Page 25 - Mechanics of Microelectromechanical Systems
P. 25
12 Chapter 1
plane of the thin microcantilever, and there is no stress acting about the z-
direction. As a consequence, and according to its definition, a state of plane
stress is setup in the microcantilever under this particular load.
Figure 1.9 Thin microbeams under the action of a tip force: (a) perpendicular to the plane;
(b) in-the-plane
Example 1.3
A thin-film microbar, having the configuration and dimensions of
Fig. 1.10 is subject to a state of extensional residual stresses (this condition
will be detailed in Chapter 6) after microfabrication. The state of residual
stress will generate an axial deformation of the bar, which can be monitored
experimentally, as sketched in Fig. 1.10. By using the theory of elasticity
equations, determine the residual stress in the film. Known are:
and E=120GPa.
Figure 1.10 Displacement sensing for residual stress measurement in a microbar
Solution:
This particular state of stress, where only the normal stresses about the x-
direction are non-zero, is called state of uniaxial stresses. Hooke’s law Eqs.
(1.26) simplify to the following form:
