本文主要為應用三維準穩態奈米力學奈米切削模式，模擬在不同的奈米級切削參數下對單晶矽材料的奈米級正交切削，並分析其切削力、切削形狀、等效應變及等效應力等的模擬的結果。本文所探討的不同奈米級切削參數為在其他文獻當中尚無較完整分析之單晶矽奈米正交切削參數，並進行模擬分析，故本文所探討的切削奈米級參數為(1)在固定切削深度5.45Å，且後斜角皆是15度，針對不同的刀鼻半徑5Å、10Å，以及尖銳刀具的單晶矽奈米正交切削行為之比較。(2)固定切削深度5.45Å，固定刀鼻半徑5Å，針對不同後斜角-30度、-15度、15度及30度，來進行單晶矽奈米級正交切削的切削行為的分析與探討。(3)固定後斜角15度及固定刀鼻半徑5Å，針對不同的切削深度2.72 Å、5.45Å 與10.90Å的單晶矽奈米正交切削行為之探討。
本文使用三維準穩態奈米靜力學奈米切削模式對單晶矽進行切削模擬，其為計算每個原子的運動軌跡方法來直接求解每個原子移動一小距離時，應用之力平衡之概念，並以最佳化的方法來求解力平衡方程式，求出新的運動位置，並逐步推算出切削時切屑的行為，本文利用被切削單晶矽中間斷面所計算出的單晶矽原子之位移以及利用有限元素法裡的形狀函數的概念來計算出被切削單晶矽中間斷面等效應變。再由塑流應力-應變曲線(flow stress-strain)的關係式計算出等效應力的數值進而得到被切削單晶矽中間斷面的等效應變與等效應力的分布趨勢。而為了驗證本文切削單晶矽之三維準穩態分子靜力學奈米級切削模式之正確性，本文模擬一後斜角為-30度鑽石刀具，正交切削2個單晶矽結晶寬度之單晶矽工件以及4個單晶矽結晶寬度之單晶矽工件，並將模擬結果與Komanduri【29】的數值做比較，其結果證明本文所建立之三維準穩態分子靜力學奈米級正交切削單晶矽的模擬模式為可行。

The study applies the nano-scale cutting model of three-dimensional quasi-steady nano-scale dynamics to simulate the nano-scale orthogonal cutting of monocrystalline silicon material under different nano-scale cutting parameters, and analyzes the simulated results of its cutting force, cutting shape, equivalent strain and equivalent stress. The different nano-scale cutting parameters investigated by the paper are the nano-scale orthogonal cutting parameters of monocrystalline silicon that did not have complete analysis in the past literature, so the paper is going to perform simulated analysis of them. The nano-scale cutting parameters investigated in this paper are: (1) Comparison of different cutting edge radii of 5Å and 10Å, as well as the nano-scale orthogonal cutting behavior of monocrystalline silicon by sharp cutting tool under the conditions that the cutting depth is fixed at 5.45Å and all rake angles are 15o. (2) Analysis and investigation of the cutting behavior of nano-scale orthogonal cutting of monocrystalline silicon at different rake angles of -30o, -15o, 15o and 30o under the conditions that the fixed cutting depth is 5.45Å and the fixed cutting edge radius is 5Å. (3) Investigation of the nano-scale orthogonal cutting behavior of monocrystalline silicon under the different cutting depths of 2.72 Å, 5.45Å and 10.90Å.
Regarding the simulated cutting of monocrystalline silicon performed by the paper by using the nano-scale cutting model of three-dimensional quasi-steady nano-scale statiics, it is a concept that the method of calculating the movement track of each atom is used to directly acquire the applied equilibrium force when each atom moves for a small distance. The paper uses optimized method to solve the equation of equilibrium force, find out the new movement position, and step by step calculate the cutting behavior in times of cutting. The paper uses the displacement of monocrystalline silicon atoms calculated from the middle cross-section of the cut monocrystalline silicon, and uses the shape function concept in finite element method to calculate the equivalent strain of the middle cross-section of the cut monocrystalline silicon. Through the relation equation of flow stress-strain curve, the paper calculates the numerical value of equivalent stress, and acquires the distribution trend of the equivalent strain and equivalent stress of the middle cross-section of the cut monocrystalline silicon. In order to prove the correctness of the paper’s nano-scale cutting model of three-dimensional quasi-steady molecular statics for the cutting of monocrystalline silicon, the paper simulates the orthogonal cutting of a monocrystalline workpiece with the width of 2 monocrystalline silicon crystals and that of monocrystalline workpiece with the width of 4 monocrystalline silicon crystals by a diamond cutting tool with rake angle -30o. The simulation result is compared with the numerical value achieved by Komanduri [29]. As proved from the result, the simulated nano-scale orthogonal cutting model of three-dimensional quasi-steady molecular statiics established by the paper is feasible.

