Structure and relations of a multi-level mathematical model for describing microcracks formation during polycrystals deformation

K. A. Kurmoiartseva   ; N. V. Kotelnikova   ; P. S. Volegov

Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 163 (2021) no. 2, pp. 197-213

Résumé

The mechanical behavior of parts is significantly affected by the material's internal defective structure and its evolution. The paper aims to build a complex physically based mathematical model for describing the behavior of metals in the deformation and destruction process. The main deformation mechanisms of metals and alloys are considered. The mechanism and criterion for the microcrack nucleation, as well as a method for microcracks describing, are outlined. The structure and main relations of the developed model are presented, including a description of the most significant mechanisms carriers evolution implemented at each structural-scale level. A submodel of the evolution of dislocation densities during deformation due to such mechanisms as the new dislocations generation and opposite dislocations annihilation on close slipping systems is described. The algorithm for implementing the model and the results of modeling the dislocation structure evolution are presented. The multi-level approach based on the crystal plasticity and the introduction of internal variables is found to be sufficiently effective for describing both the propagation and nucleation of microcracks in metals.

Détail

Keywords: mathematical modeling, physical plasticity theories, crystal plasticity, deformation of polycrystalline materials, dislocation densities, microcrack nucleation, damage.

Bibliographie

[1] Griffith A. A., “The phenomena of rupture and flow in solids”, Philos. Trans. R. Soc., A, 221:582–593 (1921), 163–198 | DOI | Zbl

[2] Orowan E., “Energy criteria of fracture”, Welding J. Res. Suppl., 34:3 (1955), 157–160

[3] Irwin G. R., “Analysis of stresses and strain near the end of crack traversing a plate”, J. Appl. Mech., 24:3 (1957), 361–364 | DOI

[4] Parton V. Z., Morozov E. M., Mechanics of Elastoplastic Fracture, Nauka, M., 1985, 502 pp. (In Russian)

[5] Pestrikov V. M., Morozov E. M., Fracture Mechanics. A Course of Lectures, TsOP “Professiya”, St. Petersburg, 2012, 552 pp. (In Russian)

[6] Taheri S., Vincent L., Le-Roux J.-C., “Classification of metallic alloys for fatigue damage accumulation: A conservative model under strain control for 304 stainless steels”, Int. J. Fatigue, 70 (2015), 73–84 | DOI

[7] Li L., Flores-Johnson E.A, Shen L., Proust G., “Effects of heat treatment and strain rate on the microstructure and mechanical properties of 6061 Al alloy”, Int. J. Damage Mech., 25:1 (2015), 26–41 | DOI

[8] Cao T. S., Vachey C., Montmitonnet P., Bouchard P.-O., “Comparison of reduction ability between multi-stage cold drawing and rolling of stainless steel wire – Experimental and numerical investigations of damage”, J. Mater. Process. Technol., 217 (2015), 30–47 | DOI

[9] Brünig M., Gerke S., Schmidt M., “Damage and failure at negative stress triaxialities: Experiments, modeling and numerical simulations”, Int. J. Plast., 102 (2018), 70–82 | DOI

[10] Tang X. S., Wei T. T., “Microscopic inhomogeneity coupled with macroscopic homogeneity: A localized zone of energy density for fatigue crack growth”, Int. J. Fatigue, 70 (2015), 270–277 | DOI

[11] Volegov P. S., Gribov D. S., Trusov P. V., “Damage and fracture: Review of experimental studies”, Phys. Mesomech., 19:3 (2016), 319–331 | DOI

[12] Kachanov L. M., Fundamentals of Fracture Mechanics, Nauka, M., 1974, 312 pp. (In Russian)

[13] Rabotnov Yu.N., Introduction to Fracture Mechanics, Nauka, M., 1987, 388 pp. (In Russian)

[14] Walton C. A., Horstemeyer M. F., Martin H. J., Francis D. K., “Formulation of a macroscale corrosion damage internal state variable model”, Int. J. Solids Struct., 51 (2014), 1235–1245 | DOI

[15] Martínez-Pañeda E., Betegón C., “Modeling damage and fracture within strain-gradient plasticity”, Int. J. Solids Struct., 59 (2015), 208–215 | DOI

[16] Martínez-Pañeda E., Niordson C., “On fracture in finite strain gradient plasticity”, Int. J. Plast., 80 (2016), 154–167 | DOI

[17] Aslan O., Forest S., “Crack growth modelling in single crystals based on higher order continua”, Comput. Materials Sci., 45 (2009), 756–761 | DOI

[18] Lemaitre J., “A continuous damage mechanics model for ductile fracture”, J. Eng. Mater. Technol., 77 (1985), 335–344 | DOI

[19] Horstemeyer M. F., Bammann D. J., “Historical review of internal state variable theory for inelasticity”, Int. J. Plast., 26:9 (2010), 1310–1334 | DOI | Zbl

[20] Maugin G. A., “The saga of internal variables of state in continuum thermo-mechanics (1893–2013)”, Mech. Res. Commun., 69 (2015), 79–86 | DOI

[21] Volegov P. S., Gribov D. S., Trusov P. V., “Damage and fracture: Crystal plasticity models”, Phys. Mesomech., 20:2 (2017), 174–184 | DOI

[22] Trusov P. V., Shveikin A. I., Multilevel Models of Mono- and Polycrystalline Materials: Theory, Algorithms, Examples of Application, Izd. Sib. Otd. Ross. Akad. Nauk, Novosibirsk, 2019, 605 pp. (In Russian) | DOI

[23] Hirth J. P., Lothe J., Theory of Dislocations, Atomizdat, M., 1972, 600 pp. (In Russian)

[24] Vladimirov V. I., The Physical Nature of Metals Fracture, Metallurgiya, M., 1984, 280 pp. (In Russian)

[25] Pozdeev A. A., Trusov P. V., Nyashin Yu.I., Large Elastoplastic Deformations: Theory, Algorithms, Applications, Nauka, M., 1986, 232 pp. (In Russian)

[26] Ivanova V. S., Gordienko L. K., Geminov V. N., The Role of Dislocations in the Hardening and Fracture of Metals, Nauka, M., 1965, 180 pp. (In Russian)

[27] Finkel' V.M., Physics of Fracture, Metallurgiya, M., 1970, 375 pp. (In Russian)

[28] Stroh A. N., “The formation of cracks as a result of plastic flow”, Proc. R. Soc. London, Ser. A, 223 (1954), 404–414 | DOI | Zbl