Transient analysis of a suddenly-opening crack in a coupled thermoelastic solid with thermal relaxation

Abstract

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.