ON THE QUESTION OF THE MECHANICAL FRACTURE OF SOLID DIELECTRICS UNDER THE ACTION OF SHORT ELECTRIC PULSES

A. A. VOROB'EV

Three forms of breakdown of solid dielectrics are distinguished: thermal, electrochemical, and electrical. The thermal and electrochemical forms of breakdown are associated with ionic processes in the dielectric. The electrical form of breakdown is described as an electronic process in a solid dielectric, associated with the motion and interaction of electrons with the lattice [1].

The electrical strength of ionic crystals increases with increasing lattice energy. The hardness and elastic moduli of crystals also increase with increasing lattice energy. Crystals having higher mechanical strength also have higher electrical strength, which is a consequence of the identical dependence of electrical and mechanical strength on the lattice energy.

It has repeatedly been proposed to explain the electrical breakdown of solid dielectrics as their mechanical fracture in an electric field.

The breakdown site of a dielectric under the action of short electric pulses presents a typical picture of mechanical fracture, with characteristic cracking along the edges of the channel. Such a picture is observed in brittle fracture of a material. If the energy of the pulse is large, the dielectric is broken into separate pieces.

The connection between electrical and mechanical fracture of solid dielectrics, with the aim of explaining electrical breakdown by the mechanical rupture of bonds between particles of the body, has repeatedly been attempted [1].

One of the first explanations of the phenomenon of electrical breakdown of solid dielectrics by mechanical fracture as a result of the rupture of bonds between ions by an electric field was proposed by Rogowski [1].

Calculations using the formulas of the theory of electrostatic rupture of bonds led to an electrical strength two orders of magnitude higher than the values measured in practice.

This was one of the main reasons for rejecting Rogowski’s theory and other analogous explanations of breakdown.

Lemkehaus [1] assumed that, in the breakdown of dielectrics by pulses with a front of less than \(10^{-7}\) sec, mechanical fracture of the material occurs. The short-term action of the electric wave produces a mechanical shock and a crushing effect.

Certain regularities of electrical breakdown known at the present time make it possible to reconsider the possibility of mechanical destruction of dielectrics in an electric field.

Numerous investigations of the influence of mechanical deformations on the electric strength of various solid dielectrics have led to the conclusion that secondary processes during deformation have a complex influence on electric strength. Compaction of the material during deformation entails an increase in its electric strength; cracking is accompanied by a decrease in electric strength.

Despite the complexity of the secondary phenomena in both electrical and mechanical destruction of solid dielectrics, a connection has nevertheless been noted between identical changes in the electric strength and hardness of crystals and changes in their lattice energy.

Under the action of an electric field \(E\) in a dielectric whose dielectric constant is \(\varepsilon\), mechanical stresses arise. The magnitude of the pressure in \(\mathrm{dyn}/\mathrm{cm}^2\) is determined by the formula [1]:

\[ P=\frac{\varepsilon E^2}{8\pi}. \]

The mechanical forces in dielectrics increase in proportion to the field strength.

The table presents the value of the electric strength at constant voltage and the pressure, calculated by formula [1], that arises in a dielectric under such a field.

Since, simultaneously with an increase in the electric strength of alkali-halide crystals, their dielectric constant also increases as a consequence of the increase in the density of the substance, the mechanical stresses in these crystals [1] increase faster than in proportion to the square of the electric-field strength, as is seen in Fig. 1.

According to data of V. D. Kuznetsov [2], the strength of crystals of alkali-halide salts has not been precisely determined. The tensile strength of KI crystals varies within the limits from 15 to 35 \(\mathrm{kg}/\mathrm{cm}^2\); for KBr—from 16 to 40 \(\mathrm{kg}/\mathrm{cm}^2\); for rock-salt crystals—from 16 to 50 \(\mathrm{kg}/\mathrm{cm}^2\), etc.

Table

The pressure experienced by the dielectric before breakdown at constant voltage is only an order of magnitude smaller than the measured mechanical strength of it and several times smaller than the value of the minimum mechanical strength.

With increasing lattice energy, the magnitude of the mechanical forces sustained by the crystal before breakdown increases, as follows from Fig. 2. The quadratic dependence shown in Fig. 2 is a consequence of the approximately linear dependence between the magnitude of the electric strength and the lattice energy.

The propagation of discharges in deformed rock-salt crystals under various conditions was studied [1]. Mechanical stresses

in crystals were observed by an optical method. Electrical discharges, while destroying the crystal, do not create mechanical stresses in it.

Experiments showed that discharges in crystals proceed along the boundary of mechanically stressed regions, where the gradient of mechanical stresses is greatest.

Fig. 1. Dependence of the mechanical stresses arising in crystals before breakdown on the square of the breakdown field strength.

Figure 3 shows a discharge from the positive point in a rock-salt crystal and the mechanical stresses in it, when observed in a direction perpendicular to the propagation of the discharge. The discharge went along the boundary of the region of plastic deformation and, having reached the face of the crystal, was reflected from it into the interior of the crystal.

