Progressive and Critical Changes in Outer Minor-Axis Length of Elliptical-Square Tubes Subjected to Cyclic Bending

This study investigates the progressive and critical variations in the outer minor-axis length of 6063-T5 aluminum alloy elliptical-square tubes, each with one of four outer major-to-minor axis length ratios (1.5, 2.0, 2.5, and 3.0), subjected to cyclic bending. The variations in the outer minor-axis length and the critical conditions leading to structural instability were systematically examined. Experimental observations revealed that the relationship between the changes in outer minor-axis length and the number of cycles could be divided into three distinct stages: (1) a rapid increase during the first stage, (2) a gradual and stable growth during the second stage, and (3) a saturation stage where further increase became negligible before final failure. The results showed that higher controlled curvature values corresponded to greater critical variations in the outer minor axis length, while larger axis-length ratios also led to increased critical variations. Furthermore, a modified version of the empirical ovalization model originally proposed by Lee et al. for SUS304 stainless steel circular tubes was employed. Nonlinear regression using the least-squares method yielded fitting parameters that describe the relationship between changes in the outer minor-axis length and the number of bending cycles during the first and second stages. In addition, a logarithmic-linear correlation was established between the critical change in the outer minor-axis length and the controlled curvature. The strong agreement between theoretical predictions and experimental results confirms the reliability and accuracy of the proposed empirical model and its parameterization.