Coefficient of Thermal Expansion in Metals

The coefficient of thermal expansion (CTE) determines how much a metal expands with temperature changes. CTE mismatch between joined materials causes thermal stress, distortion, and fatigue in multi-material assemblies.

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## What Is CTE? CTE (alpha) is the fractional change in length per degree of temperature change, in 10^-6/degree C. A 1-meter steel bar (alpha = 12) heated by 100 degrees C expands 1.2 mm. ## CTE of Engineering Metals | Metal/Alloy | CTE (10^-6/degree C) | |------------|----------------------| | Invar 36 (36% Ni) | 1.2 | | Tungsten | 4.5 | | Kovar (29Ni-17Co-Fe) | 5.3 | | Carbon steel | 11-12 | | Titanium Ti-6Al-4V | 8.6 | | 304 Stainless | 17.3 | | Copper | 17.0 | | Aluminum 6061 | 23.6 | | Magnesium AZ31B | 26.0 | ## CTE Mismatch: Thermal Stress When two materials with different CTEs are bonded, temperature change creates differential expansion: sigma = E x delta-alpha x delta-T. **Steel-to-aluminum joints**: CTE mismatch of 12 ppm/degree C. A 1-meter joint with 100 degree C change develops 1.2 mm differential expansion. **Stainless-to-carbon steel welds**: Mismatch of ~6 ppm/degree C. Cyclic thermal stress at every startup and shutdown. ## Low-CTE Alloys **Invar 36**: CTE 1.2 ppm/degree C via magnetovolume effect. Applications: LNG membrane tanks, precision instruments, optical benches, composite layup molds (matched CTE to carbon fiber). **Kovar**: CTE 5.3 ppm/degree C, matching borosilicate glass. Used for hermetic glass-to-metal seals in electronics. ## Practical Implications **Piping**: 30 m of stainless at 300 degrees C above ambient expands 15.6 mm. Expansion loops or bellows are mandatory. **Bolted joints**: Aluminum flanges with steel bolts: temperature increase raises bolt tension (aluminum expands more). Temperature decrease can cause joint separation. **Glass-to-metal seals**: CTE match must be within ~0.5 ppm/degree C. Kovar (5.3) matched to borosilicate (5.0). **Bimetallic thermostats**: Deliberately exploit CTE mismatch. Invar (low CTE) bonded to brass (high CTE) bends with temperature change to actuate switches. ## Temperature Dependence CTE generally increases with temperature. Design calculations must use the mean CTE over the actual operating range, not the room-temperature value. Invar loses its anomaly above the Curie temperature (~200 degrees C), where CTE jumps to 10+ ppm/degree C.