Development of mathematical models of plastic media for resource-saving metal systems technologies
https://doi.org/10.22405/2226-8383-2019-20-2-462-477
Abstract
The development of technology puts forward more complex problems, the effective solution
of which is associated with the refinement of mathematical models of the studied plastic forming
processes of metal systems (metals, steels, non-ferrous alloys) of various chemical compositions
and production technologies (traditional ingot processing, powder production, nanostructured
materials). To build a solution, the integration of differential equations to describe the physical
processes occurring during plastic flow or a variation approach based on the construction of
the original functional is used, but in either case the accuracy of the mathematical modelling
of the process will depend on the accepted mathematical model of the medium. The paper
discusses the development stages of different models of plastic media, from a simple rigidplastic
model, without taking into account the change in the material properties, to more
complex ones - a viscoplastic model that regards the appearance of viscosity with increasing
processing temperature and a dilating model that allows to take into consideration changes in
material density and thereby predict strain destruction. The correct use of mathematical models
of plastic media makes it possible to improve the accuracy of technological regimes calculation,
thereby reducing the time to develop the new product, and can be used for the development
of technological processes for obtaining products by means of the additive technology based
on laser sintering and fusing the powder alloys, thermoplastic processing technologies and
processes of thermochemical hardening and heat treatment of metallic systems of different
chemical compositions.
of which is associated with the refinement of mathematical models of the studied plastic forming
processes of metal systems (metals, steels, non-ferrous alloys) of various chemical compositions
and production technologies (traditional ingot processing, powder production, nanostructured
materials). To build a solution, the integration of differential equations to describe the physical
processes occurring during plastic flow or a variation approach based on the construction of
the original functional is used, but in either case the accuracy of the mathematical modelling
of the process will depend on the accepted mathematical model of the medium. The paper
discusses the development stages of different models of plastic media, from a simple rigidplastic
model, without taking into account the change in the material properties, to more
complex ones - a viscoplastic model that regards the appearance of viscosity with increasing
processing temperature and a dilating model that allows to take into consideration changes in
material density and thereby predict strain destruction. The correct use of mathematical models
of plastic media makes it possible to improve the accuracy of technological regimes calculation,
thereby reducing the time to develop the new product, and can be used for the development
of technological processes for obtaining products by means of the additive technology based
on laser sintering and fusing the powder alloys, thermoplastic processing technologies and
processes of thermochemical hardening and heat treatment of metallic systems of different
chemical compositions.
About the Authors
Gennadiy Modestovich ZhuravlevRussian Federation
Aleksander Evgenievich Gvozdev
Russian Federation
Andrey Pavlovich Navoev
Russian Federation
Anatoly Alekseevich Zhukov
Russian Federation
Nikolai Nikolaevich Dobrovol’sky
Russian Federation
Aleksandr Anatolyevich Shatulskiy
Russian Federation
Dmitry Vladimirovich Maliy
Russian Federation
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Review
For citations:
Zhuravlev G.M., Gvozdev A.E., Navoev A.P., Zhukov A.A., Dobrovol’sky N.N., Shatulskiy A.A., Maliy D.V. Development of mathematical models of plastic media for resource-saving metal systems technologies. Chebyshevskii Sbornik. 2019;20(2):462-477. (In Russ.) https://doi.org/10.22405/2226-8383-2019-20-2-462-477
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