PARTIAL DISCHARGES DURING MECHANICAL FRACTURE OF SOLID DIELECTRICS

V. S. DMITREVSKII, L. I. KORNILOVA

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

Mechanical fracture of solid dielectrics is associated with the rupture of intramolecular and intermolecular bonds. The rupture of intramolecular bonds is accompanied by the formation of radicals [1] and by charge separation [2—4], which leads to the formation of high electric fields at the site of fracture.

Electrical phenomena that occur during the mechanical fracture of solid dielectrics have the following stages: 1) rupture of bonds with separation of charges remaining on opposite walls of cracks; 2) an increase in the distance between the crack walls is accompanied

Fig. 1. Schematic of the fracture boundary of a solid dielectric with ionic structure

by an increase in the potential difference between them; 3) at a certain potential difference, a discharge occurs in the gas filling the space between the cracks.

The density of the charges formed on the crack walls and the field strength in the cavity can be estimated if it is assumed that fracture of the dielectric occurs along the direction 1—1 (Fig. 1):

\[ q=\kappa q_{0} z \frac{N_A \rho a}{M}, \tag{1} \]

\[ E=\frac{q}{\varepsilon_0\varepsilon}=\frac{\kappa}{\varepsilon_0\varepsilon}\frac{zN_A\rho a}{M}, \tag{2} \]

where \(q\) is the charge density on the crack surface;
\(q_0\) is the electron charge;
\(N_A\) is Avogadro’s number;
\(z\) is the ratio of the ion charge to the electron charge;
\(\rho\) is the density of the dielectric;
\(a\) is the lattice constant;
\(M\) is the molecular weight;
\(\varepsilon_0\) is the electric constant;
\(\varepsilon\) is the dielectric permittivity of the gas filling the crack;
\(\kappa\) is a coefficient taking into account the decrease in charge density due to deviation of the fracture direction from \(1\text{—}1\).

The calculated charge density upon rupture of an LiF crystal is \(1.96\ \mathrm{C/m^2}\). Experiments on rupture of an LiF crystal in vacuum gave a charge density of \(4.8\cdot10^{-5}\ \mathrm{C/m^2}\) [4], i.e., approximately \(10^5\) times smaller than the calculated value. In cleavage of mica, the measured charge density reached \(0.33\ \mathrm{C/m^2}\) [2], which is considerably closer to the theoretically calculated value. Table 1 gives the values of \(q\) and \(E\), calculated from formulas (1) and (2) under the assumption that \(\kappa=10^{-3}\). The same table also gives the value of the crystal-lattice energy \((W_k)\), taken from [5].

Table 1

The crack formed during mechanical fracture is filled with air. The potential difference between the crack walls may cause a discharge in the gas, provided that the electric strength of air is less than or equal to the field intensity in the crack. The electric strength of air depends on the size of the gap between the walls:

\[ \ln E_{\mathrm{pr}}=\frac{46.8}{\ln 2.4\cdot10^6 x}, \tag{3} \]

where \(E_{\mathrm{pr}}\) is the electric strength of air in \(\mathrm{kV/cm}\);
\(x\) is the gap size in \(\mathrm{cm}\).

Equating \(E_{\mathrm{pr}}\) in formula (3) to the field intensity produced during mechanical fracture of a solid dielectric, we find the minimum crack width at which a discharge in air (a partial discharge) will occur. The crack widths \(x_1\) and \(x_2\) calculated from this condition are given in Table 1. The value \(x_1\) was calculated for \(\kappa=10^{-3}\), and \(x_2\) for \(\kappa=1\). The calculations showed that gas breakdown in the crack should be observed at a minimum width from \(0.2\) to \(2.5\ \mu\mathrm{m}\).

