PSI - Issue 75

Tomáš Karas et al. / Procedia Structural Integrity 75 (2025) 150–157 T. Karas et al. / Structural Integrity Procedia 00 (2025) 000–000

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pad r = 1 mm and 9.36 kN for pad r = 50 mm) and remained constant across all tested stress levels. Once this is finished, the proving ring is tilted in order to ensure that the field of vision of the thermal camera is not obscured. The final part of the set-up is mounting a reference sample for temperature di ff erential measurement. Finally, the samples were loaded by axial force oscillating at a frequency of approximately 125 Hz with the intention of reaching either a run-out condition at N = 10 7 cycles or a frequency drop of 5 Hz, at which point the sample was considered cracked and the test was terminated. The temperature evolution on the surface of the sample and the fretting pads was monitored throughout each fretting fatigue test to obtain the stabilised temperature for the given configuration. This was done using an Optris PI450i thermal imaging camera, which has a thermal resolution of 40 mK and 382x288 pixels of optical resolution. An output of the data acquisition software in conjunction with the thermal camera view is shown in Fig. 2. (b), with highlighted areas of interest. Specifically, analysis of Area 7 provides T 7 temperature of the sample, while T 4 refers to the temperature in the Area 4 related to the temperature of the reference sample. As mentioned in Section 1., the self-heating method aims to derive the fatigue limit estimate from the reduced number of samples. This is mainly possible due to the nature of the monitored parameter Θ , which is a stabilised temperature increase obtained once the di ff erence between T 7 and T 4 stabilises. Since the sample stabilised temperature at the selected load level usually occurs after a relatively low number of cycles, the test does not have to be carried out to failure, and the same sample can be reused several times to obtain a set of stabilised temperatures for a range of loads. This is a fundamental principle of a so-called step-test procedure. This allows for the estimation of the fatigue limit from as few as one or two samples. Thermal measurement was carried out during both conventional fretting fatigue tests and self-heating tests. However, the fatigue limit estimation was based mainly on self-heating test data. The thermal measurement from conventional fretting fatigue tests was used to observe the temperature stabilisation process for a given material, which first determines whether stabilisation occurs and secondly helps designing a step-test procedure. In addition, these results can be included as extra data points for the fatigue limit estimate. The key di ff erences between the Luong (1998), La Rosa and Risitano (2000) and Matusˇu˚ et al. (2024) approaches can be seen in Fig. 3., where each method interpolates the S-H curve in a di ff erent way. Luong (1998) utilises a bilinear regression, where the elastic part / primary regime below the FL and the plastic part / secondary regime above the FL are separated. The fatigue limit is then estimated as the intersection of the primary and secondary regimes. La Rosa and Risitano (2000) also use a linear regression, but assumes that the stabilised temperature increase Θ is close to zero for amplitudes below the FL. Therefore, only the secondary regime is evaluated and the FL is estimated for Θ= 0. A completely di ff erent approach proposed by Matusˇu˚ et al. (2024) can be seen in Fig. 3. (c), where all measured data points are interpolated by one curve. An iterative process is used to construct linear and exponential parts, which, when combined, produce the best fit to the measured data, the LinExp curve. The method then searches for σ a with a maximumof ∆Θ , the maximum di ff erence between the elastic and plastic parts (curves) of the stabilised temperature increase. 2.4. Self-Heating Method

(b)

(a)

(c) Fig. 3. (a) Luong (1998); (b) La Rosa and Risitano (2000); (c) Matusˇu˚ et al. (2024).