[1]. Komanduri, R, Chandrasekaran N and Raff L. M., “Simulation of nanometric cutting of single crystal aluminum—effect of crystal orientation and direction of cutting” , Wear, Vol.242, No. 60, pp.8 (2000).
[2]. Shimada, S., “Molecular Dynamics Analysis as Compared with Experimental Results of Micromachining,” Ann. CIRP, Vol.41, No. 1, pp.117-120(1990).
[3]. Childs, T. H. C., and Maewaka, K., “Computer-aided Simulation and Experimental Studies of Chip Flow and Tool Wear in the Turning of Flow Alloy Steels by Cemented Carbide Tools” ,Wear, Vol. 139, No.2, pp. 235-250(1990).
[4]. Belak, J., and Stowers, I. F., “A Molecular Dynamics Model of the Orthogonal Cutting Process,” Proc. Am. Soc., Precision Eng., pp.76-79(1990).
[5]. Kim, Jeong-Du., and Moon, Chan-Hong., “A study on microcutting for the configuration of tools using molecular dynamics” ,Journal of Materials Processing Technology , pp. 309-314(1995).
[6]. Fang, F. Z., Wu, H., Zhou, W., and Hu, X. T., “A study on mechanism of nano-cutting single crystal silicon” , Journal of Materials Processing Technology, pp. 407-410(2007).
[7]. Pei, Q. X., Lu,C., Fang, F. Z., and Wu, H., “Nanometric cutting of copper: A molecular dynamics study,” Computational Materials Science, pp.434-441(2006).
[8]. Inamura, T., and Takezawa, N., “Cutting Experiments in a Computer Using Atomic Models of a Copper Crystal and a Diamond Tool,” Int. J. Japan Soc. Prec. Eng., Vol. 25, No. 4, pp. 259-266(1991).
[9]. Inamura, T., and Takezawa, N., “Atomic-Scale Cutting in a Computer Using Crystal Models of Copper and Diamond,” Annals of the CIRP, Vol. 41, No. 1, pp. 121-124(1992).
[10]. Inamura, T., Takezawa, N., and, Kumaki, Y., “Mechanics and energy dissipation in nanoscale cutting”, Annals. CIRP, Vol.42, No.1, pp.79-82(1993).
[11]. Cai, M. B., Li*, X. P., Rahman,M., “ Study of the mechanism of nanoscale ductile mode cutting of silicon using molecular dynamics simulation” ,International Journal of Machine Tool & Manufacture pp.75-80(2007).
[12]. Cai, M. B., Li*, X. P., Rahman,M., “ Characteristics of “dynamic hard particles” in nanoscale ductile mode cutting of monocrystalline silicon with diamond tools in relation to tool groove wear” , wear ,pp.1459-1466(2007).
[13]. Cai, M. B., Li*, X. P., Rahman,M., “ Study of the temperature and stress in nanoscale ductile mode cutting of silicon using molecular dynamics simulation”, Journal of Materials Processing Technology,pp.607-612(2007).
[14]. Cai, M. B., Li*, X. P., Rahman,M., “ Crack initiation in relation to the tool edge radius and cutting conditions in nanoscale cutting of silicon” , International Journal of Machine Tool & Manufacture ,pp.562-569(2007).
[15]. Tanaka1, H., Shimada, S., “ Requirements for Ductile-mode Machining Based on Deformation Analysis of Mono-crystalline Silicon by Molecular Dynamics Simulation”,Annals of the CIRP, Vol.56/1(2007).
[16]. Tang, Q. H., “ MD simulation of dislocation mobility during cutting with diamond tip on silicon”,Materials Science in Semiconductor Processing,Vol.10 ,pp.270-275(2007).
