Promyoo Thesis S'08

Molecular Dynamics Simulation of Molecular Dynamics Simulation of Nanometric Machining Under Realistic Nanometric Machining Under Realistic

Cutting Conditions Using LAMMPS Cutting Conditions Using LAMMPS

Rapeepan PromyooThesis Presentation

Advisor: Dr. Hazim El-Mounayri

Department of Mechanical EngineeringPurdue School of Engineering and Technology, IUPUI

February 18th, 2008

2/18/2008 MSE Thesis Defense 1

OutlineOutline

• Introduction• Problem Definition• Previous Work• Current Work • Results• Conclusions and Future Work• Acknowledgement

OutlineOutline

• Introduction> Nanometric Machining> Molecular Dynamics Simulation

• Problem Definition• Previous Work• Current Work • Results• Conclusions and Future Work• Acknowledgement

Nanometric MachiningNanometric 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.

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.

Machining parameters in nanometric machining

Cutting speed: normally below 10 m/s.Feed rateDepth of cut: 1 – 100 nmTool geometry

Rake angleClearance angleTool edge radius

Chip Formation and Cutting Forces

Fc = Cutting Force

Ft = Thrust Force

R = Resultant Force

Fs = Shear Force

F = Friction Force

Molecular Dynamics SimulationMolecular Dynamics Simulation

Molecular Dynamics (MD) is an effective tool to study the mechanism of chip formation process at the atomic scale.

Length scale = 10-10 m.Time scale = 10-12 s.

Molecular Dynamics SimulationMolecular Dynamics Simulation

Overview of MD simulation

OutlineOutline

• Introduction

• Problem Definition• Previous Work

• Current Work• Results• Conclusions and Future Work• Acknowledgement

Problem DefinitionProblem 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.

OutlineOutline

• Introduction

• Problem Definition

• Previous Work• Current Work• Results• Conclusions and Future Work• Acknowledgement

Previous WorkPrevious Work

Molecular Dynamics Modeling of Nanometric Cutting ProcessPotential 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 crystalaluminum 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 usedin the real process.

Previous WorkPrevious Work

Molecular Dynamics Modeling of Nanometric Cutting ProcessAtomistic 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 ofcopper.

Zhang and Tanaka [5] conducted 2-D MD simulation model to study the mechanism of wear and friction in nanometric cutting process.

OutlineOutline

• Introduction• Problem Definition • Previous Work

• Current Work > Objectives> Methodology> Computational Models

• Results• Conclusions and Future Work• Acknowledgement

ObjectivesObjectives

1. Develop MD simulation models of nanometric cutting using a general-purpose MD code called LAMMPS (Large-scale 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.

OutlineOutline

• Introduction• Problem Definition • Previous Work • Current Work

> Objectives> Methodology

* Principles of MD simulation* LAMMPS* Parallel Computing

> Computational Models • Results• Conclusions and Future Work• Acknowledgement

Principles of MD SimulationPrinciples of MD Simulation

Principles of MD simulation> Atomistic Interaction in Nanometric Machining

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.

Workpiece

at time t

at time t + ∆t

Principles of MD SimulationPrinciples of MD Simulation

The atoms move due to the forces acting on them according to Newton’s second law of motion:

The resultant force F can be obtained from a potential energy, U(r), which is a function of all atomic positions.

dtdvmmaF ===

∂∂

−=)(

Principle of MD SimulationPrinciple of MD Simulation

Potential Energy FunctionPotential 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.

Potential Energy Function1. Morse Potential

r is the distance between the atomsre is the equilibrium bond distanceD is the well depth (the characteristic energy parameter)

is a parameter controlling the width of the potential

The single independent variable in the equation is r.The constant parameters, re, , 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.

( )[ ] [ ]{ })(exp22exp)( ee rrrrDrU −−−−−= αα

Potential Energy Function2. Embedded-Atom Method (EAM)

is a two-body central potential between atom i and jrij is the separation distance between atom i and j

is the embedding energyis the electronic density of atom i due to the surrounding

atoms, which is given by

is the contribution to electronic density of atom i due to atom j at a distance rij from atom i

( ) ( )∑∑≠

ii rFrU φρ21)(

( )ijij rφ

( )iiF ρ

( )∑≠

ijii rρρ

Time Integration AlgorithmDue 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.

( ) ( ) ( ) ( )

( ) ( ) tm

tFttFtvttv

tmtFttvtrttr

Δ+Δ+

Δ+Δ+=Δ+

General Flow Chart in MD Simulation

LAMMPSLAMMPS

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.

LAMMPSLAMMPS

LAMMPS Input Script

1. Initialization

2. Atom definition

3. Settings

4. Run a simulation

LAMMPSLAMMPS

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 filessnapshots of atoms and various per-atom values and are written at a specified frequency.

LAMMPSLAMMPS

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.

LAMMPSLAMMPS

LAMMPS Post-Processor => Pizza.pyPizza.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.

