| A model is suggested which describes fracture toughness of ceramics and nanocrystalline metals containing graphene (nano)platelets with random orientations. Within the model, the toughening is primarily associated with two-dimensional deflection of cracks that bypass graphene nanoplatelets. Using the boundary element method, it is demonstrated that two-dimensional crack deflection can increase fracture toughness by up to 90 percent. It is shown that the optimum graphene concentration that corresponds to maximum toughening is determined by the aspect ratio of graphene nanoplatelets. The results of the model explain the results of the experiments demonstrating strong toughening of ceramics containing graphene nanoplatelets. The situation where graphene nanoplatelets have the same orientation is also briefly discussed. |
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