本文是研究不同圓孔方向與不同圓孔直徑的EMT碳鋼圓孔管在循環彎曲下的行為，其中圓孔的方向有:0°、30°、60°與90°，而不同的圓孔直徑有：2、4、6、8與10 mm。本文將EMT碳鋼圓孔管在不同的控制曲率下進行循環彎曲至疲勞損壞的實驗，所擷取的實驗數據有：曲率、彎矩、橢圓化與循環至損壞圈數。從彎矩-曲率關係中顯示，不論圓孔方向和圓孔直徑是多少，其彎矩-曲率關係都會呈現一穩定的迴圈，而當圓孔直徑越小時，其彎矩的上下限值會稍大，不過差異不會非常明顯，也就是說，圓孔方向與圓孔直徑對彎矩-曲率關係並無顯著的影響。從橢圓化-曲率關係中顯示，橢圓化的程度會隨著循環彎曲的圈數增多，呈現出棘齒、不對稱的成長趨勢，而當圓孔直徑越小或圓孔方向越接近90°時，橢圓化的成長速率就越慢，該關係也越趨於對稱。從控制曲率-循環至損壞圈數的關係中顯示，當控制曲率越大、圓孔直徑越大或圓孔方向越小時，循環至損壞圈數就越少。當考慮在同一圓孔方向下，五種不同圓孔直徑的EMT碳鋼圓孔管承受循環彎曲負載下的控制曲率與循環至損壞圈數雙對數座標關係呈現出五條近乎平行的直線。最後，本文使用Lee等人於2019年所提出的公式並加以修改後，同時根據實驗結果求得EMT碳鋼圓孔管的相關材料常數，接著，利用理論公式進行相關的模擬，在與實驗結果進行比較後顯示，理論能合理的描述實驗結果。

This paper is to study the behavior of EMT carbon steel round-hole tubes with different hole directions and different hole diameters under cyclic bending. The directions of the holes are: 0°, 30°, 60° and 90°,and diameters of the holes are: 2, 4, 6, 8 and 10 mm. In this study, the EMT carbon steel round hole-tubes are subjected to cyclic bending to fatigue failure under different control curvatures. The experimental data collected include: curvature, moment, ovalization and the number of cycles needed to ignite failure. From the moment-curvature relationship, no matter what the direction and diameter of the holes are, the moment-curvature relationship shows a stable loop. When the hole diameter is smaller, the upper and lower limits of the bending moment will be slightly larger, but the difference is not very significant. From the ovalization-curvature relationship, the ovalization increases with the number of cycles, showing a trend of ratcheting, asymmetry and growth. When the hole diameter is smaller or the hole direction closes to 90°, the slower the growth rate of ovalization, the more symmetrical the relationship becomes. From the relationship between the control curvature and the number of cycles needed to ignite failure, when the control curvature is larger, the hole diameter is larger, or the hole direction is smaller, the number of cycles needed to ignite failure is less. When considering the same hole direction, five different hole diameters correspond to five nearly parallel straight lines for the control curvature-number of cycles needed to ignite failure relationships in double logarithmic coordinates. Finally, this study modifies the formula proposed by Lee et al. in 2019, and at the same time obtains the material constants of the EMT carbon steel round-hole tube according to the experimental. It has been shown 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 the 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 the 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).