and (3) (Formula presented.) is the zone where the fatigue life follows asymptotic length dependence. The asymptotic threshold normalized length, (Formula presented.), can be evaluated by the asymptotic weakest-link Weibull model. To validate the proposed model, 3 previously published datasets are used: (1) the fatigue data of Picciotto yarn, (2) hipo-eutectoid steel wire with different lengths, and (3) the fatigue data of high-strength steel wire with different lengths and different constant stress ranges. Finally, the results obtained by the proposed model are compared with those from the literature and discussed in detail. The analytical solutions obtained using the proposed model allows for assessment of the fatigue life of certain components and structures that are beyond current testing capabilities. In particular, the length effects on the fatigue life of the high-strength steel wire in stay cables are investigated to gain insight into issues regarding safe designs.