Stresses Caused by Thermal Contraction

Abstract

Although there are exceptions over limited temperature ranges, materials generally have positive thermal expansion coefficients. Usually, the temperature change from ambient to cryogenic temperature will amount to as much as 200 K (360 °F) or greater. This large temperature decrease will cause a significant thermal contraction in any material being cooled from ambient temperature to cryogenic temperature. However, the thermal expansion coefficient is also a function of temperature, decreasing as the temperature is lowered. Figure 4.1 shows the temperature dependence of the thermal expansion coefficient of copper.¹ Although there is still further contraction below the temperature of liquid nitrogen, usually over 90% of the total contraction from room temperature to any lower temperature will have already taken place at 77 K because of the decrease in the thermal expansion coefficient for many materials with temperature. Consequently, in cooling from ambient temperature to any cryogenic temperature, there will be a thermal contraction of about 0.3% in iron-based alloys, over 0.4% in aluminum, and well over 1% in many plastics. The first two of these figures give useful rule-of-thumb values for quick estimates. The more accurate values needed for system design can be obtained from published tables of integrated thermal contraction over the temperature range of interest. Tables 4.1 and 4.2 give some representative examples.² Figure 4.2 shows the total integrated thermal contraction from ambient temperature down to any cryogenic temperature for several materials.³