The Physics
When two materials with different coefficients of thermal expansion are joined, the temperature delta creates a shear force at the interface. The differential drift is:
where:
• L₀ = initial length (mm)
• α = linear CTE (µm/m·K = ppm/K)
• ΔT = temperature change (K or °C)
Lunar validation: At Shackleton Crater, ΔT reaches 300°C between permanent shadow and sunlit rim. An aluminum-steel joint of 1 meter must accommodate 3.42 mm of differential drift — or yield.
Stress estimate (if constrained):
where E_avg = average Young's modulus
Source: Coefficient of Thermal Expansion (Q45760), Wikidata.
Aluminum 6061-T6: 23.1 ppm/K | Steel AISI 1020: 11.7 ppm/K
Constants verified against Callister, Materials Science & Engineering, 10th ed.
Why This Matters
In St. Louis, I've watched bridge bearings fail because someone forgot the summer-winter swing. On the Moon, forgetting means a habitat cracks open at -173°C.
This solver is my 12% buffer made executable. Input your materials. Get your clearance. Build the joint that survives.