design, manufacture and evaluation of laminated carbon-epoxyi-beams in bending

8/7/2019 Design, manufacture and evaluation of laminated carbon-epoxyI-beams in bending

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Design, manufacture and evaluation of laminated carbon/epoxyI-beams in bending

G. Zhou*, J. Hood

Department of Aeronautical and Automotive Engineering, Loughborough University, Loughborough, Leicestershire LE11 3TU, UK

Received 1 April 2004; revised 6 December 2004; accepted 6 January 2005

Abstract

Composite I-beams of several different lengths were fabricated by using a hot press with an open mould. Several manufacturing-related

issues were addressed. The bending behaviour of these I-beams was evaluated both experimentally and analytically in terms of bendingstiffness, strength and manufacturing quality. A particular attention was paid to the potential change of the damage characteristics induced by

a variation of the length-to-depth ratios of the beams. The manufacturing features were shown to be insensitive to the sectional flexural

modulus and the latter was in good agreement with the predicted. The sectional shear modulus could not be properly estimated

experimentally due to limited web in-plane shear. The joint reinforcement and/or segment laminate symmetry did not have the significant

effect on the flexural strength due likely to the substantial laminate thickness and as well as to small length-to-depth ratios. It was shown that

the ultimate failure was initiated at the bent fillet regions, which were in high local stresses. The presence of ply discontinuity could be the

most significant contributing factor. Decreasing the length-to-depth ratios of the beams led to the change of the damage mechanisms from

flexural failure to flange delamination. It was demonstrated that the present manufacturing method is viable for fabricating composite I-

beams of a good quality and that an established analytical methodology is useful for further bending investigations of I-sections through

cross-sectional dimension and lay-up designs.

q 2005 Elsevier Ltd. All rights reserved.

Keywords: I-beam

1. Introduction

Thin-walled I-beams are well-established and widely-

used basic load-bearing structural components. In general,

flanges are intended to provide nearly all the bending

resistance whereas the web provides most of the through-

the-thickness (TTT) shear resistance. In recent years, they

have been made with fibre-reinforced composite materials in

the aerospace industry [1–9] and civil construction industry

[10–13], because of their light weight, high specific strength

and/or stiffness, good corrosion resistance and superb fatiguestrength limit. As a result, their bending behaviour becomes

very complex due to the anisotropic nature of composite

materials and to the manufacturing techniques used to form

the I-sections. Therefore, their bending performance has

been investigated experimentally [1–10,12,14], analytically

[2,4,6,9–12,14] and numerically [8,13], though various other

types of load were also dealt with. These investigations

covered unsurprisingly a wide range of composite I-beams

and involved specific design concepts of I-section forming

with different cross-sectional dimensions and used different

composite materials along with very different manufacturing

techniques. Although, relatively speaking, the bending

mechanical behaviour has been studied substantially [1–

14], there is limited research that reports the bending damage

characteristics of these composite I-beams [1,3–9]. In

particular, there is no report on the potential change of thedamage characteristics of composite I-beams induced by a

variation of their length-to-depth ratios. Moreover, an

analytical evaluation of such bending performance could

be difficult if specific composite materials detail and

manufacturing characteristics of I-section forming are not

taken into account. Therefore an improved engineering

analytical methodology is very desirable for laminate stress

analysis in preliminary structural design and for assessing

quality of the manufacturing techniques.

Composites: Part A 37 (2006) 506–517

www.elsevier.com/locate/compositesa

1359-835X/$ - see front matter q 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.compositesa.2005.01.005

* Corresponding author. Tel.: C44 1509 223 434; fax: C44 1509 223

946.

E-mail address: [email protected] (G. Zhou).

http://www.elsevier.com/locate/compositesa

http://www.elsevier.com/locate/compositesa



In the aerospace industry, composite I-beams have often

been used as helicopter rotor blades [2], discrete stiffeners

[1,3–5] and aircraft wing spars [6,8,9]. They were usually

fabricated with one of two basic approaches. One was that

solid flanges and web were co-cured in one piece [1–5,7,14].

The other was that flat flange and web segments were

separately cured first and then were bonded together byusing adhesive without [6,9] or with laminated angle corner

pieces [8]. A further weight reduction and thus a greater

structural efficiency could be achieved in the latter by

replacing the solid web section with sandwich construction

[6,9]. The conventional curing method for aeronautical

composite I-beams is based on expensive autoclaving. One

potential alternative is to use low-cost hot pressing [14].

