A platinum wire has Poisson’s ratio ν = 0.39, and resistivity ρ of 1.06 x 10-7 ohm-meter. When the wire is pulled, the axial strain εA is 0.08 and the resistivity increases to 1.07 x 10-7 ohm-meter. What is the gauge factor of the platinum wire?
Answers
Gauge factor is defined as the ratio of per unit change in resistance to per unit change in length.
Gf=(ΔR/R)(ΔL/L)
ΔRR=Gf×ΔLL=Gf×ε
where ε=strain= ΔLL
ΔRR=ΔLL+2v×ΔLL+Δρρ
∴ Gauge FactorGf=1+2v+((Δρ/ρ))ε
where
Term 1 – resistance change due to change of length
2v – resistance change due to change in area i.e. Poisson’s ratio
((Δρ/ρ))ε – resistance change due to piezo resistive effect
The strain is usually expressed in terms of micro strain. 1 micro strain = 1 μm/m. If the change in the value of resistivity of a material when strained is neglected, the gauge factor is:
Gf = 1 + 2v
The common value for Poisson's ratio for wires is 0.3. This gives a gauge factor of 1.6 for wire wound strain gauges. Poisson's ratio for all metals is between 0 & 0.5. This gives a value of 2.
Example – A resistance wire strain gauge uses a soft iron wire of small diameter. The gauge factor is +4.2. Neglecting the piezo resistive effects, calculate the Poisson's ratio.
Solution –The gauge factor is given by equation, Gf = 1 + 2v = 4.2
Poisson's ratio = v = (4.2 -1)/2 = 1.6
Strain gauges are broadly used for two major types of applications and they are:
Experimental stress analysis of machines and structures.
Construction of force, torque, pressure, flow and acceleration transducers.