experimental response of glass-reinforced plastic cylinders under … · 2006-03-27 ·...

*Corresponding author.

Marine Structures 11 (1998) 347—371

Experimental response of glass-reinforced plasticcylinders under axial compression

A.Y. Elghazouli*, M.K. Chryssanthopoulos, A. Spagnoli

Department of Civil Engineering, Imperial College of Science, Technology and Medicine,London SW7 2BU, UK

Received 27 July 1998; received in revised form 16 October 1998; accepted 19 October 1998

Abstract

This paper presents the results of buckling tests on laminated composite cylinders made fromglass fibre reinforced plastic (GFRP). The laminates used are of type ‘DF1400’ consisting ofwoven glass fibre roving within a polyester resin matrix. In total, six cylinders constructed fromtwo-ply laminates, in which the main variable is the laminate orientation, were tested underaxial compression. The specimen details, experimental set-up and loading arrangements aredescribed, and a detailed account of the test results is given. The results include thickness andimperfection mapping, and displacement, load and strain measurements. Use was made of anautomated laser scanning system, which was developed for measuring the initial geometricimperfections as well as buckling deformations during various stages of loading. The results ofthis experimental study demonstrate the influence of laminate orientation on the bucklingstrength of composite cylinders, and provide detailed information necessary for analytical anddesign investigations. ( 1999 Elsevier Science Ltd. All rights reserved.

Keywords: Buckling; Composites; Axial compression; Cylinders; GRP structures; Shells

1. Introduction

The use of composite materials in the marine and offshore industries has beengaining ground in recent years. However, the limited availability of design criteria forcomposite structures has generally restricted the efficient use of many forms ofcomposite materials. In particular, the lack of buckling strength design criteria isdeemed to be a prohibitive factor in a more widespread use of monolithic laminatedcomposite shells in marine construction.

0951—8339/98/$ — see front matter ( 1999 Elsevier Science Ltd. All rights reserved.PII: S0951—8339(98)00017—3

One of the possible applications of GRP shells is in pipework. Composite pipes incargo and ballast systems in tankers were an early application. More recently, pipelinedesigns in topside modules have been developed using GRP. Their design generallyinvolves several load cases including pressure and axial stress. In this paper the focusis on axial compression and emphasis is placed on local shell buckling, hence theradius-to-thickness ratio examined is in the intermediate range.

Due to the complexity of the shell buckling phenomenon, it has attracted a largeresearch effort over many years [1,2]. Early tests were mainly conducted in order tounderstand the buckling phenomenon, or in order to provide straightforward esti-mates for the buckling strength using formulae for linear critical loads and empiricaltest-based ‘knock-down’ factors. More recently, within the last 20 years or so, theobjectives of shell buckling tests, whether on metal or on composite specimens, haveinvolved accurate measurement of characteristic input and response parameters priorto and during testing. These measurements are used to provide input for numericaland analytical models, which, subsequent to validation by comparison with testresponse parameters, may be employed in wider parametric studies.

In the case of composite shells, the methodology of integrating a reasonable numberof experiments with a complementary computational activity, becomes the only viableapproach. The very large number of input parameters (including basic lamina proper-ties, orientations and number of laminae as well as all the geometric and loadparameters associated with isotropic homogeneous shells) prohibits a pure experi-mental approach. To this end, the measurement of relevant properties and responseparameters during the testing programme is essential to the development of analyticalprocedures and design guidelines for buckling strength prediction. As a result, anddue to the imperfection sensitivity of shells subjected to axial compression, accuratemeasurement and mapping techniques form an important part of experimentalstudies.

Tennyson [3] has presented a concise account of early buckling tests on laminatedcomposite cylinders, whereas Simitses et al. [4] have focused on the attempts tocorrelate tests with theoretical and numerical predictions. More recently, Fuchs et al.[5] have also studied experimental response for cylinders in bending. In mostinvestigations dealing with laminated cylinders, the models are extremely thin walledand made of graphite-epoxy systems, since the intended applications lie in theaeronautics industry. Comparatively, only few glass-fibre composite shells have beentested, and results reported do not enable an analytical or numerical validation studyto be undertaken.

