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Multiscale Constitutive Modeling and Numerical Simulations of the Thermomechanical Response of Polycrystalline NiTi Shape Memory Alloy

  • Author(s): Sengupta, Arkaprabha
  • Advisor(s): Papadopoulos, Panayiotis
  • et al.
Abstract

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.

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