Effect of Internal Stresses on the Strength of Nanocrystalline Materials (Inverse Hall-Petch Relation

the relationship between the yield strength of the nanostructure materials and the grain size is very complicated. Furthermore, when the grain size of nanostructure materials is smaller than a critical value, the inverse Hall–Petch relation is observed [1-3]. As the inverse Hall–Petch phenomenon has not yet been clearly identified, numerous studies are carried out to make it more clear [4-5]. General conclusions of cited articles are based on this fact that as the size of the crystalline grain reduces, the influence of grain boundaries can be very important. That is because as the size of the crystalline grain reduces into the nanometer range the volume fraction of the grain boundaries and triple junctions increases very rapidly [6, 7] and consequently the activity of grain boundaries increases [8, 12]. Thus, it seems that for an accurate investigation, two above roles of grain boundaries should be considered simultaneously. In the present work, a new approach for considering the effects of grain boundary was made