Alumina tube cracked on fast cooling from 1000 °C: how is thermal shock resistance estimated?

The damage comes from temperature differences inside the part, not from the temperature level. When the surface cools faster than the interior it tries to contract, the hot interior holds it back, and the surface goes into tension. For a surface that is fully restrained the stress is σ = E × α × ΔT / (1 - ν).

For dense alumina, with E about 380 GPa, α about 8 × 10^-6 per K and ν about 0.22, a difference of 100 K gives 380,000 × 8 × 10^-6 × 100 / 0.78 = about 390 MPa. That is at or above the tensile strength of most alumina, around 300 MPa, and a ceramic cannot yield to relieve it, so it cracks. Cooling is the more dangerous direction because it puts the surface, where the flaws are, in tension.

Setting that stress equal to the strength gives the first thermal shock parameter, R = σ_f × (1 - ν) / (E × α), the temperature difference that the material survives in an ideally severe quench. For alumina with the values above: 300 × 0.78 / (380,000 × 8 × 10^-6) = about 77 K.

Fused silica has a strength of only about 50 MPa, but E is 72 GPa and α is about 0.5 × 10^-6 per K, which gives R = 50 × 0.83 / (72,000 × 0.5 × 10^-6) = about 1150 K. Its tiny expansion coefficient is the reason it can be quenched into water from red heat. Silicon nitride comes out at several hundred kelvin because it combines high strength with low expansion.

Treat R as a ranking number, not as a permitted temperature step. It assumes the surface temperature changes instantly, which needs an extremely high heat transfer rate. In slower cooling, such as air reaching a hot tube, heat conducts outward from the interior while the surface cools, so the real gradient is smaller than the full temperature difference. The tolerable step is then larger than R and depends on wall thickness, thermal conductivity and the heat transfer coefficient.

Thin walls and high conductivity help. This is why silicon carbide, with a conductivity several times that of alumina, handles thermal cycling well, and why a thick-walled alumina tube is more fragile in this respect than a thin one.

In practice, control the ramp rates and avoid local cold spots. Suppliers of alumina tubes give maximum heating and cooling rates, usually a few degrees per minute for larger diameters, and they apply to cooling as much as heating. Do not open a tube furnace hot, do not let cold gas blow directly on a hot wall, and keep the end seals and water-cooled flanges far enough from the hot zone that the axial gradient along the tube stays gentle. Support the tube so it can expand freely.

If the process really needs fast cycling, change the material: fused quartz up to roughly 1100 °C, or mullite, cordierite or silicon carbide, depending on temperature and atmosphere.

Bricks and castables that spall or burst in an oven are a related but different failure. Porous fireclay products often survive thermal shock better than dense ceramics, because their pores and microcracks stop cracks from running far; they lose a little strength with each cycle instead of breaking outright. What makes a brick or a fresh castable lining burst is usually trapped water turning to steam faster than it can escape.

The prevention is a slow first firing with holds a little above 100 °C and again at a few hundred degrees to drive off free and chemically bound water, following the manufacturer's dry-out schedule. Stay clear of a new lining during its first heat-up.