Superplasticity is considered as a special state of the polycrystalline material plastically deformed at the low level of the stress with the retaining of the ultrafine-grained structure – structural superplasticity received at the previous stage or arised during hot deformation independently from the initial grain size – dynamic superplasticity. For realization of the dynamic superplasticity it has to substitute an initial structural condition of material another, allowed to realize a superplasticity. The mentioned above changes are caused by the conforms of the proper strain rates and structural (phase) transformations of the evolutionary type in the open nonequilibrium systems. It is proposed an approach applying to the modelling of the deformation processes at the superplastic flow of commercial aluminum alloys taking into account the boundary regions in the framework the theory of self-organization of dissipative structures. An examples of the theoretical and experimental data correlation are given.

Formulation of the model suitable for the description of the full material deformation diagram is considered, with axial compression applied, and a loosening component added to elastic and plastic deformation. The materials involved are initially heterogeneous environments like rocks and artificial construction materials, like concrete. Such materials, being in a stationary state, stable for small disturbances, can be interpreted as dissipative structures after the limit of elasticity is reached. The deformation and destruction processes are analysed as instability hierarchy, resulting from self-organization. Methods of mathematical catastrophe theory are applied for the model construction. The energy state function is presented as the sum of the potential function, responsible for reversible deformations and disturbances. The latter involves an imperfection parameter (a controlling one), connected with damageability and responsible for the structurization process. The state equation is obtained by energy function minimization on the order parameter and is supplemented with the kinetic equation for the imperfection parameter. The synergetic methods are shown to be advantageous for the problems of formulating physically well-grounded nonlinear defining equations.

In the submitted paper there is a speech about mathematical modeling of behavior of group of the industrial aluminum alloys with initial varying grain size structure showing superplastic properties in certain temperature and strain rate ranges. Superplasticity of dynamic type are caused by simultaneous action of deformation rates and structural (phase) transitions of evolutionary type in open nonequilibrium systems. The association of deformation process with metal flow, that has irreversible structural and phase transition of indistinct type at one of the stages, allows to use synergetic approach. The experimental study of deformation behavior of group commercial aluminum alloys with initial varying grain size structure in the wide temperature and strain rate ranges (not only in case of superplasticity, but also in the boundary fields of thermoplasticity and high-temperature creep.) has led to creation of the mathematical model formulated from positions of mechanics of solid for simple tensile and compression. At the same time the offered model contains analytically formulated conditions for transition of material to a superplastic state. With using of the theory of elasto-plastic processes of small curvature the developed mathematical model is generalized for combined stress for technological problems of volume forming with use of superplasticity for the purpose receiving a semi-finished product with fine-grained structure.

Dynamic superplasticity of aluminium alloys is considered from positions of the theory of nonequilibrium phase transitions. Evolution of the open nonequilibrium system by which temperature-rates process in materials is modelled, is investigated within the framework of worked out defining relations with attraction of thermodynamic functions of the response. It is shown, that to peak of superplasticity there corresponds a maximum of a specific thermal capacity. The entropy production in optimum thermomechanical conditions of superplasticity aspires to a minimum which corresponds to formation of qualitative ultrafine-grained structure. With use of the Focker-Plank equation mechanisms of deformation characteristic for superplasticity and boundary conditions are analyzed. It is shown, that at superplasticity the main is the mechanism grain-boundary sliding, and in metastable conditions are added diffusionary processes. Influence of the specified processes in conditions of superplasticity becomes prevailing.