13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- distribution map on the key map [6]. His map seems to be rather suitable for expressing the characteristic of the fatigue strength σw2 . So, a new map is created so that it can express the characteristic of the fatigue strength inclusive of the fatigue strength σw1. The new map is shown in Fig. 5, where the character of the notch behavior is classified into four domains; (I) Un-notch-like behavior, (II) Prototype notch behavior, (III) Long-crack-like behavior and (IV) Short-crack-like behavior. The four domains are partitioned with three characteristic lines AB, CD and BD and with the outgoing lines BE and DF drawn in the horizontal and perpendicular directions from the two intersections. The characteristic lines AB, CD and BD are expressed by the following simple formulas, ρ t =10, ρ t =10−1 and ρt L 0 =1, respectively. A straight line PR formulated as ρ t =1 expresses the size change of the circular or spherical hole that represents typical notch behavior. The distribution of the fatigue strength can be diagramed in a logarithmic scale by taking the z-axis in the direction perpendicular to space of the map. Three examples are schematically shown in Fig. 5. One is the diagram of the fatigue strength σw1 for the circular or spherical hole. The diagram makes ρt L0 a variable and it is shown as a σw1 − ρt L0 diagram on the line where ρ t =1. As mentioned later, a σth − area diagram that makes Murakami's parameter of area a variable is a particular case of the σw1 − ρt L0 diagram where ρ t =1 and ρt L0 <1. Another is Kitagawa-Takahashi diagram that makes a crack length a a2 a variable and the diagram is known as a σth −a a2 diagram [7]. The σth −a a2 diagram is depicted as a σw2 −t L0 diagram on the horizontal axis (x-axis) in Fig. (5) where the crack length a a2 is replaced by the notch depth t L0 . Moreover, Kitagawa and Takahashi prepared another critical size a1 that represents the substantial transition from large size crack to small size one. This type of transition size on the fatigue strength σw2 is expressed by replacing a1 L0 by t0 L0 ; the transition notch size is shown as t0 L0 =10 1 2 in Fig. (5). The third is the fatigue strength of the un-notch condition σw0 that is distributed on the vertical axis (y-axis) as a uniform value. This value is thought to be materialized in common where both ρ L0 and t L0 are extremely small. (a) Notch sharpness: ρ t (b) Notch size scale: ρt L0 Fig. 4 Index parameter of notch sharpness and notch size scale: ρ t and ρt L0 Fig. 5 Notch behavior map and a few typical distributions of fatigue strength threshold stress
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