Study of Materials Deformation in Nanometric Cutting by Large-scale Molecular Dynamics Simulations
© to the authors 2009
Received: 22 December 2008
Accepted: 27 January 2009
Published: 18 February 2009
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© to the authors 2009
Received: 22 December 2008
Accepted: 27 January 2009
Published: 18 February 2009
Nanometric cutting involves materials removal and deformation evolution in the surface at nanometer scale. At this length scale, atomistic simulation is a very useful tool to study the cutting process. In this study, large-scale molecular dynamics (MD) simulations with the model size up to 10 millions atoms have been performed to study three-dimensional nanometric cutting of copper. The EAM potential and Morse potential are used, respectively, to compute the interaction between workpiece atoms and the interactions between workpiece atoms and tool atoms. The material behavior, surface and subsurface deformation, dislocation movement, and cutting forces during the cutting processes are studied. We show that the MD simulation model of nanometric cutting has to be large enough to eliminate the boundary effect. Moreover, the cutting speed and the cutting depth have to be considered in determining a suitable model size for the MD simulations. We have observed that the nanometric cutting process is accompanied with complex material deformation, dislocation formation, and movement. We find that as the cutting depth decreases, the tangential cutting force decreases faster than the normal cutting force. The simulation results reveal that as the cutting depth decreases, the specific cutting force increases, i.e., “size effect” exists in nanometric cutting.
Nanometric cutting is a tool-based materials removal technique to remove materials at nanometer scale thickness in the surface. Nanometric cutting can be used to produce micro/nano-components with nanoscale surface finish and sub-micron level form accuracy for many applications such as micro-electro-mechanical systems (MEMS) and nano-electro-mechanical systems (NEMS) [1, 2]. Understanding the material removal mechanism and mechanics at atomistic scale in the surface, such as deformation evolution, chip formation, machined surface, cutting forces, and friction, is a critical issue in producing high precision components. However, as the nanometric cutting process involves only a few atomic layers at the surface, it is extremely difficult to observe the cutting process and to measure the process parameters through experiments. Therefore, theoretical analysis plays a major role in obtaining information on nanometric cutting. The widely used finite element method based on continuum mechanics for the analysis of conventional cutting is not appropriate to analyze the nanometric cutting process because of the discrete nature of materials at such a small length scale; therefore molecular dynamics (MD) simulation has become a very useful tool in the study of nanometric cutting.
A number of studies have used the MD simulations to analyze the nanometric cutting process [3–9]. The typical studies among them include: Maekawa et al.  studied the role of friction between a single-crystal copper and a diamond-like tool in nano-scale orthogonal machining. The Morse type potentials were used for the interactions between Cu–Cu, Cu–C, and C–C atoms; Zhang et al.  studied the wear and friction on the atomic scale and identified four distinct regimes of deformation consisting of no-wear, adherence, plowing, and cutting regimes; Komanduri et al. [5–7] carried out MD simulations of nanometric cutting of single-crystal copper and aluminum. They investigated the effects of crystal orientation, cutting direction and tool geometry on the nature of deformation, and machining anisotropy of the material; more recently, Zhang et al.  used MD simulations to study the subsurface deformed layers in the atomic force microscopy (AFM)-based nanometric cutting process.
All those previous studies have provided much help in understanding nanometric cutting. However, as the MD simulation of nanometric cutting is compute-intensive, small simulation models with a few thousands to tens of thousands of atoms were used in the reported studies to reduce the computing time. Although those small models have provided a lot of information on the nanometric cutting processes, a small model may induce significant boundary effects that make the results unreliable. For example, if the model is not large enough, the widely used fixed-atoms boundary in MD simulations may have strong effect on the dislocation movement and thus will affect the motion of atoms at the cutting surface. Besides, in most of the reported studies, the simulation models are two-dimensional or quasi-three-dimensional (plane strain) due to the limitation on the model size. Therefore, there is a need for large-scale MD simulations of three-dimensional (3D) nanometric cutting processes.
Another limitation of previous studies on MD simulations of nanometric cutting of metals is that the Morse potential has been widely adopted to model the interatomic force between metal atoms. Morse potential is a pair potential which considers only two-body interactions; thus, it provides a rather poor description of the metallic bonding. The strength of the individual bond in metals has a strong dependence on the local environment. It decreases as the local environment becomes too crowded due to the Pauli’s “exclusion principle” and increases near surfaces and in small clusters due to the localization of the electron density. The pair potential does not depend on the environment and, as a result, cannot reproduce some of the characteristic properties of metals, such as the much stronger bonding of atoms near surfaces. The EAM potential, which has been specially developed for metals [10–12], can better describe the metallic bonding. Therefore, the EAM potential gives a more realistic description of the behavior and properties of metals than the Morse potential. Our previous study  showed that the two different potentials resulted in quite different simulation results and suggested that the EAM potential should be used in MD simulation of nanometric cutting.
In this article, we present large-scale 3D MD simulations of nanometric cutting of copper. In our simulations, the EAM potential is employed for the interactions between Cu atoms in the workpiece. We first studied the model size effect on the simulation results with three different model sizes of about 2, 4, and 10 million atoms. Then, we used the 4-million-atom model, which is shown to be large enough to eliminate the boundary effect, to study the detailed materials deformation, dislocation movement, and cutting forces during the cutting processes.
