A physical model and constitutive equations for complete characterization of S-N fatigue behavior of metals

A physical model and constitutive equations for metal fatigue, to characterize completely the S-N fatigue behavior of structural materials, have been developed on the basis of the macroscopic behavior of fatigue crack growth. The macroscopic behavior that forms the basis is that at any time during fatigue the fractional remaining fatigue life is proportional to the fractional remaining uncracked section size. A crack growth functional has been shown to describe this behavior accurately, and universally, for a wide range of materials, test conditions, and specimen geometries. By integrating this functional and with the introduction of physical boundary conditions, a surprisingly compact constitutive equation for the stress-life (S-N) fatigue behavior is derived. The constitutive equation represents accurately the sigmoidal shape of S-N high cycle fatigue behavior of single crystals and polycrystals, including the asymptotic approach of the fatigue data toward a physical endurance limit stress. Metallurgical fatigue strengthening effects due to pre-strain, alloying and grain refinement have also been shown to be accurately predictable. The equation is then expanded to include the mean-stress effects in various forms, which facilitated the complete prediction of stress-life behavior and fatigue limit, for any mean stress, solely from the S-N behavior of fully reversed fatigue data. A very interesting consequence of this is a new, master constitutive equation capturing the mean stress effect on fatigue behavior. Extensive experimental data, generated at various mean stresses, have been used to validate the present approach.