On thermomechanics and transformation surfaces of polycrystalline NiTi shape memory alloy material
This paper is devoted to the thermomechanical description of martensitic phase transformations and associated shape emory effects in polycrystalline shape memory alloys (SMAs). The developed framework for plastic materials, employing Lagrange multipliers and Kuhn-Tucker optimality conditions, is used to derive the conditions for satisfaction of the maximum dissipation due to phase transformation in SMAs. The paper extends the earlier thermodynamic framework to include the principle of maximum transformation dissipation, and proposes a generalized phase transformation function motivated by experimental results. First, the general thermomechanical theory of SMAs is reviewed, and constraints on the evolution of internal state variables are obtained as a result of principle of maximum transformation dissipation. The discussion of the paper is more general than usually for SMAs in the sense that a broader generalized thermodynamic force-internal state variable space is considered. Then, the authors present a SMA constitutive model, and various transformation functions are discussed based on the developed thermomechanical framework. The model is capable of modeling pseudoelastic and shape memory effects, while reorientation of martensitic variants is ignored. The conditions for the onset of phase transformation are given in the form of loading/unloading conditions in stress-temperature space. The authors investigate various transformation functions, namely: J2, J2-I1 and J2-J3-I1 based transformation functions. Numerical results based on these transformation functions are compared with experimental results to determine their accuracy to predict SMA characteristics like tension-compression asymmetry, negative volumetric transformation strain and pressure dependence. By this, the experimental results for uniaxial tension and uniaxial compression are utilized to calibrate the model, while the data for hydrostatic compression, zero hydrostatic pressure and total compression are predicted by the model.
generalized phase transformation function
scientific article; zbMATH DE number 1526021