Creep and plastic flow of a spherical viscoelastic layer material at its loading and unloading

K. N. Galimzyanova ; L. V. Kovtanyuk ; G. L. Panchenko

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 23 (2019) no. 2, pp. 270-283.

Résumé

The purpose of the research is to investigate the processes of accumulation of irreversible deformations through different mechanisms: creep and plastic flow. Initially irreversible deformations are produced due to the viscous properties of solid material as creep deformations. The mechanism of the production of irreversible deformations changes to plastic when stress state reach the yield surface. On the contrary, this mechanism changes from fast plastic to slow viscous during unloading. The continuity in such increase in irreversible deformations is provided by the corresponding set of creep and plasticity potentials. These processes are considered in the framework of the mathematical theory of small deformations on the example of a one-dimensional problem of the deforming of a viscoelastoplastic hollow sphere under the influence of volumetric pressure changing with time. The processes of creep and plastic flow under increasing pressure, plastic flow at constant pressure, the medium unloading at decreasing pressure and the repeated plastic flow at the unloading were considered. The regularities of the motion of elastic-plastic boundaries in the material of the hollow sphere were established. The parameters of the stress-strain state of the medium were calculated, stress relaxation after the unloading was investigated.

Détail

Keywords: elasticity, creep, plasticity, irreversible deformations.

Bibliographie

[1] Oleinikov A. I., Pekarsh A. I., Integrirovannoe proektirovanie protsessov izgotovleniia monolitnykh panelei [Integrated design of monolithic panel manufacturing processes], Ekom, Moscow, 2009, 109 pp. (In Russian)

[2] Krupsky R. F., Krivenok A. A., Stankevitch A. V., Feoktistov S. I., Belykh S. V., “Shaping profile blanks at a sheet stretch-forming press”, Scholarly Notes of Komsomolsk-na-Amure State Technical University, 1:14, Engineering and Natural Sciences (2013), 4–8 (In Russian) | DOI

[3] Khokhlov A. V., “The nonlinear Maxwell-type model for viscoelastoplastic materials: simulation of temperature influence on creep, relaxation and strain-stress curves”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 21:1 (2017), 160–179 (In Russian) | DOI | Zbl

[4] Annin B. D., Oleinikov A. I., Bormotin K. S., “Modeling of forming of wing panels of the SSJ-100 aircraft”, J. Appl. Mech. Tech. Phys., 51:4 (2010), 579–589 | DOI | Zbl

[5] Li H., Zhang B., “A new viscoelastic model based on generalized method of cells for fiber-reinforced composites”, Int. J. Plast., 65 (2015), 22–32 | DOI

[6] Firsov S. V., “Irreversible deformations of a rotating cylinder”, Izvestiya of Altai State University, 2018, no. 4 (102), 114–117 (In Russian) | DOI

[7] Burenin A. A., Bykovtsev G. I., Kovtanyuk L. V., “A simple model of finite strain in an elastoplastic medium”, Doklady Physics, 41:3 (1996), 127–129 | Zbl

[8] Burenin A. A., Kovtanyuk L. V., Bol'shie neobratimye deformatsii i uprugoe posledeistvie [Large irreversible deformations and elastic aftereffect], Dal'nauka, Vladivostok, 2013, 312 pp. (In Russian)

[9] Begun A. S., Kovtanyuk L. V., Burenin A. A., “Large irreversible deformations under conditions of changing mechanisms of their formation and the problem of definition of plastic potentials”, Doklady Physics, 61:9 (2016), 463–466 | DOI | DOI

[10] Begun A. S., Kovtanyuk L. V., Lemza A. O., “Creep and stress relaxation in the cylindrical layer of a material at its rotational motion”, Vestnik Chuvash. Gos. Ped. Univ. im I. Ya. Yakovleva. Ser. Mekh. Pred. Sost., 30:4 (2016), 3–11

[11] Begun A. S., Kovtanyuk L. V., Lemza A. O., “Change of accumulation mechanisms of irreversible deformations of materials in an example of viscometric deformation”, Mech. Solids, 53:1 (2018), 85–92 | DOI

[12] Begun A. S., Kovtanyuk L. V., Lemza A. O., “On modelling of creep and plasticity in a problem of viscosimetric flow of a material”, Key Engineering Materials, 685 (2016), 230–234 | DOI

[13] Belykh S. V., Burenin A. A., Kovtanyuk L. V., Prokudin A. N., “On account of viscous properties of materials in the theory of large elastoplastic strains”, Chebyshevskii Sb., 18:3 (2017), 108–130 (In Russian) | DOI

[14] Prokudin A. N., Firsov S. V., “Antiplane strain of hardening elastoviscoplastic medium”, J. Sib. Fed. Univ. Math. Phys., 11:4 (2018), 399–410 | DOI

[15] Norton F. H., The creep of steel at high temperatures, McGraw-Hill Book Company, New York, 1929, v+90 pp.

[16] v. Mises R., “Mechanik der festen Körper im plastisch-deformablen Zustand”, Gött. Nachr., 1913 (1913), 582–592 (In German) http://www.digizeitschriften.de/dms/resolveppn/?PID=GDZPPN002503697 | Zbl

[17] Burenin A. A., Galimzyanova K. N., Kovtanyuk L. V., Panchenko G. L., “Matching growth mechanisms of irreversible deformation of a hollow sphere under uniform compression”, Doklady Physics, 63:10 (2018), 407–410 | DOI | DOI

[18] Galimzyanova K. N., Kovtanyuk L. V., Panchenko G. L., “Creep and plastic flow of the material of an elastoplastic spherical layer under conditions of comprehensive hydrostatic compression”, Vestnik Chuvash. Gos. Ped. Univ. im I. Ya. Yakovleva. Ser. Mekh. Pred. Sost., 32:2 (2017), 37–44 (In Russian)