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Composite cylindrical shells under static and dynamic axial loading: An experimental campaign
Progress in Aerospace Sciences ∎ (∎∎∎∎) ∎∎∎–∎∎∎
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Composite cylindrical shells under static and dynamic axial loading: An experimental campaign Chiara Bisagni Politecnico di Milano, Department of Aerospace Science and Technology, Via La Masa 34, 20156 Milan, Italy
art ic l e i nf o
a b s t r a c t
Article history: Received 14 June 2015 Accepted 15 June 2015
The results of an experimental investigation performed at the Politecnico di Milano inside the European project DAEDALOS on three composite cylindrical shells are here presented. At first, static buckling tests were performed under axial compression. Then, two types of dynamic tests were carried out: modal tests at different load levels before buckling and dynamic buckling tests applying an axial shortening of short duration. At the end, one shell was statically tested until final failure. The tests allow to understand the behavior of thin-walled cylindrical shells subjected to axial compression both in static and dynamic conditions. The results show the strength capacity of these structures to work in the post-buckling range with a capacity to sustain a load that is about 40% of the buckling load. The modal tests at different load levels allowed to observe that an increase of the load determines a reduction of the modal frequency and an increase of the damping. Large deformations are obtained before the final failure with out-of-plane displacements of almost 40 mm and a shortening equal to about 26 times the buckling shortening. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Composite shell Static buckling Dynamic buckling Compression test
1. Introduction The present work is part of the DAEDALOS project [1], funded by the European Commission in the FP7 Program. The project focuses on the development of design approaches for aircraft structures to investigate the dynamic behavior in the loading process. Indeed, although aircrafts are in the most cases subjected to high dynamic loads, today the design and certification procedures are mainly based on conservative static loading which leads to additional weight and, potentially, to a structurally unsafe aircraft. One of the objectives of the DAEDALOS project consists in developing techniques which can take into account dynamic loads into finite element analyses, considering for example damping characteristics, dynamic buckling and hysteresis. The project analyzes different structures, such as unstiffened composite cylindrical shells, and stiffened metallic and composite panels. Unstiffened cylindrical shells were largely investigated in the past years, as they are representative of several aeronautical and space components, and also because they are extremely sensitive to initial imperfections [2], and consequently a large difference can be obtained from the experimental tests respect to the simulations. To take into account the effect of initial imperfections, knockdown factors are commonly used [3]. In the last 10–15 years, several experimental tests were E-mail address: [email protected]
performed to study the buckling behavior of composite cylindrical shells under axial compression, due to the growing interest of aerospace industry for composite materials. Bisagni [4,5] performed several buckling tests on shells manufactured from unidirectional and fabric carbon fiber material, and later Bisagni and Cordisco [6] tested the shells under combined compression and torsion. Tests under combined axial and torsion loading were carried out also by Meyer-Piening et al. [7], while Hilburger and Starnes tested cylindrical shells with six different laminates and two different shell-radius-to-thickness ratios [8], taking accurate measurements of initial geometric imperfections [9]. More recently, Degenhardt et al. [10,11] performed static tests on composite cylindrical shells under axial compression. A good overview of shell buckling tests and used experimental methods is reported in the book of Singer et al. [12], while Takano presented a summary of more recent buckling tests on anisotropic thin-walled cylinders [13]. The studies regarding dynamic buckling tests of composite shells are really limited, as well as the damping measurement of these structures under axial compression. For example, Simitses [14] studied the dynamic stability of suddenly loaded structures, while Bisagni performed numerical analyses [15] and experimental tests [16] to investigate the dynamic buckling behavior of composite cylindrical shells. The results of the study performed at the Politecnico di Milano inside the DAEDALOS project on three composite cylindrical shells are here presented. In particular, static buckling tests were performed under axial compression as well as two types of dynamic
http://dx.doi.org/10.1016/j.paerosci.2015.06.004 0376-0421/& 2015 Elsevier Ltd. All rights reserved.
Please cite this article as: Bisagni C. Composite cylindrical shells under static and dynamic axial loading: An experimental campaign. Progress in Aerospace Sciences (2015), http://dx.doi.org/10.1016/j.paerosci.2015.06.004i
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tests: modal tests at different load levels before buckling and dynamic buckling tests applying an axial shortening of short duration. One of the shell was tested until final failure in static conditions of axial compression in displacement control. The experimental data can be used to validate finite element models for the design of composite cylindrical shells subjected to static and dynamic conditions. Some preliminary comparisons between the data measured during the static tests and the numerical results are also presented here.
2. Composite cylindrical shells The shells investigated in the present study have diameter equal to 500 mm and length equal to 600 mm. They were manufactured at the Deutsches Zentrum für Luft- und Raumfahrt (DLR), the German Aerospace Center, in Braunschweig, inside the European project DAEDALOS [1]. Three nominally identically cylindrical shells were tested. A photograph of the shells is reported in Fig. 1. The shells are made of unidirectional prepreg material IM7/ 8552, which nominal properties are reported in Table 1 [17]. The shells consist of four plies with sequence [ þ45°/ 45°]S, obtaining a total thickness of 0.5 mm. The shell are very thin, presenting a radius to thickness ratio equal to 1000. Ending tabs are added to the shells, so to allow applying the axial compression load. The ending tabs are realized curing at first the tabs in glass fibers, and then bonding them by means of a conical mandrel. A cold bond adhesive is used to connect the tabs to the shell. A photograph of the procedure is reported in Fig. 2. The external reinforcing tabs are 40 mm long, so the actual length of the shells results limited to the central part and is equal to 520 mm.
3. Static buckling tests Static tests were performed using a press for buckling tests designed in-house [4–6] and an MTS equipment with maximum load equal to 250 kN. All the tests were carried in displacement control. A photograph of the two load frames with installed shells are reported in Fig. 3. The press for buckling tests was designed in-house with the capability to perform buckling tests in compression and in torsion. During axial compression tests in displacement control, the load is provided by a hydraulic ram, but the load level, which is transferred smoothly to the shell, is governed by the axial displacement of the upper loading platform. Indeed, this displacement is computer-controlled, moving four stepping motors connected to four
Fig. 1. Three composite cylindrical shells before the tests.
