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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6. Conclusions A Bayesian methodology has been used to evaluate the uncertainty of fracture toughness measured with notched specimens in polyamide 12. The failure criterion has a significant impact on the proposed methodology. The epistemic errors can considerably increase the uncertainty of the fracture toughness value. The Bayesian methodology is a valuable decision-making tool for selecting local failure criteria in the study of notched fracture, with the proposed use of the WAIC value as a criterion selection method. In summary, the analysis of notches, particularly utilizing U-notch specimens, serves as a valuable tool for assessing structural integrity and optimizing designs. By employing Bayesian analysis, the proposed methodology provides a means to quantify uncertainties associated with fracture toughness evaluations, accounting for both experimental error and epistemic uncertainty. Acknowledgements The authors wish to express their gratitude to the European Union’s Horizon Europe research and innovation program for their financial support under the DIMAT project (No 101091496) and the EXPLOIT4INNOMAT project (101092339). References ASTM International, 2017. ASTM D6110-18 Standard Test Method for Determining the Charpy Impact Resistance of Notched Specimens of Plastics. West Conshohocken. Anderson, T.L., 2017. Fracture Mechanics: Fundamentals and Applications, Fourth Edition. doi: 10.1201/9781315370293. Crespo, M., Gómez-del Río, M.T., Rodríguez, J., 2017. Failure of SLS polyamide 12 notched samples at high loading rates. Theoretical and Applied Fracture Mechanics 92. doi: 10.1016/j.tafmec.2017.08.008. Crespo, M., Gómez-del Río, T., Rodríguez, J., 2019. Failure of polyamide 12 notched samples manufactured by selective laser sintering. Journal of Strain Analysis for Engineering Design 54(3). doi: 10.1177/0309324719847817. Seweryn, A., 1994. Brittle fracture criterion for structures with sharp notches. Engineering Fracture Mechanics 47(5). doi: 10.1016/0013 7944(94)90158-9. Taylor, D., Cornetti, P., Pugno, N., 2005. The fracture mechanics of finite crack extension. Engineering Fracture Mechanics 72(7), pp. 1021– 1038. doi: 10.1016/j.engfracmech.2004.07.001. Gómez, F.J., Guinea, G.V., Elices, M., 2006a. Failure criteria for linear elastic materials with U-notches. International Journal of Fracture 141(1– 2). doi: 10.1007/s10704-006-0066-7. Gómez, F.J., Elices, M., 2006b. Fracture loads for ceramic samples with rounded notches. Engineering Fracture Mechanics 73(7). doi: 10.1016/j.engfracmech.2005.11.005. Bazant, Z.P., Planas, J., 1998. Fracture and Size Effect in Concrete and Other Quasibrittle Structures. Elices, M., Guinea, G.V., Gómez, J., Planas, J., 2001. The cohesive zone model: advantages, limitations and challenges. Engineering Fracture Mechanics 69(2). doi: 10.1016/S0013-7944(01)00083-2. Lazzarin, P., Zambardi, R., 2001. A finite-volume-energy based approach to predict the static and fatigue behavior of components with sharp V shaped notches. International Journal of Fracture 112(3). doi: 10.1023/A:1013595930617. Berto, F., Lazzarin, P., 2014. Recent developments in brittle and quasi-brittle failure assessment of engineering materials by means of local approaches. Materials Science and Engineering R: Reports 75(1). doi: 10.1016/j.mser.2013.11.001. Leguillon, D., 2002. Strength or toughness? A criterion for crack onset at a notch. European Journal of Mechanics, A/Solids 21(1). doi: 10.1016/S0997-7538(01)01184-6. Gelman, A., Carlin, J.B.B., Stern, H.S.S., Rubin, D.B.B., 2014. Bayesian Data Analysis, Third Edition (Texts in Statistical Science). doi: 10.1007/s13398-014-0173-7.2. Creager, M., Paris, P.C., 1967. Elastic field equations for blunt cracks with reference to stress corrosion cracking. International Journal of Fracture Mechanics. doi: 10.1007/BF00182890. Neuber, H., 1958. Theory of Notch Stresses. Novozhilov, V.V., 1969. On a necessary and sufficient criterion for brittle strength. Prikladnaya Matematika i Mekhanika 33(2). doi: 10.1016/0021-8928(69)90025-2. Ritchie, R.O., Knott, J.F., Rice, J.R., 1973. On the relationship between critical tensile stress and fracture toughness in mild steel. Journal of the Mechanics and Physics of Solids 21(6), pp. 395–410. doi: 10.1016/0022-5096(73)90008-2. Watanabe, S., 2010. Asymptotic equivalence of Bayes cross validation and widely applicable information criterion in singular learning theory. Journal of Machine Learning Research 11.