Strain...

When an external force is applied to an elastic material, stress is generated, which Subsequently deforms the material. At this time if applied force is a tensile force, the length L of the material extends to L+DL. The ratio of DL to L, that is DL/L, is called strain. (Precisely, this is called normal strain or longitudinal strain.) On the other hand, if a compressive force is applied, the length L is reduced to L- DL. Strain at this time is (- DL)/L. Strain is usually represented as e.

Assuming a cross-sectional area A for the material and an applied force of P, the stress s will be P/A, since stress is defined as a force acting over a given cross sectional area. In the simple uniaxial stress field illustrated below, strain e is proportional to stress s, thus satisfying the equation s = E × e, provided that the stress does not exceed the elastic limit of the material. "E" in the equation is the elastic modulus (Young's modulus) of the material.

e : L: DL:

Strain Original length Change due to force P

Because a strain is a ratio between length of two parts, it is a quantity having no dimension. Usually it is represented in a unit of 1x10^-6, since the ratio of deformation is often very small. For example, supposing L to be 100mm and DL to be 0.1mm, strain e is indicated as 000x10^-6strain, because "0.1mm/100mm=0.001=1x10^-3=1000x10^-6". To indicate comparatively large strain, "% strain" is also used. In this case, 1% strain equals to 0000x10^-6 strain.

Strain and resistance change...

When a metal resistor is expanded or contracted by an external force, it experiences a change in electrical resistance. By bonding a metal resistor to the surface of a test specimen with an electrical insulator between them, the metal resistor, or gage, changes dimension according to the expansion or contraction of the test specimen, thus resulting in a change in resistance. Electrical resistance strain gages are used to detect strain in a specimen by measuring this change in resistance.

Strain gages ...

A strain gage is constructed by bonding a fine electric resistance wire or photographically etched metallic resistance foil to an electrically insulated backing, and attaching wire leads. The strain gage is then used for strain measurement by bonding it to the surface of the specimen with a special adhesive.

Strain generated in the specimen is transmitted to the gage (foil or wire resistor) through the gage backing, where expansion or contraction occurs. As a result, the resistor experiences a change in resistance. This change is proportional to the strain as indicated in the following equation:

e: R: DR: K:

Strain Gage resistance Resistance change due to strain Gage factor as shown on the package

Features of a strain gage

TML strain gages are provided with many convenient features.

• Simple construction with a small mass and volume so as not to interfere with the stresses on the specimen
• Small gage lengths for evaluation of localized stress
• Good frequency response for tracking rapid fluctuations in stress
• Simultaneous measurement of multiple points and remote points are easily
  obtained
• Electrical output provides easy data processing

However, each strain gage has its limitations in terms of temperature, the amount of strain, fatigue and the measurement environment. These limitations must be carefully considered before using a strain gage.

Strain measurement using a Wheatstone bridge circuit

Resistance of a strain gage changes proportionally to the induced strain. To measure strain is to measure this change in resistance. Since this resistance change is usually very small, it requires a Wheatstone bridge circuit to convert the resistance change into voltage output.

e: E: R1: R2~R4:

Voltage output Exciting voltage Gage resistance Resistance of fixed resistors

Assuming the value R as R=R1=R2=R3=R4, and that the strain gage resistance varies from R to R+?R due to the induced strain, the output voltage ?e due to the strain is given as follows.

When DR<<R this is approximated to.

The strain gage is connected to a strainmeter, which provides the Wheatstone bridge circuitry and proper voltage excitation. The strain e is measured on a digital or analog display on the strainmeter.