Dear all,

In recent years, it was suggested that the strength of nanoscale
structures increases with speciman size as a power-law. This has been demonstrated
many times for pillars, both experimentally and in discrete dislocation
dynamics simulations. Various values for the power-law exponent in pillars were
obtained, and most of them are about -0.6. However, I did not manage to find
any theory which explains both this typical behavior and the values of the exponent.
Is it a phenomenological law? If not, can anyone refer me a detailed model?

Thank you in advance,

Dan

Based on much experimental and theoretical work in the last decade or so, mechanical properties of materials at nano-scale are proving to significantly deviate from their bulk counterparts. This is true not only for nano-structureD materials (i.e. composed of nano-scale components like nanocrystalline materials) but also for nano structureS (surface-dominated structures like carbon nanotubes (CNT’s), nanowires, etc.). Nanoindentation has been a very effective and well-characterized technique for determination of hardness, modulus, and stiffness, and for crystalline materials the indentation hardness has been widely shown to be significantly higher at shallower indentation depths (so-called indentation size effect, or ISE). However, inserting a sharp indenter tip into a material inevitably sets up strong strain gradients in the deforming volume, which is often linked to the origin of the ISE. Moreover, the infinitesimal volumes probed via this technique are coherent with the remaining matrix, rendering the effects of free surfaces on mechanical properties inaccessible.