本計畫之主要目的在於開發一套分析金屬擠製成形極限之三維 CAE 軟體，
以動態顯函有限元素法為基礎建立模擬擠製加工之變形過程分析，並考慮大變形 時，元素主軸具有旋轉的現象，因此以 Cauchy 應力的 Jaumann 微分，做為材料 構成方程式中的應力變化率推導出剛性方程式。在處理材料由極限至破壞之模擬 方面，建立相關延性破裂準則及破裂副程式，因此能將冷擠加工製程予以正確的 分析模擬。由前述章節的數值分析結果所得結論如下：
(一)將模擬的數據予以分析結果，而且可以對材料變形之各種現象予以合理 解釋，足以證實所推導的理論及所設計的電腦程式具有相當之可信度，因此對日 後所遭遇其他類似金屬成形的問題，僅須更改邊界條件即可進行分析，因而節省 大量模具開發與製程設計之時程。
(二)對於加工時的負荷、材料的變形履歷、最大主應力、最大主應變和破裂 位置等均能有效予以預測，因此對製程的改良及模具設計皆可提供有利的參考資 料。
(三)建立後處理介面之副程式用以輸出與相關繪圖軟體相容之輸入檔，如 Ideas、AVS 與 TecPlot9.0 等。
(四)建立剛性矩陣一維化之數值計算技巧以節省矩陣之儲存空間，降低動態 記憶體之依賴性，提高可分割元素之總數以增加分析精度。
(五)對於冷擠成形中的製程規劃及模具設計，可先利用軟體模擬分析，不必 完全仰賴傳統的試誤法，因而可以節省大量前製程規劃時間，並進而提升模具設 計的水準。
參考文獻
1. C. H. Lee and S. Kobayashi, “ New Solution to Rigid-Plastic Deformation Problems Using a Matrix Method ”, Journal of Engineering for Industry, Trans.
ASME, Vol. 95, pp. 865-873, 1973.
2. C. C. Chen, S. I. Oh and S. Kobayashi, “ Ductile Fracture in Axisymmetric Extrusion and Drawing ”, Journal of Engineering for Industry, Trans. ASME, Vol.
101, pp. 23-35, 1979.
3. Y. Yamada, N. Yoshimura and T. Sakurai, “ Plastic Stress-Strain Matrix and its Application for the Solution of Elastic-Plastic Problems by the Finite Element Method ”, International Journal of Mechanical Sciences, Vol. 10, pp. 343-354, 1968.
4. K. Iwata, K. Osakada and S. Fujino, “ Analysis of Hydrostatic Extrusion by the Finite Element Method ”, Journal of Engineering for Industry, Trans. ASME, Vol.
94, pp. 697-703, 1972.
5. E. I. Odell, “ A study of Wall Ironing by the Finite Element Technique ”, Journal of Engineering for Industry, Vol. 100, pp. 31-36, 1978.
6. S. Brandal and H. Valberg, “ Analysis of the Deformation Process during Wire Drawing by means of the Finite Element Method ”, Wire Journal International, pp.
64-70, 1982.
7. H. D. Hibbitt, P.V. Marcal and J. R. Rice, “ A Finite Element Formulation for Problems of Large Strain and Large Displacement ”, International Journal of Solids and Structures, Vol. 6, pp. 1069-1086, 1970.
8. R. M. McMeeking and J. R. Rice, “ Finite-Element Formulations for Problems of Large Elastic-Plastic Deformation ”, International Journal of Solids and Structures, Vol. 11, pp. 601-616, 1975.
9. A. S. Wifi, “ Incremental Complete Solution of the Stretch Forming and Deep-Drawing of a Circular Blank Using a Hemispherical Punch ”, International Journal of Mechanical Sciences, Vol. 18, pp. 23-31, 1976.
10. Lee, E. H., Mallett, R. L. and Yang, W. H., “ Stress and Deformation Analysis of the Metal Extrusion Process ”, Computer Methods in Applied Mechanics and Engineering, Vol. 10, pp. 339-353, 1977.
11. Y. Yamada and T. Hirakawa, “ Large Deformation and Instability Analysis in Metal Forming Process ”, Applications of Numerical Methods to Forming Processes, ASME AMD-28, pp. 27-38, 1978.
12. A. S. Wifi, “ Finite Element Correction Matrices in Metal Forming Analysis (with Application to Hydrostatic Bulging of a Circular Sheet) ”, International Journal of
13. I. Yarita, R. L. Mallett and E. H. Lee, “ Stress and Deformation Analysis of Metal Rolling Process ”, Advanced Technology of Plasticity, Vol. 11, pp. 1126-1131, 1984.
14. T. Hirakawa, F. Fujita, M. Kamata and Y. Yamada, “ Analysis of Strip Rolling by the Finite Element Method ”, Advanced Technology of Plasticity, Vol. 11, pp.1132-1137, 1984.
15. A. S. Wifi, “ Studies on Large Strain Elasto-Plasticity and Finite Element Analysis of Deformation Processes ”, the University of Tokyo, June, 1978.
16. Alto A., Galantucci L. M. and Tricarico L., “ A Parametric FEM Analysis of Extrusion Using a Personal Computer ”, Journal of Materials Processing Technology, Vol. 31, pp. 335-345, 1992.
17. Kang Beom-Soo, Kim Byung-Min and Choi Jae-Chan, “ Perform Design in Extrusion by the FEM and Its Experimental Confirmation ”, Journal of Materials Processing Technology, Vol. 41, pp. 237-248, 1994.
