Strain Gauge | Sensor & Industrial Instrumentation - Electronics and Communication Engineering (ECE) PDF Download

Strain Gauge

The strain gauge is a passive resistive transducer which is based on the principle of conversion of mechanical displacement into the resistance change.
A knowledge of strength of the material is essential in the design and construction of machines and structures. The strength of the material is normally characterized in terms of stress, which is defined as the force experienced per unit area, and is expressed in pressure units. Stress as such cannot be directly measured. It is normally deduced from the changes in mechanical dimensions and the applied load. The mechanical deformation is measured with strain-gauge elements. The strain is defined as the change, (Δℓ), in length, (ℓ) per unit length and is expressed as Δℓ / ℓ in microstrains.
The stress-strain curve for a typical metal specimen is shown in Fig. 9.29.Fig. 9.29 Stress-strain curves for typical metal specimen It is observed that the curve is linear as long as the stress is kept below the elastic limits. Strain measurements are usually carried out on the free surface of a body. Normally the strain magnitude is of the order of a few micrometers per meter, which is expressed as microstrains. Since the magnitude of strain is extremely small, it is practically difficult to measure it directly. Hence, a gauge which can yield strain directly is used. Such a gauge is known as strain gauge.
The desirable characteristics of the strain gauge are gauge sensitivity, range of measurement, accuracy, frequency response, and the ambient environmental conditions it can withstand. Sensitivity is defined as the smallest value of strain that can be measured. The maximum strain measurable and the accuracy achievable depend upon the type of gauges used and the method of gauging used.
Basically stress and strain both are directly related to the modulus of elasticity. But strain can be measured easily as compared to stress, using variable resistance transducer, the resistive transducer is commonly called strain gauge.

➢ Principle of Operation and Construction of Strain Gauges
The basic principle of operation of an electrical resistance strain gauge is the fact that the resistance of the wire changes as a function of strain, increasing with tension and reducing with compression. The change in resistance is measured with a Wheatstone bridge. The strain gauge is bonded to the specimen and hence the gauge is subjected to the same strain as that of the specimen under test.
The materials used for fabrication of electrical strain gauges must possess some basic qualities to achieve high accuracy, excellent reproducibility, good sensitivity, long life and ability to operate under the required environmental conditions. Some of these qualities are attained by selecting materials with high specific resistance, low temperature coefficient of resistance, constant gauge factor, and constant strain sensitivity over a wide range of strain values. The bonding cement should have high insulation resistance and excellent transmissibility of strain, and must be immune to moisture effects.
The most common materials used for wire strain gauges are constantan alloys containing 45% nickel and 55% copper, as they exhibit high specific resistance, constant gauge factor over a wide strain range, and good stability over a reasonably large temperature range (from 0°C to 300° C). For dynamic strain measurements, nichrome alloys, containing 80% nickel and 20% chromium are used. They can be compensated for temperature with platinum.
Bonding cements are adhesives used to fix the strain gauge onto the test specimen. This cement serves the important function of transmitting the strain from the specimen to the gauge-sensing element. Improper bonding of the gauge can cause many errors.
Basically, the cement can be classified under two categories, viz, solvent-setting cement and chemically-reacting cement. Duco cement is an example of solvent-setting cements which is cured by solvent evaporation. Epoxies and phenolic bakelite cement are chemically-reacting cements which are cured by polymerization. Acrylic cements are contact cements that get cured almost instantaneously.
The proper functioning of a strain gauge is wholly dependent on the quality of bonding which holds the gauge to the surface of the structure undergoing the test.

➢ Derivation of Gauge Factor
The gauge factor is defined as the unit change in resistance per unit change in length. It is denoted as K or S. It is also called sensitivity of the strain gauge.

where,
S = Gauge factor or sensitivity
R = Gauge wire resistance
ΔR = Change in wire resistance
ℓ = Length of the gauge wire in unstressed condition
Δℓ = Change in length in stressed condition.
Derivation: Consider that the resistance wire is under tensile stress and it is deformed by Δℓ as shown in the Fig. 9.30.
Let ρ = Specific resistance of wire material in Ω-m
ℓ = Length of the wire in m
A = Cross-section of the wire in m² 
When uniform stress σ is applied to this wire along the length, the reesistance R changes to R + ΔR because of change in length and cross-sectional area.Fig. 9.30 Deformed resistance wire