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 2
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.
The components of the measuring chain
For purposes of clarity and comprehensibility, only the uniaxial stress state will be considered below. The block diagram (Fig. 6) shows the flow of the measurement signal. It also shows the influence quantities and their effect in correlation with the important features of the measurement chain. These features and effects are shown in blue if they can affect the zero point.
The measurement object (DUT)
When the measurement object under examination is loaded, the stress σ is exerted in the material. This causes a strain in the material which behaves inversely proportionally to the modulus of elasticity. This material strain can be determined as a surface strain by means of a strain gauge.
The modulus of elasticity exhibits an uncertainty (tolerance of the modulus of elasticity). Extensive examinations on structural steels have shown a variation coefficient of 4.5%. The modulus of elasticity also depends on temperature as an influence quantity and the temperature coefficient of the modulus of elasticity.
If the strain gauge is glued to a surface (such as a bending rod) that is extended convexly, the strain on the measuring grid is greater than on the surface of the component.
The reason for this has to do with the distance from the neutral fiber: The further the measuring grid is from this neutral fiber and the thinner the component, the stronger the measured value becomes. Smaller roles are played by the thickness of the adhesive and the structure of the strain gauge. The change in temperature (∆t) acting together with the temperature coefficient of expansion of the material also causes thermal expansion, which is significant for zero-point related measurements.
Elastic after-effects (caused by relaxation processes in the microstructure of the material) cause the strain of the material to diminish somewhat after spontaneous loading. The formula in the chart exhibits several uncertainties.
Index of formulas
The required input quantity is the material strain. In an ideal case it is identical to the actual strain of the measuring grid on the strain gauge:
In actual practice, however, alignment and other installation errors occur despite great care. The strain gauge, as a spring element subject to mechanical stress, creeps back along its outer edge areas after spontaneous strain due to the strain loading and also depending on the rheological properties of the adhesive and the strain gauge carrier. It also exhibits a slight hysteresis the effect of the strain gauge creeping back is used in transducer construction to minimize material after-effects, which produce an undesirable additional strain, by adjusting the lengths of the transverse bridges not sensitive to strain on the strain gauge. This compensation can only be implemented in experimental stress analysis with a great deal of effort. Increased strain may also occur due to a curved installation surface (see above).
If measuring points are not adequately protected against humidity and moisture, the adhesive and carrier may soak up moisture and swell. This will be expressed as an error fraction in the form of an unintended task-specific strain in the strain gauges.
Moisture content also affects the stability of the measured values as in all methods of measurement (see below strain gauge: insulation resistance). Especially with zero-point related measurements, a test engineer may be uncertain whether he/she is observing the relevant material strain or whether it is simply one of the other effects described above. Because of this, measuring point protection is an essential precondition for reliable results, especially with zero-point related measurements.
This produces the effect that the strain of the measuring grid does not exactly match the material strain in the stress direction.
The strain gauge
The strain gauge converts the strain in the measuring grid into a relative change in resistance proportional to the strain.
The tolerance of the K factor and its temperature sensitivity contribute to the uncertainty.
It should be noted that if the strain is not distributed homogeneously, the average of the strain under the measuring grid is converted into the relative change in resistance. As a result of this, if the wrong active length of the strain gauge is chosen, the values measured for strain and material stress will be too small or too large. This is especially important when determining the maximum values of the mechanical stress peaks metrologically.
The temperature response of the strain gauge affects the zero point. It has an impact with large temperature differences and especially with strain gauges that are poorly adapted to the thermal expansion coefficient of the material (DUT), since they interfere with the action of the compensation effects.
Self-heating (due to electrical power transformed in the strain gauge) has a similar result, as it leads to a temperature difference between the material and the strain gauge. This is the reason why it is possible to set very low excitation voltages on modern measuring amplifiers. Even small bridge output voltages can be accurately amplified by the devices. Caution is advised, however, with thin materials and materials that dissipate heat poorly.
In the case of frequent alternating strain with a large amplitude (> 1500 µm/m) fatigue may occur in the measuring grid material, resulting in a zero drift.
A transverse sensitivity of the strain gauge is present, but it does not produce any significant deviations. In the uniaxial stress state the transverse sensitivity is taken into consideration by the experimental determination of the K factor due to the way the factor is defined.
A linearity deviation of up to 1000 µm/m is negligible for strains.
Penetration of moisture and humidity reduces the insulation resistances, which in turn causes a resistance shunt to the connections of the strain gauge and is generally reflected by instability in the display of measured values. Low-ohm strain gauges are less sensitive to the influence of moisture and humidity.
The measuring amplifier
The input quantity into the measuring amplifier is the relative change in resistance of the strain gauge.
Since it is very small (at 1000 µm/m and with a K factor of 2 it is just 0.2 % or 0.24 Ω out of 120 Ω), there is an addition to the Wheatstone bridge (quarter bridge circuit) in the experimental stress analysis by means of three fixed resistors (usually in the measuring amplifier). The advantages of half- and full-bridge circuits and ways to use them to reduce measurement uncertainties will not be dealt with here.
The connection of a single strain gauge in a quarter bridge circuit is considered here. Usually the correlation between bridge unbalance and relative change in resistance is described with
The actual correlation exhibits a small degree of non-linearity, which will be examined in greater detail below.
The measuring amplifier supplies voltage to the bridge circuit, amplifies the bridge output voltage and generates the measured value.
Deliberately left out of consideration here are measurement errors that can occur due to long supply lead resistances, interference fields, thermoelectric voltages and the measurement electronics themselves.
These can be almost entirely avoided by using well-known technologies (multiwire techniques, extended Kreuzer circuits, shielding designs, modern TF measuring amplifiers).