[american institute of aeronautics and astronautics 50th aiaa/asme/asce/ahs/asc structures,...

American Institute of Aeronautics and Astronautics

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Research Activities on Buckling of Composite Structures in Italy

Chiara Bisagni1 and Vittorio Giavotto2

Politecnico di Milano, Milano, 20156, Italy

Giulio Romeo3 and Giacomo Frulla4 Politecnico di Torino, Torino, 10129, Italy

and

Daniele Fanteria5 and Agostino Lanciotti6 Università di Pisa, Pisa, Italy, 56126, Italy

The paper gives an overview of some research activities regarding buckling of composite structures performed in Italy in the last years. In particular, the activities performed at Politecnico di Milano, at Politecnico di Torino and at Universita’ di Pisa are here presented. Some investigations were performed on structures manufactured by Agusta/Westland and by Alenia Aeronautica, while other researches were funded by the Italian Ministry of Research, and other ones were funded by the European Commission within European Projects.

I. Introduction HE paper gives an overview of some research activities regarding buckling of composite structures performed in Italy in the last years.

The interest for the buckling and post-buckling behavior of composite structures is continuously growing, as a possible solution to lower the weight of some primary structures is offered by the post-buckling design. In this case, the structures would be allowed to buckle well below the limit load, but they must also withstand external loads up to the ultimate values in the buckled configuration. The effective design of this type of structures results heavily dependent on the availability of methods and tools that are based on finite element analyses, but must be validated by a quite large number of experimental tests, so to take into account all the possible variabilities, such as different structures configurations, materials, lay-ups, loading conditions…

Some of the research activities performed at Politecnico di Milano, at Politecnico di Torino and at Universita’ di Pisa are here presented. They consist on experimental tests and numerical analyses developed to investigate the buckling and post-buckling behavior of different structures, such as unstiffened and stiffened shells, flat and curved panels, closed boxes and a helicopter tailplane.

Some investigations were performed on structures manufactured by Agusta/Westland and by Alenia Aeronautica, while other researches were funded by the Italian Ministry of Research, and other ones were funded by the European Commission within European Projects.

1Associate Professor, Dipartimento di Ingegneria Aerospaziale, Via La Masa 34, [email protected], AIAA Member 2Full Professor, Dipartimento di Ingegneria Aerospaziale, Via La Masa 34, [email protected] 3Full Professor, Dipartimento di Ingegneria Aerospaziale, C.so Duca degli Abruzzi 24, [email protected] 4Associate Professor, Dipartimento di Ingegneria Aerospaziale, C.so Duca degli Abruzzi 24, [email protected] 5Assistant Professor, Dipartimento di Ingegneria Aerospaziale, via G. Caruso 8, [email protected] 6Full Professor, Dipartimento di Ingegneria Aerospaziale, via G. Caruso 8, [email protected]

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50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference <br>17th4 - 7 May 2009, Palm Springs, California

AIAA 2009-2349

Copyright © 2009 by Chiara Bisagni, Vittorio Giavotto, Giulio Romeo, Giacomo Frulla, Daniele Fanteria and Agostino Lanciotti. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.


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II. Research activity at Politecnico di Milano The research activities on buckling of composite structures here below described were performed at Politecnico

di Milano inside three different European projects: “Design and validation of imperfection-tolerant laminated shell structures (DEVILS)” (October 1994 - March

1999), in cooperation with the Institute of Mechanics of Materials and Geostructures in Greece, Eurocopter Deutschland in Germany, IFREMER in France, AGUSTA in Italy, INTERMARINE in Italy, Imperial College of Science, Technology and Medicine in the UK, National Technical University of Athens in Greece, DLR (German Aerospace Centre) in Germany, ETH Zurich in Switzerland, and CNIM in France;

“Improved post-buckling simulation for design of fibre composite stiffened structures (POSICOSS)” (January 2000 - September 2004) in cooperation with DLR (German Aerospace Centre) in Germany, AGUSTA in Italy, IAI (Israel Aircraft Industries) in Israel, Riga Technical University in Latvia, RWTH Aachen University in Germany, and TECHNION (Israel Institute of Technology) in Israel;

“Improved material exploitation at safe design of composite airframe structures by accurate simulation of collapse (COCOMAT)” (January 2004 - October 2008) in cooperation with DLR (German Aerospace Centre) in Germany, AGUSTA in Italy, Gamesa in Spain, Hellenic Aerospace Industry in Greece, IAI (Israel Aircraft Industries) in Israel, PZL Swidnik in Poland, SMR S.A. in Switzerland, Cooperative Research Centre for Advanced Composite Structures Limited in Australia, Swedish Defence Research Agency in Sweden, University of Karlsruhe in Germany, Riga Technical University in Latvia, RWTH Aachen University in Germany and TECHNION (Israel Institute of Technology) in Israel.

A. Buckling and Post-buckling of Cylindrical Shells The buckling and post-buckling behavior of unstiffened thin-walled carbon fibers reinforced plastics (CFRP)

cylindrical shells1-2 was investigated inside the European Project DEVILS. The shells were tested until collapse by means of a testing equipment, that allows axial and torsion loading,

applied separately and in combination, using a position control mode. The testing apparatus includes also a laser scanning system for the measurement in situ of the geometric imperfections as well as of the progressive change in deformations on the internal surface.

