PSI - Issue 79

Andrea Avanzini et al. / Procedia Structural Integrity 79 (2026) 88–96

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Table 1. Fatigue stress limit estimation using different thermal or energy parameters (average values among different fitting algorithms) Initial slope (dT/dt) Steady temp.  T steady Q parameter Heat Treatment Mean ± Dev [MPa] Mean ± Dev [MPa] Mean ± Dev [MPa] AN 365 ± 4.36 353 ± 1.15 350 ± 1.15 SA 440 ± 26.63 418 ± 7.21 428 ± 20.31 SR 374 ± 37.11 366 ± 18.18 299 ± 25.40 DA 292 ± N/A 287 ± N/A 268 ± N/A The second type of analysis involves examining the results obtained through the mean values of the parameters, using different fitting methods, as shown in Tab.2. A comparative example is shown in Fig. 4 for SR and AN respectively considering the initial slope dT/dt. Specifically, in this work three different fitting methods were employed to estimate the fatigue limit, the OCM and the TCM, iterative or with total error minimization. These methods were applied to the initial slope, steady temperature and Q parameters.

Table 2. Fatigue stress limit estimation using different fitting algorithms OCM TCM (iterative)

TCM (min error) Mean ± Dev [MPa]

Heat Treatment

Mean ± Dev [MPa]

Mean ± Dev [MPa]

AN SA SR DA

356 ± 9.64 420 ± 11.59 333 ± 55.81 282 ± 12.56

355 ± 4.58 417 ± 1.00 336 ± 23.03

358 ± 9.07 449 ± 21.59 370 ± 49.56

N / A

N / A

The results show how the various methods, despite the different approaches and quantities measured, provide a consistently similar prediction, which seems relatively independent of the fitting approach. Based on the comparison of the fitting methods and the related graphs reported in Fig. 4, it is clear that all fitting methods use a linear approximation of the dataset. This is a good approximation when considering datasets for materials with high ductility, such as AN specimens and SA, where the obtained data was almost bilinear.

Fig. 4. Comparative example of fatigue limit estimation from thermographic measurement fitted with different strategies (AN and SR cases).