[17]. Shimada, S.,“Molecular dynamics analysis of nanometric cutting process”, Ann. CIRP, Vol.29, No.283, pp.6(1995).
[18]. Inamura, T., Shimada, S., Takezawa, N., and Ikawa,N., “ Crack initiation in machining monocrystalline silicon”, Annals of the CIRP, Vol. 48 pp.81–84. (1999).
[19]. Inamura, T., Shimada, S., and Nakahara, N., “Brittle,“ductile transition phenomena observed in computer simulations of machining defect-free monocrystalline silicon”, Annals of the CIRP,Vol. 46 pp.31–34. (1997).
[20]. Lin, Z. C. and J. C. Huang, “A nano-orthogonal Cutting Model Based on a Modified Molecular Dynamics Technique,” Nanotechnology, Vol. 15, pp. 510-519(2004).
[21]. Irving, J. H., and Kirkwood, J. G., “The statistical mechanical theory of transport properties. IV. The equations of hydrodynamics”, J. Chem. Phys., Vol.18, pp. 817-829(1950).
[22]. Kwon, Y.W., and Jung, S. H., “Atomic model and coupling with continuum model for static equilibrium problems” Computers and Structures,Vol.82, September/October, Computational Structures Technology, pp. 1993-2000(2004).
[23]. IGOR Ye. Telitchev, OLEG Vinogradov” A method for quasi-static analysis of topologically variable lattice structures” , International Journal of Computational Methods, Vol. 3, pp. 71-81, March(2006).
[24]. Jeng, Yeau-Ren and Chung-Ming Tan,“Study of Nanoindentation Using FEM Atomic Model,” Journal of Tribology, Vol. 126, pp. 767-774(2004).
[25]. . Hu, S. Y., M. Ludwig, P. Kizler, and S. Schmauder,“Atomistic simulations of deformation and fracture of α-Fe,” Modelling Simul. Mater. Sci. Eng., Vol. 6, pp. 567–586 (1998).
[26]. Saraev, D., P. Kizler, S. Schmauder, “The influence of Frenkel defects on the deformation and fracture of alpha-Fe single crystals,” Simul. Mater. Sci.,pp.1013–1023(1999).
[27]. 陳雨樵，「以分子模擬方法研究奈米線之機械性質」，國立中正大學機械工程研究所，碩士論文，民國九十五年。
[28]. 黃維富，「銅鎳面心立方晶體之奈米切削能及切削力模式研究」，國立台灣科技大學大學機械工程研究所博士論文，民國九十五年。
[29]. R. Komanduri, N. Ch, rasekaran and L. M.Raff, “ Molecular dynamics simulation of the nanometric cutting of silicon,” Philosphimcaagl Azinbe, Vol. 81, No. 12,pp. 1989-2019(2001)
[30]. Arsenault, R.J. and J.R. Beeler, “Computer Simulation in Material Science,” Asm. International, USA(1988).
[31]. Smith, R. and M. Jakas, “Atomic and Ion Collision in Solids and At Surface: Theory, Simulation and Application,” Cambridge Universty Press, USA(1977).
[32]. 黃仁清，「綜合分子動力學與變形理論於奈米切削之研究」，國立台灣科技大學大學機械工程研究所博士論文，民國九十五年。
[33]. Girifalco, L. A., and V. G. Weizer, “Application of the Morse Potential Function to Cubic Metals,” Phys. Rev., Vol. 114, pp. 687-690(1959).
[34]. Rahman, A., “Correlations in motions of atoms in liquid atom” Phys. Rev.,A,vol.136,pp.405-411(1964).
[35]. G. V. Reklaitis, "Engineering Optimization: Methods and Application".
[36]. Lin, Z. C. and J. C. Huang, “3D nano-scale cutting model for nickel material,” Journal of Materials Processing Technology, pp.27–36 (2007)
[37]. M.F. Aly, E. Ng, S.C. Veldhuis, and M.A. Elbestawi , “Prediction of cutting forces in the micro-machining of silicon using a hybrid molecular dynamic-finite element analysis force model,” International Journal of Machine Tool & Manufacture, pp.1729-1737(2007).