Theoretical description and practical determination of the strain incompatibility in the model of a shape memory alloy | Mekhanika | kompozitsionnykh | materialov i konstruktsii
> Volume 26 > №3 / 2021 / Pages: 371-386

Theoretical description and practical determination of the strain incompatibility in the model of a shape memory alloy

Abstract:

To take into account the strain incompatibility caused by phase-structural deformation of martensite, additional terms are added to the expression for the thermodynamic potential of a shape memory alloy (SMA). These terms are expressed through two material functions. The first of them characterizes the strain incompatibility between martensite formations and the austenite matrix. The second function is associated with the strain incompatibility between differently oriented martensite formations and between different variants of martensite orientation within these formations. The issue of the sign of additional terms and the arguments of corresponding functions is considered. If chaotic martensite without hardening is taken as the base state, then the term taking into account the strain incompatibility in martensite is less than or equal to zero and increases in modulus with an increase in the degree of orientation of martensite. The term that takes into account the strain incompatibility between martensite and austenite is zero in single-phase states and positive in two-phase state. The SMA with homogeneous hardening of the martensitic part of representative volume is considered in detail. The conditions for the nonnegativity of the mechanical part of dissipation represented as a sum of terms associated with phase transitions and structural transformation are formulated. From these conditions, the restrictions imposed on the material functions, taking into account the strain incompatibility, and the shifts of characteristic temperatures of phase transitions are derived. In particular, in the case of a reverse phase transition without loading in the SMA sample having a nonzero phase-structural strain, the transition start and end temperatures increase and the transition interval narrows in comparison with the chaotic martensite sample, which is consistent with the results of a number of experiments. A technique for determining material functions characterizing the strain incompatibility in the SMA using experimental data is demonstrated. The form of these functions is chosen and constants included in their expressions are found by fitting. At the same time, the restrictions ensuring the nonnegativity of the mechanical part of dissipation are satisfied.

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