Thermal stress

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Thermal stress is stress created by any change in temperature to a material. These stresses can lead to fracture or plastic deformation depending on the other variables of heating, which include material types and contraints.[1] Temperature gradients, thermal expansion or contraction and thermal shocks are things that can lead to thermal stress. This type of stress is highly dependent on the thermal expansion coefficient which varies from material to material. In general the larger the temperature change, the higher the level of stress that can occur.

Temperature gradients[1][edit]

When a material is rapidly heated or cooled, the surface and internal temperature will have a difference in temperature. Quick heating or cooling causes localized areas of thermal expansion or contraction, this localized movement of material causes thermal stresses. Imagine heating a cylinder, first the surface rises in temperature and the center remains the same initial temperature. After some time the center of the cylinder will reach the same temperature as the surface. During the heat up the surface is relatively hotter and will expand more than the center. An example of this is dental fillings can cause thermal stress in a person's mouth. Sometimes dentist use dental fillings with different thermal expansion coefficients than tooth enamel, the fillings will expand faster than the enamel and cause pain in a person's mouth.

Thermal expansion or contraction[edit]

Example of deformation induced by thermal stress on the rails

Material will expand or contract depending on the material's thermal expansion coefficient. As long as the material is free to move, the material can expand or contract freely without generating stresses. Once this material is attached to a rigid body at one end, thermal stresses can be created.This stress is calculated by multiplying the change in temperature, material's thermal expansion coefficient and material's young's modulus (see formula below). E is young's modulus, α is thermal expansion coefficient, To is temperature original, and Tf is the final temperature.[2]


As the temperature increases the stress will be in compression due to the constraints, this is when Tf is greater than To. The opposite happens which cooling, when TF is less than To, the stress will be in tension.A welding example involves heating and cooling of metal which is a combination of thermal expansion, contraction, and temperature gradients. After a full cycle of heating and cooling, the metals left with residual stress around the weld.

Thermal shock[edit]

This is a combination of a large temperature gradient in addition to rapid change in temperature on brittle materials. The change in temperature causes stresses on the surface that are in tension, which encourages crack formation and propagation. Ceramics materials are usually susceptible to thermal shock.[2] An example is when glass is heated up to a high temperature and then quickly quenched in cold water. As the temperature of the glass falls rapidly, stresses are induced and causes fractures in the body of the glass which can be seen as cracks or even shattering in some cases.


  1. ^ a b Elements of metallurgy and engineering alloys. Campbell, F. C. (Flake C.). Materials Park, Ohio: ASM International. 2008. ISBN 9780871708670. OCLC 608624525. 
  2. ^ a b 1940-, Callister, William D., Jr.,. Materials science and engineering : an introduction. Rethwisch, David G., (8th ed.). Hoboken, NJ. ISBN 9780470419977. OCLC 401168960. 
  3. ^ F., Carter, Giles (1991). Materials science & engineering. Paul, Donald E. [Materials Park, Ohio]: ASM International. ISBN 9780871703996. OCLC 555222029.