The impossibility of modelling of sigmoid superplasticity curves using only parallel or series connections of power-law viscous elements | Mekhanika | kompozitsionnykh | materialov i konstruktsii
> Volume 25 > №3 / 2019 / Pages: 299-315

The impossibility of modelling of sigmoid superplasticity curves using only parallel or series connections of power-law viscous elements

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Abstract:

Models for superplastic deformation of materials are applicable only in case they are able to describe properly the characteristic qualitative features of test data (the main effects observed), in particular material stress-strain curves features and sigmoid shape of their dependency on strain rate (in logarithmic coordinates). One of the traditional approaches to superplasticity modelling commonly used for more than half a century is based on structural rheological models, consisting of connections of various viscous and plastic elements, particularly connections of non-linear power-law viscous elements which are governed by two material parameters. In the present paper it is proved that it is impossible to describe the sigmoid shape of superplasticity curve by only parallel or only series connections of any number of non-linear viscous elements with arbitrary parameters. It results in the necessity to combine both parallel and series connections of power-law viscous elements in the model or to add elements of other types. The analysis showed that the shape of the strain rate sensitivity curves generated by the mixed connection of three power-law viscous elements as well as the model ability to provide a sigmoid strain rate sensitivity curves depend significantly on the relation between the strain rate exponents of the elements involved. The possibility of qualitative simulation of sigmoid strain rate sensitivity curve as well as providing high values of the strain rate sensitivity index within the framework of the linear viscoelasticity theory is shown without any complex restrictions on the relaxation modulus. It means that linear integral operators of the viscoelasticity theory may be used as an “element” in construction of constitutive equations for a material with a sigmoid strain rate sensitivity curve, in particular in modelling superplastic deformation of materials.

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