This paper presents the results of a series of buckling tests on composite cylindersmade from laminates of type ‘DF1400’. The laminates are formed from E-glass fibrewoven rovings and isophthalic polyester resin. The tests are part of a project carriedout at Imperial College involving experimental and analytical investigations into thebehaviour of laminated composite shells. An automated laser scanning system,developed for measuring the initial geometric imperfections as well as bucklingdeformations during various stages of loading, was used. The material properties andspecimen details are presented, and a detailed account of the experimental results isgiven. The results include thickness and imperfection mapping, load and displacement

348 A.Y. Elghazouli et al. / Marine Structures 11 (1998) 347—371

Fig. 1. Layout of test-rig.

measurements, strain gauge readings, deformations before and after buckling as wellas salient observations regarding the elastic and buckling behaviour of each model.

2. Experimental set-up

The test rig shown schematically in Fig. 1 was used for all the buckling tests. Asindicated in the figure, axial loading is applied through a hydraulic actuator of1000 kN capacity operating in displacement control in order to enable testing in thepost-buckling range. A load cell and a displacement transducer are attached to theactuator piston to measure the central load and deflection, respectively.

The load from the actuator is transferred to the bottom end of the specimenthrough a pair of stiff circular platens which are separated by three load cells, each of500 kN capacity, placed on spherical bearings. The cells are positioned along radiiemanating from the centre of the model, each pair forming an angle of 120°. The same

A.Y. Elghazouli et al. / Marine Structures 11 (1998) 347—371 349

radial arrangement of the three load cells is also used for positioning three displace-ment transducers which measure the vertical deformation between the ends of thespecimen.

In order to create well-defined end conditions during the buckling tests, the twoends of the specimen are carefully positioned in heavy, accurately machined steelrings. The gap between the model and the rings is then filled with epoxy resin. In thetest rig, the lower ring of the cylindrical specimen is clamped to the circular platen,and the top ring is connected to the top bearing through an intermediate plate.

An automated noncontact laser scanning system was used for acquiring the initialimperfections as well as the progressive change in deformations of the inner wall ofthe specimen during loading. This measurement system has many advantages overconventional transducer-based methods. It provides faster and more reliable dataacquisition, and, unlike spring-loaded contact transducers, it does not interfere withthe transverse deformation. This effect may be particularly significant when dealingwith composite materials of inherently low moduli. Moreover, it should be noted thatthe external surface of GFRP and other fibre-reinforced shells often tends to berelatively rough and somewhat irregular because of the manufacturing process in-volved. On the other hand, the internal surface of the composite shells is relativelysmooth, owing to an initial layer of resin applied to the mandrel around which theplies are wrapped.

As indicated in Fig. 1, the laser scanning system operates inside the specimen. Themeasurement frame is supported on the lower circular platen, and passes througha central opening in the upper platen. The system allows for full circumferential andaxial travel. Vertical travel is performed through a stepper motor/gearbox/lead screwcombination, whereas circumferential movement is achieved through a stepper mo-tor/rotary table arrangement. Careful attention was given to the repeatability andaccuracy of the results. Further information on the development and verification ofthe laser system is given elsewhere [6]. In addition to the laser scanning, all loadingand data acquisition procedures were fully automated through computer-controlledtechniques.

3. Specimen details

The nominal dimensions of the cylindrical models are shown in Fig. 2a. All modelshad an internal diameter of 600 mm and an overall length of 800 mm, which com-prised a central 600 mm test length and two end parts each of 100 mm length. The endparts were significantly thicker than the middle part to ensure zero radial displace-ments along the edges and to minimise the risk of local splitting or delamination at theboundaries.

The cylindrical specimens were manufactured by a shipbuilding yard from‘DF1400’ laminates using a specially built aluminium mandrel and traditional handlay-up, as typically used in marine composite construction. The fibre material isE-glass woven roving and the resin is isophthalic polyester identified by the reference‘Synolite 0288-T-1’. The nominal glass fibre volume fraction, »

f, is 30.8% and the


Fig. 2. (a) Specimen geometry. (b) View of both sides of ‘DF1400’ woven mat (vertical: weft, horizontal: warp).

matrix volume fraction, »m, is about 50.5$0.2%. The fibres have a nominal elastic

modulus of 69 GPa, nominal density of 2.5 g/m2 and ultimate tensile strength of2.4 GPa. A close up view of the roving is shown in Fig. 2b. The tex count roving in thewarp direction is 1200 (2400/10 mm construction), and 2800 in the weft direction


Table 2Laminate nominal thickness and ply orientation for test models

Number ofspecimens

Specimenreference

Lamination Nominal plythickness (mm)

Total nominalthickness (mm)

