本論文主要針對6063-T5鋁合金橢方管，在不同外長軸/外短軸長度比與不同曲率比條件下的循環彎曲負載行為與失效特性進行實驗研究。實驗所探討的外長軸/外短軸長度比分別為1.5、2.0、2.5與3.0，曲率比則為-1、-0.5與0，其定義為最小控制曲率與最大控制曲率的比值。在循環彎曲負載下的響應包括:彎矩-曲率關係以及短軸變化-曲率關係；而破壞行為則透過曲率範圍與循環至破壞圈數之間的關係加以分析。
實驗結果顯示，在相同曲率比下，橢方管的外長軸/外短軸長度比越大，其最大彎矩越小，且隨著循環圈數增加，彎矩-曲率迴圈趨於穩定；當曲率比 = -0.5或0時，彎矩-曲率曲線出現明顯的循環鬆弛現象。橢方管的外短軸變化在所有條件下皆呈現棘齒狀且遞增的趨勢，初期增速較快，隨循環進行逐漸放緩；曲率比 = -1 時曲線呈對稱，曲率比 = -0.5與0時則偏向平均曲率值方向。在破壞行為上，當外長軸/外短軸長度比固定時，循環至破壞圈數隨曲率範圍增加而降低；當曲率範圍固定時，曲率比越接近-1，循環至破壞圈數越大；而當曲率比固定時，循環至破壞圈數則隨外長軸/外短軸長度比的增加而減少。
此外，本研究在已提出的經驗公式基礎上，修正並建立了相關參數與曲率比的關係式，並進一步將材料參數與外長軸/外短軸長度比建立函數關聯。最後，透過這些材料參數成功建立了適用於6063-T5鋁合金橢方管的曲率範圍-循環至破壞圈數理論預測模型，並與實驗結果吻合良好。

This thesis primarily investigates the cyclic bending behavior and failure characteristics of 6063-T5 aluminum alloy elliptical-square tubes under various outer major-to-minor axis length ratios and curvature ratio conditions. The outer major-to-minor axis length ratios examined in this study are 1.5, 2.0, 2.5, and 3.0, while the curvature ratios are −1, −0.5, and 0, defined as the ratio of the minimum controlled curvature to the maximum controlled curvature. Under cyclic bending loading, the mechanical responses analyzed include the moment–curvature relationship and the variation of the minor axis versus curvature. The failure behavior is evaluated through the relationship between the curvature range and the number of number of cycles to failure. The experimental results indicate that, under the same curvature ratio, specimens with a larger outer major-to-minor axis length ratio exhibit a smaller maximum bending moment. Moreover, as the number of loading cycles increases, the moment–curvature hysteresis loops gradually stabilize. When the curvature ratio is −0.5 or 0, a pronounced cyclic ratcheting behavior is observed in the moment–curvature response. The variation of the outer minor axis shows a ratcheting and monotonically increasing trend under all test conditions, with a rapid increase in the early stages followed by a gradual slowdown as cycling proceeds. For a curvature ratio of −1, the response curves are symmetric, whereas for curvature ratios of −0.5 and 0, the curves shift toward the mean curvature direction. Regarding failure behavior, when the outer major-to-minor axis length ratio is fixed, the number of number of cycles to failure decreases with an increasing curvature range. When the curvature range is fixed, specimens with curvature ratios closer to −1 and 0, the curves shift toward the mean curvature direction. Regarding the failure behavior, when the outer major-to-minor axis length ratio is fixed, the number of number of cycles to failure decreases with an increasing curvature range. When the curvature range is fixed, specimens with curvature ratios closer to −1 exhibit a larger number of number of cycles to failure. In addition, for a fixed curvature ratio, the number of number of cycles to failure decreases as the outer major-to-minor axis length ratio increases. Furthermore, based on previously proposed empirical formulas, this study modifies and establishes relationships between the relevant parameters and the curvature ratio, and further formulates functional correlations between the material parameters and the outer major-to-minor axis length ratio. Finally, using these material parameters, a theoretical prediction model for the relationship between curvature range and number of cycles to failure applicable to 6063-T5 aluminum alloy elliptical-square tubes is successfully developed, showing good agreement with 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] 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).
[3] E. Corona and S. Kyriakides, “On the collapse of inelastic tubes under combined bending and pressure”, International Journal of Solids and Structures, Vol. 24, No. 5, pp. 505-535 (1988).
[4] 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).
[5] S. Kyriakides and G. T. Ju, “Bifurcation and localization instabilities in cylindrical shells under bending – I. Experiments”, International Journal of Solids and Structures, Vol. 29, No. 9, pp. 1117-1142 (1992).
[6] 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).
[7] W. F. Pan and Y. S. Her, “Viscoplastic collapse of thin-walled tubes under cyclic bending”, ASME Journal of Engineering Materials and Technology, Vol. 120, No. 4, pp. 287-290 (1998).
[8] 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).
[9] W. F. Pan and K. L. 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] 李慶峰，” 316L不鏽鋼圓管在不同彎曲曲度率循環彎曲負載下對皺曲行為影響之實驗研究”，國立成功大學工程學研究所碩士論文(2004)。
[11] 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).
[12] 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).
[13] A. Limam, L. H. Lee, E. Corona and S. Kyriakides, “Inelastic wrinkling and collapse of tubes under combined bending and internal pressure”, International Journal of Mechanical Sciences, Vol. 52, No. 5, pp. 637-647 (2012).
[14] K. L. Lee, C. M. Hsu and W. F. Pan, “The influence of mean curvatures on the collapse of sharp-notched circular tubes under cyclic bending”, Journal of Chinese Society of Mechanical Engineering, Vol. 34, No. 5, pp. 461-468 (2013).
[15] K. L. Lee, C. M. Hsu and W. F. Pan, “Viscoplastic collapse of sharp-notched circular tubes under cyclic bending”, Acta Mechanics Solida Sinica, Vol. 26, No. 6, pp. 629- 641 (2013).
[16] 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).
[17] 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).
[18] K. L. Lee, H. Y. Liu and W. F. Pan, “Response of round-hole tubes submitted to pure bending creep and pure bending relaxation”, Advances in Mechanical Engineering, Vol. 13, No. 9, pp. 1-17 (2021).
[19] 金力中，“循環彎曲負載下平均曲率對圓孔管響應與失效影響之實驗研究”，國立成功大學工程學研究所碩士論文(2021)。
[20] 周奕錡，“不同外長軸/外短軸長度比之SUS304不鏽鋼橢方管在不同彎曲方向循環彎曲負載下行為之實驗研究”，國立成功大學工程學研究所碩士論文(2021)。
[21] 吳政諭，“不同外長軸/外短軸長度比之6063-T5鋁合金橢方管在不同彎曲方向循環彎曲負載下行為之實驗研究”，國立成功大學工程學研究所碩士論文(2024)。
[22] 鄭怡哲，“不同外長軸/外短軸長度比 SUS304不鏽鋼橢圓管在不同曲率比循環彎曲負載下行為之實驗研究”，國立成功大學工程學研究所碩士論文(2025)。