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 ^∗∗∗

Perm National Research Polytechnic University, Perm, 614990 Russia

E-mail: ^∗kurmoiartseva.k@mail.ru, ^∗∗kotelnickova@gmail.com, ^∗∗∗crocinc@mail.ru

Received November 30, 2020

ORIGINAL ARTICLE

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DOI: 10.26907/2541-7746.2021.2.197-213

For citation: Kurmoiartseva K.A., Kotelnikova N.V., Volegov P.S. Structure and relations of a multi-level mathematical model for describing microcracks formation during polycrystals deformation. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2021, vol. 163, no. 2, pp. 197–213. doi: 10.26907/2541-7746.2021.2.197-213. (In Russian)

Abstract

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.

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

Acknowledgments. The study was supported by the Russian Science Foundation (project no. 17-19-01292).

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