Buckling and postbuckling of composite structures

S

UTTE E I N

RWORTH E M A N

Composites 26 (1995) 189 199 9 1995 Elsevier Science Limited Printed in Great Britain. All rights reserved 0010-4361/95/$10.00

N

Buckling and postbuckling of composite structures K. A. Stevens*, R. Ricci and G. A. O. Davies Department of Aeronautics, Imperial College of Science, Technology and Medicine, Prince Consort Road, London SW7 2BY, UK (Received 24 May 1994; revised 20 July 1994) The postbuckling behaviour of a fiat, stiffened, carbon fibre composite compression panel has been studied, theoretically and experimentally. The panel had a collapse load in excess of three times the buckling load. An initial failure mechanism leading to eventual explosive collapse of the panel is identified and the damaging stress resultant is measured in the panel and predicted from a finite element analysis. (Keywords: I-stiffened panel; buckling behaviour; failure

mechanism)

INTRODUCTION The major part of an aircraft structure takes the form of sheet material which is stabilized for compressive loading by longitudinals, or stiffeners, Figure 1. Where the structure is lightly loaded, i.e. the skins are not too thick, it is well known that the buckling load does not represent the maximum load that the structure can carry. Indeed, failure may not occur until the applied load is several times the buckling load. This postbuckling strength capacity has significant potential for weight saving. For an aluminium airframe, postbuckled strength is amenable to analysis. In this case structural collapse is most likely to follow from yielding of the skin at known specific locations in the buckled compression panel or from crippling of a stiffener. With the advent of carbon fibre composites (CFCs) the postbuckling potential is still available, as shown in refs 1-3. However, the prediction of the collapse load is now more difficult because of the susceptibility of composites to the effect of through-thickness stresses. It follows that there are a number of locations in the panel and a variety of damage mechanisms which could lead to final collapse. Another difficultly associated with research into CFC compression panels is that the postbuckling collapse is so destructive that usually the evidence of the failure mechanism cannot be retrieved from the debris of a laboratory test. The work presented in this paper is part of a Brite Euram funded investigation into the postbuckling of CFC structures which was carried out in the Aeronautics Department at Imperial College. It is both a theoretical and experimental study of the behaviour of the I-stiffened panel, shown in Figure 1, under a compression load. A finite element analysis of the buckling and postbuckling behaviour of the panel is presented and an experimental programme confirms the postbuckling strength * To whom correspondence should be addressed

capacity and reveals the initial damage mechanism which leads to final explosive collapse. The stress resultant associated with the initial damage is measured in the panel and compared with the value predicted from a finite element (FE) model. TEST PANEL AND TEST M A C H I N E The test panels, which are manufactured in T300/914C unidirectional prepreg, have four I stiffeners as shown in Figure 1. For the investigation of postbuckling failure a panel with a high ratio of failure load to buckling load was required. The configuration chosen is similar to one of the panels tested in ref. 1, where it was shown to have a failure-to-buckling load ratio in excess of three. Elastic properties of the unidirectional (UD) laminae are given in Table 1 (BAe test data). The panel in Figure 1 has a 2 mm thick quasi-isotropic skin and the stiffeners are either co-cured or bonded to the skin. In each case a layer of BSL 322 film adhesive is incorporated between the tapered flanges of the stiffener and the skin. The triangular cleavage at the base of the stiffener web is filled with twisted tow. The loaded ends of the panels were potted in a resin and fibreglass mixture then machined flat and parallel. The unloaded edges of the panels were unsupported during the tests. These tests were carried out in a 250 tonne test machine which has been designed to have the high stiffness necessary for postbuckling research. Figure 2 shows a view of the test facility. The machine can be used for testing panels up to 1.5 m long, 1 m wide and 0.5 m deep. For our smaller panels an intermediate crossbeam is positioned as shown. The panel has been painted white for shadow Moir6 photography. To the left of the panel can be seen the telescopic arm of an in situ ultrasonic scanning facility which plays an important part in detecting the initiation of damage in the postbuckled panel. The other instrumentation in the picture is associated with data logging and acoustic emission sensing.

COMPOSITES Volume 26 Number 3 1995

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Buckling and postbuckling of composite structures: K. A. Stevens et al.

