Extension of Hasselmanʹs thermal shock theory for crack/microstructure interactions in refractories

Thermal shock damage resistance in advanced refractories depends on the crack interactions with the microstructure. These energy dissipation mechanisms during crack propagation are not directly considered in the original classical thermal shock model of Hasselman. They are imbedded within the N and γ terms of his derivations. In this extension of Hasselmanʹs work, an expression is presented, which estimates the final crack size (ℓf) as the fracture surface energy ratio between γNBT and γWOF. That expression directly considers the crack interaction mechanisms with the refractory microstructure as it includes the R-curve behavior effects. In addition, the equation presented allows a quantitative evaluation of the volumetric density of cracks in refractories.