臺灣博碩士論文加值系統

彈塑性元件並聯模式為將各組彈塑性元件以並聯方式構成的一種模式，是廣泛被利用來模擬真實材料之行為的機械模型之一。基於此類模式在目前應用上能適切地模擬一些複雜的彈塑性行為，如循環彈塑性應力─應變行為，及從材料微觀的角度來看，並聯模式之架構具有明確之物理涵義，本研究的主要目的為探討彈塑性元件並聯模式及其降伏面之演化。在研究方法上，針對彈塑性元件並聯模式在不額外增加規則，也就是模式所表現出之行為，是完全符合其組成關係之定義下進行研究，主要探討重點有兩個方向：為元件降伏先後次序問題與模式降伏面之演化。其中在模式降伏面之部分，由於並聯模式僅在各組元件中有定義降伏面，故在此透過並聯機制，並利用應力應變空間轉換的方式，將元件組中定義之降伏面，也可說是其允許應力區域之影響，對應到總應力空間中後，模式之降伏面即為所有對應允許應力區域交集而成區域之邊界。經由對並聯模式在元件降伏先後次序及降伏面之演化方面進行模擬實驗，依據所呈現出之結果，對此模式在理論與應用上作進一步之討論。
另外一個研究重點，對於彈塑性機械模型之間的共通性，藉由組成方程式之對等，可找出內在儲能機制、耗散機制，及這些機制間的的互制關係不盡相同，但在宏觀的行為是一樣的，也就是輸入─輸出關係相同的機械模型。進一步探討這些不同微觀面向的機械模型，其材料常數、內變數、塑性開關機制間之等價關係，以掌握機械模型在描述彈塑性材料力學行為上之特性。

目 錄
誌謝………………………………………………………………… 一
摘要………………………………………………………………… 三
目錄………………………………………………………………… 四
圖目錄……………………………………………………………… 七
第一章 導論
1.1 研究動機與目的……………………………………………… 1
1.2 文獻回顧……………………………………………………… 2
1.3 研究方法與內容……………………………………………… 4
第二章 彈塑性元件並聯模式
2.1 完全彈塑性元件並聯模式…………………………………… 5
2.2 雙線性彈塑性元件並聯模式………………………………… 9
2.3 其他類型模式之並聯組合…………………………………… 12
2.4 彈塑性元件並聯模式之特性………………………………… 13
第三章 彈塑性元件並聯模式之模擬與探討
3.1 元件之降伏與回復彈性次序………………………………… 14
3.1.1 範例………………………………………………………… 14
3.1.2 小結………………………………………………………… 16
3.2 敏感度分析…………………………………………………… 16
3.2.1 完全彈塑性元件並聯模式………………………………… 16
3.2.2 雙線性彈塑性元件並聯模式……………………………… 18
3.2.3 小結………………………………………………………… 19
3.3 對應允許應力區域之交集情形……………………………… 19
3.3.1 範例一……………………………………………………… 20
3.3.2 範例二……………………………………………………… 20
3.3.3 小結………………………………………………………… 21
3.4 參數對降伏面之影響………………………………………… 22
3.4.1 範例………………………………………………………… 22
3.4.2 小結………………………………………………………… 22
第四章 等價機械模型之研究
4.1 異向性雙線性彈塑性模式…………………………………… 24
4.1.1 雙線性彈塑性模型一……………………………………… 24
4.1.2 雙線性彈塑性模型二……………………………………… 26
4.2 雙線性彈塑性模型之等價關係……………………………… 28
4.3 等價關係之探討與建議……………………………………… 30
4.3.1 能量觀點…………………………………………………… 31
4.3.2 總應力空間中降伏面之觀點……………………………… 32
4.3.3 等價觀念之應用性………………………………………… 33
第五章 結論與建議 …………………………………………… 35
參考文獻…………………………………………………………… 38
附錄A 具有權重參數之完全彈塑性元件並聯模式…………… 73
附錄B 異向性彈塑性元件並聯模式…………………………… 75
附錄C Prandtl-Reuss 元件並聯模式………………………… 78

[1] P. J. Armstrong and C. O. Frederick, “A mathematical representation of the multiaxial bauschinger effect,” CEGB Report, RD/B/N731, Berkeley Nuclear Laboratories. (1966).
[2] M. Brokate and J. Sprekels, Hysteresis and Phase Transitions, Springer, New York (1996).