[45/.45/0/45/.45/02/45/-45/02/90/03/902/04/902/02]s50

Stiffener cap: t=6.25 mm

4

30.5

~1

L-

Skin: t=2.0 mm [45/-4

31.8 " ~ / / ~ /

~ S ~ .

x ~ ' ~

Stiffener web: I-2.75

6.25

|!/ 2 . 7 5 1 1 r I - ~

ii5/'45/0/45/'45/02/45/'45/02]s22 mm

[45/.45/0/45/.45/02/45/-45/02]s22

Tapered stiffener flange:

2.0

43.2

7!

Figure 1 I-stiffened panel, 865 m m • 610 ram, and stiffener detail Table 1 UD elastic properties Longitudinal Young's modulus, Eu (GPa) Transverse Young's modulus, E22 (GPa) In-plane shear modulus, Gu (GPa) Poisson's ratio, vu Nominal ply thickness (mm)

127.5 9.0 4.9 0.28 0.125

FINITE ELEMENT MODELLING

Figures 3 and 4 show the finite element models for onequarter of the test panel and a typical stiffener and skin cross-section, respectively. The modelling throughout is with nine-noded, quadrilateral, Mindlin shell elements which can model laminate properties and include transverse shear deformation. Only one element is employed through the thickness. The offset nature of the tapered flanges plus skin is realized, as shown in Figure 4, by setting the elastic constants in the 'fictitious plies' to zero. The finite element package used was our 'in house' FE77, for which some non-linear modules were devel-

oped. The postbuckling analysis could be carried through with displacement or load incrementation under arc-length control4. The non-linear postbuckling analysis was preceded by an eigenvalue calculation so that an imperfection in the form of the first eigenvector could be used to assist the non-linear analysis onto the appropriate postbuckling path. This is particularly pertinent for these panels, which have close eigenvalues for buckled mode shapes having between five and seven half-waves along the panel. INITIAL BUCKLING OF THE PANEL, THEORY AND EXPERIMENT The results of the finite element predictions for initial buckling are shown in Table 2. We see that the first three eigen modes have fairly close eigenvalues. This is very relevant to the postbuckling analysis where mode changes can cause computational difficulties. The mode shape for six half-waves is shown for half the panel in Figure 5. Experimentally four panels have been tested, two with bonded and two with co-cured stiffeners. Each panel buckled into six half-waves initially but, in each case at loads in excess of twice the buckling load, there was a mode change to seven half-waves. Table 3 summarizes initial buckling results for the four panels. The measured buckling loads of the panels are obtained from the graphs of membrane strain against load (see Figure 14 ). The agreement with predicted loads is satisfactory, but the axial compression measured at buckling is greater than the predicted values by up to 0.14 mm. This is likely to be due to the end conditions since there is an indication of a lower axial stiffness when loading starts. The axial displacement at collapse is as much as 4 mm. Table 2 FE buckling results No. of half-waves along panel

Figure 2 250 tonne panel test machine

190

COMPOSITES Volume 26 Number 3 1995

5 6 7

Axial compression (mm) 0.756 0.759 0.807

Buckling and postbuckling of composite structures: K.A. Stevens et al.

Z

xJ..u

Figure 3

FE model o f one-quarter of the test panel

Flange(45/-45101451-4510*2/45/-45/O*2) Skin

(45/-45/0"2/45/-45/90 "2) s

Flange(O'2/-4514510*21-45/45/O/-45/45)E 11 = E22 =G 12 =0

'

I Figure 4

Figure 5

'

[

'

I

1

1

l

Modelling of tapered flanges to include offset

Buckle mode shape for half the test panel

COMPOSITES Volume 26 Number 3 1995

191

Buckling and postbuckling of composite structures: K. A. Stevens et al. FAILURE MECHANISMS LEADING TO STIFFENER DISBONDING There are many examples in the literature 1-3'5 7 where the failure of a postbuckled panel has been attributed to the separation of the stiffeners from the skin. It is certainly true that in the collapsed panel the stiffeners will often appear detached, but the panel failure is so explosive and destructive of the panel that it is difficult from an inspection of the broken panel to deduce how failure was initiated. Figure 6 is a photograph of a collapsed panel which had bonded stiffeners. We see that in some places the stiffener cap has separated, in others the stiffener has come away from the skin pulling the first ply with it, while in other regions the skin under the stiffener remains intact. From this debris it is not feasible to deduce that, as we show later, the initial damage in the postbuckled panel was in the form of a crack between the stiffener flange and the skin which propagated from under the stiffener web in a particular panel location. If we are to anticipate the problem of stiffener debonding, then we Table 3 Experimental buckling results

