Local Buckling of Locally Sharp-Notched C2700 Brass Circular Tubes Subjected to Cyclic Bending
Abstract
:1. Introduction
2. Experiments
2.1. Experimental Devices
2.2. Material and Specimens
2.3. Test Procedures
3. Experimental Results and Discussion
3.1. M-κ Relationships
3.2. D/Do-κ Relationships
3.3. Controlled Curvature (κc/κo)-Nb Relationships
4. Conclusions
- (1)
- When local buckling has not yet occurred, it is observed from the experimental M-κ relationships that as κ increases, M also increases. Under cyclic bending loads, the M-κ relationship exhibits a stable loop until eventual local buckling failure. Additionally, results indicate that for different values of ϕ and a, the M-κ relationships show similar loops. This phenomenon is consistent with the experimental results reported by Lee et al. [29].
- (2)
- When local buckling has not yet occurred, it is observed from the experimental ΔD/Do-κ relationships that higher κ leads to increased ΔD/Do. Larger a or smaller ϕ values correspond to increased ΔD/Do. This phenomenon is consistent with the experimental results of Lee et al. [29]. In addition, under cyclic bending loads, the ΔD/Do-κ relationships exhibit a ratcheting, symmetrical, and growing trend. A less consistent observation with the experimental results of Lee et al. [29] is that when a is small, the ΔD/Do-κ relationships are symmetrical, but when a is large, the ΔD/Do-κ relationships are asymmetrical.
- (3)
- The experimental κc/κo-Nb relationships reveal that, when ϕ and a are fixed, larger κc/κo leads to fewer Nb. Fixing ϕ and κc/κo, larger a results in fewer Nb. Conversely, when fixing a and κc/κo, larger ϕ leads to more Nb. When ϕ is fixed, the relationships of κc/κo-Nb for five different a on double logarithmic coordinates exhibit nearly straight lines. This phenomenon is consistent with the experimental results of Lee et al. [29]. However, for a certain ϕ, they show almost-parallel lines, while we found non-parallel lines.
- (4)
- This study adopts the formula (Equation (3)) proposed by Kyriakides and Shaw [1] to describe the κc/κo-Nb relationships. The formulation of the material parameter C in Equation (4) proposed by Lee et al. [29] was used in this study. However, the material parameter m (Equation (5)) was proposed based on the experimental data. Additionally, a new equation for the material parameter α is proposed (Equation (8)), where material parameters β and γ are derived from Equations (9) and (10), respectively. Note that Equations (5), (9) and (10) are restricted to use between 0° and 90°. Finally, the theoretical Equations (Equations (3)–(5) and (7)–(10)) are employed to describe the κc/κo-Nb relationships for LSN C2700 brass circular tubes under cyclic bending with varying ϕ values: 0°, 30°, 60°, 90°, and different a (dashed lines in Figure 14a–d), and the results of experimental and theoretical analyses are reasonably consistent.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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(a) ϕ = 0° | |||||
κc/κo | a = 0.2 mm | a = 0.4 mm | a = 0.6 mm | a = 0.8 mm | a = 1.0 mm |
0.33 | 542 | 303 | 192 | 112 | 65 |
0.29 | 694 | 403 | 249 | 154 | 93 |
0.26 | 890 | 511 | 316 | 212 | 128 |
0.23 | 1125 | 703 | 432 | 292 | 196 |
0.20 | 1734 | 988 | 694 | 423 | 305 |
(b) ϕ = 30° | |||||
κc/κo | a = 0.2 mm | a = 0.4 mm | a = 0.6 mm | a = 0.8 mm | a = 1.0 mm |
0.33 | 847 | 439 | 219 | 145 | 97 |
0.29 | 986 | 571 | 309 | 182 | 131 |
0.26 | 1270 | 765 | 413 | 273 | 175 |
0.23 | 1765 | 1042 | 512 | 314 | 260 |
0.20 | 2664 | 1347 | 698 | 456 | 314 |
(c) ϕ = 60° | |||||
κc/κo | a = 0.2 mm | a = 0.4 mm | a = 0.6 mm | a = 0.8 mm | a = 1.0 mm |
0.33 | 1605 | 1028 | 657 | 442 | 298 |
0.29 | 2293 | 1476 | 1059 | 661 | 422 |
0.26 | 2958 | 1821 | 1293 | 913 | 567 |
0.23 | 4191 | 2155 | 1803 | 1201 | 704 |
0.20 | 5705 | 3792 | 2430 | 1644 | 1155 |
(d) ϕ = 90° | |||||
κc/κo | a = 0.2 mm | a = 0.4 mm | a = 0.6 mm | a = 0.8 mm | a = 1.0 mm |
0.33 | 2876 | 2277 | 1687 | 1325 | 1141 |
0.29 | 3977 | 3374 | 2257 | 1888 | 1534 |
0.26 | 5528 | 4002 | 3532 | 2587 | 1898 |
0.23 | 7297 | 6339 | 4611 | 3722 | 2936 |
0.20 | 11,338 | 8867 | 6487 | 5481 | 4930 |
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Chen, Y.-A.; Pan, W.-F. Local Buckling of Locally Sharp-Notched C2700 Brass Circular Tubes Subjected to Cyclic Bending. Metals 2024, 14, 656. https://doi.org/10.3390/met14060656
Chen Y-A, Pan W-F. Local Buckling of Locally Sharp-Notched C2700 Brass Circular Tubes Subjected to Cyclic Bending. Metals. 2024; 14(6):656. https://doi.org/10.3390/met14060656
Chicago/Turabian StyleChen, Yu-An, and Wen-Fung Pan. 2024. "Local Buckling of Locally Sharp-Notched C2700 Brass Circular Tubes Subjected to Cyclic Bending" Metals 14, no. 6: 656. https://doi.org/10.3390/met14060656