2.
Strain Gages
2.1
Strain Sensitivity and Gage Factor
For most common materials, there is a constant ratio between stress and strain. The relationship is then
expressed by Hooke's law :
E
=
σ
ε
,
(12)
where:
E
= the modulus of elasticity or Young's modulus
σ
= stress
ε
= strain
All electrically conductive materials possess a
strain sensitivity
, which is defined as the
ratio of the relative change in electrical resistance of a conductor to the applied relative
change in conductor length, or
F
=
RR
LL
s
o
o
∆
∆
(13)
where:
F
s
= strain sensitivity factor
∆
R
= resistance change (ohms)
R
o
= initial conductor resistance (ohms)
∆
L
= change in length (mm)
L
o
= initial conductor length (mm)
Note that
F
s
is a dimensionless quantity, as are both the numerator and the denominator.
The term (
∆
L
/
L
o
) =
ε
, the strain.
The electrical resistance of a conductor of uniform cross section behaves according to the
equation :
RL
A
=
ρ
(/)
(14)
where:
R
= resistance (ohms)
L
= length of conductor
A
= crosssectional area of conductor
ρ
=
resistivity constant
, a property of the specific conductor
material
If a straight
wire is stretched elastically, the length will increase and the crosssection
will decrease by Poisson's ratio,
ν
= (
∆
D
/
D
)/(
∆
L
/
L
) (
D
is the diameter of the wire), which
is about 30% for most metals used in electrical resistance wire. From eq.(14), one can
see that, provided
ρ
remains constant, the two effects are additive in
causing the
resistance to increase.
Also notice that
∆
∆
∆
∆
∆
R
R
L
L
A
A
L
L
D
D
=+
2
(15)
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View Full DocumentThe overall effect is that the percentage change in the electrical resistance of the
conductor will be 1.6 times greater than the applied strain percentage.
This also means
that
F
s
will be about 1.6 for an elastically stretched wire.
For most alloys, the specific resistivity
ρ
, is not constant.
It is affected by the applied
strain.
More precisely, resistivity changes occur when a conductor is strained because of
an elastic distortion of the lattice structure which influences electron flow through the
conductor.
It can be said then that the resistance change in a conductor is made up of a
geometrical effect plus a resistivity change due to the internal state of stress of the
conductor.
In order for the overall resistance change of a conductor to be a linear
function of the applied strain, the resistivity change must be proportional to the internal
stress level.
This requirement is met by most, but not all metals.
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 Spring '08
 Spedding
 Superconductivity, Electrical resistance, Practical Gage Design and Materials

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