Steady-state thermo-elastic field in an infinite medium weakened by a penny-shaped crack: Complete and exact solutions

• Non-axisymmetric thermo-elastic crack problem is analytically solved.
• Steady-state coupling field is exactly obtained in terms of elementary functions.
• Crack surface displacement and stress intensity factor are explicitly derived.
• The temperature is found to be independent of material properties.
• An unusual observation on the radial displacement is revealed in this study.

This paper aims to analytically study the three-dimensional steady-state thermo-elastic field in an infinite space containing a penny-shaped crack subjected to a set of temperature loadings. The material is assumed to be isotropic and the loadings are symmetrically applied on the crack surfaces. In view of the symmetry with respect to the cracked plane, the present crack problem is formulated as a mixed boundary-value problem. The corresponding boundary integral and integro-differential equations are solved by virtue of the potential theory method in conjunction with the newly developed general solution. For the crack subjected to point or uniform temperature loadings, the thermo-elastic field variables are explicitly and exactly obtained in terms of elementary functions, in a complete manner. In both non-axisymmetric and axisymmetric cases, some important parameters in fracture mechanics, e.g., the crack surface displacement, the normal stress in the intact subregion of the crack plane and the stress intensity factor are explicitly derived as well. The validity of the present solutions is discussed analytically and by virtue of finite element simulation. The obtained analytical results can be combined with experimental investigations by the infrared-thermography technique.