臺灣博碩士論文加值系統

本論文是以分子動力學(Molecular dynamics)探討銅奈米線的機械性質與原子尺度下的變形行為，所探討的參數包括外加負荷的條件(拉伸、壓縮)、應變率、方向性效應。本文提出最大區域應力的計算方法(Maximum local stress calculated method, MLS)，以正確地的描述奈米線受外力作用時的真應力的變化，改善Virial stress(VS)方法在塑變過程中容易低估奈米線流動應力的問題。此外，本文提出降伏響應最小時間的概念，以解釋提升應變率造成降伏應力上升的問題，並且結合彈性響應時間及劈裂破壞完成時間用以解釋高應變率(10^9s^-1以上)的動態的變形行為及破壞模式。此外，更提出滑動因子(slipping factor)以評估不同方向的降伏應力對應變率的敏感度。針對不同方向性的臨界剪應力變動情形，在拉伸時，可利用表面晶格扭曲效應解釋，而在壓縮時則可利用本文所提出之lattice geometrical factor進行評估。
模擬結果顯示，在較低應變率範圍中(7*10^7~7*10^9s^-1)，slipping factor及lattice geometircal factor能夠合理解釋不同條件下銅奈線之各種行為表現。而應變率效應在不同方向性奈米線的條件下會有不同的塑性變形機制，在低應變率(7*10^7s^-1)時，對於降伏應力的應變率敏感度較低的施力與方向組合條件下(<100>拉伸與壓縮及<110>拉伸)，較易形成摺疊狀的部分差排分布；而當應變率提高至7*10^8s^-1，<100>與<110>奈米線都會有雙晶變形產生，同時此雙晶變形所造成的晶格轉向會因為不同的施力與方向性條件，而形成幾何強化或幾何軟化的現象，因而造成這兩個方向的變形行為類似反對稱的關係。但是，<111>奈米線由於剛性邊界及表面的限制條件下，雙晶變形不易被啟動。當應變提高至7*10^9s^-1，對於降伏應力的應變率敏感度越高的條件(<100>及<111>的拉伸、<111>與<110>的壓縮)，則較易出現多個部分差排同時啟動的塑變行為。而在應變率條件為7*10^7~7*10^9s^-1時，在奈米線最後破斷前，由於頸縮區已失去FCC晶格結構，無法再利用差排剪滑移塑變，所以原子間鍵結的直接拉斷是主要的破壞模式，因此會造成MLS應力急遽上升的現象。
在高拉伸速率(51~3000m/s)範圍中，本文模擬結果驗証te及tc 預測模式的正確性，當拉伸速率為51~800m/s間，由於彈性響應的時間效應造成應力累積在奈米線兩端，並在te期間應力增至最大值，所累積的應力隨後傳入奈米線中；在拉伸速率超過1000m/s，拉伸張應力就會趨近其劈裂應力值，並造成劈裂破壞，且tc必小於te ；而在拉伸速率為800~1000m/s的過渡範圍，在奈米線端面與剛性邊界產生劈裂破壞過程中，由於奈米線端面少數原子產生滑動，會形成不平整的劈裂斷面。而其中在額定應變率範圍(2.2*10^10s^-1~7*10^10s^-1-拉伸速率166~512m/s)，在後續的動態變形行為中，此被累積的彈性應力對於不同的施力與方向之組合條件則會有不同的發展，對於slipping factor較小的條件下(<100>拉伸、<111>拉伸與壓縮、<110>壓縮)，會出現動態的應力波傳遞情形，並在奈米線中間形成建設性干涉現象，形成MLS應力的第二應力高峰現象；反之，彈性應力波在傳入奈米線中間區域前即被接近奈米線兩端的大量塑變所釋放。而其中，較特別的是在<100>奈米線壓縮條件下，會啟動相轉換變形而形成HCP結構。同時，此種相轉換具有過渡的動態塑性波傳的特性。

This study analyzes mechanical properties and deformation behaviors of Cu nanowires with uniaxl loading states (tension and compression), different strain rates and orientations by molecular dynamics. In this work, the maximum local stress calculated method (MLS) is proposed to validly elucidate the true stress of nanowires under uniaxial loading, in order to improve the problem that that the Virial stress(VS) is easy to undervalue the flow stress during plastic deformation. In addition, the concept of the minimum response time for yielding is proposed to explain the problem that the promotion of strain rate increases the yield stress. The combination of the elastic response time and the required time for cleavage fracture are presented to elucidate the dynamic deformation behavior as the strain rate is above . Moreover, the slipping factor is proposed to evaluate the strain rate sensitivity of yield stress. Further, the effect of lattice distortion and lattice geometrical factor can be used to explain the difference in between the different orientations under tension and compression, respectively.
Analysis results demonstrate that slipping factor and lattice geometrical factor can be used to reasonably predict the various behaviors of Cu nanowire with different condition at the strain rate(7*10^7~7*10^9s^-1). The analysis also studies the variation of deformation mechanisms for various orientations and strain rates. At the strain rate of 7*10^7s^-1, the zigzag distribution of partial dislocations is observed in the nanowires of the lower the strain rate sensitivity of yield stress. When the strain rate is 7*10^8s^-1 , twinning occurs in both <100> nanowires and <110>. The variations of lattice orientation caused by twinning can result in geometrical hardening or geometrical softening with distinct loading conditions and orientations. Therefore, the deformation mechanism of two orientations (<100> and <110>) is pseudo skew-symmetry of nanowires under tension and compression. However, twinning is not easy to be operated because of the restriction of rigid body layers and free surface. When the strain rate is 7*10^9s^-1 , many partial dislocations are operated simultaneously for the conditions of higher strain rate sensitivity of yield stress(<100>tension, <111>tension /compression, <110>compression). At the strain rate between 7*10^7s^-1 and 7*10^9s^-1, immediately before fracture, the crystal structure in necking zone loses FCC, so the dislocation slip can not be operated. Therefore, the primary failure mode becomes atomic bond breakage, causing that the MLS stress increases markedly. The simulation results verify the prediction of te and tc, as the pulling speed ranges from 51 to 3000 m/s. When the pulling speed is 51~800m/s, the effect of causes the accumulation of the stress that is applied at the beginning of tensile loading in . The stress rises to the maximum at , and then the stress accumulated in the both ends of nanowires propagate forward the middle of nanowires. As the pulling speed is above 1000m/s, the fracture mode of nanowire is the cleavage fracture and the fracture surface is flat. The maximum tensile stress can be considered as cleavage stress. In this case, tc is definitely smaller than te . When the pulling speed ranges from 800 to 1000m/s, the fracture mode of nanowire is still the cleavage fracture. However, the fracture surface is not flat, because a few atoms in both ends of nanowires slip during cleavage fracture.
For the specific strain rate 2.2*10^10s^-1~7*10^10s^-1 (pulling speed 166~512m/s), the stress accumulated in the both ends of nanowires have distinct influnences on dynamic behaviors in different orientation nanowires during the following deformation. For the conditions of the smaller slipping factor (<100>tension, <111>tension/compression, and <110> compression), the propagation of stress waves are obviously observed. The encounter of the stress wave causes constructive interference in the middle of the nanowires, producing the second peak. However, for the conditions whose the slipping factor is larger (<110>tension), stress wave are released by the large plastic deformation in both ends of nanowires before the stress waves propagate forward the middle of nanowires. Interestingly, the phase transformation mechanism that the FCC can be transformed into HCP is observed when the <100> nanowires is under compression. Further, this phase transformation mechanism expresses the characteristic of transitional plastic wave propagation.

目 錄
摘 要 I
Abstract III
誌 謝 VI
目 錄 VII
符號說明 XI
表索引 XVIII
圖索引 XIX
第一章 緒論 1
1-1 研究動機與目的 1
1-2 模式構想簡介 3
1-2-1 最小降伏時間模式( ) 3
1-2-2 彈性響應時間模式( ) 4
第二章 文獻回顧 6
2-1 分子動力學文獻回顧 6
2-2 奈米金屬線製造及機械性質實驗之文獻探討 7
2-3 分子動力學應於奈米金屬線之文獻探討 9
第三章 分子動力學基礎理論 22
3-1 分子間作用力與勢能函數 22
3-2 截斷半徑法與Verle表列法 24
3-4 運動方程式及演算法 25
3-5 原子級應力計算方法 28
3-6 Centrosymmetry parameter (CSP) 30
3-7 溫度場的評估 31
第四章 降伏最小響應時間、彈性響應時間模式 34
4-1 降伏最小響應時間 34
4-2 高應變率效應所引發的應力累積模式及劈裂破壞………...41
第五章 模擬步驟與奈米線模型的建立 46
5-1 模擬步驟 46
5-1-1 前處理(initialization) 46
5-1-1-1 預備(preliminaries) 46
1.勢能函數之選取 46
2.無因次化及系統之邊界條件 47
5-1-1-2 初始條件(initial condition) 48
1.初始位置 48
2.初始速度 48
5-1-2 平衡(equilibration) 49
5-1-3 動態模擬(production) 50
5-2 平衡後的奈米線模型及施力模式 50
5-3 電腦運算設備 51
第六章 結果與討論 53
6-1 預應力現象的探討(pre-stress phenomenon) 53
6-2 應變率為 之銅奈米線拉伸及壓縮行為分析 55
6-2-1 MLS應力曲線與VS應力曲線的差異 55
6-2-2 應變率及方向性對降伏應力的影響 57
6-2-3 應變率效應及施力條件對彈性係數的影響 59
6-2-4 降伏機制與流動應力的變動情形分析 60
6-2-4-1 <100>奈米線 60
1.拉伸行為分析 60
2.壓縮行為分析 65
6-2-4-2 <110>奈米線 67
1.拉伸行為分析 67
2.壓縮行為分析 69
6-2-4-3 <111>奈米線 72
1.拉伸行為分析 72
2.壓縮行為分析 75
6-2-4-4 各方向對應變速率敏感性分析 77
1.應變速率對不同方向奈米線塑變機制影響之綜合比較 77
2.奈米線破斷前的5-1-5奈米架橋結構分析 79
6-2-4-5 尺寸與應變率對降伏應力之綜合效應 81
1.方向性效應對臨界分解剪應力的影響 81
2.尺寸效應 84
3.尺寸與應變率的綜合效應 84
6-3 應變率條件 之銅奈米線拉伸及壓縮行為分析 85
6-3-1 MLS應力曲線與VS應力曲線的差異 85
6-3-2 高拉伸速率下的彈性響應現象與劈裂破壞現象 86
6-3-3 降伏機制與流動應力的變動分析 89
6-3-3-1 <100>奈米線 89
1.拉伸行為分析 89
2.壓縮行為分析 94
6-3-3-2 <110>奈米線 99
1.拉伸行為分析 99
2.壓縮行為分析 100
6-3-3-3 <111>奈米線 102
1.拉伸行為分析 102
2.壓縮行為分析 103
6-3-3-4 各方向對應變速率敏感性分析 104
第七章 結論與建議 107
7-1 結論 107
7-2 未來研究方向與建議 109
參考文獻 110

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