1. What is Microstrain (με)? What are the Unit and Symbol of Microstrain?
Strain refers to the local relative deformation of an object under the combined effects of external forces, temperature changes, and other factors. It is the amount of deformation per unit length, and its formula is as follows:
ε = ΔL / L
Assuming the length of a structure is L, and after being deformed by force, its length becomes L', then the change in length is ΔL = L' - L. The strain (denoted by ε) is the ratio of the change ΔL to the original length L. As can be seen from the formula, strain is a ratio, which is dimensionless, meaning it has no unit.
So what is microstrain? Since ΔL is very small, typically on the order of micrometers, the calculated strain value is also very small, with many digits after the decimal point, making it inconvenient to display and read. Therefore, the scientific notation 10–6 is introduced, which is called microstrain, denoted by the symbol με. It can be understood that the unit of microstrain is 10–6, so the value of microstrain is magnified by one million times compared to the strain value, resulting in an integer. The measurement range of our strain gauge is ±1500 microstrains, where positive indicates tension and negative indicates compression.
1ε = 106με
2. Principle of Resistance Strain Gauges:
Metal materials inherently possess a specific resistance value. Therefore, when subjected to external tension (or compression), i.e., stretching (or shortening), their resistance value increases (or decreases) accordingly. When a metal material experiences strain, assuming the resistance R changes by ΔR under this influence, the following equation holds true.
Ks is called the strain factor, a constant indicating the sensitivity of the strain gauge. The strain sensitivity coefficient for general strain gauges made of copper-nickel alloy and nickel-chromium alloy is approximately 2, with a typical range of (2.0~2.2).
3. Structure of Resistance Strain Gauges:
Use a specialized adhesive to bond the strain gauge to the measurement location. The strain generated at the measurement location is transmitted to the sensitive grid through the adhesive and the base of the strain gauge. To accurately measure strain, the selected strain gauge and adhesive must satisfy the usage conditions, such as the measurement material and operating temperature. For the method of bonding strain gauges to metal, please refer to the strain gauge bonding procedure and moisture-proof treatment.
4. Selection of Strain Gauge Structure Type
In the fields of mechanical measurement and sensor design, strain gauges are one of the most widely used core sensitive elements. Whether for structural stress analysis, material property testing, or the manufacture of various force sensors and load cells, strain gauges are indispensable. However, faced with the dazzling array of strain gauge models available on the market - such as the BF120, BF350 series, and BA series - many users encountering them for the first time often feel confused: What do the numbers and letters in the model numbers signify? What is the difference between 120Ω and 350Ω strain gauges? Should the grid length be 1mm or 3mm? This article systematically outlines the key parameters and decision-making ideas for selecting strain gauges, helping you choose the most suitable one.
4.1. The determination of strain gauge type is primarily based on the dimensional characteristics of the measured stress field and the knowability of the principal stress direction.
(Uniaxial strain gauge, AA series)
For conditions involving a one-dimensional stress state with a known principal stress direction - such as axial tension rods or pure bending beams - uniaxial metal foil or wire strain gauges are the preferred solution. This type of scenario accounts for the highest proportion of engineering stress analysis, offering mature technology and controllable implementation costs.
(Biaxial strain rosette, BA series)
Under a plane stress state, if the principal stress direction is known, a right-angle strain rosette (biaxial) should be used. During installation, ensure that one of the sensitive grids is strictly aligned with the principal stress direction to obtain the most direct strain-stress conversion relationship.
(Triaxial strain rosette, CA series)
When the principal stress direction is unknown, a three-grid or four-grid strain rosette should be adopted. By obtaining multi-directional strain data from a single application, the magnitude and direction of the principal stress can be calculated using the strain rosette formula, avoiding the efficiency loss and error accumulation caused by repeated trial applications.
4.2. In the field of strain-type sensors, the type selection must match the loading mode of the elastic element:
- Elastic elements primarily subjected to tensile/compressive or bending stresses, such as column, beam, and ring types, all use uniaxial strain gauges;
- Elastic elements targeting shear stress measurement (e.g., torque sensors) use biaxial strain rosettes arranged at a 45° angle.
From the perspective of material and process, metal foil strain gauges have become the mainstream choice for current engineering applications due to their dimensional accuracy, line uniformity, and shape customizability offered by photolithography and etching processes. Their minimum sensitive grid length can reach 0.2 mm, and their bonding performance, heat dissipation capability, and transverse effect suppression are all superior to those of wire-type structures. Metal wire strain gauges are now mainly retained for special high-temperature custom scenarios, while metal thin-film strain gauges, limited by process costs, are only applied in specific high-precision or extreme temperature situations.
5. Selection of Materials
The determination of the sensitive grid material is primarily constrained by the operating temperature range. This parameter is non-negotiable - insufficient temperature resistance of the material will directly lead to strain gauge failure or performance drift.
