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題名 | 銅奈米薄膜拉伸之分子動力學和有限元素法之耦合模式研究=A Coupled Model Combining Molecular Dynamics with FEM under Tension for a Copper Nanoscale Film |
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作者姓名(中文) | 林有鎰; 陳宗傑; 李文喜; | 書刊名 | 德霖學報 |
卷期 | 25 2011.06[民100.06] |
頁次 | 頁171-180 |
分類號 | 440.21 |
關鍵詞 | 分子動力學; 有限元素法; 銅奈米薄膜; 比例拉伸; 應力; 應變; Molecular dynamics; FEM; Copper nano thin film; Proportional tension; Stress; Strain; |
語文 | 中文(Chinese) |
中文摘要 | 本文建立一套銅奈米薄膜結構拉伸實驗之分子動力學和有限元素法之耦合模式。首先以分子動力學 模擬銅奈米薄膜比例拉伸實驗,薄膜尺寸為14a 0 ×6a 0 ×6a 0,a0為晶格常數,原子總數為2016個,拉伸 速率為0.001/步,系統溫度為293K,求出自由移動區各原子位移和等效應變,代入原子級應力公式求出 拉伸模擬的等效應力,進而繪出流變應力-應變曲線,最後配合形狀函數,求出各原子的等效應變,代入 流變應力-應變三階多項式回歸關係式計算出各原子的等效應力。結果顯示銅奈米薄膜結構在截斷半徑為 2.5 倍平衡距離的條件下,得到(1)當應變為零時,應力值為-0.79520GPa,顯示預應力確實存在於銅奈米 薄膜結構中;(2)由於銅原子間的距離是等比例的均勻增加,因此自由移動區的應變分佈和應力分佈是由 固定端往拉伸端逐步地增加。 |
英文摘要 | In this paper, a coupled model combining molecular dynamics simulation with FEM for a copper nano thin film under tension was established. Firstly, molecular dynamics was used to simulate the proportional tensile test of copper nano thin film under the conditions that the size of copper nano thin film is14a 0 × 6a 0 × 6a 0 where a 0 is lattice constant, there are total 2016 atoms in the whole structure, the tensile rate is set up at 0.001/step and the system temperature is 293K to achieve the atomic displacement and equivalent strain in the free motion zone and then equivalent stress could be calculated by using atomistic stress formula. Next, flow stress–strain curve of copper nano thin film was plotted according to the stress-strain relationship. Finally, based on shape function, the equivalent strain of every atom was obtained and the equivalent stress of every atom was then calculated by using three-order stress-strain polynomial regressive equation. The results showed that (1) when being zero strain, the stress is -0.79520GPa under the condition of truncated radius of 2.5 times equilibrium radius, that is, pre-stress exists exactly in the copper nano thin film. (2) due to proportional increase of distance between atoms, the stress and strain distributions in the free motion zone increase step by step from the fixed end to the tensile end. |
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