Page 259 - Mechanics of Microelectromechanical Systems
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246 Chapter 4
which might be selected to coincide with which marks the start of the
austenitic transformation. Assuming that the substrate has a higher
coefficient of linear expansion, the bimorph will bend, due to the
dissimilarity in the linear expansion coefficients of the two materials, in the
way shown in the generic Fig. 4.51 (b). Being in martensite phase, the SMA
is easily deformable. Further increasing the temperature from to a
temperature above the point (where all the SMA is in austenitic form)
will cause the SMA to shrink, which will produce more bending in the
bimorph. The equations which define the deformation over the first
temperature variation can be written as:
and:
Equations (4.147) and (4.148) can be solved for the curvature radius, which
is:
The bending moment M is given by Eq.(4.148). During the second phase,
new forces and a new bending moment are set by the relative shrinking of the
SMA layer, and the corresponding equations are:
and:
Similarly, Eqs. (4.150) and (4.151) are solved for the new radius, which is:
