STRAIN GAGES Fundamentals: Piezoresistive Effect

STRAIN GAGES  Fundamentals: Piezoresistive Effect

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On: 08 Jun, 2017

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Strain gages are based on the variation of resistance of a conductor or se...

Strain gages are based on the variation of resistance of a conductor or semiconductor when subjected to a mechanical stress.
For a wire having length 1, cross section A, and resistivity p. the electric resistance is
R = p
When it is stressed longitudinally, each of the three quantities that affect r R change and therefore R undergoes a change given by
= + -
The change in length that results when a force F is applied to a wire, within the elastic limit (Figure 2.4), is given by Hooke’s law,
= = Ee = E
where E is a constant for each material, called Young’s modulus, o is the mechanical stress, and r is the strain (unit deformation). r has no dimens ions, but to improve clarity, it is usually given in “microstrains” (1 micro- strain 1 r 106 rn/rn).
Consider a wire that in addition to a length I has a transverse dimension t. As a result of longitudinal stress not only does 1 change but t does too. The relationship between both changes is given by Poisson’s law
v = -
where v is the Poisson ratio. It usually ranges from 0 to 0.5; it is, for example, 0.17 for cast iron, 0.303 for steel, and 0.33 for aluminum and copper. Note that for the volume to remain constant, it should be v = 0.5.

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