Thermodynamics of Nitinol

Abstract

A self-consistent macroscopic thermodynamics is developed for the calculation of work, heat, and dissipation for thermodynamic paths of the shape memory alloy, Nitinol. The thermodynamic system analyzed is a Nitinol helix for which extensive force–length–temperature (FLT) equation of state measurements have been made. The Nitinol system exhibits significant hysteresis and is determined to be a nonequilibrium thermostatic system. A set of equations of state are provided which correlate all reversible and irreversible Nitinol thermodynamic paths to both the set of helix (FLT) thermodynamic state variables and to new ‘‘history’’ state variables. It is shown that these equations predict observed cyclic behaviors not previously interpreted. In the absence of calorimetric measurements for the Nitinol helix system, a physical assumption is made that reversible paths are of constant phase. This assumption is used to estimate the reversible path thermal and mechanical heat capacities for the Nitinol system. With the state equations and the estimated reversible path heat capacities, the nonequilibrium thermostatic formalism is employed to derive expressions for the heat flow for any Nitinol thermodynamic path. It is shown that predicted calorimetric quantities are in good qualitative agreement with measurements. It is also shown that the calorimetric quantities are sensitive to state equation coefficients, which in turn are sensitive to cold-working or ‘‘conditioning’’ of the material. The large heat of transformation, ∼2.4 cal/g, an estimated isentropic temperature change of 22 °C and the large dimensional changes associated with the shape memory effect, imply that Nitinol may be useful for many applications, including use as a working medium for low-grade thermal-energy conversion (i.e., heat engines).