# The Strain Gauge Working Principle Explained

## The structure of a strain gauge

Conventional strain gauges normally consist of a foil and an electrical conductor. Why conventional? New strain gauge technologies have also been introduced, such as optical fiber Bragg sensors, which function in a fundamentally different way. "Conventional" here means strain gauges that work with electrical foils.

To understand the structure of a strain gauge, it is helpful to consider the process used to create it, using a standard model as an example: A polyimide foil forms the basis. A layer of Constantan is applied on it. Constantan is an electrical conductor. A template is used to etch away all the areas that will not be conductive later. What remains is an extremely fine Constantan measuring grid, permanently connected with the carrier foil.

The measuring grid consists of a number of "webs" arranged in a meander pattern, which have the appearance of serpentine windings.

### By the way... what makes strain gauges so special?

Jens Boersch from HBM's product management explains in this article how a strain gauge works.

What makes strain gauges special for him:

"We don't normally focus on them but they are hidden away everywhere."

## Method of operation

"Strain gauges measure strain, but what we are actually interested in is mechanical stress," explains product manager Jens Boersch. Mechanical stress describes the degree to which internal and external forces are exerted on a material. A crucial factor of this is the points at which the forces act on the material and the intensity of the forces. These studies belong to the field of application called experimental stress analysis.

Accordingly strain gauges are generally fastened onto the materials being examined in various places and connected by a cable to a measuring amplifier. If the strain gauge is stretched or compressed, the electrical resistance of the measuring grid changes. The reason for this is that when the measuring grid is stretched, the current has to travel a greater distance – and the conductor it passes through has also become thinner, further increasing the resistance. From this change in resistance the strain of the SG can be determined. It is expressed in µm/m. By the way, strain may also refer to compression, in other words negative strain. In this case the resistance is reduced correspondingly.

However, strain is not mechanical stress. To find out what it is, two important points need to be considered first of all:

### Temperature coefficient α of the material

When the ambient temperature changes, the material also changes. This change is designated by the temperature coefficient α. Example: When a steel cylinder is heated it expands, and with it the SG glued onto it. "This temperature-dependent material strain is precisely what we do not want to measure," says Boersch. To compensate for this effect, strain gauges are adapted to a specific material and developed so that they exhibit exactly the opposite temperature behavior. Ultimately the two effects balance out, thereby compensating for material strain so that the strain gauge measures only what it is intended to measure: the strain induced by external material loading. This is referred to as a self-compensated strain gauge or strain gauge with matched temperature response.

### Modulus of elasticity (Young's modulus)

When a material is subjected to a load, it exhibits a mechanical stress. Mechanical stress is force divided by area. But how is it related to strain, which is recorded by a strain gauge? This correlation can be defined in the form of a characteristic curve for different materials by subjecting samples of materials to loads under controlled conditions. As a general rule, greater mechanical stress is matched by an increase in strain. Initially this correlation is linear. This is referred to as the elastic range and the correlation is described by the modulus of elasticity.

After a certain point, however, the material is so strongly deformed by the operant force that it is no longer able to return to its original condition. This plastic deformation continues until the material breaks. Only the linear range, where no plastic deformation occurs, is of interest for experimental stress analysis.

If the modulus of elasticity of a given material is known, the mechanical stress can be determined based on the strain: This is the objective of strain gauge measurements.

## How do strain gauges differ from each other?

"There are some important features that differentiate between strain gauges: Especially important are the geometry, measuring grid length and temperature adaptation."

– Jens Boersch

HBM alone offers over 2,500 different types of strain gauges. Different types are chosen depending on the application.

What distinguishes them is a number of features including the following important ones:

• Geometry
• Measuring grid length

### Geometry

The geometry of a strain gauge is defined by how many measuring grids it has and their alignment. Depending on material loading, different stress states to be measured may occur: In uniaxial stress states there is only one known stress direction. This is a clear case. One measuring grid is sufficient. It is aligned according to the principal stress direction.

