ON A CERTAIN ANALOGY BETWEEN THE DESTRUCTION OF SOLID NONCONDUCTING MATERIALS DURING EXPLOSIONS OF EXPLOSIVES AND PULSED ELECTRICAL BREAKDOWN

I. I. KALYATSKII, V. V. KRIVKO

(Presented by the scientific seminar of the Research Institute of High Voltages)

Advances achieved recently in the field of electrical discharge in dielectrics have made it possible to use the discharge in a number of branches of industry: electro-spark machining of metal, the treatment and destruction of solid nonconducting materials by a shock wave during an electrical discharge in a liquid, and others.

The ease of obtaining high powers in the channel of an electrical discharge, and the possibility of controlling and regulating the magnitude of the energy and the rate at which it is released, make it possible to assume the promise of a broader application of electrical discharge in the national economy.

From this point of view, it is of scientific and practical interest to establish the general laws governing the destruction of solids under pulsed electrical discharge and the energy of an explosive substance.

As shown in [12], a pulsed electrical discharge, in terms of the rate of energy release and the character of the mechanical destruction, is similar to a microexplosion of an explosive substance (ES).

During the explosion of an ES, just as during electrical breakdown, an elastic wave propagates in the solid in the form of a single pulse.

The conditions for the propagation and attenuation of the elastic wave arising during the explosion of an ES, and the consequences of its action, depend on:

1) the shape, dimensions, and properties of the solid body being destroyed;
2) the shape, dimensions, and properties of the ES material (specific energy content and detonation velocity).

During electrical breakdown, the conditions for the propagation and attenuation of the elastic wave and the consequences of its action likewise depend on:

1) the shape, dimensions, and properties of the solid body being destroyed;
2) the conditions of electrical breakdown of the discharge channel being formed and its parameters (specific energy content and the rate of energy release in the channel).

Thus, there is an external analogy between the explosion of an ES and pulsed electrical breakdown. This analogy concerns both the conditions for propagation of the destructive shock wave and the consequences of its action. In both cases the occurrence of a shock wave in the solid body being destroyed is associated with the presence of very high pressures \((3 \cdot 10^5—5 \cdot 10^5\ \text{kg}/\text{cm}^2)\) and temperatures (up to \(10^4—4 \cdot 10^5\)) [1—11], concentrated in a small volume (relative to the entire volume of the material being destroyed). In both cases the determining parameters are the specific energy content and the rate of energy release.

In comparing the destruction of solids during the explosion of explosives and during electrical breakdown, one must bear in mind the difference between the physical processes involved.

During the explosion of an explosive, a reaction of thermal decomposition of the explosive takes place; its kinetics are characterized by the power of the explosive charge, the energy density, and other characteristics [3], comparable with the characteristics of energy release during breakdown [1]. The thermal-decomposition reaction proceeds with the participation of photoionization and excitation of atoms of the body by ultraviolet radiation from the explosion region [7]. In the case of pulsed electrical breakdown, the energy is released from a capacitor in the discharge circuit.

The specific energy content of an explosive (energy per unit weight or volume of explosive) and the detonation velocity are determined by its chemical composition and structure. The specific energy content of the discharge channel during breakdown and the rate of energy release are determined by the reserve of energy in the circuit and by the conditions under which it is supplied to the channel. The specific energy content of an explosive is \(0.9 \cdot 10^3\ \text{J}/\text{cm}^3\) [11]. In the channel of a pulsed discharge, the specific energy content may reach \(6 \cdot 10^2\)—\(6 \cdot 10^3\ \text{J}/\text{cm}^3\).

The hypotheses explaining the destruction of solids during the explosion of explosives proceed from the following propositions [9]:

1. Destruction of a body by an explosion occurs due to the pressure of the gaseous products of decomposition of the explosive. The pressure, and consequently the destruction as well, are directed from the charge toward the surface of the body.

2. Destruction of bodies during an explosion occurs as a result of stress waves arising under the pulsed action of the gaseous products. In this case the waves propagate from the charge in all directions, forming a complex pattern of distribution of compressive and tensile stresses in the volume of the body, determined by the interference of waves incident upon and reflected from the surface of the body.

3. Destruction occurs both under the action of stress waves and due to the pressure of the gaseous products of detonation.

