Molecular Dynamics Simulation of Nanometric Machining Under Realistic Cutting Conditions Using LAMMPS

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1 Molecular Dynamics Simulation of Nanometric Machining Under Realistic Cutting Conditions Using LAMMPS Rapeepan Promyoo Thesis Presentation Advisor: Dr. Hazim El-Mounayri Department of Mechanical Engineering Purdue School of Engineering and Technology, IUPUI February 18 th, /18/2008 MSE Thesis Defense 1

2 Outline Introduction Problem Definition Previous Work Current Work Results Conclusions and Future Work Acknowledgement 2/18/2008 MSE Thesis Defense 2

3 Outline Introduction > Nanometric Machining > Molecular Dynamics Simulation Problem Definition Previous Work Current Work Results Conclusions and Future Work Acknowledgement 2/18/2008 MSE Thesis Defense 3

4 Nanometric Machining Machining is defined as the material removal process in which the excess material is removed in the form of small chips. In nanometric machining, the machining accuracy can be as low as 1 nm. 2/18/2008 MSE Thesis Defense 4

5 Nanometric Machining Some applications of nanometric machining are in the production of computer memory disks, camera lenses, and optical mirrors. Two types of nanometric machining Single-point Diamond Turning (SPDT) Ultra-precision Diamond Grinding (UPDG) SPDT is used in the machining of ductile materials, such as aluminum and copper. UPDG is used in the machining of brittle materials, such as silicon, ceramic, and glass. 2/18/2008 MSE Thesis Defense 5

6 Nanometric Machining Machining parameters in nanometric machining Cutting speed: normally below 10 m/s. Feed rate Depth of cut: nm Tool geometry Rake angle Clearance angle Tool edge radius 2/18/2008 MSE Thesis Defense 6

7 Nanometric Machining Chip Formation and Cutting Forces F c = Cutting Force F t = Thrust Force R = Resultant Force F s = Shear Force F = Friction Force 2/18/2008 MSE Thesis Defense 7

8 Molecular Dynamics Simulation Molecular Dynamics (MD) is an effective tool to study the mechanism of chip formation process at the atomic scale. Length scale = m. Time scale = s. 2/18/2008 MSE Thesis Defense 8

9 Molecular Dynamics Simulation Overview of MD simulation 2/18/2008 MSE Thesis Defense 9

10 Outline Introduction Problem Definition Previous Work Current Work Results Conclusions and Future Work Acknowledgement 2/18/2008 MSE Thesis Defense 10

11 Problem Definition Nanometric machining involves changes in a small region which contains only a few layers of atoms. As such it is difficult to investigate the machining process and determine the machining parameters experimentally. Experimental approach requires the use of expensive equipments. 2/18/2008 MSE Thesis Defense 11

12 Outline Introduction Problem Definition Previous Work Current Work Results Conclusions and Future Work Acknowledgement 2/18/2008 MSE Thesis Defense 12

13 Previous Work Molecular Dynamics Modeling of Nanometric Cutting Process Potential Energy Functions Komanduri [1] used Morse potential to conduct MD simulation of ultra-precision grinding process of single crystal copper. Komanduri [2] studied the effects of crystal orientation, cutting direction and rake angle on nanometric cutting of single crystal aluminum using Morse potential. Ye et al. [3] used EAM potential to conduct MD simulation of nanometric cutting of copper. However, in their study copper tools were used instead of diamond tools which are the ones used in the real process. 2/18/2008 MSE Thesis Defense 13

14 Previous Work Molecular Dynamics Modeling of Nanometric Cutting Process Atomistic Model - Due to limitation in computational time, most existing models of nanometric cutting are 2-D models consisting of a limited number of atoms (less than 15,000 atoms). Shimada [4] conducted 2-D MD simulation model to study chip removal, cutting force, and specific energy of micromachining of copper. Zhang and Tanaka [5] conducted 2-D MD simulation model to study the mechanism of wear and friction in nanometric cutting process. 2/18/2008 MSE Thesis Defense 14