18. B. Bennani and N. Bay, “ Limits of lubrication in backward can extrusion:
analysis by the finite-element method and physical modeling experiments ”, Journal of Materials Processing Technology, Vol. 61, pp. 275-286, 1996.
19. Chanda, Tapas, Zhou, Jie, Duszczyk and Jurek “ A comparative study on iso-speed extrusion and isothermal extrusion of 6061 Al alloy using 3D FEM simulation ”, Journal of Materials Processing Technology, Vol. 114, pp. 145-153, 2001.
20. K. D. Hur, Y. Choi and H. T. Yeo, “ A design method for cold backward extrusion using FE analysis ”, Finite Elements in Analysis and Design, Vol. 40, pp. 173-185, 2003.
21. H. Kudo ands K. Aoi, “ Effect of compression test conditions upon featuring of a medium carbon steel – study on cold forgeability test PartII ”, J. Jpn. Soc. Technol.
Plast., Vol. 8, pp. 17-27, 1967.
22. P. W. Lee and H. A. Kuhn, “Fracture in cold upset forging – a criterion and model ”, Metal. Trans., Vol. 4, pp. 969-974, 1973.
23. S. L. Semiatin and J. J. Jonas, “Formability and workability of metals ”, American Society for Metals, metals park, OH, 1984.
24. R. Sowerby and N. Chandrasekharan, “The upsetting and free surface ductility of some commercial steels ”, J. Appl. Metal Network., Vol. 3, pp. 101-106, 1984.
25. V. Vujovic and A. Shabaik, “A new workability criterion for ductile metals ”, Journal of Engineering Materials and Technology, Vol. 108, pp. 245-249, 1986.
26. A. M. Frudenthal, “the inelastic vehavior of metals ”, Wiley, New York, 1950.
27.M. G. Cockroft and D. J. Latham, “Ductility and the workability of metals ”, J. Inst.
Met., Vol. 96, pp. 33-39, 1968.
28. S. I. Oh, C. C. Chen and S. Kobayashi, “Ductile fracture in axisymmetric extrusion
and drawing. Part II. Workability in extrusion and drawing ”, Journal of Engineering for Industry, Vol. 101, pp. 33, 1976.
29. P. Brozzo, B. Deluca and R. Rendina, “A new method for the prediction of formability limits in metal sheet, sheet metal forming and formability ”, Proceedings of the seventh biennial conference of the international deep drawing research group, 1972.
30. D. M. Norris, J. E. Reahgh, B. Moran, and D. F. Quinnones, “A plastic mean-stress criterion for ductile fracture ”, Journal of Engineering Materials and Technology, Vol. 100, pp. 279-286, 1978.
31. A. S. Argon, J. Im and R. Safoglu, “Cavity formation from inclusions in ductile fracture ”, Metal. Trans., Vol. A6, pp. 825-836, 1975.
32. M. Oyane, T. Sato, K. Okimoto and S. Shima, “Criteria for ductile fracture and their applications ”, Journal of Engineering Materials and Technology, Vol. 4, pp.
65-81, 1980.
33. F. A. McClintock, “A criterion for ductile fracture bt the growth of holes ”, Journal of Engineering for Industry, Trans. ASME, Vol. 35, pp. 363-371, 1968.
34. 啟學出版社編輯部編譯，“鋁合金資料集”，啟學出版社，民國 70 年。
計畫成果自評
本計畫發展一套金屬擠製成形極限分析之三維動態有限元素程式，並且結合 延性破裂準則，藉以分析金屬柱材在擠製製程中，加工負荷、材料的變形歷程、
應力與應變的分佈，此外，本計畫並設計前向擠製模具，進行擠製成形實驗，期 望在擠製加工製程定案前能先預測得知工件是否會發生缺陷，以利金屬擠製製程 之設計。因此，本計畫在執行完成後的自評部分如下
1. 建立本研究室高噸位擠製機之標準操作流程，並且完成負荷、位移等相關 參數的校正，此外，本計畫也設計前向擠製模具，可供後續研究計畫之執行。
2. 本計畫在有限元素分析的前處理部分，將目前已商業化之 Ideas 與 Pro/E 等 相關 CAD 軟體進行加工模式之建立與相關參數之輸出成一標準介面的檔案 格式，並加入延性破裂的相關參數設定，以提供主分析程式之讀取；在後處 理方面，本計畫之輸出格式符合多種商業化繪圖軟體所適用之檔案格式如 AVS、TecPlot9.0 與 Ideas 等，將使得分析結果不會受到繪圖軟體的限制而影 響結果的判斷。
3. 本計畫之分析程式，以顯性動態有限元素法為基礎建立模擬擠製加工之變 形過程分析，並建立剛性矩陣一維化之數值計算技巧以節省矩陣之儲存空 間，降低動態記憶體之依賴性，提高可分割元素之總數以增加分析精度。
4. 本計畫亦提供延性破裂法則之副程式模組化在分析程式中，使得材料在擠 製過程中，若能量符合延性破裂準則的能量時，能夠使材料產生裂縫，以合 理的模擬擠製製程。
5. 本計畫所可提供總計畫有關擠製方面製程之分析，且可將分析結果建立成 資料檔(data base)，以提供相關人員參考與應用，最後能與其它子計畫整合，
成為一泛用型之金屬成形極限分析軟體。