The glass dish did not crack because it was weak. It cracked because its inside and outside disagreed about size

Four failures that look unrelated. A borosilicate dish out of a hot oven, rinsed under a tap, cracks straight across. Floor tiles on a terrace lift off with an audible bang on a May afternoon. A solder joint that carried its current perfectly for three years goes open circuit. And a tooth filling that fitted beautifully develops a stained margin and starts to leak.

None of these is a strength problem in the ordinary sense. Nothing was overloaded. In every case, two things wanted to change size by different amounts, and something had to give.

Expansion itself is completely harmless. A steel bar left free to lengthen simply lengthens. What breaks things is preventing expansion — and the stress that constraint generates is far larger than most people's intuition allows.

Everything expands, and the numbers differ more than you would think

Heat a solid and its atoms vibrate with greater amplitude, sitting slightly further apart on average. The fractional size change per degree is the coefficient of thermal expansion, usually quoted in parts per million per kelvin.

The spread across common materials is what causes all the trouble:

• Fused silica about 0.5, borosilicate glass about 3, ordinary soda-lime glass about 9
• Concrete about 10, steel about 12, copper about 17, aluminium about 23
• Most polymers between 50 and 200 — five to twenty times a metal
• Invar, a nickel-iron alloy, about 1.2

Two observations follow immediately. Plastics move enormously compared with the metals they are usually bolted to. And glass covers a huge range depending on its composition, which is why the choice between kitchen glass types is not marketing.

Constraint is the whole story

Here is the equation that does the work, in words. The stress generated in a constrained part is roughly its stiffness multiplied by its expansion coefficient multiplied by the temperature change.

Put numbers to it and the result is startling. A steel member fully restrained and heated by just 30 °C develops stress in the region of seventy megapascals — a substantial fraction of the yield strength of ordinary structural steel, produced by nothing at all except a warm afternoon. No load was applied. Nobody stood on it.

This is why thermal effects are not a minor correction in structural design but a primary load case, and why the standard answer is not stronger material but allowing movement: expansion joints in bridges and buildings, expansion loops in long pipe runs, sliding bearings, gaps between rails, and movement joints in tiling and cladding. Every one of those gaps is there because stopping the movement would cost more than accommodating it.

A temperature change does not stress anything by itself. A temperature change plus a constraint does — and the constraint is usually something an engineer added, which means thermal failures are very often design failures rather than material failures.

Thermal shock, and why thick glass is worse

A part does not need two different materials to be in trouble. A single piece is enough, if it is not all at the same temperature.

Take a hot glass dish and cool its surface suddenly. The surface tries to contract; the still-hot interior is not ready to contract with it, so the surface is held stretched. Glass is brittle and has no yielding mechanism to relieve that tension — so, as our article on brittle strength explained, the tension finds the worst surface flaw and a crack runs from it.

Two consequences, and the second surprises people.

Low-expansion glass survives much better. Borosilicate has roughly a third the expansion coefficient of soda-lime glass, so the same temperature difference generates roughly a third the stress. That is the entire reason laboratory glassware and oven dishes are borosilicate, and why fused silica — an order of magnitude lower again — can be heated red hot and quenched in water.

Thick glass is worse than thin glass. This sounds wrong, because thick sounds strong. But thermal shock is driven by the temperature difference between surface and interior, and a thick piece takes longer to equalise, so it sustains a much larger internal gradient. A thin borosilicate beaker tolerates abuse that would destroy a heavy tumbler. Strength and thermal shock resistance are different properties, and here they pull in opposite directions.

The coincidence the built world rests on

Now a fact worth pausing over, because it is close to luck.

Steel expands at about 12 parts per million per kelvin. Concrete expands at about 10. Those numbers are near enough that a reinforced concrete beam heating through an Indian summer day expands as a single body, with only modest stress at the steel-concrete interface.

If the two had differed by a factor of two — as steel and aluminium do, or as steel and polymer do — reinforced concrete as we know it would not work. Every seasonal cycle would work the bars loose from the matrix, and the composite would progressively debond itself. The entire built environment depends on a near-match between two materials chosen for completely unrelated reasons.

