Development of mathematical models of plastic media for resource-saving metal systems technologies

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 rigid-plastic 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.