The specimens were fabricated by Agusta/Westland from CFRP unidirectional tape material and from CFRP fabric tape material. The specimens were characterized by an internal diameter and an overall length of 700 mm, including two tabs provided at the top and at the bottom surfaces for attaching them to the loading equipment. The actual length was therefore limited to the central part equal to 540 mm. The unidirectional shells presented a thickness of 1.20 mm and consequently a radius-to-thickness ratio of 292, while the fabric shells presented a thickness of 1.32 mm and a radius-to-thickness ratio of 265.

The measurement of the inner surfaces of the specimens was carried out, using the laser scanning system, after each specimen was mounted in the test rig and before any load was applied, allowing to measure the geometric imperfections in situ and not in a separate rig. Each specimen was firstly tested under pure axial compression and under pure torsion, individually. The curve of axial load versus displacement as well as the curve of torsion versus rotation were recorded in real-time, during the tests. Then the shells were tested under combined axial and torsion loading. To perform combined tests, three different procedures were investigated. The first procedure consisted in twisting the specimen into one direction (clockwise or counter-clockwise) to a pre-set torsion torque level and then in axially loading it until buckling. The second one consisted in axially loading the specimen to a pre-set axial load level and then twisting it into one or the opposite direction until buckling. The third procedure consisted in applying fixed steps of axial load and torsion torque with different ratio of axial load and torsion torque levels. During all the three procedures, the axial and tangential displacements were recorded using LVDT transducers throughout the whole test, as well as the axial compression load and the torsion torque using a load cell.

All the tests were performed to reach the buckling phenomenon, were continued in the post-buckling field and then the specimens were unloaded always using the position control mode. The inner surface of the cylindrical shells was measured 15-20 times during each test using the lasers system, so to be able to measure the pre-buckling surface and to follow the development of the post-buckling deformations. This was possible as the time required to measure a complete specimen surface was limited to 4 minutes.

An example of the measurements taken on a [0°/45°/-45°/0°] fabric cylindrical shell under axial compression test is shown in Figure 1.


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The results identified the effect of

laminate orientation, showed that the buckling loads were essentially independent of load sequence and demonstrated that the shells were able to sustain load in the post-buckling field without any damage.

The measured data were also used for the development and validation of analytical and numerical high fidelity methods. The numerical models were performed using commercial finite element codes. Figure 2 shows the buckling mode obtained with an eigenvalue analysis performed using ABAQUS/Standard, and the post-buckling mode obtained with a dynamic analysis performed using ABAQUS/Explicit. The geometric imperfections measured on the real specimens were accounted for in the finite element model for the dynamic analysis. The investigation performed using the dynamic analysis showed the reliability to follow the evolution of the cylinder shape from the buckling to the post-buckling field and showed good accuracy in reproducing the experimental post-buckling behavior.

B. Buckling and Post-buckling of Cylindrical Stiffened Shells The buckling and post-buckling behavior of stiffened CFRP cylindrical shells3-4 was investigated inside the

European Project POSICOSS. In particular, four stringer-stiffened shells and two ring- and stringer-stiffened cylindrical shells were tested.

The shells were fabricated by Agusta/Westland from a CFRP fabric tape material with an internal radius of 350 mm and a length of 700 mm, according to three different configurations able to work in the post-buckling range. The analysis and design of the configurations were performed at Politecnico di Milano. In particular, the first two configurations were designed to offer a ratio between the collapse load and the first buckling load under axial compression equal to about 3. The last configuration was intentionally designed to work under torsion offering a ratio between the collapse torque and the first buckling torque equal to about 3. Consequently, two stringer-stiffened cylindrical shells were fabricated for the first configuration, two stringer-stiffened cylindrical shells were fabricated for the second configuration and two ring- and stringer-stiffened cylindrical shells for the third configuration.

After that each specimen was mounted in the test apparatus, the geometric imperfections were measured in situ and were then processed by a custom-developed software which calculated the “best-fit cylinder” through the entire grid of measured points. This widely used data processing technique permits, on one hand, an easily introduction of the imperfections into the analytical and numerical models and, on the other, can be used as inputs to the International Imperfection Data Bank for comparative studies on the effect of the manufacturing process on the magnitude and spatial distribution of the geometric imperfections.

(a) (b)

Figure 2. [0°/45°/-45°/0°] fabric cylindrical shell under axial compression: (a) eigenvalue analysis; (b) explicit dynamic analysiswith imperfections.

0

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150

0 0,4 0,8 1,2

Displacement [mm]

Axia

l loa

d [k

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(a) (b) (c)

Figure 1. [0°/45°/-45°/0°] fabric cylindrical shell under axial compression: (a) load-shortening curve; (b) laser scanning of post-buckling mode; (c) photo of post-buckling mode.


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The first specimen of each configuration was, first, tested until the local buckling load under pure axial compression and under pure torsion, individually. Then combined tests under axial compression and torsion were carried out until local buckling loads. These tests were performed 2-3 times, in order to verify the repeatability of the obtained results. Finally, the collapse test was executed. On the second specimen of each configuration, instead, only the collapse test was performed. This allowed evaluating the effect of the repeated buckling on the post-buckling cycles, by comparing the results obtained for the two nominally identical specimens of a single configuration. The modality of the collapse tests changed according to the configuration: the shells of the first and second configurations were collapsed under axial compression, while on the specimens of the third configuration the collapse tests were carried out under torsion.

The curves of axial load versus displacement and of torque versus rotation were lined in real-time, during the tests. Besides, in each test, the inner surface of the cylinders was measured several times, according to the duration of the test (typically, from seven times for a pure compression test until the first local buckling to thirty times for a collapse test). This permitted to evaluate the evolution of the surface from the undeformed pre-buckling shape to the deformed post-buckling one. Moreover, collapse tests were digitally recorded by a double high resolution camera system, in order to detect the zones of the shell where the failure started from and its modality.

