PULSED ELECTRICAL BREAKDOWN AND FRACTURE OF NONCONDUCTING MATERIALS AT ELEVATED PRESSURES

I. I. Kalyatskii, V. V. Krivko

(Presented by the scientific seminar of the Department of High-Voltage Engineering)

The technological process in certain branches of industry is associated with the fracture of very strong nonconducting materials, including rocks.

In recent years, intensive searches have been under way for new, effective methods of fracturing solid bodies. Among the fracture methods being developed, methods using electrical energy occupy a special place. Therefore, the study of the electrical characteristics of various solid materials is of scientific and practical interest.

Rocks occurring at great depths are subjected to high pressures and temperatures, which may influence the electrical characteristics of rocks and the effectiveness of their fracture during electrical breakdown.

In the published domestic and foreign literature there are no data on the pulsed breakdown voltage of rocks at elevated pressures.

The present work is devoted to studying the effect of pressure on the pulsed breakdown voltage and fracture of certain rocks and solid dielectrics.

Experimental procedure

The study of the influence of pressure (up to 150 kg/cm²) on the pulsed breakdown voltage of solid nonconducting materials was carried out on rocks: quartzite, felsite-porphyry, marble, and natural crystalline rock salt.

The rock and rock-salt specimens had a rectangular shape, with dimensions of \(40 \times 40 \times 20\) mm, with conical recesses and an applied metallic electrode layer. The thickness of the specimen at the breakdown site was measured with an IZV-1 instrument with an accuracy of up to 0.01 mm. An electrode system of the “rod–plane” type was used in the work.

Breakdown of the specimens was carried out in a special high-pressure chamber. The chamber was a steel cylinder 120 mm in diameter and 700 mm high, with hermetically sealed flanges. Pulsed voltage of up to 300 kV was introduced into the chamber through a section of RK-162 cable with the metallic braid removed. Work-

ing medium in the chamber was transformer oil with an electric strength of 30 kV in a standard breakdown tester. The pressure in the chamber was produced by means of a piston-type hydraulic press and was measured with a pressure gauge to an accuracy of 0.5 kg/cm².

As a source of single aperiodic high-voltage pulses, a seven-stage pulse-voltage generator assembled according to the Arkad’ev–Marx circuit was used in the work. The maximum generator voltage was 400 kV, the discharge capacitance \(0.0135 \cdot 10^{-6}\) F, and the pulse energy about 1000 J. The generator made it possible to obtain high-voltage pulses with a minimum front length of \(0.3 \cdot 10^{-6}\) sec. Increasing the length of the pulse front was accomplished by switching in inductance and capacitance.

Breakdown of solid materials at elevated pressures was carried out on the pulse front. The high-voltage pulses were applied to the rod electrode; the plane electrode was grounded. The amplitude and duration of the pulse were recorded with an OK-19M oscilloscope connected through an ohmic voltage divider with a resistance of 3000 ohms.

Each experimental point corresponds to the arithmetic mean of breakdown voltages obtained from processing 20 or more oscillograms.

The investigation of the influence of increased hydrostatic pressure on the efficiency of destruction of solids under pulsed electrical breakdown was carried out on rock salt. In this case the specimens had a rectangular shape with dimensions \(40 \times 40 \times 10\) mm, without a conical recess.

The efficiency of destruction of rock-salt specimens under pulsed electrical breakdown was evaluated by the magnitude of the cracking zone in the specimen. The cracking zone was determined with a Pulfrich photometer and by direct measurement.

Experimental Results

Figure 1 presents the dependence of the pulsed breakdown voltage of quartzite, felsite-porphyry, and marble on pressure. The pulses were of positive polarity, with a duration of \(0.5 \cdot 10^{-6}\) sec. Figure 1 also shows the dependence of the breakdown voltage of transformer oil on pressure for the same experimental conditions.

As can be seen from Fig. 1, the breakdown voltages of quartzite and felsite-porphyry, as the pressure increases from atmospheric to 50 kg/cm², increase by 12 and 21%, respectively (curves 2 and 4). A further increase in pressure from 50 to 150 kg/cm² has no effect on the breakdown voltage of these rocks. With an increase in pressure from atmospheric to 50 kg/cm², the breakdown voltage of marble increases from 80 to 115 kV, i.e., by 43% (Fig. 1, curve 3), and, beginning at a pressure of 50 kg/cm², it proves to be higher than the pro-

Fig. 1. Dependence of the breakdown voltage of transformer oil (1) and rocks on pressure (positive-polarity pulses with a duration of \(0.5 \cdot 10^{-6}\) sec): 2 — quartzite, 3 — marble, 4 — felsite-porphyry.

breakdown voltage of felsite-porphyry. The greatest increase in the breakdown voltage of marble (29%) occurs when the pressure is changed from atmospheric to 50 kg/cm², just as for quartzite and felsite-porphyry.

