13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- from 0.1 to 3 mm. The REQ for axial cyclic load is estimated by FEM based on Mises' equivalent stress and the factor p done as the ratio of the average equivalent stress in the notch section σeq to the nominal stress σN [1]. In Fig. 3, the colored plot represents the experimental result. From the dispersion state of a plot, it is found, the fatigue strength is systematically arranged in spite of differences of stress concentration factors and mean stress, and it is clearly separable into the two groups of σw1 and σw2 . The curved and straight lines represent the fatigue strength diagrams of σw1 and σw2 , respectively, and they are drawn on the basis of the regression equations derived in the following chapter. The horizontal axis of the graph in Fig. 3(a) can be converted from the scale of REQ to the scale of Kt eq 1− RN ∗ ( ) and K t 1− RN ( ) as shown in the lower berth of the graph; 1− REQ = Kt eq 1− RN ∗ ( ) = K t eq ΔσeqN σeqmaxN ( ) = ΔσeqNR σeqmaxN (for axial load) (7) 1− REQ = Kt 1− RN ( ) = Kt ΔσN σmaxN ( ) = ΔσNR σmaxN (for rotating bending) (8) Both the axes of the graph take the scale proportional to Kt . Therefore, it can be said that a similitude relation between the diagrams is materialized. This means that REQ is very useful as the correspondence parameter between the fatigue strength of the notched and un-notched specimen. The coincidence of a diagram in Fig. 3(b) means that the σmeanEQ -based fatigue strength diagram obtained from the fatigue data of the notched specimen turns into the σmeanN -based fatigue strength diagram of the un-notched specimen as it is. 3. Formulation of the fatigue strength diagram based on the REQ-ratio 3.1. Characterizing and mapping of the notch behavior The notch is characterized by two parameters of ρ t and ρt L0 as shown in Fig. 4(a) and (b), where the notch depth t and the notch root radius ρ are expressed as the co-ordinates after normalized by the size L0 . L0 is introduced as an index for judging large size or small size notch. In the present study, L0 =1mm is set emprically. The parameter ρ t shows the sharpness of the notch which Kt depends on and the parameter ρt does the scale of the notch which the size effect depends on. Taylor classified the character of the notch behavior into three and drew the Fig. 3 Fatigue strength diagram of SM400 steel round-bar specimen with the large-size notch (The fatigue tests were performed by cyclic axial load under mean stress [1] and rotating bending) (a) REQ vs.Kt ΔσN diagram and similarity (b) σmeanEQ vs.Kt σampN diagram and identity with that of the un-notch condition
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