PSI - Issue 79

João Alves et al. / Procedia Structural Integrity 79 (2026) 326–334

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nanotomography. As expected, both algorithms converged for similar values, and a significant improvement of the R 2 , was achieved, of 0.993. As can be seen in Table 1.

Table 1. Results for both different algorithms and different admissible areas of defects.

Algorithm Initial defect (µm) Final defect (µm)Optimal ( C,m )

Iteration number

Nelder-Mead 122.64

1000 1000 2000 2000

[6.157x10 -5 ,1.805] 49 [6.151x10 -5 ,1.807] 30 [7.104x10 -5 ,1.806] 55

SLSQP

122.64

Nelder-Mead 122.64

SLSQP [7.100x10 -5 ,1.806] 33 From the obtained optimal C and m , it was perceived that m didn’t change independently of the final defect assumed, since the slope of the curve is independent of the assumed final defect. Therefore, only C was changed to transpose the fatigue curves, to the defined final defect condition (a f = 1000 µm and a f = 2000 µm). The obtained final curves for both algorithms and assumed final defects are represented in Fig. 3. 122.64

Fig. 3. Comparison between the proposed models and the Experimental equation

Although both proposed models converged to the same output, as expected from the optimisation algorithm with a proper setup. It was compared how they would perform by changing from the two developed models, the final area of defect for which both models were optimised. Therefore, in Fig. 4 it was plotted the following curves: the model when C = 7.104x10 -5 and m=1.806, but now considering a f =1000 µm, the model when C = 7.104x10 -5 and m=1.806, but considering a f =2000 µm, to be used as a reference and when C = 6.154x10 -5 and m=1.805, however, now considering a f =2000 µm.

Fig. 4. Comparison between the proposed models and the Experimental equation