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IntroductionNanoscale 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.

MethodIn 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:

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:

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.

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.

ResultsI. Effect of Mass

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 atomsin 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

1Pure Cu 2x Mass Difference 10x Mass Difference

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6.6 Å 6.6 Å 6.6 Å

6.8 Å 7.0 Å 6.9 Å

8.6 Å 8.6 Å 8.6 Å

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 VelocityTo 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.

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.

ConclusionIt 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.

AcknowledgmentsThis work was supported by the National Science Foundation's Research Experience for Undergraduates program under grant number EEC-0754370.

References[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

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DYNAMIC EFFECTS ON NANOSCALE INDENTATION AND DISLOCATION PROPAGATION

Garrett Lahr1, Shuai Shao2, Sergey N. Medyanik2

1 Department of Science and Mathematics, Northwestern College (St. Paul, MN)2 School of Mechanical and Materials Engineering, Washington State University

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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).

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 TemperatureTo 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.