Shape memory alloys have found diverse applications in several engineering
systems including biomedical devices and thermal actuators. This
is due to their superelastic and shape-memory behavior, which occur as a result of
solid-solid transformations from a parent phase to several variants of the product
phases. The most commonly used shape-memory alloy is a nearly equiatomic
NiTi alloy known as Nitinol. Much research has been devoted to modeling
polycrystalline Nitinol under various thermomechanical loading conditions. As a result,
several phenomenological and micromechanics-based models have been proposed
to characterize the complex behavior of Nitinol in both monocrystalline and
textured polycrystalline form.
In this work, a multiscale thermomechanical model for Nitinol is developed
that takes into account the temperature-dependent multivariant phase transformations
at the single-crystal level and the interaction between various crystals in a textured
polycrystalline aggregate. The single-crystal thermomechanical model
is relevant to both thermal loading and mechanical loading at high strain-rates.
The coupled thermomechanical problem is solved using a monolithic approach
in a finite-element framework. Specializing this model to isothermal conditions leads to a
temperature-independent mechanical response, which is suitable for quasistatic
mechanical loading. Most models in literature account only for isothermal stress-induced
phase transformations between the austenite and multivariant
martensite phases in Nitinol. In this work, such a constitutive model
is extended to include the formation of intermediate multivariant
rhombohedral phase as well. In order to model the macroscopic
response of polycrystalline Nitinol, first a statistics-based method is developed
to determine the optimum size of Representative Volume Element (RVE) meant
for solving the microscale problem. The macroscale constitutive response is
then derived through computational homogenization of this RVE response.
A finite element-on-finite element architecture is employed to solve
this multiscale problem accurately. Representative numerical
simulations are performed in order to validate the modeling approach with
several experiments on thin-walled tubes.