Table 1 Ply properties. IM7/8552 Longitudinal modulus, E11 [MPa] Transverse modulus, E22 [MPa] Shear modulus, G12 [MPa] Poisson's ratio, ν12 Density, ρ [kg/m3] Thickness [mm]
150,000 9080 5290 0.32 1570 0.125
ball screws placed at the four corners of the loading platform. Two linear variable differential transformers (LVDTs) give directly the axial displacement of the shell, measuring the distance between the upper clamp and the lower clamp. The four stepping motors can be computer-controlled simultaneously but also independently. In this way it is possible to adjust the parallelism of the platforms at the beginning of the tests, and to constrain the two ends of the shells to remain parallel during the tests. The MTS load frame applies the load in a central point, and the shell is located between two plates. Two LVDTs are added to measure the distance between the plates. There is no possibility to control or modify the parallelism between the two plates during the test, so there is no possibility to correct any imperfection related to the end tabs. The decision to use two different equipments has been taken for two main reasons. The first reason is due to one of the key aspects of buckling tests, that is the parallelism of the boundary ends of the structure, in this case the cylindrical shell. The press used for buckling tests has been developed during the last 15 years and customized for accurate buckling tests in displacement control. Due to the presence of the ball screw on the four corners of the press, there is the possibility to control the parallelism during the tests. This capability is not available on the MTS machine so there was interest to perform the same tests on a different equipment to cross validate the results. The second reason is that the press is designed just for static test, while the MTS is able to perform both static and dynamic tests. Due to the need to perform the dynamic buckling tests under the MTS equipment it was necessary to repeat the static buckling also to compare static and dynamic results measured on the same equipment. In summary, the press is able to perform buckling tests in displacement control with a higher accuracy, and allows to have a better control during the test. The MTS load frame was used for the static buckling tests only as preliminary step before tests under dynamic loads. Indeed, the use of MTS load frame was the only possibility to perform dynamic buckling tests thanks to its bandwidth. Dynamic tests were not possible with the dedicated press due to its load distributions system based on four stepping motors. The boundary conditions of the tests are the same, simply supported, but without the possibility to change the orientation of the loading platform in the case of the MTS loading frame. The buckling loads measured on the three shells during the static tests using the two different load frames are reported in Table 2. From the data reported in Table 2, it is possible to see that there is a scatter among the values of buckling loads measured during the different tests. The average of the buckling loads of the three shells is equal to 14.69 kN for the tests on the buckling press, and to 13.85 kN for the tests on the MTS load frame with a difference of 5.7%. The standard deviation is 0.56 and 1.69, respectively. Two photographs taken during the static tests on Shell A and on Shell C using the press for buckling tests are shown in Fig. 4.
Please cite this article as: Bisagni C. Composite cylindrical shells under static and dynamic axial loading: An experimental campaign. Progress in Aerospace Sciences (2015), http://dx.doi.org/10.1016/j.paerosci.2015.06.004i
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Fig. 2. Application of the ending tabs.
4. Dynamic tests
Table 2 Bucking loads measured during the static tests using the two load frames.
Two types of dynamic tests were performed using the MTS load frame: modal tests at different load levels before buckling and dynamic buckling tests applying an axial shortening of short duration. The modal tests were performed using the roving hammer technique, which allowed the evaluation of the modal damping values in the range between 0 and 500 Hz for different load levels before the buckling. In particular, the modal tests were performed by impacting 48 points located in the middle of the cylindrical shell with an instrumented hammer. The hammer was used for modal excitation, while a PCB microphone was used for response measurement, in place of a classical accelerometer, to avoid any contact of the sensor with the shell and any mass loading effect. LMS TestLab software was employed for data acquisition and processing, while the identification process was based on the Polymax method available inside Testlab module. Photographs of a cylindrical shell with the instrumented hammer is reported in Fig. 5. The measurements were taken at no load and at three different levels of pre-buckling axial load: 3 kN, 5 kN and 7 kN. The frequencies and the damping values measured on Shell C are reported in Table 3 for the different modes. The measured damping are then graphically represented versus the frequency in Fig. 6. It is possible to observe that an increase of the load determines a reduction of the modal frequency and an increase of the damping. The same conclusions are drawn for the other two shells, with values that differ for the three shells in the range of about
Shell
Buckling load [kN] - Tests using the Buckling load [kN] - Tests using press MTS
Shell A 15.34 Shell B 14.33 Shell C 14.41
13.01 12.75 15.79
10%. Some modes experimentally measured on Shell C are represented in Fig. 7. It is important to note that what is measured during the modal testing is simply the modal damping. During the DAEDALOS project a large activity has been carried out to identify more accurate physical models of damping, to be implemented in finite element models for dynamic simulation. These models are complex and require specific tests on specimens to identify the constitutive model parameters [18,19]. The dynamic buckling tests were carried out imposing an axial displacement equal to 2 mm at the velocity of 60 mm/s. It was the maximum possible velocity considering the reaction force of the shells. The displacement of 2 mm was the value imposed to the MTS, that differs from the value measured by the LVDTs between the plates. The load–shortening curves measured on the three shells during the dynamic buckling tests are reported in Fig. 8; while Fig. 9 shows the time history of the resulting blended square wave axial shortening applied during the dynamic buckling tests.
Hydraulic arm Ball screws
Shell LVDT Load cell
Fig. 3. Testing equipment: in-house designed press and MTS system.
Please cite this article as: Bisagni C. Composite cylindrical shells under static and dynamic axial loading: An experimental campaign. Progress in Aerospace Sciences (2015), http://dx.doi.org/10.1016/j.paerosci.2015.06.004i
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Fig. 4. Two photographs taken during the static tests on Shell A and on Shell C.
