本論文利用分子動力學(Molecular Dynamics)，模擬奈米尺寸下的正交切削行為，使用鑽石刀具切削銅材的研究。並且改變不同的切削方向、深度、速度，探討其切屑的變形機制與差排滑動行為對切削力的影響，並探討在設定為週期性邊界條件下，模型寬度對模擬結果的影響。所使用的模型在垂直切削方向設定邊界條件，原子間勢能函數在銅原子間採用嵌入原子式模型(EAM)而銅對碳原子則採用二體的Morse勢能函數模型。
模擬的結果顯示，在(001)晶面沿[-100]方向切削中，於剪切區形成(111)或(-11-1)面為滑動系統，並藉此產生塑性變形。在(101)晶面沿[-101]方向切削中，切屑的形成是差排利用(111)平面沿著剪切平面(shear plane)射出與(1-1-1)平面的滑動系統向上滑移所造成。在(101)晶面沿[0-10]方向切削時，切屑形成方式主要為利用[-12-1]方向的原子滑移形成雙晶變形。在不同切深的條件下，隨著切入深度的增加比切削能也會減少，其主要起因於刀腹的摩擦行為。切削速度達到300m/s時在刀斜面處會發生非結晶(微融)現象並使切削力降低，但500m/s時因速度過高則反而造成切削力上升。此外，研究結果顯示周期性邊界的主胞室寬度不足時，則易使結果受影響。

The research study the nanometric cutting of singal crystal copper with the diamond tool by molecular dynamics. The effects of chip deformation and dislocation slip on cutting force are performed with the various cutting directions, depthes and speeds. The study also analyze the influneces of different widths of primary cell on the nanometric cutting process when the periodic boundary conidtion are used. The interactions between Cu atoms in the workpiece are described by a embedded-atom method(EAM) potential ,and interactions between Cu atoms and C atoms are described by two body potential.

The simulation results shows that when the cutting direction is along the [-100] direction on the (001) plane, the partial dislocations are operated on the (111) or (-11-1) slip plane in the shear zone. As the cutting direction is along the [-101] direction on the (101) plane, the formation of chip is caused by the dislocation slip with the (111) shear plane and [1-1-1] slip plane. If the cutting direction is along the [0-10] direction on the (101), twin deformation with the [-12-1] slip direction is responsible for the formation of chip. For different cutting depths, specific energy decreases with cutting depths,resulting from the friction of the tool clearance face. When the cutting speed reaches 300m/s, the amorphous (melting) phenomenon on the tool rake face is produced, causing the decrease of cutting force. However, if the cutting speed reaches 500m/s,causing the increase of cutting force. Additionally, the simulation result proves that the insufficiency of the widths of primary cell obviously influence the validity of simulation results.

1.G. Binning, H. Rohrer, Ch. Gerber, and E. Weibel, “Surface Studies by Scanning Tunneling Microscopy”, Phy. Rev. Lett., Vol.49, No.1,pp.57-61(1982).
2.約翰．道爾頓(Dalton, John)，李家玉，盛根玉譯，化學哲學新體系(A new system of chemical philosophy)，北京市，北京大學出版社，2006。
3.J. H. Irving, and John G. Kirkwood, “The Statistical Mechanical Theory of Hydrodynamics,” J. chem. phys., Vol.18, No.6,pp.817-829(1950).
4.Nicholas Metropolis, Arianna W. Rosenbluth, Marshall N. Rosenbluth, and Augusta H. Teller, Edward Teller, “Equation of State Calculations by Fast Computing Machines,” J. chem. phys.,Vol.21, No.6, pp.1087-1092(1953).
5.沉海軍，奈米科技概論，第209~213頁，北京，國防工業出版社，2007年。
6.Loup Verlet, “Computer “Experiment” on Classical Fluids. I.Thermodynamical Properties of Lennard-Jones Molecules,” Phys.rev., Vol.159, No.1, pp.98-103(1967).
7.B. Quentrec, and C. Brot, “New Method for Neighbors in Molecular Dynamics Computations,”J. comput. phys., Vol.13,pp.430-432(1973).
