本研究針對不同外長軸/外短軸長度比的SUS 304不鏽鋼橢方管在不同曲率範圍循環彎曲負載下的對外短軸變化及臨界外短軸探討進行實驗，其中不同的外長軸/外短軸長度比，各別為：1.5、2.0、2.5與3.0，所探討的控制曲率範圍κc = (±0.5 m⁻¹ 至 ±0.8 m⁻¹)。
　　根據實驗結果，外短軸變化與循環圈數關係變形歷程可分為三個階段：初始階段: 外短軸變化成長迅速，此時表面同時出現上凹面與下凹面區分；第二階段:外短軸變化成長趨緩，上凹面裂紋從應力集中的邊緣向中心穩定成長；第三階段: 外短軸變化相對微小，下凹面承受疲勞性累積損傷，裂紋緩慢成長直至試件完全斷裂。根據上述，本研究專注全階段的外短軸變化探討。實驗結果進一步發現，當外長軸/外短軸長度比固定時，控制曲率增加，而臨界外短軸變化值愈大；而且，當控制曲率固定時，外長軸/外短軸長度比增加，臨界外短軸變化值也愈大，從曲線圖可發現幾何變化越大與控制曲率越大對臨界外短軸變化值有加乘效應。
　　在模型預測方面，本研究修正Lee等人 [21] 針對圓管所提出的橢圓化經驗公式，將實驗數據透過擬合求得符合SUS 304不鏽鋼橢方管的相關材料參數，並建立預測模型，預測於全階段之外短軸變化與循環圈數對應關係，可找出外短軸變化最劇烈的時所對應的該循環圈數。最後，本研究提出可描述臨界外短軸變化與控制曲率之線性預測模型，對不同幾何形參數下，預測其外短軸臨界變化行為。

This study experimentally investigates the external minor axis variations and critical external minor axis behavior of SUS 304 stainless steel Oval-Rectangular tubes with different aspect ratios (ratio of external major axis to external minor axis) subjected to cyclic bending loads under various curvature ranges. The investigated aspect ratios are 1.5, 2.0, 2.5, and 3.0, and the controlled curvature range κc = (±0.5 m⁻¹ to ±0.8 m⁻¹). Based on the experimental results, the deformation history relating the external minor axis variation to the number of cycles can be categorized into three distinct stages: Initial Stage: The external minor axis variation grows rapidly, accompanied by the concurrent appearance of distinct upper and lower concave regions on the surface. Second Stage: The growth of the external minor axis variation slows down, during which cracks in the upper concave region propagate stably from the stress-concentrated edges toward the center. Third Stage: The variation in the external minor axis becomes relatively minor; the lower concave region undergoes cumulative fatigue damage, with cracks growing slowly until total specimen fracture. Accordingly, this study focuses on analyzing the external minor axis variation across all three stages. Furthermore, the experimental results reveal that when the aspect ratio is held constant, an increase in controlled curvature leads to a larger critical external minor axis variation value. Likewise, when the controlled curvature is fixed, an increase in the aspect ratio also results in a larger critical value. The response curves demonstrate a synergistic effect, where larger geometric variations combined with higher controlled curvatures significantly increase the critical external minor axis variation value. Regarding predictive modeling, this study modifies the empirical ovalization formula proposed by Lee et al. [21] for circular tubes. By fitting the experimental data, relevant material parameters suitable for SUS 304 stainless steel Oval-Rectangular tubes were determined, establishing a predictive model to capture the relationship between external minor axis variation and cycle count throughout all stages. This model effectively identifies the cycle count corresponding to the most severe external minor axis variation. Finally, a linear predictive model capable of describing the relationship between critical external minor axis variation and controlled curvature is proposed to predict the critical variation behavior under various geometric parameters.

1.L.G. Brazier, “On the flexure of thin cylindrical shells and other “thin sections”, Proceeding of Royal Society, Series A, Vol. 116, pp.104-114 (1927).
2.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).
3.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).
4.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).
5.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).
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.W. F. Pan and C. H. 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).
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.K. L. Lee and W. F. Pan, “Pure bending creep of SUS304 stainless steel tubes”, Steel and Composite Structures, Vol. 2, No. 6, pp. 461-474 (2002).
11.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).
12.K. H. Chang, C. M. Hsu, S. R. Sheu and W. F. Pan, “Viscoplastic response and collapse of 316L stainless steel under cyclic bending”, Steel and Composite Structures, Vol. 5, No. 5, pp. 359-374 (2005).
13.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).
14.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).
15.A. Limam, L. H. Lee and S. Kyriakides, “On the collapse of dented tubes under combined bending and internal pressure”, International Journal of Solids and Structures, Vol. 55, No. 1, pp. 1-12 (2010).
16.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 (2010).
17.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).
18.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).
19.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).
20.K. L. Lee, C. J. Lin and W. F. Pan, “Mechanical behavior and buckling failure of local sharp-notched SUS304 stainless steel tubes subjected to cyclic bending” , Journal of Science and Engineering Technology, Vol. 11, No. 1, pp. 9-19 (2015).
21.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).
22.劉林威，” 不同外長軸/短軸長度比橢圓管在循環彎曲負載下外短軸變化與臨界外短軸變化之研究”，國立成功大學工程科學研究所碩士論文(2024).
23.王重諺，” 不同外長軸/外短軸長度比之 6063-T5 鋁合金橢方管在循環彎曲負載下外短軸變化與臨界外短軸變化之實驗研究”，國立成功大學工程科學研究所碩士論文(2025).