本研究針對不同外邊長的6063-T5鋁合金方形管在不同對稱曲率循環彎曲負載下的響應與失效進行實驗研究，其中不同的外邊長分別為:20、30、40和50 mm，以及不同的對稱控制曲率分別有:±0.35、±0.4、±0.45、±0.5、±0.55和±0.6 m-1。實驗使用一系列設備，包括有：彎管實驗機、油壓伺服控制系統、橢圓化量測器和電腦監控系統等，測量並分析方形管在循環彎曲負載下的彎矩-曲率、外邊長變化(外邊長變化量/原始外邊長)-曲率以及控制曲率-循環至損壞圈數關係。
實驗結果顯示，彎矩-曲率關係呈現出迴圈的型態，外邊長較小時，迴圈會循環硬化後呈現穩定；外邊長較大時，迴圈會循環軟化後呈現穩定。而外邊長變化-曲率關係則呈現出對稱、棘齒與增加的趨勢，外邊長越大時，外邊長變化就越快。至於控制曲率-循環至損壞圈數關係則呈現，在相同的控制曲率，外邊長較大時，循環至損壞圈數就越少。若將上述的關係繪製於雙對數坐標下，則四種不同的外邊長對應出四條直線。最後，本研究針對控制曲率-循環至損壞圈數關係提出相關的理論分析，在與實驗結果比較後顯示，實驗結果與理論分析相當契合。

This study conducted experimental research on the response and failure of 6063-T5 aluminum alloy square tubes with different outer side lengths under various symmetric curvature cyclic bending loads. The different outer side lengths were 20, 30, 40, and 50 mm, and the different symmetric control curvatures were ±0.35, ±0.4, ±0.45, ±0.5, ±0.55, and ±0.6 m⁻¹. The experiments used a series of equipment, including a pipe bending test machine, a hydraulic servo control system, an ovalization measurement device, and a computer monitoring system, to measure and analyze the moment-curvature, variation of outer side length (variation of outer side length/original outer side length)-curvature, and control curvature-number of cycles required to initiate to failure relationships under cyclic bending loads.
The experimental results showed that the moment-curvature relationship exhibited a hysteresis loop. For smaller outer side lengths, the loop stabilized after cyclic hardening, while for larger outer side lengths, the loop stabilized after cyclic softening. The variation of outer side length-curvature relationship showed a symmetric, ratcheting, and increasing trend, with larger outer side lengths resulting in faster variation. Regarding the control curvature-number of cycles required to initiate to failure relationship, for the same control curvature, larger outer side lengths resulted in fewer cycles to failure. When these relationships were plotted on a double logarithmic scale, four straight lines corresponding to the four different outer side lengths were observed. Finally, this study proposed a theoretical analysis of the control curvature-number of cycles required to initiate to failure relationship, and a comparison with the experimental results showed a good agreement between the two.

[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] 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).
[5] E. Corona and S. Vaze, “Buckling of elastic-plastic square tubes under bending”, International Journal of Mechanical Science, Vol. 38, No. 7, pp. 753-775 (1996).
[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] K. H. Chang, W. F. Pan and K. L. Lee, “Mean moment effect on circular thin-walled tubes under cyclic bending”, Structural Engineering and Mechanics, Vol. 28, No. 5, pp. 495-514 (2008).
[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, H. Y. Chang and W. F. Pan, “Buckling life estimation of circular tubes of different materials under cyclic bending”, Journal of Chinese Institute Engineers, Vol. 33, No. 2, pp. 177-189 (2010).
[13] 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).
[14] 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).
[15] 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).
[16] 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).
[17] 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).
[18] C. C. Chung, K. L. Lee and W. F. Pan, “Collapse of sharp-notched 6061-T6 aluminum alloy tubes under cyclic bending”, International Journal of Structural Stability and Dynamics, Vol. 16, No. 7, 1550035 [24 pages] (2016).
[19] 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).
[20] 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).
[21] 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).