A thermo-mechanically coupled field model for shape memory alloys
P. Junker, K. Hackl.
Continuum Mechanics and Thermodynamics, 26, 859-877, (2014)
The impressive properties of shape memory alloys are produced by means of solid-to-solid phase transformations where thermal effects play an important role. In this paper, we present a model for polycrystalline shape memory alloys which takes full thermo-mechanical coupling into account. Starting from the equations of the first and the second law of thermodynamics, we derive evolution equations for the volume fractions of the different martensitic variants and a related equation for heat conduction. A thermodynamic analysis allows to formulate a complete expression for the dissipation caused by phase transformation and heat flux. This allows to model the experimentally well-documented transformation fronts in tension tests by a finite element scheme without further assumptions. Additionally, the number of required model parameters is very small in comparison with phenomenological approaches. Numerical examples are presented which show a good agreement with experimental observations. © 2014, Springer-Verlag Berlin Heidelberg.
Keyword(s): energy dissipation; finite element method; heat conduction; heat flux; intermetallics; martensitic transformations; phase transitions; tensile testing; thermoanalysis; extremum principles; finite element schemes; martensitic variants; phenomenological app
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