2 DF01 and DF02 0/0 1.753 3.5062 DF03 and DF04 0/90 1.753 3.5062 DF05 and DF06 45/!45 1.753 3.506

Table 1DF1400 ply properties obtained from two-ply (0°/0°) specimens

Property Direction Value (0°)2

Elastic modulus (GPa) 1-Weft (E1) 16.4$0.1

2-Warp (E2) 12.7$0.2

Poisson’s Ratio l12

0.20$0.01Shear modulus (GPa) G

123.1$0.1

Tensile strength (MPa) 1-Weft 192.4$12.12-Warp 163.2$14.5

(4340/10 mm construction). The resin has a nominal elastic modulus of 4.0 GPa,nominal density of 1.2 g/m2 and tensile strength of 73 MPa (ultimate tensile strain of2.4%).

Nominal properties of the ‘DF1400’ ply (1.75 mm nominal thickness) were providedby the manufacturer based on tests carried out on 6-ply 0° laminates [7]. Additionaltests were independently carried out at Politecnico di Milano [8] to the relevantASTM standards using two-ply flat specimens (the same number of plies used in thecylindrical models) and the results are reported in Table 1.

The results of the two-ply tests where in agreement with the nominal propertiesbased on 6-ply tests, with maximum variation lower than 10%. In view of theimportance of mechanical properties, and the commonly observed variation in theirvalues, further tests were carried out to confirm the material properties of corespecimens extracted from the cylindrical models as discussed later in this paper.

A total of six two-ply cylinders were tested under concentric axial compression asdescribed in Table 2. Direction 0° indicates that the ply is laid with the weft parallel tothe axis of the cylinder. Other ply orientations may be identified through the axissystem given in Fig. 2a. As indicated in Table 2, the main variable investigated was theply orientation. All the cylinders had a nominal radius-to-thickness ratio of about 86.For each laminate construction 0/0, 0/90 and #45/!45, two nominally identicalcylinders were tested.

The cylinders were manufactured by hand lay-up using a specially preparedmandrel. Fig. 3 shows the details of the overlapping procedure used for the models,in which overlaps of 50 mm nominal width were used in a staggered pattern. For the0/0 laminates, two diametrically opposite vertical overlaps were used. For the 0/90


Fig. 3. Cross-section of cylinders indicating ply construction and relative position of overlaps.

laminates, four vertical overlaps were used due to limitations in the roll widthcombined with the desirable symmetry around two perpendicular axes. In the caseof the #45/!45 laminates four overlaps, inclined at 45° were used, forwhich the cross-section at the cylinder mid-height would be similar to that of the 0/90laminate.

4. Thickness measurement

Mapping of the actual thickness of all cylinders was carried out using a grid of50 mm]50 mm covering the full circumference and the middle 500 mm of the speci-men height. This grid was refined to 25 mm]25 mm at the locations of overlaps,which were nominally of 50 mm width. Measurement of cylinder thickness wascarried out using a vernier micrometer mounted on a specially designed bracket.

Fig. 4a shows a perspective map of the thickness measurement of model DF01 (0/0)clearly depicting the position of the overlaps. As can be seen, two overlap zones (OL1and OL2) and two normal zones (N1 and N2) may be identified. Thickness statisticswithin each zone, together with an overall average value, are given in Table 3. Thethickness pattern of the nominally identical model (DF02) is very similar and istherefore not shown here, but the corresponding thickness statistics are also reportedin Table 3.

Similarly, a typical thickness map for a 0/90 model (DF03) is given in Fig. 4b. Theposition of the four overlaps may be observed, identifying four normal (N1 to N4) andfour overlap (OL1 to OL4) zones. For one of the two-angle-ply (45/!45) models, i.e.DF05, the thickness map is shown in Fig. 4c. As shown, four inclined overlaps wereintroduced but the distinction between normal and overlap zones becomes somewhatless clear, presumably due to the increased complexity in lay-up. Nevertheless, it is still


Fig. 4. Thickness measurement of cylinders.


Table 3Measured thickness of test models

Model Zone N1 OL1 N2 OL2 N3 OL3 N4 OL4 Overallmean!