Panel ident,

No. of half-waves along panel

Buckling load (kN)

Axial compression (mm)

6407~ 6414~ bonded

6 6

114 114

0.87 0.85

644l] 6442tc~

6 6

t15 tl0

0.75 0.89

need to study the nature and the magnitude of the stresses which develop at the interface between the stiffener and the skin as the panel postbuckles. These interface stresses arise due to load diffusion or transfer between the skin and the stiffener. From the initial buckling observations we have seen that the displacements vary periodically throughout the panel (Figure 5). It follows that the stress resultants and therefore the interface stresses will also have a periodic variation, so that it should only be necessary to examine conditions corr~,sponding to the buckle node lines or antinode lines, where the various stress resultants have their maximum values. These observations about the stress resultants are confirmed in a following section where the finite element postbuckling results are discussed.

Stiffener loading on the anti-nodal lines Figure 7 shows the deformed shape of the stiffener and skin at a position in the panel opposite a buckle crest, i.e. an anti-node line. The dotted line indicates the skin deformation if the stiffener had provided only a simple support condition along its length. The torsional stiffness of the stiffener and the bending stiffness of the flanges modify the buckled shape to be as shown. There are apparently two possibilities for disbonding between the stiffener and skin. 1) At A the flange presents a step change in bending stiffness to the skin moment My. Thus My has a tendency to peel the skin from the flange and interface peel stresses will develop. The alleviating effect of tapering the flanges is apparent. This problem was addressed in ref. 5, which deals with the postbuckling of stiffened shear panels. There, critical values of bending strain were evaluated by testing in fourpoint bending a narrow strip cut from the panel. 2) The moment transferred between the stiffener web and the flange/skin laminate at the foot of the web is such as to pull the flange on the tension side away from the skin. This possibility was recognized by Bushnellv, who recommends a peel strength test to provide data for his PANDA program. For the stiffeners in the test panel, torsional rigidity comes mainly from the torsion bending effect of the heavy stiffener cap. The bending moment Mw in Figure 7 then increases linearly to a maximum value at the base of the web. This moment Mw has been measured in the test panels and has been extracted from the FE analysis for comparison in a following section (on Finite element postbuckling analysis).

S t r a i n gauges M /2 w

Figure 6 I-stiffened panel. Buckling at 11 tonnes, failure at 48 tonnes

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COMPOSITES Volume 26 Number 3 1995

Figure 7 Deformation on anti-nodal line

Buckling and postbuckling of composite structures: K.A. Stevens et al. Stress resultants on the nodal line On the nodal lines there is no deformation of the cross-section. Thus the bending moments in the stiffener and the skin are zero. However, at the nodal lines the twisting moment M,.,. reaches its maximum value at the stiffeners. In Figure 8 it is apparent that to enforce compatibility between the skin and the flange there will be interface shear stresses of the type T,-_-.If these stresses reach a critical value then delamination will occur between the flange and the skin. Again, tapering of the stiffener flange will have an alleviating effect. A point to note in connection with each of these potentially damaging stress resultants is that, because of the periodic nature of the deformation, the stress resultant reverses sign with each buckle half-wave. This clearly has a bearing on whether any delamination propagates along the stiffener to the next half-wave, where the stress resultant may now be stabilizing. P O S T B U C K L I N G TESTS TO F A I L U R E We have noted that each of the four panels tested buckled initially into six half-waves along the length of the panel. Figure 9 shows a shadow Moir6 pattern of panel 6442 under a load of 30.0 tonnes, after buckling at 11 tonnes. Figure 10 is a diagrammatic representation of the buckled panel with the stiffeners labelled A - D and the half-waves numbered 1 6 so that locations in the panel can be identified.

