By using pseudopotential density functional theory within the local density approximation, calculations were made of the ideal shear strengths for slip on {110}, {112} and {123} planes; allowing for complete structural relaxation orthogonal to the applied shear. The strengths in the weak directions on all planes were found to be very nearly equal to about 18GPa (11% of the shear modulus). The shear instability also occurred at about the same applied shear strain, of 17 to 18%. This unusual isotropy was explained in terms of the atomic configurations of the high-energy saddle points which were reached during shear. The analysis of these saddle points was expected to offer a simple explanation for the prevalence of the pencil glide of dislocations on planes which contained a <111> direction in body-centered cubic metals. Calculations were also made of the ideal cleavage strength of W on {100}, and the calculated ideal shear and cleavage strengths were compared with experimental nano-indentation and whisker measurements. All of the results could be simply explained in terms of a Frenkel-Orowan model.

The Ideal Strength of Tungsten. D.Roundy, C.R.Krenn, M.L.Cohen, J.W.Morris: Philosophical Magazine A, 2001, 81[7], 1725-47