Closed-Form Solutions For Several Crack Problems In Thermo-Orthotropic Solids

The study of crack problems can give some theory basis for the reliability and server life of solids and structures. In the present paper, we study the single and two collinear cracks problems in orthotropic solids under applied uniform heat flow and mechanical loadings. Main observations are listed as follows.First, in order to investigate the effects of the thermal conductivity inside crack on crack-tip thermoelastic fields, the known crack face thermal boundary conditions have been analyzed. It is pointed out that the thermal-medium crack model is more effective to simulate an exact crack. The thermal permeable and impermeable crack models are the limiting cases of the thermal medium one.Second, applying the thermal-medium crack model, the Griffith crack problem in orthotropic solids is addressed under thermo-mechanical loadings. Based on the theories of Fourier transform, the thermoelasitc coupling partial difference equaitions are transfored to dual integral euqtions, then to singular integral equations. The thermoelastic fields in full plane are obtained. The known results can be derived by using the present ones. Numerical results are carried out to show the effects of thermal conductivity inside crack and applied mechanical loadings on the thermal stress intensity factor. The results reveal that the thermal stress intentisy factor is greatly dependont on the thermal conductivity of crack interior and applied mechanical loadings. Consequently, the effects of thermal conductivity of crack interior and applied mechanical loadings can not be disregarded in analzing detory behavior of cracked solids and constructures under thermal loadings.Finally, due to the interaction of multiple cracks, the problem of two collinear cracks in orthotropic solids is further dealt with. Making use of Fourier transform technique and singular integral equations theory, the thermo-elastic fields near inner and outer crack tips are given in closed forms. The known results in the literature have been improved. Numerical results are given to show the effects of thermal conductivity inside crack and applied mechanical loadings on the thermal stress intensity factor and the strain energy density factor.