Theoretical solution for thermo-mechanical crack-tip stress field for transversely graded materials

Abstract

The present work deals with the structure of the thermo-mechanical stress field near the crack-tip in a graded material, where properties vary along the crack front in an exponential manner. With assumptions of steady-state conditions and insulated crack faces, expansion of the temperature field around the crack-tip is obtained. Results indicate that the heat flux in the radial and angular direction has inverse square root singularity near the crack-tip. The heat flux in the direction of gradation does not have any singularity. Navier’s equation for a thermo-mechanical system is solved using the Eigenfunction expansion approach to obtain the near crack-tip stress field. The explicit form of the first four terms in the expansion of the displacement field is obtained. It is observed that terms corresponding to in the stress field are directly affected by the temperature or heat flux. Effect of temperature is observed in out-of-plane normal stress only for Considering the first two terms in the asymptotic expansion, a parametric analysis, shows that thermal stresses help relax the constraint ahead of the crack-tip when the structure is constrained in the thickness direction. It helps in the suppression of crack growth mechanisms, which delays the failure of structures.