Thermoelastic problem of an orthotropic elastic plane containing a cruciform crack

Abstract

The problems of determining the thermal stress and displacement fields in an infinite orthotropic plane containing a cruciform crack when (I) the shape of the crack is prescribed and (II) the cracks are opened by given normal pressures, are reduced to mixed boundary value problems for the quarter plane. An integral transform technique, based upon displacement potentials, is employed for the case of a steady-state temperature field. Closed form solution is obtained for problem I, whereas the solution of problem II has been reduced to solving a Fredholm integral equation of second kind with non-singular kernel. The expressions for the stress intensity factor and the energy of crack formation are derived. In problem II, numerical results are presented for the case of linear loading functions.