15 Outline Introduction Problem Definition Previous Work Current Work > Objectives > Methodology > Computational Models Results Conclusions and Future Work Acknowledgement 2/18/2008 MSE Thesis Defense 15

16 Objectives 1. Develop MD simulation models of nanometric cutting using a general-purpose MD code called LAMMPS (Largescale Atomic/Molecular Massively Parallel Simulator). 2. Develop a pre-processor for generating the atomistic model of workpiece and tool material. 3. Validate MD as a technique for simulating nanometric machining. 4. Investigate the effect of different potential energy functions on the MD simulation results. 5. Simulate MD Simulation of nanometric machining under realistic cutting conditions. 2/18/2008 MSE Thesis Defense 16

17 Outline Introduction Problem Definition Previous Work Current Work > Objectives > Methodology * Principles of MD simulation * LAMMPS * Parallel Computing > Computational Models Results Conclusions and Future Work Acknowledgement 2/18/2008 MSE Thesis Defense 17

18 Principles of MD Simulation Principles of MD simulation > Atomistic Interaction in Nanometric Machining V c F ij Tool i at time t Workpiece at time t + t For each time increment ( t), every atom changes its position and interacts with its surrounding neighbor atoms in a manner that can be determined from the interatomic potential function. 2/18/2008 MSE Thesis Defense 18

19 Principles of MD Simulation The atoms move due to the forces acting on them according to Newton s second law of motion: dv F = ma = m = dt m 2 d r 2 dt The resultant force F can be obtained from a potential energy, U(r), which is a function of all atomic positions. F U ( r) = r 2/18/2008 MSE Thesis Defense 19

20 Principle of MD Simulation Potential Energy Function Potential energy function plays an important role in MD simulation: * Determines accuracy of MD simulation * Determines computational time The selection of an appropriate potential energy function depends on the type of material. The potential energy functions that are employed in this research are the pair-wise Morse potential and the embedded atom potential. 2/18/2008 MSE Thesis Defense 20

21 Principle of MD Simulation Potential Energy Function 1. Morse Potential { exp [ 2α ( r r )] 2 exp [ ( r r )]} U ( r ) = D e α e r is the distance between the atoms r e is the equilibrium bond distance D is the well depth (the characteristic energy parameter) is a parameter controlling the width of the potential α The single independent variable in the equation is r. α The constant parameters, r e,, and D, can be determined on the basis of the physical properties of the material. It is frequently used to describe the properties of cubic metals. 2/18/2008 MSE Thesis Defense 21

22 Principle of MD Simulation Potential Energy Function 2. Embedded-Atom Method (EAM) ( ) U ( r ) = i 1 ( ρ i ) + φ ij ( ij ) F i r 2 φ ij r ij is a two-body central potential between atom i and j r ij is the separation distance between atom i and j F i ( ρ i ) is the embedding energy ρ i is the electronic density of atom i due to the surrounding atoms, which is given by ρ i = i ρ i is the contribution to electronic density of atom i due to atom j at a distance r ij from atom i 2/18/2008 MSE Thesis Defense 22 j ρ i i j ( r ) ij

23 Principle of MD Simulation Time Integration Algorithm Due to the complex nature of potential energy functions, there is no analytical solution to the integration of Newton s equation. Thus, time integration algorithms are used. The time integration algorithm used in this research is called velocity Verlet Algorithm. r i ( t + Δt) = r () t + v () t Fi v ( t + Δt) = v ( t) + i i i i Δt + ( t) Fi 2m ( t + Δt) + F ( t) 2m Δt i 2 Δt 2/18/2008 MSE Thesis Defense 23

