Page 343 - Mechanics of Microelectromechanical Systems

330 Chapter 5
times the length of the free-fixed microcolumn‚ which gives a value of
for the sought maximum postbuckling deflection.

8. COMPOUND STRESSES AND YIELDING

8.1 Introduction

Often times‚ normal and tangential stresses are produced concomitantly
in deformable MEMS components. In such cases‚ the loading produced
through actuation needs to ensure that the microcomponents that do deform‚
do so within the elastic range‚ so that the part regains its original shape after
loading is relieved‚ and that they do not fail.

Figure 5.62 Normal tangential and resultant (p) stresses on a cross-section

Figure 5.62 shows the cross-section of a MEMS component where
normal (perpendicular to the plane) and tangential (within the plane) stresses
are produced and combined vectorially to get the resultant stress p. The
normal stress can be produced by either bending or axial loading whereas
the tangential stress which is contained in the yz plane of the cross-section
and which has components about the principal axes y and z‚ can be generated
by torsion or shearing‚ as discussed in Chapter 1. The total stress p can be
found as:

Failure in MEMS‚ as the situation where a microcomponent does no
longer perform as expected/designed‚ can occur in the forms of fracture (in
the case of brittle materials)‚ yielding (for ductile materials where the stresses
exceed the yield limit)‚ excessive deformation (either elastic or plastic)‚
buckling or creep (deformation under constant load‚ especially at elevated
temperatures) – see for more details Boresi‚ Schmidt and Sidebottom [3] or
Cook and Young [8].