PSI - Issue 79

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

333

The results showed a small reduction in the accuracy when changing the considered admissible defect. Although a slightly better performance was seen for the model of C = 7.104x10 -5 and m=1.806, when considering the a f = 1000 µm. Furthermore, the last-mentioned model revealed to be more conservative, indicating that the higher the C , will lead to more conservative predictions, positioning the curve under most of the experimental points Concerning the optimisation algorithms, as was seen in a previous work (Alves et al., 2025), the fastest to converge was the SLSQP. Fig. 5 shows the optimisation process and the convergence of the values. It is noticeable a typical up and down in each iteration, linked to the movements of reflection, expansion, and contraction that the simplex uses to optimise the solution. This typical behaviour of algorithms with the absence of gradient, using instead the simplex, led to an increased number of iterations, especially noticeable when compared to the results obtained by SLSQP. However, as can be seen in Fig. 5, the relatively fast convergence of the SLSQP, enhanced by the information regarding the derivatives of the cost function (gradient), came with the cost of less smooth convergence, where C and m values drifted away from the optimal solution, indicating a typically flat region or non-convex landscape. For both a f =1000 µm and a f =2000 µm, the convergence process was similar for the two used algorithms, although the SLSQP revealed higher peaks while converging for an admissible defect of 1000 µm.

Fig. 5. Optimisation process: a) For a f =1000 µm; b) a f =2000 µm

6. Conclusion A new methodology is proposed to predict of a Ti-6Al-4V alloy manufactured by SLM. The proposed S-N curves consider the intrinsic manufacturing defects obtained by nanotomography. It was concluded from the results analysis that the models properly fit the data (R 2 = 99.3%), with an equal accuracy of the Basquin equation (R 2 = 99.3%), possibly presenting a higher generalisation capacity than the model proposed by Basquin, although further research is needed to draw such a conclusion. Regarding the proposed methodology, after optimisation, there is no significant difference between models, appearing 2 different sets of constants from the present work: C= 6.157x10 -5 and m=1.806 and C= 7.104x10 -5 and m=1.806 Furthermore, it was concluded that for the model where C= 7.104x10 -5 and m=1.806, assuming a final allowable defect of 1000 µm, showed to be the most conservative and therefore, for real-world applications, the preferable, since a slight decrease in R 2 , it is advantageous to improve the overall design safety. Concerning the optimisation algorithms, for the proposed application, it was concluded that the most suitable is the Nelder-Mead, since although it takes more iterations to converge, the computation power is not demanding, and therefore, the Nelder-Mead was found to be the easiest to set up, due to the possible flat region or non-convex landscape. This is typically harder for the SLSQP to optimise, and the possible reason behind the difficulty of setting the initial conditions of optimisation for the last-mentioned algorithm. In conclusion, the proposed framework reveals an alternative path to the development of new models that better fit the fatigue data by considering the existence of intrinsic manufacturing defects, gathered through nanotomography. This proposal suggests an approach to access a deeper understanding of the quality of the manufactured parts, defining more precisely the limits of acceptance while using the most advanced techniques of defect analysis.