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In order to understand the origin of the size effect at the sub-micrometer scale, one should consider the underlying dislocation activity. In bulk metals, the effect of microstructural scale on mechanical strength is understood either in terms of dislocation pile-up (Hall–Petch), dislocation sources (Frank-Read) or obstacles to dislocation migration (Orowan strengthening, dislocation forest, solute strengthening, etc.). However, these concepts should be reconsidered as the microstructural length scales reaches dimensions as small as the average spacing between dislocations—typically the sub-micro and nano-regimes. At this scale, strength is commonly controlled by dislocation nucleation, activation of single-ended dislocation sources (a truncated Frank-Read dislocation source which is pinned on one side and terminates on the surface on the other side) and the efficiency of dislocations to escape at the surfaces in the so-called dislocation starvation regime.
This complex handful of dislocation mechanisms brings with it a great challenge in relating quantitatively dislocation activity at the atomic level to the macroscopic deformation. In most cases, phenomenological constitutive laws are being employed in Finite Element Method (FEM) simulations. However, these laws break down at the sub-micrometer scale. In particular, these constitutive relations consider only material properties and are non-local in the sense that they are size and shape independent. Thus, it is commonly accepted that a constitutive law for specimens of nanoscale dimensions should be constituted on the basis of its building blocks – dislocation mechanisms. This is not an easy task since the typical time and length scales of each dislocation mechanism are different and require different simulation techniques.
At the Nanomechanics Simulations Laboratory we propound a path to towards this goal, which will bridge between the length scales and will allow us to understand plasticity at the nanoscale. For instance, with the help of molecular dynamics (MD) simulations and Finite Elements Modelling (FEM) we analyzed the high strengths exhibited by Au nanoparticles under compression and the manifested size effect. With the MD simulations we concluded that the deformation is controlled by dislocation nucleation at the vertices of the nanoparticle. Moreover, a significant size effect on strength is identified in the MD simulations, which fits to a power-law with an exponent similar to the experimental one. In FEM simulations we found that the stress levels reached at the onset of plasticity approach the theoretical shear strengths of Au along the slip planes, on which the dislocations are. Based upon the FEM analysis and the MD simulations, we proposed a dislocation nucleation model in a non-uniform stress field.