DYNAMIC EFFECTS ON NANOSCALE INDENTATION
AND DISLOCATION PROPAGATION
Garrett
1
Lahr ,
1 Department
2 School
Nanoscale plastic deformation in metals is dominated by the
nucleation and propagation of small defects in the crystal structure –
called dislocations. Understanding the mechanisms of dislocation
nucleation and propagation is important for predicting the mechanical
properties of nanoscale metallic materials. Nanoindentation is one
way to analyze the mechanical properties of nanoscale metallic
materials. Nanomechanical problems, such as nanoindentation, can
be studied conveniently through atomistic simulations. There are
generally two ways to perform atomistic simulations: molecular
mechanics (MM) and molecular dynamics (MD). Many studies of
nanoindentation have been done using the MM method, in which
various dynamic parameters such as mass, loading velocity, and
temperature are not taken into account. These variables may play an
important role in how dislocations propagate through a material.
Sergey N.
2
Medyanik
of Science and Mathematics, Northwestern College (St. Paul, MN)
of Mechanical and Materials Engineering, Washington State University
difference (63.55 amu on top, 127.1 amu on bottom), and ten times
mass difference (63.55 amu on top, 635.5 amu on bottom).
180
160
140
1
120
Force (eV/Å)
Introduction
Shuai
2
Shao ,
100
2
80
pure Cu
3
2x
60
From the graph we can see that higher temperatures seem to
dampen the load displacement curve. At point 1, the higher
temperatures nucleate more dislocations. At point 2, the no
temperature case has propagated a full dislocation through while the
higher temperature cases have not. At point 3, we only see full
dislocations for the no temperature case and mostly partial
dislocations for the higher temperature cases.
III. Effect of Loading Velocity
10x
To study the effect of loading velocity, simulations were run with
three different indenter velocities: 0.5 m/s, 1 m/s, and 5 m/s.
40
20
0
0
2
4
6
8
10
12
14
16
180
Indentation Depth (Å)
Pure Cu
2x Mass Difference
160
10x Mass Difference
140
1
In order to study the effect of the dynamic parameters, MD
simulations should be performed. MD is performed by solving a
system of differential equations based on Newton’s second law, so
mass, velocity, and temperature are taken into account. Each variable
will be isolated so its affects on dislocation propagation can be
studied. The simulations are performed using LAMMPS (Large-scale
Atomic/Molecular Massively Parallel Simulator)[1]. The inter-atomic
forces are modeled using the embedded atom method (EAM) which
allows for the modeling of a large system of atoms[2]. The total
energy of a system of atoms is given by the following:
1
Etot ∑ Fi ( ρi ) + ∑ φij ( Rij )
=
2 i, j
i
where Fi is the embedding energy which is a function of the electron
density ρi, and φij is the pair potential between atoms i and j, which is
a function of Rij, the distance between the atoms.
To render the atomistic configurations, the visualization software
Atomeye is used [3]. Dislocations are located by evaluating each
atom’s centrosymmetry parameter, which is defined as follows:
=
P
∑ R +R
i =1,6
i
2
i +6
where Ri and Ri+6 are vectors corresponding to the pairs of opposite
nearest neighbors in the lattice [4]. Atoms in a perfect lattice
structure will have a value of zero; atoms that are part of a defect will
have a non-zero value for P. Only atoms with P > 0.3 are displayed.
120
6.6 Å
6.6 Å
6.6 Å
100
0.5 m/s
2
80
1 m/s
5 m/s
60
3
40
2
20
0
6.8 Å
7.0 Å
8.6 Å
8.6 Å
8.6 Å
At point 2, we see that pure Cu and 2x mass difference have already
propagated through a full dislocation while 10x mass difference has
not. At point 3, we see that pure Cu has propagated through two full
dislocations, 2x mass difference has propagated one and is in the
process of another, and 10x mass difference has only propagated
through one full dislocation.
II. Effect of Temperature
To study the effect of temperature, simulations were run with no
temperature controls and system temperatures kept at 10 and 300
degrees Kelvin. It should be noted that in the first case, the system is
initially 0 Kelvin with no further temperature control.
180
160
140
1
Force (eV/Å)
120
100
no temp
80
60
3
300K
40
20
Results
0
0
I. Effect of Mass
2
4
6
8
10
12
14
16
Indentation Depth (Å)
No Temperature Control
10 K
2
4
6
8
10
12
14
16
Indentation Depth (Å)
0.5 m/s
1 m/s
5 m/s
6.6 Å
6.7 Å
6.8 Å
6.8 Å
6.9 Å
6.9 Å
8.6 Å
8.6 Å
8.6 Å
1
2
3
At point 3, the 0.5 m/s case has propagated two full dislocations, the
1 m/s case has propagated one, and the 5 m/s case has partial
dislocations. At higher velocities, the dislocations do not have
enough time to relax the structure so at identical indentation depths,
the dislocations in the higher velocity cases have not propagated as
far.
Conclusion
10K
2
0
6.9 Å
3
The computational domain for the simulations was approximately 170
x 60 x 170 Å with a nearly rigid spherical indenter of radius 40 Å. The
lateral sides are fixed while the top and bottom sides are free.
To study the effect of mass, it would not work to simulate a metallic
bi-layer of different materials (Cu-Ni for example) because there
would be other variables affecting dislocation propagation in addition
to mass (namely, the interference of the interface on dislocation
propagation). To isolate the effect of mass, a ‘virtual’ interface was
created within a single material: copper, in this work. All of the atoms
in the simulation are Cu, but the bottom half of the material was
changed to have a greater mass than regular Cu. The above figure
shows the initial configuration where the blue atoms are regular Cu
and the red atoms are ‘greater mass’ Cu (2x and 10x). Three
simulations were run: pure Cu (63.55 amu), two times mass
Force (eV/Å)
Method
1
300 K
1
It was found that the dynamic parameters did affect the propagation
of dislocations. Dislocation propagation was slowed down when
going from a smaller to a larger atomic mass. High temperature
facilitated the nucleation of dislocations but inhibited further
propagation. Higher loading velocities, when compared to lower
velocities at the same indentation depth, propagated dislocations a
shorter distance.
Acknowledgments
6.6 Å
6.5 Å
6.4 Å
7.2 Å
7.1 Å
7.1 Å
References
9.4 Å
[1] S. J. Plimpton, Fast Parallel Algorithms for Short-Range Molecular Dynamics, J Comp Phys,
117, 1-19 (1995). http://lammps.sandia.gov
[2] M.S. Daw, S.M. Foiles, M.I. Baskes, Mater. Sci. Rep. 9 (1993) 251-301
[3] J. Li, Modeling Simul. Mater. Sci. Eng. 11 (2003) 173
[4] C.L Kelchner, S.J Plimpton, J.C Hamilton, Phys. Rev. B 58 (1998) 11085-11088
2
3
9.4 Å
9.4 Å
This work was supported by the National Science Foundation's
Research Experience for Undergraduates program under grant
number EEC-0754370.