A constitutive equation for the S–N fatigue behavior of metal single crystals and validation by the physical definition of fatigue endurance limit

Abstract

A phenomenological constitutive equation for the stress–life (S–N) fatigue behavior of metal single crystals is presented and is validated on the basis of physical definition of fatigue endurance limit. The constitutive equation is developed here on the basis of probabilistic arguments for fatigue fracture in cyclic loading. The physical endurance limit for fatigue is taken as the stress amplitude corresponding to the critical resolved shear stress for dislocation slip initiation in ductile single crystals. It is shown that the constitutive equation is surprisingly compact and very flexible to accurately describe a wide range of S–N behaviors, as found in fatigue of nickel-based superalloy single crystals as well as in Fe and Zn single crystals. The S–N constitutive equation is also expanded by the superposition of the mean stress effect and the cyclic effect in fatigue. A remarkable outcome of this is a master S–N fatigue equation that yields S–N curves for any mean stress, on the basis of the S–N parameters for fully reversed fatigue behavior. The application of the presented equations to characterize the S–N behavior of polycrystalline materials is quite promising.