臺灣博碩士論文加值系統

本文以實驗及理論的方式來探討五種不同材料圓管在循環彎曲負載下彈塑性力學行為及皺曲損壞之行為。實驗是以『彎管實驗機』及『曲度-橢圓化量測器』對圓管進行實驗，而理論則是採用內涵時間理論及虛功原理來分析圓管在循環彎曲負載時彎矩、曲度及橢圓化關係。從彎矩-曲度的實驗曲線中顯示，在對稱曲度循環彎曲負載時，本文所採用所有不同材料圓管皆呈現循環硬化的現象，而經過了一些循環圈數後迴圈會變的較穩定。而從橢圓化-曲度的實驗曲線中顯示，在對稱曲度循環彎曲負載時橢圓化會漸增且呈對稱棘齒的變化，橢圓化量會一直增加直到圓管發生皺曲。從控制曲度及循環至皺曲圈數的實驗曲線中顯示，控制循環曲度量越大時，循環至皺曲圈數就越少。最後，本文修改1987年Kyriakides與Shaw所提出的理論模式，使該理論架構可用來描述不同材料圓管在循環彎曲負載時控制曲度和循環彎曲至皺曲圈數的關係。理論分析和實驗結果進行比較後發現，理論能合理的描述實驗結果。

This paper discuss the thin and circular tubes of five kinds of different materials by the way of experiments and theories, including SUS 304 is managed with 316L stainless steel, 7005- T53 aluminum tube and C2700 copper tube and titanium alloy tube ,which were researched the mechanical behavior of the elasticity and plasticity, and buckling failure of circular tubes subjected to cyclic bending. The experiment of circular tubes subjected to cyclic bending is in charge of the experiment with the “tube bending machine” and “curvature-ovalization measurement apparatus.” The theory part is to adopt the endochronic theory for the basic theory of the deformation of the elasticity and plasticity, cooperate with the principle of virtual work to derive the essential balance equation. We also use one group of Fourier series to approximate to in charge of every some displacement on the section while being round to spread, trying to get the relationship of the moment, curvature and ovalization from the each other corresponding parameter. Shown by the experiment and theory result: Circular tubes of different materials subjected to symmetrical and cyclic bending, we will get the situation of the strain hardening. After the cyclic bending, the moment and the curvature will get the steady states gradually.The diameter of tube will present the behavior of ovalization , the ovalization of the tube cross-section increases in a ratcheting manner with the number of cycles.Owing to the progressive accumulation of the ovalization of the tube cross-section during cyclic bending.In addition as controlled curvature getting bigger, the number of cycles of buckling failure is getting less. Conversely, the controlled curvature getting less, the number of cycles of buckling failure is getting bigger.Finally, the relationship of the controlled curvature from the experiment and the number of cycles of buckling failure, we will use the theory which advanced by Kyriakides and Shaw in 1987, try to get the corresponding parameters.

摘要-----------------------------------------------------Ⅰ
Abstract-------------------------------------------------Ⅱ
誌謝-----------------------------------------------------Ⅳ
目錄-----------------------------------------------------Ⅵ
表目錄---------------------------------------------------Ⅸ
圖目錄---------------------------------------------------Ⅹ
符號表-------------------------------------------------ⅩⅣ
第一章 緒論----------------------------------------------1
1-1 研究動機----------------------------------------------1
1-2 文獻回顧----------------------------------------------2
1-3 論文內容----------------------------------------------6
第二章 內涵時間塑性理論----------------------------------7
2-1 基本理論----------------------------------------------7
2-1-1 內涵時間定義----------------------------------------7
2-1-2 材料函數的定義--------------------------------------8
2-1-3 材料性質的假設--------------------------------------9
2-2 增量式內涵時間塑性理論-------------------------------10
2-3 圓管在純彎曲作用下，增量式內涵時間理論的推導---------12
第三章 虛功法與里茲法應用於圓管內涵時間理論之推導-------16
3-1 圓管應變的推導---------------------------------------16
3-1-1 軸向應變的推導-------------------------------------16
3-1-2 圓周方向應變的推導---------------------------------17
3-2 圓管受彎曲負載下虛功法的描述-------------------------20
3-3 圓管受彎曲負載下的數值計算---------------------------21
第四章 圓管彎曲計算流程---------------------------------26
4-1 模擬過程---------------------------------------------26
4-2 切割管壁、積分與運算---------------------------------27
4-3 計算流程---------------------------------------------27
第五章 實驗材料、實驗設備與實驗方法---------------------33
5-1 實驗材料---------------------------------------------33
5-2 實驗設備---------------------------------------------33
5-3 實驗原理---------------------------------------------35
5-4 實驗量測方法-----------------------------------------36
5-5 實驗步驟---------------------------------------------37
第六章 理論分析與實驗結果-------------------------------51
6-1 力學行為實驗與理論的比較-----------------------------51
6-2 皺曲損壞之實驗結果-----------------------------------52
第七章 結論---------------------------------------------72
參考文獻-------------------------------------------------74