A photo of a ring- and stringer-stiffened cylindrical shell during a test under torsion is shown in Figure 3, where it is possible to see also the buckling test equipment.

As an example, Figure 4 shows some data of the collapse test on the ring- and stringer-stiffened cylindrical shell configuration. The laser scanning taken in the post-buckling field at 19 kNm on one of the two shells shows that the skin is completely buckled. The cylinder presented two diagonal half-waves in each sector delimited by two stringers in the circumferential direction and by the external reinforcing ring in the axial direction. These waves were perfectly defined and had a regular shape with a normal displacements of 5.5 mm inward and 3.5 mm outward. By increasing the torque, at about 39 kNm, the central reinforcing ring started to debond from the skin. Once the central ring was debonded, the skin pattern suddenly changed, as it can be seen from the photo. The superimposition of the torque vs rotation curves obtained for the two cylinders of this configuration is also shown. It is possible to observe that the behavior of the two specimens was very close both in the prebuckling and in the postbuckling range up to the separation between the cylinder skin and the central ring. The differences in the collapse torque and in the corresponding rotation were equal to 10% for torque and 23% for rotation. The ratio between the collapse torque and the first buckling torque resulted equal to about three.

(a) (b) (c)

Figure 4. Torsion test of a stiffened shell: (a) laser-scanning; (b) photo; (c) load-shortening curves.

Figure 3. Buckling test equipment with a stiffened shell during a torsion test.


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The data acquired during the first nondestructive tests and during the destructive collapse tests demonstrated that the shells were able to sustain load in the post-buckling field without any damage. Indeed, neither failure mechanisms nor any other hazards were visible in the post-buckling range. On the other hand, the collapse, due to the failure of the stringers both under axial compression and under torsion, was sudden and destructive. It caused extensive fracture in the skin and in the stringers, so that, after the collapse, the load suddenly dropped to about zero. The experimental data showed clearly the strength capacity of these structures to work in the post-buckling range, with a ratio between the collapse load and the first buckling load higher than 3, allowing for the further weight savings likely to be required in the near future for the construction of aerospace structures.

C. Static and Cyclic Buckling of Undamaged and Pre-Damaged Curved Stiffened Panels The design, testing and validation of closed box structures made of CFRP stringer stiffened curved panels5-7 was

performed inside the European research project COCOMAT. In particular, static and cyclic buckling tests were performed up to collapse aiming to exploit the post-buckling field of CFRP panels by means of experimental tests, and to develop validated tools able to capture the damage mechanisms.

The design phase was carried out using ABAQUS/Explicit with the purpose to obtain a structure with a ratio between the collapse and the buckling load greater than three under axial compression and greater than two under torque. Five box were then manufactured by Agusta/Westland and tested at Politecnico di Milano.

At the beginning, two boxes were tested, one (box SN1) under static loads and one (box SN2) under static and cyclic loads. Then three boxes with pre-damages, obtained with Teflon inserts between three stringers and the skin, were tested. The first one (box SN3) was tested under static loads and the other two (box SN4 and box SN5) under static and cyclic loads. In particular, box SN4 was tested in the same conditions and number of cycles of box SN2, while box SN5 with higher loads and number of cycles. All the five boxes were then tested until collapse in the same conditions with combined compression and torsion. In this way, it was possible to find out, from one hand, the influence that static and cyclic combined post-buckling loads have on undamaged and pre-damaged structures and, from the other hand, the effect that initial pre-damages have on the global response of these structures in the post-buckling field up to collapse.

The comparison between the results under combined axial compression and torque loads obtained in the collapse test on box SN1 and in the FE analysis reproducing the collapse are shown in Figure 5. A good correlation was obtained, both in the buckling and post-buckling behavior and in the collapse modality, demonstrating the capability of the dynamic explicit analyses to catch the highly non-linear response of the aeronautical panels.

After the tests on all the five boxes, under static and cyclic loads, it was possible to observe that the CFRP boxes here investigated showed, from one hand, a large capability to safely work in the post-buckling field, reaching ratios between collapse load and buckling load higher than 3.5. On the other hand, the boxes did not suffer any loss of structural performances when they were subjected to loads up to 300% of the buckling one, even if the post-buckling field was reached thousands of times during the operative life.

Besides, the boxes did not show any propagation of pre-damages, neither due to the static or to the cyclic post-buckling combined loading, as it was observed by several C-scans performed using an ultrasound system directly in-loco during the tests.

0 100 200 300 400 500 600 700

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Figure 5. Deformed shape recorded in the collapse test and in the FE analysis at 300% TBUCKL: (a) Test: moiré fringes; (b) Test: laser equipment; (c) FE: displacement contour plot


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D. Post-Buckling Behavior of Stringer-Stiffened Laminated Composite Helicopter Tailplane. A composite laminated helicopter tailplane8, whose lower panels were subjected to buckling phenomena during

the life envelope, was analyzed and tested inside the European project POSICOSS. The structure, manufactured by Agusta/Westland, was

made of carbon fabric, carbon unidirectional and honeycomb. Two different types of lower laminate composite panels were investigated: Z stringer-stiffened panels and L stringer-stiffened panels. At the beginning three Z stringer-stiffened and three L stringer-stiffened laminate composite lower panels were tested until 85% of the target load.

