PSI - Issue 17

Jürgen Bär et al. / Procedia Structural Integrity 17 (2019) 300–307 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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2.2. Evaluation of the Fatigue tests

For a mathematical description of a part or the complete S-N-curve several functions can be used. An overview about common functions is given by Kohout and Vĕchet (2001). For a description of the complete S-N-curve the function (1) suggested by Gecks and Och (1977) can be used. Besides the Ultimate tensile strength  UTS and the fatigue limit  FL two parameters  and  are used to fit this function on the determined cyclic lifetimes: = + − ( ) (1) To describe the scatter of the measured cyclic lifetimes lines for a failure probability of 10% and 90% are calculated. Therefore, the deviation between the experimental lifetimes and the fitted curve is calculated using equation (2): = − (2) With the deviation r i virtual data x i can be calculated for a given stress  i using equation (3). = ∙ (1 + ) (3) This corresponds to the shift of a data point with the adapted function (1) to a given cyclic lifetime. Assuming a normal distribution, the mean value ̅ and the standard deviation s for all x i can be obtained. With this values and a statistical factor ′ depending on the number of data points and a given confidence level, an upper and lower tolerance limit T 10% and T 90% for a failure probability of 10 % and 90 % can be calculated with equation (4): 10%/90% = ̅ ± ′ ∙ (4) With this tolerance limits and the mean value the factors k 10% and k 90% are calculated: 10%/90% = 10%/90% ̅ (5) These factors allow a shift of the S-N-curve to higher and lower stresses to get the curves for the given failure probabilities according to equation (6): 10%/90% = 10%/90% ∙ ( + − ( ) ) (6) 3. Results

3.1. Fatigue Tests

The results of the fatigue tests were evaluated according to the procedure described in chapter 2.2. The results of the evaluation with all valid experiments are given in table 1. Invalid experiments are run out specimen loaded again on a higher loading level resulting in cyclic lifetimes shorter than expected as well as a run out specimen tested at a too low loading level.