Size Effect in Nanomaterials
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By size effect we mean a dependence of a material parameter such as Young’s modulus on a specimen size which is used for the parameter determination.
In mechanics of materials at the macroscale, the size effect may appear in many cases as a result of influence of dislocations, microcracks, voids, grains, and subgrains (see, e.g., reviews Bažant 1999, 2000; Diebels and Steeb 2002). At the nanoscale the size effect may appear at the level of a single crystal, and it is mostly determined by surface-/interface-related phenomena. Indeed, a nanostructured material can be characterized by high ratio of material particles localized in the vicinity of a surface or interfaces to ones located in the bulk. A typical dependence of a material property P on a specimen of characteristic size L is shown in Fig. 1. Here P∞ corresponds to the value of P at the macroscale, which formally corresponds to the limit L →∞. ℓ...
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