Connecting atomistic and experimental estimates of ideal strength Page: 3 of 16
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Atomistic and experimental estimates of ideal strength
able circumstances, one may observe experimental strengths approaching the ideal
strength of a material.
The discrepancy is resolved by reanalyzing both theory and experiment. First, the theo-
retical solution must be modified to reproduce the geometry of the indentation load. The
calculations reported in Refs. 7 and 8 assumed a fully relaxed shear load. However, the
actual stress state at the point of maximum shear under the indenter is triaxial. This
triaxial stress stabilizes the structure and raises the ideal strength in shear. Second, the
experimental numbers must be corrected for the non-linearity in the stress-strain relation
at finite strain, and also require a (smaller) correction to orient the shear onto the appro-
priate crystallographic plane.9 These corrections substantially lower the maximum shear
stress that can be inferred from the experimental hardness data. The net effect is to
remove the apparent discrepancy: to within the accuracy of our analysis, the measured
shear strengths are either equal to or slightly below the computed ideal strengths, as they
should be. Moreover, the difference between the measured shear strengths and the
predictions of theory are now less than the uncertainties in the analysis (< 5%).
The next section of this paper presents the computational approach and results. This is
followed by a discussion section and the conclusions.
Computational Procedures and Results
To quantify the effect of triaxial loading on the ideal strengths of W and Mo, we used the
local density approximation (LDA) to density functional theory within an ultra-soft
pseudopotential total-energy scheme10' 11 to calculate the stress-strain response for the
active shear system in W and Mo (<111>1110}). (The calculations were done with the
VASP package. 12-14 ) The stress states considered included relaxed simple shear (as in
Krenn, Roundy, Cohen, Chrzan & Morris
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Krenn, C.R.; Roundy, D.; Cohen, M.L.; Chrzan, D.C. & Morris Jr., J.W. Connecting atomistic and experimental estimates of ideal strength, article, April 1, 2001; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc741551/m1/3/: accessed September 24, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.