The load–shortening curves present a large jump in the measurement of the displacement after buckling due to the LVDTs, which are not able to keep up with the dynamic of the load frame. The maximum load of the curves corresponds to the dynamic buckling load, and resulted higher than the static values in all the performed tests. For example, the dynamic buckling load of Shell C results equal to 16.62 kN, compared to the static buckling value of 15.79 kN measured during the static test on the MTS. Identical behavior was observed during the tests on the other two shells. For all three cylindrical shells the ratio between the dynamic buckling load and the static one resulted equal to approximately 1.05. Even if it appears as a consistent trend, it is not yet possible to state that the increase of the buckling loads of 5% is due to the dynamic effects, as the number of tested structures is limited, and as this increase falls into the range of the scatter of the measured buckling loads. Besides, in the case of dynamic buckling the mode shapes play the same role of the geometrical imperfections, as pointed out by Simitses [14]. This mechanism is mainly related to the bandwidth of the external excitation, or, in other words, to how many modes is able to excite. Also other important aspects play a relevant role, like inertia forces, damping, and so on. In the case of MTS machine, the maximum bandwidth available, for such high compression loads, is not sufficient to switch on the mechanism, so the difference between static and dynamic buckling loads is not significant. Unfortunately, it was not possible to perform further tests with a higher velocity of imposed displacement due to the limit of the load frame.
5. Numerical analysis and correlation Finite element analyses are performed using the commercial code ABAQUS [20]. The mesh of the cylindrical shell is chosen after a convergence study, and is composed of 9360 S4R shell elements and 9516 nodes, with element dimensions of about 10 mm 10 mm. Boundary conditions are applied in order to simply reproduce the clamping conditions of the compressive tests. In particular, nodal constraints of fixed displacement in three directions are imposed on one side of the shell, while nodal constraints in the radial and tangential directions and free displacement in the axial direction are imposed on the other side. At first, a modal analysis is performed. Table 4 reports the obtained natural frequencies, while the first modal shape is presented in Fig. 10. The natural frequencies measured during the modal tests are compared to the values obtained from the finite element analyses. The difference for the first frequency is limited to 3%, and is of the same order also the difference for the second frequency. It grows for the higher frequencies, and results equal to about 10% for the third one, and around 16% for the fourth and fifth ones. Then, an eigenvalue buckling analysis is performed without any initial imperfection. The buckling load results equal to 23.99 kN, to which corresponds axial displacement of 0.89 mm. The first buckling shape is presented in Fig. 11. The static buckling loads measured on the shells vary between a minimum of 12.75 kN and a maximum of 15.79 kN. The numerical value obtained without any initial imperfection from the eigenvalue analysis is equal to 23.99 kN, so is significantly higher
Fig. 5. Cylindrical shell ready for the modal tests, and detail of the microphone used for response measurement.
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Table 3 Frequencies and damping values measured on Shell C. Mode
1 2 3 4 5 6 7 8 9 10
0 kN
3 kN
5 kN
7 kN
Freq. [Hz]
Damping
Freq. [Hz]
Damping
Freq. [Hz]
Damping
Freq. [Hz]
Damping
– 194.00 212.57 239.05 271.23 307.63 347.34 391.85 438.00 487.81
– 0.52 0.60 0.42 0.36 0.32 0.34 0.34 0.28 0.24
191.02 194.81 210.13 234.82 265.54 300.45 336.99 377.85 427.42 475.08
0.87 0.55 0.60 0.39 0.36 0.33 0.39 0.37 0.32 0.30
188.99 191.76 205.85 230.60 260.35 293.13 328.37 368.14 418.48 464.49
0.72 0.54 0.51 0.42 0.39 0.46 0.50 0.38 0.35 0.34
185.35 188.87 202.06 226.32 254.57 286.86 320.34 359.49 409.35 453.48
0.79 0.70 0.51 0.43 0.45 0.45 0.48 0.44 0.36 0.37
Fig. 8. Comparison between dynamic buckling tests on three shells. Fig. 6. Damping versus frequency for different load levels.
Mode 1
Mode 2 Fig. 9. Applied shortening during dynamic buckling test.
Table 4 Natural frequencies obtained by finite element analysis.
Mode 5
Mode 7
Mode
Natural frequencies [Hz]
No. 1 No. 2 No. 3 No. 4 No. 5
199.47 206.28 214.13 227.60 257.97
Fig. 7. Experimentally measured modes of Shell C.
than the experimental one. Better and more realistic comparisons are obtained introducing initial geometric imperfections and performing dynamic analysis. A dynamic analysis is so carried out imposing a constant compressive displacement velocity in the axial direction on one side of the shell. The imposed compressive velocity is chosen equal to 4 mm/s for 0.75 s of simulation, representing a good compromise
between CPU time and result accuracy. The buckling load, obtained from a dynamic implicit analysis including initial imperfections given by the combination of the first and third mode and having maximum amplitude of 0.1 mm, equal to 20% of the thickness, is equal to 18 kN. The comparison of the post-buckling shapes is shown in Fig. 12, where a photograph of Shell A is reported together with the post-buckling deformation obtained from the analysis.
Please cite this article as: Bisagni C. Composite cylindrical shells under static and dynamic axial loading: An experimental campaign. Progress in Aerospace Sciences (2015), http://dx.doi.org/10.1016/j.paerosci.2015.06.004i
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Fig. 13. Load–shortening curve of Shell B until final failure.
Fig. 10. First modal shape obtained by finite element analysis.
Fig. 11. First buckling shape obtained by finite element analysis.
