本文係研究不同外徑/壁厚比與不同圓孔直徑的6061-T6鋁合金圓孔在循環彎曲負載下的橢圓化成長與臨界橢圓化，其中不同外徑/壁厚比有:16.5、31.0與60.0，而不同的圓孔直徑有:2、4、6、8與10 mm。本文選用6061-T6鋁合金圓孔管在不同控制曲率下進行循環彎曲至損壞的實驗，而在實驗過程中會量測曲率、橢圓化與循環圈數。根據實驗結果顯示，橢圓化成長與循環圈數的曲線大略可分成三個階段：初始階段、第二階段與第三階段，而大多的循環圈數都在初始階段與第二階段。最後，當裂痕出現時，橢圓化成長進入第三階段並急遽的上升，最後導致6061-T6鋁合金圓孔管的斷裂。接著，本文採用Lee等人【10】所提出的關係式，並將不同外徑/壁厚比與不同圓孔直徑變數導入相關的材料參數中，則該關係式可用來描述初始階段與第二階段的橢圓化-循環圈數關係。此外，本文採用胡庭源【16】所提出的關係式，並將不同外徑/壁厚比與不同圓孔直徑變數導入相關的材料參數中，則該關係式可用來描述臨界橢圓化-控制曲率的關係。經由理論分析與實驗結果相互比較後發現，理論可合理的描述實驗結果。

This paper studies the ovalization growth and critical ovalization of 6061-T6 aluminum alloy round-hole tubes with different diameter-to-thickness ratios and different hole diameters subjected to cyclic bending. The different diameter-to-thickness ratios include: 16.5, 31.0 and 60.0, while the different hole diameters include: 2, 4, 6, 8 and 10 mm. In this paper, the 6061-T6 aluminum alloy round-hole tube is selected for the experiment of cyclic bending to failure under different controlled curvatures. The curvature, ovalization and number of cycles will be measured during the experiment. It can be seen that the experimental ovalization-number of cycles relationship can roughly divided into three stages: the stage I, second stage II and stage III. However, most of the number of cycles are in the stages I and II. Finally, when the crack appears, the ovalization growth enters the stage III and increases sharply, which finally leads to the fracture of the 6061-T6 aluminum alloy round-hole tube. Next, this study adopts the empirical formulation proposed by Lee et al. [10], and induces diameter-to-thickness ratio and hole diameter into the relevant material parameters. Thus, the empirical formulation can be used to describe the ovalization-number of cycles relationship in the stages I and II. In addition, this study adopts the empirical formulation proposed by Hu [16], and induces diameter-to-thickness ratio and hole diameter into the relevant material parameters. Therefore, the empirical formulation can be used to describe the critical ovalization-controlled curvature relationships. After comparing the theoretical analysis with the experimental results, it is found that the theory can reasonably describe the experimental results.

1. P. K. Shaw and S. Kyriakides, “Inelastic analysis of thin-walled tubes under cyclic bending”, International Journal of Solids and Structures, Vol. 21, No. 11, pp. 1073-1100 (1985).
2. 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).
3. K. L. Lee, W. F. Pan and J. N. 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, No. 14, pp. 2401-2413 (2001).
4. S. Kyriakides and P. K. Shaw, “Inelastic buckling of tubes under cyclic loads”, Journal of Pressure Vessel Technology, Vol. 109, No. 2, pp. 169-178 (1987).
5. K. L. Lee, C. M. Hsu, W. F. Pan, “Endochronic Simulation for the response of 1020 carbon steel tubes under symmetric and unsymmetric cyclic bending with or without external pressure”, Steel and Composite Structures, Vol. 8, No. 2, pp. 99-114 (2008).
6. E. Corona and S. Kyriakides, “An experimental investigation of the degradation and buckling of circular tubes under cyclic bending and external pressure”, Thin-Walled Structures, Vol. 12, No. 3, pp. 229-263 (1991).
7. K. H. Chang and W. F. Pan, “Buckling life estimation of circular tubes under cyclic bending”, International Journal of Solids and Structures, Vol. 46, No. 2, pp. 254-270 (2009).
8. K. L. Lee, C. Y. Hung and W. F. Pan, Variation of ovalization for sharp-notched circular tubes under cyclic bending, Journal of Mechanics, Vol. 26, No. 3, pp. 403- 411 (2010).
9. K. L. Lee, C. M. Hsu and W. F. Pan, “The influence of diameter-to-thickness ratios on the response and collapse of sharp-notched circular tubes under cyclic bending”, Journal of Mechanics, Vol. 28, No. 3, pp. 461-468 (2012).
10. K. L. Lee, C. C. Chung and W. F. Pan, “Growing and critical ovalization for sharp-notched 6061-T6 aluminum alloy tubes under cyclic bending”, Journal of Chinese Institute of Engineers, Vol. 39, No. 8, pp. 926-935 (2016).
11. K. L. Lee, K. H. Chang and W. F. Pan, “Effect of notch depth and direction on stability of local sharp-notched circular tubes subjected to cyclic bending”, International Journal of Structural Stability and Dynamics, Vol. 18, No. 7, 1850090 [23 pages] (2018).
12. K. L. Lee, M. L. Weng and W. F. Pan, “On the failure of round-hole tubes under cyclic bending”, Journal of Chinese Society of Mechanical Engineering, Vol. 40, No. 6, pp. 663-673 (2019).
13. K. L. Lee, Q. Y. Wen and W. F. Pan, “Response of round-hole tubes with different hole sizes and positions under pure bending relaxation”, Informatica Journal, Vol. 32, No. 8, pp. 48-65 (2021).
14. K. L. Lee, C. M. Hsu and W. F. Pan, “Response of sharp-notched circular tubes under bending creep and relaxation”, Mechanical Engineering Journal, Vol. 1, No. 2, pp. 1-14 (2014).
15. K. L. Lee, Y. C. Tsai and W. F. Pan, “Mean curvature effect on the response and failure of round-hole tubes submitted to cyclic bending”, Advances in Mechanical Engineering, Vol. 13, No. 11, pp. 1-14 (2021).
16. 胡庭源，“圓孔管在循環彎曲負載下橢圓化成長與臨界橢圓化之研究”，國立成功大學工程科學研究所碩士論文(2021).