Answer
The maximum stress during installation occurs when the ring is expanded over a shaft or contracted into a housing. The installation stress $S_i$ is calculated as $S_i = \frac{E \cdot t \cdot (D_g - D_f)}{D_f \cdot D_g}$, where $E$ is the modulus, $t$ is the material thickness, $D_g$ is the installation diameter (shaft or housing), and $D_f$ is the free diameter of the ring. To prevent permanent set (plastic deformation), $S_i$ must not exceed the yield strength $\sigma_y$ of the material. If $S_i > \sigma_y$, the ring will not return to its original free diameter, leading to a loose fit in the groove. For materials like SAE 1070, the limit is typically $200,000$ psi. If the application requires excessive expansion, the ring must be designed with multiple turns or a thinner cross-section to distribute the bending strain.