6. Static compression test until final failure Shell B was tested under axial static compression until the final failure. The test was performed in displacement control using the press for buckling tests designed in-house. The load–displacement curve measured during the test is presented in Fig. 13. The pre-buckling response of the shell is characterized by a linear load–shortening response with a stiffness of about 200 kN/ mm. The buckling load was equal to 13.9 kN with a shortening of 0.58 mm. The shell presented a large, almost flat, post-buckling
Fig. 14. Shell B during the static compression test until final failure.
field, with a load of approximately 6 kN in the first part, decreasing then to about 4.4 kN. The post-buckling load results so equal to about 40% of the buckling load in the first part of the post-buckling field, and then it decreases to less than 30%. The final failure happened at a shortening of 15.58 mm, equal to about 26 times the buckling shortening. The load was 3.8 kN before dropping down, with the shell no more able to sustain any load. A photograph of the testing equipment with the shell in the post-buckling field is shown in Fig. 14. During the test two cameras were installed: one on the socalled front side of the shell and one on the rear side. Fig. 15 shows the evolution of the post-buckling shape of the shell. In particular,
Fig. 12. Experimental–numerical comparison of static post-buckling shape.
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Fig. 15. Photographs taken on front and rear side of Shell B during the test until final failure: (a) shortening¼0.65 mm; (b) shortening¼4.02 mm; (c) shortening¼8.22 mm; (d) shortening¼15.55 mm.
two photographs are reported for four different shortening values of the tests. The first photograph is taken from the camera located on the front side and the second photograph is taken from that one on the rear side. The shell appears different from the two cameras. Different lights were on the two sides of the shell, as in one case the natural light is predominant respect to the artificial light. There is also a difference of light on the photographs of the front side, as the test lasted several hours and the natural light changed during the day. In any case, the main difference between the photographs taken from the two cameras is a different post-buckling shape. It is due to the geometric imperfections of the shell, together with probably a load not evenly distributed. Immediately after the buckling (Fig. 15a) the deformation is characterized by the
presence of two/three small half-waves on the front side, while presents a regular central buckling half-wave on the rear side. Increasing the axial displacement, the post-buckling deformation evolves, remaining irregular on the front side. At a shortening of about 4 mm (Fig. 15b), three irregular half-waves can be noted on the front side, while the rear side presents almost perfect diamond waves, similar to a Yoshimura buckle pattern. The out-of-plane displacement increases significantly with the increase of the axial displacement. Fig. 15c shows the deformation for a shortening equal to 8.22 mm, while Fig. 15d reports the photographs taken just before the final failure at a shortening of 15.55 mm. It is possible to note that the front side presents large waves, some of them developed from the union of the previous waves. On the opposite, the rear side of the shell did not changed
Please cite this article as: Bisagni C. Composite cylindrical shells under static and dynamic axial loading: An experimental campaign. Progress in Aerospace Sciences (2015), http://dx.doi.org/10.1016/j.paerosci.2015.06.004i
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Fig. 16. Out-of-plane displacement just after buckling and before final failure.
Fig. 17. Failure of Shell B visible from outside and from inside.
shape, but presents the same number of shell with larger out-ofplane displacement. The large out-of-plane displacements cause sharp corners on the deformations towards the interior of the shell and especially to the outside. Fig. 16 reports two photographs that show the out-of-plane displacement just after buckling and before final failure. A straight plate in aluminum alloy helped to point out the displacements. Just after the buckling the deformation is highlighted by the shadow of the plate. Before final failure, the out-of-plane displacement can be measured and is equal to almost 40 mm. The test was stopped when the shell was not able to sustain the load any more. Small failures developed on the sharp corners of the half-waves, due to the large strain values. Some of the failures were on the deformations towards to the outside, and were visible on the shell outer surface. When the shell was removed from the testing equipment, several failures were visible on the inner surface. Probably they happened in the last part of the test, when small noises were heard, but no cracks were noted from the outside of the shell. The failures were mainly fiber fractures both on the inner and outer surfaces. Very small and localized fiber pullouts were also present in two/three points at the end of the test. Two photographs of the shell failure are reported in Fig. 17. 7. Conclusions The results of the study performed at the Politecnico di Milano
inside the European project DAEDALOS on three composite cylindrical shells were presented. In particular, static buckling tests under axial compression and two types of dynamic tests were performed. The dynamic tests were modal tests at different load levels before buckling and dynamic buckling tests with an applied axial shortening of short duration. One of the shell was then tested until final failure under axial compression. A scatter among the values of buckling loads was measured during the static buckling tests for the three shells using two different load frames. The average of the buckling loads of the three shells is equal to 14.69 kN for the tests on the buckling press, and to 13.85 kN for the tests on the MTS load frame with a difference of 5.7%, while the difference between the buckling values measured on the same shell using the two different load frames is between 9% and 15%. The scatter is due to the high sensitivity of unstiffened thin-walled cylindrical shells to imperfections, such as initial geometric imperfections but also imperfections related to the boundary conditions and to the loading application. The modal tests at different load levels allowed to observe that an increase of the load determines a reduction of the modal frequency and an increase of the damping. The dynamic buckling tests revealed that the dynamic buckling loads are higher than the static ones of about 5%. Even if it appears as a consistent trend, it is not yet possible to state that the increase of the buckling loads of 5% is due to the dynamic effects, as the number of tested structures is limited, and because this increase falls into the range of the scatter of the measured buckling loads. The results of the static compression tests until final failure show the strength capacity of these structures to work in the postbuckling range with a capacity to sustain a load that is about 40% of the buckling load. Large deformations are obtaining before the final failure with out-of-plane displacements of almost 40 mm and a shortening equal to about 26 times the buckling shortening. The tests investigated the behavior of thin-walled cylindrical shells subjected to axial compression both in static and dynamic conditions. The importance of having measurements of both static and dynamic buckling loads, as well as measurements of damping values for structures in composite materials is fundamental for the development and validation of numerical models.
Acknowledgments The research leading to these results has partially received funding from the European Union's Seventh Framework Programme [FP7/2007-2013] under grant agreement “DAEDALOSDynamics in Aircraft Engineering Design and Analysis for Light Optimized Structures” No. 266411. The author would also like to thank Potito Cordisco for helping in performing the tests. An initial version of this paper was presented at AIAA SciTech, 55th AIAA/ ASMe/ASCE/AHS/SC Structures, Structural Dynamics, and Materials Conference, 13–17 January 2014, National Harbor, Maryland, USA.