8.D. C. Rapaport, “Large-Scale Molecular Dynamics Simulation Using Vector and Parallel Computers,” Comput. phys. rep., Vol.9,pp.1-53(1988).
9.Madeleine Meyer and Vallilis Pontikis, “Computer Simulation in Material Science:Interatomic Potentials, Simulation Techniques and Applications,” Kluwer Academic Publishers, USA,(1991).
10.W. G. Hoover, C. G. Hoover and I. F. Stowers, ”Interface tribology by nonequilibrium molecular dynamics fabrication technology”,Mater Res. Soc. Symp.,140 (1989).
11.Stowers I., Belak J. F., F.,Lucca D. A., Komanduri R.,Rhorer R. L.,Moriwaki T.,Okuda K.,Ikawa H., Shimada S., Tanaka H., Dow T. A. and Drescher J. D., ”Molecular Dynamics Simulation of the Chip Forming Process in Single Crystal Copper and Comparison with Experimental Data Proc”,6th Annu. Conf. AM. Soc. Prec. Eng.pp.100-103.
12.J. Belak and I. F. Stowers,”A Molecular Dynamics Model of the Orthogonal Cutting Process Proc. Am. Soc. Prec. Eng.pp.76-9(1990).
13.J. Belak,”Modelling Atoms when Surfaces Collide”, Nanotribology
(Energy and Technology Review),p13(1994).
14.Murray S. Daw, and M. I. Baskes, “Embedded-Atom Method: Derivation and Application to Impurities, Surfaces, and Other Defects in Metals,” Phy. Rev. B., Vol.29, No.12, pp.6443-53(1983).
15.M.E. Riley, M.E. Coltran and D.J. Diestler. J. Chem., ” A velocity reset method of simulating thermal motion and damping in gas–solid collisions”, Phys.Vol.88, p.5934(1988).
16.N. Ikawa, S. Shimada, H. Tanaka and G. Ohmori, ”An Atomistic Analysis of Nanometric Chip Removal as Affected by Tool-Work Interaction in Diamond Turning,”Ann. CIRP,Vol.40,No.1,551(1991).
17.Shimada et al, ”Structure of Micromachined Surface Simulated by
Molecular Dynamics Analysis,” Ann. CIRP,Vol.43,No.9, 51(1994).
18.S. Shimada, N. Ikawa, G. Ohmori, H. Tanaka and J. Uchikoshi, “Molecular Dynamics Analysis as Compared with Experimental Results of micromachining,” Ann.CIRP,Vol.41,No.1,117(1992).
19.S. Shimada et al, “Feasibility Study on Ultimate Accuracy in Microcutting Using Molecular Dynamics Simulation,” Ann. CIRP,Vol.42,No.1,91(1993).
20.Shimada et al, “Molecular Dynamics Analysis of Cutting Force and Chip Formation Process in Microcutting”, J.JSPE,Vol.59,No.12,pp.51-51(1993).
21.T. Inamura, H. Suzuki and N. Takezawa, “Cutting experiments in a computer using atomic models of a copper crystal and a diamond tool”, Int. J.Japan.Soc.Prec., Eng.,Vol.25,pp.259-266(1991).
22.T. Inamura,N. Takezawa and N. Taniguchi, ”Atomic-scale cutting in a computer using crystal models of copper and diamond”, Ann.CIRP,Vol.41,pp.121-124(1992).
23.T. Inamura, N. Takezawa and Y. Kumaki,” Mechanics and energy dissipation in nanoscale cutting”, Ann.CIRP, Vol.42,pp.79-82(1993).
24.T. Inamura, N. Takezawa,Y. Kumaki and T. Sata,” On a possible mechanism of shear deformation in nanoscale cutting”, Ann.CIRP,Vol.43,pp.47-50(1994).
25.R. Komanduri, N. Chandrasekaran nad L. M. Raff, ”Effect of tool geometry in nanometric cutting: a molecular dynamics simulationapproach,” Wear, Vol.219, 84-97(1998).