This method was reported to be very effective in

manufacturing composite parts with thermoplastic matrix

[15]. Thus it is very desirable to ensure that composite

components manufactured via this cost-effective method

have an adequate mechanical performance.

Therefore, the present work is intended to design,

fabricate, test and evaluate quasi-isotropic carbon-epoxy I-

beams co-cured by using a purpose-made open mould with a

hot press and low temperature moulding prepregs. The

beams of various lengths were made. The evaluation of the

mechanical behaviour of these I-beams in bending was

carried out both experimentally and analytically. Damage

characteristics and load-bearing capacity of the I-beams

were examined with focus on flange-web joint reinforce-

ment, length-to-depth ratio and manufacturing quality.

Because of this co-curing nature, the TTT shear in the I-

beams could be affected when their length-to-depth ratios

were altered. This paper represents the first attempt toexamine both experimentally and analytically the potential

change of the damage characteristics induced by a variation

of the length-to-depth ratios of these co-cured I-beams.

2. Design of moulding device

In the design of an I-beam moulding device for a

hydraulic hot press, major requirements considered were

ease of specimen fabrication, removal of the cured speci-

men, cross-sectional mould dimensions associated with

conduction heat loss, the length (L )-to-overall-depth (h)

ratios (L / hs) of specimens and the radius of fillets between

the flanges and the web section. Aluminium alloy was

chosen for the mould, rather than steel, due primarily to its

ease of machining. The hydraulic press was capable of

delivering a pressure up to 2.1 MPa (300 psi) with a

temperature up to 300 8C. A four-piece open mould was

designed in such a way that the first two requirements were

readily satisfied. It consisted of two press plates at the top

and bottom and two side pieces, as its cross-sectional profile

shows in Fig. 1. The heated top and bottom platens of the hot

press directly distributed heat to the respective top and

bottom press plates of the mould during cure and also

applied hydraulic pressure to close the mould therebyshaping the I-section. In addition, the applied pressure could

force partially molten resin to fill up any potential voids.

Two side pieces as shown in Fig. 1 have cavities machined

out to ensure that heat flow could be directed effectively

towards the regions that would make contact with the web

section. The fillet radius of 2 mm for the flange-web joints

was a trade-off between minimal stress concentrations

caused by the extension of 908 and angle plies in the web to

the flanges and minimal cavities at the centre of the flange-

web joints (Fig. 10). A smaller fillet radius was preferred

here as a greater fillet radius may lower the maximum

bending stress [13]. In addition, resin bleed from the flangesduring cure was directed to resin sink channels that were

located near both ends of the flanges as shown in Fig. 1.

Since an important part of this investigation was to

validate the sectional stiffness of the I-beams by using an

established analytical method [6,9,10,14] and to develop a

stress analysis capability. This required these I-beams to

have the slenderness ratios in such a range that both flexural

and web in-plane shear failures would occur in a mixed-

mode but reciprocal manner. Since the cross-sectional

dimensions could affect these failure modes, they had to be

chosen carefully. Nevertheless, these dimensions, once

selected, were kept constant in the present investigation, and

thus the more convenient L / hs were used instead. The

maximum length of the beams was restricted to 420 mm due

to dimensional constraints of the platens on the hot press.

Consequently, the overall cross-sectional dimensions were

limited to the overall depth of 40 mm so that the L / hs of 6 to

11 could be obtained. On the basis of the experimental

results from composite I-beams [9] as well as solid

rectangular composite beams [16,17], the mixed-mode

failure was common among the beams with the L / hs

between 6 and 14. The flange width of 30 mm was selected

first to ensure that the width-to-depth ratio was less than

unity as the I-beams with the wider flanges could have

Fig. 1. Unassembled view of four-piece open mould for fabricating

laminated I-beams.

G. Zhou, J. Hood / Composites: Part A 37 (2006) 506–517 507



the lower bending resistance [7]. The additional consider-

ation was in order for a high critical buckling strain of the

compressive flange via

3bucklingZK

1Kn212

t f

b1

2

(1)

in which a bucking coefficient K is 0.58 for the presentboundary conditions, n12 is the Poisson’s ratio of carbon/

epoxy. The flange thickness t f of 3 mm (or 24 plies) was

selected so that a half free flange width b1 was 13.5 mm.

This finally ensured that the compressive flange had a

relatively high critical buckling strain of 3200 m3.

