PSI - Issue 43

Kamila Kozáková et al. / Procedia Structural Integrity 43 (2023) 178–183 Kamila Koza´kova´ / Structural Integrity Procedia 00 (2023) 000–000

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2.2. Determination of the length parameter

To determine the length parameter l , it is necessary to know the Wo¨hler curve of smooth specimens and a repre sentative curve of notched specimens. A curve with notch radius r = 0 . 2 mm was chosen as the representative of the notched specimens because this approximation has the smallest value of a sum of squared errors. The length parameter l was calculated from these two curves (smooth and notched) and the corresponding distribution of the axial stress of the notched specimen ( r = 0 . 2 mm). The remaining experimental fatigue data were used for the verification of fatigue lifetime predictions. The principle of the method is based on the equality of stress ratios (see Eq. 1 below and Fig. 5). Stresses on the left hand side of the equation, σ n a and σ s a represent the fracture stresses of notched and smooth specimens for a specific but equal number of cycles to fracture. These stresses are determined from Wo¨hler curves. The principle of the prediction method is to find the distance l from the notch tip for which the ratio of the stresses σ n a and σ s a is equal to the ratio of stresses σ y , nom , and σ y ( l ) (Eq. 1). These stresses can be found in the stress distribution of the notched specimen (eq. 2, eq. 3 and Fig. 5). Stress σ y , nom represents the average stress over the cross-section of the notched specimen. Stress σ y ( l ) is firstly obtained from the formula 1 and it represents an average stress over the distance l . Finally, the length parameter is determined from the stress distribution, so that eq. 3 applies. This calculation is repeated for di ff erent numbers of cycles to failure. σ n a σ s a = σ y , nom σ y ( l ) (1)

1 R

R 0 σ y dx

(2)

σ y , nom =

1 l

l 0 σ y dx

(3)

σ y ( l ) =

smooth

notched

Fig. 5. Prediction method: Wo¨hler curves and axial stress distribution

2.3. The length parameter and fatigue lifetime predictions of notched specimens

The output of previous calculations is the dependence of the distance l on the number of cycles to fracture (see Fig. 6). The distance, calculated from the fatigue lifetime curve of notched specimens with a notch radius of 0 . 2 mm, can be used to predict the Wo¨hler curves of other specimens with di ff erent notch radii. The fracture stresses of the specimens with di ff erent notch radii were calculated inversely. The length parameter was applied to various axial stress distributions of di ff erent notches (calculated numerically) and their Wo¨hler curves were obtained. These Wo¨hler curves represent fatigue lifetime predictions (see Fig. 7). To assess the safety of this prediction method, the prediction data are compared to the experimental approximations.

3. Discussion and SEM observation

Fatigue lifetime prediction of notched specimens with radius r = 0 . 1 mm is very similar to the approximation of experimental data (see Fig. 7). The predicted lifetime curves of notched specimens with radii r = 0 . 8 mm and r =