Unified Theory of Thermal Shock Fracture Initiation and Crack Propagation in Brittle Ceramics

Abstract

A fracture‐mechanical theory is presented for crack propagation in brittle ceramics subjected to thermal shock. The criteria of crack stability are derived for a brittle solid uniformly cooled with triaxially constrained external boundaries. Thermal stress crack instability occurs between two values of critical crack length. For short initial crack length, crack propagation occurs kinetically, with the total area of crack propagation proportional to the factor S t 2 (1‐2 v )/EG, where S t is tensile strength, v is Poisson's ratio, E is Young's modulus, and G is surface fracture energy. Under these conditions the newly formed crack is subcritical and requires a finite increase in temperature difference before propagation will proceed. For long initial crack length, crack propagation occurs in a quasi‐static manner and can be minimized by maximizing the thermal stress crack stability parameter R st = [G/α 2 E ] 1/2 , where α is the coefficient of thermal expansion. For heterogeneous brittle solids, such as porous refractories, the concept of an “effective flaw length” is introduced and illustrated on the basis of experimental data in the literature. The relative change in strength of a brittle solid as a function of increasing severity of thermal shock is estimated. Good qualitative agreement with literature data is found.