Page 250 - Mechanics of Microelectromechanical Systems

4. Microtransduction: actuation and sensing 237
It is assumed that in state 1, the SMA wire is in martensitic phase and is
deformed by the gravity force exerted on it through the attached weight. In
case the temperature increases over the critical reversed transformation value,
the austenitic transformation takes place and the natural tendency of the wire
is to shrink and remember its original austenitic phase. In order to keep the
wire’s length unchanged, an external force directed downward has to be
applied. This scenario is indicated by the sequence 1-2 in Figs. 4.49 and 4.50,
which attempt to explain the change in force by the jump from the martensite
characteristic (point 1) to the austenite characteristic (point 2).
As a consequence, the force gain during the 1-2 phase is equal to:

where A and M stand for austenite and martensite, respectively. For a wire,
the stiffness can be expressed as:

where A is the cross-sectional area, l is the length and E is Young’s modulus.
It is therefore clear that the force of Eq. (4.125) is due to the difference in
Young’s moduli between austenite and martensite. Obviously, this simple
force generation mechanism can be used in actuation.

Figure 4.50 Force and stroke potentially gained through SMA transformation in the wire-
weight device

Conversely, when no external force is applied during the heating and the
corresponding martensite-austenite transformation, the SMA wire will shrink,
as sketched in the 1-2’ sequence of both Figs. 4.49 and 4.50. The
displacement gained in this case is: