Asymptotic form of the stress intensity coefficients in quasistatic temperature problems for a domain with a cut
Plane quasistatic thermoelasticity problems are investigated for domains of arbitrary shape with a cut in the case of an instantaneous temperature change on the boundary. The asymptotic form of stresses is investigated in the neighbourhood of a crack tip. Quasistationary thermoelasticity problems are investigated for domains with cut in a more general asymptotic sense. A plane domain with a cut whose boundary is instantaneously cooled or heated is examined in Sects. 1-3. Since the shape of the domain contour can be arbitrary, it is impossible to speak of the explicit solution of the thermoelasticity boundary value problem. Nevertheless, an expression is successfully found for the principal terms of the asymptotic form of the stress intensity coefficients at the most dangerous initial times (from the viewpoint of crack propagation). In particular, the asymptotic form of the fracture time is determined as a function of the temperature jump at the crack tip. Note that the principal term of the tensile stress intensity coefficient is independent of the contour shape, and agrees with the intensity coefficient of the same problem for a plane with a cut. Analogous results are obtained in Sec. 4 for the problem of an instantaneous change in the endface temperature of a thin plate from whose side surfaces heat is transferred to the external medium, where the stress intensity coefficients found are explicitly expressed in terms of those in the absence of heat transfer. This enables an asymptotic analysis to be made of the stresses near a crack tip at the initial times. The results obtained in this paper emerge from the asymptotic solution of the heat conduction equations as \(t\to 0\) for a domain with a cut and the method proposed by the second author and \textit{B. A. Plamenevskij} [Math. Nachr. 76, 29-60 (1977; Zbl 0359.35024)] for calculating the stress intensity coefficients.
instantaneous change in the endface temperature
scientific article; zbMATH DE number 3986729