Multiple buckling

Several cylinders are tested repeatedly in axial compression. The test set-up is not changed compared to the single buckling tests, except that the Aramis system is only measuring in the postbuckling regime.

For cylinder 1.6, the set-up is changed after 11 tests with the last four buckling loads being almost equal in magnitude. The load introduction is changed to the fixed mount-ing and three more bucklmount-ing tests are performed.

Figure 5-33 shows the decline of buckling load in the subsequent tests after the first buckling test. After a certain number of tests that varies individually for each cylinder, the curve suggests that a plateau of bearable buckling load (difference less than 2%) is reached. The buckling load level achieved here in % of the load reached in the respec-tive first buckling is summarised in Table 5-13 and lies between 70-90%.

Table 5-13 Buckling load at plateau level in % of first occurring buckling load

1.1 1.2 1.6 2.2

69% 87% 73% 70%

The Aramis measurements show a two-row buckling pattern that moves slightly after the third test to the top – a former depression is now deformed outwards and con-versely. A correspondence between switch in the mode and decrease of buckling mode cannot be found.

The change of mounting for Z1.6 leads to a significant increase in buckling load from around 45 kN to about 55 kN, the latter forming a plateau again for three subsequent

tests. The corresponding Aramis-measurement, depicted in Figure 5-33, also shows a two-row pattern with depressions and heights being situated close together.

For cylinder 2.2 an additional thermography measurement has been performed after each test. The resulting pictures are assigned to the corresponding test in Figure 5-34.

No delaminations are present prior to testing.

Figure 5-33 Buckling loads of cylinders tested repeatedly, postbuckling pattern Z1.6 After the first buckling test, a delamination area is observed, oriented at 60° with re-spect to the z-axis of the cylinder. The size of the delamination increases slightly after the second test: an additional, slightly fainter spot is visible that is oriented approxi-mately at -30° with respect to the cylinder axis (marked in second picture in Figure 5-34). From the second test onwards, no growth of the delamination is observed. Cor-respondingly, the buckling load drops significantly after the first test from 61.7 kN to 44 kN, the last four tests show almost identical buckling loads, varying between 43.4 kN and 43.1 kN.

The buckling pattern itself does not change, but the buckles are deeper for the tests following when compared to the first one (Figure 5-35).

Figure 5-34 Thermography of cylinder 2.2 at 270° after each buckling test

Figure 5-35 Postbuckling patterns of cylinder 2.2 after each test

All cylinders tested multiple times showed significant reduction in buckling load. How-ever, the four cylinders under investigation showed very different behaviour when it comes to a comparison of the load reduction in relation to the number of tests. While cylinders 1.1 and 2.2 reach a certain load level quickly (Z1.1 after 3 tests, Z2.2 after the first test), Z1.2 and 1.6 reach the plateau gradually after 5 and 8 tests respectively.

In situ thermography is undertaken for Z2.2 only. In that case, the plateau is reached after the first test. It seems plausible, that if the damage in the structure does not grow, the structure behaves in the same way repeatedly, leading to similar buckling loads, described as plateau here.

The white circle in the left picture of Figure 5-35 shows the position of the delamina-tion corresponding to thermography pictures of Figure 5-34. The delaminadelamina-tion hence occurs at the edge of the buckle where the deformation gradient has a maximum.

5.6 Summary and discussion

Although optical thickness measurements were taken for cylinders of set Z2 by using the ATOS system to measure the inner and the outer surface, thickness measures were evaluated by analysing micro sections in order to identify and leave out the outer resin layer in further computations. This was considered necessary since the resin layer does not contribute to the load carrying capacity of the cylinders.

The analysis of micrographs generally showed a good quality of the cylinders in terms of void content and fibre volume fraction. While the analysis of specimens from set Z1 and set Z2 showed strong similarities, the coupon specimens showed remarkable devi-ations although an effort was made to resemble the manufacturing process of the cylinders. However, since the manufactured sheets needed to be straightened and the edge constraint were missing during the curing process, the sheet material could spread and bleed resulting in thinner layers and higher fibre volume fraction as com-pared to the cylinder specimens. The fibre orientation showed slightly higher scatter which might be due to the manual handling during the straightening process.

The autocorrelation analysis showed very low absolute values above a lag length of 62.5 µm. Also, correlation of thickness and fibre volume content was not found on the scale considered (up to 1000 µm). These two possible correlations are hence neglected in the Monte Carlo simulations.

The outer resin layer that stems from the manufacturing process influenced the optical measurement of the outer surface on a small scale. The same accounts for the peel ply fibre that stuck to the surface in a regular pattern. For the analysis of the geometric imperfection these very short-waved influences can be filtered by reducing the number of Fourier coefficients used to approximate surface geometry (refer to Appendix A7).

The power spectral analysis shows how the spectrum of the cylinders is clearly domi-nated by the first three to four half-waves. This dominance by low half-wave numbers was also found by [Kep13].

Although it is shown that the rms value of the geometric deviations from the perfect cylinder surface vary with height due to the potting process, a mean rms value is calcu-lated in order to be able to compare to data found in literature.

The structural tests in the elastic regime showed a high compliance between structural tension and compression stiffness. Regarding buckling tests, high speed shootings show the inition of buckling at a single buckle. Thermography shows delaminations after buckling that occur preferably close to manufacturing flaws in the case of the second set of cylinders. To investigate the relation between occurring delamination and

reduc-tion of buckling load, the in situ observareduc-tion should be employed for future buckling tests.

Notable is also the increase in buckling load by about 22 % when changing from a load i t odu tio that allo s tilti g at u kli g to a la ped setup he e the li de is effectively kept in straight position. This effect should be considered when evaluating test data as basis for practical designs since there the structure will tilt at buckling.

The cylinders tested contribute to the creation of a database for CFRP cylinders close to practical applications. This is important since the layup and manufacturing method can have a large influence on the geometric imperfections.

6 Nu eri al a al sis

Within this section the structural tests are recomputed deterministically using finite element methods and compared to the test results. The role of the stiffness of the cylinder mounting is treated separately.