24 Principle of MD Simulation General Flow Chart in MD Simulation 2/18/2008 MSE Thesis Defense 24

25 LAMMPS LAMMPS stands for Large-scale Atomic/Molecular Massively Parallel Simulation. LAMMPS is a free open-source code. LAMMPS is a C++ code capable of modeling atomic, polyatomic, biological, metallic or granular molecules using a variety of force fields and boundary conditions. LAMMPS is designed for parallel applications. LAMMPS can model systems with only a few particles up to millions or billions. The maximum number of atoms that can be modeled in a simulation depends on computational power. 2/18/2008 MSE Thesis Defense 25

26 LAMMPS LAMMPS Input Script 1. Initialization 2. Atom definition 3. Settings 4. Run a simulation 2/18/2008 MSE Thesis Defense 26

27 LAMMPS LAMMPS Output There are two basic types of LAMMPS output. 1. Thermodynamic output a list of quantities printed every few time steps to the screen and log file. 2. Dump files snapshots of atoms and various per-atom values and are written at a specified frequency. 2/18/2008 MSE Thesis Defense 27

28 LAMMPS LAMMPS Pre-processor A pre-processor is developed using LabVIEW for generating the atomistic model of workpiece and tool material. Cutting parameters (such as depth of cut, tool rake angle, tool clearance angle, and tool edge radius) can be easily changed through the graphical user interface. The visualization of initial atom coordinates of tool and workpiece is provided to visually check the correctness of the initial model. 2/18/2008 MSE Thesis Defense 28

29 LAMMPS LAMMPS Post-Processor => Pizza.py Pizza.py is a collection of tools that provide post-processing capability for the LAMMPS molecular dynamics package. Pizza.py Include several tools to create input files, convert between file formats, process log and dump files, create plots, and visualize and animate simulation snapshots. Pizza.py is distributed free-of-charge. Pizza.py is written in Python scripting language. 2/18/2008 MSE Thesis Defense 29

30 Parallel Computing Big Red supercomputer is used to perform MD simulation of nanometric cutting in this work. Big Red is configured for massively parallel computing. LAMMPS code runs in parallel using distributed memory message passing techniques and spatial decomposition of simulation domain. In spatial decomposition, the simulation domain is divided into a set of equal smaller sized domains. Each sub-domain is distributed to different processor for calculation. 2/18/2008 MSE Thesis Defense 30

31 Parallel Computing Computational Time Number of atoms Computational time (seconds) 1 processor 4 processors 8 processors 10, , /18/2008 MSE Thesis Defense 31

32 Outline Introduction Problem Definition Previous Work Current Work > Objectives > Methodology > Computational Models * Atomistic Modeling of Material * Nanometric Cutting Model * Boundary Condition Results Conclusions and Future Work Acknowledgement 2/18/2008 MSE Thesis Defense 32

33 Computational Models Atomistic Modeling of Material Atomistic description of material properties considers crystal structure, lattice constants and orientation. The crystal structure is composed of a unit cell, a set of atoms arranged in a particular way, which is periodically repeated in three dimensions on a lattice. The unit cell is given by its lattice parameters, the length of the cell edges and the angles between them. The lattice parameters of the unit cell identify its shape such as cubic or hexagonal. The selection of the lattice structure to be modeled for the simulation is determined from the shape of the unit cell. 2/18/2008 MSE Thesis Defense 33

34 Computational Models Atomistic Modeling of Material Lattice Structure Face centered cubic (FCC) structure Diamond cubic structure 2/18/2008 MSE Thesis Defense 34

35 Computational Models Nanometric Cutting Model Direction of cutting Rake angle Tool Depth of cut Clearance angle Workpiece y x z 2/18/2008 MSE Thesis Defense 35

36 Computational Models Nanometric Cutting Model Tool is modeled as a rigid body. The initial displacement of the workpiece and the tool can be created from the crystal structure of the material. The thermostat atoms are applied to the MD simulation model to ensure that the heat generated during the cutting process can conduct out of the cutting region properly. The Newtonian zone is determined solely by the forces derived from the potential energy function and the Newton s equation of motion. 2/18/2008 MSE Thesis Defense 36

