Variation of the 90° Redundant-hole Diameter Effect on the Response and Failure of Round-hole 6061-T6 Aluminum Alloy Tubes under the Cyclic Bending

This paper presents an experiment and an analysis for examining the variation of the 90° redundanthole diameter effect on the cyclic bending mechanical behavior and fracture failure of round-hole 6061-T6 aluminum alloy tubes. In this investigation, a round-hole 6061-T6 aluminum alloy tube with a 6 mm hole diameter was drilled to obtain a 90° redundant hole but with different hole diameter of 2, 4, 6, 8, or 10 mm. It can be observed that from the first bending cycle, the bending moment-curvature curve describes a stable loop. The diameter of the 90° redundant hole has little effect on the bending moment-curvature relationship. However, when the number of bending cycles increases, the ovalization-curvature curve shows an increasing, asymmetrical, ratcheting, and bow-like tendency. The diameter of 90° redundant-hole shows a significant influence on the ovalization-curvature relationship. In addition, five non-parallel straight lines corresponding to five different 90° redundant hole diameters were discovered for the controlled curvature-number of bending cycles necessary to cause failure relationship on the double logarithmic coordinates. Finally, a formula was presented to simulate the above relationship. It is found that the experimental and analytical data were in good agreement.


Introduction
Round-hole tube (abbreviation: RHT) is a tube drilled with a round hole. RHT is usually used as a connection for automobile, motorcycle or bicycle parts. When RHT bears a bending load, the circular cross section will gradually become elliptical as the degree of bending increases. The bending stiffness of the RHT will gradually decrease, which is called deterioration. A quantity "ovalization" is used to describe the deterioration, which is the decrease in the outer diameter (ΔDo) divided by the original outer diameter (Do). ΔDo/Do increases with the number of cycles in cyclic bending load. Eventually, RHT will suffer fracture damage when a certain number of cycles is attained.
So far, the research on the cyclic bending of smooth circular tubes has achieved important results. In 1987, Professor Kyriakides and his research team designed a mechanical device for cyclic bending tests on various round pipes (6061-T6 aluminum alloy pipe, 1018 steel pipe, 304 stainless steel pipe, 1020 steel pipe and NiTi pipe) with or without internal or external pressure, many experiments and theoretical studies have been conducted under monotonic or cyclic bending [1][2][3][4][5][6]. In addition, many scholars have also presented related research. Elchalakani et al. [7] carried out experimental tests on C350 steel pipes with different diameter/thickness ratios (Do/t ratio) under bending. Jiao and Zhao [8] examined the bending response of very-high-strength steel pipes. Houliara and Karamanos [9] studied the in-phase bending buckling of pressured thin-walled tubes. Yazdani and Nayebi [10] studied the fatigue damage and ratcheting behavior of thin-walled pipes subjected to cyclic bending with a stable internal pressure. By using the measured strain in the plastic bending test, the new ductile slenderness limits of the CFT structural plastic design was determined by Elchalakani et al. [11]. Li and Wang [12] studied the stability of reinforced single-layer lattice shells under earthquake action. Chegeni et al. [13] explored the influence of corrosion shape and depth on the response of internal pressure bending pipes.
In 2010, Pan et al. began to study the response of notched tubes under cyclic bending loads. Lee et al. [14] studied the cyclic bending change of ΔDo/Do of sharp-notched circular tubes. Lee et al. [15] discussed the rupture of sharp-notched SUS304 stainless steel pipes periodically bent under different curvatures. This work also studied the changes in curvature and notch depth. Chung et al. [16] studied the cyclic bending stability of the sharp-notched 6061-T6 aluminum alloy tube. However, all of the above-mentioned studies are for circumferential notched tubes. Thereafter, Lee et al. [17] inspected the cyclic bending degradation and failure of 6061-T6 aluminum alloy tubes with local sharp cuts. In addition, the relationship between bending moment (M)-curvature (κ) and ΔDo/Do-κ was analyzed by ANSYS. Lee et al. [18] studied the cyclic bending response of SUS304 stainless steel pipes with local sharp grooves. In their research, ANSYS also analyzed the M-κ and ΔDo/Do-κ relationships.
In this study, the effect of 90° redundant hole diameter on the response and failure of round-hole 6061-T6 aluminum alloy tubes (abbreviation: Al 6061-T6 RHTs) subjected to cyclic bending was investigated. Al 6061-T6 RHT with a 6 mm hole diameter was drilled to obtain a 90° redundant hole but with different hole diameter of 2, 4, 6, 8, or 10 mm. The experimental study is a cyclic bending test of curvature control. The M, κ and ΔDo/Do were measured by the test device. In addition, the number of bending cycles necessary to cause failure (Nf) was also recorded. process. Based on the angle change, the κ can be obtained by simple calculation. The calculated version can be discovered in the paper by Pan et al. [19]. The ΔDo/Do can also be measured in the central part of the device including the magnetic detector and the magnetic block.

Material and specimens
The 6061-T6 aluminum alloy round tube is used in this study. Its chemical composition (weight percentage) is Mg 0.916, Si 0.733, Cu 0.293, Ti 0.268, Fe 0.256, Mn 0.132, Zn 0.0983, Cr 0.0682, Ni 0.0056, and Pb 0.005, Sn <0.001 and Al remains. The mechanical properties of the material are: yield stress of 282 MPa, ultimate tensile stress of 313 MPa, and percentage elongation of 13%.
In this study, we drilled the original 6061-T6 aluminum alloy tube with outer diameter (Do) of 35.0 mm and wall thickness (t) of 3.0 mm to obtain RHT with a 6 mm-hole-diameter. Next, we drilled a φ = 90° redundant hole on the same cross section, and its redundant hole diameter (d) was 2, 4, 6, 8 or 10 mm. Fig. 3 demonstrates a schematic diagram of the RHT with a φ redundant hole, and Fig. 4 depicts the dimensions of Al 6061-T6 RHT with a φ = 90° redundant hole. Note that the same cross section is the A-A cross section. As shown in Fig. 3, the direction of the round hole on the RHT is the y direction. Since the cyclic bending moment is in the z direction, the cyclic bending causes the most serious deterioration and damage to the RHT.

Test procedures
The experiment was a curvature controlled cyclic bending test, and the curvature rate was a constant at 0.03 m −1 s −1 . The M is measured by two load cells (Fig. 1) installed in the pipe bender. As shown in Fig. 2, the κ and ΔDo/Do were measured by a curvature-ovalization measurement device. The Nf was also recorded. Figs. 6(a)-6(c) respectively depict the experimental cyclic ΔDo/Do-κ relationships for Al 6061-T6 RHTs with φ = 90° and d = 2, 6 and 10 mm redundant holes subjected to cyclic bending. It is observed that as the number of bending cycles increases, the ΔDo/Do-κ relationship shows an increasing, asymmetrical, ratcheting, and bow-like tendency. In addition, when the round hole is under tension, ΔDo/Do continues to increase. However, when the round hole is under compression, ΔDo/Do continues to decrease. Fig. 7 presents the experimental controlled curvature (κc/κo)-Nf relationships for Al 6061-T6 RHTs with φ = 90° and different d redundant holes under cyclic bending. Note that the κc was normalized by κo = t/Do 2 . Next, the data in Fig. 7 was plotted on double logarithmic coordinates, and five non-parallel straight lines were found in Fig.  8. Note that these lines were obtained by the method of least squares.

Fracture failure
In our research, the failure type was fatigue fracture. Therefore, the empirical formula proposed by Kyriakides and Shaw [1] was modified to: Here, C is the value of κc/κo when Nf is equal to 1, and α is the slope of the straight line of the log-log graph.
According to the experimental data in Fig. 8, five magnitudes of C were respectively obtained for d = 2, 4, 6, 8 and 10 mm from Eq. (1b) to be 0.331, 0.312, 0.356, 0.310 and 0.320. According to the experimental data in Fig.   8, five magnitudes of α were respectively determined for d = 2, 4, 6, 8 and 10 mm from Eq. (1b) to be 0.165, 0.152, 0.174, 0.159 and 0.163. Fig. 9 depicts the relationship between C and d/t. The following formulation was proposed: where c 1 , c 2 and c 3 are material parameters. When the d/t value is 0.667, the value of c 1 can be determined to be 0.331. The value of c 2 is the amplitude of the periodic function and the value of c 3 is the parameter of the correction period. Therefore, from Fig. 9, the values of c 2 and c 3 can be respectively determined to be 0.025 and 1.125. Fig.   10 depicts the relationship between α and d/t. The following formulation was proposed: where a 1 , a 2 and a 3 are material parameters. When the d/t value is 0.667, the value of a 1 can be determined to be 0.165. The value of a 2 is the amplitude of the periodic function and the value of a 3 is the parameter of the correction period. Therefore, from Fig. 10, the values of a 2 and a 3 can be respectively obtained to be 0.012 and 1.132. Finally, using Eqs.

Conclusions
The response and failure of Al 6061-T6 RHTs with φ = 90° and different d redundant holes subjected to cyclic bending were explored. Based on the results of experiments and simulations, this study draws the following conclusions: (1) The experimental M-κ relationships for Al 6061-T6 RHTs with φ = 90° and different d redundant holes subjected to cyclic bending display stable loops from the first bending cycle. Since the redundant holes were small and local, the M-κ curves for Al 6061-T6 RHTs with φ = 90° and different d redundant holes under cyclic bending were almost the same.
(2) The experimental ΔDo/Do-κ relationships for Al 6061-T6 RHTs withφ = 90° and different d redundant holes subjected to cyclic bending reveal increasing, asymmetrical, ratcheting, and bow-like tendency with the increase in the number of bending cycles. In addition, ΔDo/Do continues to increase when the round hole is under tension. However, ΔDo/Do continues to decrease when the round hole is under compression.
(3) The empirical formula proposed by Kyriakides and Shaw [1] was modified to describe the κc/κo-Nf relationships for Al 6061-T6 RHTs with φ = 90° and different d redundant holes submitted to cyclic bending. Based on the experimental data, the material parameters C and α were proposed in Eqs. (2) and (3), respectively.

Acknowledgement
This research was carried out with the support of the Ministry of Science and Technology, and the research project was MOST 106-2221-E-006-097. We sincerely thank them for their assistance.