New data are reported which show that the cycles to failure for NiTi are related exponentially to cyclic strain extent (difference between maximum and minimum cyclic strain) to at least 2×105 cycles. The relationship is apparently insensitive to thermodynamic cycle type or to stress/strain mode, but does show strong dependence on the NiTi martensite transition temperature.

A self-consistent thermodynamics is developed for nonrelaxation hysteretic processes. This theory, nonequilibrium thermostatics, is based upon macroscopic empirical descriptions of hysteretic behavior and the laws of thermodynamics. It is shown that the empirical behavior of hysteretic systems does not satisfy the conditions required for application of either equilibrium or relaxation nonequilibrium thermodynamics. Therefore, modified thermodynamic assumptions are proposed which are consistent with empirical hysteretic behavior. The principal new assumptions are (1) that processes (energy dissipation permitted) consists of a differential sequence of nonequilibrium states; (2) that three new ‘‘state variables’’ describe all of the ‘‘history dependence of a state;’’ (3) that at least some ‘‘reversible’’ processes exist; (4) that the time-independent ‘‘modified Gibbs relation’’ can be used to describe the Second Law constraints. With these assumptions, it is shown that the thermodynamic relationships derived from the First Law are identical to those for standard equilibrium thermodynamics, but Second Law implications are significantly different, e.g., a new ‘‘dissipation’’ state function is derived; it is proven that hysteretic behavior is a positive indication of a dissipative process and that dissipation always causes hysteresis. It is concluded that nonequilibrium thermostatics provides a self-consistent theory which extends the useful domain of thermodynamics to include nonrelaxation, hysteretic (dissipative)processes. A comparison of detailed predictions and experimental measurements of heat capacities, adiabatic paths, etc., for a hysteretic system is provided in a separate paper.

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).

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