Multiscale Investigation of Strain Energy Density for Fatigue Life Prediction

A fatigue life prediction method using strain energy density as a prediction parameter has had success predicting the lifetimes greater than 10⁵ cycles for room and elevated temperatures under axial, bending, and shear loading for different material systems. This method uses monotonic strain energy density determined at the macroscale as a damage parameter for fatigue, despite the differences in damage behavior of static and dynamic loading. Recent studies have brought this method into question, as cyclic energy for low cycle fatigue loading has been found to be significantly greater. Amendments of the fatigue life model have addressed this discrepancy for continuum level measurements, but have yet to examine the localized effects of machined notches. This study investigates strain energy density for static and dynamic loading at cycle counts from one (monotonic) to 10⁵ for plain and notched specimens, exposing the differences between damaging strain energy density at continuum and local length scales. Continuum level strain energy density is simply determined by using the load and strain feedback from a standard mechanical test procedure using a common extensometer and a servohydraulic load frame. Local strain energy density is determined more elaborately by using three methods. Localized energy is determined from compliance and a closed form relationship between stress intensity factor and strain energy density. The influence of the notch is considered in the stress intensity calculation, but its influence on stress concentration is disregarded. All calculations are based on the net section stress and linear elasticity is assumed. The analyses revealed two distinct groups, but one data set indicated coincidence with total accumulated strain energy density. These data also corroborate the theory that average strain energy density at the continuum level changes mechanisms governing damage evolution. Monotonic strain energy density is refuted as an appropriate damage parameter to predict fatigue lifetimes, and a statically equivalent strain energy density is proposed. An amended continuum level model is proposed, increasing prediction accuracy over fatigue lifetimes less than 10⁶. Additionally, a localized model is proposed, expanding prediction capability to geometries with notch like features.