In this paper, several multiaxial fatigue damage parameters taking into account non-proportional additional hardening are reviewed. According to the way non-proportional additional hardening is considered in the model, the damage parameters are classified into two categories: (i) equivalent damage parameters and (ii) direct damage parameters. The equivalent damage parameters usually define a non-proportional coefficient to consider non-proportional additional cyclic hardening, and make a combination of this non-proportional coefficient with stress and/or strain quantities to calculate the equivalent damage parameters. In contrast, the direct damage parameters are directly estimated from the stress and strain quantities of interest. The accuracy of four multiaxial fatigue damage parameters in predicting fatigue lifetime is checked against about 150 groups of experimental data for 10 different metallic materials under multiaxial fatigue loading. The results revealed that both Itoh’s model, one of equivalent damage parameters, and Suemel’s model, which belong to direct damage parameters, could provide a better correlation with the experimental results than others assessed in this paper. So, direct damage parameters are not better than the equivalent damage parameters in predicting fatigue lifetime.
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