本文研究之目的，乃在以ULF(updated Lagrangian formulation)的觀念建立一彈塑性大變形有限元素法分析模式，以解析軸對稱條件下金屬管端成形過程中所需之參數對製程的影響，以及考慮非線性加工硬化之均向性與正交異向性材料之變形行為。
本文以rmin法則來精確的計算邊界條件，包含不斷在變形中發生變化的節點切入與分離及摩擦方向變換等問題，還有應變增量與旋轉增量的線性化及變形之彈塑性狀態的轉換問題之處理。本文引用修正之庫侖摩擦法則，適當的描述黏滯與滑動現象之摩擦作用。上述相關之運算與模式可結合至整體剛性矩陣中，進而構成整體的剛性統制方程式。
依上述發展之有限元素模式，首先分析軸對稱金屬管端擴口及縮口成形加工，在計算成形之過程中，可得除荷過程的管端變形形狀與衝頭負荷分佈，並配合相關文獻之實驗結果，探討不同加工製程參數對衝頭負荷與除荷回彈後之最後成形形狀的作用與影響，以期得到正確的衝頭負荷與管端成形形狀。於分析擴口和縮口之成形過程中，加工參數包含衝頭半角、材料性質、摩擦係數、擴口率(或縮口率)、最適衝頭半角、管材厚度與管材平均直徑比值等對衝頭負荷與除荷後回彈作用的影響。
此外，並將選擇減少積分法技巧偶合入所建立之有限元素法程式，並用來分析管端向外卷邊製程，探討各因素如衝頭半角及其入口圓弧半徑、管材厚度與管材平均直徑比值、機械性質、潤滑等對管端向外卷邊成形的影響。並將數值解析的結果與相關文獻之實驗結果比較，以驗證理論之正確性與程式之可信性。由結果得知，當衝頭入口彎曲半徑小於或等於臨界彎曲半徑，則管端形成卷邊成形，反之，則管端形成擴口成形。
本文所建立之分析模式，證明能正確地處理各種複雜變形與接觸之邊界條件之管端成形加工製程，且對有關管端成形現象與問題提供了進一步的了解與認識，於製程改良與模具設計上，將有相當之助益。

An elasto-plastic finite-element computer code based on an updated Lagrangian formulation is developed to analyze the influence of manufacturing parameters in axisymmetric tube end forming processes. The behavior of isotropic and normal anisotropic material is examined in a non-linear work hardening process.
An extended rmin algorithm is utilized to formulate boundary conditions, such as nodal penetration and separation, alteration frictional sliding direction, which varies throughout the entire process of tube end forming, establishing linear strain and rotational increments, and the altered state of elasto-plastic material. A modified Coulomb’s friction law is introduced to describe the alternation state of frictional sliding-sticking at the contact interface. After incorporating the modified Coulomb’s friction matrix and corresponding solution algorithms, the govering stiffness equation used in the tube end forming process is derived.
Based on the developed finite-element code, the tube-flaring and tube-nosing processes are first simulated under axisymmetric condition. Simulation results are compared with experiment data to clarify the process conditions of tube-flaring and tube-nosing operation for the correct punch load of tube end forming and precise final shape of products after unloading. The punch load and the effects of process variables, such as optimum punch-semi angle, friction coefficient, mechanical properties, tube wall thickness to mean diameter of tube, on the final shape of the product after unloading are discussed in detail.
Furthermore, introducing the reduced and selective integration method into the computer code present the deformation mechanics of tube-curling. The effects of variables, such as the half-apex angle of punch and its radius, the ratio of the thickness of the tube to its mean diameter, the mechanical properties and lubrication on the tube’s outward curling are investigated. The results of numerical simulations have exhibited a good consistency with the experimental results. Simulation findings indicate that, if the bending radius at punch inlet is smaller than the critical bending radius, curling is present at the tube end. On the contary, the tube end experiences flaring.
The simulation clearly demonstrates the efficiency of the code in conducting various tube end forming processes that proceed under complicated deformation and contact history. This study has provided a greater understanding of the tube end forming process, which will inevitably improve the manufacturing processes and the designing of tools for such processes.

中文摘要-------------------------------------------------------I
英文摘要------------------------------------------------------Ⅲ
誌 謝---------------------------------------------------------Ⅴ
目 錄---------------------------------------------------------Ⅵ
符號索引------------------------------------------------------Ⅷ
圖表索引-----------------------------------------------------XII
第一章　緒論---------------------------------------------------1
1.1 前言-------------------------------------------------------1
1.2 文獻回顧---------------------------------------------------3
1.3 論文之構成-------------------------------------------------8
第二章　基本理論----------------------------------------------10
2.1 有限變形之應變與應變率------------------------------------10
2.2 有限變形之應力與應力率------------------------------------12
2.3 有限變形之Total Lagrangian Formulation--------------------15
2.4 有限變形之Updated Lagrangian Formulation--------------16
2.5 材料之彈塑性構成關係式------------------------------------17
2.6 材料降伏之判定法則----------------------------------------21
2.7 有限元素法之公式------------------------------------------24
2.8 選擇減少積分法 (Selective Reduced Integration)------------30
2.9 穩定矩陣法 (Stabilization Matrix)-------------------------32
第三章　數值分析----------------------------------------------39
3.1 彈塑性界面與接觸節點的處理--------------------------------39
3.2 摩擦的處理------------------------------------------------42
3.3 除荷之設定------------------------------------------------44
3.4 數值分析之流程--------------------------------------------44
第四章　管端擴口與縮口成形加工分析----------------------------52
4.1 管端擴口成形加工------------------------------------------52
4.1.1 數值分析----------------------------------------------- 53
4.1.2 邊界條件----------------------------------------------- 54
4.1.3 結果與討論--------------------------------------------- 55
4.2 管端縮口成形加工------------------------------------------66
4.2.1 數值分析----------------------------------------------- 67
4.2.2 邊界條件----------------------------------------------- 68
4.2.3 結果與討論--------------------------------------------- 69
第五章　管端向外卷邊成形加工分析------------------------------78
5.1 數值分析--------------------------------------------------79
5.2 邊界條件--------------------------------------------------81
5.3 結果與討論------------------------------------------------82
第六章　結論--------------------------------------------------96
6.1 結論------------------------------------------------------96
6.2 未來研究之展望--------------------------------------------99
參考文獻-----------------------------------------------------100
作者簡介-----------------------------------------------------109
授權書-------------------------------------------------------110

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