Thermal Shock Resistance Parameter R

Drop something hot into cold water and the surface tries to contract while the interior, still hot, holds it out. The surface goes into tension. If that tension reaches the fracture strength, it cracks. Kingery's 1955 paper in the Journal of the American Ceramic Society turned that sentence into a parameter: $R = \sigma_f(1-\nu)/(E\alpha)$, which is simply the temperature difference at which the thermal stress equals the strength.

The algebra is honest and it comes straight from restrained thermal expansion. A surface prevented from contracting by the bulk beneath it is restrained in two directions at once, which gives the biaxial stress $\sigma = E\alpha\Delta T/(1-\nu)$; set that equal to $\sigma_f$, solve for $\Delta T$, and $R$ is what comes out. The $(1-\nu)$ is the biaxial correction and nothing more.

And now the thing that must be said before anything else on this page: $R$ is a RANKING PARAMETER, not a survivable temperature drop. The derivation assumes an infinite Biot number — the surface of the body arriving instantaneously at the quench temperature while the interior has not moved at all. Nothing real achieves that. A small specimen plunged into cold water gets closest and still falls short; an air blast is nowhere near it. Because a real quench develops a smaller temperature difference than the idealised one, $R$ systematically understates what a real part will take, sometimes by a large factor. And the equation contains nothing about the size of the part, its shape, its surface finish, or how vigorously it is being cooled — all of which matter enormously.

The practical consequence is worth stating plainly: two materials can be ranked correctly by $R$ and both fail at temperature differences it does not predict. Use it to choose between candidate materials. Never use it to set a process limit. The honest way to qualify a part against thermal shock is to quench real parts and count what breaks, which is what the standard quench tests do.

Read the structure of the equation and it teaches something durable. Strength on top; stiffness and expansion coefficient underneath. Expansion coefficient is the term with the widest range across real ceramics — from about $0.5\times10^{-6}$/K for fused silica to $10\times10^{-6}$/K for alumina, a factor of twenty, against maybe a factor of five in strength and six in modulus. That is why fused silica can be taken red-hot from a furnace and dropped in water without complaint: the numerator barely matters when $\alpha$ is that small. It is why borosilicate replaced soda-lime in laboratory glassware — not because it is stronger, but because its expansion is a third as much. It is why cordierite, not alumina, carries catalytic converters, and why near-zero-expansion lithium aluminosilicate glass-ceramics make ceramic hobs that survive a wet cloth.

Stiffness is a liability here, which is worth sitting with for a moment, because everywhere else in engineering it is an asset. A compliant material accommodates the thermal strain elastically instead of turning it into stress. That is why a porous refractory brick outlives a dense one in a furnace lining, and why fibrous insulation boards survive flame impingement that would shatter the same oxide fully dense. Porosity lowers $E$ fast — but it lowers $\sigma_f$ too, as the Ryshkewitch page shows, so the trade is real rather than free.

One last honesty, which connects this page to the rest of the category: $\sigma_f$ is not a number. It is the Weibull distribution from the first half of this shard, so $R$ inherits all of that scatter, and an $R$ computed from a mean strength and an $R$ computed from a design allowable differ by tens of percent. Two $R$ values are only comparable if they were built on the same choice.