本研究主要探討S45C中碳鋼直角扇形管於不同彎曲方向條件下，在對稱控制曲率循環彎曲載重作用時之力學行為與破壞特性。實驗中選用四種不同外半徑之直角扇形管，分別為20、30、40及50 mm，並施加六種對稱控制曲率條件，分別為±0.5、±0.55、±0.6、±0.65、±0.7及±0.75 m⁻¹。此外，試件依據截面擺放方向設定四種彎曲方向，分別為0°、15°、30°及45°，且所有試件之壁厚均固定為1 mm，以進行循環彎曲試驗及相關力學特性分析。
實驗結果顯示，由彎矩－曲率關係可知，所有S45C中碳鋼直角扇形管在循環彎曲載重作用下，最終皆形成穩定的彈塑性迴圈。當彎曲方向固定時，隨著外半徑增加，試件所對應之最大彎矩值亦隨之提高；反之，在外半徑固定的情況下，彎曲方向角度愈大，所需承受之彎矩值亦愈高。此外，由外半徑變化－曲率關係可觀察到，不論外半徑尺寸或彎曲方向為何，各試件皆呈現棘齒狀逐漸增長的變化特徵，且隨循環次數增加而持續累積，顯示其對試件截面變形具有明顯影響。
在控制曲率與循環至損壞圈數之關係方面，實驗結果顯示，於相同控制曲率條件下，外半徑較大的直角扇形管其循環壽命較短，亦即達到損壞所需之循環圈數較少。進一步將實驗數據繪製於雙對數座標圖中，可發現不同外半徑之試件分別形成四條近似直線。最後，本研究根據實驗結果建立一套理論模型，用以描述不同外半徑S45C中碳鋼直角扇形管於各彎曲方向條件下，在對稱控制曲率循環彎曲載重作用時，控制曲率與循環至損壞圈數之間的關聯性。理論分析結果與實驗數據具有良好的一致性，證明所建立之模型能有效預測S45C中碳鋼直角扇形管於循環彎曲載重下之損壞圈數與破壞行為。

This study investigates the mechanical behavior and failure characteristics of S45C medium-carbon steel right-angle sector tubes subjected to symmetric curvature-controlled cyclic bending under different bending directions. Four types of right-angle sector tubes with outer radius of 20, 30, 40, and 50 mm were employed. Six symmetric curvature-controlled loading amplitudes, namely ±0.5, ±0.55, ±0.6, ±0.65, ±0.7, and ±0.75 m⁻¹, were applied during the cyclic bending tests. In addition, four bending directions (0°, 15°, 30°, and 45°) were considered according to the orientation of the tube cross-section. The wall thickness of all specimens was maintained at 1 mm to investigate their cyclic bending behavior and mechanical characteristics.
The experimental results indicate that all S45C medium-carbon steel right-angle sector tubes eventually developed stable elastoplastic hysteresis loops in the moment-curvature relationship under cyclic bending. When the bending direction was kept constant, the maximum bending moment increased with increasing outer radius. Conversely, for specimens with the same outer radius, the maximum bending moment increased as the bending direction angle increased. Furthermore, the outer-radius change-curvature relationship revealed that all specimens exhibited a progressive ratcheting behavior regardless of the outer radius or bending direction. The accumulated deformation increased continuously with the number of loading cycles, indicating a significant influence of cyclic bending on the cross-sectional deformation of the tubes.
Regarding the relationship between the controlled curvature and the number of cycles to failure, the experimental results showed that, under the same controlled curvature, specimens with larger outer radius exhibited shorter fatigue lives, requiring fewer loading cycles to reach failure. When the experimental data were plotted on double-logarithmic coordinates, the results for the four outer radius formed four approximately straight lines. Based on these experimental observations, a theoretical model was established to describe the relationship between the controlled curvature and the number of cycles to failure for S45C medium-carbon steel right-angle sector tubes with different outer radius under various bending directions. The theoretical predictions showed good agreement with the experimental results, demonstrating that the proposed model can effectively predict the fatigue life and failure behavior of S45C medium-carbon steel right-angle sector tubes subjected to symmetric curvature-controlled cyclic bending.

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