本文應用動顯函有限元素法進行圓杯微深引伸成形製程之分析，探討不同模具圓弧角對沖頭負荷與衝程關係、成形歷程、杯高分佈、應力分佈與塑性應變分佈，並將數值分析與實驗結果相比較，以驗證本文所用有限元素分析程式的可信度。
在實驗方面，首先依據ASTMD-412-F之規範，進行微拉伸試驗取得電解銅箔之材料參數，其最大真應力值約為359.99MPa，最大真應變值約為0.128。其次，參考ASTM-D1894規範進行摩擦力試驗取得動摩擦係數，沖頭與壓料板相對料片之動摩擦係數為0.111，沖模相對料片之動摩擦係數為0.102。最後本文設計六組不同尺寸之微深引伸模具，以進行圓杯微深引伸成形實驗，並與數值分析結果相比較。
經數值分析與實驗結果比較得知，最大沖頭負荷會隨著沖頭與沖模圓弧角增加而降低，降低沖模圓弧角可有效減少皺摺之發生，並避免於圓杯微深引伸時發生二次負荷。成形杯高則隨著沖頭圓弧角增加而增加，因此本文所使用之動顯函有限元素分析程式，可合理的模擬圓杯微深引伸成形製程。

In this study, the dynamic-explicit finite element program was applied to analyze the forming process in the micro deep drawing of cylindrical cup. The present study discussed the relationship between punch load and punch stroke, the deformation history, distribution of height of cup, distribution of von Mises stress and strain for various arc radii of tools. The reliability of the finite element program could be proved by the comparison between numerical analysis and experiment. 
There were three experiments for this study. First, the material parameter of electrolytic copper foil was obtained by micro-tensile test of ASTMD-412-F specification for experiment. The maximum true stress was about 359.99MPa and the maximum true strain value was 0.128. Then, the kinetic friction coefficient was obtained by the friction test of ASTM-D1894 specification. The kinetic friction coefficient of punch and holder relative to blank was 0.111, and the one of die relative to blank was 0.102. Finally, the six different geometric sizes of tools were designed to compare with numerical analysis results for experiment of micro deep drawing of cylindrical cup in this study. 
According to the comparison results between numerical analysis and experiment, the maximum punch load decreased as the arc radius of punch increased. When the arc radius of die decreased, the wrinkles of workpecies decreased, and the second load disappeared during the micro deep drawing process of cylindrical cup. The height of cup increased as the arc radius of punch increased. The dynamic-explicit finite element program could simulate the micro deep drawing of cylindrical cup reasonably in this study.