DF01 Mean 3.70 4.57 3.60 4.53 — — — — 3.65Cov" 0.07 0.10 0.07 0.10 — — — —

DF02 Mean 3.80 4.96 3.63 4.52 — — — — 3.72Cov 0.06 0.06 0.08 0.07 — — — —

DF03 Mean 3.94 4.92 3.90 4.96 3.92 5.02 3.99 5.24 3.94Cov 0.06 0.09 0.12 0.08 0.08 0.15 0.09 0.11

DF04 Mean 4.01 4.66 4.10 4.99 3.93 5.14 3.99 5.05 4.00Cov 0.10 0.06 0.10 0.11 0.09 0.07 0.07 0.08

DF05 Mean 3.52 4.56 3.45 4.49 3.71 4.51 3.81 4.40 3.62Cov 0.07 0.12 0.07 0.15 0.08 0.13 0.07 0.10

DF06 Mean 3.58 4.37 3.70 4.66 3.79 4.34 3.81 4.44 3.72Cov 0.08 0.08 0.09 0.12 0.05 0.11 0.07 0.14

!Excluding overlaps."Coefficient of variation.

possible to classify the model into zones and the results for both models are alsosummarised in Table 3.

It is worth noting that the measured thickness may be up to 15% higher than thenominal values in the normal two-ply zones of some models. Since these values do notinclude any overlaps, the relative increase must be associated with excess resin whichis introduced during the cylinder lay-up process.

As evidenced from Fig. 4, the thickness measurement is particularly useful indetermining the exact location of overlaps, which would be required for detailednumerical investigations. The thickness mapping may also be used to explain, inconjunction with imperfections and accidental load eccentricities, any asymmetries orirregularities in the observed buckling mode. However, the reported thickness vari-ations should be used carefully in comparative numerical or analytical studies. Asmentioned previously, the increase in thickness is mainly due to excess resin which,owing to its relatively low elastic modulus compared to that of the fibres, should beproperly accounted for in modifying the overall laminate properties.

5. Initial imperfections

Imperfection sensitivity has long been recognised as the main factor for discrepan-cies between experimental buckling loads and analytical predictions for shell struc-tures in general, and for cylindrical shells subject to axial compression in particular[9,10].

Detailed measurement of initial geometric imperfections was carried out in thistesting programme. The automated laser scanning system was first used to obtain theimperfections of the specimen after it was mounted in the test rig and before any load


was applied. The internal surface of the specimen, which was painted in white in orderto enhance the performance of the laser sensor, was measured in a radial direction at2232 points. The measuring grid consisted of 31 axial stations (with an interval of20 mm) and 72 circumferential stations (with an interval of 5° or 26.2 mm).

In order to generate a reference surface for the measurements taken on thespecimen, the internal surface of an accurately machined steel ring with a diameter of540 mm was also scanned at 5° intervals. The scan was undertaken at three verticallocations (100, 400 and 700 mm above the bottom platen) by bolting the steel ring ona set of three solid circular columns of corresponding heights. Thus, using thesereference measurements, a datum for all imperfection and deflection measurementswas created.

The ‘raw’ imperfection data were then processed using the so-called ‘best-fit’cylinder concept [11]. This concept accounts for possible misalignments between thelongitudinal axes of the specimen and the measuring frame. Furthermore, it facilitatescomparative studies on the effect of the manufacturing process on the magnitude andspatial distribution of initial imperfections. It has been used successfully in previousimperfection measuring studies on composite shells [12].

Following the ‘best fit’ procedure, the resulting imperfections were analysed usingtwo-dimensional harmonic analysis to produce a set of Fourier coefficients. Theadvantage of this widely used data processing technique is that measured imperfec-tions can be readily fed into analytical and numerical models. Specifically, thefollowing expression was used:

w0(x, h)"

mT

+m/1

nT+n/0

mmn

sinmnx

¸

sin(nh#/mn

), (1)

where: 0)x)¸ and 0)h)2n, w0(x, h) is the initial imperfection function of the

cylinder at any point, m is the number of axial half-waves, n is the number ofcircumferential waves, and m

mnand /

mnare the initial imperfection amplitude and

phase angle associated with mode (m, n), respectively.The imperfection surface was thus described by a set of coefficients, m

mnand /

mn,

with mT"15 and n

T"36, these upper limits being determined from the number of

readings taken axially and circumferentially. Eq. (1) represents a half-range sineexpansion in the axial direction, thus, imposing zero imperfection values at the twocylinder ends. Although this is not correct, the error introduced is strictly confined tothe end regions, with other parts of the Fourier expansion representing very closelythe imperfection surface [6]. It is also useful to plot the distribution of Fourierimperfection coefficients as such a plot may be used to identify dominant features ofthe imperfection pattern produced by this manufacturing method.