37 Computational Models Nanometric Cutting Model of Copper Workpiece material Workpiece dimension Crystal orientation Tool material Tool dimension Tool rake angle Tool clearance angle Width of cut Depth of cut Cutting speed Cutting Direction Bulk temperature Time steps Copper 21a 1 x 20a 1 x 4a 1 ; a 1 = nm (001) Diamond 10a 2 x 14a 2 x 5a 2 ; a 2 = nm -75º to +45º 5º nm nm 5 and 500 m/s [100] 293 K 2 fs (2 x s) 2/18/2008 MSE Thesis Defense 37

38 Computational Models Nanometric Cutting Model of Aluminum Workpiece material Workpiece dimension Crystal orientation Tool material Tool dimension Tool rake angle Tool clearance angle Width of cut Depth of cut Cutting speed Cutting Direction Bulk temperature Time steps Aluminum (Al) 30a 3 x 25a 3 x 4a 3 ; a 3 = nm (001) Diamond (C) 12a 2 x 20a 2 x 5a 2 ; a 2 = nm 0º,10º, and 40º 5º 1.62 nm nm 500 m/s [100] 293 K 2 fs (2 x s) 2/18/2008 MSE Thesis Defense 38

39 Computational Models Boundary Condition Two types of boundary conditions are used in MD simulation studies 1. Fixed boundary conditions 2. Periodic boundary conditions Fixed boundary conditions are applied to the boundary atoms. The atoms are fixed in the position to reduce the edge effects and maintain the symmetry of the lattice. Periodic boundary conditions are maintained along the z direction. 2/18/2008 MSE Thesis Defense 39

40 Computational Models Periodic Boundary Condition The simulation box and its surrounding boxes are exactly the same in every detail. Whenever an atom leaves the simulation box, it is replaced by another with exactly the same velocity, entering from the opposite cell face. An atom may interact with one in the neighboring cell because it is within the cutoff radius (r cut ). Beyond the cutoff radius, interactions are small enough to be neglected. Periodic boundary conditions in MD simulation 2/18/2008 MSE Thesis Defense 40

41 Outline Introduction Problem Definition Previous Work Current Work Results Conclusions and Future Work Acknowledgement 2/18/2008 MSE Thesis Defense 41

42 Results MD Simulation of Nanometric Cutting of Copper t = 0 ps t = 4 ps t = 7 ps t = 10 ps Animation of Nanometric Cutting Process with 15ºTool Rake Angle and Depth of Cut of nm. 2/18/2008 MSE Thesis Defense 42

43 Results MD Simulation of Nanometric Cutting of Aluminum t = 0 ps t = 4 ps t = 7 ps t = 10 ps Animation of Nanometric Cutting Process of Aluminum with 15ºTool Rake Angle and Depth of Cut of 1.62 nm. 2/18/2008 MSE Thesis Defense 43

44 Results Effect of Tool Rake Angle on Chip Formation (Copper) Rake angle = -5º Rake angle = 5º Chip Dimension of Copper Rake angle = 10º Rake angle = 30º 2/18/2008 MSE Thesis Defense 44

45 Results Effect of Tool Rake Angle on Chip Formation (Aluminum) Rake angle = 0º Rake angle = 10º Rake angle = 40º Chip Dimension of Aluminum 2/18/2008 MSE Thesis Defense 45

46 Results Effect of Tool Rake Angle on Forces (Copper) Cutting and Thrust Forces at t = 10 fs Force Ratio 2/18/2008 MSE Thesis Defense 46

47 Results Effect of Tool Rake Angle on Other cutting parameter(copper) Friction Angle Shear Angle 2/18/2008 MSE Thesis Defense 47

48 Results Effect of Tool Rake Angle on other cutting parameters (Aluminum) Friction Angle Shear Angle 2/18/2008 MSE Thesis Defense 48

