Thermal Properties

thermal stress

Pour boiling water into a cold thick glass and it cracks. The glass wants to expand where it is hot, but the cold parts hold it back — that internal tug-of-war is thermal stress. Whenever a material's natural expansion is prevented, stress builds up as surely as if you had clamped it in a vise.

If a bar is fully clamped so it cannot change length and you change its temperature by delta_T, the stress is sigma = E x alpha x delta_T, where E is Young's modulus and alpha is the expansion coefficient. Worked example: a steel rail (E = 200 GPa, alpha = 12 x 10^-6 per K) held rigid and warmed 40 degrees C carries sigma = 200e9 x 12e-6 x 40, which is 96 MPa of compression — enough, over a long rail, to buckle the track sideways. Notice the stress does not depend on length: a short clamped bar and a long clamped bar reach the same stress for the same delta_T (though the long one, if it were free, would move much more).

Thermal stress arises three ways: from external constraint (clamped pipes, welded rail), from temperature gradients within one part (a hot surface pulling against a cold interior, as in the cracked glass), and from mismatch between two bonded materials. It drives thermal fatigue in engines and cracking in castings. The defenses are always the same: let it move (expansion joints, flexible loops), lower alpha, lower E, or reduce the temperature swing.

A welded steel pipe clamped at both ends and heated 50 degrees C by the fluid inside builds sigma = 200e9 x 12e-6 x 50, which is 120 MPa of compression — a large fraction of typical steel yield strength, so pipelines add expansion loops to bleed it off.

Constrained expansion turns a modest temperature change into a large, dangerous stress.

Thermal stress from full constraint is independent of the part's length — doubling the bar does not double the stress. What length changes is how much a free part moves, not how hard a clamped one pushes.

Also called
熱應力溫度應力