本文首先以動顯函有限元素法模擬銅箔U型精微彎曲，接著使用靜隱函有限元素法分析銅箔除荷後之回彈。並假設材料於等向性之條件下進行數值分析，以探討U型精微彎曲之沖頭負荷與衝程關係、成形歷程、除荷後之工件角度、回彈量，及側壁蜷曲現象。另設計一組U型精微彎曲之模具進行實驗比較，以驗證本文之有限元素分析程式可合理模擬U型精微彎曲成形製程。
    本文針對沖模圓弧角半徑與間隔墊片厚度之改變，對除荷後之工件角度、回彈量，及側壁蜷曲之影響進行探討。經數值分析與實驗結果比較得知，沖頭負荷會隨著沖模圓弧角半徑增加而遞減，除荷後鄰近沖頭角隅處與鄰近沖模圓弧角之工件角度、回彈量，及蜷曲半徑則隨之遞增。此外，沖頭負荷會隨著間隔墊片厚度增加而遞減，除荷後鄰近沖頭角隅處之工件角度與回彈量亦隨之遞減，然而鄰近沖模圓弧角之工件角度、回彈量，及蜷曲半徑則隨之遞增。由於數值分析均與實驗結果相符合，故本文之有限元素分析程式可有效預測U型精微彎曲成形與回彈分析。

This study first simulated the U-shaped micro bending of copper foil using the dynamic-explicit finite element method, and then analyzed the springback of unloaded copper foil using the static-implicit finite element method. The numerical analysis was conducted under the assumption that materials were isotropic in order to explore the relationship between punch load and punch stroke, deformation history, workpiece angle after unloading, springback amount, and sidewall curl. In addition, another U-shaped micro bending mold was designed for comparison, to verify that the finite element method proposed in this study can reasonably simulate the process of U-shaped micro bending. 
    This study explored the influence on changes in arc radius of die and spacer thickness on unloaded workpiece angle, springback amount, and sidewall curl. According to the results of the numerical analysis and experiment results, when arc radius of die increased, punch load decreased, and workpiece angle, springback amount, and radius of curvature near punch corner and die arc increased after unloading. Besides, when spacer thickness increased, punch load decreased, and workpiece angle and springback amount near punch corner also decreased after unloading, while workpiece angle, springback amount, and radius of curvature near die arc increased after unloading. The results of the numerical analysis and the experiment were consistent; thus the finite element method proposed by this study can effectively predict deformation and springback of U- shaped micro bending.

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	2
1.3文獻回顧	3
1.4論文之構成	7
第二章 基本理論	8
2.1基本假設	8
2.2應變與應變率之定義	8
2.2.1 Green應變張量 	9
2.2.2應變率張量 	9
2.2.3應變率張量 與Green應變率張量 之關係	10
2.3大變形之應力張量轉換	11
2.3.1體積於變形前與變形後座標間之關係	11
2.3.2面積於變形前與變形後座標間之關係	12
2.3.3應力張量之轉換關係	14
2.3.4應力平衡方程式之推導	17
2.4 Updated lagrangian formulation之虛功率原理方程式	18
第三章 有限元素分析	21
3.1動顯函有限元素法	21
3.1.1有限元素近似解	21
3.1.2內力、外力及慣性力	22
3.1.3離散化之運動方程式	24
3.1.4中央差分法	24
3.3靜隱函有限元素法	26
3.4薄殼元素	27
3.5接觸問題	27
第四章 U型精微彎曲之實驗與數值分析	29
4.1實驗設備	29
4.2實驗方法	30
4.3材料參數	31
4.4 U型精微彎曲之數值分析	32
4.4.1數值分析	32
4.4.2邊界條件	32
4.4.3回彈分析之拘束點設定	33
4.4.4工件角度與蜷曲半徑之定義	33
4.5數值分析與實驗結果之比較	35
4.5.1 U型精微彎曲於沖頭達指定衝程除荷後工件之比較	35
4.5.2不同沖模圓弧角半徑對U型精微彎曲之影響	36
4.5.2.1沖頭負荷之比較	36
4.5.2.2成形歷程	37
4.5.2.3應力分佈	37
4.5.2.4除荷後工件角度之比較	38
4.5.2.5除荷後工件蜷曲半徑之比較	39
4.5.2.6數值分析與實驗工件影像套疊之比較	40
4.4.3不同間隔墊片厚度對U型精微彎曲之影響	41
4.5.3.1沖頭負荷之比較	41
4.5.3.2除荷後工件角度之比較	41
4.5.3.3除荷後工件蜷曲半徑之比較	42
4.5.3.4數值分析與實驗工件影像套疊之比較	43
第五章 結論與未來展望	72
5.1 結論	72
5.2 未來展望	73
參考文獻	75
符號索引	78

