 Advances in Technology Innovation , vol. 1, no. 1, 2016, pp. 25 - 27 25 Copyright © TAETI Buckling Experiment on Anisotropic Long and Short Cylinde rs Atsushi Takano Department of Mechanical Engineering, Kanagawa University , Yokohama, Japan. Received 02 February 2016; received in revised form 22 March 2016; accept ed 25 March 2016 Abstract A buckling e xpe riment was performed on anisotropic, long and short cylinders with various radius -to-thickness ratios . The 13 cylinders had symmetric and anti-sy mmetric layups, were between 2 and 6 in terms of the length-to-radius ratio, between 154 and 647 in radius -to-thickness ratio, and made of t wo kinds of carbon fiber re inforced plastic (CFRP) prepreg with high or low fiber modulus. The theoretical buckling loads for the cylinders were calculated fro m the previously published solution by using linear bifurcation theory considering layup anisotropy and transverse shear deformat ion and by using deep shell theory to account for the e ffect o f length and compared with the test results. The theoretical buckling loads for the cy linders were calculated fro m the previously published solution by using linear bifurcation theory considering layup anisotropy and transverse shear deformation and by using deep shell theory to account for the effect of length. The knockdown factor, defined as the ratio of the e xperimental value to the theoretical value, was found to be between 0.451 and 0.877. The test results indicated that a large length-to-radius ratio reduces the knockdown factor, but the radius -to-thickness ratio and other factors do not affect it. Keywor ds : buckling, cylinders, anisotropy 1. Introduction Many buckling tests have been performed on orthotropic and anisotropic cylinders , which a re often made fro m CFRP. As summarized by the author [1] and as shown in Fig. 1, the values of the knockdown factor have been calculated from these tests are scattered between 50% and 100% . Fig. 1 Knockdown factor and r/t [1] Note that the theoretical buckling loads were calculated by using the solution with the least amount of simplificat ion in the linear b ifurcation theory from a mong the previously published solutions [2]. The previous experiments and evaluations , however, main ly concentrated on the effect of the radius to thickness ratio (r/t). Recently, long CFRP cy linders have started to be used in large satellites [3], but no information is yet availab le on the effect of length on the knockdown factor. Thus, buckling tests were performed on long and short CFRP cy linders, and the results were used to calculate the knockdown factors. 2. Method 2.1. Mak ing Specimens The CFRP prepregs used to ma ke the cylinders were TR350J075S, EL = 114.7GPa (hereafter ca lled “T R”) and HSX350C075S, EL = 260.3GPa (hereafter called “HSX” ); both were made by M itsubishi Rayon Co., Ltd. Here , EL is the longitudinal Young’s modulus measured in a tensile test, and the transverse Young’s modulus ET and shear modulus GLT we re assumed to be 6 GPa and 4GPa, respectively. * Corresponding aut hor, Email: at akano@kanagawa-u.ac.jp Advances in Technology Innovation , vol. 1, no. 1, 2016, pp. 25 - 27 26 Copyright © TAETI The test specimens (CFRP cylinders) we re made in-house by hand-layup. CFRP prepregs were layered manually on an alu min iu m mandre l (150 mm in dia meter), and heat shrinkable tape was wound around them. The layup sequence is shown in Table 1. The CFRP prepregs on the mandrel were therma lly cured in an oven kept at 130°C for 2 hours. The cured cylinders were cut by grinders, and both ends were bonded to steel rings by epoxy adhesive. To prevent therma l residual stress on the cylinders, the curing of the epoxy adhesive was conducted at room temperature. Twelve sheets of three-axis strain gages were bonded on the top and bottom (5 mm fro m the steel end rings) and middle (the center of the length) of the cylinders in the circumferentia l direction, each separated by 90°. 2.2. Test Method A typical compression test configuration is shown in Fig. 2. Section paper was la id under the specimen to align the centers of the cylinder and the universal testing instrument (Shimad zu A G-I 100kN). To make the load uniform, a rubber sheet and a silicone rubber sheet were laid on the top end of the cylinder, a 20 mm thic k stainless plate was put over the sheets, and a rubber sheet was la id on the bottom end of the cy linder. To minimize the offset of the load, a sma ll compression load was applied, and the strain outputs in the middle were checked. When a significant difference between the strains was observed, the location of the cylinder on the universal testing instrument was adjusted. When the difference between the strains no longer changed or a la rge offset was observed between the centers of the cylinder and the universal testing instrument, however, the difference between the strains was ignored and the test proceeded to the next step. Fig. 2 Photograph of buckling test The half leve l co mpression test (applying half the e xpected buckling load, including 0.5 of the knockdown factor) was performed to check for anoma lies in the data. After that, the full level co mpression test was performed to buckle the cylinder. Load was applied until the cross -head displacement reached 1.5 of the buckling displacement. 