[3] D. Y. Chiang and J. L. Beck, “A new class of distributed-element models for cyclic plasticity-I. Theory and application,” International Journal of Solids and Structures, Vol.31, No.4, pp.469-484 (1994).
[4] D. Y. Chiang and J. L. Beck, “A new class of distributed-element models for cyclic plasticity-II. On important properties of material behavior,” International Journal of Solids and Structures, Vol.31, No.4, pp.485-496 (1994).
[5] D. Y. Chiang, “A phenomenological model for cyclic plasticity,” Journal of Engineering Materials and Technology, ASME, Vol.119, pp.7-11 (1997).
[6] D. Y. Chiang, “Modeling and identification of elastic-plastic systems using the distributed-element model,” Journal of Engineering Materials and Technology, ASME, Vol.119, pp.332-336 (1997).
[7] D. Y. Chiang, K. H. Su, and C. H. Liao, “A study on subsequent yield surface based on the distributed-element model,” International Journal of Plasticity, Vol.18, pp.51-70 (2002).
[8] J. L. Chaboche, K. Dang Van and G. Cordier, “Modelization of the strain memory effect on the cyclic hardening of 316 stainless steel,” Transactions of 5th International Conference on Structural Mechanics in Reactor Technology, Vol. L, Paper No. L11/3. North-Holland (1979).
[9] J. L. Chaboche, “Cyclic Plasticity Modeling and Ratchetting Effects,” in Desal et al., (eds), Proceedings of Second International Conference on Constitutive Laws for Engineering Materials: Theory and Applications, Tucson, Arizona, Elsevier, pp.47-58 (1987).
[10] J. L. Chaboche, “Constitutive equations for cyclic plasticaity and cyclic viscoplasticity,” International Journal of Plasticity, Vol. 5, pp.247-302 (1989).
[11] J. L. Chaboche, “On some modifications of kinematic hardening to improve the description of ratchetting dffects, International Journal of Plasticity, Vol. 7, pp.661 (1991).
[12] J. L. Chaboche, D. Nouailhas, D. Pacou and P. Pauimier, “Modeling of the cyclic response and ratchetting effects on Inconei-718 Alloy,” European Journal of Mechanics, A/Solids, Vol. 10, pp.101 (1991).
[13] P. Dupont, V. Hayward, B. Armstrong and F. Altpeter, “Single state elastoplastic friction models,” IEEE Transactions on Automatic Control, Vol. 47, No. 5, pp.787-792 (2002).
[14] M. Francois, “A plasticity model with yield surface distortion for non proportional loading,” International Journal of Plasticity, Vol.17, pp.703-717 (2001).
[15] W. N, Findley, J. S. Lai and K. Onaran, Creep and relaxation of nonlinear viscoelastic materials, with an introduction to linear viscoelasticity, North-Halland, Amsterdam, New York (1976).
[16] D. E. Helling, A. K. Miller and M. G. Stout, “An experimental investigation of the yield loci of 1100-0 aluminum, 70:30 brass and an overaged 2040 aluminum alloy after various prestrains,” Journal of Engineering Materials and Technology, ASME, Vol.108, pp.313-320 (1986).
[17] H. K. Hong and C. S. Liu, “Prandtl-Reuss elastoplasticity: on-off switch and superposition formulae,” International Journal of Solids and Structures, Vol.34, pp.4281-4304 (1997).
[18] H. K. Hong and C. S. Liu, “On behavior of perfect elastoplasticity under rectilinear paths,” International Journal of Solids and Structures, Vol.35, pp.3539-3571 (1998).
[19] H. K. Hong and C. S. Liu, “Internal symmetry in bilinear elastoplasticity,” International Journal of Non-Linear Mechanics, Vol.34, pp.279-288 (1999).
[20] H. K. Hong and C. S. Liu, “Internal symmetry in the constitutive model of perfect elastoplasticity,” International Journal of Non-Linear Mechanics, Vol.35, pp.447-466 (2002).
[21] A. Yu. Ishlinsky, “Some applications of statistics to description of laws of body deformation,” Reports of the Academy of Science of the USSR, ONT, No.9, pp.583-590 (1944).
[22] A. Yu. Ishlinsky, “On equations of spatial deformation of not completely elastic and elastoplastic bodies,” Reports of the Academy of Science of the USSR, ONT, No.3 (1945).