Typical imperfection results are given hereafter, with a full account of the measure-ments given elsewhere [13]. Fig. 5 shows a perspective view of the ‘best-fit’ imperfec-tion scan for model DF01, in which positive/negative values refer to outward/inwarddirections, respectively. The starting point of the scan (i.e. zero circumferential angle)coincides with the starting point of the thickness measurement. A plot of the Fouriercoefficients, as represented by Eq. (1), corresponding to the imperfection measurement


Fig. 5. Best-fit imperfections of Model DF01.

Fig. 6. Fourier coefficients of imperfections of Model DF01.

of DF01 is depicted in Fig. 6. A circumferential side view of the imperfectionmeasurement of all models is given in Fig. 7a—f.

In general, the results indicate that dominant imperfection wavelengths along boththe circumferential and the axial direction are ovalisation (n"2) and barrelling(m"1), with maximum imperfection amplitudes being, on average, between 40 to


Fig. 7. Side view of the imperfection surface of all models.

60% of the shell thickness. Ovalisation is often associated with manufacturinginvolving the use of a mandrel, especially when this is constructed from two semi-cylindrical parts joined together through bolts. However, it should be noted that


Table 4Peak load and corresponding strains for the cylindrical models

Model Lamination Bucklingload (kN)

Axialstrain (%)

Circumf.strain (%)

Diagonalstrain (%)

DF01 0/0 285 !0.24 0.045 —DF02 0/0 285 !0.25 0.047 —DF03 0/90 346 !0.31 0.057 —DF04 0/90 355 !0.34 0.061 —DF05 #45/!45 235 !0.44 0.28 !0.14DF06 #45/!45 232 !0.42 0.22 !0.12

whereas lower imperfection modes exhibit high amplitudes, higher low-amplitudemodes in both the axial and circumferential directions need to be adequately repre-sented in analytical models as these could be more sympathetic to cylinder bucklingmodes under axial compression.

6. Buckling tests

6.1. Experimental response

As mentioned before, the buckling tests were carried out under displacementcontrol. The displacement was increased gradually using the computer-controlledhydraulic actuator. The cylinder wall deformation was captured through the lasersystem prior to and directly after buckling.

Table 4 presents the buckling loads obtained in the tests alongside the measuredstrains at the point of buckling (i.e. at the peak load). The strains given are the averagevalues obtained from at least three gauges. For the cross-ply models (i.e.DF01—DF04), three groups of gauges, each consisting of one vertical (axial) and onehorizontal (circumferential) gauge, were placed at mid-height of the cylinder at equalcircumferential distances. In the case of the angle-ply models (i.e. DF05 and DF06),each group consisted of a rosette with vertical, horizontal and diagonal gauges, inaddition to independent vertical and horizontal gauges.

The compressive axial load versus end-shortening relationships for all six cylindersare given in Figs. 8—10. As illustrated, the behaviour of nominally identical cylinderswas very similar, in terms of stiffness, buckling load and post-buckling response. In thecase of Models DF01 and DF02, the displacement was increased gradually up toa load of about 200 kN at which point the elastic scan was performed. Upon furtherloading, buckling occurred suddenly, and audibly, at a load of approximately 285 kNin both models. The load then dropped sharply to less than 100 kN. The deformedshape at this reduced load was associated with fairly localised deformations and somefibre fracture on the crests and troughs of the buckling waves.

Under increased displacements in the post-buckling range, the specimens picked upa relatively small amount of load accompanied by significant deformation growth and


Fig. 8. Load—displacement relationship for DF01 and DF02 (0/0).

Fig. 9. Load-displacement relationship for DF03 and DF04 (0/90).

substantial noise indicating matrix cracking and possibly further fibre fracture. Theapplied displacement was finally reduced incrementally and the specimen was un-loaded. In this stage, the specimens had regained their cylindrical shape (as can beinferred from the spring-back nature of the unloading paths) but material damage wasclearly evident at positions where large buckling deformations had taken place.


Fig. 11. (a) Post-buckling wall deformation scan of Model DF01 (0/0). (b) View of Model DF01 (0/0) afterfailure.

Fig. 10. Load—displacement relationship for DF05 and DF06 (#45/!45).

