Many devices have been made for measuring deformation (or strain). Strictly speaking, since gauge lengths are always finite, we measure deformations. While we frequently calibrate our output signal to give average strain over the gauge length, we are in reality sensing finite deformation over a finite gauge length.
Deformation measuring devices include innumerable devices employing mechanical, optical, electrical resistance, electrical inductance, electrical capacitance and piezoelectric principles. The large variety of devices which have been developed to measure deformations (or strain) is much too extensive to even mention here. We shall consider in some detail the electrical resistance strain gauge.

Fig - Strain Gauge
The use of mechanical extensometers (either dial gauges or LVDT type) gives us a reusable measuring device for determining deformation over fairly long gauge lengths (typically 2" or 8"). Average strains are then obtained by dividing the measured deformations by the gauge length. This approach is satisfactory provided the strain is essentially constant over the gauge length, provided we do not require very short gage lengths, and there is adequate space to mount the extensometer on the specimen. Accurate measurement of strain in regions of high strain gradient (strain changing rapidly with position), on curved surfaces or in close quarters (i.e. inside a hole) are generally not practical, if not impossible, using mechanical measuring devices.
The primary advantages of mechanical extensometers and other mechanical strain (actually deformation) measuring devices is the ease with which they can be used, their relatively low cost and the fact that they are reusable. Additionally, some types require no special instrumentation. Their primary disadvantages lie in their relatively bulky size, long gauge lengths and the fact that the variety of practical applications is extremely limited.
Electrical resistance strain gauges overcome most of the disadvantages of mechanical gauges. Resistance strain gauges come in gauge lengths from as little as a few thousandths of an inch to gauges of several inches in length. Extremely short gauge lengths are used for applications involving high strain gradients or where measurements are required in areas of small radius of curvature. At the other extreme, some very long special purpose gauges are made to be embedded in non homogeneous materials such as concrete where they automatically average the strain over a more representative sample of the material.
With proper surface preparation and choice of adhesive, resistance strain gauges can be used on most materials (e.g. metals, glass, wood and plastics). In most applications gauge lengths of 0.25 to 0.50 inch are very satisfactory. These relatively short gauge lengths would suffice in all but the most demanding applications and yet they are long enough to make installation relatively easy.
Electrical resistance strain gauges are relatively inexpensive (costs vary from about $3 for a single element gauge to $35 or more for more sophisticated multi - gauge configurations). Special measuring instruments are required when using resistance strain gauges. The instrumentation must be connected to the gauges via lead wires, but it may be remote from the specimen if that is needed or desired. Also, the gauges are good only for a single installation (i.e. you can't remove and reuse them on another specimen). They can be reused only to the extent that they remain undamaged and on the original specimen.
Electrical resistance strain gauges have their primary advantages in that they come in such a wide range of gage configurations and lengths, are extremely accurate, have a sensitivity of about one micro-strain, and are relatively inexpensive to use. Their primary disadvantage lies in the fact that strain gauge installation is somewhat of an art (but it can be mastered with a little practice).
A comprehensive coverage of electrical resistance strain gauges would require an entire text. Our intent here is to simply introduce you to this vast and important area of strain measurement. Strain gauges come in thousands of sizes, shapes, and configurations. Additionally one can select from a wide assortment of gauge foil alloys, carrier matrix (backing), and electrical resistance. Additionally, temperature operating range and maximum strain range capability varies with gauge material. Some gauges are designed primarily for dynamic testing while others are normally used for static testing. Special purpose gauges may compensate for temperature change or lateral sensitivity. The possibilities are almost endless, but they all operate on the same basic principles.
As an example to give you some idea of the operating range of electrical resistance strain gauges, we note the following fairly typical values for a Constantan foil gauge encapsulated in polyimide (Micro-Measurements):
·         Universal general-purpose strain gauges primarily used for general purpose static and dynamic testing.
·         Normal temperature range: -100o to +350oF
·         Strain range: ±5% (±50,000 micro-strain) for gauge lengths over 1/8 inches.

The theory of operation of the electrical resistance strain gage is based on Lord Kelvin's discovery that the electrical resistance of a wire changes when the wire is deformed. The electrical resistance R of a wire of length L and cross-sectional area A is given by:

R      =     ρL/A

Where ρ is electrical resistivity of the material. If the wire is stretched the length L increases and the cross sectional area A decreases resulting in a increase in electrical resistance of the wire. The resistivity ρ is a function of the material and is one of those "engineering constants" that is actually a variable. The resistivity increases with strain for most materials, but it may be nearly constant or decrease with strain for other materials. It is also temperature dependent. Gauges were originally made of wire but are now typically etched from thin foil (about 0.0001 inch thick). The wire or foil forms a pattern of parallel elements and is bonded to a non-conducting carrier or backing. The carrier may be paper or a thin flexible plastic film. Hundreds of shapes and sizes of gauges are manufactured, but the examples shown (enlarged) are fairly typical of single-element gauges:

Foil gauges are preferred since they can be manufactured in shorter gauge lengths than wire gauges and have less sensitivity to transverse strains. Foil gauges also have a flatter construction which makes them less susceptible to mechanical damage and allows them to conform to curved surfaces more easily.

The gauge (actually its carrier) is cemented to the specimen. As the specimen is loaded, and thus deformed, the gauge is deformed along with it, the gauge length is changed and its electrical resistance changes proportionally. Since the gauge is securely bonded to the specimen it can contract as well as elongate with the specimen, thus we can detect both tensile and compressive strains. In order to measure these changes we need instrumentation which will allow us to accurately measure very small changes in electrical resistance. These changes in electrical resistance permit us to determine the strain (average strain over the gauge length). The governing relationship is as follows:
ϵavg = ∆R/R / GF
Where R is the electrical resistance of the gauge (typically 120 ohms), is the measured change in electrical resistance and GF is the gauge factor. The gauge factor (GF) is a function of the gauge material and is supplied by the manufacturer. A value of about 2±20% is typical.


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