Atomistic Simulations of Nanoindentation
G. Ziegenhain and H. Urbassek
Indentation experiments in which a hard
tip is indented into a substrate allow research on basic material
properties. Indentation in general is an important technique for
determining the elastic properties of
materials Tabor (1996,2000). Besides the reduced elastic
Oliver and Pharr (1992); Hertz (1882); Chaudhri (2000)
one can determine the contact hardness
Force-Depth Curve - (100) Indentation into Copper
Contact Hardness - (100) Indentation into Copper
For small length scales
Gane and Bowden (1968)
properties differ from the macroscopic expectations. Particularly the
force-depth curve has characteristic dips (the so-called pop-ins) at the
Göken and Kempf (2001). This and the
overestimated theoretical shear stress
that atomistic effects play an important role for the macroscopic length
scale material behavior; namely these atomistic effects are
Phillips (2001); Hull and Bacon (1992). The indented surface
itself is also of interest: pile-up effects and regeneration are only
two important topics.
Therefore an understanding of the atomistic plasticity is of great
importance for material modeling on larger length scales and for
understanding the material properties (hardness, elasticity) at all.
Apart from that this the current length scale of electronic devices has
already reached the nm-scale and atomistic effects itself are becoming
important for industrial production.
The big advantage of simulations in contrast to the experiment is a
total control of the system. Therefore simulations are predicted to
research the atomistic effects. By using molecular dynamics (MD)
Frenkel and Smit (1996); Plimpton and Ziegenhain (2006); Allen and Tildesley (2002) the onset of plasticity has
been investigated in various systems
Smith et al. (2003); Mulliah et al. (2003); Lilleodden et al. (2003); Christopher et al. (2001).
The elastic properties are treated in detail in
Lilleodden et al. (2003) and preliminary simulations for anisotropical
effects have been done Tsuru and Shibutani (2007). Alternatively one
could choose finite-element simulations for the modeling
Durst et al. (2002,2004); these operate
inherently on larger scales and are therefore not reasonable for
atomistic length scales. Nevertheless it is promising to exploit the
concurrent length scales of the physical system by coupling both
simulation methods McGee et al. (2006). This strategy will not
be pursued in the present project.
In our simulations we model the indenter as an external constraint
using the potential proposed in Kelchner et al. (1998):
Lattice Defects under (100)-Indentation into Copper
Lattice Defects and Mises Stress under (100)-Indentation into Copper
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G. Ziegenhain - 24.10.2007