Answer
Fatigue life is dictated by the stress range between the initial preload height $H_1$ and the final operating height $H_2$. The alternating stress $\sigma_a$ is defined as $(\sigma_{max} - \sigma_{min}) / 2$, and the mean stress $\sigma_m$ as $(\sigma_{max} + \sigma_{min}) / 2$. Utilizing a Goodman diagram, engineers must ensure that the point $(\sigma_m, \sigma_a)$ lies within the safe region for the specific material, such as SAE 1070 Carbon Steel. In dynamic hydraulic valves, if the deflection $f$ exceeds 50 percent of the available travel, the probability of fatigue crack initiation at the wave crests or troughs increases due to micro-plasticity. Precise work height control ensures the stress remains below the endurance limit $\sigma_e$.
