Page 345 - Mechanics of Microelectromechanical Systems
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332 Chapter 5
in uniaxial tension/compression. As a consequence‚ the equivalent stress by
the Tresca criterion is formulated as:
where and are the maximum and minimum values of the three
principal stresses and which can be calculated as solutions of the
third-degree algebraic equation:
with and – the stress invariant – being defined in terms of the three-
dimensional state of stress components as:
In a plane stress situation‚ the Tresca theory predicts that:
Both von Mises and Tresca yielding criteria are working well for ductile
materials.
Example 5.23
A microcantilever of constant rectangular cross-section is utilized in a
AFM reading experiment‚ where‚ at a given moment in time‚ the following
forces act at its tip‚ as shown in Fig. 5.63: and
Determine the maximum stress induced in the microcantilever when its
narrow cross-section is defined by and The length of the
microcantilever‚ is measured between the vertex of its tip and the
anchor root‚ and the distance h is equal to The microcantilever is
metallic with a yield stress of
Solution:
The most loaded cross-section of the microcantilever is the one located at
the anchor root. Bending moments and axial tension combine to produce
normal stresses‚ whereas the tangential stresses are generated by torsion
when shearing is ignored. The loading at the microcantilever’s fixed root
comprises the following components:
