Many industrial granular processes involve desired or undesired fragmentation of grains. However, despite experimental measurements and numerical modelling approaches, the mechanisms of single grain fragmentation and its effects on the behaviour of granular materials are still poorly understood. In this work, we investigate thefracture and fragmentation of a single grain due to a single impact, using three dimensional DEM simulations by means of the Contact Dynamics method. The grains are assumed to be perfectly rigid but modelled as an assembly of glued polyhedral Voronoï cells. The strength of the glue represents the internal cohesion of the grain along normal and tangential directions. The numerical method allows us to calculate the forces and torques at the interface zones between cells. The inter-cell joints can open eitherin tension (mode 1) or by slippage (mode 2) when the fracture strength is reached and a certain amount of energy is absorbed by the relative fragments movement. A series of simulations for a range of different values of parameters (number of cells, fracture strength, impact velocity) were performed in order to test the energetic aspects of the dynamic fragmentation of grains.