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On the mechanisms of production of large irreversible strains in materials with elastic, viscous and plastic properties

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Abstract

A thermodynamically and geometrically consistent mathematical model of large strains of materials with elastic, viscous and plastic properties is proposed. The viscous properties of a material are considered to provide a creep process and, therefore, the slow growth of irreversible strains during unloading and the stage preceding plastic flow. Under the fast growth of irreversible strains under the conditions of plastic flow, the viscous properties emerge as a mechanism that resists to this flow. Thus, the accumulation of irreversible strains initially occurs in the creep process, then under the plastic flow condition and finally because of material creep (during unloading). The change in the mechanism of irreversible strain growth occurs on elastoplastic boundaries moving in the deformed material. This change is only possible under the conditions of the continuity of irreversible strains and their rates. This continuity requires the coordination in the definitions of irreversible strain rates in the dependence on stresses, i.e. in laws of creep and plasticity. The change in the production mechanisms of irreversible strains means a different setting of the sources in differential equations of change (transfer equations) for these strains. Thus, irreversible strains are not divided into creep and plastic ones. The hypothesis of the independence of thermodynamic potentials (internal energy, free energy) from irreversible strains is applied with the aim of most visibility of the model relations. Under the condition of the acceptance of this hypothesis, an analogue of the Murnaghan formula is obtained, i.e. the stresses are completely determined by the level and distribution of the reversible strains as in the classical elastoplasticity theory. The main statements of the proposed model are illustrated by a boundary value problem solved in the framework of the model. This problem is about the deformation of an elastoviscoplastic material placed in the gap between two rigid cylindrical surfaces under the rotation of one of them and the material slipping in the neighbourhood of the internal surface.

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Acknowledgements

The reported study was funded by Russian Foundation for Basic Research (RFBR) according to the research Projects Nos. 19-31-50001 and 18-01-00038.

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Authors and Affiliations

  1. Institute of Automation and Control Processes of FEB RAS, Radio St. 5, Vladivostok, Russia, 690041

    Alexandra S. Begun & Larisa V. Kovtanyuk

  2. Institute of Machinery and Metallurgy of FEB RAS, Metallurgov St. 1, Komsomolsk-na-Amure, Russia, 681005

    Anatoly A. Burenin & Alexander O. Lemza

  3. Far Eastern Federal University, Sukhanova St. 8, Vladivostok, Russia, 690950

    Alexander O. Lemza

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  1. Alexandra S. Begun
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  2. Anatoly A. Burenin
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  3. Larisa V. Kovtanyuk
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  4. Alexander O. Lemza
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Correspondence to Alexander O. Lemza.

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Begun, A.S., Burenin, A.A., Kovtanyuk, L.V. et al. On the mechanisms of production of large irreversible strains in materials with elastic, viscous and plastic properties. Arch Appl Mech 90, 829–845 (2020). https://doi.org/10.1007/s00419-019-01641-x

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