13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- b) Approximation to a semi-elliptical notch. The specimen notch is approximated by a semi-elliptical notch with semi-axes b and c (see Fig. b). The value of c can be expressed as a function of the notch root tip ρ, c b/ 2 =ρ . From an elastic stress analysis, considering the C(T) as a cantilever beam, the nominal stress range applied at the notch can be calculated as ( ) ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − + ⋅ + ⋅ ⋅ − Δ Δ = W b W b t W b P n 1 3 σ (1) Therefore, after the value of nσΔ is determined by solving the system of equations in Eq. (11), the load PΔ to be applied to the specimen will be found by applying Eq. (12), in the next section are presented the numerical results for that combination. 3. Numerical results Assuming the fatigue limit of smooth specimen as u L S S ⋅ =' 0.5 , for a load ratio 1 =− R (fully reversed loading), by Goodman it can be interpolated for 0 = R (pulsating tension), resulting in 2 /3 0 uS Δ = ⋅ σ . Following the Frost’s statement, it is the difference between tK and f K that define the generation of non-propagating cracks. The figure also shows the stress concentration factor tK and how its value tends to f K as the notch root ρ increases. Therefore, for this material and specimen configuration, notch with root radii ~1.5 <ρ will be able to generate non-propagating cracks (see Fig. 5). 0 5 10 15 20 25 30 0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5 Kt, Kf ρ(mm) Kt Kf (ETS) Kf (TCD) Fig. 5 Comparison of predictions of the notch fatigue factor f K with the stress concentration tK as a function of the notch root ρ. In addition to f K , the model also allows calculating the largest non-propagating crack max a that can arise from fatigue alone. Fig. shows the value of max a as a function of the notch root ρ.
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