3. Results and Discussion Typical load and displace ment results are shown in Fig. 3 and 4. Fig. 3 TR 6 ply, L/D=1, gap allowed. Fig. 4 TR 6 ply, L/D=3, gap allowed. Table 1 summa rizes the test results. Note that an e xtre me ly low knockdown factor 0.397 was caused by 8mm of offset load , and the modified knockdown factor considering the offset is 0.481. Accordingly, the knockdown factors are scattered between 0.451 and 0.877. The knockdown factors of the longer cylinders are lowe r than those of the shorter cylinders, while other factors (symmetric or anti-symmetric, ply gap, fiber modulus and L/r) seem to have no effect on the trend. Thus , a regression analysis with categorical variab les was conducted to check the effects . The results are shown in Table 2. A regression analysis can be used instead of an analysis of variance (ANOVA) when the samp le size is unbalanced like in this case. He re, r/t (thickness) and the symmetric or anti-symmet ric factor a re Advances in Technology Innovation , vol. 1, no. 1, 2016, pp. 25 - 27 27 Copyright © TAETI mu lticollinear; thus , the symmetric or anti-symmetric factor should be e xc luded fro m the regression analysis. Table 1 Summary of the test results Table 2 Regression Tables The mean of the knockdown factors is 0.611 with 0.02% of P-value, and it is smalle r than 5% (standard statistical criteria); hence, the value is statistically significant. Other effects , however, are not significant because their P-values are higher than 5%. Only the P-va lue of L/r, which is 19.23%, is smaller than the others . The mean of the knockdown factors is 0.627 for L/r=2 and 0.537 for L/r=6. The s ma lle r va lue is 14.4% smaller than the larger va lue. Thus , the length may affect the knockdown factor. To c larify its effect, more buckling tests are required. 4. Conclusions Thirteen buckling tests were performed on symmetric and anti-sy mmetric, long and short cylinders to investigate effect of varying the length. The diffe rence in the mean knockdown factor between lengths was found to be 14.4% . A regression analysis , however, indicated that the diffe rence was not statistically significant. More buckling tests considering other factors should be conducted in order to find the cause of the scatter in the knockdown factor. References [1] A. Takano, “Statistical knockdown factors of buckling anisotropic cylinders under axial compression,” Journal of Applied Mechanics, vol. 79, 051004, pp 1-17, 2012. [2] A. Takano, “Improvement of Flügge’s equations for buckling of moderately thick anisotropic cylindrical shells,” AIAA Journal, vol. 46, no. 4, pp. 903-911, 2008. [3] Y. Takano, T. Masai, H. Seko, A. Takano, and M. Miura, “Development of the lightweight large composite-honeycomb-sandwich central cylinder for next-generation satellites,” Aerospace Technology Japan, vol. 10, pp. 11-16, 2012. Theory P a [N] Test P a [N] TR 6 ply L/r=2 (-70/70/0/0/70/-70) 0.488 136 21983 13197 0.600 Gap TR 6 ply L/r=4 (-70/70/0/0/70/-70) 0.488 287 21986 11870 0.540 Gap TR 6 ply L/r=6 (-70/70/0/0/70/-70) 0.488 436 21987 11537 0.525 Gap HSX 6 ply L/r=2 (-70/70/0/0/70/-70) 0.349 136 21123 12997 0.615 Gap HSX 6 ply L/r=6 (-70/70/0/0/70/-70) 0.349 443 21873 12647 0.578 Gap HSX 3 ply L/r=2 (-70/0/70) 0.175 148 2060 1806 0.877 Overlap HSX 3 ply L/r=6 (-70/0/70) 0.175 443 2061 1437 0.697 Overlap TR 6 ply L/r=2 (-70/70/0/0/70/-70) 0.488 136 21983 12665 0.576 Overlap TR 6 ply L/r=6 (-70/70/0/0/70/-70) 0.488 436 21987 8738 0.397 * Overlap HSX 6 ply L/r=2 (-70/70/0/0/70/-70) 0.349 136 21123 10366 0.491 Overlap HSX 6 ply L/r=6 (-70/70/0/0/70/-70) 0.349 436 21873 9875 0.451 Overlap HSX 2 ply L/r=2 (-50/50) 0.116 136 964 583 0.605 Overlap HSX 2 ply L/r=6 (-50/50) 0.116 436 944 464 0.492 Overlap *Not e: 8mm of load offset was observed and modified knockdown fact or considering t he offset load is 0.481. Specimen name Layip sequence Thick- ness t [mm] Length L [mm] Buckling load Ply gap or overlap Knock- down factor Coefficients Std Error t P-value Lower 95% Upper 95% Intersept 0.611 0.095 6.459 0.02% 0.393 0.829 gap/overlap -0.052 0.080 -0.646 53.62% -0.236 0.133 TR/HSX 0.047 0.087 0.542 60.28% -0.154 0.249 L /r -0.025 0.017 -1.424 19.23% -0.065 0.015 r /t 0.000 0.000 0.782 45.70% 0.000 0.001