The increase in the pulse voltage of the rocks studied with increasing pressure is apparently associated with two factors:

1) with a certain strengthening of the gas pores of the rock under pressure;
2) with intensive penetration into the pores of the rock of transformer oil, whose breakdown voltage, for a pulse duration of \(0.5 \cdot 10^{-6}\) sec, is higher than the breakdown voltages of quartzite, felsite-porphyry, and marble and does not depend on pressure (Fig. 1, curve 1).

The compressibility of rocks in the pressure range up to 150 kg/cm² amounts to a few percent [1–3] and cannot affect the formation of the discharge or the magnitude of the breakdown voltage. With increasing hydrostatic pressure, the rate of penetration of the working (insulating) liquid into the pores of the rock increases. The volume of the specimen impregnated with liquid during the time the specimen remains in the chamber during the breakdown experiment also increases. For example, at a pressure of 50 kg/cm², in 2 min a quartzite specimen measuring \(40 \times 40 \times 20\) mm is impregnated to a depth of 3 mm, while at a pressure of 150 kg/cm² it is impregnated to 8 mm. It should be noted that the ratios of the percentage increases in the breakdown voltages of quartzite, felsite-porphyry, and marble when the pressure is changed from atmospheric to 150 kg/cm²—equal to 12, 21, and 43%, respectively—are approximately proportional to the ratios of their porosity values, which are respectively 2.7, 3.0, and 5.4%. Thus, the greatest increase in breakdown voltage with increasing pressure is observed in the rock with the greatest porosity (in this case, marble).

The possible influence of impregnation of rocks with transformer oil under pressure on the magnitude of their breakdown voltages is confirmed by the results of additional experiments.

Fig. 2. Dependence of the breakdown voltage of marble on pressure for positive-polarity pulses of duration \(0.5 \cdot 10^{-6}\) sec.
1 — specimens without lacquer coating; 2 — specimens coated with Bakelite lacquer.

Figure 2 presents the dependence of the pulsed breakdown voltage of marble on hydrostatic pressure. The pulses were of positive polarity, with a duration of \(0.5 \cdot 10^{-6}\) sec. One batch of marble specimens was prepared as indicated above. The surface of the specimens of the other batch was covered with a film of Bakelite lacquer. The thickness of the lacquer coating was 0.01 mm. The lacquer film eliminated

impregnation of the marble specimens with transformer oil during their breakdown in the pressure chamber. It is evident from Fig. 2 that, for specimens without a varnish film (curve 1), the breakdown voltage increases by approximately 40% as the pressure is raised from atmospheric to 150 kg/cm² (as in the first experiments). For specimens protected by a film (curve 2), the breakdown voltage remains constant as the pressure is varied within the indicated interval.

Pulsed electrical breakdown of solids is accompanied by a powerful short-time release of energy in a narrow conducting channel. With sufficient energy and power in the channel of a pulsed discharge in a solid, the high-pressure shock waves that arise lead to mechanical destruction of the body, caused by rupture of its continuity and crack formation. By varying the parameters of the discharge circuit, as well as the parameters of the pulse, it is possible to regulate the amount and rate of energy release in the discharge channel, and consequently the effectiveness of destruction of solid nonconducting and semiconducting bodies during their pulsed electrical breakdown.

Fig. 3. Dependence of the diameter of the cracking zone in rock salt during through pulsed breakdown on pulses of positive polarity of duration \(0.6\cdot 10^{-6}\) sec and different amplitudes.
\(1\)—254 kV, \(2\)—210 kV, \(3\)—170 kV, \(4\)—120 kV.

Figure 3 presents the dependence of the diameter of the cracking zone in rock-salt specimens during pulsed breakdown on hydrostatic pressure. The pulses were of positive polarity, with duration \(0.5\cdot 10^{-6}\) sec and amplitudes of 120, 170, 210, and 254 kV. The discharge capacitance of the generator was 13,500 pF.

Since, at atmospheric pressure, the rock-salt specimens used were completely destroyed into 3–4 parts or more during breakdown by pulses of minimum amplitude (120 kV), a pressure of 25 kg/cm² was taken as the initial pressure.

As is evident from Fig. 3, with increasing pressure from 25 to 150 kg/cm², the diameter of the cracking zone decreases. The relative decrease in diameter with increasing pressure in this interval is about 30% and is approximately the same for pulse amplitudes of 120–154 kV.

The destruction of solid dielectrics and other nonconducting bodies during their pulsed breakdown, in our opinion, occurs owing to compressive stresses at the shock-wave front, as well as tensile stresses caused by reflection of elastic waves from the free surfaces of the specimens.

Under conditions of elevated pressures, the specimen being broken down is subjected to compressive deformation caused by the external pressure. Consequently, in this case, for destruction of the specimen during pulsed breakdown it is necessary to expend energy: first, to overcome the compressive forces and, second, to overcome the intermolecular cohesive forces of the specimen, i.e.,

\[ P_{\mathrm{k}} = P_{\mathrm{p}} + P_{\mathrm{vn}}, \tag{1} \]

where \(P_{\mathrm{k}}\) is the pressure in the discharge channel;

$P_{\mathrm{ext}}$ — external (hydrostatic) pressure;

$P_{\mathrm{r}}$ — the pressure required to fracture the specimen.