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Composite cylindrical shells under static and dynamic axial loading: An experimental campaign Chiara Bisagni Politecnico di Milano, Department of Aerospace Science and Technology, Via La Masa 34, 20156 Milan, Italy
art ic l e i nf o
a b s t r a c t
Article history: Received 14 June 2015 Accepted 15 June 2015
The results of an experimental investigation performed at the Politecnico di Milano inside the European project DAEDALOS on three composite cylindrical shells are here presented. At first, static buckling tests were performed under axial compression. Then, two types of dynamic tests were carried out: modal tests at different load levels before buckling and dynamic buckling tests applying an axial shortening of short duration. At the end, one shell was statically tested until final failure. The tests allow to understand the behavior of thin-walled cylindrical shells subjected to axial compression both in static and dynamic conditions. The results show the strength capacity of these structures to work in the post-buckling range with a capacity to sustain a load that is about 40% of the buckling load. The modal tests at different load levels allowed to observe that an increase of the load determines a reduction of the modal frequency and an increase of the damping. Large deformations are obtained before the final failure with out-of-plane displacements of almost 40 mm and a shortening equal to about 26 times the buckling shortening. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Composite shell Static buckling Dynamic buckling Compression test
1. Introduction The present work is part of the DAEDALOS project [1], funded by the European Commission in the FP7 Program. The project focuses on the development of design approaches for aircraft structures to investigate the dynamic behavior in the loading process. Indeed, although aircrafts are in the most cases subjected to high dynamic loads, today the design and certification procedures are mainly based on conservative static loading which leads to additional weight and, potentially, to a structurally unsafe aircraft. One of the objectives of the DAEDALOS project consists in developing techniques which can take into account dynamic loads into finite element analyses, considering for example damping characteristics, dynamic buckling and hysteresis. The project analyzes different structures, such as unstiffened composite cylindrical shells, and stiffened metallic and composite panels. Unstiffened cylindrical shells were largely investigated in the past years, as they are representative of several aeronautical and space components, and also because they are extremely sensitive to initial imperfections [2], and consequently a large difference can be obtained from the experimental tests respect to the simulations. To take into account the effect of initial imperfections, knockdown factors are commonly used [3]. In the last 10–15 years, several experimental tests were E-mail address: [email protected]
performed to study the buckling behavior of composite cylindrical shells under axial compression, due to the growing interest of aerospace industry for composite materials. Bisagni [4,5] performed several buckling tests on shells manufactured from unidirectional and fabric carbon fiber material, and later Bisagni and Cordisco [6] tested the shells under combined compression and torsion. Tests under combined axial and torsion loading were carried out also by Meyer-Piening et al. [7], while Hilburger and Starnes tested cylindrical shells with six different laminates and two different shell-radius-to-thickness ratios [8], taking accurate measurements of initial geometric imperfections [9]. More recently, Degenhardt et al. [10,11] performed static tests on composite cylindrical shells under axial compression. A good overview of shell buckling tests and used experimental methods is reported in the book of Singer et al. [12], while Takano presented a summary of more recent buckling tests on anisotropic thin-walled cylinders [13]. The studies regarding dynamic buckling tests of composite shells are really limited, as well as the damping measurement of these structures under axial compression. For example, Simitses [14] studied the dynamic stability of suddenly loaded structures, while Bisagni performed numerical analyses [15] and experimental tests [16] to investigate the dynamic buckling behavior of composite cylindrical shells. The results of the study performed at the Politecnico di Milano inside the DAEDALOS project on three composite cylindrical shells are here presented. In particular, static buckling tests were performed under axial compression as well as two types of dynamic
http://dx.doi.org/10.1016/j.paerosci.2015.06.004 0376-0421/& 2015 Elsevier Ltd. All rights reserved.
Please cite this article as: Bisagni C. Composite cylindrical shells under static and dynamic axial loading: An experimental campaign. Progress in Aerospace Sciences (2015), http://dx.doi.org/10.1016/j.paerosci.2015.06.004i
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tests: modal tests at different load levels before buckling and dynamic buckling tests applying an axial shortening of short duration. One of the shell was tested until final failure in static conditions of axial compression in displacement control. The experimental data can be used to validate finite element models for the design of composite cylindrical shells subjected to static and dynamic conditions. Some preliminary comparisons between the data measured during the static tests and the numerical results are also presented here.
2. Composite cylindrical shells The shells investigated in the present study have diameter equal to 500 mm and length equal to 600 mm. They were manufactured at the Deutsches Zentrum für Luft- und Raumfahrt (DLR), the German Aerospace Center, in Braunschweig, inside the European project DAEDALOS [1]. Three nominally identically cylindrical shells were tested. A photograph of the shells is reported in Fig. 1. The shells are made of unidirectional prepreg material IM7/ 8552, which nominal properties are reported in Table 1 [17]. The shells consist of four plies with sequence [ þ45°/ 45°]S, obtaining a total thickness of 0.5 mm. The shell are very thin, presenting a radius to thickness ratio equal to 1000. Ending tabs are added to the shells, so to allow applying the axial compression load. The ending tabs are realized curing at first the tabs in glass fibers, and then bonding them by means of a conical mandrel. A cold bond adhesive is used to connect the tabs to the shell. A photograph of the procedure is reported in Fig. 2. The external reinforcing tabs are 40 mm long, so the actual length of the shells results limited to the central part and is equal to 520 mm.
3. Static buckling tests Static tests were performed using a press for buckling tests designed in-house [4–6] and an MTS equipment with maximum load equal to 250 kN. All the tests were carried in displacement control. A photograph of the two load frames with installed shells are reported in Fig. 3. The press for buckling tests was designed in-house with the capability to perform buckling tests in compression and in torsion. During axial compression tests in displacement control, the load is provided by a hydraulic ram, but the load level, which is transferred smoothly to the shell, is governed by the axial displacement of the upper loading platform. Indeed, this displacement is computer-controlled, moving four stepping motors connected to four
Fig. 1. Three composite cylindrical shells before the tests.