26.R. Komanduri, N. Chandrasekaran nad L. M. Raff, ”Simulation of nanometric cutting of single crystal aluminum-effect of crystal orientation and direction of cutting,”Wear,Vol.242,pp.60-68(2000).
27.R. Komanduri, N. Chandrasekaran nad L. M. Raff, ”Simulation of indentation and scratching of single crystal aluminum“, Wear, Vol.240, No.1-2, pp.113-143(2000).
28.R. Komanduri, N. Chandrasekaran nad L. M. Raff, ”Molecular dynamics simulation of atomic-scale friction”, Phys. Rev.B,Vol.61, pp.14007-14019(2000).
29.R. Komanduri, M. Lee, L. M. Raff, ”The significance of normal rake in oblique machining”, International Journal of Machine Tools and
Manufacture, Vol.44, No.10,pp.1115-1124(2004).
30.K. Maekawa, and A.Itoh, “Friction and tool wear in nano-scale machining – A molecular dynamics approach”, Wear, Vol.188,155(1995).
31.Y. Y. Ye, R. Biswas, J. R. Morris, A. Bastawros and A. Chandra, ”Molecular dynamicm simulation of nanoscale machiningof copper”, Nanotechnology, Vol.14, pp.390-396(2003).
32.Q.X. Pei, C. Lu, F. Z. Fang, H. Wu, ”Nanometric cutting of copper: A molecular dynamics study”, Computational Materials Science,Vol.37, No.4, pp.434-441(2006).
33.Q.X. Pei, C. Lu, H. P. Lee,” Large scale molecular dynamics study of nanometric machining of copper”, Computational Materials
Science,Vol.41, pp.177–185(2007).
34.陳露生，科學發展，400期，第62~67頁，行政院國家科學委員會，2006年。
35.J.E. Lennard-Jonse, “The Determination of Molecular Fields. I. From the Variation of the Viscosity of a Gas with Temperature”, Proc.Roy.Soc.(Lond.), Vol.106A, 441(1924).
36.L.A. Girifalco and V.G. Weizer, “Application of the Morse Potential Function to Cubic Metals”, Phys.Rev.,Vol.114, No.3,pp.687-90(1959).
37.Murray S. Daw, and M. I. Baskes, “Semiempirical, Quantum Mechanical Calculation of Hydrogen Embrittlement in Metals,” Phy. Rev. Lett.,Vol.50, No.17, pp.1285-1288(1983).
38.Murray S. Daw, and M. I. Baskes, “Embedded-Atom Method: Derivation and Application to Impurities, Surfaces, and Other Defects in Metals,” Phy. Rev. B., Vol.29, No.12,pp.6443-53(1983).
39.C. W. Gear, Numerical Initial Value Problems in Ordinary Differential Equations,Prentice-Hall, Englewood Cliffs, NJ,(1971).
40.J. M. Haile, Molecular Dynamics Simulation,John Wiley and Sons, New York, (1992).
41.Cynthia L. Kelchner, S. J. Plimpton, J. C. Hamilton, “Dislocation Nucleation and Defect Structure During Surface Indentation,” Phy. Rev. B., Vol.58, No.17, pp.11085-11088(1998).
42.R. A. Johnson, “Analytic Nearest-Neighbor Model for FCC Metals,”Phy. Rev. B., Vol.37,No.8, pp.3924-3931(1988).
43.R. A. Johnson, “Alloy Models with the Embedded-Atom Method,”Phy. Rev. B., Vol.39, No.17, pp.12554-12559(1989).
44.Dar-Jen Pen and Yuan-Ching Lin, “Transition wave in Cu nanowires at ultra-high strain rate with molecular dynamics method”, Taiwan-Tohoku Joint International Symposium for Mechanical Science Based on Nanotechnology, National Taiwan University of Science and Technology, Taiwan, pp.122-125(2007).
45.M. C. Shaw,Metal cutting principles, Oxford, NewYork,
pp.42-3(1984).