13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Formulation and Characterization of Fatigue Strength Diagrams of Notched Specimens Based on Equivalent Cyclic Stress Ratio, Attending Especially to Material Dependence and Notch Size Effects Hiroshi Matsuno1,* 1 Department of MECHANICAL ENGINEERING, SOJO University, Kumamoto 860-0082, Japan * Corresponding author: hi-matsuno@par.odn.ne.jp Abstract In the present paper, a fatigue strength diagram is formulated and characterized as a function of an equivalent cyclic stress ratio (named as REQ-ratio). The REQ-ratio is derived from a hypothesis of plastic adaptation that reflects micro-mechanical behavior of a fatigue slip band, and it was proposed as a corresponding parameter between cyclic stress-conditions of notched and un-notched specimens in the previous paper. The REQ-ratio is given as a function of a theoretical stress concentration factor Kt and a nominal cyclic stress ratio RN, and it is noteworthy that the REQ-ratio materializes a similitude relation between the fatigue strength diagrams of notched and un-notched specimens in the case where the notch depth is greater than about 1mm (where the notch size effect is negligible). Therefore, the REQ-ratio can be applied as a main variable to the formulation of the fatigue strength diagram. The formulation is extended to the case of the extremely shallow notch where the size effect is dominant, and finally the generalized equations expressing the fatigue strength diagrams are proposed. These equations are applied to regression analyses on fatigue data of practically used metallic materials. Consequently, the material- and size- dependence in notch effects are considered and characterized. Keywords Fatigue strength diagram, Cyclic plastic-adaptation, Equivalent cyclic stress ratio (REQ-ratio), Notch behavior map, Notch size effect 1. Introduction A fatigue strength diagram is formulated and characterized as a function of an equivalent cyclic stress ratio (named as REQ-ratio). The REQ-ratio is derived from a hypothesis of cyclic plastic adaptation that reflects micro-mechanical behavior of a fatigue slip band, and it was proposed as a corresponding parameter between cyclic stress condition of notched and un-notched specimens in the previous paper [1]. A graphic method estimating the REQ-ratio on the basis of the hypothesis is developed in the present paper. It is described that the REQ-ratio materializes a similitude relation between the fatigue strength diagrams of the notched and un-notched specimen in the case where the notch depth is comparatively large size of mm-order (where the notch size effect is negligible). It means that the REQ-ratio can be applied as a main variable to the formulation of the fatigue strength diagram. Next, the notch behavior is characterized and mapped by making the notch root radius and depth into variables. The notch size effect is discussed on the basis of the notch behavior map and the size effect factors are introduced. As a result, the formulation of the fatigue strength diagram can be extended to the case of the extremely small size notch, such as the depth of 10 and 100 µm-order, where the size effect is dominant, and finally the generalized equations expressing the fatigue strength diagrams are proposed. These equations are applied to regression analyses on fatigue data of practically used metallic materials. 2. Graphic method estimating an equivalent cyclic stress ratio (REQ-ratio) 2.1. A hypothesis of cyclic plastic-adaptation Irreversible microscopic expansion developing in the slip direction of a crystal of a persistent slip
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