Definitions

# strain gauge

A strain gauge (alternatively: strain gage) is a device used to measure the strain of an object. Invented by Edward E. Simmons and Arthur C. Ruge in 1938, the most common type of strain gauge consists of an insulating flexible backing which supports a metallic foil pattern. The gauge is attached to the object by a suitable adhesive, such as superglue. As the object is deformed, the foil is deformed, causing its electrical resistance to change. This resistance change, usually measured using a Wheatstone bridge, is related to the strain by the quantity known as the gauge factor.

## Physical operation

A strain gauge takes advantage of the physical property of electrical conductance's dependence on not merely the electrical conductivity of a conductor, which is a property of its material, but also the conductor's geometry. When an electrical conductor is stretched within the limits of its elasticity such that it does not break or permanently deform, it will become skinnier and longer, changes that increase its electrical resistance end-to-end. Conversely, when a conductor is compressed such that it does not buckle, it will broaden and shorten, changes that decrease its electrical resistance end-to-end. From the measured electrical resistance of the strain gauge, the amount of applied stress may be inferred. A typical strain gauge arranges a long, thin conductive strip in a zig-zag pattern of parallel lines such that a small amount of stress in the direction of the orientation of the parallel lines results in a multiplicatively larger strain over the effective length of the conductor—and hence a multiplicatively larger change in resistance—than would be observed with a single straight-line conductive wire.

## Gauge factor

The gauge factor $GF$ is defined as:
$GF=frac\left\{Delta R/R_G\right\}\left\{epsilon\right\}$
where
$R_G$ is the resistance of the undeformed gauge,
$Delta R$ is the change in resistance caused by strain, and
$epsilon$ is strain.

For metallic foil gauges, the gauge factor is usually a little over 2. For a single active gauge and three dummy resistors, the output $v$ from the bridge is:

$v=frac\left\{BV cdot GF cdot epsilon\right\}4$
where
$BV$ is the bridge excitation voltage.

Foil gauges typically have active areas of about 2-10 mm2 in size. With careful installation, the correct gauge, and the correct adhesive, strains up to at least 10% can be measured.

## Gauges in practice

Foil strain gauges are used in many situations, different applications place different requirements on the gauge. In most cases the orientation of the strain gauge is significant.

Gauges attached to a load cell would normally be expected to remain stable over a period of years, if not decades; whilst those used to measure the response in a dynamic experiment may only need remain attached to the object for a few days, be energized for less than an hour, and operate for less than a second.

### Variations in temperature

Variations in temperature will cause a multitude of effects. The object will change in size by thermal expansion, which will be detected as a strain by the gauge. The resistance of the gauge will change, and the resistance of the connecting wires will change.

Most strain gauges are made from a constantan alloy. Various constantan alloys and Karma alloys have been designed so that the temperature effects on the resistance of the strain gauge itself cancel out the resistance change of the gauge due to the thermal expansion of the object under test. Because different materials have different amounts of thermal expansion, self-temperature compensation (STC) requires selecting a particular alloy matched to the material of the object under test.

Even with strain gauges that are not self-temperature compensated (such as isoelastic alloy), using a Wheatstone bridge arrangement it is possible to compensate for temperature changes in the specimen under test and the strain gauge. To do this in a Wheatstone bridge made of four gauges, two gauges are attached to the specimen, and two are left unattached, unstrained, and at the same temperature as the specimen and the attached gauges. Murphy's Law was originally coined in response to a set of gauges being incorrectly wired into a Wheatstone bridge.

Temperature effects on the lead wires can be cancelled by using a "3-wire bridge" or a "4-wire Ohm circuit (also called a "4-wire Kelvin connection").

## Other gauge types

For measurements of small strain, semiconductor strain gauges, so called piezoresistors, are often preferred over foil gauges. A semiconductor gauge usually has a larger gauge factor than a foil gauge. Semiconductor gauges tend to be more expensive, more sensitive to temperature changes, and are more fragile than foil gauges.

In biological measurements, especially blood flow / tissue swelling, a variant called mercury-in-rubber strain gauge is used. This kind of strain gauge consists of a small amount of liquid mercury enclosed in a small rubber tube, which is applied around e.g. a toe or leg. Swelling of the body part results in stretching of the tube, making it both longer and thinner, which increases electrical resistance.

## Mechanical types

Simple mechanical types (such as illustrated here) are used in civil engineering to measure movement of buildings, foundations, and other structures. In the illustrated example, the two halves of the device are rigidly attached to the foundation wall on opposite sides of the crack. The red reference lines are on the transparent half and the grid is on the opaque white half. Both vertical and horizontal movement can be monitored over time. In this picture, the crack can be seen to have widened by approximately 0.3mm (and no vertical movement) since the gauge was installed.

More sophisticated mechanical types incorporate dial indicators and mechanisms to compensate for temperature changes. These types can measure movements as small as 0.002 mm.