[23] H. Ishikawa and K. Sasaki, “Yield surfaces of SUS304 under cyclic loading,” Journal of Engineering Materials and Technology, ASME, Vol.110, pp.364-371 (1988).
[24] H. Ishikawa and K. Sasaki, “Stress-strain relations of SUS304 stainless after cyclic preloading,” Journal of Engineering Materials and Technology, ASME, Vol.111, pp.417-423 (1989).
[25] W. D. Iwan, “A distributed-element model for hysteresis and its steady-state dynamic response,” Journal of Applied Mechanics, ASME, Vol.33, No.4, pp.893-900 (1966).
[26] W. D. Iwan, “On a class of models for the yielding behavior of continuous and composite systems,” Journal of Applied Mechanics, ASME, Vol.34, No.2, pp.612-617 (1967).
[27] Y. Jiang and P. Kurath, “Characteristics of the Armstrong-Frederick type plasticity models,” International Journal of Plasticity, Vol. 12, No. 3, pp.387-415 (1996).
[28] C. S. Liu and H. K. Hong, “The contraction ratios of perfect elastoplasticity under biaxial controls,” European Journal of Mechanics, A/Solids, Vol.19, pp.827-848 (2000).
[29] N. Ohno and J. D. Wang, “Transformation of a nonlinear kinematic hardening rule to a multi-surface form under isothermal and nonisothermal conditions,” International Journal of Plasticity, Vol. 7, pp. 879 (1991).
[30] N. Ohno and J. D. Wang, “Kinematic hardening rules with critical state of dynamic recovery, part I:Formulation and basic features for ratchetting behavior,” International Journal of Plasticity, Vol. 9, pp.375-390 (1993).
[31] N. Ohno and J. D. Wang, “Kinematic hardening rules with critical state of dynamic recovery, part II: Application to experiments of ratchetting behavior, International Journal of Plasticity, Vol. 9, pp.391-403 (1993).
[32] N. Ohno and J. D. Wang, “Kinematic hardening rules for simulation of ratchetting behavior,” European Journal of Mechanics, A/Solids, Vol. 13, pp. 519 (1994).
[33] A. Phillips and J. L. Tang, “The effect of loading path on the yield surface at elevated temperatures,” International Journal of Solids and Structures, Vol.8, pp.463-474 (1972).
[34] A. Phillips and C. W. Lee, “Yield surfaces and loading surfaces. Experimants and recommendations,” International Journal of Solids and Structures, Vol.15, pp.715-729 (1979).
[35] A. Phillips and W. Y. Lu, “An experimental investigation of yield surfaces and loading surfaces of pure aluminum with stress-controlled and strain-controlled paths of loading,” Journal of Engineering Materials and Technology, ASME, Vol.106, pp.349-354 (1984).
[36] L. Prandtl, “Ein Gedankenmodell zur kinetischen Theorie der festen Korper,” Zeitschrift für angewandte mathematik und mechanic, Vol. 8, pp.85-106 (1928).
[37] V. Palmov, Vibrations of elasto-plastic bodies, Springer, New York (1998).
[38] H. C. Wu and W. C. Yeh, “On the experimental determination of yield surfaces and some results of annealed 304 stainless steel,” International Journal of Plasticity, Vol.7, No.8, pp.803-826 (1992).
[39] R. H. Wu and P. C. Tung, “Studies of stick-slip friction, presliding displacement, and hunting,” Journal of Dynamic System, Measurement, and Control, ASME, Vol.124, pp.111-117 (2002).
[40] R. H. Wu and P. C. Tung, “Fast pointing control for systems with stick-slip friction,” Journal of Dynamic System, Measurement, and Control, ASME, Vol.126, pp.614-626 (2004).
[41] I. R. Whiteman, “A mathematical model depicting the stress-strain diagram and the hysteresis loop,” Journal of Applied Mechanics, ASME, Vol.26, pp.95-100 (1959).
[42] 鄭正義，多晶材料微觀量測與其力學行為探討，國立臺灣大學應用力學研究所，台北 (1992)。
[43] 王智睿，鋁銅鎳微觀拉伸實驗，國立台灣大學土木工程研究所，台北 (1996)
[44] 倪亮傑，微觀雙滑移模式銅鎳拉伸實驗，國立台灣大學土木工程研究所，台北 (1998)。
[45] 蘇愷宏，材料後續降伏面之研究，國立成功大學航空太空工程研究所，台南 (1998)。