Measurement of Plastic Deformations Using Resistance Strain Gauges

MEASUREMENT OF PLASTIC DEFORMATIONS USING RESISTANCE STRAIN GAUGES

A. V. Anfilofiev, E. N. Muranov

(Presented by the scientific seminar of the Department of Strength of Materials)

Special strain gauges make it possible to measure deformations within the range of 4–15%; ordinary wire gauges, produced in series, within 0.7–4% [1, 2]. The upper measurement limit is reached when only the grid is bonded, since the connection of the wire to the lead is the weakest point of the gauges.

The use of ordinary strain gauges for solving problems of plasticity is of definite practical interest.

In the present work, two methods of bonding gauges for measuring plastic deformations on the surface of deformable bodies are considered.

The first method is based on the known operating principle of transducers of the dynamometric-clip type [3]. By its design the gauge is a rod made of a composite material: constantan strain filaments and a film or paper backing. In the transverse section of the gauge, the strain filaments occupy a very small area and are displaced relative to the central axis in order to ensure electrical strength in the object–gauge contact. The stiffness of the gauge is determined mainly by the stiffness of the backing. The design features of the gauge make it possible to use the strain effect that occurs when it is bent. The gauges are bonded along the arc of a circle in such a way that the strain grid remains unbonded. When the object being strain-measured is deformed, the change in curvature of the arc causes a change in the resistance of the gauge.

The main disadvantages of this bonding method, as compared with the ordinary one, are the low sensitivity of the gauges and the possibility of damaging them during tests. These disadvantages can be partly eliminated if the gauge is first bonded to a bracket made of elastic metal foil with the dimensions of the gauge backing, and the corresponding amplifying equipment is used. In this case, repeated use of the microclip thus formed is possible, analogous to the existing method [4].

Figure 1 presents comparative data on the strain sensitivity of PKB-10-200 gauges with ordinary bonding and in a bent form on a base equal to half the length of the strain grid. Gauges bonded to foil 0.1 mm thick have a sensitivity six times higher than simply bent ones. Deformations were measured with a lever strain meter.

Gutenberger and a VST-3 strain-measuring station. The bent gauges were used to record tensile diagrams of specimens. The maximum permissible strain values were limited by the strength of the adhesive bond between the object and the gauge and amounted to 15–16%. The accuracy of strain measurement was \(10^{-2}\).

When studying the distribution of plastic strains, in many cases the principal directions are known or are determined by preliminary investigations. Therefore, a method of bonding gauges may be applicable here, the essence of which is explained in Fig. 2. In the general case, by orienting the gauges in the directions \(\alpha\) and \(\beta\), from their readings \(\varepsilon_\alpha\), \(\varepsilon_\beta\), the principal strains \(\varepsilon_1\) and \(\varepsilon_2\) can be determined graphically from Mohr’s circle or from the formulas:

Fig. 1. Strain sensitivity of gauges:
○ — under ordinary bonding, × — of a bent gauge,
● — of a bent gauge on metal foil

\[ \varepsilon_1 = \frac{\varepsilon_\alpha \cos^2 \beta + \varepsilon_\beta \cos^2 \alpha} {\cos^2 \beta - \cos^2 \alpha}, \]

\[ \varepsilon_2 = \frac{\varepsilon_\alpha \sin^2 \beta + \varepsilon_\beta \sin^2 \alpha} {\cos^2 \beta - \cos^2 \alpha}. \tag{1} \]

In special cases, for example in torsion, \(|\varepsilon_1| = |\varepsilon_2|\), both gauges are bonded at equal angles to the principal strains. With the angle \(\gamma = \alpha - \beta\) between the gauges, from (1) we obtain

\[ \varepsilon_1 + \varepsilon_2 = \frac{\varepsilon_\alpha + \varepsilon_\beta}{\sin \gamma}. \tag{2} \]

If one strain is sufficiently small, one intermediate direction may be used: \(\varepsilon_2 = \varepsilon_{\min}\), \(\beta = 0\),

\[ \varepsilon_1 = \frac{\varepsilon_\alpha + \varepsilon_2}{\sin^2 \alpha} - \varepsilon_2 . \tag{3} \]

PKB-10-200 gauges, permitting a relative elongation of up to 2%, were used in plastic torsion and bending.

Figure 2 presents theoretical and experimentally calculated data for plastic bending of a strip \((40 \times 80 \times 800\ \text{mm})\) of St. 3 steel. The strains were calculated by (3), taking into account the change in the angle \(\alpha\), which was measured before and after deformation with a toolmaker’s microscope. The error in determining the strains reaches 12% and is evidently caused by a change in the strain-sensitivity coefficient of the gauges [5]; therefore, in order to achieve greater accuracy, it is necessary to have strain-sensitivity curves for the gauges in the plastic region.

The use of two gauges makes it possible to extend the limits of the measured strains by a factor of 2; therefore, this method may be recommended—

...should be used for studying small plastic deformations, while bonding gauges in a bent form is advisable for static measurements of large deformations.

Fig. 2. Plastic bending of a strip (theoretical curve and experimental-calculated deformation values)

REFERENCES

1. S. M. Kutepov. Wire strain gauges for measuring plastic deformations in vessels and apparatus. Khimicheskoe i neftyanoe mashinostroenie, 1968, No. 4.

2. Hoffman Karl. Die Auswahl geeigneter Dehnungmessstreifen (DMS). Automatik, 14, No. 1, 10–17, 1969.

3. A. M. Turichin, P. V. Novitskii. Wire transducers and their technical application. Moscow–Leningrad, Gostekhizdat, 1967.

4. Abramowicz Marian. Sposób kilkakrotnego użycia tensometrycznego czujnika elektrooporowego. Pomiary, automatyka, kontrola, 11, No. 8, 343–344, 1965.

5. I. A. Kozlov, V. G. Bazhenov, V. V. Matveev, V. M. Leshchenko. Study of the strength of machine parts using resistance strain gauges. Kiev, Tekhnika, 1967.