A multivariant model for shape memory alloys

A general 3-D multivariant model based on thermodynamics and micromechanics for single crystal shape memory alloy (SMA) behavior is presented in this thesis. This model is based on the habit planes and transformation directions for the variants of martensite in a given material. From this information, the single crystal behavior of the material to temperature and mechanical loads is derived using the concept of a thermodynamic driving force. The Eshelby-Kroner approach is utilized to determine the interaction energy between the variants, where it is assumed that variants can be subdivided into several self-accommodating groups in which variants can grow together compatibly.; This model is examined initially for a simple 2-variant case and then extended to the typical 24 variant case. The multivariant model is shown to exhibit appropriate responses for uniaxial results on single crystals: the transformations occur instantaneously when the critical stress/temperature is reached; both pseudoelasticity and the shape memory effect are captured. The model is also examined for responses to multiaxial loadings and the distinction between perfectly compatible and imperfectly compatible variants (with nonzero volumetric transformation strain) is discussed.; An averaging scheme is also developed to simulate the behavior of a polycrystalline SMA specimen. In the simulation, the polycrystalline SMA specimen is assumed to be formed by a number of randomly oriented single crystal grains. The grains are assumed to be spherical. The Eshelby-Kroner approach is used again to formulate the interaction between the grains, then the single crystal model is applied to each single crystal grain. The polycrystalline simulation successfully captures several features of a polycrystalline SMA specimen.