It is not a perfect match, and where the remaining difference matters it shows up exactly as you would predict: at surfaces, at joints and in thin cover, which is one of several reasons cover thickness and joint spacing are specified rather than left to judgement — and which compounds the reinforcement corrosion problem once cracks let moisture in.

Why Indian summers are hard on buildings

Thermal movement scales with temperature swing, and India supplies large ones — a daily range of twenty-five to thirty degrees in many places, plus seasonal variation, plus dark surfaces in direct sun reaching sixty or seventy degrees while the shaded structure beneath them stays far cooler.

The visible consequences are familiar to anyone who has maintained a building here. Terrace and façade tiles debonding — often with a bang — because the tile, the adhesive and the substrate all move differently and no movement joints were provided. Cracks in plaster appearing exactly at the junction between two materials, which is precisely where a differential-movement crack should appear. Metal roofing that creaks in the evening as it cools and slides against its fixings. Long pipe runs that bow or tear at a rigid anchor.

Almost none of these is fixed by using a stronger tile or a better adhesive. They are fixed by movement joints, by fixings that allow sliding, and by not rigidly connecting two materials with very different expansion over a long unbroken run.

Why switching a device on and off is worse than leaving it running

The electronics version of this problem is the dominant wear-out mechanism in assembled hardware, and it produces genuinely counterintuitive advice.

A surface-mount component sits on a circuit board, joined by solder. The component body — ceramic or silicon-based — might expand at 3 to 7 parts per million per kelvin. The board is a glass-fibre and epoxy composite expanding at perhaps 14 to 18 in plane. The solder joint between them is the only thing that can absorb the difference.

Every time the device powers up and warms, then powers down and cools, that joint is strained. It is a small strain, but it repeats — and solder creeps and fatigues. After enough cycles a crack initiates and grows, and eventually the joint goes open, usually intermittently first. This is thermal cycling fatigue, and it is why reliability engineers count power cycles rather than operating hours for many assemblies, why underfill adhesive is applied beneath large packages to share the strain, and why large ceramic components are the most vulnerable.

The practical inversion is real: equipment that runs continuously often outlasts identical equipment that is switched on and off frequently, because the continuous unit accumulates far fewer thermal cycles. The same logic sits behind the old observation about light bulbs and about industrial machinery, and it applies with full force to electronics.

When two materials must be joined permanently

Sometimes movement cannot be allowed, and then the only option is to match the expansion.

Glass-to-metal seals are the classic case. A hermetic electrical feedthrough — in a vacuum tube, a sensor, a pressure transducer, a battery terminal — needs glass bonded to metal with no leak path, permanently, through repeated temperature cycles. You cannot use an arbitrary metal, because on cooling from the sealing temperature the two would part or crack the glass.

So an alloy was designed specifically to solve it. Kovar, an iron-nickel-cobalt alloy, exists essentially because its expansion curve follows that of borosilicate glass closely over a wide range. It is a material whose entire reason for existence is a thermal expansion coefficient — which is an unusual and instructive thing for a metal to be.

Invar is the other famous case, with an anomalously low expansion coefficient arising from a magnetic effect that happens to cancel most of the normal thermal expansion. It is used where dimensions must not change: precision instruments, surveying tapes, and the membranes of liquefied-gas tankers, where the cargo is at −160 °C and ordinary steel would shrink unacceptably.

And in a component this site has already discussed, the catalytic converter substrate is typically cordierite — a ceramic chosen largely because it has very low thermal expansion, which is what lets a thin-walled honeycomb survive being heated from ambient to several hundred degrees within a minute of a cold start, thousands of times.

The material that shrinks when you heat it

The nanomaterials contribution here is smaller than in some of this catalogue's subjects and includes one genuinely strange thing.