The pre-buckling (elastic) scans for the models are not presented herein for com-pactness, but can be found elsewhere [13]. The elastic deformations (differencebetween pre-buckling and imperfection scans) are predominantly associated withoutward barelling, with a maximum amplitude of about 0.5 mm. The post-bucklinglaser scan for DF01 taken directly after buckling, is shown in Fig. 11a, and a view of


Fig. 11. (Continued.)

the cylinder is given in Fig. 11b. The buckling mode extended over about half thecircumference, and consisted of three circumferential waves and two axial half-waves,with a maximum inward deformation of about 25 mm. The failure was concentratedin the lower half of the cylinder. Similar behaviour was observed in Model DF02.

The same procedure of loading was used in 0/90 cross-ply models (i.e. DF03 andDF04), as shown in Fig. 9. Whereas the stiffness of these two models was about 10%lower than that of models DF01 and DF02, the buckling load was, on average, about23% higher (346 kN for DF03 and 355 kN for DF04). Buckling failure was brittle withcombined radial deformations and more extensive fibre fracture than in the 0/0models. The shape and amplitude of pre-buckling deformations were similar to thoseobserved in the cross-ply 0/0 models. The post-buckling scan of Model DF04 isdepicted in Fig. 12a, and a view of the same model after failure is shown in Fig. 12b.


Fig. 12. (a) Post-buckling wall deformation scan of Model DF04 (0/90). (b) View of Model DF04 (0/90)after failure.

The maximum amplitude of the deformation was about 30 mm in an inwardsdirection.

As shown in Fig. 10, the stiffness of the angle-ply cylinders (DF05 and DF06) wassignificantly lower than the other models (approximately 50% of models DF01 andDF02). The buckling loads were also lower than the other models as shown in Table 4.Pre-buckling deformations measured at a load of about 190 kN indicated moresignificant outward ‘‘barrelling’’ deformations of the walls compared to other models,with a maximum amplitude of about 1.0 mm. Moreover, the response of the angle-plymodels was associated with pronounced cracking noises also in the pre-bucklingstages. Although failure was generally similar to the previous models, it occurred lesssuddenly with a more gradual development of the buckling mode. The post-bucklingscan for DF05 is shown in Fig. 13a, and a view of the model at failure is given inFig. 13b. In both DF05 and DF06, radial deformations were primarily confinedbetween overlaps, with a maximum inward deformation of about 30 mm.

6.2. Axial stiffness

As indicated in the load versus end-shortening plots depicted in Figs. 8—10, the axialstiffness of the three cylinder configurations (i.e. 0/0, 0/90 and#45/!45) are signifi-cantly different. The experimental elastic stiffness of the cylinders is estimated in Table5. In order to compare these values with simplified analytical expressions, it isnecessary to determine the appropriate equivalent material elastic properties in thedirection of the cylinder axes.

Based on classical laminate theory and using the material properties given inTable 1, the apparent elastic modulus (E

x) in the axial direction (i.e. along the cylinder



length) and the two Poisson’s ratios may be determined, as shown in Table 5. Thesevalues are in agreement with the results obtained directly from tests carried out oncore specimens taken from the cylinders. The results for the latter are shown in Fig. 14and it was estimated that discrepancies with corresponding values in Table 5 werewithin $5%.

Using the apparent properties, an approximate value for the cylinder axial stiffnessmay be predicted from

kx"

Exh

(1!vxy

vyx

), (2)

in which kx

represents the normalised in-plane membrane stiffness for a unit circum-ferential and a unit axial length of the cylinder, and h is the cylinder wall thickness.


Fig. 13. (a) Post-buckling wall deformation scan of Model DF05 (#45/!45). (b) View of Model DF05(#45/!45) after failure.

Considering nominal geometry and apparent material properties (Ex, l

xy, l

yx) given in

Table 5, the membrane stiffness (in kN/mm) is estimated and presented in the sametable.

Whereas the stiffness of the cross-ply 0/0 cylinders appears to be well predicted bythe above expression, the stiffness of the 0/90 cylinders is somewhat overestimatedpossibly due to the membrane/flexural coupling caused by mid-plane section asym-metry. This discrepancy is more pronounced in the angle-ply cylinders where moresignificant coupling effects are present in addition to notable nonlinearity in thematerial behaviour.

In general, both the experimental results and analytical predictions indicate that thehighest axial stiffness is obtained from the 0/0 cylinders, with relatively lower valuesexhibited by the 0/90 cylinders. This is a direct consequence of the orthotropic elasticproperties. Furthermore, it is clearly indicated that considerably lower axial stiffness isprovided by the angle-ply cylinders.

