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博碩士論文 etd-0716109-185504 詳細資訊
Title page for etd-0716109-185504
論文名稱
Title
數位影像相關法於三維變形量測之新應用
A New Approach of DIC on the 3-D Deformation Measurement
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
144
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2009-06-24
繳交日期
Date of Submission
2009-07-16
關鍵字
Keywords
最佳化法則、有限元素法、蒲松氏比、楊氏係數、薄膜、數位影像相關法
finite element method, optimization method, Possion's ratio, Young's modules, membrane, digital image correlation
統計
Statistics
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中文摘要
本研究之目的是建立起一套成本遠較奈米壓痕計便宜之量測系統以測定薄膜材料機械性質,基本概念為對薄膜施力,使薄膜產生面外位移,依據所測得之面外位移以逆向工程之概念推算薄膜之楊氏係數和蒲松氏比。首先為了固定薄膜以方便施力,本研究設計了一個模具以便能夠準確定位施力位置和測量面外位移的點。爲了測量薄膜面外位移,本研究使用數位影像相關法,並開發出一套比文獻所述更簡易之具有三維位移測量功能之數位影像相關法系統,並以懸臂樑配合ESPI驗證其正確性,結果顯示依據本研究之設備品質,可量測之最小面內位移量約為2 μm,可量測之最小面外位移量約為6 μm,誤差在10 %以內。
爲了測量薄膜機械性質,本研究結合了三維數位影像相關法所測量之薄膜面外位移、有限元素法與最佳化法則,依據逆向工程原理計算薄膜材料機械性質,在有限元素法部份乃使用套裝軟體ANSYS進行模擬,在最佳化法部份則討論數種方法,並比較其於本研究主題之適用性。最後將所測定之楊氏係數比對於奈米壓痕計之量測值,結果顯示誤差值約在3 %至12 %左右。
關鍵詞:數位影像相關法、薄膜、楊氏係數、蒲松氏比、有限元素法 、 最佳化法則
Abstract
In this study, a simple and inexpensive membrane mechanical property measuring system was developed. By applying the force on a membrane and recording the corresponding out-of-plane displacement fields, then the Young’s modules and Possion’s ratio of the membrane can be obtained from those deformations through the inverse approach. Firstly, a loading frame was designed to fix the membrane and allow the membrane can be loaded and its deformations can be measured precisely. In order to measure the out-of-plane displacement fields of the loaded membrane, the digital image correlation (DIC) was used and an easier 3-D DIC measuring method was proposed in this study. The proposed 3-D DIC measuring method was verified by using a loaded cantilever beam with ESPI. The error was within in 10%. In this study, the smallest in-plane displacement that can be measured by proposed method is 2 μm and the smallest out-of-plane displacement that that can be measured is 6μm.
In this study, in order to determine the mechanical properties of the membrane, digital image correlation, finite element method (FEM) and optimization method were combined with the measured out-of-plane displacement fields, then the Young’s modules and Possion’s ratio of the membrane were determined through the inverse approach. The FEM simulations were performed by using ANSYS. Several optimization theorems were adopted and their corresponding merits on this study were compared The obtained Young's modulus was compared with the results obtain from the nano-indentor and the error was within in 3% ~ 12%.
Keyword: digital image correlation, membrane, Young’s modules, Possion’s ratio, finite element method, optimization method.
目次 Table of Contents
目錄 I
表目錄 V
圖目錄 VII
符號表 XI
摘要 XIII
Abstract XIV

第一章緒論 1
1.1研究動機與目的 1
1.2文獻回顧 2
1.2.1 數位影像相關法源起 2
1.2.2數位影像相關法應用和薄膜材料性質量測 4
1.2.3 數位影像相關法三維量測之發展 6
1.2.4 DIC法結合有限元素法和最佳化法則 8
1.3 全文架構 9
第二章基礎理論 10
2.1 數位影像相關法 10
2.1.1 簡述圖片資訊 10
2.1.2 影像重建 11
2.1.2.1 雙線性內插法 11
2.1.2.2 雙立方內插法 12
2.1.3 物體平面變形理論 12
2.1.4 影像相關原理 13
2.1.5求取最佳位移參數 15
2.1.6 特徵搜尋 17
2.2 最佳化法則原理 19
2.2.1 設計變數 19
2.2.2 目標函數 19
2.2.3 限制條件 20
2.2.4 最佳化設計流程 21
2.3有限元素法原理 22
2.4 旋轉座標理論 23
2.5 有限插分法 24
第三章研究方法 33
3.1 實驗儀器與設備 34
3.1.1 硬體儀器 34
3.1.2 軟體設備 35
3.2 數位影像相關法環境參數測定 37
3.2.1 比例因子 37
3.2.2 影像重建誤差 38
3.2.3 數位影像相關法的解析度和精準度 41
3.2.4 分析結果的正確性 44
3.3 三維數位影像相關法量測理論推導 44
3.3.1 三維DIC公式推導 45
3.3.2 三維DIC量測的量測範圍 49
3.3.3 三維DIC量測的角度設定 50
3.4 三維數位影像相關法之驗證 51
3.4.1 新式三維DIC位移場量測的剛體位移驗證 51
3.4.2 新式三維DIC一般位移場量測驗證 52
3.5 薄膜固定模具設計 53
3.6 薄膜面外變形場量測 54
3.7 有限元素法建模 55
3.8 最佳化目標函數建立 56
第四章結果與討論 83
4.1 三維數位影像相關法之驗證結果 83
4.1.1 剛體位移量測驗證結果 83
4.1.2 一般位移場量測驗證結果 84
4.1.3 各種三維數位影像關係法比較 86
4.2 最佳化求解薄膜機械性質 87
4.2.1 可用與不可用之最佳化方法分析 87
4.2.2 最佳化方法求解薄膜材料參數 88
4.3 實驗結果與奈米壓痕實驗值之比較 91
第五章結論與未來展望 109
5.1 結論 109
5.2 未來展望 110
參 考 文 獻 112
附錄 121
附錄一 121
附錄二 123
附錄三 125
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