Finite-element modeling of phase transformation in shape memory alloy wires with variable material properties

Abstract

In this paper, we address the issue of modeling the temperature distribution in a shape memory alloy (SMA) wire with variable thermal and electrical properties. This is done in the context of a one-dimensional (1D) boundary value problem where an initially martensitic SMA wire is electrically heated under zero-stress conditions. The model accounts for an evolution in the thermal conductivity, electrical resistivity and heat capacity during the phase transformation. The evolution in the 1D temperature field is found by implementing a Galerkin-based finite-element method. This is used in combination with a recursive iteration scheme to accurately determine the change in the material properties during a time step. The numerical approach is validated by comparing it with a known analytical solution with variable thermal properties. A parametric study on the SMA phase transformation indicates that, based on the considered values for the material properties, the heat capacity is the least important factor that needs to be accounted for, whereas the electrical resistivity is the most important. It is also demonstrated that the time required to complete a martensite to austenite transformation for a SMA wire subjected to an adiabatic boundary condition is lower if the model accounts for property variations. In fact, when the cyclic response of a SMA wire actuator subjected to an adiabatic boundary condition is the issue at hand, a model that does not account for property variations will predict a lower frequency of actuation than a model that does account for the property variations, as dealt with in this paper.

Finite element analysis of 2D SMA beam bending

“…For given applied stress σ(t) and Joule heating j(t), we can evaluate phase fraction x α (t) and temperature T (t) by Finite element analysis of 2D SMA beam bending 741 integrating the ODEs of Eqs. (13) and (14) simultaneously, and then calculate the resulting strain ε(t) from Eq. (12).…”

“…More and more researchers have concentrated on thermomechanical coupling model and simulation [13][14][15][16][17][18].…”

FEM model of middle ear prosthesis with pseudo-elastic effect

“…The paper [13] considers the influence of variable thermal conductivity and electrical resistivity on the cyclic thermal response of a shape memory alloy (SMA) wire. The specific boundary value problem of an SMA wire under zero-stress conditions is considered, wherein the wire, in an initially martensitic state, is heated by electrical current and cooled by convection.…”

1D Phenomenological Modeling of Shape Memory and Pseudoelasticity in NiTi Alloys

“…Within this context the use of numerical modeling techniques, to simulate both mechanical and functional behavior of SMAs, is of major concern and, consequently, many studies have been focused on this topic in the last few years [9,10], with the aim to model the non-linear hysteretic behavior that describes the phase transformation, and the related functional properties. Some of these models are based on microscopic and mesoscopic approaches [10], where the thermo-mechanical behavior is modeled starting from molecular level and lattice level, respectively; other models are based on macroscopic approaches, where only phenomenological features of the SMAs are used [11][12][13][14][15][16][17][18][19][20][21][22][23][24]. In this field, some authors proposed one-dimensional models based on an assumed polynomial-free energy potential [11,12] while other models are based on an assumed phase transformation kinetic and consider simple mathematical functions to describe the phase transformation behavior of the material [13][14][15].…”

“…Furthermore, other models are based on the elastoplasticity theory [16][17][18][19][20][21][22] which are capable of describing the functional behavior of the material using plasticity concepts. Finally, some researchers used the Galerkin method to describe thermo-mechanical behaviors of shape memory alloys [23,24]. More recently, a 1-D phenomenological approach to simulate both the shape memory effect [27][28][29] and pseudoelastic effect [30] in NiTi-based shape memory alloys has been developed and it is described in the following sections.…”