PSI - Issue 53

Martin Matušů et al. / Procedia Structural Integrity 53 (2024) 29 – 36 Author name / Structural Integrity Procedia 00 (2019) 000–000

34 6

Fig. 5. The SH tests result for four different HTs. A close-up of the region between 30-90 MPa was taken to observe the transition from the region under the fatigue limit with points. The lines between points are there only to emphasize the trends, they do not represent any function. 3. S-N curve life prediction Based on the assumption presented by [6; 7; 8], the area below the temperature evolution curve (Fig. 4) can be used to define a parameter known as limiting energy Φ . This parameter is considered constant independent of the load amplitude. As long as the testing conditions remain identical (including the material, stress ratio, frequency, etc.), this assumption can be used for further analyses. The limiting energy is calculated as follows: ߔ ൌ׬ܶ ሺܰ ሻ ܰ݀ڄ ே ೑ ଴ (3) Here, N f is the number of cycles to failure, and T ( N ) is temperature during cyclic loading. Temperature can be modeled as a function of the number of cycles. In most cases, it can be assumed that the specimen will remain in the second phase of the temperature evolution for most of its life. Therefore, Eq. (3) can be simplified to: , . f N const   (4) There are two approaches to determining the limiting energy. The first one sets this value based on a specimen tested at a single stress amplitude until failure. The second approach involves summing the partial areas obtained from an SH test conducted with varying stress amplitudes. Relying solely on results from a single specimen can be deceptive as it neglects the statistical distribution of fatigue damage. To account for this, the S-N curve was established using at least 10 specimens in the experiments referenced in this paper. Additionally, more than three of these specimens were used to determine the limiting energy value, with up to 9 samples being used in some cases. Eq. (4) of Fargione's theory has another intriguing application. It allows for the experimental determination of the S-N curve using just two test specimens. One specimen is used to determine the limiting energy value, while the other is monitored during the SH test. By recording the temperature during each level of the step test and knowing the limiting energy, it is possible to estimate the S-N curve at different evaluated stress levels. Table 3 reports on retrieved limiting energy values. As seen in the last row, the averaged limiting energy values for series 41, 42, and 44 are consistent. For series 43 however, the value from constant amplitude test is nearly double of the averaged value from the SH test. Due to this fact, the S-N curve estimates will be greatly influenced by the selection of the source for evaluating the limiting energy value. The parameter of limiting energy is further investigated in other publications [5; 8; 9], where it is evaluated as a non-constant parameter. To assess the fit quality, R 2 coefficient of determination was employed. The overall results of S-N curve estimates in Figs. 6 and 7 demonstrate that the difference of limiting energy input is insignificant for series 41, 42, and 44. For series 43, the results are considerably different (Fig. 7), where the input from SH test yields a better fit.