Analysis of spatial stress and velocity fields in plastic flow processes
https://doi.org/10.22405/2226-8383-2019-20-2-325-335
Abstract
The method of analysis of spatial fields of stresses and velocities in pro-cesses of plastic flow
is given, based on mapping of flow zones in deviator space of stresses. A generalized Mises flow
function corresponding to numer-ous experimental data is taken as the loading surface. It is
shown that the generalized Mises model is convenient for analysis of spatial deformation processes
with the power of a special depicting parametric space. The numer-ical implementation
of the method is illustrated by the example of plastic compression of a material under threedimensional
deformation conditions. It is shown that the distribution of stresses and flow rates
depends on the current ratio of layer sizes during settling.
About the Authors
Nikolai Dmitrievich TutyshkinRussian Federation
Vadim Yurievich Travin
Russian Federation
References
1. Ilyushin A. A., 1963, “Plasticity: Fundamentals of General Mathematical Theory”, M.: AN SSSR, 271 p. (In Russian)
2. Ivlev D. D., 2001, “Mechanics of Plastic Environments: in 2 vol. Vol.1.: Theory of Perfect Plasticity”, М.: Fizmatlit, 232 p. (In Russian)
3. Tutyshkin N. D., Tregubov V. I., 2016, “Related problems of the theory of plasticity and damage to deformable materials”, Tula: TulGU, 248 p. (In Russian)
4. Tutyshkin N. D., Lofink P., M‥uller W. H., Wille R., Stahn O., 2017, “Constitutive equations of a tensorial model for strain-induced damage of metals based on three invariants”, International Journal Continuum mechanics and thermo-dynamics, vol. 29, pp. 251–269.
5. Tutyshkin N. D., M‥uller W. H., Wille R., Zapara M. A., 2014, “Strain-induced damage of metals under large plastic deformation: Theoretical framework and experiments”, International Journal of Plasticity, vol. 59, pp. 133–151.
6. Rozhdestvenskiy B. L., Yanenko N. N., 1978, “Systems of quasilinear equations and their applications to gas dynamics”, M.: Science, 687 p. (In Russian)
7. Brigadnov I.A., 1996, “Mathematical correctness and numerical methods for solving initialboundary problems of plasticity”, Izvestiya RAN. Solid mechanics, № 4, pp. 62–74. (In Russian)
8. Yanenko N. N., Boyarintsev Yu. I., 1964, “Theory and methods of integration of systems of nonlinear partial differential equations”, Trudy IV Vsesoyuznogo math. s”ezda, M., vol. 2., pp. 613–621. (In Russian)
9. Tutyshkin N. D., 2005, “Metal plastic straining processes with predictable mechanical and constitutive properties modeling”, IASME Transactions, vol. 2, № 9, pp. 1819–1825.
10. Sokolovskiy V. V.,1969, “Plasticity theory”, M.: Higher School, 608 p. (In Russian)
Review
For citations:
Tutyshkin N.D., Travin V.Yu. Analysis of spatial stress and velocity fields in plastic flow processes. Chebyshevskii Sbornik. 2019;20(2):325-335. (In Russ.) https://doi.org/10.22405/2226-8383-2019-20-2-325-335
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