13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- where, γ, C1, C2 : Material constants. 4. Regression analysis on the fatigue data currently introduced in literature Eq. (19) and (20) are applied to the regression analyses of fatigue data picked up from literatures. It is confirmed whether the function form of the equation derived in the preceding chapter 3 is appropriate as a regression equation. A part of the result is described below. Fig. 6 shows the result of a rotating bending test of S45C annealed steel with a round-bar specimen containing a small drill-hole. In the experiment [9], the diameter of a hole d was changed in the range from 0.04 to 0.5 mm and the depth t changed from 0.04 to 1 mm. The fatigue strength σw1 is shown as a function of area -parameter in Fig. 6. The plot represents the experimental result and the curve shows the calculated result from the regression equation. The horizontal line represents the strength level of an un-notched specimen σw0 is calculated backward from the regression equation. It turns out that the regression equation fits the experimental result very well. Fig. 7 shows the result of a rotating bending test of S45C annealed steel with a round-bar specimen containing an extremely shallow circumferential-notch. In the experiment [10], the notch root radius ρ was changed in the range from 0.01 to 0.6 mm and the depth t changed from 0.005 to 1.5 mm. The fatigue strength σw1 and σw2 were measured and they were shown as a function of a stress concentration factor Kt in Fig. 7(a) and (b), respectively. The colored plot represents the experimental result and the colored thin curve/line shows the calculated result. The horizontal thick gray line represents the strength level of an un-notched specimen σw0 calculated backward from the regression equation. The thick gray curve obtained by dividing σw0 by Kt is drawn for reference. In both Fig. 7(a) and (b), it turns out that the regression equation fits the experimental result very well. The regression analysis using the proposed equation has applied to the fatigue testing result of the total Fig. 6 Result of a regression analysis on rotating bending fatigue strength of S45C round-bar specimens containing small drill-holes (data from Ref. [9]) (a) Fatigue strength σw1 (b) Fatigue strength σw2 Fig. 7 Result of a regression analysis on rotating bending fatigue strength of S45C round-bar specimens containing small size circumferential notches (data from Ref. [10])
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