6.3. Buckling strength

As shown in Table 4 and Figs. 8—10, the experimental load corresponding tobuckling of the two cross-ply 0/0 models (DF01 and DF02) was 285 kN compared toan average buckling load of about 350 kN in the 0/90 models (DF03 and DF04). Onthe other hand, the angle-ply models (DF05 and DF06) exhibited significantly lowerbuckling loads, of 234 kN on average.

Preliminary analytical predictions were carried out in order to determine theupper-bound linear buckling strength of the cylinders. For this purpose, the finiteelement program ABAQUS [14] was used to estimate the buckling loads using linear



eigenvalue analysis. This type of analysis does not account for nonlinearities, andin-particular the effect of initial geometric imperfections is not considered. Thecylinder was modelled using 9-noded doubly curved shell elements (type S9R5), with24 and 72 elements in the axial and circumferential directions, respectively. Thematerial properties given in Table 1 were used in conjunction with nominal uniformwall thickness, thus thickness imperfections were not included. The parameters of thefinite element model were determined following a number of benchmark and conver-gence studies carried out as part of the project [15].

The numerical linear buckling loads obtained for the cylinders are given in Table 6.As shown, the estimated loads are similar for the 0/0 and 0/90 cylinders, withmarginally higher loads predicted for the angle-ply #45/!45 models. Furtherestimations may be carried out using available simple theoretical methods, but thesewould generally impose some limitations. For example, expressions given by Vinson


Table 5Comparison of experimental and analytical axial stiffness

Model reference DF01/02(0/0)

DF03/04(0/90)

DF05/06(#45/!45)

Apparent elastic modulus Ex

(GPa) 16.4 14.3 9.3Poisson’s ratio l

xy0.20 0.18 0.47

Poisson’s ratio lyx

0.16 0.18 0.47Analytical membrane stiffness (kN/mm) 149 139 104Experimental stiffness (kN/mm) 148 134 81Ratio of experimental/analytical stiffness 0.99 0.96 0.78

Fig. 14. Stress—strain relationships of specimens cut from the cylinders along the vertical axis.

and Sierakowski [16] result in an overestimation of the numerical buckling load by4% for 0/0 and 0/90 cylinders, and about 14% for the angle-ply models. However, itshould be noted that these expressions are based on ideal boundary conditions andspecial orthotropy rules which do not strictly apply to the tested cylinders, parti-cularly the angle-ply models.

The ratio between the experimental buckling strength and the linear buckling loadsgives an indication of the ‘knock-down’ factors for these cylinders. Knock-downfactors are important for design purposes as they are used to reduce theoreticalbuckling predictions of nominal shells in order to account for the influence ofimperfections. In addition to the significant influence of initial geometric imperfec-tions, other factors such as thickness variation, overlapping and slight load eccentrici-ties would also affect these ratios.


Table 6Comparison of linear numerical buckling loads with experimental results

Model reference DF01/02(0/0)

DF03/04(0/90)

DF05/06(#45/!45)

Numerical eigen value (Linear FE) 463.96 464.20 470.35"Experimental load! (kN) 285 350 234Ratio of experimental/numerical load 0.62 0.75 0.50"

! Average of the two nominally identical cylinders."Based on initial elastic properties of angle-ply.

As shown in Table 6, the ratio of experimental-to-linear buckling strength isestimated as 0.62 for the 0/0 models and about 0.75 for the 0/90 models. The higherexperimental buckling strength obtained for the 0/90 cylinders, which is not reflectedin the linear eigenvalue analysis using nominal geometry, may be largely attributed tothe relatively higher thickness due to excess resin as well as the additional overlapsused in these models. Nevertheless, this requires further investigation using nonlinearnumerical analysis with due account of geometric and stiffness imperfections as well asadequate consideration of the influence of excess resin on laminate material proper-ties.

On the other hand, a relatively lower ratio of about 0.5 is indicated in Table 5 forthe angle-ply cylinders. It should be noted however that the numerical eigenvalueresult is based on the initial elastic moduli of the angle-ply laminate. As shown inFig. 14, the stress—strain relationship of the #45/!45 specimen is essentially nonlin-ear. Consequently, at the point of buckling significantly reduced moduli, compared toinitial values, would be effective. For example, if the elastic moduli are reduced toreflect the nonlinearity in the constitutive relationships corresponding to the level ofstrain at buckling, the buckling loads would reduce by more than 20% and the‘knock-down’ ratio would exceed a value of 0.6. Appropriate consideration of thiseffect in numerical studies would necessitate the use of nonlinear material models.

