Thermal and electromechanical dielectric breakdown

Dielectric breakdown is the sudden large increase of current through an insulator when the applied field exceeds a critical value (the dielectric strength), so that the material loses its insulating property, usually permanently in solids.

Thermal breakdown

1. When an AC or DC voltage is applied, a small leakage current and dielectric loss ($W = \omega\varepsilon_0\varepsilon_r'E^2\tan\delta$ per unit volume) heat the insulator.
2. The conductivity of an insulator rises steeply (exponentially) with temperature, and $\tan\delta$ also rises.
3. More conductivity gives more current and more heat. If heat is generated faster than it can be conducted away to the surroundings, the temperature rises without limit (thermal runaway).
4. The material melts, chars or burns, forming a conducting path, usually at the hottest point in the middle.

Features: it takes seconds to minutes to develop. The breakdown strength falls with higher frequency, higher ambient temperature and longer application time, and also with thicker insulation, because the interior is cooled less well. It is the most common breakdown mode in power equipment insulation (e.g. cable insulation).

 heat
  ^       generated
  |         /
  |        /   ...lost (cooling)
  |  .....'
  |  stable / unstable -> runaway
  |____________________> T

Electromechanical breakdown

1. A voltage $V$ across a soft solid dielectric of thickness $d$ produces an electrostatic attraction between the electrodes (Maxwell stress) of $\frac{1}{2}\varepsilon_0\varepsilon_r\frac{V^2}{d^2}$ per unit area.
2. This compressive force squeezes the material, so $d$ decreases.
3. The field $V/d$ then increases, the force grows further, and the material is compressed even more.
4. If the elastic restoring stress (Young's modulus $Y$) cannot balance it, the insulation collapses mechanically and then breaks down.

Balancing the stresses, the material becomes unstable when $d$ falls to about $0.6\,d_0$, which gives the highest apparent field

$$E_{max} \approx 0.6\sqrt{\frac{Y}{\varepsilon_0\varepsilon_r}}$$

It occurs mainly in soft materials such as polymers (polyethylene, rubber) and at high temperature, where $Y$ is low.