本研究主要針對不同尺寸的SUS304不鏽鋼方形管在各種循環彎曲負載下行為進行實驗研究，其中方形管有四種外邊長的截面，分別為：20、30、40和50 mm，方形管主要受六種對稱控制曲率分別有：±0.5、±0.55、±0.6、±0.65、±0.7和±0.75 m-1。實驗係以彎管實驗機進行循環彎曲負載的測試，實驗結果包含在循環彎曲負載下的彎矩-曲率及外邊長變化率-曲率的關係來呈現力學行為，並以控制曲率-循環至損壞圈數的關係來呈現失效損壞。
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，較快速達到穩定迴圈，外邊長較大時，迴圈會先循環軟化後才呈現穩定。外邊長變化率-曲率關係呈現出對稱、棘齒與隨時間增加的趨勢，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呈現，在相同的控制曲率下，外邊長較大時，循環至損壞的圈數就越少。若將控制曲率-循環至損壞圈數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進行理論分析，在與實驗結果比較後，顯示實驗結果與理論分析有一致性。

This research experimentally investigated the mechanical behavior and failure characteristics of SUS304 stainless steel square tubes with varying outer side lengths subjected to cyclic symmetric bending under different curvature levels. The tube side lengths examined were 20 mm, 30 mm, 40 mm, and 50 mm, while the applied symmetric curvatures were ±0.35, ±0.4, ±0.45, ±0.5, ±0.55, and ±0.6 m⁻¹. A comprehensive test setup, 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 rate of outer side length (variation rate 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 loop pattern. When the outer side length was smaller, a stable loop was reached more quickly; when the outer side length was larger, the loop stabilized after undergoing cyclic softening. The outer side length variation rate–curvature relationship displayed a symmetric, ratcheting, and progressively increasing trend, where larger outer side lengths led to faster changes in side length. Regarding the control curvature–number of cycles to failure relationship, under the same control curvature, specimens with larger outer side lengths failed in fewer cycles. When this relationship was plotted on a double logarithmic scale, the four different outer side lengths corresponded to four distinct straight lines. Finally, a theoretical analysis of the control curvature–number of cycles to failure relationship was conducted, and comparison with the experimental results showed good consistency between theory and experiment.

1.L. G. Brazier, “On the flexure of thin cylindrical shells and other thin sections”, Proceedings of the Royal Society, Series A, Vol. 116, No. 773, pp. 104-114 (1927).
2.R. M. Korol, “Critical buckling strains of round tubes in flexure”, International Journal of Mechanics and Science, Vol. 21, No. 12, pp. 719-730 (1979).
3.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).
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.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).
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.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).
8.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).
9.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).
10.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).
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. 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).
16.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).
17.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).
18.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).
19.M. C. Yu and W. F. Pan, “Failure of elliptical tubes with different long-short axis ratios under cyclic bending in different directions”, Metals, Vol. 13, No. 11, 1891, (2023).
20.W. F. Pan and Y. A. Chen, “Response and fracture of EMT carbon steel round-hole tubes with different hole orientations and different hole diameters under cyclic bending”, Applied Sciences, Vol. 14, No. 13, 5475 (2024).