In pulsed electrical breakdown of solids of limited dimensions, compressive stress waves propagate from the breakdown channel to the free surface of the body and are reflected from it [1]. Destruction of the material may occur both under the action of compression waves and of tensile waves. Here the conditions for reflection of waves from the free surface are influenced by the shape and dimensions of the body being destroyed.

The occurrence of stress waves from gaseous products in a pulsed discharge is unlikely.

In an underground explosion of an explosive, three explosion zones are conventionally distinguished [10]: the near zone, the middle zone, and the far zone.

Their dimensions are mainly determined by the weight of the charge and by the type of rock. In the nearest zone, two regions are further distinguished: the compression region and the destruction region. In the compression region there exists a shock wave with a discontinuous front. Because of the enormous loads, the rock is crushed and compacted. Its boundary during the explosion of TNT charges is determined by the empirical formula

\[ R_c = 19K_c, \]

where \(R_c\) is the relative radius of the compression region;
\(K_c\) is an empirical coefficient depending on the type of rock.

The destruction region is characterized by a violation of the continuity of the rock and by the appearance of cracks, and is determined as

\[ R_p = 19K_p, \]

where \(R_p\) is the relative radius of the sphere of destruction;
\(K_p\) is an empirical coefficient.

The middle zone of an underground explosion, where elastic-plastic deformations of the rock occur, extends approximately to a distance of about \(100 R_{03}\) (\(R_{03}\) is the radius of the charge), and the far zone of the explosion is conventionally limited to the range of distances from 100 to \(1000R_{03}\).

The comminution and crushing of material during an explosion of explosives, occurring in the immediate vicinity of the charge, are caused by the front of the full impulse of the explosion and take place with a small expansion of the detonation products. This is the so-called brisant action of the explosion. The greater part of the total work of the explosion, determined by the passage of the entire impulse, goes into the destruction and throwing off of material and constitutes the overall, or heaving, action of the explosion [10]. The magnitude of the brisant forms of the work of the explosion represents a small part of the total work and depends strongly on the detonation velocity of the explosive. The magnitude of the heaving form of the work of the explosion is determined by the total energy of the explosion, less losses, and does not depend on the detonation velocity.

Under conditions of pulsed electrical breakdown of solids, two forms of the work of the shock wave arising in the discharge channel can likewise be distinguished. As in the explosion of explosives, the comminution and crushing of material in pulsed electrical breakdown occur in the immediate vicinity of the discharge channel. The brisance of the discharge action is determined by the rate of energy release in the discharge channel and increases as the rate increases. The magnitude of the complete destruction of the body is determined by the amount of energy released in the discharge channel during the first half-period of the current oscillation after breakdown.

In the explosion of explosives, in addition to the mechanical destruction of a solid by stress waves, thermal destruction of some volume of the body is also possible, owing to the high temperatures and considerable amount of heat released during the explosion.

Thermal destruction of a solid (melting, evaporation) under the action of high temperatures takes place in small volumes also in electrical breakdown of solid dielectrics. In this case, the energy spent on melting the walls of the discharge channel may amount to as much as 10% of all the energy released in the channel [2].

Thus, as a consequence of a certain analogy between the destruction of solids during the explosion of explosives and during pulsed electrical breakdown, first, in individual cases it is in principle possible to use a pulsed electric discharge effectively instead of explosives, with a number of advantages (absence of danger in storing and transporting explosives, simple production of energy in the circuit, controllability of the process, etc.); second, it is possible to calculate the explosive action of a pulsed electric discharge using the formulas of hydrodynamics for the explosion of explosives; third, in the destruction of solids by pulsed electric discharges there is, in comparison with the use of explosives, a greater possibility of regulating the rate of energy release in the discharge channel and its total amount, as well as the possibility of carrying out directed destruction by using the conditions for selective directionality of the path of an electric discharge in a dielectric medium.

LITERATURE

1. A. A. Vorob'ev, E. K. Zavadovskaya. Electrical strength of solid dielectrics. GITTL, 1956.
2. V. I. Obukhov, A. I. Litsyn. IFZh, 1, 1963.
3. S. I. Andreev, M. P. Vanyukov. ZhTF, 31, issue 8, 1961; 32, issue 6, 1962.
4. Yu. V. Skvortsov, V. S. Komel'kov, N. M. Kuznetsov. ZhTF, 30, 10, 1959.
5. N. A. Roi, D. P. Frolov. Sound formation during spark discharges in water. Report 1, Moscow, 1957.

