PSI - Issue 68

F.J. Gómez et al. / Procedia Structural Integrity 68 (2025) 734–740 F.J. Gómez, T. Gómez-del-Rio, J. Rodríguez/ Structural Integrity Procedia 00 (2025) 000–000

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5.2. Influence of the failure criteria The measurement procedure is based on the assumption of a fracture criterion. The posterior distributions can be calculated with the six failure criteria proposed on section 3. a) b)

Fig. 3. Posterior distributions of the fracture toughness of polyamide12 calculated with six different failure criteria, a) with orientation 0 and b) with orientation 90. Figure 3 depicts the posterior distribution of fracture toughness calculated using the six failure criteria under study. Epistemic uncertainty significantly increases the total uncertainty. With the data obtained from orientation 0, the relative error is approximately 10%, indicating that the procedure could be useful. However, with the data obtained from orientation 90, the relative error is too high, near 50%. 5.3. Failure criteria selection. The epistemic uncertainty estimated at the previous subsection can be reduced or eliminated selecting the failure criteria that better fit the experimental results. The Watanabe-Akaike information criterion (WAIC) (Watanabe 2010) is a commonly used method for Bayesian Model Selection. = −2 ( − LM"% ) (14) = ∑ 3 7 ) < ( $% | "% ) + ( $% | )>4 : NO7 LM"% = < ( $% | "% )>+ < ( $% | )> Table 2. WAIC value in polyamide12. Criterion Orientation 0 Orientation 90 TCD-1 43.73 -27.50 TCD-2 62.08 -27.59 CSED 45.52 -27.50 FFM 64.59 -27.43 CZM-L 55.30 -27.31 Phen 56.71 -28.78 WAIC can be used to compare models with different numbers of parameters and provide a measure of their relative goodness of fit. WAIC can be formulated as expression (15). Calculating WAIC in the four failure criteria studied the next table is obtained. Lower WAIC values indicate better model fit and are preferred for model selection. The models that better fit the experimental results in polyamide12 with orientation 0 are the theory of critical distance with the maximum stress failure criteria and the mean strain energy density. Both criteria have a similar WAIC value significantly lower than the other four. There is no criterion that better fit with orientation 90.