A gas discharge is accompanied by visible luminescence and electromagnetic radiation. These phenomena were observed during the formation of microcracks in LiF [6]. We have investigated the number of electromagnetic pulses (the number of partial discharges) arising during flexural fracture of several solid dielectrics. The specimens

the dielectrics were beams of rectangular cross section, freely mounted on two supports. On the lower side, at the center of the beam, a notch was made in order to localize the fracture site. The load was applied at the center of the beam. Some experiments were carried out on beams fixed at one end and with a load applied at the other end. Silicate glass, polymethyl methacrylate, epoxy resin, and polystyrene were chosen as the specimen materials. The cross-sectional area of the specimens was 0.5–0.75 cm\(^2\), and only the polystyrene specimens had a cross-sectional area of 3 cm\(^2\). The number of partial discharges was measured with a PS-10000 counter with a sensitivity of \(10^{-2}\) V. To detect electromagnetic radiation, two electrodes were used, which were glued to the specimen.

The investigations showed that partial discharges appeared during the mechanical fracture of dielectrics: inorganic ones with ionic bonds (silicate glass) and organic ones with covalent bonds, both polar (polymethyl methacrylate, epoxy resin) and nonpolar (polystyrene). The charge density \(q\) and the field strength in the crack will be greater the higher the density of the bonds being broken. From Table 1 it is seen that \(q\) and \(E\) increase with increasing energy of the crystal lattice. In [7] it was established that the strength properties of ionic dielectrics (stress under mechanical fracture, electrical—

Fig. 2. Dependence of the number of partial discharges on the mechanical strength of a solid dielectric under bending

strength) are determined by the energy of the crystal lattice, i.e., by the strength and density of bonds in the material. Later it was shown that the electrical strength of inorganic and organic dielectrics depends on the energy of channel formation, which is defined as the energy of dissociation of bonds and ionization of the atoms constituting a molecule of the substance, referred to a mole of material [8].

Thus, it may be expected that the number of partial discharges arising during the fracture of solid dielectrics should be related to the strength properties of the material.

In Figs. and 3 the dependence is given of the number of partial discharges \((n)\) arising during the mechanical fracture of solid dielec-

...dielectrics, on their electrical and mechanical strength. The values of the electrical and mechanical strength were taken from [9, 10]. Each point on the graphs corresponds to the mean value of \(n\) from 20–25 observations. The dependence of \(\lg n\) on the electrical and mechanical strength of dielectrics is well fitted by a straight line.

Attempts to relate the number of partial discharges arising during the mechanical fracture of solid dielectrics to their specific resistance and dielectric constant showed that no such relation exists.

On the basis of the experiments carried out, the following conclusions may be drawn:

1. The mechanical fracture of solid dielectrics is accompanied by the formation of charges on the opposite walls of the fracture crack.

2. In the process of mechanical fracture, a partial discharge develops in the crack.

3. The number of partial discharges does not depend on the nature of the bonds being broken (ionic, covalent).

Fig. 3. Dependence of the number of partial discharges on the electrical strength of solid dielectrics

1. The number of partial discharges during mechanical fracture correlates well with the strength characteristics of the dielectric (electrical strength and bending strength).

LITERATURE

1. A. Ya. Savostin, E. T. Tomashevskii. Fizika tverdogo tela, 1970, 12, No. 10, 2857–2864.

2. N. A. Krotova, V. D. Karasev. DAN SSSR, 1953, 92, No. 3, 607.

3. L. M. Belyaev, V. Z. Nabatov. Kristallografiya, 1962, 7, No. 6, 576–580.

4. M. I. Kornfeld. Fizika tverdogo tela, 1968, 10, No. 8.

5. Brief Handbook of Physicochemical Quantities. Moscow, “Khimiya,” 1967.

6. L. M. Belyaev, V. V. Nabatov, Yu. N. Martyshev, G. G. Bendrikova. In: Breakdown of Dielectrics and Semiconductors. Moscow, “Energiya,” 1964, 343–346.

7. A. A. Vorob'ev. Insulating Properties, Strength, and Fracture of Dielectrics. Novosibirsk, Publishing House of the Siberian Branch of the USSR Academy of Sciences, 1960.

8. Yu. N. Vershinin. Electrical Breakdown of Solid Dielectrics. Novosibirsk, “Nauka,” 1968.

9. J. Artbauer, J. Griac. Acta techn. CSAV, No. 3, 1966, II, 416–428.

10. Handbook of Electrical Engineering Materials. Vol. I, Part 1. Edited by Yu. V. Koritskii and B. M. Tareev. Moscow, Gosenergoizdat, 1958.