Breakdown in Solid Dielectrics

The crucial difference between a solid and the fluids of the last two chapters is that a solid cannot flow back together. A gas re-mixes, a liquid closes over a discharge channel and recovers most of its strength, but a punctured solid carries a permanent carbonised track that short-circuits it forever. A single breakdown is the end of the component's life. The design goal is therefore not "survive one breakdown" but "never break down at all", across thirty or forty years of continuous stress.

That long horizon exposes the central subtlety: a solid does not have one breakdown strength, it has many, depending on how long the voltage is applied. Under a microsecond impulse the only mechanism fast enough to act is the electronic intrinsic one, and the strength is at its highest. Stretch the time to milliseconds and electromechanical and thermal processes get their chance; stretch it to hours and years and slow discharge, treeing and ageing processes dominate, and the strength falls dramatically. Plotting strength against time-to-breakdown gives a descending staircase — the single most important picture in the chapter.

Intrinsic breakdown is the purely electronic limit, reached only in a flawless sample, at low temperature, under a fast-rising voltage that gives no slower mechanism time to intervene. A few conduction electrons, present even in a good insulator, are accelerated by the field; if they gain energy from the field faster than they lose it to the lattice, their energy climbs until they ionize the lattice by collision, and an avalanche multiplies through the solid in nanoseconds — the same runaway condition we have now met in gases and liquids.

Because the process is electronic and the lattice is dense, intrinsic strengths are enormous — of the order of \(10^{6}\text{–}10^{7}~\mathrm{V/cm}\) (hundreds of \(\mathrm{kV/mm}\) to a few \(\mathrm{MV/mm}\)) — and they represent the ceiling a perfect solid could reach. No practical insulation gets near it: a real component always carries a flaw that one of the slower mechanisms exploits at a far lower field. Intrinsic strength is thus a benchmark, not a service value, and the rest of the chapter is about why service values are so much lower.

A charged capacitor's plates attract one another, and when the dielectric between them is a soft solid, that attraction physically squeezes it. The compressive electrostatic (Maxwell) stress on a slab of permittivity \(\varepsilon_r\) under field \(E = V/d\) is:

The solid resists with its mechanical (Young's-modulus) stiffness. As the slab thins, the field \(V/d\) rises, so the squeezing stress rises faster than the restoring stress — a positive feedback. Stark and Garton showed this becomes unstable once the slab has been compressed to a definite fraction of its original thickness:

Here \(Y\) is Young's modulus. The mechanism matters most for soft polymers and at higher temperature, where \(Y\) falls; a stiffer or cooler material resists longer. It is one of the medium-speed rungs on the staircase — slower than intrinsic, faster than thermal.

No real dielectric is perfectly lossless; under AC each cycle dissipates a little energy as heat, set by the loss tangent \(\tan\delta\). The power generated per unit volume is:

This heat must be conducted away to the surfaces. The danger is that the loss usually rises with temperature (conductivity and \(\tan\delta\) climb), while the cooling — proportional to the temperature difference — rises only linearly. If at some point the heat generated grows faster with temperature than the heat removed, equilibrium is lost: the temperature, and with it the loss, runs away until the material melts or chars. That is thermal runaway.

Three consequences follow for design. Thermal strength falls as frequency and \(\tan\delta\) rise, so AC and high-frequency stress are far more punishing than DC. It falls as the insulation gets thicker, because the heat at the centre has farther to travel out — making thermal breakdown the limiting mechanism for bulky insulation like large bushings and thick cables. And it is the reason a low loss tangent is prized: every reduction in \(\tan\delta\) buys margin against runaway.

The mechanism that kills most solid insulation in service is none of the above acting on the bulk, but a slow erosion that begins in a tiny gas-filled cavity — a void left by imperfect manufacture, a delamination, a gas pocket. The cavity is the solid's version of Chapter 8's bubble, and it is dangerous for exactly the same two reasons: the field inside it is enhanced, and the gas it contains is weak.

Once the cavity field reaches the gas's breakdown value, a small spark — a partial discharge (PD) — fires inside the void, again and again, on every voltage cycle. Each tiny discharge is harmless in itself, but its ions and ultraviolet bombard the cavity walls, slowly eroding and chemically degrading the surrounding polymer. Over months and years the cavity grows, the erosion concentrates the field at its tip, and a conducting channel begins to push into the solid — which is treeing, the next section. PD is therefore both a destroyer and a diagnostic: because each discharge injects a measurable charge pulse, detecting and quantifying PD is the single most powerful way to find ailing insulation before it fails, the subject of Chapter 19.

An electrical tree is a branching, hollow, carbonised channel that grows through a solid under prolonged stress, almost always starting from a PD site, a sharp contaminant, or a field-concentrating defect. Each branch advances by partial discharges at its tip, which erode fresh polymer and extend the channel a little further; under a microscope the result looks startlingly like a bush or a lightning bolt frozen in the plastic. Once a tree bridges the insulation, breakdown follows. Trees can take years to cross thick insulation, which is precisely why they are the dominant ageing mechanism of cables and machine insulation.

A subtler relative haunts polymer cables in wet environments: the water tree. Where moisture and an electric field act together on polyethylene, diffuse, fan-shaped trees of water-filled micro-channels grow at fields far below those needed for electrical trees. Water trees do not themselves puncture the insulation, but they degrade it and seed the electrical trees that eventually do — the chief reason early XLPE cables failed and why modern cables use water-tree-retardant compounds and tight moisture control.

Not every solid failure happens in the bulk; many occur along the surface, especially for outdoor insulators exposed to pollution and damp. A film of contamination — salt, dust, industrial deposit — wetted by dew or drizzle becomes weakly conducting, and the leakage current it carries heats the surface unevenly. Where the film dries fastest, a dry band forms; almost the whole voltage then appears across this narrow band, igniting small arcs across it. These arcs carbonise organic surfaces into a permanent conducting track, which extends with each event until a continuous path flashes the insulator over. A material's resistance to this is graded by its comparative tracking index (CTI).

Surface flashover is doubly important because the flashover voltage of a contaminated surface can be a small fraction of the bulk strength, so for outdoor apparatus the surface, not the volume, sets the rating. The defence is partly geometric — long creepage paths, sheds that shelter dry zones — and partly material: hydrophobic surfaces that bead water into isolated droplets rather than letting it form a continuous conducting film. Silicone-rubber housings, whose hydrophobicity recovers even after pollution, have become the modern answer, and assessing that hydrophobicity is itself an active diagnostic field.

For each item, first name the mechanism it tests — intrinsic, electromechanical, thermal, partial discharge, treeing, or tracking — then work it through. Difficulty rises down the list.