We study the creep rupture of viscoelastic fiber bundles under uniaxial constant tensile loading, assuming global load sharing (GLS) for the redistribution of load following fiber failure. We consider loading paths such that the stress raises to a value sigma0 under a time-independent loading (negligible creep strain) and remains fixed thereafter. Motivated by experimental observations, we introduce an "effective" strain controlled failure criterion to incorporate damage into the system, thus damage is distributed over time. In addition, when a "limit" value for the effective stress is reached, failure of the remaining alive fibers is instantaneous. This enables us to show both analytically and numerically that creep rupture occurs for external loads above a critical value that is less than the static fracture bundle's strength in accordance with experimental observations. An analytical expression for this critical load is given. For stress levels below the critical value, the system suffers only partial failure since the deformation tends to a stationary solution for which the effective stress is below the limit value giving rise to an infinite lifetime. On the other hand, if the time-independent loading process ends in the softening regime, the deformation of the system monotonically increases in time resulting in global failure at finite time irrespectively of the applied load. Moreover, the applied model is found to be consistent with the experimentally observed increase of the creep rupture displacement with decreasing steady external load (above the critical value).