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Molecular dynamics (MD) simulations are performed to study the nanoindentation onto three different crystal structures including the single crystalline, polycrystalline, and nanotwinned polycrystalline copper. To reveal the effects of crystal structure and twin-lamellae-thickness on the response of nanoindentation, we evaluate the evolution of crystalline structure, dislocation, strain, indentation force, temperature, hardness, and elastic recovery coefficient in the deformation zone. The results of MD simulations show that the hardness, elastic recovery ratio and temperature of those three nanocrystalline copper strongly depend on crystal structure and twin-lamellae-thickness. It is also revealed that as nanoindenter goes deeper, the extent of plastic zone becomes substantially larger. Initial dislocation always nucleates at the beneath of indenter, and the discrete drops of indentation force observed at certain indentation …