An energy-equilibrium model for complex stress effect on fatigue crack initiation

Based on Tanaka and Mura’s fatigue model and Griffith theory for fracture, an energy-equilibrium model was proposed to explain the complex stress effect on fatigue behavior. When the summation of the elastic strain energy release and the stored strain energy of accumulated dislocations reach the surface energy of a crack, the fatigue crack will initiate in materials. According to this model, for multiaxial stress condition, the orientation of the crack initiation and the initiation life can be deduced from the energy equilibrium equation. For the uniaxial fatigue loading with mean stress, the relation between the maximum stress or the minimum stress and the stress amplitude is in agreement with an ellipse equation on the constant life diagram. If the ratio of the mean stress to stress amplitude is less than a critical value ?0.17, and the stress amplitude keeps constant, the fatigue crack initiation life will decrease with the increase of the compress mean stress. In this model, the mean stress does not cause damage accumulation with the fatigue cycles in crack initiation. For this reason, the loading sequence of different load levels would induce the cumulative damage to deviate from the Palmgren-Miner cumulative damage rule. The procedure of estimating the damage under random loading is also discussed.