Three-dimensional fundamental thermo-elastic field in an infinite space of two-dimensional hexagonal quasi-crystal with a penny-shaped/half-infinite plane crack

In the present work, a penny-shaped/half-infinite plane crack problem is investigated in the framework of thermo-elasticity of two-dimensional quasi-crystals. In view of the symmetry with respect to the crack plane, the original problem is formulated by a mixed boundary-value problem defined in a half-space. The boundary integral equations are derived by virtue of the general solution and the method of generalized potential theory. For the crack subjected to a pair of point temperature loadings, the corresponding fundamental thermo-elastic field variables are exactly and explicitly obtained in terms of elementary functions. Furthermore, the physical quantities on the crack plane, which are important in fracture mechanics, are given. Numerical calculations are carried out to discuss the validity of the present solutions and to characterize the thermo-phonon-phason coupling effect. The present analytical solutions may serve as benchmarks for future computational fracture mechanics of QCs and as a guide for the infrared thermography techniques in non-destructive detection.