3. Design considerations of laminate lay-up

As mentioned in Section 1, two approaches have been

used to form the composite I-sections. The bonding

approach [6,8,9] has the advantage that the formed I-section

could preserve material symmetry with respect to the mid-

plane of the cross section when ready-made flat flange and

web laminates were bonded together. Consequently, lay-up

design as well as analysis of its mechanical and structural

behaviour could be substantially simplified because of fewer

couplings. The disadvantage of the approach is that design

of the corner angles and bonding quality could become very

critical to section integrity because of the complete lack of

fibre continuity through the flange-web joints.

On the contrary, the advantage and disadvantage of the

co-curing approach [1–5,7,14] seem to be the opposite of

the above. Lay-up design with this approach could beextremely complicated, if angle plies are involved [18].

Since the angle plies in the inner halves of the flange

laminates are extended from the web laminate, a change of

ply orientations means that both the flange and web

laminates cannot have a symmetric lay-up at the same

time, as illustrated in Fig. 2(a) and (b). For the flange

laminate to have a symmetric lay-up with respect to its own

mid-plane (Fig. 2(a)), the angle plies from both the flanges

have to be completely anti-symmetric with respect to the

mid-plane of the cross section. Those angle plies in the inner

halves of the flange laminates are also discontinuous with

respect to the vertical axis, though their fibre orientations

are continuous. Consequently, the angle plies in the web

laminate are completely anti-symmetric. For the web

laminate to have a symmetric lay-up with respect to its

own mid-plane (or bending plane), the angle plies in the

inner halves of the flange laminates (Fig. 2(b)) have to be

discontinuous not only in material crossing the vertical axis

but also in fibre orientations. However, they may have

partial symmetry with respect to the mid-plane of the cross

section, in addition that the two outer halves (two flat stacks

in Fig. 3) can still be made symmetric. The additional

shortcomings of this approach are that the angle (and

transverse) plies in the inner halves of the flange laminates

are discontinuous across the respective lamination planes inboth cases. Therefore, it is generally impossible to have

complete symmetry with respect to the mid-plane of the

cross section if the angle plies are present. Therefore,

possessing some degree of couplings in the co-cured

composite I-beams is inevitable whatever the lay-up design

one adopts, and the effect of such couplings on sectional

stiffness could be significant if the segment laminates are

relatively thin. In general, the flange laminates with

Fig. 2. (a) Flange laminate with a symmetric lay-up. (b) Flange laminate

without a symmetric lay-up.

Fig. 3. Four ply-group stacks for forming the composite I-section.




a symmetric lay-up with respect to its own mid-plane may

have less degree of coupling than the one without.

In the present investigation, both the lay-up designs with

either symmetric flanges or symmetric web were adopted

with the co-curing approach. The composite system,

T700/LTM45-EL (from Advanced Composites Group),

was selected mainly because LTM45-EL epoxy can beeasily cured at low temperature and its mechanical property

database is available at Loughborough University. The UD

mechanical properties of this composite system were

measured as E 1 of 127 GPa, E 2 of 9.1 GPa, G12 of

5.6 GPa, G23 of 3.9 GPa and n12 of 0.31. A total

of 24 plies in a quasi-isotropic symmetric lay-up of

(G458/08/908)3s with a ply thickness of 0.128 mm were

used to construct balanced I-beams. Again, selecting the

quasi-isotropic lay-up was due to the same reasoning as the

above, that is, some strength data from coupon tests is

available and they will be required later in the evaluation of

load-bearing capacity of the I-beams. Otherwise a more

conventional multidirectional lay-up, for example,

(G458/(08)2)3s may have been used, and so manufactured

I-beams could be stronger in terms of bending resistance.

4. Fabrication of I-beam specimens

Each laminated I-beam in the present investigation was

formed by assembling four sublaminate stacks in the mould.

It consisted of two identical flat rectangular top and bottom

stacks of 12 plies each, and two channel section stacks of

12 plies each, as illustrated in Fig. 3. Extra UD strips of

the same composite material were inserted at the flange-web

joints to prevent creation of voids in some selected

specimens. Two different amounts of the strips were

experimented as indicated in Table 1. The outer faces of

the I-beams used G458 plies to provide shear resistance in

the web section. Because the inner halves of the flanges had

to be extended from the flanges of two channel sections, a908 folding of G458 plies at the corner bends led to anti-

symmetry with respect to the mid-plane of the cross section.

The central area of the web section was the most remote

region to the press plates of the hot press. Thus, it was

difficult for the entire cross-sectional area of the I-beam to

have the same curing temperature of 90 8C during curing.

Therefore, heat from the press plates required to achieve

such temperature had to be greater because of the additional

loss through heat transfer. A simple heat transfer analysis

was carried out on the basis of a crude assumption that a

distribution of temperature across the mould was linear.

Consequently the temperature of the press plates for

achieving 90 8C along the longitudinal axis of the I-beams

was estimated to be 138 8C.

To fabricate each specimen, three coats of a release

medium (Dexter Frekote 700-NC) were applied to the

interior of the mould pieces for specimen removal at the end

of the curing cycle. After each of the first two coats, the

mould interior surface was wiped with cloth. Then two 12-

ply channel stacks were wrapped on the two side pieces in a

correct sequence and were brought together with the two flat

stacks before the mould was assembled. Finally, the

assembled mould was placed in between the two press

plates of the hot press. A vice system was used to provide

Table 1

Bending test results on carbon/epoxy I-beams

Support

span (mm)

L / h Segment with

a symmetric

lay-up

T-joint

reinforce-

ment

Max. load

(kN)

Max. total

displ. (mm)

Max. ten-

sile strain,

3tensil (m3)

Compr.

strain,

3compr (m3)

Max. web shear

strains 1 (m3)

Max. web

shear strains

2 (m3)

180 4.50 Flanges None 21.7 2.3 5731 K4436 K490,K595 –

210A 5.25 Web 5!3 mm 17.5 3.3 5833 K4375 242,K875 –

210B 5.25 Flanges None 22.7 3.6 11185 K11074 K2647,K400 –

210C 5.25 Flanges None 19.0 3.1 6584 K3125 K850a,K1020 –

250 6.25 Web 3!2 mm 17.7 3.6 5756 K4474 K809a,K390 K2499, 2110

270A 6.75 Web 5!3 mm 20.8 4.0 7684 K5684 K1346,K756 –

270B 6.75 Flanges None 18.3 4.4 7710 K7250 K936a,K695 –

270C 6.75 Flanges 3!2 mm 18.8 5.7 8104 – K754,K662 –

290 7.25 Flanges None 17.1 6.8 13981 K10192 K37a,K314 –300 7.50 Flanges 5!3 mm 17.9 4.8 7155 – K826,K251a –

310 7.75 Flanges 3!2 mm 19.1 5.6 8492 K6728 K1375a,K599 K2484, 2148

330A 8.25 Web 5!3 mm 20.5 7.0 10357 K8750 1500,K1742 –

330B 8.25 Flanges None 17.7 6.2 7999bK5400 K987,K329 –

360 9.00 Flanges None 16.0 6.6 8214 K6769 K1129,K836 –

370A 9.25 Flanges None 17.5 8.3 10968 K9355 33a,K96 –

370B 9.25 Flanges 3!2 mm 14.2c 7.5c 7168cK5604 K506,K1334 K1342, 1528

390 9.75 Flanges None 15.1 7.6 8739 K4316 K948,K615 –

L/D denotes the ratio of support span to depth of a beam.a The sign of strain was opposite initially.b Strain gauge broke before the maximum load.c Premature failure at one support. 1 and 2 in the web strain columns denote the mid-span and a longitudinal quarter locations, respectively, each for bothC

458 andK458 ply orientations.




horizontal forces to ensure that the side pieces of the mould

remained stationary and closed during the cure, asillustrated in Fig. 4. All the specimens were cured under a

pressure of 0.69 MPa (100 psi) for 2 h 38 min. A total of

seventeen I-beams were fabricated with a range of the

overall lengths from 240 to 420 mm.

5. Experimental procedures

All the I-beam specimens were strain-gauged at various

selected positions to monitor bending and shear behaviour,

especially sign of damage initiation and propagation. One

single-element strain gauge (SG) was bonded at the centre

of the bottom/tensile flange at the mid-span and one at

15 mm away from the loader on the compressive flange on

all the specimens as indicated in Fig. 5. One or two-element

rosettes of 908 apart were bonded on the web at G458

orientation with respect to the longitudinal axis of the

I-beams to monitor the web shear (Fig. 5). The additional

rosette orientated in the 0 and 908 directions was bonded on

the under surface of the compressive flange at the mid-span

to examine the compressive flange deformation. In sometests, a LVDT was positioned about 5 mm away from the

polymer base of the SG on the tensile flange to examine the

potential local indentation.