Fig. 2. Dependence of the mechanical stresses arising in crystals before breakdown on the energy of the crystal lattice.

Figure 4 shows the mechanical stresses in polarized light after strong plastic deformation of the crystal and a discharge in it [3].

In plastically deformed crystals, a discharge, crossing a slip plane, changes its direction at its boundary. In crystals only slightly disturbed by deformation, discharges propagate along the boundary of mechanically stressed volumes.

Fig. 3. Photograph of a discharge in rock salt from the positive point in the presence of mechanical stresses

Fig. 4. Mechanical stresses in crystals under strong fields (photograph in polarized light) and an electric discharge

Cooper and Wallace [3] observed the occurrence of plastic deformation in single crystals of KCl in a uniform electric field under the action of a voltage pulse (50 μsec) [1]. The observations were carried out with the field applied in the directions of a cube face, a face diagonal of the cube, and a body diagonal of the cube. Before the action of the voltage pulse on the specimen, mechanical stresses in it were not observed by the optical method.

Fig. 5. Photograph of the observed field brightening in polarized light under the action of high voltage

... If breakdown of the specimens as a result of their defectiveness occurred at a field strength of about \(0.7\ \mathrm{MV/cm}\), then after exposure to a field of such strength no plastic deformation was observed in the specimens. After exposure to a field strength on the order of \(0.8\ \mathrm{MV/cm}\) and higher, residual deformation was observed optically in all specimens, as is seen in Fig. 5. With increasing field strength, the dimensions of the deformed region increased. Breakdown of specimens with higher electric strength was preceded also by greater deformation.

Thus, after exposure to an electric field of high strength, residual mechanical stresses arise in the crystals, and electrical breakdown of crystals having high strength is always preceded by plastic deformation and, possibly, by mechanical fracture.

According to the theory of impact ionization by electrons, the electric strength of ionic crystals should decrease with decreasing temperature and with decreasing scattering of electrons by phonons.

In Fig. 6 are presented the dependences of the electric strength of potassium salt on temperature at constant voltage according to the theories of Fröhlich [1] and V. A. Chuenkov [4] and according to experimental data of various authors [1], [4]. In the region of high temperatures, after the maximum value is reached, the electric strength decreases with increasing temperature as a result of thermal breakdown.

Fig. 6. Temperature dependences of the electric strength of certain crystals of alkali-halide salts.

1—according to Hippel’s theory, 2—according to Chuenkov’s theory, 3—according to the data of Hippel and Alger, 4—according to the data of Calderwood and Cooper, 5—according to the data of V. D. Kuchin, 6—according to Fröhlich’s theory, 7—according to the data of Buehl and Hippel.

The experimentally observed increase in the electric strength of ionic crystals with increasing temperature at constant voltage, in thermal and electrical breakdown of rock salt, agrees with the theoretically expected dependence.

In Fig. 7 is presented the dependence of electric strength on temperature for single crystals of NaCl, KCl, KBr, and KI under breakdown by short pulses with a front duration of \(3 \cdot 10^{-8}\ \mathrm{s}\), according to measurements by V. D. Kuchin [5].

The magnitude of the electric strength of ionic single crystals increases with increasing lattice energy and does not depend on temperature in the interval investigated.

The independence of the electrical strength of crystals from temperature over a wide interval under short electric pulses contradicts the theory of impact ionization by electrons and is in agreement with the conclusions of the theory of electrostatic ionization.

Fig. 7. Temperature dependences of the electrical strength of single crystals of NaCl, KCl, KBr, and KI, obtained at an exposure of \(3 \cdot 10^{-8}\) sec.

Stark and Garton [6], measuring the electrical strength of polyethylene irradiated with electrons of energy \(4\) MeV at a dose of 150–300 mkrad, found that the change in the electrical strength of polyethylene with temperature is analogous to the change in Young’s modulus with temperature.

From a comparison of the theoretical and experimental results, the authors came to the conclusion that, in the case studied, a new form of breakdown takes place, associated with the mechanical deformation of the dielectric.

Under the action of a short voltage pulse of \(10^{-8}\) sec, when the electrical strength exceeds the static strength by several times, the mechanical stresses arising in the dielectric cause its destruction before prebreakdown electronic processes can develop.

REFERENCES

1. Vorob’ev A. A. and Zavadovskaya E. K. Electrical Strength of Solid Dielectrics. G.I.T.T.L., 1956.
2. Kuznetsov V. D. Physics of the Solid State. Izd. “Krasnoe Znamya,” Tomsk, 1941.
3. Cooper R. and Vallance A. A. Proc. Phys. Soc. B. 66, 1113 (1953).
4. Chuenkov V. A. Izv. Tomskogo politekhn. in-ta, 91, 45, 1956.
5. Kuchin V. D. DAN SSSR, 114, 301, 1957.
6. Stark K. H., Garton C. G. Nat 176, No. 4495, 1225, 1955.