A rate independent inelasticity model with smooth transition for unifying low-cycle to high-cycle fatigue life prediction

Abstract

A three-dimensional rate independent inelastic constitutive model has been developed to predict the fatigue behavior of metals spanning low to high cycles, based solely on the monotonic stress strain curve and a cyclic test for a few cycles ( < 1000). The key to the development of the model is that the “microplastic response” before full yield is accounted for by a new approach to inelastic modeling while retaining a rate independent response. A numerical algorithm based on the one-dimensional version of the constitutive theory has also been implemented into a computer code to model fatigue loading under simple tension/compression i.e. uniaxial loading conditions. The material parameters in the constitutive model were calibrated through fitting the constitutive model to the monotonic stress–strain curve obtained from a simple compression test experiment. By adopting the total inelastic work dissipation (which is related to the configurational entropy created due to damage) as the failure criteria and integrating the rate of entropy generation (under isothermal conditions) over a typical stabilized hysteresis cycle (including the small scale effects due to microplasticity), a close-formed expression for stress-fatigue life prediction is also derived for zero mean stress. Finally, it is shown that the model and numerical algorithm are able to predict the experimental stress-life and strain-life (with and without mean stress) responses quite well.