The pressure in the discharge channel ($P_{\mathrm{k}}$) is determined by the magnitude of the energy of the discharge channel and by the rate at which it is released.

The pressure required for mechanical fracture of the specimen during breakdown ($P_{\mathrm{r}}$) depends on the mechanical strength of the specimen material and on its linear dimensions. The external hydrostatic pressure determines the magnitude of the compressive deformation of the specimen. With increasing hydrostatic pressure, at constant pulse energy, and also with unchanged energy density and power in the discharge channel, the part of the energy expended in overcoming compressive forces increases; consequently, the fracture effect will decrease.

The change in the diameter of the crack-formation zone in rock-salt specimens during breakdown under elevated pressures up to 150 kg/cm² is described by the equation

\[ d_{\mathrm{t}} = d_{\mathrm{t}0} e^{-\alpha P}, \tag{2} \]

where $d_{\mathrm{t}0}$ is the diameter of the crack-formation zone at atmospheric pressure, $P$ is the hydrostatic pressure, and $\alpha = 0.004$ is a coefficient characterizing the relative decrease in the diameter of the crack-formation zone with increasing pressure.

Fig. 4. Dependence of the diameter of the crack-formation zone in rock salt on pulse energy during through breakdown (pulse duration $0.6 \cdot 10$ sec).
1 — change in energy by means of the discharge capacitance; 2 — change in energy by means of the voltage amplitude (calculated curve); 3 — change in energy by means of the voltage amplitude (experimental curve).

With increasing pulse energy by changing the pulse amplitude or the discharge capacitance, the diameter of the crack-formation zone increases. For example, with an increase in the pulse amplitude from 120 to 170 kV, the diameter of the crack-formation zone at a pressure of 25 kg/cm² increases from 15 to 17.5 mm.

Figure 4 gives the dependence of the diameter of the crack-formation zone in rock salt during breakdown under a pressure of 50 kg/cm² on the pulse energy. The pulse energy was varied by increasing the discharge capacitance (curve 1) and the amplitude (curve 3). The numbers beside curve 3 indicate the magnitude of the overvoltage

\[ n = \frac{U_{\mathrm{appl}}}{U_{\mathrm{br}}}, \tag{3} \]

where $U_{\mathrm{appl}}$ is the voltage applied to the specimen;
$U_{\mathrm{br}}$ is the breakdown voltage.

As follows from Fig. 4, from the energy standpoint it is most rational to increase the effectiveness of fracture of solid bodies during their pulsed breakdown by changing the discharge capacitance, rather than the pulse amplitude. Beginning with an overvoltage of $n = 1.7$, the curve of the change in the diameter of the crack-formation zone with pulse energy appears to tran—

enters the saturation region, and a further increase in the pulse amplitude becomes ineffective. This circumstance is explained as follows. With an increase in the overvoltage on the specimen being broken down, the fraction of energy released in the discharge channel during the first half-period of current oscillation after breakdown decreases. Since the destruction of solids during their pulsed electrical breakdown occurs mainly during the first half-period of current oscillation after breakdown, then, despite the increase in pulse energy with increasing amplitude, the relative increase in the diameter of the fracture-formation zone decreases. If this effect did not occur, the increase in the diameter of the fracture-formation zone with increasing pulse amplitude would be linear. Line 2 in Fig. 4 is the calculated dependence of the diameter of the fracture-formation zone on the change in pulse energy.

Conclusions

1. It has been established that the pulsed electric strength of rocks increases only slightly as the pressure is increased from atmospheric to \(150\ \mathrm{kg/cm^2}\). The greatest increase in pulsed strength occurs at pressures up to \(50\ \mathrm{kg/cm^2}\) and amounts to 20–40%. As the pressure is changed from 50 to \(150\ \mathrm{kg/cm^2}\), the pulsed electric strength remains practically unchanged and, for a voltage exposure time of \(0.5 \cdot 10^{-6}\ \mathrm{s}\), is \(220 \div 250\ \mathrm{kV/cm}\).

2. The efficiency of destruction of solid materials during their pulsed electrical breakdown decreases by 30% as the pressure is increased from 25 to \(150\ \mathrm{kg/cm^2}\).

3. It is expedient to increase the efficiency of destruction of solid materials during their pulsed electrical breakdown under elevated-pressure conditions by increasing the discharge capacitance.

References

1. Zisman W. A., Proc. Nat. Acad. Sein. 19, 66, 1933.
2. Zisman W. A., Proc. Nat. Acad. Sein. 19, 680, 1933.
3. Zisman W. A., Gerland Beitz, Z. Geophys. 39, 408, 1933.
4. I. I. Kalyatskii, A. G. Sinebryukhov. Izv. vuzov SSSR, Energetika, 3, 1963.