7 Design Criteria for Thermal Stress

The allowable stress for thermal expansion and other deformation-induced stresses is substantially higher than for sustained loads. This is due to the difference between load-controlled conditions, such as weight and pressure, and deformation-controlled conditions, such as thermal expansion or end displacements (e.g., due to thermal expansion of attached equipment).

When a load-controlled stress is calculated, it is an actual stress value. It is governed by equilibrium. For example, the stress in a bar when a tensile force is applied to it is the force divided by the area of the bar. This is not the case for thermal stresses. In the case of thermal stresses, it is the value of strain that is known. The elastically calculated stress is simply the strain value times the elastic modulus. This makes essentially no difference until the stress exceeds the yield strength of the material. In that case, the location on the stress-strain curve for the material is determined based on the calculated stress for load-controlled, or sustained, loads. The location on the stress-strain curve for the material is determined based on the calculated strain (or elastically calculated stress divided by elastic modulus) for deformation-controlled (e.g., thermal expansion) loads. This is illustrated in Fig. 7.1. Because the stress analyses are based on the assumption of elastic behavior, it is necessary to discriminate between deformation-controlled and load-controlled conditions in order to properly understand the post-yield behavior.