Atomistic Simulations of Orientation Dependent
Hardness in Aluminum
Arulselvi Selvaraja and Christopher Weinberger
Drexel University, Mechanical Engineering and Mechanics
Introduction
Nanoindentation is an advanced, non-destructive method
developed to measure the hardness of a small volume of a
material. Experimental results have demonstrated that the
hardness of the material varies with the angle the indenter
relative to single crystals on which it indents.
The goal of this work is to use atomistics to theoretically
investigate nanoindentation and study the hardness.
• The force and residual depth were
plotted during every time step for
comparison.
• The atomistic simulations were
visualized using OVITO to
determine the best method for
acquiring residual area.
Motivation
• The hardness (𝐻 =
Figure 3 :- The graph between Force and depth for different orientations
Figure 2 :- Effective resolved shear stress factor on the
{110} < 11̅0> and {111} < 11̅0> slip systems as a function
of indenter orientations [1]
Figure 2.2 Nanoindentation with
different orientation [2]
• The hardness measurements made with a Leitz microhardness machine using a Knoop (Pyramidal Diamond)
indenter depicted a periodic relation between hardness
and the orientation with respect to the [100] on the (100)
surface of a single crystal.
• Aluminum favors a {111}<1͞10> slip system.
Results
Atomistic Data and Analysis
Figure 4 :- Graph between different orientations (angle with respect (001)) and their
residual depths
𝐹
)
𝐴
versus
indenter angle was plotted using
different methods for calculating
the force and area:
Possibilities for force
o Force = Average of Force over
hold
o Force= Force at the end of hold
Possibilities for Area
o 𝐴𝑟𝑒𝑎 = (𝜋 × 𝐷𝑒𝑝𝑡ℎ)(202.5 ×
10−10 ) i.e. curvature*length of
side of the area taken
o 𝐴𝑟𝑒𝑎 = (2 × 𝐷𝑒𝑝𝑡ℎ)(202.5 ×
10−10 )i.e linearly approximated
curvature*length of side
Preferred slip
direction
Cylindrical Indenter
(Hold)
Method/Conditions
• Atomistic simulations were carried out using LAMMPS with
different indenter orientations.
• Simulations used the molecular dynamics method which
𝑑𝑝
directly integrates the equations of motion (𝐹 =
).
𝑑𝑡
• Simulations were carried at constant Temperature,
T=300K.
• Aluminum was chosen as a model metal due to its well
defined slip systems.
• Interatomic interactions where evaluated using the
Embedded Atom Method (EAM) parameterized by Mishin
et al. (conversion by C. A. Beker) [3]
• Indenter is modeled as a rigid cylinder moving with a
constant velocity. Indentation occurs in (001) plane, hence
the angles are taken with respect to <100> or <010>
Fig 5.1 Starting atomistic stimulation (time step
0)
Fig 5.3a Hold Left View ( time step 145000)
Fig 5.2 Loading (time step 51500)
Fig 5.4a Final Depth - Left View ((time step
250000)
Figure 4 :- Atomistic simulation pathway for 45 degree indenter orientation
Fig 5.3a Hold 3D view ( time step 145000)
Fig 5.4a Depth Left View (time step 250000)
Figure 6 Graph between orientation and hardness
• The hardness computed from these simulations do not
exhibit the trend expected from a single crystal indented on
the (100) surface with <110>{111} slip systems.
• However, analysis of this dislocations confirms <110>{111}
slip in all cases.
• Orientation dependent hardness can be observed despite
the excess deviation with a 45 degree orientation, but it is
not definite
Conclusion and Future Works
• Results do not demonstrate a conclusive orientation
dependent hardness that is in agreement with experiments
or analytical theory.
• The variation in the observed trend may be due to
 Domination by dislocation nucleation rather than
propagation.
 The role of pre-existing defects under the indenter
affect the observed hardness anisotropy in experiments
• Further work will investigate the role of indentation rate
and system size, to understand their role in affecting these
results.
References & Acknowledgement
I would like to thank the STAR research program for providing the opportunity
to conduct this research and I acknowledge the following references as having
inspired and influenced this research..
[1] D. d, Rowcliffe and G. E. Hollox Journal of Material Sciences 6,1971, pp.
1271.
[2] C. A. Brookes, J. B. O'Neill and B. A. W. Redfern Proceedings of the Royal
Society of London. Series A, Mathematical and Physical Sciences, Vol. 322,
No. 1548 (Mar. 23, 1971), pp. 73-88
[3] Y. Mishin, D. Farkas, M.J. Mehl, and D.A. Papaconstantopoulos,
"Interatomic potentials for monoatomic metals from experimental data and ab
initio calculations," Phys. Rev. B59, 3393 (1999).