Thermal Shock:

It expands if the material is not constrained, and one or more of its dimensions increases. The thermal expansion coefficient (α) associates the fractional change in length ? l/l, called thermal strain, to modify in temperature per degree ?T.

α = (? l/l)/?l                                                                                                (3-1)

? l/l  = α?T                                                                                      (3-2)

where:

l = length (in.)

?l = change in length (in.)

α =  denotes linear thermal expansion coefficient (°F^-1)

?T = change in temperature (°F)

The below table lists the coefficients of linear thermal expansion for various generally-encountered materials.

In the easy case where two ends of a material are strictly constrained then the thermal stress could be calculated by using Hooke's Law through equating values of ?l/l from Equations (3-1), (3-2), and (3-3).

E = stress/strain =(F/A)/( ?l/l)                                                               (3-3)

Or

?l/l = (F/A)/E                                                                                             (3-4)

α?T = (F/A)/E

F/A = Eα?T                                                                                                (3-5)

where:

F/A = thermal stress (psi)

E = modulus of elasticity (psi)

α = denotes linear thermal expansion coefficient (°F^-1)

T = change in temperature (°F)