Room temperature strain gauges (-30°C to 80°C): Constantan is the industry standard choice. Its strain sensitivity coefficient is approximately 2.0, with a low temperature coefficient of resistance, mature process technology, stable supply chain, and reasonable cost structure.
At the backing material level, the current mainstream choice is adhesive-based materials, including special fibers, epoxy resin, phenolic resin, and polyimide, with a typical thickness of 0.03 to 0.07 mm. The backing must simultaneously meet requirements for mechanical strength, flexibility, adhesion, electrical insulation, moisture resistance, and must be free of mechanical hysteresis and creep.
6. Selection of Resistance Value
The standard resistance series includes 120Ω, 350Ω, and 1000Ω. In engineering practice, 120Ω and 350Ω are dominant, and their selection logic is as follows:
When using a resistance strain indicator for stress analysis, 120Ω is the standard matching resistance. This specification is compatible with the bridge circuit design of mainstream strain indicators and can be directly connected without additional impedance matching.
In the development of strain gauge sensors, 350Ω is the recommended specification. Its advantages include: allowing a higher operating voltage, correspondingly improving output sensitivity; a lower operating current, reducing temperature rise caused by self-heating, which benefits long-term stability; and a better signal-to-noise ratio in dynamic measurement scenarios. Currently, the sensor industry shows a clear trend towards higher resistance values. When long cables are subsequently connected, higher resistance offers better anti-interference, but the bridge excitation voltage is limited by the amplifier's input range.
Typical excitation voltage range (e.g., 5~10V is common for 350Ω, and 2~5V for 120Ω), the excitation current is usually controlled within 10～15mA (the limit can reach 30mA on materials with good heat dissipation).
When physical space and circuit conditions permit, higher resistance values should be preferred. An increase in resistance will simultaneously raise the allowable operating voltage and output voltage, thereby increasing sensitivity, while reducing the operating current and thermal effects, which positively contributes to measurement accuracy.
7. Size Selection: Balancing Spatial Resolution and Averaging Effect
The determination of the sensitive grid length (base length) requires comprehensive consideration of stress gradient, material uniformity, and dynamic response requirements.
For areas with uniform specimen material and significant stress gradients - such as stress concentration zones and notch roots - a small grid length (0.2mm to 3mm) should be selected. A shorter grid length improves spatial resolution, allowing more accurate capture of local strain extremes.
For non-uniform materials (such as concrete) or components with gentle stress distribution, a larger grid length (3mm to 100mm) is recommended. A longer grid length produces an averaging effect, making the measurement results more representative of the overall strain level in the area, thus avoiding data dispersion caused by local material differences.
In impact load or high-frequency dynamic measurement scenarios, the sensitive grid length should be minimized as much as possible. Grid length is inversely correlated with the upper measurable frequency limit; shortening the grid length effectively improves dynamic response capability, ensuring that the measurement signal truly reflects the measured strain time history.
Reference for common engineering specifications: The minimum grid length for foil strain gauges is 0.2mm, suitable for precision measurements; general stress analysis primarily uses 1mm to 3mm; for sensor applications, the grid length is matched according to the size of the elastic element's stress zone, with a common range of 1mm to 5mm.
8. Strain Gauge Bonding Process and Protection
The performance of a resistance strain gauge depends not only on the quality of the gauge itself but also on its correct usage. For commonly used bonded strain gauges, the bonding process is a critical step. The following are the key steps and points summarized:
Common problems after bonding:
Abnormal resistance value
Under normal circumstances, the resistance value of the strain gauge remains unchanged or changes slightly after bonding. If the resistance value changes significantly, it may be caused by the following factors:
- Excessive pressure during pressure curing leads to abnormal resistance after bonding; reduce the pressure appropriately;
- Uneven pressure during curing causes deformation of the strain gauge's sensitive grid and abnormal resistance. This issue is mainly due to non-standard pressure fixtures, resulting in uneven stress on the strain gauge;
- The curvature radius of the fixture design does not match the component, causing deformation or bulging of the strain gauge and abnormal resistance;
- If the resistance becomes abnormal after a period of use, the main reasons include bubbles inside the strain gauge, individual voids, or unreliable factors during welding;
- If the resistance remains abnormal after multiple attempts, check whether the multimeter is faulty.
Major defects
The main defects in bonding include voids, bulging (abnormal bridge zero), uneven adhesive layer (strain gauge detachment), excessively thick adhesive layer (poor sensor creep), adhesive ridges, pressure pits, and misalignment (actual strain gauge value smaller than the true value). To address these defects, a visual inspection must be performed after bonding to eliminate defective ones and ensure bonding quality. At the same time, the resistance value and insulation resistance should be checked to avoid waste in subsequent processes.
Wire connection
Check whether the welding is reliable and whether there is any risk of short circuits. Avoid contact resistance.
Resistance strain gauge, Strain measurement, Microstrain, Sensor selection, Stress analysis, Strain, Bonding process, Mechanical testing, Experimental mechanics, Sensor design, Strain indicator, Mechanics of materials, Piezoresistive effect, Industrial measurement.
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