A few materials have negative thermal expansion — they contract when heated. The best known is zirconium tungstate, a metal oxide whose framework structure responds to heating by rotating its linked polyhedra in a way that pulls the structure inward. It is not a curiosity of the last decimal place; the effect is substantial and works over a wide temperature range.

That makes it useful as a filler for expansion tailoring: blend a negative-expansion or very-low-expansion powder into a matrix and the composite's net coefficient can be dialled down towards zero, or towards matching whatever it must be bonded to. This is a real strategy in electronics packaging and precision optics, where matching a substrate matters more than any absolute value.

The honest limits are worth stating. Mixing rules for composite expansion are approximations rather than laws, because the phases constrain each other internally. Expansion coefficients themselves vary with temperature, so a composite matched carefully at 25 °C may be mismatched at 150 °C — which is exactly the range that matters for electronics. And as everywhere else in this catalogue, a filler only delivers its property if it is genuinely dispersed rather than agglomerated.

Why it matters for students and researchers

The transferable idea is that stress does not require a load. A constraint plus a temperature change is sufficient, and the stress it produces can exceed anything in the design load case. Students who instinctively add "and what happens when this gets hot, while held" to their checking will catch a whole class of failure that no static analysis reveals.

The second idea is matched expansion as a selection criterion. Beginners choose materials on strength, stiffness, corrosion resistance and price. Experienced designers joining two materials permanently look at the expansion coefficients early, because a mismatch cannot be fixed downstream — it can only be accommodated or designed around. Kovar exists as proof of how far industry will go to satisfy that one number.

The open problems are practical. Life prediction for solder-joint thermal fatigue remains semi-empirical, and models calibrated on one package geometry transfer poorly to another. Matching expansion across a wide temperature range, rather than at one point, is genuinely difficult and is the binding constraint in several precision applications. Negative-expansion materials are mostly brittle oxides with their own processing problems, which limits where they can be used. And for Indian construction specifically, movement-joint practice in tiling and cladding is frequently below what the local temperature range requires, which makes it a workmanship and specification problem more than a materials one.

Frequently asked questions

Why did my glass dish crack when I put it in water?

Thermal shock. The surface cooled and tried to contract while the interior was still hot and not contracting with it, which put the surface into tension — and brittle materials fail in tension from their worst surface flaw. Borosilicate resists this roughly three times better than ordinary glass because its expansion coefficient is about a third as large, and thinner glass resists it better than thick because it equalises temperature faster.

Why do terrace or façade tiles pop off with a bang?

Because the tile, the adhesive and the concrete beneath all expand by different amounts, and if no movement joints were provided the accumulated stress has nowhere to go until the bond fails suddenly. It is a design omission rather than a bad tile, and the remedy is movement joints at appropriate spacing, a flexible adhesive rated for the application, and not running a large unbroken tiled field in direct sun.

Is borosilicate cookware worth paying for?

For anything involving sudden temperature changes, yes. Its lower expansion coefficient means a given temperature difference produces roughly a third of the stress, which is a large safety margin in a kitchen. It is not indestructible — a thick borosilicate piece taken from a hot oven to a cold wet surface can still fail — and it is no stronger than ordinary glass against mechanical impact, which is a different property entirely.

Why did a solder joint fail after three years of working perfectly?

Almost certainly thermal cycling fatigue. Each power-up and cool-down strains the joint slightly, because the component and the board expand by different amounts, and solder creeps and accumulates damage. After thousands of cycles a crack grows through the joint. This is why counting power cycles predicts electronics failures better than counting hours, and why equipment left running continuously often outlives the same equipment switched on and off daily.

Why do bridges and railway tracks have gaps in them?

Because the alternative is enormous stress. A restrained steel member heated by thirty degrees generates stress comparable to a substantial fraction of its yield strength, from temperature alone, and over the length of a bridge the unrestrained movement would be measured in centimetres. Expansion joints, sliding bearings and rail gaps exist to let that movement happen harmlessly — and continuously welded rail, where gaps are eliminated, requires the rail to be deliberately pre-stressed and anchored precisely because the movement cannot simply be ignored.