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During cooling the internal heat generation term was dropped. The material properties of the SMAs were taken from the product literature for the low temperature wires, and the properties of water and air were implemented in a look-up table for increased accuracy, taken from White (1999).

Performance in air for a variety of wire diameters was first examined to verify the model in relation to the published performance data. While the cooling simulation was quite accurate, the heating simulation required less current than published to attain the required transition temperatures in the wires. The simulation was then repeated using the properties of water, where the high heat transfer coefficients were found to greatly increase the required current when heating, and drastically reduce the cooling times, as reported in the product specifications. Figures 10 and 11 show the simulation results for heating and cooling respectively, along with the finish temperatures for the phase transitions. The numbers in 0 indicate the wire diameter in |im, and both results used an ambient temperature of 10°C. The results for heating and cooling in water agree with both the product literature and experimentation with a number of test specimens.

Based on this data, the 250|m low temperature wires were chosen for the prototype, and the power supply was sized to deliver up to 3A per wire, since not all wires would be actuated simultaneously.

Since no feedback mechanism was designed into the prototype, an accurate simulation of the mechanical behaviour of the wires was essential. The thermomechanical behaviour of SMAs is only just being to be carefully studied and quantified. The literature commonly refers to a dual kriging model to describe the behaviour of SMAs, relating temperature, strain, and applied stress on a three-dimensional surface, shown in Figure 12.

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Fig. 10. The Flexinol 250 |m Diameter Wire Heating for Various Current Values
Fig. 11. Flexinol wire cooling in water for diameters of 100, 150, 250, 300 375|m

In order to determine the correct position in that volume at any time, subject to any imposed mechanical or thermal loading, the initial condition of the material must be known. A simpler model of the SMA relates only temperature and strain level, and is adequate for this application. Figure 13 illustrates this relationship, including the transition from martensite to austenite on heating and the reverse phase transition upon cooling and straining. Ms and As indicate the temperatures at which the phase transitions are estimated to start, while Mf and Af denote the finish temperatures of the phase change. As stated in the introduction, in order for the wire to return to its initial strain level, an external biasing force must be applied. Therefore, the wire is assumed to start at an initial pre-strain, point 'A', and shorten to zero strain on heating, point 'B'. While cooling, a force is applied to the wire allowing it to return to its initial strain level along the lower path. The maximum strain level must be kept below 5% in order to ensure the longevity of the wire. On the fish prototype, the wires are strained back to their initial level by a combination of the set of wires on the opposing side and the spline's bending stress.

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