A model for degradation of $eta$-$Al_2O_3$ is derived from sress generated by Poiseuille pressure capillary effect and effulent flux in charging process of Na-S Battery. Critical current density for degradation increase with increasing the crack length and crack tip radius. radius 10-7cm and crack length 10-5cm Dependence of crack growth velocity on crack lengh is seperated two regions that is for a large crack length it is predominated by Poiseuille pressure and effulent fluex but in the case of small crack length it is controlled by capillary effect.