Nanomaterials, due to their fine grain sizes, exhibit enhanced mechanical properties. However, their low stability at also relatively low temperatures might limit their future applications. In the present work, a statistical model has been proposed in order to study grain growth processes in nanomaterials. The Hillert’s approach has been extended by incorporating two mechanisms of growth for an individual grain: grain boundary migration – GBM - (diffusion based - continuous) and grain-rotation coalescence – GRC - (discontinuous). The influence of the grain size distribution on the grain growth process has been studied. The results show that the inclusion of GRC mechanisms results in a departure from the parabolic law of grain growth. Such a deviation has also been observed experimentally, especially in nanomaterials. The results reveal that grain growth rate increases with higher dispersion of the fine grains and the rotation mechanism can initiate growth even with low dispersion. This causes a steady increase in the coefficient of variation which, after some time interval, decays to homogeneity. This paper also demonstrates that the average rotation mobility which is a consequence of the varying misorientation angle contributes up to about 50% of the overall average boundary mobility.

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Predicting the properties of a material from knowledge of the internal microstructures is attracting significant interest in the fields of materials design and engineering. The most commonly used expression, known as Hall-Petch Relationship (HPR), reports on the relationship between the flow stress and the average grain size. However, there is much evidence that other statistical information that the grain size distribution in materials may have significant impact on the mechanical properties. These could even be more pronounced in the case of grains of the nanometer size, where the HPR is no longer valid and the Reverse-HPR is more applicable. This paper proposes a statistical model for the relationship between flow stress and grain size distribution. The model considered different deformation mechanisms and was used to predict mechanical properties of aluminium and copper. The results obtained with the model shows that the dispersion of grain size distribution plays an important role in the design of desirable mechanical properties. In particular, it was found that that the dependence of a material’s mechanical properties on grain size dispersion also follows the HPR to Inverse-HPR type of behaviour. The results also show that copper is more sensitive to changes in grain size distribution than aluminium.

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.