Transient concentrated thermal/mechanical loading of the faces of a crack in a coupled-thermoelastic solid

A near-tip, transient, coupled thermoelastodynamic solution is presented for the plane stress/strain problem of a crack subjected to a concentrated thermal and/or mechanical loading, which is suddenly and symmetrically applied to the crack faces. Interest is focused on the stress field in the immediate vicinity of the crack during a small time-interval right after the application of loading and, therefore, the cracked body is considered of infinite extent and the crack itself of semiinfinite length. The loading consists of a pair of line heat sources or sinks (thermal loading) placed at the crack faces and/or a pair of equal, but opposite, line concentrated normal forces (mechanical loading) applied on the crack faces. These loadings may have an arbitrary time dependence (our analysis can deal with such cases), but here only the case of a step-function variation (the loadings act suddenly on the faces and are maintained there for all subsequent time) has been worked out. The thermoelastic wave propagation problem, which contains a characteristic length associated with the forcing function, is solved exactly in the time Laplace-transform domain by an analyticfunction method. The inversion of the time Laplace-transformed stress intensity factor is carried out through a numerical technique. The present solution provides the Greenʹs function for thermoelastic cracked bodies under more general spatially non-uniform loadings. © 1998 Elsevier Science Ltd