Thermal Expansion Coefficients (CTE): Impact on Cryogenic Tightening

In our article on preload, we mentioned differential thermal expansion as one of the sources of in-service preload loss — sometimes the most significant one. This article is entirely dedicated to it, with a particular focus on cryogenic environments, where this effect becomes critical.

What is CTE?

The coefficient of thermal expansion (CTE, often denoted α) characterizes how much a material's dimension changes per degree of temperature variation. Generally expressed in ×10⁻⁶/°C (or ppm/°C), it indicates a part's relative elongation per degree: a CTE of 12×10⁻⁶/°C means a 1000mm part elongates by about 0.012mm per degree of warming.

In a bolted joint, two distinct CTEs come into play: that of the bolt (usually steel) and that of the clamped parts (which may be a very different material — aluminum, composite, cryogenic alloy...).

Why the gap between materials matters

As long as the bolt and clamped parts share the same CTE, a temperature change expands or contracts them identically, with no net effect on preload. The problem appears as soon as the CTEs differ: the bolt and parts don't "move" at the same rate with temperature, which mechanically alters the tension in the bolt — without any additional torque having been applied.

Depending on the sign of the gap and the direction of the temperature change, this effect can either increase preload (yielding risk) or decrease it (slipping or separation risk) — which is why it's essential to check both extremes of the service temperature range, not just the reference assembly temperature.

Common CTE values

Typical orders of magnitude at room temperature — actual values vary by exact alloy and should be verified against the material datasheet used:

• Steel (common bolt material) — approximately 11 to 13 ×10⁻⁶/°C
• Austenitic stainless steel — approximately 16 to 18 ×10⁻⁶/°C, noticeably higher than carbon steel
• Aluminum — approximately 22 to 24 ×10⁻⁶/°C, often double that of steel
• Titanium — approximately 8.5 to 9.5 ×10⁻⁶/°C, closer to steel
• Composites (depending on fiber orientation) — highly variable, sometimes near zero or even negative along the fiber direction

The most frequently problematic pairing: steel bolts on aluminum parts, with a CTE gap close to double — exactly the type of configuration that warrants a rigorous thermal check rather than a default assumption.

The special case of cryogenics

In cryogenic applications (propellant tanks, cooling systems, space instrumentation), two factors worsen the CTE effect compared to a room-temperature application:

• The ΔT magnitude is much larger — a gap of 200 to 300°C between assembly temperature and cryogenic service temperature is nothing unusual, versus a few tens of degrees for most industrial applications.
• CTE itself isn't constant with temperature — the assumption of a linear CTE, reasonable over a narrow range around room temperature, becomes a coarser approximation over such a wide range extending down to very low temperatures.

For a rigorous cryogenic justification, it's better to use a mean CTE integrated over the actual temperature range (often tabulated separately in material databases for low temperatures) rather than the room-temperature value applied as-is.

How the thermal effect changes preload

The thermally-induced preload loss (or gain) depends on the CTE gap between bolt and clamped parts, the magnitude of the temperature change, and the respective stiffnesses of the bolt and parts (their compliances δb and δc). The larger the CTE difference and the ΔT magnitude, the greater the effect on preload — and the higher the joint's compliances (a "softer" joint), the more this effect is amplified.

This is why the thermal check can't be decoupled from the rest of the preload calculation: it must be integrated into the full Fv,min/Fv,max bracket, at both extremes of the service temperature range.

Mitigation strategies

• Choose materials with close CTEs when the design allows it — directly reduces the magnitude of the thermal effect.
• Belleville washers or elastic elements — absorb part of the preload variation by adding controlled compliance to the joint.
• Compensation via tightening preload — target an initial preload that remains within an acceptable range even after the thermal effect at both extremes, rather than a preload optimal only at room temperature.
• Low-temperature characterization — for critical cryogenic applications, use CTE values measured over the actual range rather than generic room-temperature values.

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