Answer
Groove deformation occurs when the compressive stress on the groove wall exceeds the yield strength of the material ($S_{yh}$). The maximum load $P_g$ is limited by $P_g = \frac{D d S_{yh} \pi}{K}$. As the wall deforms, it creates a 'ramp' effect. The axial force on the ring then generates a radial component $F_r = P \tan(\theta)$ where $\theta$ is the angle of the deformed wall. Once $F_r$ exceeds the friction and the ring's inherent radial tension, the ring expands and is ejected. This is common when using steel rings in soft housings (Aluminum or Magnesium) without considering a larger safety factor or a deeper groove.