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Thermodynamics of one-way shape memory effect at complex stress state and unrestricted strains

Bogdan Raniecki 

Polish Academy of Sciences, Institute of Fundamental Technological Research (IPPT PAN), Świętokrzyska 21, Warszawa 00-049, Poland


The early phenomenological thermodynamic theory of pseudoelasticity (RL model) is generalized to account for one-way shape memory effect under single thermomechanical cycle (arbitrary path in the temperature-stress space). The thermoelasticity of austenite (high temperatures), pseudoelasticity (moderately high temperatures), R - plastic flow (low temperatures), and the complex deformation behaviour consisting in combined reorientation and phase transition - p.t. (moderately low temperatures) are encompassed into the single theoretical framework.

The basic concepts:

- In micro-scale the phases are thermoelastic solids having the same thermal properties, the motion of interfaces is the only source of the entropy production,

- The macroscopic RVE is a single component, three-phase system (austenite and two compounds: self-accommodated martensite - Msa, and oriented martensite – Mor) being in constrained equilibrium with respect to the global amounts of Msa and Mor at each instant of a homogeneous process,

- the concept of optimal internal rearrangement of martensite objects (RVE is in unconstrained equilibrium with respect to all possible microscopic phase orientation variables) leading to the notion of macroscopic phase strain energy,

- the second law of thermodynamics acts as the exclusion principle. It indicates which p.t. processes are admissible and it establishes their onset (macroscopic phase strain energy reaches the critical value),

- the multiplicative decomposition of the deformation tensor is applied to extend the infinitesimal theory into the range of unrestricted strains.

The preliminary verification procedure showed that at simple tension, the theoretical isothermal stress-strain (212K<T<336K) and isostress strain-temperature hystereses (30MPa < Sig=const < 400MPa) follow 15 experimental plots (TiNi alloy) with an error acceptable in the structural engineering.


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Presentation: Invited at E-MRS Fall Meeting 2007, Symposium E, by Bogdan Raniecki
See On-line Journal of E-MRS Fall Meeting 2007

Submitted: 2007-05-07 12:54
Revised:   2009-06-07 00:44