49 Results Effect of Depth of Cut on Chip Formation (Aluminum) As the depth of cut increase, > the deformations ahead of the tool and under the tool increase > the chip thickness and chip length increase 2/18/2008 MSE Thesis Defense 49

50 Results Effect of Depth of Cut on Forces (Aluminum) Cutting and Thrust Forces at t = 10 fs. Force Ratio 2/18/2008 MSE Thesis Defense 1

51 Results Effect of Potential Energy Function (Copper) Morse Potential EAM Potential Rake angle = 0º Rake angle = 15º Rake angle = 30º 2/18/2008 MSE Thesis Defense 2

52 Results Effect of Potential Energy Function (Aluminum) Morse Potential EAM Potential Rake angle = 0º 2/18/2008 Rake angle = 10º MSE Thesis Defense Rake angle = 40º 3

53 Results Effect of Potential Energy Function on Forces Cutting and Thrust Forces 2/18/2008 MSE Thesis Defense 4

54 Outline Introduction Problem Definition Previous Work Current Work Results Conclusions and Future Work Acknowledgement 2/18/2008 MSE Thesis Defense 5

55 Conclusions Development of a pre-processor for generating the atomistic model of workpiece and tool material Development of MD simulation models of nanometric machining using LAMMPS Validation of MD technique as a tool for nanometric machining Simulation of nanometric machining under realistic cutting conditions Investigation of the effect of different potential energy functions The EAM potential is found to describe the metallic bonding character more accurately than the Morse potentials 2/18/2008 MSE Thesis Defense 6

56 Future Work 1. Simulate a machining process at micro-level 2. Create a model of defects and imperfections in the crystal structure of the work material. This would require the formulation of a new Potential energy function 3. Consider tool and workpiece interaction in a model to investigate wear and deformation in the cutting tool 2/18/2008 MSE Thesis Defense 7

57 Acknowledgements Dr. Hazim El-Mounayri Major Advisor Dr. Hasan U. Akay Committee Member Dr. Xiaoping Yang Committee Member Dr. Guofeng Wang Dr. Erdal Yilmaz Resat Payli Robert Meagher Colleagues from the AEML, ME department, and IUPUI 2/18/2008 MSE Thesis Defense 8

58 References [1] R. Komanduri, N. Chandrasekaran, and L. M. Raff, "Some aspects of machining with negative-rake tools simulating grinding: a molecular dynamics simulation approach," Philosophical Magazine B, Vol. 79, pp , [2] R. Komanduri, N. Chandrasekaran, and L. M. Raff, "M.D. Simulation of nanometric cutting of single crystal aluminum effect of crystal orientation and direction of cutting," Wear, Vol. 242, pp , [3] Y. Y. Ye, R. Biswas, J. R. Morris, A. Bastawros, and A. Chandra, "Molecular dynamics simulation of nanoscale machining of copper," Nanotechnology, Vol. 14, pp , [4] S. Shimada, N. Ikawa, H. Tanaka, G. Ohmori, J. Uchikoshi, and H. Yoshinaga, " Feasibility study on ultimate accuracy in microcutting using molecular dynamics simulation " CIRP Annals, Vol. 42, pp , [5] L. Zhang and H. Tanaka, "Towards a deeper understanding of wear and friction on the atomic scale - A molecular dynamics analysis," Wear, Vol. 211, pp , /18/2008 MSE Thesis Defense 9

59 Questions?? 2/18/2008 MSE Thesis Defense 10

60 Thank you 2/18/2008 MSE Thesis Defense 11

SIMULATION OF NANO-SCALE CUTTING WITH MOLECULAR DYNAMICS

SIMULATION OF NANO-SCALE CUTTING WITH MOLECULAR DYNAMICS American Journal of Nanotechnology 5 (2): 17-26, 2014 ISSN 1949-0216 2014 Angelos P. Markopoulos et al., This open access article is distributed under a Creative Commons Attribution (CC-BY) 3.0 license