A Mesoscopic-Stress Based Fatigue Limit Theory - A Revised Dang Van's Model

Dang Van (Dang Van et al., 1982 and Dang Van, 1993) states that for an infinite lifetime (near fatigue limit), crack nucleation in slip bands may occur at the most unfavorable oriented grains, which are subject to plastic deformation even if the macroscopic stress is elastic. Since the residual stresses in these plastically deformed grains are induced by the restraining effect of the adjacent grains, it is assumed that the residual stresses are stabilized at a mesoscopic level. These stresses are currently approximated by the macroscopic hydrostatic stress defined by the normal stresses to the faces of an octahedral element oriented with the faces symmetric to the principal axis; mathematically they are equal to each other and they are the average of the principal stresses. This paper proposes and supports the novel hypothesis of normal stress to the maximum shear stress plane being an alternative to the octahedral normal stress, and better aligning with the restraining effect of the adjacent grains defined by Dang Van Multi Scale Approach.