## 5 Conclusions  
The high-stress and long-lifetime operating conditions of modern composite flywheel rotors create the necessary conditions for viscoelastic failure modes not included in contemporary quasi-static failure analyses. In this study, a computational algorithm, based on an accepted analytical modeling approach, was developed to investigate the viscoelastic behavior of fiber reinforced polymer composite rotors during their lifetimes. Additionally, the Tsai-Wu failure criterion was used to compute strength ratios along the rotor radial direction. The values were used to assess the conditions for rotor failure. A composite flywheel rotor design was considered that meets capacity requirements to support an electrical vehicle charging system or solar PV residential electric grid. The rotor consists of a press-fit assembly of an aluminum hub with a carbon fiber polymer composite rim. The viscoelastic behavior of the flywheel rotor was studied for two cases: (i) a worst-case scenario of the rotor operating with an angular velocity at the failure threshold for a simulated lifetime of 10 years, and (ii) a charging/discharging cycle in which the rotor experiences a minimum, intermediate, and maximum velocity for 8 h each per day over a one-year period. The case 1 simulation indicated that due to viscoelastic stress relaxation, the radial and circumferential stresses in the composite rotor reduce over time. After 10 years, peak stress in the radial and circumferential directions were found to decrease by approximately 1% and 5%, respectively. Given that rim stresses continually decrease over time, the risk of rim failure is diminishing during operation, provided no external factors, such as matrix cracking, affect the rotor's structural integrity. In contrast, circumferential stresses in the aluminum hub increase while radial stresses decrease. This behavior was attributed to an increasing compliance of the composite rim, allowing it to deform radially outward. Thus, radial compressive stresses in the rotor are reduced, and in turn, circumferential stresses in the hub are increased. The peak strength ratio for the composite rim decreases by approximately 4% compared to an 8% increase in the hub after 10 years. The latter is of concern, as the peak strength ratio in the aluminum hub converges toward unity, suggesting an increased risk of hub failure. The interfacial press-fit pressure is subject to the largest decrease, approximately 36%. Still, taken on its own, this behavior represents a low risk to the flywheel rotor's structural integrity as long as the rotor design prescribes a sufficient initial press-fit interference that upholds compressive interfacial pressure over the rotor's lifetime. Based on the observation in case 1, failure may occur in the rim at startup if the rotor reaches a critical velocity, but would decrease over time even if the critical velocity is maintained as viscoelastic stress relaxation improves the overall stress state in the composite rim. However, this behavior does not preclude possible failure due to other effects such as fatigue and matrix cracking, which warrants including such effects in flywheel rotor design and analysis. The daily charge-discharge cycle considered in case 2 imposes cyclic loading conditions upon the rotor. In this scenario, strength ratios never reached unity, so failure is not predicted for any part of the rotor. Consistent with case 1, viscoelastic stress relaxation allows the radial and circumferential stress in the composite rim to decrease over time, creating a more favorable stress state regardless of angular velocity or time. However, the viscoelastic effects that improve the stress state for the rim are detrimental to the metallic hub. Moreover, charge-discharge cycles were found to impose fatigue loading with a negative stress ratio, positive mean stress, and a comparatively high stress range at the inner surface of the hub.