DEFECTS IN METALS AND SIMULATION OF MECHANICAL ...

The load at yielding is also sensitive to indentation velocities, with 20 m/s yielding at loads
substantially lower than at 100 m/s for the same vacancy concentrations. This is similar to the
work of Schiotz [ 27 ] who studied the plastic deformation of nanocrystalline copper, in which
reductions in the strain rate by a factor of 10 caused a15 % reduction of flow stress. If the same
mechanism of yielding is present at the strain rates where experimental tests are performed, it
will be expected to exhibit a similar mild decrease in yield point phenomena with vacancy
concentration.
While the simple Hertzian approximation for spherical indentation is not strictly valid at
depths that are significant fractions of the contact probe radius [ 28 , 29 ], for simple comparisons to
other published results a first order approximation of the maximum shear stress, τ max under the
indenter tip can be made using
τ
max 3 2
1
* 2 3
⎛ 6( E ) ⎞
= 0.31⎜ ⎟
⎝ π R ⎠
P
1/3
(1).
From the data presented in Fig. 2-7, the typical; shear stress from (1) is on the order of 7 GPA for
defect free crystals; similar to that proposed by other investigators [ 12 ].
It s important to show a Hertzian fit along with our simulations with different indentation
different values of indenter stiffness K, in Fig. 2-9 we show a Hertzian fit for the force
displacement curve along with previous curves that were obtained.
17