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

737

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• TCD-1: Mean stress criterion (Neuber 1958 and Novozhilov 1969) $% = "% 01+ ' * + ( !" ,

(3)

where

,- =3 . #$ / ! 4 )

(4)

• TCD-2: Maximum stress criterion (Ritchie at al 1973) $% = "% 01+ ' * + ( !" − *((+123')'( !" 2)'() %

(5)

• CSED: Mean strain energy density criterion (Lazzarin and Zambardi 2001, Berto and Lazzarin 2014) $% = "% 01+ ' * + ( !" − *5+ !" *65'+5(2)( !"

(6)

• FFM: Finite fracture mechanics (Leguillon 2002) $% = "% 61+ ' * + ( !" + %. & % . & ( %

676 ) &+ ! * " 28 ) &+ ! * " 279 %.%, * & + !" +:;72 %.%, * & + !" < 76 %.%, * & + !" +:;72 %.%, * & + !" <

(7)

• CSZ-L: Cohesive Zone Model with linear softening curve (Gómez et al, 2006b) $% = "% 71+ ' * + ( !" + 6=.?@3A* + * !" 6).7B138 + * !" 9 % 27@.1=78 + * !" 9 . 6*3.7B?8 + * !" 9 & 7277?.A78 + * !" 9 &

(8)

• Phen: Phenomenological formulation (Gómez and Elices 2006a) . /$ . #$ =0 72=.*?A@)(( + !" ⁄ )2).7A3)(( + !" ⁄ ) % 2'/*(( + !" ⁄ ) . 72(( + !" ⁄ ) %

(9)

When applying failure criteria to notches, a pivotal aspect lies in the process of ascertaining the criteria's parameters. Within this study, all criteria analyzed have two material parameters and use a similar methodology, the experimental tests used are the crack case and the smooth specimen. 4. Bayesian analysis Bayesian inference is a powerful statistical framework that allows for the incorporation of prior knowledge and updating uncertainties based on observed data (Gelman et al 2014). By using Bayes' theorem, Bayesian inference enables the estimation of uncertain parameters in a coherent manner. The Bayes theorem gives this posterior probability of the parameters as a function of the prior probability, the likelihood and the marginal likelihood: ( "% , , | ) = #E F "% , , G#(. #$ ,/ ! ) #(IJKJ) (10)