Thermal expansion coefficient (CTE)

Thermal expansion coefficient converts a temperature change into strain. For a material with an average coefficient α over the interval being assessed, multiply α by the starting length and the temperature change to estimate the free change in length. The value is a material property, not a weld-process setting, and it may change with temperature and material condition. NIST’s thermal-expansion work defines the linear coefficient from change in length, original length and change in temperature, and notes that the coefficient can depend on temperature.

Welding makes the property important because a joint rarely heats uniformly. A local thermal gradient makes neighbouring regions attempt different amounts of expansion and contraction. Restraint prevents some of that free movement, turning the mismatch into distortion and residual stress.

Worked distinction: coefficient and thermal gradient

Take two illustrative one-metre strips heated through the same 100 K interval. Give strip A an average coefficient of 12 µm/(m·K) and strip B an average coefficient of 18 µm/(m·K). If each is free to move, the formula gives 1.2 mm growth for A and 1.8 mm for B: a 0.6 mm difference. Those values are invented for the example and do not represent named alloys.

The coefficient explains why the two materials respond differently to the same temperature change. The thermal gradient explains how temperature varies from one position to another. A component can have a uniform temperature change with no spatial gradient and still expand; it can also have one material coefficient while a steep gradient produces different local movement. In a dissimilar metal weld, both effects can act together, so the calculation needs the coefficient for each actual material and the temperature interval in service rather than a generic room-temperature label.

The formula estimates free expansion. It does not establish the stress in a restrained weldment without geometry, elastic-plastic properties, boundary conditions and the thermal history of the heat-affected zone.