We present a new model for the fragmentation of dust beds in laboratory shock tube experiments. The model successfully explains the formation of layers in the bed using mass and momentum conservation. Our model includes the effect of wall friction, inherent cohesion, and gravitational overburden. We find that the pressure changes caused by the expansion wave take time to penetrate into the bed, while simultaneously increasing in magnitude. By the time the pressure difference is large enough to overcome wall friction, the overburden and the intrinsic cohesion of the bed, it has penetrated ~8-15 bead diameters into the bed, thus causing a layer of dust to be lifted off. We have found the dependence of layer size upon bead diameter and found a good match to experiment. We have also predicted the dependence of layer size and fragmentation time on bead density.