Panel loaded until explosive collapse The first panel tested was no. 6407. This panel buckled at ll tonnes and collapsed explosively at about 48 tonnes, Figure 6. Testing had proceeded cautiously with frequent ultrasonic scans but no sign of a failure initiation had been detected. The end result of this test was salutary since the destruction was so comprehensive that no evidence of the failure mechanics was apparent. However, this panel did confirm the large postbuckling strength potential. The remaining three panels all behaved in a similar way. The only differences between the bonded and cocured examples will be referred to at the end of this section.

Figure 9 Shadow Moir6 pattern of panel 6442 under load of 30 tonnes (failures at B4 and C3) F a i l u r e site 3 Failure

site I

Failure site 2

1

Test procedure Jor damage initiation In each case the panel was loaded very slowly until such time as an indication from the acoustic emission or any of the transducers suggested that a damage mechanism was active. In the event the panel would then be unloaded slightly for ultrasonic inspection. This meant that in the course of a test the panel might be reloaded 15 20 times. On successive reloadings no significant

xj

Figure 8

~

y

~

Mxy

Shear stresses due to M,~, are m a x i m u m on nodal lines

D

Figure l0

Buckling mode and failure sites (viewed through skin)

change was noticed except that, where a mode change occurred, this tended to happen at a slightly lower load as the load cycling progressed. When the higher loads were being applied it was sometimes necessary to wait up to 30 min between load increments for all acoustic emission activity to cease. Figure 11 shows the location of displacement transducers and some strain gauges on the skin at points corresponding to buckle crests. Strain gauges were also attached to the stiffener web so that the bending strain associated with Mw (Figure 7) could be measured.

COMPOSITES Volume 26 Number 3 1995

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Buckling and postbuckling of composite structures: K. A. Stevens

Test observations Overall panel behaviour. Figure 12 shows the axial load versus axial contraction for two panels. It is noticeable that there is very little loss of stiffness at buckling, because of the substantial proportions of the stiffeners. Lateral buckling displacements are shown in Figure 13. We see that there is some overall bowing of the panel as shown by the deflection of the stiffener. The bowing, which is towards the stiffener rather than the skin, continues throughout the test and is attributed to imperfections in the panel and inaccuracy in the preparation of the panel loaded ends. The lateral displacement is up to about 3 mm at the centre of the panel, i.e. over a length of 865 mm. For the purpose of studying postbuckled failure the overall bowing was not considered to be a problem since the initial failure starts as a very localized phenomenon. Figure 14 shows the reversal at buckling of the membrane strain increase with load for the three buckle crests in bay 3. Again, the separation of the curves at the knee is due to the overall bowing of the panel. Figure 15 records the bending strain in the web of stiffener C at buckle crests in bays 4--6. At each buckle crest strain is measured near the stiffener cap and 4.5 mm from the top surface of the skin. The bending strain

Stif Bay

C e n t r e line

Node line

|

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U Figure

S t r a i n gauge 11

et al.

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50000'

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1000

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Panel load versus axial displacement (6441, co-cured panel; 6414, bonded panel) LHF~ BAY (AB4)

Sr[e~ER(B4) 2000'

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Figure 13

194

Lateral displacement on anti-node line of bay 4 for co-cured panel 6442

COMPOSITES Volume 26 Number 3 1995

Buckling and postbuckling of composite structures: K.A. Stevens et al.

/!,,,,/!

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Variation of bending strain in the web of stiffener C at anti-nodes, C4 to C6 near the skin and near the stiffener cap for co-cured

panel 6442

is very low at the cap and increases to a maximum value at the base of the web. This was anticipated in the discussion of the torsion-bending of the stiffener. Notice that these stiffener bending strains only arise in the postbuckled state, load > 110 kN. The bending moments near the skin also decrease slightly from 4-6. This is attributed to the effect of the panel bowing. The jump in the strain values at about 43 tonnes is associated with a mode modification - the centre bay changed from six halfwaves to seven half-waves. This mode switching was experienced in all the panels tested and is to be expected in panels loaded as far into the postbuckled state. Experimental measurements showed that, because of the narrow width of skin at the edges of the panels, the web bending moments in the outer stiffeners, A and D, are significantly less than those in stiffeners B and C at any given load. This was confirmed by the FE analysis

(see Figure 20b). The experimental measurements of the web bending strains also showed that in any panel the web bending strains at corresponding locations such as B3, B4, C3 and C4 all have similar magnitudes (i.e. before damage in the form of localized stiffener/skin failure, described next, occurs).