1.S.Kyriakides and P.K.Shaw,“Inelastic Buckling of Tubes Under Cyclic Bending”,Journal of Pressure VesselTechnology,Vol.109,pp.169-178(1987)。

2.E.Corona and S.Kyriakides,“On the Collapse of Inelastic Tubes Under Combined Bending and Pressure”,Int. J. Solids Structures,Vol.24,No.5,pp.505-535(1988)。

3.E.Corona and S.Kyriakides,“An Experimental Investigation Degradation and Buckling of Circular Tubes Under Cyclic Bending and Buckling of Circular Tubes Under Cyclic Bending and External Pressure”, Thin-Walled Structures Vol.12, pp.229-263(1991)。

4.S.Kyriakides and G.T.Ju,“Bifurcation and Localization Instabilities in Cylindrical Shells Under Bending-Ⅰ. Experiments”,Int. J. Solids Structures,Vol.29,No.9,pp.
1117-1142(1992)。

5.W.F.Pan,T.R.Wang and C.M.Hsu,“A Curvature-ovalization Measurement Apparatus for Circular Tubes Under Cyclic Bending”, Experimental Mechanics Vol.38,No.2,pp.99-102 (1998)。

6.Wen-Fung Pan and Yung-Shun Her,“Viscoplastic Collapse of Thin-Walled Tubes Under Cyclic Bending”,Journal of Engineering Materials and Technology,Vol.120,pp.287-290 (1998)。

7.Wen-Fung Pan and Chun-Huei Fan,“An Experimental Study on the Effect of Curvature-Rate at Preloading Stage on Subsequent Creep or Relaxation of Thin-Walled Tubes under Pure Bending”,JSME International Journal Series A,Vol.41, No.4,pp.525-531(1998)。

8.Kuo-Long Lee, Wen-Fung Pan and Ju-Nan Kuo,“The Influence of the Diameter-to-thickness Ratio on the Stability of Circular Tubes Under Cyclic Bending”,International Journal of Solids and Structures Vol.38,pp.2401-2413 (2001)。

9.Wen-Fung PAN and Kuo-Long LEE,“The Effect of Mean Curvature on the Response and Collapse of Thin-Walled Tubes Under Cyclic Bending”,JSME International Journal Series A,Vol.45, No.2,pp.309-318(2002)。

10.W.F.Pan,T.H.Lee and W.C.Yeh,“Endochronic Analysis for Finite Elasto-Plastic Deformation and Application to Metal Tube Under Torsion and Metal Rectangular Block Under Biaxial Compression”Int. J.ofplasticity,Vol.12,No.10,pp.1287-1316(1996)。

11.W.F.Pan and K.T.Leu,“Endochronic Analysis for Viscoplastic Collapse of Thin-Walled Tube under Combined Bending and External Pressure”, JSME Int. J.Series A,Vol.40,No.2,pp.189-199(1997)。

12.W.F.Pan and C.H.Chern,“Endochronic Description of Viscoplastic Behavior of Materials Under Multiaxial Loading”,Int.J.of Solids Structures, Vol.34.No.17,pp.2131-2160(1997)。

13.W. F. Pan and W. J. Chiang,“Endochronic Simulation for Multiaxial Creep”, JSME Series A,Vol.41,No.2,pp.204-210(1998)。

14.W.F.Pan,W.J.Chiang and C.K.Wang,“EndochronicAnalysis for Rate-dependent Elasto-plasticDeformation”,Int.J.of Solids and Structures,Vol.36,pp.3215-3237(1999)。

15.K.C.Valanis,“A Theory of Viscoplasticity Without a Yield Surface, Part Ⅰ: General Theory; Part Ⅱ: Application to Mechanical Behavior of Metals”, Arch.Mech.,Vol.23,pp.517-551(1971)。

16.K.C.Valanis,“Fundamental Consequences of a New Intrinsic Time Measure Plasticity as a Limit of the Endochronic Theory”,Arch.Mech.,pp.171-191(1980)。

17.H.C.Wu and R.J.Yang,“Application of the Improved Endochronic Theory of Plasticity to Loading with Multiaxial Strain-Path”,Int.J.Nonlinear Mech.,Vol.18,pp.395-409 (1983)。

18.K.C.Valanis and J.Fan,“Endochronic Analysis of Cyclic Elastoplastic Strain Fields in a Notched Plate”,Journal of Applied Mechanicsc,Vol.50,pp.789-793(1983)。

19.洪健中,“應用內涵時間理論描述鈦合金管在循環彎曲負載下粘塑性之材料行為”,國立成功大學碩士論文(2000)。

20.許哲榮, “316L不锈鋼管在循環彎曲負載下黏塑性力學行為及皺曲損壞之理論分析,”國立成功大學碩士論文, 2004

21.林慶原, “7005-T53鋁合金管在循環彎曲負載下彈塑性力學行為及皺曲損壞之研究,”國立成功大學碩士論文, 2005