Thermal shock in a domain with a crack

Abstract

Thermal shock, i.e., the action of stresses caused by an abrupt change in temperature, in a plane with a semi-infinite slit, is investigated. It is assumed that the plane has zero temperature at the initial instant, and a certain non-zero temperature acts instantaneously on the slit. The main result is the representation (5.8) of the tensile stress intensity factor SIF). The Laplace transform of the SIP is found by using a method proposed in /1/ for evaluating the coefficients in the asymptotic form of the solutions of elliptical boundary value problems near a boundary singularity. Such an approach enables one to find the SIF bypassing the solution of the initial dynamical thermoelasticity problem. Asymptotic expressions for the SIF are derived from the formulas for the SIF, as well as for the time of fracture under instantaneous cooling of the crack edges. Thermal shock is also considered in a bounded plane domain with a rectilinear slit. It is shown that the principal term of the SIF asymptotic form for small values of time agrees with the SIF for the same problem in a plane with a slit. The expectation value of the heat shock can be obtained by the simultaneous solution of the heat conduction equation and the thermoelasticity system taking inertial terms into account. The first analytic solution of such a dynamic problem was found in /2/, where the thermal shock was considered in an elastic half-space for sudden heating of its boundary. References to other literature in the same area can be found in /3/.