本文旨在建立結合分子動力學與變形理論，藉以探討奈米正交切削、圓錐刀具奈米直線切削與圓錐刀具奈米曲線切削等不同切削型態與不同切削深度與切削速度等加工參數對工件所產生之應變與應力及切削力之影響。同時亦進行奈米拉伸之研究，以提供所需之奈米級塑流曲線。
本文提出原子視為節點，晶格視為元素，結合分子動力學與有限元素法中形狀函數，以探討在奈米切削時單晶銅中央截面所產生的等效應力與等效應變的分布趨勢。本文亦提出一個在奈米拉伸時之應力計算方法-剛體邊界層介面力之奈米級應力計算模式，並發現應變速率對塑流曲線之K值與n值影響相當大。本文結合前述發展之奈米級塑流曲線與應變硬化率，推導出可應用於奈米切削之變形理論彈塑性關係矩陣，以探討奈米切削後之已加工面之殘留應力與殘留應變現象，且進一步分析不同切削速度對奈米級切削時工件的應力與應變分佈趨勢與切削力之影響。
本文進一步探討圓錐刀具之奈米直線加工，以探討不同切削參數對奈米級切削時工件的應力與應變分佈趨勢與切削力之影響。且提出奈米尺度切削力轉換因子，藉以估算實際奈米加工時之切削力，並以鑽石探針進行實際奈米直線加工實驗來相互驗證。本文亦探討銅材料之奈米曲線加工，並分析奈米曲線加工後之切屑堆積與已加工表面殘留應力與殘留應變等現象之影響。提出以插值法的觀念，將以多段等長小線段來形成奈米曲線動路，並以模擬退火演算法來得到等長直線動路的插值點。且以鑽石探針進行實際奈米曲線加工實驗，以探討應用插值法於實際的奈米曲線加工之可行性。並將奈米尺度切削力轉換因子，應用於實際奈米曲線加工時之切削力估算。本文結合以極低負荷之奈米壓痕試驗進行單晶鎳之楊氏係數量測值，進一步探討單晶鎳在圓錐刀具奈米切削時所產生的應力與應變。
期望本文的研究成果可做為奈米加工製程參數研究以及建構殘留應變與殘留應力分析模型的重要參考。

By the combination of molecular dynamics and finite deformation theory, the objective of this thesis is to investigate into the effect of different cutting types such as nano orthogonal cutting, conical shaped tool nano straight line cutting and nano curve cutting, and processing parameters such as different cutting depth and cutting speed towards the strain and stress, as well as the cutting force produced towards the workpiece. Also, it carried out a nano tensile research, so as to provide the required nanoscale flow curve. By taking atoms as nodes and lattics as elements, and by combining molecular dynamics and the shape function of the finite element method, this study investigates into the distribution trend of the equivalent strains and equivalent stress produced on the central cross section of the single crystal copper during nano cutting. This thesis also proposes a rigid boundary layer interface force (RIF) model for nanoscale stress calculation, so as to investigate into the strain-stress behavior of the nanoscale single copper crystal during the nano tension by means of molecular dynamics. Upon simulation, the effect of the strain rate towards the K and n values of the flow curve is very significant. By combining the abovementioned nanoscale flow curve developed and the strain hardening rate, this study derives the elastic-plastic relationship equation of nano-scale finite deformation theory that can be applied to nano cutting, so as to investigate into the phenomenon of residual strain, residual stress on the machined surface and the cutting force by the different cutting speed during nano cutting. This thesis also investigates into the effect of different cutting parameters towards the distribution trend of the strain and stress of the workpiece, as well as its cutting force during nano cutting by the conical shaped tool. Also, this thesis proposes a nanoscale action-force transfer factor (NAT factor), so as to predict the cutting force during practical nano cutting. Finally, it uses diamond probe to practice practical nano linear cutting experiment for verification. This thesis further investigates into the nano curve cutting of the single crystal copper, as well as analyzes into the heap of chip the nano curve after cutting, and the effect of the phenomenon such as the residual strain and residual stress of the machined surface. It proposes to use the concept of interpolation method to form nano curve path by many small segments. Also, by using the simulated annealing algorithm, the interpolation point of curve path having equal length can be acquired. With the use of diamond probe, practical nano curve processing experiment is executed, so as to investigate into the feasibility of applying interpolation method on the practical nano curve processing. This thesis then applies the NAT factor on the estimation of the cutting force during practical nano curve cutting. In order to understand the effect of processing parameters such as different material, different E value and lattic size etc. towards the cutting force and residual strain and residual stress, this study combines a nano indentation test having a very low loading to obtain Young's modulus of the single crystal nickel, so as to further investigate into the strain and stress produced by single crystal nickel by the conical shaped tool during nano cutting.
It is expected that the research result of this thesis can supply as an important reference for the researches on the parameters of nano cutting procedure, as well as the construction of the analytical models of residual strain and residual stress.

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