PSI - Issue 13

K. Solberg et al. / Procedia Structural Integrity 13 (2018) 1762–1767 K. Solberg / Structural Integrity Procedia 00 (2018) 000–000

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Fig. 2. Top: Coordinate system used to describe notch geometry plotted for different values of η. Bottom: Coordinate system used to describe the components of the stress field.

Fig. 3. Boundary conditions, load and mesh used in Abaqus for the different notch geometries.

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Table 2. Parameters used for describing analytical stress field. Specimen geometry ρ [mm] 2α [°]

r 0 [mm]

λ 1

µ 1

Unnotched

30.31

0 0

15.16

0.500 0.500 0.545

-0.500 -0.500 -0.345

1.000 1.000 0.810

Semi-circular V-shaped notch

5.00 1.00

2.50 0.33

90

4. Results The analytical and numerical stress fields are shown along the notch bisector line in Fig. 4. The analytical stress field is fitted with the numerical one by the maximum stress. Based on the maximum stress obtained from the numerical solution, the elastic stress concentration factors k t were calculated for each geometry, shown in Table 3. The error between the numerical and analytical stress field in the center of the specimen were calculated for each geometry, 10.07% for the unnotched, 20.45% for the semi-circular and 22.89% for the v-shaped notch. The data obtained from fatigue testing of the three different geometries was normalized with the ultimate tensile strength and compared in Fig 5. Haibach confidence bands (at 50 %) were calculated in the software Faticaw. The fatigue notch factor, k f , was obtained considering the ratio between the unnotched fatigue strength and the notched fatigue strength at 2 × 10 6 , shown in Table 3. As expected the fatigue notch factor for the v-shaped notch was higher