PSI - Issue 23

Petr Kubík et al. / Procedia Structural Integrity 23 (2019) 15–20 Petr Kubík et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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Unfortunately, the force rapidly decreased in the case of dog-bone specimen beyond the ultimate tensile strength (Fig. 3). This was caused by wrong prediction of deformations in the necking zone (Fig. 4). The equivalent plastic strain was also localized in that part and its magnitude was more than threefold, when compared to von Mises model of plasticity, which predicted the necking with correspondence with experiment. There was no such misconduct in the case of the flat grooved specimen. Wrong predictions of deformations and stress states of yield criteria depending on the third invariant of deviatoric stress tensor might be fou nd in other works as well (Kroon and Faleskog, 2013; Šebek et al., 2017; Kubík et al., 2018). The prediction of correct stress state is crucial especially when the ductile fracture criteria are calibrated. The contribution presented the validation of two yield criteria. The widespread von Mises yield criterion was compared with the one proposed by Kroon and Faleskog (2013). Two tensile tests of dog-bone and flat grooved specimen were analyzed. Plasticity model according to von Mises predicted correctly the deformations of both specimens and correct force response of the dog-bone specimen, while false response for the flat grooved specimen. It was in contrast with the Kroon – Faleskog plasticity model, which predicted a correct force response for the flat grooved specimen and a wrong one for the dog-bone specimen, which was caused by false prediction of deformations. This is a problem accompanied with wrong predictions of stress states under plane strain condition. Then, the non quadratic plasticity model tends to predict the stress state close to uniaxial tension instead of generalized shear. This is one of the reasons for studying the capabilities of non-associated plasticity models. Acknowledgements This work was supported by the Czech Science Foundation under contract No. 19- 20802S “A coupled real -time thermo- mechanical solidification model of steel for crack prediction.” The authors would also like to thank Mr . Ondřej Kalivoda for the design and execution of experiments in Siemens. Bai, Y., Wierzbicki, T., 2008. A new model of metal plasticity and fracture with pressure and Lode dependence. International Journal of Plasticity 24(6), 1071–1096. Coulomb, C.A., 1776. Essai sur une application des règles de maximis & minimis à quelquels problèmes de statique, relatifs à l’architecture. Mémoires présentés à l’Académie des Sciences, 343–384 (in French). Drucker, D.C., Prager, W., 1952. Soil mechanics and plastic analysis or limit design. Quarterly Journal of Mechanics &Applied Mathematics X(2), 157–165. Hershey, A.V., 1954. The plasticity of an isotropic aggregate of anisotropic face-centered cubic crystals. Journal of Applied Mechanics 53–A-63, 241–249. Hosford, W.F., 1972. A generalized isotropic yield criterion. Journal of Applied Mechanics 39(2), 607–609. Kroon, M., Faleskog, J., 2013. Numerical implementation of a J 2 - and J 3 -dependent plasticity model based on a spectral decomposition of the stress deviator. Computational Mechanics 52(5), 1059–1070. Kubík, P., Šebek, F., Petruška, J., 2018. Notched specimen under compression for ductile failure criteria. Mechanics of Materials 125, 94–109. Mises, von R., 1913. Mechanik der festen Körpern im plastisch-deformablen Zustand. Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-physikalische Klasse, 582–592 (in German). Mohr, O., 1900. Welche Umstände bedingen die Elastizitätsgrenze und den Bruch eines Materiales? Zeitschrift des Vereins deutscher Ingenieure 45, 1524–1530 (in German). Petruška, J., Kubík, P., Hůlka, J., Šebek, F., 2013. Ductile fracture criteria in prediction of chevron cracks. Advanced Materials Research 716, 653– 658. Šebek, F., Kubík, P., Petruška, J., 2018. Application of coupled ductile fracture criterion to plane strain plates. Defect and Diffusion Forum 382, 186–190. Šebek, F., Petruška, J., Kubík, P., 2017. Behavior of Lode dependent plasticity at plane strain condition and its implication to ductile fracture. Solid State Phenomena 258, 213–216. Španiel , M., Mareš, T., Kuželka, J., Šebek, F., Džugan, J., 2017. Uncoupled material model of ductile fracture with directional plas ticity. In: Proceedings of the 14th International Conference on Computational Plasticity, 596–605. Tresca, M. H., 1864. Mémoire sur l’écoulement des corps solides soumis à de fortes pressions. Compte Rendu des Séances de l’Académie des Sciences, 754–758 (in French). 6. Summary References