Geometric aspects of the ideal shear resistance in simple crystal lattices

Abstract

We present and analyze results of a large series of atomistic calculations of crystal resistance to shearing along rational planes of different orientations. The data computed for bcc and fcc crystals suggests that the interplanar spacing, d, is not a pertinent scaling parameter for the ideal shear resistance and that instead, plane orientation angle, θ, is a more appropriate predictor of the resistance variations among crystal planes in the same crystallographic zone. By counting the interatomic bonds reaching across the shear plane, we obtain interpolation functions that accurately match the computed resistances in the whole range of plane orientations. Entirely defined by the lattice symmetries and geometry, the interpolation functions are universal for a given crystallographic class of materials. Within a given class, material specificity of the shear resistance is accounted for with just a few scaling parameters entering the interpolation functions.