A Phenomenological Model for the Anisotropic (Positive/Zero/Negative) Thermal Expansion in Shape Memory Alloys and its dependence on Phase Transformation and (Re)orientation of Martensite Variants

Thermal expansion (TE) is inherent material property and a critical design parameter in applications in which dimensional stability and/or thermal fatigue resistance over a wide range of temperatures are required. Examples include high precision instruments, satellite antennas, and optical instruments. Metallic materials that undergo martensitic transformation have been recently shown to exhibit tailorable bulk TE due to the TE anisotropy of the low-crystallographic-symmetry martensite lattice. In these materials, the TE anisotropy of bulk polycrystals can be exploited through martensite variant "orientation" upon deformation processing. This work proposes a constitutive model for tailoring the anisotropic CTE in shape memory alloys (SMAs) during martensite variant texturing, which is validated against experimental data from NiTiPd. A description of the evolution of the anisotropic macroscopic thermal expansion (TE) tensor of bulk shape memory alloys (SMAs) during phase transformation and martensite (re)orientation is proposed. Given that the tailorability of the TE of SMAs originates from the crystallographic TE anisotropy of the low-crystallographic-symmetry martensite, the TE tensor is approximated by a function of the oriented martensite volume fraction and the orientation direction unitary tensor. The proposed model is validated against recent experiments on tailoring TE through martensite orientation in a NiTiPd high temperature SMA. In those experiments, the TE tensor component in the loading direction of NiTiPd in the martensite state was shown to decrease with increasing inelastic strain induced by uniaxial tensile loading. According to the model, the TE tensor components in the transverse to the loading directions decrease with increasing tensile inelastic strain.