本研究的目的主要在於瞭解金屬板材帽形引伸成形製程的條件，基於材料的伸張性質與所使用模具的幾何形狀，本研究提出一個能夠正確地預估引伸過程沖頭的負載，並且可預估除荷回彈後產品的最終外形的模式。經一系列的模擬都指出所提出的計算法，可有效地應用在這個理論上，在整個有限元素分析方法中都仔細地考慮整個變形過程與在變形期間應力與應變的分佈，在這個研究結果中，很明顯地證明了這個計算法，能夠有效地模擬帽形引伸成形製程。
此增量型彈塑性大變形三維有限元素分析程式之理論採用有限變形理論及Updated Lagrangian Formulation (ULF)的觀念，結合Prandtl-Reuss塑流法則和Hill的降伏條件，應用選擇簡化積分法及四邊形四節點退化殼元素所推導之形狀函數偶合入剛性矩陣中，使用廣義r_min法則處理板材成形時元素降伏之判斷、元素之變化增量及模具與料片之間節點之接觸或分離等問題。
最後本研究配合金屬板材帽形引伸成形實驗，設計兩組帽形引伸模具(包含圓帽及方帽引伸模具)，於50噸油壓成形機上做金屬板材帽形引伸成形之引伸實驗，並將有限元素分析所得之結果與實驗結果作比較，以驗證本文所發展的彈塑性有限元素分析程式之可靠性。

This study is aiming for clarifying the process conditions of the hat-type drawing of a sheet metal of steel. It provides a model that predicts not only the correct punch load for drawing, but also the precise final shape of products after unloading, based on the tensile properties of the material and the geometry of the tools used. A series of simulations were performed to validate the formulation in the theory, leading to the development of the computer codes. The whole deformation history and the distribution of stress and strain during the forming process were obtained by carefully considering the moving boundary condition in the finite-element method. Results in this study clearly demonstrated that the computer code for simulating the hat-type drawing process was efficient.
The methodology of elasto-plastic three-dimensional incremental finite element model is based on updated lagrangian formulation (ULF). It associated Prandtl-Reuss flow rule and Hill’s yield criterion respectively. The shape function derived from a four-node quadrilateral degenerated shell element associated and used selective reduced integration into the stiffness matrix to constitute the finite element model. An extended r_min algorithm is proposed to formulate the altered elasto-plastic state of material, the increment of element and the nodal penetration or separation of mold and blank.
Two sets of hat-type drawing mold are designed for experiments. The experiments are set on the 50 tons hydraulic forming machine to simulate the hat-type drawing process of metal sheet. The simulation and experimental results are compared to verify the reliability about the development of elasto-plastic finite element program in this project.

中 文 摘 要 i
英 文 摘 要 ii
誌 謝 iv
目 錄 v
表 目 錄 viii
圖 目 錄 ix
符 號 說 明 xii
第 一 章 緒論 1
1.1 前言 1
1.2 研究動機與目的 3
1.3 研究方法 4
1.4 文獻回顧 6
1.5 本論文之架構 9
第 二 章 基礎理論 11
2.1 基本假設與基礎理論 11
2.2 有限變形之應變與應變率 12
2.3 有限變形之應力與應力率 13
2.4 有限變形之Update Lagrangian Formulation (ULF) 18
2.5 材料之彈塑性構成關係式 21
第 三 章 有限元素分析理論 26
3.1 有限元素分析簡介 26
3.2 剛性統制方程式 26
3.3 虛功原理之離散化 28
3.4 退化殼元素(Degenerated Shell Element) 30
3.5 不同積分法則推導退化殼元素之剛性矩陣 33
3.6 摩擦處理 35
3.7 三維曲度修正方程式 38
3.8 除荷之設定 40
3.9 靜態顯函(static explicit) 40
3.10 廣義r_min法之增量步驟的計算 41
第 四 章 金屬板材圓帽引伸實驗與數值分析 46
4.1 金屬板材帽形引製程分析簡介 46
4.2 研究步驟 47
4.3 實驗設備簡介 50
4.4 實驗流程 59
4.5 潤滑處理 64
4.6 材料參數 64
4.7 圓帽引伸數值模擬分析 65
4.7.1 圓帽有限元素網格化處理 66
4.7.2 圓帽數值模擬之邊界條件 68
4.7.3 彈塑性與接觸問題的處理 69
4.7.4 除荷處理 69
4.8 圓帽引伸成形之數值模擬與實驗結果分析 70
4.8.1 圓帽變形歷程 70
4.8.2 圓帽沖頭負荷與沖程關係 72
4.8.3 圓帽反作用力分佈 73
4.8.4 圓帽應力分佈 75
4.8.5 圓帽應變分佈 76
4.8.6 圓帽厚度分佈 78
4.8.7 圓帽斷面輪廓分析 79
4.8.8 圓帽外形輪廓分析 82
4.8.9 圓帽引伸耳緣流入量分析 83
第 五 章 金屬板材方帽引伸實驗與數值分析 85
5.1 方帽引伸設備簡介 85
5.2 方帽有限元素網格化處理 93
5.3 方帽數值模擬之邊界條件 95
5.4 方帽引伸成形之數值模擬與實驗結果分析 96
5.4.1 方帽變形歷程 96
5.4.2 方帽沖頭負荷與沖程關係 97
5.4.3 方帽反作用力分佈 99
5.4.4 方帽應力分佈 100
5.4.5 方帽應變分佈 102
5.4.6 方帽厚度分佈 103
5.4.7 方帽斷面輪廓分析 106
5.4.8 方帽外形輪廓分析 111
5.4.9 方帽引伸耳緣流入量分析 111
第 六 章 結論 113
6.1 結論 113
6.2 未來研究之展望 114
參考文獻 116

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