STUDY OF THE DYNAMIC SHEAR MODULUS OF POLYMER FILMS

V. M. ANIKEENKO, G. M. KRIVORUCHKO

(Presented by the scientific seminar of the Department of Electrical Insulation and Cable Engineering)

The elastic moduli of polymers are used to characterize the service properties of products. Since the operating conditions of products differ in the presence of mechanical effects in the form of static and dynamic loads, the action of elevated temperatures and moisture, and also the duration of their action, the degree of their manifestation in the form of deformations and internal stresses will be different. Often these effects can be evaluated using the actual values of the elastic modulus [1, 2], which we must have for the entire temperature interval.

In the case of polymer films, especially those used in winding wires, knowledge of the elastic modulus makes it possible to determine the internal stresses in the insulation at elevated temperatures.

Various methods may be used to study the elastic modulus in polymer materials, making it possible either to estimate the value of the modulus directly from the magnitude of the deformation or to find it through the shear moduli [3, 4, 5, 6].

For the study of polymer films, the method of freely damped oscillations [6] was chosen. This method makes it possible to measure the dynamic characteristics of films in all physical states, i.e., over a wide temperature interval. For the study, an instrument was reproduced and a torsion fiber 0.1 mm in diameter made of steel wire was selected, with the calculation that the rigidity of the film specimens would be higher than the rigidity of the torsion fiber.

The experiment was carried out with continuous heating of the films at a rate of 0.5–1 degree/min.

For the study, a polyimide film and films of polyester (F-35), polyurethane (UL-1), polyepoxyimide (PE-955), polyepoxycyanurate (PE-958), and polyvinylformal-ethylal varnishes (VL-931) with a thickness of 30–50 μm were used. The film specimens were double-sided paddles with a length of the working part of 30 mm and a width of 4 mm.

The experiment showed that, for calculating the dynamic shear modulus \((G)\) [6], the formula

\[ G=\frac{I f \omega_k^2}{\omega_2^2} \left[ \omega_k^2\left(1+\frac{\lambda_k^2}{4\pi^2}\right)-\omega_2^2 \right] \]

can be simplified, since \(\lambda_k\) varies within the limits 0.1–0.4,

and therefore the quantity \(\lambda_k^2/4\pi^2\) may be neglected. For the calculation we used the expression

\[ G=\frac{I}{K}\left(\omega_k^2-\omega_2^2\right), \]

where \(I\) is the moment of inertia of the system;
\(K\) is the shape factor of the specimen [4];
\(\omega_k\) is the oscillation frequency of the “specimen—torsion” system;
\(\omega_2\) is the natural oscillation frequency of the torsion element.

Figures 1 and 2 present the results of studying the films as a function of temperature in the range \(20\text{--}200^\circ\mathrm{C}\).

Fig. 1. Dependence of \(\lg G\) on temperature for films: 1—polyimide, 2—polyester \((F=35)\)

Fig. 2. Dependence of \(\lg G\) on temperature for enamel-varnish films:
1—VL-931; 2—PE-955; 3—UL-1; 4—PE-958

All the films, with the exception of the polyimide film, are thermosetting polymers with varying degrees of structuring, with a value of

sections—segments between cross-linking nodes and, consequently, have different mobility of the links. A polyimide film contains a large number of rings in the molecule and therefore has a rigid structure. The mobility of the segments of a polyimide molecule is small and changes little with temperature. This is what determines the character of the change in \(G\) with temperature (Fig. 1). In the temperature interval \(20\text{–}200^\circ\mathrm{C}\), the value of \(G\) changes by practically a factor of 1.05. For films of VL-931 varnish this change amounts to a factor of 1.2, UL-1—a factor of 1.23, PE-955—a factor of 1.24, etc.

During aging of enamel films for 240 hours at \(180^\circ\mathrm{C}\), the shear modulus increases within the range of 1.05–1.2 times, but the character of the dependence \(\lg G = f(t^\circ)\) in the given interval of aging time practically does not change. This indicates additional structuring of the film during aging under the specified conditions.

Thus, in structured films the shear modulus changes only slightly, and this can be explained by the fact that in the temperature range \(20\text{–}200^\circ\mathrm{C}\) no substantial rearrangement of molecules occurs; this is observed least of all in rigid-chain, polycyclic polymers.

REFERENCES

1. I. P. Zemlyakov. Strength of Plastic Parts. Mashgiz, 1972.
2. A. N. Raevskii. Polyamide Bearings. Mashgiz, 1967.
3. Yu. G. Yanovskii, E. A. Dzyura. “Factory Laboratory,” 1969, No. 1.
4. Yu. G. Yanovskii. “Factory Laboratory,” 1966, No. 6.
5. Yu. G. Yanovskii, E. A. Dzyura. “Mechanics of Polymers,” 1968, No. 6.
6. Yu. G. Yanovskii. “Factory Laboratory,” 1969, No. 12.