Experimental characterization of free convection during thermal phase transformations in shape memory alloy wires

Abstract

This paper has experimentally addressed the determination of the convection coefficient for a nichrome and nickel-titanium (NiTi) shape memory alloy (SMA) wire subjected to constant load, heated by electrical current and cooled by free convection (with the current switched off). The entire cycle of actuation is such that the temperature field is allowed to reach a steady state during heating, and the ambient temperature during cooling. The experiments, in conjunction with a phenomenological model, suggest that the convection coefficient can be represented as h = a 0 + a 1 I , where I is the electric current in the wire. The parameter h is highly sensitive to the material (nichrome or SMA) through the zeroth-order coefficient (a 0 ) whereas it is weakly sensitive to I (or the strength of the heat source) through the first-order coefficient (a 1 ). Further, for a given material, h (through a 0 ) is strongly dependent on whether the wire is being heated or cooled. This is in contrast with the customary practice in the literature where h is taken to be identical for heating and cooling. Finally, a simple empirical model in terms of a convection-like parameter, α, is also tested (with a view towards control applications) and is found to be highly accurate in simulating the experimental results.

A homogenized free energy model for hysteresis in thin-film shape memory alloys

“…Having specified the chemical free energy ∆β (T ) in (18), we wish to determine the explicit temperature-dependence of the local transformation stresses (14) and (15). Expressions for the transformation stresses in SMAs typically are determined from an approximation of a modified Clausius-Clapeyron equation, which describes the effect of hydrostatic pressure on transformation temperatures in a thermodynamic system [1,41,71,82,103].…”

“…We describe temperature changes in the material via a simplified balance of internal energy, similar to the developments in [14,26,94]. In this case,…”

“…For Bi ¿ 1, the temperature changes within the material are negligible relative to temperature differences between the surface and surroundings [47]. For SMAs such as NiTi, the conductivity k α is on the order of 10 Wm −1 K −1 and h c is on the order of 1 and 10 2 Wm −2 K −1 , depending on ambient flow conditions [14,69]. Furthermore, for rectangular geometries of thickness d, width w and length L,…”

A free energy model for thin-film shape memory alloys

“…In general, h c is temperature and geometry dependent. For this paper, we assume h c is constant and we refer the reader to [3,7,24] for discussions of variable h c pertinent to bulk and thin-film SMAs. Equation (30) also accounts for rate-dependent heat generation and loss due to phase transformations, where the specific enthalpies h α have the form…”

“…We computed a log-normal distribution about δ using a variance of (27 MPa) 2 , and we used an effective stress variance of (5 MPa) 2 with a normal distribution. [ 3,8,21]. The results of the full model with the identified parameters is compared with the data in Figure 3.…”