Critical energy approach for the fatigue life calculation under blocks with different normal stresses amplitudes

More than 60 fatigue models have been proposed since Palmgren damage accumulation concept was introduced in 1924. The Palmgren–Miner linear cumulative damage rule is still used in design due to its simplicity, but it does not take into account the material behaviour (linear or nonlinear), the influence of mean stress, load rate and deteriorations. Some cumulative damage rules derived from Palmgren–Miner's rule are presented in the present paper.The problem of fatigue life is discussed and a new method and new relationships for fatigue life calculation is proposed taking into account the superposition of fatigue loadings, considering the dependence of critical stress value on the number of loading cycles, as well as the nonlinear behaviour of the material along with the influence of the mean stress, cyclic loads rate and deteriorations.Relationships have been established for superposition of different effects in the case of cyclic fatigue loading with only one block of stress;—several blocks of normal stresses.For the endurance: - domain (N≥N0) a relationship under constant fatigue life an approach is proposed in the case of loading with only one block of normal stress. The influence of the mean stress sign (tension or compression), as well as the influence of the loading rate is analysed.The obtained results are discussed taking into account some other empirical relationships, as well as the ASME Code—Section VIII, PD 5500 and Euronorme recommendations. Recommendations for the practical use of the cumulative fatigue damage rules proposed in this paper are presented along with numerical examples. These may be useful for engineering design.

► New method for fatigue life calculation has been proposed for nonlinear and cracked materials.
► The influence of mean stress and its sign, of cyclic loads rate and of the deterioration is shown.
► Relationships have been established for fatigue life due to several blocks of normal stresses.
► Relationships for constant fatigue life in the endurance domain have been deduced.