It may also be noteworthy that although, in theory, initial imperfections have asignificant effect on buckling strength reduction, this may not be necessarily corre-lated with the modes found to exhibit a large amplitude in physical models. Asindicated in Fig. 7, whereas nominally identical cylinders such as DF05 and DF06may have different maximum imperfection amplitude, they exhibit similar experi-mental buckling loads. This suggests a probable significance of imperfection modeswith small wavelength and low amplitude, a factor which has to be adequatelyrepresented in nonlinear numerical simulations.

7. Conclusions

The buckling behaviour under axial compression of laminated woven GFRPcylinders was investigated in this paper. The main experimental aspect examined was


the influence of ply orientation on the response of the composite cylinders. Itwas shown that using reliable automated techniques, systematic data acquisition ofthe salient experimental parameters may be carried out. The experimental resultspresented provide data for the calibration and verification of analytical models. Theseare needed for assessing and quantifying the response of cylinders of various geomet-ric and material properties, and for conducting parametric and design studies. Par-ticular observations and conclusions of this experimental study are summarised asfollows:

1. Automated laser scanning provided an accurate and reliable non-contact measure-ment method for initial imperfections and change in wall deformations of thecomposite shells prior to and after the occurrence of buckling. Integrating thissystem with computer-controlled loading techniques significantly enhances theprecision as well as efficiency of shell buckling tests.

2. The average measured thickness of the cylindrical models was about 5—15% higherthan the nominal values. This does not include the effects of overlaps, but isassociated with excess resin introduced through the manual lay-up process. Thethickness mapping is important in accurately identifying the locations of overlaps,as may be required for numerical modelling.

3. Imperfection scans have revealed that long imperfection wavelengths are dominantwith maximum imperfection amplitudes being, on average, between 40 and 60% ofthe shell thickness. The laser scans provide information on manufacturing imper-fections, which with the support of analytical and statistical studies, can find its wayinto tolerance specification. This is an important objective in shell buckling codes,and controls can be applied on the specific manufacturing conditions to improveproduct performance.

4. The effect of laminate orientation on the elastic axial stiffness of the cylinder wasclearly observed. As expected, the highest axial stiffness was provided by the 0/0models, with about 10% and 55% lower stiffness for the 0/90 and #45/!45cylinders, respectively. This was in agreement with analytical predictions based onthe apparent properties in the axial direction.

5. In terms of buckling strength, the highest axial resistance was exhibited by the 0/90cylinders. As expected, the experimental buckling load was significantly lower thanthe linear buckling strength due to imperfection sensitivity, indicating a knock-down value of about 0.75 in the case of the 0/90 cylinders.

6. Although the numerically estimated linear buckling load, based on uniform nom-inal properties, indicate similar linear buckling strengths for the 0/0 and 0/90models, the experimental loads of the 0/0 models were about 18% lower than their0/90 counterparts. The knock-down factor for the 0/0 models was estimated as0.62. The relatively higher strength of 0/90 laminates is largely attributed to theextra resin and additional overlaps introduced in these models. This aspect war-rants closer analytical examination.

7. The buckling strength of the angle-ply laminates was considerably lower than thecross-ply models. This is in contradiction to the prediction of linear analysis whichresults in marginally higher buckling loads for the angle-ply cylinders as compared


to the cross-ply. However, it was shown that this may be primarily due to thesignificant nonlinearity of the material when the angle-ply laminate is tested alongthe cylinder axis. This causes a significant reduction in the buckling strengthcompared to that obtained from predictions adopting the initial values of materialproperties.

The results presented in this paper form part of a large project dealing with thebehaviour of several types of composite cylindrical shells under various loadingscenarios. Further numerical and parametric studies are underway, with a view toproviding design recommendations.

Acknowledgements

The work presented in this paper was sponsored by the European Commissionunder a Brite-Euram programme (Project BE-7550: Design and Validation of Imper-fection-Tolerant Shell Structures). Thanks are due to Intermarine-Spa for providingthe specimens, to Prof. Poggi of Politecnico di Milano for carrying out materialproperty tests, and to all the other partners for many productive discussions. Theauthors would also like to express their gratitude to Mr T Boxall and Mr R Millwardof the Structures Laboratories at Imperial College for their dedication and profes-sionalism in conducting the tests.

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