Answer
In cryogenic environments (e.g., liquid nitrogen at -196 C), the yield strength $\sigma_y$ and tensile strength of stainless steels like 302 or 316 increase, but ductility decreases. The thrust load capacity formula $P_g = (D \cdot d \cdot \pi \cdot \sigma_y) / S_f$ suggests an increase in capacity. However, the risk of brittle fracture becomes the dominant failure mode. The safety factor $S_f$ must be increased from 2 to 4 to account for the reduced fracture toughness $K_{IC}$. Furthermore, the thermal contraction of the ring ($L = L_0 \cdot \alpha \cdot \Delta T$) must be calculated to ensure that the ring does not contract so much that it binds on the shaft or expands out of the groove due to differential cooling rates between the ring and the housing.
