The mechanism of fragmentation processes in aqueous nanodroplets charged with ions is studied by molecular dynamics (MD) simulations. By using constant-temperature MD, the evaporation of the water is naturally taken into account and sequences of ion fragmentation events are observed. The size of the critical radius of the charged droplet just before the fragmentation and the distribution of the sizes of the fragments are estimated. Comparison of the Rayleigh critical radius for fragmentation and simulation data is within 0.23 nm. This seemingly small difference arises from a large difference in the number of water molecules that makes fragmentation an activated process as in the ion evaporation mechanism (IEM). This finding is in agreement with the predictions of Labowsky et al. [Anal. Chim. Acta 2000, 406, 105-118] for charged aqueous drops. The size of the daughter droplets is larger than the prediction of Born's theory by 0.1 to 0.15 nm. The nature and the dynamics of the intermediate states of the fragmentation process characterized by a bridge formed between the mother droplet and the evaporating ion or thorned structures where the ion sits on the tip are important for the outcome of the size-distribution of the fragments, while they are is missing in Born's theory.