Defining and measuring strain: part 1

A metallic foil strain gauge can detect how a test specimen responds when subjected to axial stress.

In a previous series, we investigated the Wheatstone-bridge circuit topology and described how strain-gauge elements could be used in the bridge legs.

Q: At that point, I asked the question, what is strain, and what are its units?
A: Right, so we’ll take up that question in this new series. Figure 1 at the top shows a specimen under test of length l. In the center image, we apply an axial stress in the form of tension to the specimen, and it lengthens by an amount Dl. The strain, indicated by a lower-case epsilon, is

In addition, as shown at the bottom, if you apply axial compression to a specimen, it shrinks in length, and you’ll have a negative strain.

Figure 1. A test specimen of length l increases by length Dl when subjected to axial tension and decreases by length Dl when subjected to axial compression. (Image: Rick Nelson)

Like the radian, strain is a ratio of lengths and is therefore dimensionless. It can be helpful, however, to think of it in units such as meters per meter. You’ll also see strain expressed in microstrain, abbreviated µe, which is 1 millionth of e. If you have a specimen 1 meter long and you apply tension that expands its length by 1 micron, you’ll have a strain of 1 µe.

Q: OK, given that we’ve defined strain, what’s an effective way to measure it?

Figure 2. A metallic strain gauge (left) presents an increase in resistance under tension (center) and a decrease in resistance under compression (right). (Image: Rick Nelson)

A: Just as we can use a thermocouple to measure temperature or an accelerometer to measure vibration, we can use a metallic strain gauge to measure strain. The metallic strain gauge consists of a conductive foil pattern on a flexible insulating backing, such as the one shown in Figure 2, with the conductive foil shown in black and the insulating backing, called a carrier, shown in blue. The image on the left shows the strain gauge in an unstrained state, for which it has a resistance R. When a test specimen on which the gauge is mounted undergoes tension, as shown in the center, the vertical conductive elements of the pattern elongate and become thinner, and their resistance increases by an amount DR. Conversely, under compression, as shown on the right, the resistance decreases by DR.

Q: How do we relate strain-gauge resistance changes to test-specimen length changes?
A: Your strain gauge will have a parameter called gauge factor, abbreviated GF, which you will find on the data sheet. GF, usually about 2 for a metallic strain gauge,^[1] relates to gauge resistance and specimen length as follows:

Now we can solve for strain as a function of the resistances and gauge factor:

Q: So we just glue the strain gauge to the specimen, and we are all set.
A: Right, but you’ll need to use a special adhesive, such as cyanoacrylate, methacrylate, or epoxy resin, that can accurately transfer your specimen’s deformation to the strain gauge. Factors that influence which adhesive you use include the strain and temperature ranges.^[2]

Q: How do we measure strain using the Wheatstone bridge?
A: Figure 3 is an alternate view of Figure 2 from part 4 of our previous series. Here, R_X is an active strain gauge, and R₂ is a dummy strain gauge used for temperature compensation. Note that the long, thin wires of R₂ are mounted perpendicular to the direction of tension, so their resistance is unaffected by the strain, and you will not need a special adhesive. However, if you use two different adhesives, you should ensure that their thermal properties are similar.

Figure 3. In this configuration, RX is an active strain gauge element, and R2 is a dummy used for temperature compensation. (Image: Rick Nelson)

Q: So how do we calculate strain?
A: We’ll look at the details of the calculation next time, after which we’ll discuss some additional strain-gauge considerations. For example, Figure 3 shows a half-bridge application with one active strain-gauge element, but other configurations are possible. We’ll also look at optimizing the excitation voltage (V_IN in Figure 3). Finally, strain-gauge applications often involve large structures, such as wide-body airframes, antenna towers, stadiums, buildings, or bridges, so we’ll look at lead-resistance and signal conditioning considerations.