An Energy-Based Torsional-Shear Fatigue Lifing Method

On the anelasticity and fatigue fracture entropy in high-cycle metal fatigue

“…The gradual decline in the area of the hysteresis loop with the decreasing frequency indicates that the amount of anelastic energy contained within a hysteresis loop reduces with the decrease of the frequency. The trend of this plot agrees with the results reported by Wertz et al [26] and Wegel and Walther [31]. Thus, by continuing the reduction of frequency, it is possible to arrive at a frequency when further reduction does not decrease the area of hysteresis loop.…”

“…The experimental work of Wegel and Walther [31] showed that the internal friction increases at higher frequencies. Wertz et al [26] revealed that the area of a hysteresis loop decreases by several fold as the frequency of Nomenclature A i thermodynamic forces associated with internal variables C specific heat (J kg À1 K À1 ) E s elasticity modulus at magnetic saturation (GPa) E 0 elasticity modulus at zero magnetism (GPa)…”

“…Although the effect of vibration/oscillation, thermal current, dislocation movements, and ferromagnetism is less at a lower stress level, the influence of test frequency is considered to be the most influential parameter on the internal friction [26,31]. In order to determine the effect of test frequency on the hysteresis area, experiments are performed at different frequencies and stress levels.…”

“…According to the published literature [1,26,27], most of the area of a cyclic hysteresis loop in HCF represents a non-damaging anelastic energy generated by the magnetoelastic coupling, thermoelasticity, atomic diffusion, etc. The presence of the anelastic energy in a hysteresis loop occurs due to the effect of internal friction in the material, Q À1 , that causes a phase lag, /, between the stress and the resulting strain [26,28,29].…”

“…The presence of the anelastic energy in a hysteresis loop occurs due to the effect of internal friction in the material, Q À1 , that causes a phase lag, /, between the stress and the resulting strain [26,28,29]. Wertz et al [26] successfully showed that the anelastic energy from a hysteresis loop can be eliminated by gradually decreasing the loading frequency, f, to a value such that further decrease of the frequency does not reduce the area contained within the hysteresis loop. Application of this novel method requires one to repeat an HCF test at different frequencies with identical stress level and load ratio (defined as the ratio of minimum to the maximum stress in a load cycle), L R .…”