A photo of the helicopter tailplane in the test rig is shown in Figure 6. During the tests, the applied load was measured using a load cell, the displacement of the tailplane ends using potentiometers and the panels strains using strain gauges. Moire’ fringes were also installed to highlight the panels deformation in the lower part of the structure.

The last L stringer-stiffened panel was then tested until collapse. The buckling load happened at 63% of the target load, while the collapse happened at 90%.

At the same time, the finite element analyses of the tailplane structures with both Z stringer-stiffened and L stringer-stiffened panels were performed, simulating the dynamic of a slow compression test, using LS-DYNA.

The comparison between the numerical and the experimental deformations for the L stringer-stiffened panel are shown in Figure 7. The deformations are not very similar, due also to the fact that the Moire’ fringes allowed to highlight only the lower part of the panel.

The load-displacement curve obtained from the finite element analysis for the L stringer-stiffened panel is compared in Figure 8 to the ones measured during the test on the second and the fourth panels. The correlation was good until about 70% of the target load.

In any case, the collapse of the structure was predicted by the finite element analyses at 93% of the target load and experimentally happened at 90%.

Figure 7. Comparison between the numerical and the experimental deformations for the L stringer-stiffened panel at 88% of the target load.

Figure 8. Comparison between the numerical and the experimental load-displacement curves for the L stringer-stiffened panel.

Figure 6. Helicopter tailplane and test rig.


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III. Research activity at Politecnico di Torino Both buckling and post-buckling of composite plate under combined biaxial compression and shear loads were

analyzed by means of the in-house development of specific numerical procedures in order to evaluate the critical condition and the post-critical configuration under combination of loads9. The theoretical calculations have been compared when possible to experimental results by means of a new loading machine available at the Department. The presence of specific loading configuration more consistent with the real cases such as linearly varying load along edges, were also taken into consideration in some panel schemes10-11. Non-linear evaluation of the wing box behavior under bending loads and under pure torsion including the effect of crushing pressure and shear in-plane panel loads was studied pointing out different contribution to the demonstrated non-linear phenomenon12-13. Cyclical compressive loading of panels with defects have been also studied in order to evaluate their effect in the panel behavior and their possible growing under repetitions. The progressive nature of failure is a characteristic property of laminated composites. Fatigue failure is usually accompanied by extensive damage that multiplies throughout the specimen volume. Experimental activity is fundamental in this phase due to the nature of different empirical coefficients included in typical Paris-law formula.

A. Buckling and Post-buckling of Flat Anisotropic Panels

The application of the stationary value principle of total potential provided the working out of the buckling condition of flat anisotropic panels with the definition of in-house developed Fortran code EMASTER5. The considered boundary conditions are: clamped-clamped, simply supported, clamped-simply supported. Combined compression and shear loads are included with the possibility of linearly varying in-plane loads configuration specific for situations more consistent to real cases. The EMASTER5 code includes also the buckling of I,T,Ω stiffened plates under in-plane combined compression and shear. The same principle provided the determination of the equilibrium equations, solved by Galerkin method in POBUCK Fortran code, in order to identify the post-critical behavior of the flat anisotropic panels under similar boundary conditions. This in-house developed code included combined constant compressive and shear loads with an extension to the linearly varying in-plane loads as representative of more real situations. The research activity has been developed autonomously in combination with several experimental tests starting from the 1995 up to now. The experimental activity became possible after the acquisition of new testing machine (Figure 9) capable of combined loading of panels up to 1000 x 700 mm in dimensions. It was used for wide experimental activity in order to validate and compare the numerical results to the experimental ones. The testing machine was upgraded to include non conventional loading configuration that is in-plane bending and linearly varying load configuration. Typically the machine is able to apply a longitudinal tension/compression load up to 500kN, a transverse tension/compression load of 200 kN and a shear load of 200 kN. The loads can be also distributed linearly along the

Table 1. Numerical/experimental buckling load comparison (Px – kN) for different boundary conditions and γy=0.

EMASTER5 NASTRAN Applied biaxial load ratios

γx

S-S C-C C-S C-C C-S

Test

(-1,0) 0 -108.9 -222.4 -194.6 -247.5 -212.9 -225.4

(-1,-0.6) 0 -71.9 -177.9 -163.8 -198.7 -179.3 -186.5

(-1,-1) 0.5 -62.0 -166.3 -150.0 -158.6 -142.6 -166.6

(-1,-1) 1 -72.5 -180.2 -157.3 -176.2 -153.4 -176.4

(-1,-1) 2 -88.5 -205.8 -170.3 -195.7 -158.7 -196.0

Figure 9. Schematic view of new combined testing machine (biaxial compression and shear loading equipment) at Politecnico di Torino.


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boundary. Longitudinal load is applied by two separately controlled servo-actuators with a maximum load of 250 kN in compression and 225 kN in tension respectively. The transverse load application system is similarly controlled by two separated servo-actuators with a maximum load of 100kN in compression as well as in tension respectively. It

floats not interfering with longitudinal and shear loads. A displacement control is used to keep the panel ends parallel to each other during shear load application. The test rig is completely loop-controlled via electronic modules which are closed by nine transducers. Several experimental and numerical buckling results and some post-buckling numerical and analytical comparison are presented in9-11. A summary of the more recent numerical and experimental buckling comparisons in the case of linearly varying load configuration are reported in Table 1. The results are related to a flat anisotropic graphite-bismaleimide (T800-5250) panel with dimensions of 1000x700 mm and lay-up of [452/905/-452/02/902]2s. The group of data related to longitudinal compression and in-plane bending for a clamped configuration (Figure 10) is reported as an example. The reversal of the SG strains in the maximum buckle point indicates the presence of a critical condition. A confirmation of the buckle shape is detected by the out-of-plane displacement plot and by the Moiré plot. The comparison confirmed the accuracy of the developed procedure. POBUCK buckling loads for in-plane different configurations are reported in table 2 in order to validate the procedure with respect to EMASTER5 and FE results previously reported. The post-buckling behavior of the same anisotropic plates under in-plane bending condition is reported in Figure 11 from POBUCK and FE analysis. he comparison is quite satisfactory.