中文摘要	I
英文摘要	II
目  錄	IV
圖表索引	VII
第一章 緒論	1
1.1 前言	         1
1.2 研究動機與目的	1
1.3 文獻回顧	2
1.4 論文之構成	6
第二章 基本理論	7
2.1 基本假設	7
2.2 應變與應變率之定義	7
2.2.1 Green應變張量 	7
2.2.2 應變率張量 	8
2.2.3 應變率張量 與Green應變率張量 之關係	9
2.3 大變形之應力張量轉換	10
2.3.1 體積於變形前與變形後座標間之關係	10
2.3.2 面積於變形前與變形後座標間之關係	11
2.3.3 應力張量之轉換關係	13
2.3.4 應力平衡方程式之推導	16
2.4 Updated Lagrangian Formulation之虛功率原理方程式	17
2.5 Total Lagrangian Formulation之虛功原理方程式	19
第三章 有限元素分析	23
3.1 Updated Lagrangian Formulation	23
3.1.1 有限元素近似解	23
3.1.2 內力、外力及慣性力	25
3.1.3 離散化之運動方程式	26
3.2 中央差分法(Central Difference Method)	26
3.3 選擇簡化積分(Selective-Reduced Integration)	29
第四章 圓杯微深引伸成形之實驗與數值分析              32
4.1 實驗設備	32
4.2 實驗程序	32
4.2.1 微拉伸試驗	32
4.2.2 摩擦力試驗	34
4.2.3 圓杯微深引伸成形實驗	35
4.3 數值分析	36
4.4 數值分析與實驗結果之比較	37
4.4.1 圓杯微深引伸成形沖頭負荷之比較	37
4.4.2 模具圓弧角對最大沖頭負荷影響之比較 38
4.4.3 圓杯微深引伸成形工件與影像套疊圖	39
4.4.4 圓杯微深引伸之成形歷程	39
4.4.5 圓杯微深引伸成形工件杯高分佈之比較	40
4.4.6 圓杯微深引伸成形之應力與塑性應變分佈	40
第五章 結論與未來展望                         71
5.1結論	71
5.2未來展望	72
參考文獻	73
符號索引	76
圖表索引
圖2-1 物體變形前後及內部不連續曲面	22
圖4-1 拉伸試片之尺寸示意圖	42
圖4-2 厚度 電解銅箔之應力－應變曲線	42
圖4-3 厚度 電解銅箔正面之摩擦試驗曲線圖	43
圖4-4 厚度 電解銅箔背面之摩擦試驗曲線圖	43
圖4-5 圓杯微深引伸成形實驗之模具尺寸示意圖	44
圖4-6 圓杯微深引伸成形沖頭之網格分割	45
圖4-7 圓杯微深引伸成形沖模之網格分割	46
圖4-8 圓杯微深引伸成形壓料板之網格分割	46
圖4-9 圓杯微深引伸成形初始料片之網格分割	47
圖4-10 初始料片之邊界條件設定	47
圖4-11  , 之圓杯微深引伸數值分析與實驗結果之沖頭負荷與衝程關係之比較	48
圖4-12  , 之圓杯微深引伸數值分析與實驗結果之沖頭負荷與衝程關係之比較	48
圖4-13  , 之圓杯微深引伸數值分析與實驗結果之沖頭負荷與衝程關係之比較	49
圖4-14  , 之圓杯微深引伸數值分析與實驗結果之沖頭負荷與衝程關係之比較	49
圖4-15  , 之圓杯微深引伸數值分析與實驗結果之沖頭負荷與衝程關係之比較	50
圖4-16  , 之圓杯微深引伸數值分析與實驗結果之沖頭負荷與衝程關係之比較	50
圖4-17 不同沖頭底部圓弧角於 之最大沖頭負荷比較	51
圖4-18 不同沖頭底部圓弧角於 之最大沖頭負荷比較	51
圖4-19  , 之圓杯微深引伸成形歷程上視圖	58
圖4-20  , 之圓杯微深引伸成形歷程側視圖	58
圖4-21  , 之圓杯微深引伸成形歷程上視圖	59
圖4-22  , 之圓杯微深引伸成形歷程側視圖	59
圖4-23  , 之圓杯微深引伸成形歷程上視圖	60
圖4-24  , 之圓杯微深引伸成形歷程側視圖	60
圖4-25  , 之圓杯微深引伸成形歷程上視圖	61
圖4-26  , 之圓杯微深引伸成形歷程側視圖	61
圖4-27  , 之圓杯微深引伸成形歷程上視圖	62
圖4-28  , 之圓杯微深引伸成形歷程側視圖	62
圖4-29  , 之圓杯微深引伸成形歷程上視圖	63
圖4-30  , 之圓杯微深引伸成形歷程側視圖	63
圖4-31 不同沖頭底部圓弧角於 之杯口周緣杯高分佈比較	64
圖4-32 不同沖頭底部圓弧角於 之杯口周緣杯高分佈比較	64
圖4-33  , 之圓杯微深引伸貫穿成形後之von.Mises應力分佈圖	65
圖4-34  , 之圓杯微深引伸貫穿成形後之von.Mises應力分佈圖	65
圖4-35  , 之圓杯微深引伸貫穿成形後之von.Mises應力分佈圖	66
圖4-36  , 之圓杯微深引伸貫穿成形後之von.Mises應力分佈圖	66
圖4-37  , 之圓杯微深引伸貫穿成形後之von.Mises應力分佈圖	67
圖4-38  , 之圓杯微深引伸貫穿成形後之von.Mises應力分佈圖	67
圖4-39  , 之圓杯微深引伸貫穿成形後之塑性應變分佈圖	68
圖4-40  , 之圓杯微深引伸貫穿成形後之塑性應變分佈圖	68
圖4-41  , 之圓杯微深引伸貫穿成形後之塑性應變分佈圖	69
圖4-42  , 之圓杯微深引伸貫穿成形後之塑性應變分佈圖	69
圖4-43  , 之圓杯微深引伸貫穿成形後之塑性應變分佈圖	70
圖4-44  , 之圓杯微深引伸貫穿成形後之塑性應變分佈圖	70
表4-1 圓杯微深引伸成形之模具參數44
照片4-1 圓杯微深引伸成形實驗 3.0mm之圓形料片	45
照片4-2  , 之圓杯微深引伸貫穿成形工件52
照片4-3  , 之圓杯微深引伸貫穿成形後數值模擬與實驗工件套疊比較	52
照片4-4  , 之圓杯微深引伸貫穿成形工件	53
照片4-5  , 之圓杯微深引伸貫穿成形後數值分析與實驗工件套疊比較	53
照片4-6  , 之圓杯微深引伸貫穿成形工件	54
照片4-7  , 之圓杯微深引伸貫穿成形後數值. 分析與實驗工件套疊比較	54
照片4-8  , 之圓杯微深引伸貫穿成形工件	55
照片4-9  , 之圓杯微深引伸貫穿成形後數值. 分析與實驗工件套疊比較	55
照片4-10  , 之圓杯微深引伸貫穿成形工件		56
照片4-11  , 之圓杯微深引伸貫穿成形後數..值分析與實驗工件套疊比較	56
照片4-12  , 之圓杯微深引伸貫穿成形工件		57
照片4-13  , 之圓杯微深引伸貫穿成形後數..值分析與實驗工件套疊比較	57

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