Cracks are usually observed at the edge of materials deformed by accumulative roll bonding from conventional materials to nanostructure materials. The observed cracks then propagate in the materials during grain refinement. The cracks propagation affects the yield stress and the effective fracture energy of nanocrystalline materials. In this study, the impacts of crack propagation when measured as a function of grain size variants on nanocrystalline materials' yield stress are investigated for a material deformed by accumulative roll-bonding. The study employs experimental data and theoretical concepts of severe plastic deformation and cracks processes in nanocrystalline materials. The current studies also focus on nano-cracks that will not lead to rapid materials failure during grain refinement. The study revealed that crack propagation varied as a function of grain size variants during grain refinement. The study also revealed that nano-crack increased during the deformation of nanostructured materials. The study also revealed that the effective fracture energy decreased as grain refinement took place. The study revealed that nanomaterials yield stress decreased with the increase in effective fracture energy. The current study suggests a theoretical model that shows the generation of nanomaterials cracks during grain refinement as a function of grain size variants. In the model, the cracks propagate on nanocrystalline materials due to the compressive load applied to a material. The model predicts that the generation of cracks as functions of grain size variants impacts the energy level in nanocrystalline materials.