On the definition of elastic strain energy density in fatigue modelling

Fatigue modeling for wrought magnesium structures with various fatigue parameters and the concept of highly strained volume

“…Finally, the regressions of Eqs. (26) and (27) lead to regression planes for the fatigue parametersε * a , P SWT , ΔW t and ΔW t mss and to a regression surface for the fatigue parameterε * ,el a +ε * ,pl a , plotted with green color in Figs. 8, 9, 10 and 11.…”

“…A further reason for the deviation could be the calculation approach of the positive elastic strain energy density ΔW +el , which considers the mean stress. Roostaei et al states in [27] that wrought Mg alloys show positive mean stress even during fully reversed strain-controlled tests with strain ratio R ε = −1. By using their calculation approach of ΔW +el , they improve their fatigue model especially for the load ratio R = 0.5.…”

“…The total strain energy density is defined as the positive elastic strain energy density ΔW +el and the plastic strain energy density ΔW pl . Among the different calculation methods for the positive elastic strain energy density [5,16,19,27], the equations…”

“…In addition, [10] shows that common fatigue parameters such as strain amplitude, Smith-Watson-Topper or energy-based fatigue parameters, taken from inside BTGs, have higher values, which corresponds to the observation that the initial macroscopic crack is always within BTGs. Further challenges in fatigue modeling of basal textured wrought Mg alloys are anisotropic and asymmetric yield strengths, almost ideal plastic material behavior during twinning and sigmoidal shaped stress-strain hystereses [20,27,31].…”

“…In recent years, several works have been published on fatigue modeling, that deal with the complex deformation behavior of Mg alloys [5,19,23,26,27]. All these researches use a total strain energy density fatigue parameter, first introduced by Ellyin et al [12].…”