The cutting speed used in the MD simulations ranges from 50 to 500 m/s, while the cutting depth ranges from 0.8 to 4 nm. The cutting is in the (001) plane and along the  direction of the workpiece. The initial temperature of the workpiece is 300 K. The three layers of atoms adjacent to the fixed-atom boundary at the workpiece bottom are set as the thermostat atoms, in which the temperatures are maintained at 300 K by rescaling the velocities of the atoms. The velocity Verlet algorithm with a time step of 2 fs is used for the time integration of Newton’s equations of motion.
where is a pair potential energy function;D is the cohesion energy;α is the elastic modulus;r ij andr0are the instantaneous and equilibrium distance between atoms,i andj, respectively.
where is the contribution to the electronic density at atom,i, due to atom,j, at distance,r ij , from the atom,i.
There are three different atomic interactions in the MD simulations of nanometric cutting processes: (1) the interaction in the workpiece; (2) the interaction between the workpiece and the tool; and (3) the interaction in the tool. For the interaction between the copper atoms in the workpiece, we used the EAM potential for copper constructed by Johnson . For the interaction between the copper workpiece and the diamond tool, as there is no available EAM potential between Cu and C atoms, we still use the Morse potential for the workpiece–tool interaction with the parameters adopted from reference  being D = 0.087 eV, α = 5.14, and r0 = 2.05 Å. Since the diamond tool is much harder than the copper workpiece, it is a good approximation to take the tool as a rigid body. Therefore, the atoms in the tools are fixed relative to each other, and no potential is needed for the interaction among the tool atoms.
where R i and Ri+6 are the vectors corresponding to the six pairs of opposite nearest neighbors in the FCC lattice. By definition, the centro-symmetry parameter is zero for an atom in a perfect FCC material under any homogeneous elastic deformation and non-zero for an atom which is near a defect such as a cavity, a dislocation, or a free surface.
The large-scale MD simulations of nanometric cutting are carried out on the IBM p575 supercomputer at the Institute of High Performance Computing (IHPC). The multi-processor parallel computing is used for the simulations. The parallel computing is realized by using message passing interface (MPI) library. The calculation time for each simulation case depends on the model size, cutting speed, cutting distance, as well as the number of CPUs used. For example, it took about 3 weeks to finish the simulation run for the 10-millino-atom model with the cutting speed of 100 m/s using 32 CPUs.
For a MD simulation, the larger the model size, the less obvious the boundary effect on the simulation results. However, a very large model will take unnecessarily long computing time. Therefore, it is necessary to study the model size effect, so that we can find a suitable model size for the MD simulations of nanometric cutting. The model size should be moderate with diminished boundary effect on the simulation results.
Thereafter, we performed simulations using the 4-million-atom model in Fig. 1b with the workpiece thickness (y direction) two times that of the 2-million-atom model. The simulation results in Fig. 3b show that the 4-million-atom model could eliminate the boundary effect of the periodic boundaries. We also carried out simulations with the 10-million-atom model in Fig. 1c. In the 10-million-atom model, the workpiece is larger than that of the 4-million-atom model in all the three dimensions with very obvious increase in both thex andz directions to test the boundary effects in these two directions. We found that the simulation results with the 10-million-atom model, shown in Fig. 3c, did not show obvious difference from those of the 4-million-atom model. Therefore, for the cutting speed of 100 m/s and cutting depth of 4 nm, the 4-million-atom-model is shown to be large enough to ignore the boundary effect in the simulations.
MD simulations were also carried out to study the effect of cutting speed and cutting depth on the boundary effect. The simulation results show that reducing cutting speed results in more obvious boundary effect, while reducing cutting depth results in less obvious boundary effect. This is because a slower cutting speed means longer cutting time, and therefore the dislocations have more time to move and are more possible to reach the boundaries, which makes the boundary effect stronger. A smaller cutting depth means less material deformation, and therefore results in a weaker boundary effect. As the cutting speed and cutting depth may make the boundary effect stronger, it is important to consider those process parameters in choosing the model size for MD simulations of nanometric cutting.
We have performed a series of large-scale 3D MD simulations using the EAM potential to study the nanometric cutting process. Three different model sizes of 2-million-atom, 4-million-atom, and 10-million-atom are used with different cutting speeds and cutting depths. It is shown that the 2-million-atom model, though quite large compared with the models used in the previously reported studies, is not large enough to eliminate the boundary effect for the simulation conditions used. It is also shown that the 4-million-atom model is large enough to eliminate the boundary effect at the cutting speed of 100 m/s and cutting depth of up to 4 nm. A detailed study on the material deformation, lattice defects, dislocation movement, and cutting forces during the cutting process is made with the 4-million-atom model. It is observed that the nanometric cutting process is accompanied by complex material deformation, chip formation, lattice defect generation, and dislocation movement. It is found that as the cutting depth decreases, both the tangential and normal cutting forces decreases; however, the tangential cutting force decreases faster than the normal cutting force. It is also found that as the cutting depth decreases, the specific cutting force increases, which reveals that the “size effect” exists in nanometric cutting.
This work has been supported by the Agency for Science, Technology and Research (A*STAR), Singapore. Thanks also go to the staffs of the Computational Resource Centre at the Institute of High Performance Computing, who have provided the assistance in the large-scale computing and visualization.