Our series of articles addresses possible sources of error when strain gauges are used in experimental stress analysis and shows how to successfully assess measurement uncertainty already in the design stage

# Series of articles: Measurement accuracy in experimental stress analysis – part 4

Strain gauge technology has been optimized over the course of decades with a wide range of options to compensate for errors. Yet there are still effects that have a negative impact on measurements. The objective of this paper is to point out the numerous (and often avoidable) sources of errors when using strain gauges in experimental stress analysis and to provide some help in estimating the measurement uncertainty early on in the planning phase.

## Estimating the measurement uncertainty for zero-point related measurements

In these measurements, the zero point is important. These are typically long-term measurements on buildings and fatigue tests on components. If the zero point changes during measurement tasks of this type, the result is an additional measurement error. The measurement uncertainties discussed already in the last part of this series must be added to the ones noted in this section.

## Thermal expansion of the DUT, temperature response of the strain gauge, radius of curvature

It is assumed below that under unfavorable circumstances, it will not be possible to eliminate the temperature effect with an additional compensation strain gauge in the bridge circuit.

The material of the component has a coefficient of thermal expansion. The thermal expansion will not be measured, as it is simply the result of temperature as an influence quantity. The measuring grid also has a coefficient of thermal expansion as well as a temperature coefficient of the specific electrical resistance. Since only strains induced by loading are of interest in ESA, the strain gauges that are offered are adapted to the thermal expansion of specific materials. However, all these temperature coefficients are themselves a function of the temperature so this compensation will not be entirely successful. The remaining deviation ΔƐ can be calculated with a polynomial. The coefficients of the polynomial are determined batch-specifically and are specified by the manufacturer on the strain gauge package.

An example of a strain gauge (HBM type LY-6/120) can be found here.

The current should be inserted in °C (but without dimensions). Then the remaining deviation (apparent strain) will be determined in μm/m. For a temperature of 30 °C, the resulting apparent strain is -4.4 μm/m.

If the ambient temperature deviates significantly more from the reference temperature (20 °C) or if the strain gauge is actually adjusted incorrectly, much greater deviations will occur. These are systemic in nature and can be eliminated by calculations (online as well). On the other hand, the equation already exhibits an uncertainty that increases by 0.3 μm/m per Kelvin of temperature difference from 20 °C. At a temperature of 30 °C, the uncertainty of the polynomial is 3 μm/m.

The only requirements for the correction calculation are to know the thermal expansion coefficient of the material and the ambient temperature.

## Self-heating

This refers to the increase in temperature resulting from converted electrical power in the strain gauge. The heat output is determined as follows:

For a root mean square value of 5 V for the bridge excitation voltage and a 120 Ω strain gauge the resulting heat output is 52 mW. A strain gauge with a measuring grid length of 6 mm applied with a thin layer of adhesive on steel or aluminum is able to give off the heat sufficiently to the measurement object. A small temperature difference will nevertheless arise between the strain gauge and measurement object, which will lead to an apparent strain (see above):

If the temperature of the adjusted strain gauge is just one Kelvin above the material temperature, there is already an apparent strain of -11 μm/m (ferritic steel) or -23 μm/m (aluminum). The measurement uncertainty can be roughly determined with a simple experiment - the excitation voltage is connected while the load is not applied to the component. In the temperature increase phase, the measured value will drift slightly (zero drift). The greatest difference between measured values during this thermal compensating process corresponds roughly to the maximum expected deviation.

Lower excitation voltages provide a remedy (1 V generates only 2 mW). Strain gauges with higher resistances are also advantageous in this respect.

*For components with poor heat conductance (plastics, etc.) and when very small strain gauges are used, lowering the excitation voltage is indispensable. Caution is always advised when working with rapidly changing temperatures. Compensation effects resulting from adjusting the metal foil of the strain gauge to the material being examined have a time constant.*

## Swelling of adhesive and measuring grid carrier

The main cause of this is the high mobility of water molecules and the hygroscopic properties of the adhesives and carrier materials. The effect is a zero drift that is not clearly discernible (or distinguishable from the material strains). It may take on considerable values. A strain is measured which does not exist, at least in the component being examined. This parasitic strain is only partially reversible, which is probably due to the sorption hysteresis. Unfortunately there is no way to “grab a hair dryer” and drive out the water molecules. The speed at which the measured value drifts depends on the measuring point protection and ambient conditions. The time constant may be in the range of many hours. A high temperature and a high relative humidity are especially critical. Unfortunately no concrete formulas or figures can be given here.