1. K. K. Andreev. Thermal Decomposition and Combustion of Explosive Substances. GEI, 1957.
2. F. I. Bowden, A. Yoffe. Initiation and Development of Explosion in Solids and Liquids. IL, 1955.
3. G. I. Pokrovskii. Physical Foundations of Blasting. Znanie, 1956.
4. O. E. Vlasov. Fundamentals of the Theory of Explosion. VIA Publishing House, 1957.
5. Yu. S. Yakovlev. Hydrodynamics of Explosion. Sudpromgiz, 1961.
6. V. A. Assonov. Blasting Operations. Ugletekhizdat, 1958.
7. I. I. Kalyatskii, A. G. Sinebryukhova. Izvestiya VUZov—Energetika, 3, 1963.

\(C_0\)—the partial capacitance of one transporter relative to the stator,

\(U_{\mathrm{v}}\)—the excitation voltage.

The transporters were taken with a circular cross section because this electrode shape is the most effective for moving charges in a region of high gradient [5].

The value of the recharging coefficient can be determined from the formula [6]

\[ K_i=\sqrt{1+4\frac{C_1}{C_0}}, \tag{2} \]

where \(C_1\) is the partial capacitance between neighboring transporters.

The dependences of the partial capacitances \(C_0\) and \(C_1\) were determined by modeling in an electrolytic bath. As a result of processing the experimental data, empirical dependences were obtained for these quantities for a single-row arrangement of transporter-conductors:

\[ C_0=\frac{4.3\,\mathrm{E}\,la}{D_{\mathrm{pr}}}, \tag{3} \]

\[ \frac{C_1}{C_0} = \frac{1}{3} \left( \frac{D_{\mathrm{pr}}}{2r}-1 \right) \left( \mathrm{sc}\,\frac{\pi r}{a}-1 \right)^{0.8}, \tag{4} \]

where \(\mathrm{E}\) is the dielectric constant of the resin,

\(l\)—the length of the transporter,

\(a\)—the distance between the axes of the transporters,

\(r\)—the radius of the transporter.

\[ D_{\mathrm{pr}}=d_{\mathrm{sm}}+2r+\mathrm{E}d_{\mathrm{voz}}, \]

\(d_{\mathrm{sm}}\)—the thickness of the dielectric,

\(d_{\mathrm{voz}}\)—the air gap.

Fig. 1. Graph of the dependence \(I_{\mathrm{kz}}=f(U_{\mathrm{v}})\) of rotors with different numbers of transporters: 1—for a rotor with \(m=27\), 2—for a rotor with \(m=45\), 3—for a rotor with \(m=54\), 4—for a rotor with \(m=74\).

Taking into account dependences (3) and (4), equation (1) can be written as:

\[ I_{\mathrm{kz}} = U_{\mathrm{v}}\cdot n\cdot 2\cdot m \frac{4.3\mathrm{E}la}{D_{\mathrm{pr}}} \sqrt{ 1+4 \left[ \frac{1}{3} \left( \frac{D_{\mathrm{pr}}}{2r}-1 \right) \left( \mathrm{sc}\,\frac{\pi r}{a}-1 \right)^{0.8} \right] } \]

or

\[ I_{\mathrm{kz}} = \frac{8.6\,U_{\mathrm{v}}nm\mathrm{E}la} {d_{\mathrm{sm}}+2r+\mathrm{E}d_{\mathrm{voz}}} \sqrt{ 1+ \frac{4}{3} \left( \frac{d_{\mathrm{sm}}+2r+\mathrm{E}d_{\mathrm{voz}}}{2r}-1 \right) \left( \mathrm{sc}\,\frac{\pi r}{a}-1 \right)^{0.8} }. \tag{5} \]

When the transporter radius \(r\) is changed, leaving \(U_{\mathrm{v}}, n, a, l, d_{\mathrm{sm}}, d_{\mathrm{voz}}=\mathrm{const}\), it is evident that \(I_{\mathrm{kz}}\) will increase as the radius \(r\) decreases and the number of transporters \(m\) increases. Therefore, in order to obtain the maximum short-circuit current in a generator with an unchanged rotor disk radius, it is necessary to increase the number of transporter-conductors and decrease their radius. However, decreasing the radius of the transporters is associated with manufacturing difficulty.