Table 2. Numerical/experimental buckling load comparison (Px – kN) for C-C boundary conditions and γy=0:

Applied biaxial load ratios

γx POBUCK

(-1,-0.6) 0 -177.9 (-1,-1) 0.5 -166.4 (-1,-1) 1 -180.3 (-1,-1) 2 -206.3

Figure 10. Experimental results for a clamped panel under longitudinal and in-plane-bending-transverse compression. a) typical SG behavior, b) out-of-plane deflection, c) Moiré plot at longitudinal load of 275 kN.

Figure 11. a) FE result for in-plane bending condition and FE/analytical comparison. b) Maximum non-dimensional deflection in function of longitudinal load ratio.


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B. Wing Box Behavior under Pure Bending/Torsion Anisotropic panels are usually considered as subjected to in-plane loads and separately from the main structure. This is an erroneous approach : additional effects are created on the skin panels when all of the wing-box beams are subjected to bending moment12 or pure torsion moment13.

As a result of pure bending moment the whole box is curved while the upper and lower panels are subjected to an induced transversal load resulting in a lateral pressure. Lateral pressure interacts with the existing in-plane loads from bending, causing a specific loading configuration that has an influence on the buckling and post-buckling behavior of the lower/upper skin panels. A nonlinear analysis was developed to investigate the effect of the presence both of the lateral pressure and the classical in-plane loading situations. POBUCK code was used in order to work out the buckling and post-buckling behavior of the compressed panel under this condition, on the basis of smeared stiffness approximation. The pure bending test machine was already available at the Department12. The structural tested configuration consists in a composite box as in Figure 12 with a length of 0.688m. Material CFRP characteristics were experimentally determined and can be found in12. Deflections were measured by a dial deflectometer that ran on a guide independent from the box structure connected to an x-y recorder. The strain behavior of the compressed part of the wing-box, is reported in Figure 13. The effect of the lateral pressure combined with compression is very evident: the compressed stiffener moves from compression to tension at high bending moment while the panel remains in the tension field. The analytical/experimental correlation is

Figure 13. Longitudinal strain behavior on the stiffener web.

Figure 12. a)Overall view of the bending machine and (b) wing-box SG scheme and dimensions.

Figure 14. a) Wing box for test configuration and (b) testing equipment for puretorsion at Politecnico di Torino


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quite good: as an effect of the lateral pressure the stiffener is subjected to a local bending moment that drastically alters the hypothesis of a uniform compression longitudinal loading of the panel. A similar loading configuration can be determined as a result of pure torsion moment applied to wing-boxes. A load perpendicular to both the upper and lower panels arise due to the derived torsion curvature associated with the panel shear loads. Additional effects are created by the structure when the panels are in the post-buckling range. A diagonal shear stress field appears and the effective shear modulus diminishes as the applied stress increases. Consequently the torsional stiffness of the whole wing-box is considerably reduced. A very large change in the area enclosed by the mid-line of the box, due to relevant out-of-plane skin panel deflection in highest post-buckling phase is possible thus causing a reduction in the box torsional stiffness. The experimental test configuration is shown in Figure 14a. The pure torsion testing machine available at the department is shown in Figure 14b. The load is applied by the hydraulic jack (I) while the other corners are fixed. The two end plates can rotate in order to apply pure torsion to the box. A maximum torsion of 20kNm was applied to the specimens. The materials used for the boxes are: M40/914 for the first one and T300/F263 for the second one. The two configurations were tested without a central rib and with it. Overall dimensions are: L= 790mm,B=404mm, H=135 mm. Thickness of the flat upper/lower plates is 2 mm while for the lateral plate is 4 mm. The effect of the variation in shear stiffness of the skin plates of the box for the incomplete diagonal tension field, is included in the theory as reported in Figure 15 and identified with (IDT), while the effect of the enclosed area variation is indicated by ∆A. The angle of twist of the second box configuration is presented in Figure 15 in function of the applied torsion moment. The effect of the enclosed area is less effective for torsion moment up to 10-11 kNm where the diagonal tension field is predominant. The effect of the enclosed area variation becomes larger for higher torsion moment as the post-buckling panel deflection is substantially increased. The correlation with experimental results is revealing, in a quite satisfactory way, the correct approach to the problem.

C. Damaged Flat/Stiffened Anisotropic Panels The activity was focused on the evaluation of damage effect on critical and post-critical behavior of flat /stiffened composite panels also in presence of cyclic compressive loads with a possible identification of damage grow under cyclic in-plane compressive loads in combination with critical conditions and in order to identify and determine specific formulation of structural damage propagation problems. Delamination is known to degrade the overall stiffness and strength of the structures, severely reducing the load-carrying capacity of the laminate under compressive loads. Local/global critical behavior is modified as a damage effect in terms of de-bonding between skin and stiffeners. In these cases it is important to assess and characterize damage, as well as how to identify the progression of damage and the convenient design procedures. This activity was partially supported by PRIN2002 funding project devoted to “Development and numerical-experimental validation of models for advanced fuselage structures” and continued under the partial support of PRIN2004 funding project devoted to “Fully Composite Fuselage for Medium and Large Pressurized Aircraft”. The testing equipment for the experimental activity is the same as the one described in sub-section A after updating with the possibility of cyclic tension-compression loads in longitudinal and transversal directions.

