Stress Intensity Relaxation at the Tip of an Edge Crack in a Functionally Graded Material Subjected to a Thermal Shock

We analyze thermal stresses and the stress intensity factor in an edge-cracked strip of a functionally graded material (FGM) subjected to sudden cooling at the cracked surface. It is assumed that the shear modulus of the material decreases hyperbolically with the higher value at the surface exposed to the thermal shock and that the thermal conductivity varies exponentially. Volume fractions of the constituents in a ceramic-metal FGM are then determined with the assumed shear modulus gradient using a three-phase model of conventional composites. The differences between the other assumed material properties and those predicted by the three-phase model are delineated and the applicability of the assumed FGM is discussed. It is shown that the maximum tensile thermal stress in the strip without cracks is substantially reduced by the assumed thermal conductivity gradient and that the magnitude of the compressive stress is increased. A strong compressive zone just away from the thermally shocked surface is developed especially at the very initial stage of the thermal shock. Thermal stress intensity factors (TSIF) are numerically calculated based on a singular integral equation derived from the dislocation density along the crack faces. It is shown that while TSIF is relatively insensitive to the shear modulus gradient, it is significantly reduced by the thermal conductivity gradient.