Axisymmetric thermo-elastic field in an infinite one-dimensional hexagonal quasi-crystal space containing a penny-shaped crack under anti-symmetric uniform heat fluxes

Abstract

This paper is dedicated to investigating the problem of an infinite one-dimensional hexagonal quasi-crystal medium weakened by a penny-shaped crack and subjected to a pair of anti-symmetric and identical uniform heat fluxes. In view of the anti-symmetry with respect to the crack plane, this problem is formulated by a mixed boundary value problem of the half-space. Based on the general thermo-elastic solution, the mixed boundary value problem is solved by means of the generalized potential theory method. The thermo-elastic field variables in the entire three-dimensional space are explicitly expressed in terms of elementary functions. Some important physical quantities on the crack plane, e.g., temperature, crack slip displacement, shear stress and stress intensity factor, are also presented in closed-forms. Numerical calculations are carried out to validate the present analytical solution and to graphically show the distribution of the thermo-elastic coupling field around the crack. The present solution may be served as a benchmark for the experimental investigations by infrared-thermography technique.