Table 1 Ply properties. IM7/8552 Longitudinal modulus, E11 [MPa] Transverse modulus, E22 [MPa] Shear modulus, G12 [MPa] Poisson's ratio, ν12 Density, ρ [kg/m3] Thickness [mm]
150,000 9080 5290 0.32 1570 0.125
ball screws placed at the four corners of the loading platform. Two linear variable differential transformers (LVDTs) give directly the axial displacement of the shell, measuring the distance between the upper clamp and the lower clamp. The four stepping motors can be computer-controlled simultaneously but also independently. In this way it is possible to adjust the parallelism of the platforms at the beginning of the tests, and to constrain the two ends of the shells to remain parallel during the tests. The MTS load frame applies the load in a central point, and the shell is located between two plates. Two LVDTs are added to measure the distance between the plates. There is no possibility to control or modify the parallelism between the two plates during the test, so there is no possibility to correct any imperfection related to the end tabs. The decision to use two different equipments has been taken for two main reasons. The first reason is due to one of the key aspects of buckling tests, that is the parallelism of the boundary ends of the structure, in this case the cylindrical shell. The press used for buckling tests has been developed during the last 15 years and customized for accurate buckling tests in displacement control. Due to the presence of the ball screw on the four corners of the press, there is the possibility to control the parallelism during the tests. This capability is not available on the MTS machine so there was interest to perform the same tests on a different equipment to cross validate the results. The second reason is that the press is designed just for static test, while the MTS is able to perform both static and dynamic tests. Due to the need to perform the dynamic buckling tests under the MTS equipment it was necessary to repeat the static buckling also to compare static and dynamic results measured on the same equipment. In summary, the press is able to perform buckling tests in displacement control with a higher accuracy, and allows to have a better control during the test. The MTS load frame was used for the static buckling tests only as preliminary step before tests under dynamic loads. Indeed, the use of MTS load frame was the only possibility to perform dynamic buckling tests thanks to its bandwidth. Dynamic tests were not possible with the dedicated press due to its load distributions system based on four stepping motors. The boundary conditions of the tests are the same, simply supported, but without the possibility to change the orientation of the loading platform in the case of the MTS loading frame. The buckling loads measured on the three shells during the static tests using the two different load frames are reported in Table 2. From the data reported in Table 2, it is possible to see that there is a scatter among the values of buckling loads measured during the different tests. The average of the buckling loads of the three shells is equal to 14.69 kN for the tests on the buckling press, and to 13.85 kN for the tests on the MTS load frame with a difference of 5.7%. The standard deviation is 0.56 and 1.69, respectively. Two photographs taken during the static tests on Shell A and on Shell C using the press for buckling tests are shown in Fig. 4.
Please cite this article as: Bisagni C. Composite cylindrical shells under static and dynamic axial loading: An experimental campaign. Progress in Aerospace Sciences (2015), http://dx.doi.org/10.1016/j.paerosci.2015.06.004i
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Fig. 2. Application of the ending tabs.
4. Dynamic tests
Table 2 Bucking loads measured during the static tests using the two load frames.
Two types of dynamic tests were performed using the MTS load frame: modal tests at different load levels before buckling and dynamic buckling tests applying an axial shortening of short duration. The modal tests were performed using the roving hammer technique, which allowed the evaluation of the modal damping values in the range between 0 and 500 Hz for different load levels before the buckling. In particular, the modal tests were performed by impacting 48 points located in the middle of the cylindrical shell with an instrumented hammer. The hammer was used for modal excitation, while a PCB microphone was used for response measurement, in place of a classical accelerometer, to avoid any contact of the sensor with the shell and any mass loading effect. LMS TestLab software was employed for data acquisition and processing, while the identification process was based on the Polymax method available inside Testlab module. Photographs of a cylindrical shell with the instrumented hammer is reported in Fig. 5. The measurements were taken at no load and at three different levels of pre-buckling axial load: 3 kN, 5 kN and 7 kN. The frequencies and the damping values measured on Shell C are reported in Table 3 for the different modes. The measured damping are then graphically represented versus the frequency in Fig. 6. It is possible to observe that an increase of the load determines a reduction of the modal frequency and an increase of the damping. The same conclusions are drawn for the other two shells, with values that differ for the three shells in the range of about
Shell
Buckling load [kN] - Tests using the Buckling load [kN] - Tests using press MTS
Shell A 15.34 Shell B 14.33 Shell C 14.41
13.01 12.75 15.79
10%. Some modes experimentally measured on Shell C are represented in Fig. 7. It is important to note that what is measured during the modal testing is simply the modal damping. During the DAEDALOS project a large activity has been carried out to identify more accurate physical models of damping, to be implemented in finite element models for dynamic simulation. These models are complex and require specific tests on specimens to identify the constitutive model parameters [18,19]. The dynamic buckling tests were carried out imposing an axial displacement equal to 2 mm at the velocity of 60 mm/s. It was the maximum possible velocity considering the reaction force of the shells. The displacement of 2 mm was the value imposed to the MTS, that differs from the value measured by the LVDTs between the plates. The load–shortening curves measured on the three shells during the dynamic buckling tests are reported in Fig. 8; while Fig. 9 shows the time history of the resulting blended square wave axial shortening applied during the dynamic buckling tests.
Hydraulic arm Ball screws
Shell LVDT Load cell
Fig. 3. Testing equipment: in-house designed press and MTS system.
Please cite this article as: Bisagni C. Composite cylindrical shells under static and dynamic axial loading: An experimental campaign. Progress in Aerospace Sciences (2015), http://dx.doi.org/10.1016/j.paerosci.2015.06.004i
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Fig. 4. Two photographs taken during the static tests on Shell A and on Shell C.
