13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- = ac (i.e., the critical distance) will allow the determination of an expression for the fatigue notch factor of the form 1 3 1 2 2 1 c c 1 1 1 2 2 2 2 ρ ρ ρ ρ = + + + ∫ b b b n f e V k dV V V a a (26) Assuming that the critical distance is constant for the notched component with a notch root radius ρ, Eq. (26) reduces to 3 1 2 2 1 c c 1 1 2 2 2 2 ρ ρ ρ ρ = + + + b n f e V k V a a (27) The above equation for kf was derived using the fatigue damage process zone based on critical distance, probabilistic framework based on the weakest link, and the Glinka’s closed form solution based on the notch root stress distribution. The expression in Eq. (25) has been shown to give a good prediction of the stress field for relatively blunt U-notches and be used over a distance of 3ρ from the notch root with an accuracy of approximately 7% [15]. 6. Results and Discussion The stress distribution obtained from the finite element analysis was used in determining the average kf for the geometry using the proposed probabilistic framework based on Weibull’s weakest link and extreme-value statistics. Also as a further validation of the proposed approach, the value of kf was calculated using the closed form solution for fatigue notch factor in Eq. (27) and the result is compared to experimental results determined by R.A. Naik et al [15] as shown in Table 2. Both results are in agreement with the experimental results with minimal difference. The kf determined using the Weibull’s weakest link approach, when the loading ratio R =-1, is more accurate than for every other loading ratios tested. Table 2. Comparison of measured and predicted Kf using FEM and closed form analysis Test Case Kt Notch radius, (mm) Notch depth, h (mm) R- ratio Experimental average Kf Kf using Weibull’s weakest link Kf using closed-form analysis 1 2.78 0.330 0.729 -1 2.79 2.73 2.66 2 2.78 0.330 0.729 0.1 1.80 1.89 1.88 3 2.78 0.330 0.729 0.5 1.75 1.82 1.84 4 2.78 0.203 0.254 0.1 1.71 1.86 1.80 5 2.78 0.203 0.254 0.5 1.74 1.83 1.83 6 2.78 0.127 0.127 0.1 1.98 2.05 2.01 7 2.78 0.127 0.127 0.5 1.65 1.72 1.77 Also, the radius of curvature at the notch root plays a vital role on the stress gradient at the notch. This effect is captured by the fatigue notch sensitivity factor q given in Equation 3. Figure 6 gives a plot of the notch sensitivity factor as a function of the notch root radius for the different load ratio. The
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