Localized stiffener/skin failure. In the co-cured panel 6442 a characteristic local mode of failure was detected at three separate locations in the panel. This same type of failure also occurred in the other two panels tested. The description of the phenomenon will be referred to measurements from 6442. We have seen above that high bending moments occur in the postbuckled panels at the base of the stiffener webs on the anti-nodal lines. These bending moments are at their largest at the locations B3, B4, C3 and C4 (Figure

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195

Buckling and postbuckling of composite structures: K. A. Stevens et al.

10) and it was also observed above that such bending moments could lead to a debond of the flange on the tension side of the web. Figure 16 shows a record of the bending strain in a web at the anti-node position C4. At a load of 45 tonnes there is a sudden drop in the bending moment in the web. This sudden drop was associated with an audible crack. Subsequent ultrasonic scanning of the region revealed a crack which started in the triangular region at the base of the web and propagated outwards into the flange/skin. Figure 17 shows a typical micrograph of the region. Further incremental loading of the panel produced similar failures at locations C3 and B4 (see Figure 10). Loading of the panel was continued with some long dwell periods at high loads to examine how the localized damage might propagate. At two failure locations B4 and C3 the crack propagated to the free edge of the tension flange, which opened up over a length of about 20 mm, Figure 18. At the base of the web the damage extended along the stiffener for 35 mm each side of the anti-node line. (The buckle half wavelength is approximately 140 mm.) No further extension of these damage 50000'

I

t

bending

load(daN)

due

strain

areas along the stiffeners was recorded. The explanation for this is related to the periodic variation of the web bending moment. In the buckle half-wave adjacent to a damage site, the web moment is of reverse sign and would tend to peel away the opposite flanges of the stiffener. Also, when the detamination reaches the free edge of the flange the web bending moment has become very small, as shown in Figure 19 at B4.

Panel collapse. In panel 6442 at this stage there are two locations, B4 and C3, where the stiffener has been 'unzipped' to the free edge of the tension flange, and there is a location C4 where delamination is present under the tension flange. Loading was continued in an attempt to observe the mechanics of the final collapse. Figure 19 is a record of the web bending strains at three anti-node positions. Explosive collapse occurred at 45.6 tonnes. The failure was too sudden to observe the process. However, there are indications on Figure 19 that further reductions in bending strain, and thus increases in delamination, are occurring at locations B4 and C4 as the final failure is approached.

I

reduction

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to delaminatiort !

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40000' []

1

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r.

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Figure 16

1000

5000 6000 bending strain C4 (I.te)

Web bending strain near the skin at C4 for co-cured panel 6442

Figure 17

196

2000

Crack under flange of co-cured specimen

COMPOSITES Volume 26 Number 3 1995

Buckling and postbuckling of composite structures: K.A. Stevens et al. D E S I G N M E T H O D O L O G Y FOR P O S T B U C K L E D PANELS

Node line

Node line Figure 18

The stiffened panel which has been studied in this investigation has exhibited a failure load exceeding the initial buckling load by a factor of four. In order to take advantage of this strength reserve in design, the load at which the characteristic localized initial failure occurs has to be predicted theoretically. Not only this, but also the type of failure has to be identified from the other possibilities described above9 The FE model has been shown to evaluate correctly the stress resultants in the buckled panel, so the problem reduces to determining the values of the stress resultants to cause failure9 The theoretical possibilities are then concerned with relating these stress resultants to critical values of the interface stresses or to an energy release analysis. Both of these methods are being examined but, bearing in mind the complexity of the laminate structure in the failure region, it is considered that the stateof-the-art in both methods is not up to an a priori prediction of the failure load without further developments. A number of researchers 54 have suggested that an alternative approach might be to establish critical values of stress resultants by testing suitably loaded components cut from a test panel. Component tests have been done for the flange free edge delaminations, and also for the mode of failure identified in this work. The components are chordwise sections taken from panels and loaded to establish critical values of the moments in each case. These components are economical to test and the results to date, which are reported in ref. 9, do replicate the panel failure mode and therefore give some encouragement that designs can be evaluated with a minimum of full-scale testing.

