13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- band is released on the surface and forms surface relief [2-4]. On the other hand, it is inside restrained and produces inherent compressive stress. A hypothesis that reflects such microscopic mechanical behavior in the persistent slip band is introduced from a viewpoint of macro-mechanics as follows. At the weakest spot of a surface layer, a notch root and a fatigue crack tip, the elastic expansion arising at the maximum stress is transformed into the irreversible expansion inherent in fatigue. As a result, the maximum stress at the weakest spot is substantially decreased and the elastic energy is relieved. Therefore, it is termed as the hypothesis of cyclic plastic-adaptation by author. Such stress relief is materialized for each maximum principal stress in a multi-axial stress condition, too. The expansion arising by the plastic adaptation behaves as a mechanical misfit and lowers the mean stress of substantial cyclic stress. Accordingly, the cyclic behavior of stress can be imaged as shown in Figs. 1(a)-(c). They show the cases of uni-axial stress (a), bi-axial stress where the change is the same (b) and opposite sign (c). At the weakest spot of the surface layer, the stress path moves from a site ab to a site ef, in common in each figure, though the outward path remains at a site ab. The cyclic plastic-adaptation is accomplished completely at the site ef. As mentioned later, it should be noted that the movement of the stress path caused by growth of irreversible expansion means not a change of itself but the movement of the potential field that it has. 2.2. Derivation of the equivalent cyclic stress ratio (REQ-ratio) How to reproduce the cyclic stress potential field at a notch root as that in the surface layer of the un-notch condition is illustrated based on the hypothesis of cyclic plastic-adaptation. Concretely speaking, the cyclic stress that activates microscopic slip behavior in the un-notch condition as much as the cyclic stress does at the notch root is pictured on the diagram of the stress path. From this diagram, the equivalent cyclic stress ratio REQ and the equivalent mean stress σmeanEQ are graphically estimated. REQ and σmeanEQ behave just like a hydrostatic stress ratio and hydrostatic mean stress in the process of the cyclic plastic-adaptation, respectively. This is due to the following reasons; (1) the irreversibility of expansion caused by cyclic plastic-adaptation and (2) the addibility of volume expansion which is produced under each principal cyclic stress. These two matters give the important hint to quantitative interpretation of cyclic plastic-adaptation; it is the potential described by Mises' equivalent stress that generates a driving force advancing cyclic plastic adaptaion and it is the algebraic sum of the maxmum value of principal stresses that provides the capability producing the cyclic plastic-adaptation. So, in the present study, in order to estimate the Fig. 1 Change of the stress path under cyclic plastic-adaptation (a) Uni-axial stress (b) Bi-axial stress where the change is the same sign (c) Bi-axial stress where the change is the opposite sign
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