In biaxial stress states, multiple stress directions occur together, for example tension, pressure, bending or torsion. In some cases the measurement engineer may not know the direction of the principal stress. Strain gauges with three measuring grids aligned differently are available for these applications. This makes it possible to determine the magnitude of the principal and secondary stress as well as their direction.

### Measuring grid length

Depending on the material and measurement application, the length of the measuring grid plays a role: For example when measuring the stress curve (stress gradients) in a workpiece very precisely. In this case it is better to place many short measuring grids next to each other to achieve a fine grid or analyze a key point precisely. On the other hand if the general load (arithmetic mean) is important, one longer measuring grid is sufficient.

Different surface structures represent a similar challenge: Concrete, for example, is uneven and small pebbles are embedded in it. If the measuring grid is too short in this case, embedded bits may distort the measurement result because a tiny, independent stress field applies in that spot. To prevent this, a longer measuring grid should be chosen: The measured stress is averaged over the length of the measuring grid.

Temperature adaptation of strain gauges for a specific material ensures that the material strain caused by a change in temperature is compensated for as described above. Therefore it is important to select the right SG for the material.

### Other selection criteria

Aside from the features described above, there are a few others that should be briefly mentioned here: Strain gauges are generally available with different commonly used resistances (120, 350 or 1000 ohms, etc.). Choosing the right one often depends on the constraints of the measurement, for example the completion resistors that can be selected in the amplifier or the anticipated interference pulses. The carrier material, conductor material or type of connection may also vary. Some strain gauges can be delivered pre-wired, while others have to be soldered by the user. Pre-wired strain gauges take less time and therefore reduce job set-up costs.

## Using strain gauges

Some basic requirements must be met to ensure that strain gauges function correctly: The most important is for them to be very firmly connected with the material so that they actually participate in every material strain. Because of this, strain gauges are usually glued with a very brittle adhesive, or sometimes they are also welded. Some points should also be considered when selecting an adhesive, since of course the consistency of the adhesive changes with temperature variations. Installation of the strain gauge on the material is a small science in itself: For example, no air bubbles are permitted between the strain gauge and the material or between the strain gauge and the adhesive.

Nevertheless, strain gauges alone are practically useless. "The changes in resistance are so minute that they always have to be amplified before they can be measured at all," explains Jens Boersch. This is done by measuring amplifiers, which are available in many different variants for different applications.

### Fields of application

There are two main fields of application for strain gauges: Either they are used in transducer construction or to test durability. Transducer construction is a topic in its own right with a different purpose: For example it is important for the transducer material to be as fatigue-free as possible. The purpose of strain gauges is to measure the operant physical quantities such as force or torque.

Fatigue (which should if possible play no role in transducer construction) is by contrast the main focus in experimental stress analysis. Product manager Jens Boersch: "The question is: When does the material fail under constant load?" These loads are simulated by test cycles in which the material is repeatedly subjected to loading. The load is normally so low that the material is not destroyed immediately. Thus it varies within the elastic range, as described above, where strain and mechanical stress are still linearly dependent on each other.

The question of fatigue is interesting in many areas: In tests of aircraft parts, infrastructure facilities like bridges or railways, or even in electrical printed circuit boards and motherboards. The components are thoroughly tested to find out whether the required durability is provided so they will withstand the expected loads.

The fatigue curve for the materials being tested is known from laboratory tests. Thus it can be predicted after how many test cycles and under what load the material will fail. The material life is shortened with every load. The more cars that drive over a bridge, for example, the closer it comes to the point where one of its components will be damaged. The heavier the load, the fewer cycles the material is able to withstand. Heavy trucks are a much more significant load than small cars.

"This is a fascinating question: Which will be the load that actually does damage to the material," says Jens Boersch. "This is the key question in an application I have found particularly fascinating: To estimate how long a railway bridge would be able to stand up to the load. But it had already been in operation for decades at the time of the tests. The operators of the relevant section were able to look back through old documentation to retrace exactly how many trains weighing how much had traveled over the bridge in all those years. That was really quite fascinating."