Buckle valley

F l a n g e d e l a m i n a t i o n to flange edge at B4

Bonded~co-cured stiffeners. In each case an adhesive layer was included between the stiffener flange and the skin. The bonded stiffeners seemed to be marginally more effectively adhered to the skin than the co-cured examples. Thus failure-initiation occurred at a slightly higher load. Also the crack tended to remain in the flange rather than entering the first ply of the skin, Figure 17. F I N I T E E L E M E N T P O S T B U C K L I N G ANALYSIS

Figures 20a and b plot the stress resultants in the skin and skin/flange laminations at an axial compression in the panel of 3.584 ram. Experimental points at a similar end compression, measured in two test panels, are shown. The plot, which corresponds to an anti-nodal line in the buckled panel, extends from the free edge (FE) to the centre line (CL). The moment ( M ) transfer between the skin and the stiffener near the edge (290 N) is much less than for the central stiffener (470 N). The moment distribution in the web of a central stiffener, from the loaded edge (LE) to the CL, is shown in Figure 21. The moment which corresponds to M,, is M,..The value of this moment intensity at the buckle crests varies between 400 and 470 N. Of all resultants the stiffener moment looks to have the biggest disagreements from predicted values, but this is mostly due to the fact that the web laminates were very badly distorted and so the surface strains are affected by the varying rigidity. Note that in Figure 20b panel 6407 has buckles in the opposite sense to 6411. The experimental values show that the theoretical prediction is reasonably accurate.

CONCLUSIONS A stiffened panel with either co-cured or bonded stiffeners has been shown to delaminate under the stiffener web at points in the panel where the web bending moment is a maximum, i.e. at points opposite the buckling crests.

50000' lead (daN)

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2000

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6000

Web b e n d i n g strains n e a r skin at C4, B3 and B4 up to explosive collapse for co-cured panel 6442

COMPOSITES Volume 26 Number 3 1995

19"/

Buckling and postbuckling of composite structures: K. A. Stevens et al. CL

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Figure 21

Web base m o m e n t resultants along central stiffener

This crack under the flange on the tension side of the web is, to an extent, stabilized by the reversal of the sign of the stress resultants in the neighbouring bays. Eventual collapse of the panels occurred at a load of over four times the buckling load. The collapse was explosive and very destructive of the panel.

198

COMPOSITES Volume 26 Number 3 1995

ACKNOWLEDGEMENTS The authors would like to acknowledge the support of the EEC Brite Euram Directive and the co-operation of their colleagues in this joint venture: British Aerospace, the project leaders and panel manufacturers, SAAB, Dassault and CASA.

Buckling and postbuckting of composite structures: K.A. Stevens et al. REFERENCES 1 Starnes, J.H., Knight, N.F. and Rouse, M. AIAA J, 1985, 23(8), 1236 2 Knight, N.F. and Starnes, J.H. AIAA J. 1988, 26(3), 344 3 Romeo, G. AIAA J. 1986, 24(11), 1823 4 Crisfield, M.A. Computers and Structures 1981, 13, 55 5 Hachenberg, D. and Kossira, H. ICAS-90-4.3.1, pp. 511-521 6 McConne[[, P. 'AGARD 74th Structures and Materials Meeting',

Patras, Greece, 1992 7 Bushnell, D. Computers and Structures 1987, 4, 469 8 Paul, P.C., Saff, C.R., Sanger, K.B., Mapler, M.A., Kan, H.P. and Kentz, E.F. 'Sth DOD/NASA/FAA Conf. on Fibrous Composites in Structural Design', Norfolk, VA, November 1989, pp. 263-279 9 Stevens, K.A., Davies, G.A.O. and Ricci, R. '19th ICAS Conf.', Anaheim, CA, 1994, ICAS-94-9.8.3, pp. 2975-298t

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