In each three-point bending test, the outer surfaces of the

flange ends of the beam were secured by a pair of purpose-

made fixtures as illustrated in Fig. 5. Four pairs of bolts

through steel plates were gently tightened such that an

amount of holding force (not measured) would not induce

local damage on the beam. As could be seen, each holding

fixture consisted of a pair of H-shaped steel plates of

115 mm in the longitudinal direction with the inner edge of

the lower one (on the tensile side of the I-beam) being

smoothed out to minimise local crushing and to accommo-

date bending rotation. Although each secured region of the

I-beam was about 20 mm long, the effective length in

contact with the ends of the beam was less than 15 mm. A

steel block with the same height as the I-beams was used to

fill out the remaining end region to provide a uniform

holding pressure, but the spaces between the two inner

Fig. 4. Assembled view of four-piece I-beam mould in hot press.

Fig. 5. Experimental setup of a secured composite I-beam with strain gauge locations.




flange surfaces on both sides of the web within the

supported end regions were not supported. As a result, the

longitudinal movement of the beams was not prevented and

in particular, the mid-plane of the I-beams was completely

free to rotate with the tensile flanges as well as part of the

compressive flanges. Hence the present boundary condition

was considered essentially as simply supported. This type of the end condition was intended to mainly provide the

current I-beams with stability against lateral buckling.

A cylindrical loader with a flat contact surface of 14 mm

wide (in the longitudinal direction of the I-beam) was firmly

bolted on the ram of a servo-hydraulic MAND universal

testing machine. Each specimen was quasi-statically loaded

monotonically to failure at a speed of 5 mm/min. Its data in

terms of load, displacementand strainreadings were recorded

through an Orion delta 3530D acquisition system at the

samplingrateofoneortwodatapointspersecond.Theoverall

resultsaresummarisedin Table1,inwhichthesupportspanof

each I-beam was also used as the specimen identity.

6. Laminate I-beam stiffness analysis

Because the 3 mm wall thickness in the present I-beams

is quite substantial with respect to other cross-sectional

dimensions, the bending behaviour of these beams is

expected to be dominated by the linear elastic deformation

before appreciable damage occurs. As the L / hs of these I-

beams are relatively short, a shear deflection has to be taken

into account as in Eqs. (2a) and (2b). Thus, the deflection w

of a simply-supported composite beam for the given load P

is provided by

wZPL 3

48Dx

CPL

4kS x(2a)

in which Dx is the sectional flexural rigidity of the beam as

given by Eq. (3), S x is the sectional shear rigidity, L is the

support span and a shear correction factor k is close to unity

for the present cross-sectional dimensions by using charts in

Fig. 3 of [11]. Since the TTT shear of the web is effectively

the in-plane shear of the web laminate, thus Eq. (2a)

becomes

wZ PL 3

48Dx

C PL 4k ðG12AÞ

; AZ ðhK2t f Þt wC2bt f (2b)

in which A is an area of the cross section, b is the flange

width and t w is the web thickness. Also as the flange

laminates could not be completely symmetric with respect

to their own respective mid-planes, the flexural rigidity Dx

of the composite I-beams must thus be defined [14] by

DxZE xI z2b

ðd 011Þf

CðhK2t f Þ

3

12ða11Þw

(3)

in which d 011, d 012, d 016 and a11 are respective elements of

the inverted [D 0]f matrix for the flanges and the inverted [A]

matrix for the web. The [D0]f matrix must be calculated with

respect to the centroidal axis of the cross section [19] as

½D0�f Z ½D�C2

hK t f

2

½B�C

hK t f

2

2

½A�z½D�

C hK t f

2

2

½A� (4)

in which [D], [A] and [B] are the bending, extensional and

coupling stiffness matrices with respect to the flange

centroidal axis. For the I-beams with the nearly symmetric

flanges, the contribution of the coupling stiffness matrix [B]

is assumed to be zero, as a first-order approximation,

although practically ply discontinuity in the inner halves of

the flanges exists (Fig. 2(a)). Using the basic lamina data

given earlier, the effective flexural modulus E x of the beam

was estimated to be 57.1 or 48.5 GPa if the flange coupling

terms d

0

12 and d

0

16 are neglected as in [6,9,10,14]. For the I-beams with the non-symmetric flanges (i.e. with a

symmetric web), the contribution of the coupling stiffness

matrix [B] may not be zero. However, as there was no

similar analytical method available for taking into account

the unique feature in defining the I-beam stiffness, Eq. (4)

was used again in the corresponding stiffness calculations

for such I-beams, as a first-order simplification.

