The delayed failure of SiC fibers is commonly described by a power law relating the growth rate to the stress intensity factor KI, itself following the classical fracture mechanics law with a constant geometrical factor. For low stress levels, relevant for ceramic matrix composite (CMC) applications, this model predicts crack lengths exceeding the specimen size and unrealistic times to failure. Indeed, discrepancies between this model prediction and experiments have been reported. This paper proposes a model improvement with a simple and accessible analytical solution to work around this shortcoming. First, a more accurate description of fracture mechanics is introduced which yields physically reasonable estimates of the crack size at failure. Then, the contribution of silica scale formation to oxidation embrittlement (OE) is evaluated. If the corrected slow crack growth (SCG) model and the OE model are irrelevant when taken separately, their simultaneous presence accurately depicts the observations: OE prevails under low stresses, resulting in a finite lifetime below 150 MPa, whereas SCG takes over above 800 MPa. This result brings new insight for the design of CMC and may as well apply to other types of materials, prone to environment-assisted and stress-accelerated degradation.