Glossary

Thermal stress is the internal stress that develops within a material when it experiences a change in temperature that causes it to expand or contract. Because different parts of the material may heat or cool at different rates—or because the material’s expansion is physically constrained—uneven thermal expansion or contraction generates internal forces. These forces resist the dimensional changes and create stress within the structure.

When a material is heated, it tends to expand, and when cooled, it contracts. The amount of expansion or contraction depends on the coefficient of thermal expansion (α), the temperature change (ΔT), and the original dimensions of the object. If this movement is restricted (for example, by fasteners, joints, or other structural components), the material cannot freely deform, and internal stress builds up. The basic relationship for thermal stress in a fully constrained material is:

σ = EαΔT

where 𝜎 is the thermal stress, 𝐸 is the modulus of elasticity, 𝛼 is the coefficient of thermal expansion, and 
Δ𝑇 is the temperature change.

If the temperature increases, the material wants to expand. When expansion is prevented, compressive stress develops. Conversely, if the temperature decreases and contraction is restrained, tensile stress occurs. Over time, repeated heating and cooling cycles can lead to thermal fatigue, a form of failure caused by the continual buildup and release of these stresses, often resulting in microcracks that grow with each cycle.

Thermal stress is particularly critical in metals, ceramics, and composite materials used in environments with large temperature gradients, such as turbine blades, engines, bridges, piping systems, and electronic components. For example, in a steel bridge exposed to day-night temperature swings, expansion during the day and contraction at night create alternating stresses that must be accounted for in the design.

Designers manage thermal stress by allowing for expansion (using expansion joints or flexible connections), selecting materials with compatible coefficients of thermal expansion, or applying thermal treatments that reduce residual stresses.