| A phase mixture model was considered in which nanocrystalline materials are treated as a mixture of crystalline phase, intercrystalline phases (grain boundary, triple line junction and quadruple node) and pores. In order to investigate the effects of grain size and porosity on the elastic modulus, Budiansky`s self-consistent method in conjunction with the phase mixture model was employed. The calculated results are compared with the experimental measurements in the literature. The elastic modulus of nanocrystalline materials decreases with a decrease of the grain size and the decrement is relatively large at grain sizes below about 10 ㎚. The effect of porosity, however, is substantially greater than the grain size effect. |
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