Thermal stresses arise in materials when they are heated or cooled. Thermal stresses effect the operation of industrial facilities, both because of the large components subject to stress and because they are affected by the way in which the plant is operated. This chapter describes the concerns associated with thermal stress.
Thermal shock (stress) can lead to excessive thermal gradients on materials, which lead to excessive stresses. These stresses can be comprised of tensile stress, which is stress arising from forces acting in opposite directions tending to pull a material apart, and compressive stress, which is stress arising from forces acting in opposite directions tending to push a material together. These stresses, cyclic in nature, can lead to fatigue failure of the materials.
Thermal shock is caused by non-uniform heating or cooling of a uniform material, or uniform heating of non-uniform materials. Suppose a body is heated and constrained so that it cannot expand. When the temperature of the material increases, the increased activity of the molecules causes them to press against the constraining boundaries, thus setting up thermal stresses.
If the material is not constrained, it expands, and one or more of its dimensions increases. The thermal expansion coefficient relates the fractional change in length, called thermal strain, to the change in temperature per degree.
Table 1 lists the coefficients of linear thermal expansion for several commonly-encountered materials.
Table 1 Coefficients of Linear Thermal Expansion
In the simple case where two ends of a material are strictly constrained, the thermal stress can be calculated using Hooke's Law by equating values of from Equations (3-1), (3-2), and (3-3).
Example: Given a carbon steel bar constrained at both ends, what is the thermal stress when heated from 60F to 54F?
Thermal stresses are a major concern in industrial systems due to the magnitude of the stresses involved. With rapid heating (or cooling) of a thick-walled vessel such as a pressure vessel, one part of the wall may try to expand (or contract) while the adjacent section, which has not yet been exposed to the temperature change, tries to restrain it. Thus, both sections are under stress. Figure 1 illustrates what takes place.
A vessel is considered to be thick-walled or thin-walled based on comparing the thickness of the vessel wall to the radius of the vessel. If the thickness of the vessel wall is less than about 1 percent of the vessel's radius, it is usually considered a thin-walled vessel. If the thickness of the vessel wall is more than 5 percent to 10 percent of the vessel's radius, it is considered a thick-walled vessel. Whether a vessel with wall thickness between 1 percent and 5 percent of radius is considered thin-walled or thick-walled depends on the exact design, construction, and application of the vessel.
When cold water enters the vessel, the cold water causes the metal on the inside wall to cool before the metal on the outside. When the metal on the inside wall cools, it contracts, while the hot metal on the outside wall is still expanded. This sets up a thermal stress, placing the cold side in tensile stress and the hot side in compressive stress, which can cause cracks in the cold side of the wall.
Stress on Reactor Vessel Wall
The heatup and cooldown of the vessel and the addition of makeup water to the system can cause significant temperature changes and thereby induce sizable thermal stresses. Slow controlled heating and cooling of the system and controlled makeup water addition rates are necessary to minimize cyclic thermal stress, thus decreasing the potential for fatigue failure of system components.
Operating procedures are designed to reduce both the magnitude and the frequency of these stresses. Operational limitations include heatup and cooldown rate limits for components, temperature limits for placing systems in operation, and specific temperatures for specific pressures for system operations. These limitations permit material structures to change temperature at a more even rate, minimizing thermal stresses.