## Insulation resistance

Residue of flux material can also absorb water molecules. This appears in practical applications as a “breathing display” which is often discernible in fluctuating measured values due to a draft or similar cause. Experienced testers will recognize the warning and meticulously clean all contact points. “Baking out” the residue is also possible in some circumstances. However, all these countermeasures require that the moist parts are not already enclosed under the protective cover of the measuring point, which they often are for good reason. It has proven practical when the measuring point is prepared for covering, to heat it a few degrees Kelvin compared to the prevailing ambient temperature, and then cover it immediately. This will exclude the possibility of condensation forming later under the cover. If the insulation resistances are too low, zero drift of measured values will occur. The insulation resistances within the bridge circuit are extremely critical in this case. Faulty electrical insulation of strain gauge contacts between each other is comparable to a resistance shunt. It cannot be measured directly, but due to its nature, is similar in magnitude to the insulation resistance. The correlation between the apparent strain and shunt is as follows:

This eq. shows that the effect is lower with high-resistance strain gauges. The following measurement errors are determined for 120 Ω strain gauges (gauge factor = 2):

Under “normal” circumstances, insulation resistances greater than 50 MΩ can be achieved and the deviations of less than **1.2 μm/m** are negligible.

At 500 kΩ and with a measured value of 1000 μm/m. the zero error would already be -12%! This shows clearly that a significant drop in insulation resistances could cause the measuring point to fail. Strain gauge transducers have insulation resistances of several GΩ.

A high relative humidity with high temperature at the same time (such as saturated vapor) is critical because it leads to a high water vapor pressure. The tiny water molecules push forward and gradually overcome the measuring point protection. It is impossible to predict without a test whether the measuring point will fail after just a few days or several years.

## Fatigue

Signs of fatigue in the strain gauge measuring grid appear during dynamic loading of the component that are expressed in a zero drift (apparent strain in the material). The greater the alternating strain amplitude and the greater the number of load cycles, the greater the effect (Fig. 10).

The installation and the arithmetic mean of the strain also affect the zero drift. If the average is negative, the fatigue life improves. If the value is positive, it deteriorates. Practically no zero drift may be expected for alternating strains with an amplitude up to 1000 μm/m. Greater amplitudes are more critical. A zero error of 10 μm/m may be expected for:

1500 μm/m and approx. 2 mil. load cycles

2000 μm/m and approx. 100,000 load cycles

2500 μm/m and approx. 4000 load cycles

3000 μm/m and approx. 100 load cycles

Note that the test specimen also undergoes fatigue. If its resistance to alternating loads is greater than that of the foil strain gauge, use of optical strain gauges should be considered (fiber Bragg grating).

## Summary of all partial uncertainties

While the deviations in section 3.3 are multiplicative in effect and are indicated as a percentage of the measured value, the deviations in this section have an additive effect. The unit of measurement is μm/m and they are practically independent of the measured value. If the relative deviation is calculated with eq.,

the value is comparable to those in section 3.3.

If the values in bold type above are combined using Pythagorean addition, the result is 16.01 μm/m. Since measurement uncertainties should not be rounded, the uncertainty for the zero point is **17 μm/m**. With a strain of 1000 μm/m, the deviation expressed as a percentage is 1.7%, which is certainly reasonable. It is clearly critical with small strains: 17 μm/m of 100 μm/m is already **17%**.

Now the uncertainty of the zero point (1.7% or 17%) must still be added to the uncertainty from section 3.3 (3% for the strain measurement).

The result of Pythagorean addition is:

4% with a measured value of 1000 μm/m,

18% with a measured value of 100 μm/m.

Usually the mechanical stress is the actual measured quantity so its uncertainty must be estimated. The uncertainty of the stress measurement calculated in section 3.3 is 6%. Including the uncertainty of the zero point (1.7% or 17%) with Pythagorean addition, the result is:

7% with a strain of 1000 μm/m,

19% with a strain of 100 μm/m.

Large relative measurement errors occur with zero-point related measurement tasks, especially with small strains.

## Installed Strain gauges

## The effect of the installer

It has been assumed so far that the installation of the strain gauge measurement point was well planned and conscientiously executed. For this reason, only a few of the individual deviations in the examples above exceeded the set range. Although it is unfortunately necessary to point out that if the installation is performed very poorly, the measurement errors could assume arbitrarily large values. Imagine for a moment that a very long strain gauge was used to try to measure a notch stress, or that contact resistances to the strain gauge fluctuate by 0.24 Ω (equivalent to a strain error of 1000 μm/m for a 120 Ω strain gauge).

Especially in zero-point related measurements over long periods of time, the importance of measuring point protection cannot be overestimated. An excellent example is the 44 strain gauge measuring points on the FINO 1 research platform (overall height 129 m) in the North Sea (45 km North of Borkum Island). The strain gauges are located 5 to 25 m below the surface of the ocean. Their task was to measure loading strains on the support frame of the platform caused by pile drivers and by waves and wind. After two years in North Sea water, 42 measuring points were still fully functional.

Another gross error is if the strain gauge has only a partial internal connection with the surface of the component being examined. Causes may include: poor cleaning or improper handling of the application surface and superimposed adhesive. These causes must and can be avoided. The rubber eraser test generally clarifies the situation. Although it may be possible to dispense with measuring point protection for a short-term measurement (tensile test), installation of strain gauges requires a conscientious approach and frequently a good measure of experience. There is probably no other method of measurement in which the knowledge and experience of the person performing the task play such an important role. This is why companies and institutes are more and more frequently taking advantage of the possibility of certifying their personnel according to VDI/VDE/GESA 2636 on various qualifying levels.