Atomistic Finite Deformation Simulations: A Discussion on Length Scale Effects in Relation to Mechanical Stresses

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Abstract
In this study, atomistic finite deformation calculations employing the Embedded Atom Method show three items of interest related to continuum field theory. First, a spatial size scale effect on the yield stress is found. In these calculations, mechanical yield point occurred from dislocation initiation at the edge of the numerical specimens. The spatial size scale continued to affect the plastic response up to strains of 30 percent in simple shear for nickel oriented at ⟨011⟩. The second point is related to the continuum mechanics observation about oscillating global shear stress under simple shear conditions is shown to dampen as the spatial size scale increases. As the spatial length scale increases, the continuum rotational effect coupled with the increase in dislocation population reduces the oscillatory behavior. This confirms the notion proposed by Bammann and Aifantis (1987) in that when more dislocations are initiated with different orientations of the Burger’s vectors then the oscillations decrease. Finally, a length scale bridging idea is proposed by relating a continuum single degree of freedom loss coefficient, which relates the plastic energy to the total strain energy, to varying sizes of blocks of atoms. This study illustrates the usefulness of employing the Embedded Atom Method to study mechanisms related to continuum mechanics quantities.

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