| Title |
A Composite Model for Hardness of Nanocrystalline Materials |
| Abstract |
Nanocrystalline materials have been modeled as a mixture of crystallite and intercrystallite phases in order to investigate the effect of grain size on hardness of the nanocrystalline materials. The hardness has been calculated using the rule of mixtures based on the volume fractions of crystallite and intercrystallite phases. The critical grain size, d_c, concept suggested by Nieh and Wadsworth was applied for the calculation of the hardness as a function of grain size. The theoretical hardness as a function of grain size were compared with the published experimental data. The calculated hardness showed a change in gradient and a negative Hall-Petch plots which can be observed in some experimental results. The inverse H-P relationship doesn`t occur and just the gradient changes at dc when d_c>d_(peak), (d_(peak) is the grain size at the peak hardness point, eq.(9)). On the other hand, the inverse H-P relationship appears when d_c |