Connecting atomistic and experimental estimates of ideal strength Page: 4 of 16
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Atomistic and experimental estimates of ideal strength
Ref. 7) and a triaxial stress determined numerically from the finite element modeling of
nanoindentation described below. Using a plane-wave energy cut-off of 17 Ry with a
Monkhorst-Pack 17x17x17 k-point grid proved sufficient to achieve precision of better
than 0.01 eV in the calculated energies and better than 0.6 GPa in peak stress.1 The
triaxial stress increased the shear strength (tenrt) of W from 20.0 to 22.7 GPa and the
strength of Mo from 17.1 to 18.2 GPa. (The unconstrained strength of W is higher than
the value (18.2 GPa) calculated by Roundy et al., presumably because different pseudo-
potentials are used in the two calculations). Figure 1 shows the normalized stress-strain
curves for W and Mo. They are similar with peak stresses near a shear strain of 17% as
expected for the bec structure.7
To correct the reported values of the experimental strengths we must examine how they
are generated from the raw data. In Bahr et al.'s study of tungsten,4 a sharp diamond with
a tip radius of approximately 400 nm is pressed into a single crystal with a polished
surface. Yielding is marked by a sudden increase in the depth of penetration during
loading. Prior to yielding, the load-displacement (P-S) response of the system is fit well
by the Hertzian model of elastic contact: 16
P R3 , (1)
where R is the radius of the indenter tip. Since the stress is not measured directly, the
Hertzian stress field is used to deduce the maximum shear stress underneath the indenter
at the yield point. However, the Hertzian stress field assumes linear stress-strain behavior
in both the indenter and the substrate. This assumption fails when the shear stress
approaches the ideal strength (Fig. 1).
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/m1/4/: accessed November 15, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.