Figure 15. Experimental/analytical wing box angle of twist comparison for the case with a central rib box configuration.

Figure 17. Experimental results.

Figure 16. Experimental damage buckling.


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The effect of an artificial damage introduced into a flat composite panel (T300/epoxy) 1000x700mm with symmetric layup ([[-45/703/903/703/45]s ]s) and assumed thickness of 6.5mm, was investigated14 firstly. During the laying up process, a Teflon insert of 100 by 70mm was introduced in the mid-width mid-length position as an intermediate layer. This configuration was not effective in order to enhance the damage effect on panel behavior under loads so a stiffened panel with a skin-stiffener de-bonding was considered. The intention was to identify a possible damage grow under cyclic in-plane compressive loads in combination with local critical conditions for the damaged area15. a) Preliminary Numerical Analysis. A M40/epoxy flat T-stiffened panel with an artificially simulated defect (skin-stiffener de-bonding) is investigated 7. Stiffener width and height of 30mm is assumed with the following laminate lay-ups: [(+-45)2/0/(+-45)/90]S for the panel, [(+-45)2/06/(+-45)/0]S for the stiffener cap and [(+-45)2/06/(+-45)/05]S for stiffener web. Panel average thickness of 2.8mm is considered. Overall panel dimensions are 1000x700mm. Uniaxial compression and two biaxial cases were considered in this preliminary numerical analysis with an overall load per unit length ratio of 0.15 and 0.2. A de-bonded length of the order of the stiffener distance is considered : type A introduces a de-bonding length of 100mm in the central part of one stiffener, type B duplicates the same de-bonding in the central part of two stiffeners, while type C considers a de-bonding length of 200mm in the central part of one stiffener. The C-type damage reveals an evident local buckling in the de-bonded area at a load level compatible with the experimental machine range and with a well behaved buckle for experimental strain measuring. Type-C configuration is chosen as the experimental configuration for the testing panel with a damage extension of 220 mm. A FE model has been developed. The applied longitudinal load is twice the critical load of the panel between two stringers15 for the biaxial cases, while the uniaxial one is limited to 400kN considered sufficient for damage activation. An evident damage buckling at a load level ratio of about 0.72 is confirmed15. As a conclusion of this preparatory activity, it is important to point out that in the uniaxial case a damage buckling is expected to occur in a well behaved shape. In the biaxial one the damage buckling is not so evident and a damage-global buckling coupling seems to occur at high transversal load. b) Experimental Static Behavior . A flat stiffened panel, were manufactured for testing activity. No initial imperfection seems detectable on the panel. Several strain gages are bonded back-to-back along mid-line and quarter-line panel position. Biaxial compression test is considered at first with the application of a load per unit length ratio Ny/Nx of 0.1515. The load level reached during the test was maintained low with the aim of the activation of the panel deflection in the damage position and have possibility for a subsequent cyclical loading phase. The longitudinal numerical-experimental strain comparison revealed the tendency of the panel to move towards the stiffener avoiding the buckling of the damaged area. A subsequent uniaxial compression is applied to the panel. The experimental results (Figure 16) demonstrate the activation of damage deflection at the load level ratio of about 0.52. The restoring curve proceeds along a different path up to a load ratio of about 0.42 where it remains over the previous loading one. The damage position demonstrates very clearly the snap local buckling effect as also detected in strain distribution in Figure 17. c) Preliminary Fatigue Results. The uniaxial compression case is considered for this preliminary fatigue test. A low frequency (0.1Hz) loading condition is performed in order to evaluate the behavior of the damage and in order to asses the testing equipment. The load cycle is characterized by a maximum load ratio of 0.6, a minimum load ratio of 0.5 and an amplitude of 0.05. The cycling curves follow the “after snap “ path as indicated during static phase. The present evaluation is focused on the evaluation of damage effect on the panel behavior so time histories are not reported here. The uniaxial loading phase is presented in Figure 18 showing the “snap” effect at 0.52 load level as previously determined. The same loading phase is compared after the execution of this preliminary fatigue test. The snap condition seems slightly modified in strain behavior as a result of damage accumulation: higher strain is detected for the same load level after snap. A stiffness parameter is evaluated according to6 in order to detect the damage effect. Damage level is experimentally evaluated and reported in Figure 19. Very slight variation in equivalent stiffness is determined according to results in Figure 19. A relatively little higher variation in D parameter is determined for SG24 (defect point) directly connected with a change in damage dimension during loading repetitions.

Figure 19. Damage parameter behavior.

Figure 18. Uniaxial loading phase at different number of cycles.


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IV. Research activity at Universita’ di Pisa Significant weight reduction of future commercial aircraft will depend on the effective capacity of the designers

to deploy the advantageous feature of new high performance materials such as fibrous carbon composites. A possible solution to lower the weight of some primary structures (fuselage, wing spars) is offered by the post-critical design: the structure is allowed to buckle well below the limit load and it must withstand external loads up to the ultimate values in the buckled configuration. The effective design of this type of structures is heavily dependent on the availability of methods and tools that are necessarily numerically based and therefore need a comprehensive verification and validation process prior to their use and acceptance by certification authorities.