Parallel ComputingParallel 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.

Parallel ComputingParallel Computing

Computational Time

Number of

Computational time (seconds)

1 processor 4 processors 8 processors

10,000 113.999 101.566 59.2076

100,000 1626.06 944.138 499.498

OutlineOutline

• 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

Computational ModelsComputational Models

Atomistic Modeling of MaterialAtomistic 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.

Atomistic Modeling of MaterialLattice Structure

Face centered cubic (FCC) structure

Diamond cubic structure

Nanometric Cutting Model

Workpiece

Direction of cutting

Depth of cut

Clearanceangle

Rake angle

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 processcan 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.

Nanometric Cutting Model of Copper

Workpiece materialWorkpiece dimensionCrystal orientationTool materialTool dimensionTool rake angleTool clearance angleWidth of cutDepth of cutCutting speedCutting DirectionBulk temperatureTime steps

Copper21a1 x 20a1 x 4a1 ; a1 = 0.362 nm(001)Diamond10a2 x 14a2 x 5a2 ; a2 = 0.357 nm-75º to +45º5º1.418 nm0.724 – 2.172 nm5 and 500 m/s[100]293 K2 fs (2 x 10-15 s)

Nanometric Cutting Model of Aluminum

Workpiece materialWorkpiece dimensionCrystal orientationTool materialTool dimensionTool rake angleTool clearance angleWidth of cutDepth of cutCutting speedCutting DirectionBulk temperatureTime steps

Aluminum (Al)30a3 x 25a3 x 4a3 ; a3 = 0.405 nm(001)Diamond (C)12a2 x 20a2 x 5a2 ; a2 = 0.357 nm0º ,10º, and 40º5º1.62 nm0.81– 1.62 nm500 m/s[100]293 K2 fs (2 x 10-15 s)

Boundary ConditionTwo types of boundary conditions are used in MD simulation

studies1. Fixed boundary conditions2. 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.

Periodic Boundary ConditionThe 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 (rcut).

Beyond the cutoff radius, interactions are small enough to be neglected.

Periodic boundary conditions in MD simulation

OutlineOutline

• Introduction

• Problem Definition• Previous Work• Current Work

• Results• Conclusions and Future Work

• Acknowledgement

ResultsResults

MD Simulation of Nanometric Cutting of Copper

t = 0 ps

t = 10 ps t = 7 ps

t = 4 ps

Animation of Nanometric Cutting Process with 15ºTool Rake Angle and Depth of Cut of 0.724 nm.

ResultsResults

MD Simulation of Nanometric Cutting of Aluminum

t = 0 ps

t = 10 ps t = 7 ps

t = 4 ps

Animation of Nanometric Cutting Process of Aluminum with 15ºTool Rake Angle and Depth of Cut of 1.62 nm.

ResultsResults

Effect of Tool Rake Angle on Chip Formation (Copper)

Rake angle = -5º Rake angle = 5º

Rake angle = 30ºRake angle = 10ºChip Dimension of Copper

ResultsResults

Effect of Tool Rake Angle on Chip Formation (Aluminum)

Chip Dimension of Aluminum

Rake angle = 0º

Rake angle = 40º

Rake angle = 10º

ResultsResults

Effect of Tool Rake Angle on Forces (Copper)

Cutting and Thrust Forces at t = 10 fs

Force Ratio

ResultsResults

Effect of Tool Rake Angle on Other cutting parameter(Copper)

Friction Angle Shear Angle

ResultsResults

Effect of Tool Rake Angle on other cutting parameters (Aluminum)

Friction Angle Shear Angle

ResultsResults

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

ResultsResults

Effect of Depth of Cut on Forces (Aluminum)

Cutting and Thrust Forcesat t = 10 fs.

Force Ratio

ResultsResults

Effect of Potential Energy Function (Copper)

Rake angle = 30ºRake angle = 15º

Morse Potential

Rake angle = 0º

EAM Potential

ResultsResults

Effect of Potential Energy Function (Aluminum)

Rake angle = 40ºRake angle = 10º

Morse Potential

Rake angle = 0º

EAM Potential

ResultsResults

Effect of Potential Energy Function on Forces

Cutting and Thrust Forces

OutlineOutline

• Introduction

• Problem Definition• Previous Work• Current Work• Results

• Conclusions and Future Work• Acknowledgement

ConclusionsConclusions

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

Future WorkFuture 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

AcknowledgementsAcknowledgements

Dr. Hazim El-Mounayri – Major AdvisorDr. Hasan U. Akay – Committee MemberDr. Xiaoping Yang – Committee MemberDr. Guofeng Wang Dr. Erdal YilmazResat PayliRobert MeagherColleagues from the AEML, ME department, and

ReferencesReferences

[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. 955-968, 1999.

[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. 60-88, 2000.

[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. 390-396, 2003.

[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. 91-94, 1993.

[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. 44-53, 1997.

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