It was worth noting that Eq. (2b) predicted only the

maximum beam deflection without consideration for local

indentation a. Such local indentation consideration is

necessary for improving correlation of prediction with

experimental data only if the beams are subjected to three-

point bending, as in the present case. In order to compareprediction of Eq. (2b) with experimental data, the local

indentation has to be taken into account through

dtotalZwCa (5)

where dtotal is a displacement directly measured by the

testing machine. Then Eq. (2b) can be rearranged as

4AðdtotalKaÞ

PL Z

1

12E x

L

r

2

C1

G12

(6)

in which r is the radius of gyration of the cross section as

given by r2ZI / A. Eq. (6) describes a linear relationship

between the reciprocal of stress, 4A(dtotalKa)/ PL , and the

squared slenderness ratio of the I-beams, (L / r)2. Thus, a

reciprocal of the slope of Eq. (6) should reflect the sectional

flexural modulus of the I-beams, and accordingly, a

reciprocal of the intercept on the ordinate reflects the

sectional shear modulus. Therefore, Eq. (6) is more accurate

than the similar equations without correction for local

indentation as presented in [9,10,12,14]. Obviously, if the L /

hs of beams were relatively large, say, greater than 16, the

effect of local indentation could be negligible.




7. Experimental results for sectional stiffness

The analytical predictions in terms of load-deflection

relationship as described in Section 6 did not account for

either the effect of ply discontinuity (angle and transverse

plies) in the inner halves of the flanges or the effect of

potential voids at the flange-web joints in some I-beams. Asa result, such prediction (Eq. (6)) could provide only the

upper-bound estimate of the sectional flexural stiffness. As

these effects are unlikely to affect the web shear, they may

not make a noticeable contribution to the estimation of the

sectional shear stiffness. Nevertheless, comparison with

experimental data could still provide an effective means for

assessing the sectional stiffness and thereby manufacturing

quality of these composite I-beams.

Fig. 6 shows load-displacement curves from four I-

beams of different support spans (210C, 270B, 330B and

390) plus two analytical predictions. The experimental

results (in solid symbols) showed reasonably linearresponses and indicated that the I-beams deformed elasti-

cally throughout major part of the loading process. The

prediction for the 390 mm beam agreed well with the

experimental result whereas the prediction for the 210C mm

beam underestimated the experimental result by about 15%.

The latter may be attributed to the less well developed

flexural behaviour at such low L / h. The strain responses of a

web rosette bonded at the quarter span location (of the

310 mm beam) in Fig. 7 showed the similar linear features.

In-plane shear in the web seemed limited with no sign of the

usual non-linearity due likely to the presence of 908 plies.

For the I-beams with voids or incompletely filled-up voidspresent at the flange-web joints, some local indentation

could easily be substantiated. The test result from a 270 mm

long I-beam (270A) showed an indentation of about

0.38 mm at the load of 10 kN. This indentation value was

measured from a location which is 10 mm away from the

mid-span in order to avoid contact with the mid-span SG.

Previous experimental results in [20] demonstrated that the

maximum longitudinal bending strain in laminated

rectangular beams could be extrapolated linearly using

strain data measured from locations away from the mid-

span. For the present case, an indentation of about 0.45 mm

was estimated for the mid-span. Therefore, for simplicity, a

local indentation of 0.45 mm was linearly added to the beam

deflections at the same load. In this way, the correlation

between the experimental and the predicted was in much

better agreement, as shown in Fig. 6. This also implied that

the discontinuity of three ply groups in the inner halves of

the flanges may not have had a noticeable effect on the

bending stiffness of the I-beams, unlike initially anticipated.

After all, 08 plies, which were supposed to provide the most

resistance of the bending load, were not affected.

As mentioned earlier, the sectional flexural and shear

moduli of the I-beams were evaluated by using Eq. (6). Tothis end, the displacement data of all the individual tests

were taken at the load of 10 kN, at which the beams were

not considered potentially initiating or experiencing any

damage in any circumstances. Such data (in cross) are

presented in Fig. 8 along with prediction of Eq. (6). In the

figure, the data appear in a band, and this could reflect the

effects of three different flange-web joint reinforcements

0

2

4

6

8

10

12

14

16

18

20

22

0 1 2 3 4 5 6 7 8

Displacement, mm

Load, kN

210C 270B

330 390

210C 390

Experimental

390

210C

Prediction by Eq. 6 with

0.45-mm indentation

270B330

Fig. 6. Load-displacement curves of four composite I-beams.

