Modeling solid-solid phase transformations: from single crystal to polycrystal behavior

We introduce a framework for modeling elastic properties of shape memory alloy polycrystals by coupling orientational degrees of freedom with elastic strains. Our method allows us to span the length scales from single crystal to that appropriate to obtain polycrystal properties. The single crystal free energy coefficients can be determined from microscopic calculations (such as electronic structure and molecular dynamics) and/or available experimental structural, phonon and thermodynamic data. We simulate the microstructure and determine the stress-strain response of the polycrystal and compare it with that of a single crystal. For FePd parameters we find that the recoverable strain for a polycrystal is ∼ 40% of that for a single crystal. The polycrystal information can, in principle, serve as input to the engineering scale of calculation, where the finite element method is appropriate. Mathematical subject classification: 74B20, 74N10, 74N15.