The micromechanic analysis of a fatigue band in the most favorably oriented crystal at the free surface of a polycrystal is reviewed. The localization of plastic strain in thin slip bands under monotonic loadings and the ratchet mechanism of fatigue bands provided by the stress fields of two closely located parallel thin slices sliding in opposite directions are shown. Each of these two thin slices slides monotonically. The alternate sliding of the two thin slices results in the macroscopic forward and backward plastic strain in cyclic loading.

Single crystals are used in turbine engine parts. The fatigue band analysis of polycrystals is extended to analyze the fatigue band in single crystals. Hysteresis loops of a single crystal under constant stress amplitudes and under constant plastic strain amplitudes are shown. Two sets of these hysteresis loops, one with small initial stress and one with large initial stress, are presented. These calculated hysteresis loops explains the two diagonal sharp corners in each loop to be due to reversals of loadings.

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