# Extensometer for Determining Strains on a Tensile and Torsion Simultaneous Load

## Abstract

**:**

## 1. Strains Compounded at Simultaneous Loading on an Axial Tensile Force and Torsion Moment

## 2. Comparisons with Other Types of Similar Devices, Description of the Extensometer and Measurement Mode

- The sharp tips 9 are mounted on sample 10, which is loaded under a tensile–torsion combined load;
- The extensometer is mounted on the sample using elastic bands 11 or arcs that pass through the cuttings 8, thereby forcing the easy penetration of the sharp tips through the surface of the sample;
- Once the loading starts, the signals for the strains are retrieved from the two transducers: the tensile and torsional beams;
- Using calibration constants, which will be determined according to the steps below, the real strains will be calculated: tensile strain ε and torsional (shear) strain γ.

_{t}. Thus, the signal retrieved in this case will be:

_{r}).

_{r}results from the torsional loading and is the residual moment for the tensile beam. When the tensile beam is loaded under the bending moment, My

_{r}(Figure 3) the strain gauges mounted on the tensile beam deform as follows:

- The strain gauges m
_{t1}and m_{c1}provide the tensile strains (+ε) that occur on the middle part of the beam 5 subjected to tensile due to the residual moment, My_{r}; - The strain gauges m
_{t2}and m_{c2}provide the compression strains (-ε) that occur on the middle part of the beam 5 subjected to compression due to residual moment, My_{r}.

_{r}(residual for the tensile beam), given by the torsion load, the signal of the linear deformation transducer (the tensile beam) will be zero. Similarly, when the torsion beam is loaded with the bending moment Mz

_{t}(residual for the torsion beam) given by the tensile load, the signal of the torsion deformation transducer (the torsion beam) will be zero. In this way, each specific deformation transducer will provide signals according to the load for which it was designed: tensile or torsion.

## 3. Calibration for Tensile Loading

Observation: This coefficient is valid for the extensometer we built, with its specific shape, used materials, strain gauge placement, dimensions, etc. For any other extensometer built following this description, a proprietary calibration will be required. The calibration tensile coefficient results are characteristic only for our own extensometer.

_{1}, and point B in B

_{1}, when the tensile loading takes place. If the torsional loading continues, point A

_{1}moves to A’

_{1}and point B

_{1}to B’

_{1}. Finally, both initial points (A and B) where the extensometer was mounted will be in A’

_{1}and B’

_{1}after the tensile–torsion loading.

_{0}is the initial length of the bar; Δl is the total elongation of the bar due to tensile loading; γ is the torsional (shear) strain due to torsional loading; a is the initial distance between the mounting points of the extensometer; Δa is the elongation of the bar in the mounting area of the extensometer (a) if only the tensile stress takes place. When the sample is subjected to only tensile loading, the tensile strain is given by the following relation:

_{ext}, will be higher than ε

_{real}because A’

_{1}B’

_{1}> A

_{1}B

_{1}. Under these conditions, the measured signal will contain an error that can be removed based on a computational relationship that will be presented in the following.

_{real}under simultaneous tensile–torsion loading will be calculated based on the signal given by the tensile strain transducer, ε

_{ext}, and torsional strain γ, using Relation (10). The torsional strain is determined based on the signal received via the torsion beam, multiplied by a calibration constant, as shown below.

- ε
_{ext}= 600 με = 600·10^{−6}m/m (where the dimension of με is μm/m); - γ = 250 με = 250·10
^{−6}m/m.

## 4. Calibration for Torsional Loading

_{real}.

Observation: This coefficient is valid for the extensometer we built (i.e., with the specific characteristics, shape and materials, strain gauge positioning, and dimensions. For any other extensometer built as we described, a new calibration needs to be done in order to obtain an appropriate calibration coefficient.

## 5. Conclusions

## Funding

## Conflicts of Interest

## References

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**Figure 4.**Tensile calibration with the Wheatstone bridge connected to the Vishay bridge P3—the signals from the extensometer and control sample are in με.

**Figure 5.**The drawing of the displacement of the fixing points on the sample under tensile–torsion loading.

**Figure 7.**Measuring torsion strain using tensiometric transducers (two strain gauges): (

**a**) mounting strain gauges on the control sample; (

**b**) linking strain gauges in a half-bridge Wheatstone.

**Figure 8.**Calibration with all links of the Wheatstone bridge on the Vishay P3 bridge—the signal from the extensometer is in με.

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**MDPI and ACS Style**

Goanta, V.
Extensometer for Determining Strains on a Tensile and Torsion Simultaneous Load. *Sensors* **2020**, *20*, 385.
https://doi.org/10.3390/s20020385

**AMA Style**

Goanta V.
Extensometer for Determining Strains on a Tensile and Torsion Simultaneous Load. *Sensors*. 2020; 20(2):385.
https://doi.org/10.3390/s20020385

**Chicago/Turabian Style**

Goanta, Viorel.
2020. "Extensometer for Determining Strains on a Tensile and Torsion Simultaneous Load" *Sensors* 20, no. 2: 385.
https://doi.org/10.3390/s20020385