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Identification of Initial Critical Resolved Shear Stresses Using of a Two-Level Model of Inelastic Deformation

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Abstract

The problem of identifying the initial critical resolved shear stresses (CRSS) of slip systems is considered in the framework of a two-level statistical model of inelastic deformation. We propose a three-stage method for determining critical stresses. The problem is solved on the basis of an experimental data set that includes the ‘‘\({{{\sigma}}}-{{{\varepsilon}}}\)’’ diagrams for a polycrystal (subjected to uniaxial loading at different temperatures) and the anisotropic elastic moduli of single crystals. Analysis of the experimental loading diagrams makes it possible to determine the yield strength at the macrolevel. Using the two-level model, an optimization problem is formulated to determine the CRSS values corresponding to the experimentally established yield strength of a polycrystalline macrosample at a fixed temperature. The obtained CRSS are approximated by an exponential temperature dependence; there is good agreement between this approximation and the considered critical stresses. The problem parameters are determined for a copper polycrystal. The obtained results can be used to investigate inelastic deformation by means of multilevel models, in which the activation of slip systems is determined by the the Schmid law.

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Funding

The study was carried out with a financial support from the Ministry of Education and Science of the Russian Federation as part of the implementation of the national project ‘‘Science and Universities’’ (the state task fulfillment in the laboratory of multilevel structural and functional materials modeling, project no. FSNM-2021-0012).

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Authors and Affiliations

  1. Laboratory of Multilevel Structural and Functional Materials Modeling, Perm National Research Polytechnic University, 614990, Perm, Russia

    N. S. Kondratev & D. S. Bezverkhy

  2. Department of Mathematical Modeling of Systems and Processes, Perm National Research Polytechnic University, 614990, Perm, Russia

    P. V. Trusov

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  1. N. S. Kondratev
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  2. P. V. Trusov
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  3. D. S. Bezverkhy
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Correspondence to N. S. Kondratev, P. V. Trusov or D. S. Bezverkhy.

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(Submitted by A. M. Elizarov)

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Kondratev, N.S., Trusov, P.V. & Bezverkhy, D.S. Identification of Initial Critical Resolved Shear Stresses Using of a Two-Level Model of Inelastic Deformation. Lobachevskii J Math 44, 2306–2316 (2023). https://doi.org/10.1134/S1995080223060240

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