• Evaluation of modeling features in simulating creep and fatigue responses. • Need of coupling continuum damage model to unified constitutive model (UCM). • Issues in simulating creep strains at low temperatures by the modified UCM. • Issues in simulating fatigue responses at high temperatures by the modified UCM. • Challenges of UCM in simulating elevated temperature creep and fatigue responses. A unified constitutive model (UCM) specifies that its flow rule for inelasticity computes both the plastic and creep strains as a single state variable. A Chaboche framework based UCM with the modeling features of strain range-dependence, strain rate-dependence, static recovery and mean stress evolution was developed and experimentally validated against a broad set of fatigue and fatigue-creep responses of Haynes 230 (HA 230) under isothermal and anisothermal temperature conditions. This article demonstrates that this advanced Chaboche-based UCM can simulate the secondary minimum creep strain rates reasonably, but is unable to predict the tertiary creep strain responses. To simulate the tertiary creep strain responses a continuum damage model is needed to be coupled to the UCM. This study also evaluated three different unified flow rules, Norton's power law, exponential Norton and sine-hyperbolic Norton for calculating the inelastic strain rates. It is found that the choice of flow rule is important in simulating the stress amplitude saturation rate of fatigue responses, but has minimal effect in simulating the tertiary creep strains. However, the damage coupled UCM independent to the unified flow rules listed above can adequately simulate fatigue, fatigue-creep including the stress relaxation during strain dwell, and creep strain up to the tertiary range for HA 230. The drawbacks of the damage coupled UCM are the hysteresis loop softening at very high temperatures and asymptotic simulation at low creep temperatures, which are identified as challenges to be overcome towards developing a universal UCM for robust design and analysis of high temperature components.