thermal stress
Thermal stress is stress that a material generates against itself when it is heated or cooled and cannot expand or contract freely — no external push required, only expansion that is somehow blocked. Heat a bar that is clamped at both ends and it cannot lengthen, so it pushes hard against its clamps and squeezes itself in compression. Heat a thick block unevenly and the hot part wants to grow while the cold part holds it back, so the block strains against itself. Every part of the block is loaded, yet nothing outside is pushing on it.
The size of the stress is easy to estimate. For a bar fully prevented from expanding while heated by delta-T, the stress is sigma = E times alpha times delta-T (uniaxial), where E is the elastic modulus and alpha the expansion coefficient; for a constrained surface layer the biaxial version sigma = E times alpha times delta-T divided by (1 - nu) applies, with nu the Poisson ratio. Put numbers in: alumina with E about 380 GPa, alpha about 8 x 10^-6 /K, and delta-T of 100 degrees gives roughly 380 x 10^9 times 8 x 10^-6 times 100, near 300 MPa — comfortably enough to fracture it. Thermal stress rises with stiffness E, with expansion alpha, and with the temperature difference; it does not care how strong the part is until it is time to crack.
Three situations create it in real ceramics. External constraint, as when a rigid frame stops a heated part from growing. Internal temperature gradients, as when a quenched surface is held by a hot core — the classic route to thermal shock, and the reason the surface goes into dangerous tension on cooling. And expansion mismatch between joined materials — a coating on a substrate, a glaze on a body, a second phase in a matrix — where the two want to change size by different amounts. Managing thermal stress is the whole game of high-temperature ceramic design: keep E and alpha low, avoid sharp constraints, heat and cool gradually, and match the expansion of anything you bond together.
A glaze whose expansion coefficient is higher than the clay body beneath it ends up stretched in tension as the pot cools, and above a threshold it cracks into the fine network called crazing. Choosing a glaze with slightly lower expansion than the body instead leaves the surface in mild compression — stronger and craze-free.
Expansion mismatch between a coating and its substrate is thermal stress made visible — tune it to leave the surface in compression, not tension.
Thermal stress depends only on modulus, expansion, and temperature difference — not on strength. A very strong ceramic still builds the same thermal stress as a weak one; strength only decides at what stress it finally cracks.