Thermal Shock Resistance Parameter R′

Kingery's $R$ has a famous embarrassment, and this parameter is the fix. Work out $R$ for alumina — 350 MPa strength, 380 GPa modulus, $\alpha = 8.1\times10^{-6}$/K — and you get about 89 K. Work it out for ordinary soda-lime window glass — 70 MPa, 70 GPa, $\alpha = 9\times10^{-6}$/K — and you get about 87 K. Essentially identical. $R$ says these two materials are equally good in thermal shock, and every cook, every glazier and every kiln operator knows they are not.

What is missing is conduction. $R$ assumes the surface arrives instantly at the quench temperature and the interior does not move at all, so heat flow through the material is irrelevant by construction. Real quenches are slower than that. The interior follows the surface part of the way down, and how far it follows depends on how well the material conducts. A good conductor never develops the temperature difference that a poor one does, and so never generates the stress.

Multiply $R$ by the thermal conductivity and the ranking changes completely. Alumina conducts at about 30 W/(m·K); soda-lime glass at about 1. $R'$ separates them by a factor of thirty, and that is the number that matches what actually happens when hot things meet cold water. $R$ ranks a quench nothing achieves; $R'$ ranks the ones that occur.

The units are worth a moment because they look odd. Watts per metre — the same dimension as heat loss per metre of pipe, and that is not a coincidence. Both are a heat flow spread along a length. Physically $R'$ is proportional to the maximum heat flux a surface can sustain in steady state without cracking, times a length scale; it is the finite-Biot companion to $R$'s infinite-Biot limit, and the two together bracket the real behaviour rather than either one describing it.

This is why silicon carbide dominates in kiln furniture and high-temperature heat exchangers. Its strength is good but not extraordinary; its conductivity of 100 to 150 W/(m·K) is four or five times alumina's, and that multiplies straight through this parameter. It is also why porosity hurts twice over in a thermal-shock application: a porous body conducts worse and breaks sooner, so both terms move the wrong way at once — which is a genuine tension with the fact that porosity also lowers $E$ and helps.

Neither parameter is a survivable $\Delta T$. That has to be said again here because $R'$ is more useful than $R$ and therefore more tempting to over-read. Kingery's family continues past these two: $R''$ and $R'''$ address crack propagation and damage tolerance rather than crack initiation, and a refractory that is expected to craze and go on working is selected on those instead — a material with a low initiation resistance and a high propagation resistance may outlast one that resists the first crack better and then shatters. All of them are ranking parameters. All of them are shortcuts around a transient thermal stress analysis, which is what you actually do when the answer matters, and none of them replaces quenching real parts and counting what breaks.