The coupled criterion, using both stress and energy conditions, satisfactorily predicts the crack nucleation starting from a stress concentration point in brittle or quasi-brittle materials under monotonic loading. But it is a priori difficult to generalize to fatigue. A first fatigue model was established based on a Dugdale cohesive zone model but in turn it proved difficult to be extended to complex loadings. The present work is twofold: (i) showing how to generalize the coupled criterion to take into account both shear and tensile strengths as well as mode I and II toughness to predict crack nucleation under monotonic complex loadings; (ii) extending this criterion to the crack nucleation under fatigue cycles by considering a gradual degradation along the presupposed crack path. One parameter is identified so that the rate of advance coincides with that of a Paris law in case of a pre-existing long crack. As derived from the model, the growth is intermittent which provides an explanation for the striations observed in experiments. A relationship is established between the initial crack velocity and the exponent of the singularity characterizing the stress concentration, showing that the weaker the singularity and the smaller the crack advance rate. From these considerations one can deduce that the short crack range can be characterized by the distance required to reach a steady velocity.