臺灣博碩士論文加值系統

冷作成形製程常透過成形極限圖來判斷材料是否會破壞。透過成形極限圖上的成形極限曲線，CAE工程師在設計階段即可評估產品之製造可行性。建構材料之成形極限曲線需透過大量的可成形性實驗及應變量測程序，且不易獲得包含全應變值域的完整曲線。此外，透過成形極限圖判斷破壞是否發生並非總是準確。造成誤判的原因可能為：1.建構成形極限曲線因人為因素導致的誤差、2.材料變形時不遵循線性應變路徑。本論文將能量準則導入成形極限圖的建立過程中，以改善傳統方法評估結果不準確的缺點。以既有之能量準則可評估材料受到拉伸-壓縮狀態之極限應變，但大部分的能量準則無法準確預估材料在雙軸拉伸狀態下的成形極限。因此在本論文中以提出一修正能量準則來解決此問題。
本論文將冷作成形製程問題分為線性應變路徑及非線性應變路徑兩大類。針對線性應變路徑條件下板材之可成形性評估，本論文將應變路徑變化之概念用於修正Cockcroft與Latham提出之能量準則。在準則中加入主應變比值項，可反映材料第二主應變與第三主應變比值對破壞發生之影響。能量準則透過解析解方式，可預估材料在不同應變狀態下之極限應變，進而預估建立材料之完整成形極限曲線。由實驗結果比對證實，本論文提出之修正準則評估結果優於C＆L準則，並可適用於不同強度及厚度的板材上。針對線性應變路徑下塊材之可成形性評估，本研究使用圓柱壓縮及圓柱側壓兩種實驗方式，搭配C＆L準則亦可預估材料之成形極限曲線。透過實驗及有限元素模擬求得的材料極限能量密度值，可作為判斷破壞發生與否之依據。本論文中針對具凹槽設計之圓柱試件進行分析，發現凹槽設計之所以能加速破壞發生，導因於凹槽處應力集中與應變集中之效應。若僅從應力或應變之觀點無法準確預估材料是否發生破壞，必須以能量密度之概念才能進行完整評估。
若材料變形時遵循非線性應變路徑，利用線性應變路徑建構出的成形極限曲線無法準確預估材料之成形極限。本論文透過試件幾何設計，使試件在變形過程中遵循具有一次轉折的二階段應變路徑。由實驗結果可知，以本研究使用之模具及試件幾何設計，可在變形過程的第一階段產生雙軸拉伸狀態之預應變。在第二階段的應變路徑變化，根據試件幾何設計的不同可造成雙軸拉伸、平面應變及拉伸-壓縮等三種不同狀態。除透過實驗決定材料成形極限外，本論文亦以提出之能量準則進行二階段應變路徑情形下的可成形性分析。
總括而言，進行冷作成形製程之可成形性評估時，應變路徑變化具有相當重要的影響性。在線性及非線性應變路徑情況下，以本論文提出之能量準則進行冷作製程之可成形性評估，評估能力均優於C＆L能量準則評估結果。