Given the existence of a number of advanced analysis tools, whose simulation capabilities are continuously expanded, the development of proper modeling and simulation strategies and their validation by means of significant experimental data is a subject of undisputed interest for both the academic and industrial communities. Such interest is demonstrated by the many scientific papers on the subject1,3,16-20 and by the number of recently funded research projects21-22.

In the paper an overview will be given of some experimental activities carried out at the Department of Aerospace Engineering of the University of Pisa within a research project funded by the Italian Ministry of Research. The objective of the project consists in developing and validating coherent procedure for modeling and simulating stiffened composite structures in order to both predict the buckling load and capture the post-buckling behavior. In particular results are presented relevant to a test campaign conducted on two sets of CFRP flat stiffened panels designed and manufactured by Alenia Aeronautica using different technologies to join the stiffeners to the skin: co-curing and co-bonding. The results of the experimental campaign permits a first assessment of the postbuckling behavior of the two types of panels which is achieved by comparing the results of uni-axial

compression tests in terms of load-end shortening curves, strains and out-of-plane deflections.

A. Test preparation and procedure Test articles

The test articles are flat panels, made of carbon fiber reinforced plastic, stiffened by five stringers with I-shaped cross section of the same material along the longitudinal direction and by two frames with L-shaped cross-section in transversal direction (Fig. 20). The panels have a width of about 800 mm, a length of about 1200 mm and the two frames, centered with respect to the middle of the panel, have a spacing of about 600 mm; the five stringers are equally spaced and centered with respect to the longitudinal axis of the panel (Fig. 20). Some details of geometry and dimensions of the stringers are shown in Fig. 21. The frames are connected to the skin by means of titanium hi-loks and to the stringers by means of composite angular clips, joined by means of titanium hi-loks as well.

The materials are of composite type with epoxy matrix reinforced by carbon fibres, the basic material is a Fiberite Europe 934-37-4K –T400HB-145 Prepreg tape. Two sets, of three panels each, were manufactured: panels of the first set (no. 1-3) have co-cured stringers, panels of the second set (no. 4-6) have pre-cured stringers bonded to a fresh skin during the final cure process (co-bonded).

Test equipment

The experimental tests have been conducted on an axial machine (Fig. 22) having a maximum loading capacity of 1500 kN, equipped with flat fixture grips to

Figure 20. Geometry of the stiffened panels.

Figure 21. Detail of the stringer geometry.


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which the potting frames, at both the extremities of the panels, are fixed. The load cell and the position transducer integrated in the actuator of the test machine have been used to measure both the total axial load and the end-shortening of the test article. On the flat side of the panel a screen was mounted for the visualization, by means of

the “Shadow Moirè” method, of the interference fringes caused by out-of-plane deformations that occurred when the buckling load was exceeded (Fig. 22a). On the stringers side an equipment is mounted that permits the sliding along the loading direction of three displacement transducers (LVDT) in the region between the panel frames (Fig. 22b). Such transducers are used to measure the out-of-plane deflections of the central stiffener and of the skin in the adjacent bay. In order to correctly reproduce the constraint conditions during testing, a special fixture has been employed to attach the panel frames to the columns of the testing machine (Fig. 22c): the frames have been connected to shaped plates in steel, which are supported by flexible crossbows anchored to the machine columns. The fixture allows translations along the loading direction

a) front view (skin side) b) rear view (stringers side)

c) side view Figure 22. Equipped test machine.

Figure 23. Position of displacement transducers (LVDT) and strain gauges.


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while providing a very stiff constraint for displacements in transversal direction.

Preparation of the test articles Each panel was instrumented by means

of twenty-two uni-axial strain-gauges, bonded back-to-back, and two rosette strain-gauges bonded, still in the back-to-back configuration, to the web of the central stringer. The general configuration of the strain-gauges is shown in Fig. 23; in the same figure the locations of the LVDTs are indicated. Letter M in Fig. 23 designates the middle section between frames while letter S indicates a section located at a distance of about 80 mm from the previous one. The

choice of instrumenting two quite close sections between the frames assured that some of the strain gauges were always in correspondence of a skin buckle. The panels have been painted white on the flat side in order to enhance the interferometric fringes produced by the “Shadow Moirè” method.

Test procedure The test procedure is articulated in three main phases. In the first phase the axial load is incremented in steps up

to about 2.5 times the design buckling load (visually recognized by the occurrence of buckles of the skin). At each load increment strain levels are monitored by means of the back-to-back strain-gauges and the out of plane deflections, between the frames, are measured by means of the sliding LVDT transducers system. Successively, the external load is removed and strain levels checked in order to verify that residual deformations with respect to the initial test conditions do not occur. Sliding LVDT transducers are removed from the actuation system to avoid damage in the subsequent test to failure.

Finally, the axial load is incremented up to failure (a slow ramp displacement is requested to the test machine). During this phase strain levels are monitored by means of the back-to-back strain-gauges while the out of plane deflections are monitored by means of the Shadow Moiré fringes. During this phase the panel is video recorded from both sides in order to document the failure mode of the panel.

B) Test Results

Load-end shortening curves Figure 24 shows the load-end shortening curves of four of the six tested panels (only panels 2, 3, 5 and 6

produced complete sets of usable data, results are normalized using the design buckling load and the corresponding measured end-shortening): the two types of test articles exhibit a similar behavior with curves that maintain a linear shape up to 2 times the design buckling load; co-bonded panels have higher failure loads.

