V. D. Solovei

POSSIBLE VELOCITY DISTURBANCES IN THE LAG ZONE AND ON THE FREE BOUNDARY IN A VISCOPLASTIC STRIP UNDER ROLLING

The isothermal slow plane flow of a viscoplastic strip under rolling is considered. The Prandtl friction law is assumed to be valid on the contact surface between the strip and the roller. Integral equations are found for possible tangential velocity disturbances in the lag zone and normal velocity disturbances on the free boundary for the special stationary flow of a strip at any time moment.

References:

1. Gorelik S.S. Rekristallizatsiya v metallakh i splavakh [Recrystallization in metals and alloys]. Moscow, Metallurgia Publ., 1978, 568 p. (In Russian).
2. Gubernatorov V.V., Sokolov B.K., Gervasyeva I.V., Vladimirov L.R. Formation of band structure in structurally homogeneous materials during deformation. Fizicheskaya mezomekhanika, 1999, vol. 2, no. 1–2, pp. 157–162. (In Russian).
3. Gubernatorov V.V., Sycheva T.S., Vladimirov L.R., Matveeva V.S., Pyatygin A.I., Melnikov M.B. Corrugation and formation of structure and texture in metallic materials during deformation and recryctallization: 2. Alloys of cubic system. Fizicheskaya mezomekhanika, 2002, vol. 5, no. 6, pp. 95–99. (In Russian).
4. Glensdorf P., Prigozhin I. Termodinamicheskaya teoriya struktury, ustoychivosti i fluktuatsiy [Thermodynamic theory of structure, stability and fluctuations]. Moscow, Mir Publ., 1973, 280 p. (In Russian).
5. Solovei V.D. Stability of flow and Prigogine’s theorem for the stationary flow of a viscoplastic body. Inzhenerno-fizichesky zhurnal, 2011, vol. 84, no. 6, pp. 1293–1296. (In Russian).
6. Lamb G. Gidrodinamika [Hydrodynamics]. Moscow-Leningrad, GITTL Publ., 1947, 930 p. (In Russian).
7. Ilyushin A.A. Deformation of a viscoplastic body. Uchebniye zapiski MGU. Mekhanika, 1940, no. 39, pp. 3–81. (In Russian).
8. Freudental A., Geiringer H. Matematicheskie teorii neuprugoy sploshnoy sredy [The mathematical theories of the inelastic continuum]. Moscow, Fizmatgiz Publ., 1962, 432 p. (In Russian).
9. Коlmogorov V.L. Mekhanika obrabotki metallov davleniem [Mechanics of metal forming]. Moscow, Metallurgia Publ., 1986, 688 p. (In Russian).
10. Grudev А.P. Teoriya prokatki [Theory of rolling]. Moscow, Metallurgia Publ., 1988, 239 p. (In Russian).
11. Alekseev А.Е. Nonlinear laws of dry friction in contact problems for the linear theory of elasticity. Prikladnaya mekhanika i tekhnicheskaya fizika, 2002, vol. 43, no. 4, pp. 161–169. (In Russian).
12. Ishlinsky А.Yu. On the stability of the viscoplastic flow of a strip and a round rod. Prikladnaya matematika i mekhanika, 1943, vol. VII, pp. 109–130. (In Russian).
13. Solovei V.D. Possible velocity disturbances in the lag zone in the rolling of a perfectly plastic strip. Deformatsiya i razrushenie materialov, 2014, no. 12, pp. 23–26. (In Russian).
14. Solovei V.D. Trukhin V.B. The stability of upsetting of a viscoplastic parallelepiped without friction. Deformatsiya i razrushenie materialov, 2014, no. 2, pp. 9–13. (In Russian).

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