圖表索引
圖2-1  物體變形前後及內部不連續曲面	20
圖4-1  U型精微彎曲實驗之模具尺寸示意圖	44
圖4-2  U型精微彎曲之矩形料片尺寸圖	45
圖4-3  拉伸試片幾何尺寸	46
圖4-4  斷裂後之拉伸試片	46
圖4-5  厚度0.035mm壓延銅箔經拉伸試驗所得之應力-應變
       曲線	47
圖4-6  U型精微彎曲沖頭之網格分割	48
圖4-7  U型精微彎曲沖模之網格分割	49
圖4-8  U型精微彎曲壓料板之網格分割	50
圖4-9  U型精微彎曲初始料片之網格分割	51
圖4-10 初始料片之邊界條件設定	51
圖4-11 四分之一對稱模型回彈拘束節點之設定位置.	52
圖4-12 除荷後回彈之工件角度與蜷曲半徑之定義	52
圖4-13 U型精微彎曲於沖頭達指定衝程除荷前後工件之正視
       圖	53
圖4-14 U型精微彎曲於沖頭達指定衝程除荷後工件角度之比
       較	54
圖4-15 U型精微彎曲於沖頭達指定衝程除荷後回彈量之比較	54
圖4-16 U型精微彎曲於沖頭達指定衝程除荷後蜷曲半徑之比
       較	55
圖4-17 U型精微彎曲於沖模圓弧角半徑0.20mm數值分析與
       實驗之沖頭負荷與衝程關係比較	55
圖4-18 U型精微彎曲於沖模圓弧角半徑0.35mm數值分析與
       實驗之沖頭負荷與衝程關係比較	56
圖4-19 U型精微彎曲於沖模圓弧角半徑0.50mm數值分析與
       實驗之沖頭負荷與衝程關係比較	56
圖4-20 U型精微彎曲之成形歷程	57
圖4-21 U型精微彎曲於沖模圓弧角半徑0.20mm沖頭衝程達
5.00mm之von Mises應力分佈圖	58
圖4-22 U型精微彎曲於沖模圓弧角半徑0.20mm除荷後之
von Mises應力分佈圖	58
圖4-23 U型精微彎曲於沖模圓弧角半徑0.35mm沖頭衝程達
5.00mm之von Mises應力分佈圖	59
圖4-24 U型精微彎曲於沖模圓弧角半徑0.35mm除荷後之
von Mises應力分佈圖	59
圖4-25 U型精微彎曲於沖模圓弧角半徑0.50mm沖頭衝程達
5.00mm之von Mises應力分佈圖	60
圖4-26 U型精微彎曲於沖模圓弧角半徑0.50mm除荷後之
von Mises應力分佈圖	60
圖4-27 U型精微彎曲實驗於除荷後工件角度之量測圖	61
圖4-28 U型精微彎曲於不同沖模圓弧角半徑除荷後工件角度
       之比較	61
圖4-29 U型精微彎曲於不同沖模圓弧角半徑除荷後工件回彈
       量之比較	62
圖4-30 U型精微彎曲於不同沖模圓弧角半徑除荷後工件蜷曲
       半徑之比較	64
圖4-31 U型精微彎曲於沖模圓弧角半徑0.20mm之數值分析
       與實驗工件之影像套疊圖	64
圖4-32 U型精微彎曲於沖模圓弧角半徑0.35mm之數值分析
       與實驗工件之影像套疊圖	65
圖4-33 U型精微彎曲於沖模圓弧角半徑0.50mm之數值分析
       與實驗工件之影像套疊圖	65
圖4-34 U型精微彎曲於間隔墊片厚度0.055mm數值分析與實
驗之沖頭負荷與衝程關係比較	66
圖4-35 U型精微彎曲於間隔墊片厚度0.070mm數值分析與實
驗之沖頭負荷與衝程關係比較	66
圖4-36 U型精微彎曲於間隔墊片厚度0.080mm數值分析與實
驗之沖頭負荷與衝程關係比較	67
圖4-37 U型精微彎曲於不同間隔墊片厚度除荷後工件角度之
比較	67
圖4-38 U型精微彎曲於不同間隔墊片厚度除荷後工件回彈量
       之比較	68
圖4-39 U型精微彎曲於不同間隔墊片厚度除荷後工件蜷曲半
徑之比較	70
圖4-40 U型精微彎曲於間隔墊片厚度0.055mm數值分析與實
       驗工件之影像套疊圖	70
圖4-41 U型精微彎曲於間隔墊片厚度0.070mm數值分析與實
       驗工件之影像套疊圖	71
圖4-42 U型精微彎曲於間隔墊片厚度0.080mm數值分析與實
       驗工件之影像套疊圖	71
表4-1  U型精微彎曲模具之主要尺寸	45
表4-2  U型精微彎曲於不同沖模圓弧角半徑除荷後工件角度
       、回彈角度，及蜷曲半徑之數據	63
表4-3  U型精微彎曲於不同間隔墊片厚度除荷後工件角度、
       回彈角度，及蜷曲半徑之數據	69

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