Figure 24. Load – end shortening curves.

a) b) c) d) Figure 25. Out of plane deflections: a) small buckles (P/Pcr = 1), b) transition (P/Pcr = 1.2), c) 3 buckles shape (P/Pcr = 2), d) central stringer peeling (P/Pcr = 3.6).


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Small differences exist in the curves of the co-bonded set: at the same end-shortening panel 6 shows higher loads than panel 5.

Out-of-plane deflections Figure 25 shows the typical evolution of

the Moiré fringe patterns, that give a measure of the out-of-plane deflections, as the external load is increased. At the design buckling load, small buckles appears in the skin in the region between the frames (Fig. 25a), then a transition phase starts at about 1.2Pcr (Fig. 25b) that evolves in a stable three buckles shape at 2Pcr (Fig. 25c). Increasing the load, this pattern is maintained up to about 3.6Pcr when a de-bonding (peeling) of the central stringer from the skin occurs (Fig. 25d). However the panel maintains its load carrying capacity and the external must be increased further (up to about 4.4Pcr) to produce the final failure.

The only exception to the evolution of the test just described is represented by panel 6 (of co-bonded type) which showed a transition to a four buckles shape and reached the failure load with no occurrence of stringer peeling.

Figure 26 shows two examples of the measures of the out-of-plane deflections, taken positive when a point moves toward the stringer side, by means of the sliding LVDT transducers (the displacements are normalized using the skin thickness, while the transducer excursion is referred to the frames pitch). Both panels show deflections at the design buckling load even though the small buckles pattern visible from the Moiré fringes is not detectable from measures. Transition to large buckles patterns at higher loads is confirmed and also the different behavior of panel 6 (transition to 4 buckles pattern evident from Fig. 26b). The measures shown in Fig. 26 point out that the small buckles are confined to the area of bare skin between the stringer flanges while the large buckles pattern involves also the stringer flanges and pads.

Strain measurements Figure 27 shows two examples of the

axial strains readings, by means of the back-to-back strain gauges, as a function of the applied load (normalized using the design buckling load).

a) panel 2: co-cured

b) panel 6: co-bonded Figure 26. Out-of-plane-measures.

a) panel 2 (co-cured): section M

b) panel 6 (co-bonded): section S Figure 27. Strain measures.


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The results of panel 2 (Fig. 27a) come from instrumented section M while the results relevant to panel 6 (Fig. 27b) come from section S since section M coincides with a nodal line for the 4 buckles deformation pattern. For panel 2 (representative of the results of all the tests except for panel 6) the small buckles pattern at design critical load is confirmed to essentially involve the skin: the first bifurcation of the strain curves is very limited in the readings taken on the stringer flange (Strain gauges 13-14).

The following sudden changing in the graphs (at 1.4Pcr) coincides with the transition to the 3 buckles pattern: the sign change in the bending strains (difference of the signals coming from the back-to-back strain gauges) confirms the sign change of the out-of-plane deflections at transition reported in Fig. 26a. The last abrupt change in the strain gauges reading (at 3.6Pcr) is due to the de-bonding of the central stringer from the skin.

Strain gauges readings relevant to panel 6 (Fig. 27b) account for the 4 buckles pattern that follows the transition phase and confirm that such pattern involves the stringers flanges and pads (Strain gauges 23-24). Moreover it is confirmed that the peeling phenomenon was absent for this panel.

Failure modes Co-cured panels failure is a two phases phenomenon (Fig. 28): first a de-bonding (peeling) of the central stringer

from the skin occurs (at about 3.6Pcr), after that some residual load carrying capacity is maintained and failure occurs (at about 4.4Pcr) when all the stringers collapse at the same time. No appreciable growth of the de-bonded region was observed prior to the final failure.

Co-bonded panels exhibit an analogous failure mode except for panel 6, which reaches the final failure load (the highest of all the panels tested) without any occurrence of de-bonding events.

V. Conclusions The paper has given an overview of some research activities regarding buckling of composite structures

performed in Italy in the last years. In particular, the activities performed at Politecnico di Milano, at Politecnico di Torino and at Universita’ di Pisa were here presented. They consisted on experimental tests and numerical analyses developed to investigate the buckling and post-buckling behavior of different structures, such as unstiffened and stiffened shells, flat and curved panels, closed boxes and a helicopter tailplane. Different loading conditions were investigated: compression loads, but also torsion on closed structures, applied statically but also cyclically. Some pre-damaged structures were tested to investigate the possible damage propagation due to buckling conditions.

In all the cases, the structures show a large possibility to work in the post-buckling field, allowing for the further weight savings likely to be required in the near future for the construction of aerospace structures.

Acknowledgements Chiara Bisagni and Vittorio Giavotto are grateful to the several graduate students that worked on these research

activities and in particular to Potito Cordisco. The work was supported by the European Commission, Competitive and Sustainable Growth Programme, projects DEVILS, POSICOSS and COCOMAT. The information in this paper is provided as is and no guarantee or warranty is given that the information is fit for any particular purpose. The user thereof uses the information at its sole risk and liability.

Daniele Fanteria e Agostino Lanciotti are grateful to Luisa Boni for her valuable work in the research program presented in the paper.

a) b) c) Figure 28 Failure mode example (pan. 2): a) stringer pad strain, b) peeling (P/Pcr = 3.6), c) failure (P/Pcr = 4.4).


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19Caputo, F., Esposito, R., Perugini, P., and Santoro, D., “Numerical-Experimental Investigation on Post-Buckled Stiffened Composite Panels”, Composite Structures, Vol. 55, No. 3, 2002, pp. 347-357.

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