本文使用有限元素軟體ANSYS Workbench 17.0分析相同截面不同孔徑多餘圓孔的6061-T6鋁合金圓孔管在循環彎曲負載下的力學行為，其中圓孔管的圓孔位於截面角度0o (y-方向，主圓孔)圓孔直徑固定為6 mm，而位於截面90o (x-方向，多餘圓孔)有五種不同多餘圓孔直徑，分別為:2、4、6、8與10 mm，至於相關的力學行為包含有：彎矩-曲率關係與橢圓化-曲率關係。
　　由朱柏穎【18】的實驗結果可看到，改變不同直徑的多餘圓孔對彎矩-曲率關係幾乎沒有明顯的影響，且從第一圈循環開始，該曲線即為一穩定迴圈。而橢圓化-曲率關係皆呈現棘齒狀且不對稱的形式成長，且當多餘圓孔直徑為2 mm和4 mm時，橢圓化值最小；而多餘圓孔直徑10 mm時橢圓化值最大。ANSYS分析與實驗結果互相比對後，證實模擬與實驗結果相當吻合。由於實驗試件的毀損型態是疲勞破壞，因此本文使用一個簡單的疲勞模式來估算疲勞壽命。根據計算的最大應力及最小應力數值上並無太大的差異，所以平均應力影響不列入考慮。根據分析結果顯示，本文所提出的疲勞模式能適當的預測相同截面但不同孔徑多餘圓孔的6061-T6圓孔管在循環彎曲負載下的疲勞壽命。

In this study, the finite element software ANSYS Workbench 17.0 is used to analyze the mechanical response of round-hole 6061-T6 aluminum alloy tubes with a redundant hole of different diameters on the same cross-section under cyclic bending load. The circular hole of the round- hole tubes is located on the section at the angle 0o (y-direction) with a fixed diameter of 6 mm. The redundant hole is on the section at the angle 90o (x-direction) with five different diameters of 2, 4, 6, 8, and 10 mm. The mechanical response includes the moment-curvature and ovalization- curvature relationships.
It can be seen from the experimental results of Zhu [18] that changing the diameters of the redundant hole has no obvious influence on the moment- curvature relationship. It is a stable loop from the first bending cycle. The ovalization-curvature relationships show a ratcheting and asymmetrical look. The ovalization is smaller when the redundant hole diameters are 2 mm and 4 mm, and the ovalization is the largest when its diameter is 10 mm. After comparing with the ANSYS analysis and the experimental results, it is confirmed that the simulation was similar with the experimental results. Since the fatigue failure is the fracture pattern, a simple fatigue model is used to estimate the fatigue life. There is not much difference between the maximum stress and the minimum stress, so the mean stress effect is not considered. According to the analysis results, the fatigue mode proposed in this study can properly predict the fatigue life of round-hole 6061-T6 aluminum alloy tubes with a redundant hole on the same cross-section but with of different diameters under cyclic bending.

1. Kyriakides, S. and Shaw, P. K. “Response and Stability of Elastoplastic Circular Pipe Under Combined Bending and External Pressure,＂International Journal of Solids and Structures, Vol. 18, No. 11, pp. 957- 973, 1982.

2. Shaw, P. K. and Kyriakides, S. “Inelastic Analysis of Thin-Walled Tubes Under Cyclic Bending,＂International Journal of Solids and Structures, Vol. 21, No. 11, pp. 1073-1100, 1985.

3. Pan, W. F., Wang, T. R. and Hsu, C. M. “A Curvature-Ovalization Measurement Apparatus for Circular Tubes Under Cyclic Bending,” Experimental Mechanics, Vol. 38, No. 2, pp. 99-102 , 1998.

4. Lee, K. L., Pan, W. F. and Hsu, C. M. “Experimental and Theoretical Evaluations of the Effect Between Diameter-to-Thickness Ratio and Curvature-Rate on the Stability of Circular Tubes Under Cyclic Bending,” JSME International Journal, Series A, Vol. 47, No. 2, pp. 212-222, 2004.

5. Lee, K. L., Hung, C. Y. and Pan, W. F. “Variation of Ovalization for Sharp-Notched Circular Tubes Under Cyclic Bending,” Journal of Mechanics, Vol. 26, No. 3, pp. 403- 411, 2010.

6. Lee, K. L., Hsu, C. M. and Pan, W. F. “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.

7. Lee, K. L. Chan, Y. T. and Pan, W. F. “Finite Element ANSYS Analysis of the Behavior for 6061-T6 Aluminum Tubes under Cyclic Bending with External Pressure,” Journal of Civil Engineering and Architecture, Vol. 8, No. 6, pp. 673-679, 2014.

8. Lee, K. L., Wang, Y. and Pan, W. F. “Finite Element Analysis on the Response of Local Sharp-notched Circular Tubes under Cyclic Bending,” Key Engineering Materials, Vol. 626, pp. 34-39, 2015.

9. Y. Miyano, M. Nakada, H. Kudoh and R. Muki “Prediction of tensile fatigue life Under temperature environment for unidirectional CFRP,” Advanced Composite Materials, Vol. 8, No. 3, pp. 235-246, 1999.

10. 林煒凱，「有限元素ANSYS分析橢圓形凹槽薄壁管在循環彎曲負載下之力學行為」，國立成功大學工程科學研究所碩士論文，2008。

11. 葉弘文，「有限元素分析尖銳凹槽SUS304不鏽鋼圓管在循環彎曲負載下之力學行為」，國立成功大學工程科學研究所碩士論文，2012。

12. 洪揚銘，「有限元素分析局部尖銳凹槽圓管在循環彎曲負載下之行為」，國立成功大學工程科學研究所碩士論文，2013。
13. 孟慶勳，「有限元素分析局部凹痕圓管在循環負載下之行為」，國立成功大學工程科學研究所碩士論文，2014。

14. 曾詠茹，「有限元素分析不同外徑/壁厚比局部圓形凹痕圓管在循環彎曲負載下之行為」，國立成功大學工程科學研究所碩士論文，2016。

15. 陳伯宜，「圓形凹痕圓管在循環彎曲負載下毀損模式之研究」，國立成功大學工程科學研究所碩士論文，2017。

16. 吳尚儒，「有限元素分析圓孔管在循環彎曲負載下之行為」，國立成功大學工程科學研究所碩士論文，2018。

17. 林均澤，「相同截面不同方向的多餘圓孔對圓孔管承受循環彎曲負載下行為影響之研究」，國立成功大學工程科學研究所碩士論文，2019。

18. 朱柏穎，「相同截面不同孔徑的多餘圓孔對圓孔管承受循環彎曲負載下行為影響之研究」，國立成功大學工程科學研究所碩士論文，2019。

19. Kyriakides, S. and Shaw, P.K., “Inelastic Buckling of Tubes under Cyclic Load”, ASME Journal of Pressure Vessel Technology, Vol. 109, pp. 169- 178,1987.