本文採用動態顯函有限元素法，結合材料彈塑性理論，發展出一套增量型彈塑性大變形之三維顯性動態有限元素分析程式，並利用九節點元素來定義模具外形，亦發展出彈性棒元素來處理料片與模具之接觸問題，將此彈性棒與三維實體元素偶合後，進行金屬板材圓杯拉伸成形製程之分析，並探討圓杯拉伸成形之沖頭負荷與衝程之關係、厚度分佈、變形歷程、成形極限，及探討位移增量、彈性棒面積和質量密度於動態顯函解法上之影響，其目的是為了瞭解料片在拉伸過程中，不同條件對工件成形性之影響與變形行為。
本文設計一組含引伸扣緣之圓柱形沖模來進行圓杯拉伸成形實驗，以探討圓杯拉伸成形之破裂情況與厚度變化情形，進而得到圓杯拉伸成形極限。經數值分析與實驗結果比較得知，在拉伸過程中，其料片之圓弧轉角會受到最大拉伸應力，此拉伸應力會使得圓弧轉角的厚度明顯的薄化。數值分析之結果皆可合理的模擬實驗結果，故本動態顯函有限元素分析程式可合理的模擬圓杯拉伸成形製程。

The objective of this study was to observe the deformation when the work pieces were stretched under various conditions. The study applied  an analytical program model which integrated dynamic explicit finite element and elasto-plastic theory. The nine-node element was also adopted to define the tool surface geometric characteristic. An elastic bar element was developed to handle the contact problems. After coupling the elastic bar to the solid element in the finite element model, the analysis of three-dimensional stretching proceeds and the simulation results included the relationship between punch load and punch stroke, the various thickness of the work pieces, the deformation history, the forming limit, and effect of displacement increment, elastic bar area and mass density in the dynamic explicit solution.
A set of drawbead cylindrical-cup tools was designed to explore the forming of blank in arc corner and the variation of thickness so as to achieve the maximum stretching stress, which significantly thinned the thickness of arc corner. The simulation results show good agreement with the experiments that can be used to verify the reliability and accuracy of the elasto-plastic finite element program in this study.

目  錄
中文摘要 Ⅰ
英文摘要 Ⅱ
目    錄 Ⅲ
圖表索引 Ⅵ
第一章 緒論 01
1.1 前言 01
1.2 研究動機與目的 02
1.3 文獻回顧 03
1.4 論文之構成 05
第二章 基本理論 07
2.1 基本假設 07
2.2虛位移原理 07
2.2.1虛位移原理方程式 09
2.2.2 Total Lagrangian formulation 10
2.2.3 Updated Lagrangian formulation 12
2.2.4線性化平衡方程式 14
     2.2.4.1 Total Lagrangian formulation 16
            2.2.4.2 Updated Lagrangian formulation 18
2.3材料的構成式 20
2.4工具面之描述 22
第三章 動態顯函有限元素分析 24
3.1動態顯函有限變形之TLF與ULF 24
3.2動態顯函有限元素方程式 25
3.2.1動態顯函有限元素計算程序 25
3.2.2有限元素離散化 26
3.2.3動態顯函有限元素之運動方程式 27
3.3接觸力的推算 28
第四章 圓杯拉伸成形之實驗與數值分析 33
4.1實驗設備 33
4.2 實驗原理與步驟 33
4.3 邊界條件 35
4.4 材料參數 35
4.5 數值模擬分析 36
4.6 數值分析與實驗結果之比較 36
4.6.1沖頭負荷之比較 37
     4.6.1.1圓杯拉伸成形於不同位移增量之數值分析與實驗之沖頭負荷與衝程關係之比較 37
    4.6.1.2 圓杯拉伸成形於不同彈性棒面積之數值分析與實驗之沖頭負荷與衝程關係之比較 37
     4.6.1.3圓杯拉伸成形於不同質量密度之數值分析與實驗之沖頭負荷與衝程之比較 38
4.6.2工件厚度分佈之比較 38
4.6.3圓杯拉伸成形歷程之比較 39
第五章 結論 65
5.1 結論 65
5.2 未來展望 66
參考文獻 67
符號索引 70
圖表索引
圖2-1  工具構成介面之種類 23
圖2-2  料片節點與工具之接觸判斷 23
圖3-1  動態顯函有限元素分析之流程圖 31
圖3-2  八節點實體元素之示意圖 32
圖3-3  Penalty法計算節點之外力 32
圖4-1  實驗設備之整體系統配置圖 41
圖4-2  圓杯拉伸製程的模具外形圖 42
圖4-3  圓杯拉伸製程之模具尺寸圖 42
圖4-4  圓杯拉伸成形四分之一料片之網格分割及邊界條件設定 45
圖4-5  圓杯拉伸成形沖頭之元素分割 46
圖4-6  圓杯拉伸成形沖模之元素分割 46
圖4-7  圓杯拉伸成形壓料板之元素分割 47
圖4-8  圓杯拉伸成形於不同位移增量之數值分析與實驗之沖頭負荷 與衝程關係之比較 47
圖4-9  圓杯拉伸成形於不同彈性棒面積之數值分析與實驗之沖頭負 荷與衝程關係之比較 49
圖4-10圓杯拉伸成形於不同質量密度之數值分析與實驗之沖頭負荷與衝程關係之比較 50
圖4-11沖頭衝程達13mm時之數值模擬與實驗之工件厚度分佈之比較 50
圖4-12圓杯拉伸成形之沖頭衝程達13mm之數值模擬與實驗的成形工件之比較 51
圖4-13不同位移增量於圓杯拉伸成形模擬時之工件變形歷程 52
圖4-14 位移增量0.001之成形歷程 63
圖4-15 位移增量0.0008之成形歷程 63
圖4-16 位移增量0.0005之成形歷程 63
圖4-17 位移增量0.0002之成形歷程 64
表4-1  模具與料片有限元素網格分割之相關數據 45
表4-2  不同位移增量與沖頭衝程設定下之數值分析與實驗之工件於沖頭圓弧轉角最小厚度值 62
照片4-1   圓杯拉伸成形之沖頭 43
照片4-2   圓杯拉伸成形之沖模 43
照片4-3   圓杯拉伸成形之壓料板 44
照片4-4   工件之量測方法 44
照片4-5   圓杯拉伸實驗之沖頭衝程達13mm時之成形工件 48
照片4-6   圓杯拉伸實驗之沖頭衝程達14.6mm時發生頸縮之工件 48
照片4-7   圓杯拉伸實驗之沖頭衝程達15.17mm後發生破裂之工件 49

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