For a semiinfinite crack that opens in an unbounded thermoelastic solid
initially at rest under uniform plane-strain tension at uniform temperature, the
governing equations contain as special cases the Fourier model, and two
thermal relaxation models with, respectively, one and two relaxation times.
Integral transforms reduce the initial/mixed boundary value problem to a
Wiener–Hopf equation. Its solution produces analytical expressions for temporal
transforms of normal stress and temperature change near the crack edge.
For 4340 steel, numerical inversions allow comparisons of the crack edge
stress for the three thermoelastic models with the isothermal result, and
temperature change at the crack edge for the two thermal relaxation models with
the Fourier model result. Calculations indicate that thermoelasticity has a
mild relaxation effect on the stress, and that temperature changes for the
thermal relaxation model are much larger than those that arise for the Fourier
model just after the crack opens. After a time interval in the order of a
nanosecond, however, the Fourier changes are larger, although the deviation is
minuscule.