The load–shortening curves present a large jump in the measurement of the displacement after buckling due to the LVDTs, which are not able to keep up with the dynamic of the load frame. The maximum load of the curves corresponds to the dynamic buckling load, and resulted higher than the static values in all the performed tests. For example, the dynamic buckling load of Shell C results equal to 16.62 kN, compared to the static buckling value of 15.79 kN measured during the static test on the MTS. Identical behavior was observed during the tests on the other two shells. For all three cylindrical shells the ratio between the dynamic buckling load and the static one resulted equal to approximately 1.05. Even if it appears as a consistent trend, it is not yet possible to state that the increase of the buckling loads of 5% is due to the dynamic effects, as the number of tested structures is limited, and as this increase falls into the range of the scatter of the measured buckling loads. Besides, in the case of dynamic buckling the mode shapes play the same role of the geometrical imperfections, as pointed out by Simitses [14]. This mechanism is mainly related to the bandwidth of the external excitation, or, in other words, to how many modes is able to excite. Also other important aspects play a relevant role, like inertia forces, damping, and so on. In the case of MTS machine, the maximum bandwidth available, for such high compression loads, is not sufficient to switch on the mechanism, so the difference between static and dynamic buckling loads is not significant. Unfortunately, it was not possible to perform further tests with a higher velocity of imposed displacement due to the limit of the load frame.
5. Numerical analysis and correlation Finite element analyses are performed using the commercial code ABAQUS [20]. The mesh of the cylindrical shell is chosen after a convergence study, and is composed of 9360 S4R shell elements and 9516 nodes, with element dimensions of about 10 mm 10 mm. Boundary conditions are applied in order to simply reproduce the clamping conditions of the compressive tests. In particular, nodal constraints of fixed displacement in three directions are imposed on one side of the shell, while nodal constraints in the radial and tangential directions and free displacement in the axial direction are imposed on the other side. At first, a modal analysis is performed. Table 4 reports the obtained natural frequencies, while the first modal shape is presented in Fig. 10. The natural frequencies measured during the modal tests are compared to the values obtained from the finite element analyses. The difference for the first frequency is limited to 3%, and is of the same order also the difference for the second frequency. It grows for the higher frequencies, and results equal to about 10% for the third one, and around 16% for the fourth and fifth ones. Then, an eigenvalue buckling analysis is performed without any initial imperfection. The buckling load results equal to 23.99 kN, to which corresponds axial displacement of 0.89 mm. The first buckling shape is presented in Fig. 11. The static buckling loads measured on the shells vary between a minimum of 12.75 kN and a maximum of 15.79 kN. The numerical value obtained without any initial imperfection from the eigenvalue analysis is equal to 23.99 kN, so is significantly higher
Fig. 5. Cylindrical shell ready for the modal tests, and detail of the microphone used for response measurement.
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Table 3 Frequencies and damping values measured on Shell C. Mode
1 2 3 4 5 6 7 8 9 10
0 kN
3 kN
5 kN
7 kN
Freq. [Hz]
Damping
Freq. [Hz]
Damping
Freq. [Hz]
Damping
Freq. [Hz]
Damping
– 194.00 212.57 239.05 271.23 307.63 347.34 391.85 438.00 487.81
– 0.52 0.60 0.42 0.36 0.32 0.34 0.34 0.28 0.24
191.02 194.81 210.13 234.82 265.54 300.45 336.99 377.85 427.42 475.08
0.87 0.55 0.60 0.39 0.36 0.33 0.39 0.37 0.32 0.30
188.99 191.76 205.85 230.60 260.35 293.13 328.37 368.14 418.48 464.49
0.72 0.54 0.51 0.42 0.39 0.46 0.50 0.38 0.35 0.34
185.35 188.87 202.06 226.32 254.57 286.86 320.34 359.49 409.35 453.48
0.79 0.70 0.51 0.43 0.45 0.45 0.48 0.44 0.36 0.37
Fig. 8. Comparison between dynamic buckling tests on three shells. Fig. 6. Damping versus frequency for different load levels.
Mode 1
Mode 2 Fig. 9. Applied shortening during dynamic buckling test.
Table 4 Natural frequencies obtained by finite element analysis.
Mode 5
Mode 7
Mode
Natural frequencies [Hz]
No. 1 No. 2 No. 3 No. 4 No. 5
199.47 206.28 214.13 227.60 257.97
Fig. 7. Experimentally measured modes of Shell C.
than the experimental one. Better and more realistic comparisons are obtained introducing initial geometric imperfections and performing dynamic analysis. A dynamic analysis is so carried out imposing a constant compressive displacement velocity in the axial direction on one side of the shell. The imposed compressive velocity is chosen equal to 4 mm/s for 0.75 s of simulation, representing a good compromise
between CPU time and result accuracy. The buckling load, obtained from a dynamic implicit analysis including initial imperfections given by the combination of the first and third mode and having maximum amplitude of 0.1 mm, equal to 20% of the thickness, is equal to 18 kN. The comparison of the post-buckling shapes is shown in Fig. 12, where a photograph of Shell A is reported together with the post-buckling deformation obtained from the analysis.
Please cite this article as: Bisagni C. Composite cylindrical shells under static and dynamic axial loading: An experimental campaign. Progress in Aerospace Sciences (2015), http://dx.doi.org/10.1016/j.paerosci.2015.06.004i
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Fig. 13. Load–shortening curve of Shell B until final failure.
Fig. 10. First modal shape obtained by finite element analysis.
Fig. 11. First buckling shape obtained by finite element analysis.
