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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As the parameters K IC and s c do not influence the denominator and the final output is normalized, only two terms have been considered in calculations: ( "% , , | ) ∝ ( | "% , , ) ( "% , , ) (11) The experimental data are the critical notch stress intensity factors depending on the notch radius. < "% , , = $% ( )> ∝ ( $% | , "% , , ) ( "% , , ) (12) The statistical distribution of the critical notch stress intensity factors is modelled as normally distributed with equal variance. The mean value depends on the notch tip radius following the failure criteria proposed. ( $% | , "% , , ) ∼ ( , ) (13) = "% D (. ( #$ / ! ⁄ ) % E The prior distributions studied are non-informative ones. PyMC3 python library has been used to build and fit the model. The posterior distributions have been calculated numerically following a NUTS (No U-Turn Sampler) algorithm sampling (Gelman et al 2014) with 2000 iterations and 3 chains. 5. Results 5.1. TCD maximum stress.

Table 1. Initial prior distributions. Orientation 0 Orientation 90 !" ∼ (1 − 5) (MPam 0.5 ) !" ∼ (0.1 − 3) (MPam 0.5 ) # ∼ (1 − 150) (MPa) # ∼ (1 − 150) (MPa) ∈∼ (1,1) ∈∼ (1,1) b)

a)

Fig. 2. Posterior distributions of the fracture toughness of polyamide12 calculated with the maximum stress criteria a) with orientation 0 and b) with orientation 90.

Following the initial work (Crespo et al 2017, 2019) the theory of local distance with a maximum stress criterion has been selected. The posterior distribution has been calculated with expression (5) using the prior non-informative distributions of Table 1. The posterior distributions are shown in Figure 2. The pink area corresponds to a 99% probability interval. Fig 2 displays a mean fracture toughness centred and relatively small uncertainty.