In many situations where assets are used in the field, knowledge of the stresses and strains that are applied to a structure is an important tool for identifying potential problems [1]. In addition, it is essential to prevent high deformations from compromising the purpose for which the structure or equipment was intended. One of these methods is extensometry.

Generally, mathematical models such as those developed in analyses using the finite element method (FEM) are necessary to predict the behavior of the stresses in a structure. There are some situations, however, in which there is no knowledge of the loads being applied to the object under analysis, compromising the modeling, the reproduction of reality, the results and the definitions of the actions required. In these cases, to avoid these mistakes, experimentation can be an interesting way forward.

Various methods can be used, such as fiber optic sensors, piezoelectric sensors, photoelastic sensors and digital image correlation. In this first part of the article, we will highlight the use of strain gauges as a form of experimentation.

What is an extensometer?

Before introducing the concept, a very interesting fact is that the strain gauge was invented by two different people at almost the same time. Professor Arthur Ruge, from the Massachusetts Institute of Technology (MIT), was one of these inventors; the other was Edward Simmons. At the California Institute of Technology (Caltech) in 1936, Simmons was investigating the stress-strain behavior of metals under shock loads. He was, at the time, a student working as a research assistant at the Institute. The interesting thing is that they were both in very distant places and at that time didn't know each other. [3]

In practice, an extensometer is a sensor that can be fixed and glued to the surface of the object being studied, from which you want to know the deformations and consequently the stresses. It can be, for example, uniaxial or triaxial, as shown in Figure 1. This methodology is very important for checking these parameters, especially when the object (be it a structure, component or piece of equipment) is in operation.

Figure 1: Uniaxial extensometer (left) and triaxial or rosette (right) - SOURCE: SILVA (2019).

Therefore, extensometry refers to the use of this device to measure deformations between two points on solid bodies, which occur when one of them is subjected to a force. This sensor obeys the mechanical deformation of the solid being instrumented as a function of the force/load applied. Basically, these strain gauges experience a change in an electrical parameter, usually resistance, which causes a variation in current. This current variation in the milliamp range is collected and its measured values are interpreted by the data acquisition board and the available computer tool. This interpretation allows the deformation values of the object studied to be known. From there, using Hooke's Law, the deformation values can be transformed into mechanical stress and evaluated in comparison with the structural analysis being carried out. [2]

Hooke's Law

Stress evaluations are based on the work of Robert Hooke ("The power of any springy body is in the same proportion with the extension"), which relates the stresses applied to a given material to the resulting deformation. The law is named after the 17th century British physicist who tried to demonstrate the relationship between the forces applied to a spring and its elasticity.

Extending Hooke's exploration of springs, it becomes apparent that most materials act like springs with force directly proportional to displacement. But compared to springs, other materials have an area that must be accounted for.

The reasoning is that if, for example, a steel cylinder is pulled, the force applied to the object is directly proportional to the deformation caused in the elastic region. In this way, there is a constant relationship between the deformation and the force applied to the object. This means that the force to neutralize the pulling force is generated in the internal structure of the material.

The definition of the magnitude/value of the force applied to the object per unit area is called stress. Basically, stress can be understood as a vector, with its value and direction presented using MPa (megapascal) or any other unit of force value over the unit area. In general, materials commonly used in engineering have the property of stretching when they are pulled and shrinking when they are compressed.

Figure 2 shows the relationship between stress and strain in a given metal specimen that is being tensioned. Up to the point _σE the stress is directly proportional to the strain, where you can see a practically linear slope in the graph. This region is known as the elastic region, where Hooke's law applies.

Figure 2: Stress x strain curve - SOURCE: BEER (2011).

By checking the principle of proportionality observed in the elastic region on the graph and considering that all the material is tensioned in this region, a relationship is obtained between the initial and final length, arriving at Equations 1 and 2:

Equation 1: Strain calculation - SOURCE: BEER (2011).

Equation 2: Calculation of the stress and strain ratio - SOURCE: BEER (2011).

Where:

∆L = change in length [m or other unit of length].

L= object length [m or other length unit].

ε = Strain - specific deformation [dimensionless].

σ = Stress - stress value that is measured by the average force per unit area [Mpa or other unit of force over area].

E = longitudinal modulus of elasticity (Young's modulus) [GPa or other unit of force over area], which is a specific proportionality constant for each material.

When and how to use extensometry?

The use of strain gauges to solve non-conformities in structural assets, components and equipment is important for promoting Structural Integrity. The installation on a yard machine can be seen in Figure 3. In short, various engineering disciplines (Aeronautical, Civil, Mechanical, Geotechnical, among others) regularly use strain gauges to detect faults in structures and assets, where these non-conformities would have a major human and financial impact.

Figure 3: Yard machine instrumentation using extensometer - SOURCE: Kot Collection.

There are other ways of promoting the Structural Integrity of assets, one of which can be seen here. This non-destructive test can also be carried out preliminarily and in conjunction with extensometry, for example, to identify non-conformities and then carry out an instrumentation plan.

A common application is in the structural evaluation of rail and road vehicles. Instrumentation can be carried out on cars, trucks, trailers, wagons, rails, couplings or other structures from which it is desired to obtain the deformations during the operation of the asset. Initially, the installation points for the sensors are determined, and then the plan is carried out.

It should be noted that knowledge of all the theory behind extensometry and asset instrumentation methods is crucial for a correct structural assessment. Often, the use of strain gauges is possible, but will not bring the desired results. On other occasions, the use of FEM in conjunction with this method is recommended. 

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References:

[1] SILVA, Anderson Langone et al. A study of strain and deformation measurement using the Arduino microcontroller and strain gauges devices. Revista Brasileira de Ensino de Física, v. 41, n. 3, 2019.

[2] ŞTEFĂNESCU, Dan Mihai. Strain gauges and Wheatstone bridges-Basic instrumentation and new applications for electrical measurement of non-electrical quantities. In: Eighth International Multi-Conference on Systems, Signals & Devices. IEEE, 2011. p. 1-5.

[Technology and practical use of strain gages: with particular consideration of stress analysis using strain gages. John Wiley & Sons, 2017.

[4] BEER, Ferdinand P. et al. Mechanics of materials. Amgh, 2011.

[5] BIELEN, Paul; LOSSIE, Mieke; VANDEPITTE, Dirk. A low cost wireless multi-channel measurement system for strain gauges. In: Proceedings of ISMA. 2002. p. 663-670.