6. Static compression test until final failure Shell B was tested under axial static compression until the final failure. The test was performed in displacement control using the press for buckling tests designed in-house. The load–displacement curve measured during the test is presented in Fig. 13. The pre-buckling response of the shell is characterized by a linear load–shortening response with a stiffness of about 200 kN/ mm. The buckling load was equal to 13.9 kN with a shortening of 0.58 mm. The shell presented a large, almost flat, post-buckling
Fig. 14. Shell B during the static compression test until final failure.
field, with a load of approximately 6 kN in the first part, decreasing then to about 4.4 kN. The post-buckling load results so equal to about 40% of the buckling load in the first part of the post-buckling field, and then it decreases to less than 30%. The final failure happened at a shortening of 15.58 mm, equal to about 26 times the buckling shortening. The load was 3.8 kN before dropping down, with the shell no more able to sustain any load. A photograph of the testing equipment with the shell in the post-buckling field is shown in Fig. 14. During the test two cameras were installed: one on the socalled front side of the shell and one on the rear side. Fig. 15 shows the evolution of the post-buckling shape of the shell. In particular,
Fig. 12. Experimental–numerical comparison of static post-buckling shape.
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Fig. 15. Photographs taken on front and rear side of Shell B during the test until final failure: (a) shortening¼0.65 mm; (b) shortening¼4.02 mm; (c) shortening¼8.22 mm; (d) shortening¼15.55 mm.
two photographs are reported for four different shortening values of the tests. The first photograph is taken from the camera located on the front side and the second photograph is taken from that one on the rear side. The shell appears different from the two cameras. Different lights were on the two sides of the shell, as in one case the natural light is predominant respect to the artificial light. There is also a difference of light on the photographs of the front side, as the test lasted several hours and the natural light changed during the day. In any case, the main difference between the photographs taken from the two cameras is a different post-buckling shape. It is due to the geometric imperfections of the shell, together with probably a load not evenly distributed. Immediately after the buckling (Fig. 15a) the deformation is characterized by the
presence of two/three small half-waves on the front side, while presents a regular central buckling half-wave on the rear side. Increasing the axial displacement, the post-buckling deformation evolves, remaining irregular on the front side. At a shortening of about 4 mm (Fig. 15b), three irregular half-waves can be noted on the front side, while the rear side presents almost perfect diamond waves, similar to a Yoshimura buckle pattern. The out-of-plane displacement increases significantly with the increase of the axial displacement. Fig. 15c shows the deformation for a shortening equal to 8.22 mm, while Fig. 15d reports the photographs taken just before the final failure at a shortening of 15.55 mm. It is possible to note that the front side presents large waves, some of them developed from the union of the previous waves. On the opposite, the rear side of the shell did not changed
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Fig. 16. Out-of-plane displacement just after buckling and before final failure.
Fig. 17. Failure of Shell B visible from outside and from inside.
shape, but presents the same number of shell with larger out-ofplane displacement. The large out-of-plane displacements cause sharp corners on the deformations towards the interior of the shell and especially to the outside. Fig. 16 reports two photographs that show the out-of-plane displacement just after buckling and before final failure. A straight plate in aluminum alloy helped to point out the displacements. Just after the buckling the deformation is highlighted by the shadow of the plate. Before final failure, the out-of-plane displacement can be measured and is equal to almost 40 mm. The test was stopped when the shell was not able to sustain the load any more. Small failures developed on the sharp corners of the half-waves, due to the large strain values. Some of the failures were on the deformations towards to the outside, and were visible on the shell outer surface. When the shell was removed from the testing equipment, several failures were visible on the inner surface. Probably they happened in the last part of the test, when small noises were heard, but no cracks were noted from the outside of the shell. The failures were mainly fiber fractures both on the inner and outer surfaces. Very small and localized fiber pullouts were also present in two/three points at the end of the test. Two photographs of the shell failure are reported in Fig. 17. 7. Conclusions The results of the study performed at the Politecnico di Milano
inside the European project DAEDALOS on three composite cylindrical shells were presented. In particular, static buckling tests under axial compression and two types of dynamic tests were performed. The dynamic tests were modal tests at different load levels before buckling and dynamic buckling tests with an applied axial shortening of short duration. One of the shell was then tested until final failure under axial compression. A scatter among the values of buckling loads was measured during the static buckling tests for the three shells using two different load frames. The average of the buckling loads of the three shells is equal to 14.69 kN for the tests on the buckling press, and to 13.85 kN for the tests on the MTS load frame with a difference of 5.7%, while the difference between the buckling values measured on the same shell using the two different load frames is between 9% and 15%. The scatter is due to the high sensitivity of unstiffened thin-walled cylindrical shells to imperfections, such as initial geometric imperfections but also imperfections related to the boundary conditions and to the loading application. The modal tests at different load levels allowed to observe that an increase of the load determines a reduction of the modal frequency and an increase of the damping. The dynamic buckling tests revealed that the dynamic buckling loads are higher than the static ones of about 5%. Even if it appears as a consistent trend, it is not yet possible to state that the increase of the buckling loads of 5% is due to the dynamic effects, as the number of tested structures is limited, and because this increase falls into the range of the scatter of the measured buckling loads. The results of the static compression tests until final failure show the strength capacity of these structures to work in the postbuckling range with a capacity to sustain a load that is about 40% of the buckling load. Large deformations are obtaining before the final failure with out-of-plane displacements of almost 40 mm and a shortening equal to about 26 times the buckling shortening. The tests investigated the behavior of thin-walled cylindrical shells subjected to axial compression both in static and dynamic conditions. The importance of having measurements of both static and dynamic buckling loads, as well as measurements of damping values for structures in composite materials is fundamental for the development and validation of numerical models.
Acknowledgments The research leading to these results has partially received funding from the European Union's Seventh Framework Programme [FP7/2007-2013] under grant agreement “DAEDALOSDynamics in Aircraft Engineering Design and Analysis for Light Optimized Structures” No. 266411. The author would also like to thank Potito Cordisco for helping in performing the tests. An initial version of this paper was presented at AIAA SciTech, 55th AIAA/ ASMe/ASCE/AHS/SC Structures, Structural Dynamics, and Materials Conference, 13–17 January 2014, National Harbor, Maryland, USA.
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Please cite this article as: Bisagni C. Composite cylindrical shells under static and dynamic axial loading: An experimental campaign. Progress in Aerospace Sciences (2015), http://dx.doi.org/10.1016/j.paerosci.2015.06.004i