Peridynamic models of dynamic brittle fracture have been able to explain the reasons behind crack branching in dynamic brittle fracture ([1]). Under certain conditions, as in the case of impact, damage fronts in brittle systems can move at supershear speeds, with or without branching ([2,3]). An interesting case is that of \textbf{cascading crack branching} from quasi-static loading conditions of thin glass slides with a defect/notch ([4]). In the experiments conducted in [4], the "severity" of the notch was shown to lead to changes in crack morphology: the dynamic crack can grow as a single straight crack, or branch once, or branch multiple times (cascade branching). We investigate the performance of the Fast Convolution-Based Method (FCBM) discretization of peridynamic (PD) models for this problem using two different damage models: a critical bond-strain in a bond-based PD implementation available in PeriFast ([5]), and a new Christensen-based failure model in a PD-correspondence model. While the 3D PeriFast code is explicit, the quasi-static loading conditions are mimicked by imposing an initial velocity with a linear profile along the loading direction. We discuss the highly sensitive nature of cascade branching in brittle materials. Being able to predict the behavior of dynamic cracks in brittle materials has applications ranging from protective glass in aerospace, construction, and defense industries, to microelectronics under extreme conditions.