Formability of material in cold forming processes is often evaluated by the Forming Limit Diagram (FLD) method. CAE engineers can judge if their design succeeds virtually by this tool, and saves the cost of trial-and-error experiments. However, massive formability tests and strain measurements must be conducted in order to obtain the FLD of material, and sometimes the information is not sufficient to plot the complete Forming Limit Curve (FLC). Besides, the predictions made by FLC are not always very accurate. The errors may come from two aspects: 1. Errors in strain measurement caused by human factors. 2. Errors result from complex strain states. In this dissertation, energy criteria were introduced into the procedures for establishing the FLD of material for better prediction accuracy. Most of the existed energy criteria could be used for evaluating the formability under tension-compression conditions, but the predictions made under biaxial tension conditions were not so accurate. Therefore, a modified energy criterion would be proposed in this dissertation.
In this dissertation, problems encountered in cold forming processes were classified as linear strain path problems and non-linear strain path problems. For the formability evaluation under linear strain path conditions, an energy criterion modified from the one proposed by Cockcroft and Latham was proposed. The modified criterion introduced a ratio of the secondary principal stress to the third principal stress for reflecting the influences of strain ratio changes on fracture initiation. The limit strain data under different strain states could be predicted by analytical solutions of energy criteria. Experimental results supported that the modified criterion had better prediction capability than the C＆L criterion, and was capable of predicting FLCs of material under different strengths and thicknesses. For the formability evaluation of bulk material under linear strain paths, the predicted FLC could be established by the C＆L criterion with limit strain data obtained from cylinder upsetting tests and cylinder side pressing tests. The energy density constant in the C＆L criterion could be viewed as a critical value for indicating the fracture initiation. In this dissertation, the energy density constant was used for evaluating the notch designs on cylinder specimens. The notch designs were capable of accelerating fracture initiation because they had created both stress concentration effects and strain concentration effects on cylinder specimens. Since it is a combined phenomenon, the formability evaluation would not be accurate if only the stress terms or strain terms were taken into consideration.
When material deforms under non-linear strain path, engineers could not simply use the FLC obtained under linear strain paths for fracture predictions. Therefore, formability test specimens with special designs were utilized in this dissertation for constructing non-linear strain path conditions. Results showed that the specimens deformed under two-step strain paths. By using the proposed die and specimen designs, pre-strains could be applied on the specimens without unloading the specimens from the die sets. At the first step of strain paths, pre-strains under biaxial tension state were observed. At the second stage of strain paths, three different strain states, namely the biaxial tension state, the plane-strain state, and the tension-compression state, could be created by altering the specimen designs. Also, predictions made by the proposed energy criterion were obtained for formability evaluation.
To sum up, strain paths in cold forming processes played an important role when conducting formability evaluations. The modified energy criterion proposed in this dissertation showed a better prediction capability than the C＆L criterion not only under linear strain path conditions, but also under non-linear strain paths.

中文摘要 I
Abstract II
致謝 IV
Table of Contents VI
List of Tables VIII
List of Figures IX
Nomenclature XI
Chapter 1 Introduction 1
1.1 Research Background 1
1.2 Literature Review 2
1.2.1 Cold Forming Processes 2
1.2.2 Formability and Forming Limit Diagram 3
1.2.3 Forming Limit Stress Diagram 8
1.2.4 Energy Criteria 9
1.2.5 Hybrid Methods for Formability Evaluation 12
1.3 Objectives and Methodologies of this Dissertation 13
1.3.1 Objective of this dissertation 13
1.3.2 Applicable range of the study 13
1.3.3 Methodologies adopted in the dissertation 15
1.4 Outline of the Dissertation 17
Chapter 2 Theoretical Background 20
2.1 Energy Criteria for Formability Evaluation 20
2.2 Modifications of Energy Criteria 24
2.3 Predicting Forming Limit Curve by Energy Criteria 28
Chapter 3 Experimental and Numerical Methods 33
3.1 Strain Measurement Techniques 33
3.2 Linear Strain Path Formability Tests 41
3.2.1 Experimental Setup for Sheet Material 41
3.2.2 Experimental and Simulation Setup for Bulk Material 46
3.3 Two-step Strain Path Formability Tests 51
3.3.1 Study of Strain Path Effects under Non-linear Strain Path Conditions 51
3.3.2 Experimental Setup for Two-step Strain Path Formability Tests 54
3.3.3 Simulation Setup for Two-step Strain Path Formability Tests 59
Chapter 4 Results and Discussions 64
4.1 Formability Evaluation for Sheet Material 64
4.2 Formability Evaluation for Bulk Material 75
4.3 Formability Evaluation under Two-step Stain Paths 82
4.3.1 Results of Tube Hydroforming Process with Non-linear Strain Paths 82
4.3.2 Results of Two-Step Strain Path Formability Tests with Special Specimen Designs 85
Chapter 5 Conclusions and Future Works 94
5.1 Conclusions 94
5.2 Future Works 95
References 96
Appendix A Derivation of Analytical Forms for Predicting FLC 102
Appendix B Prediction of Limit Strain by Zhuang’s Criterion 106

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