0

2

4

6

8

10

12

14

16

18

20

22

24

-3000 -2500 -2000 -1500 -1000 -500 0 500 1000 1500 2000 2500 3000

Microstrain

Lo

ad, kN

+45 Degree

-45 Degree

Fig. 7. Web strainresponse curves from a rosette located at a quarterspan of

an I-beam.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 100 200 300 400 500 600 700 800

(L/ρ)2

4 A (δtotal - α)/PL, mm

2/kN

---- Linear fit of experimental data

Prediction of Eq. 6

Fig. 8. Graphic presentation of normalised bending stresses for the

determination of sectional flexural and shear moduli.




and the sectional symmetrical characteristics in addition to

experimental errors. Nevertheless, as the individual contri-

butions of these features were considered insignificant, the

data trend, ignoring these differences, was linearly fitted (in

dashed line) so that both the slope and the ordinate intercept

of the line trend could be used to estimate, respectively, the

sectional flexural and the sectional shear moduli. Interest-ingly, the estimated sectional flexural modulus of about

47.3 GPa differed from the predicted value of 57.1 GPa by

17% or only by 3% if compared to 48.5 GPa. This

reasonable agreement may well be because the underlining

deformation mechanism was dominated by the flexural

behaviour. However, the estimated sectional shear modulus

of about 3.5 GPa was slightly more than half the predicted,

and both were considerably lower than the experimental

value of 17.9 GPa [21]. The reason for this could be that the

degree of the induced web shear was very limited due to the

quasi-isotropic lay-up and the substantial web thickness. As

a result, this low value may reflect the shear behaviour of the

flanges rather than the web.

8. Stress analysis

To evaluate the load-bearing capacity of the I-beams

leading to the ultimate failure, a detailed three-dimensional

state of stress is usually required inevitably with appropriate

failure criteria. Although such information could be

obtained from finite element modelling [8,13], prediction

of damage initiation and ultimate failure can still be a

tremendous challenge. Thus a simple engineering method

on the basis of mechanics of composite laminates is still

very desirable to carry out structural design studies in order

to allow the effects of structural as well as material

parameters to be evaluated effectively. With the present I-

section forming concept, the web laminate is like a usual

solid laminate whereas the flange laminates are not, due to

the presence of the angle plies and the transverse ply

discontinuity in addition to the change in ply orientations forthe I-beams without symmetric flanges.

The maximum bending stresses smax on the surfaces of

the flanges at the mid-span can be calculated by

smaxZ1

t f a11

PmaxLh

8Dx

(7)

in which 1/ t f a11 is the longitudinal flexural modulus of the

flanges. The maximum bending stress values calculated by

Eq. (7) for all the I-beams are given in Table 2. They were

also estimated by using the maximum tensile strain and the

compressive strain values in conjunction with the flexural

modulus, as included in the table. The experimental bending

stress values in Fig. 8 are lower than the predicted,

especially for the I-beams with the relatively large L / hs.

In particular, all the estimated bending stresses in Table 2

are low when compared to the flexural strength 701 MPa

of the present solid carbon/epoxy beam, though the radius of

gyration of the I-beams could be much greater than that of

solid beams for the same overall sectional dimensions.

However, the maximum strain values at failure on the

tensile flange (in Table 1) are quite substantial. The load-

based maximum bending stresses are less than the tensile

strain-based maximum bending stresses in nearly half of all

the tests. In the meanwhile, the compressive strain-based

Table 2

Bending stress results on carbon/epoxy I-beams

Support span

(mm)

L / h Max. Load,

Pmax (kN)

Max. bending

stress based

on Pmax

(MPa)

Max. bending

stress based

on 3tensil(MPa)

Differ. of the

two left col-

umns (%)

Bending stress

based on

3compr (MPa)

T-joint

reinforce-

ment

Major failure

mode

180 4.50 21.7 261 287 K9 222 None B

210A 5.25 17.5 246 292 K16 219 5!3 mm B

210B 5.25 22.7 319 559 K43 554 None A

210C 5.25 19.0 267 329 K19 156 None B

250 6.25 17.7 296 288 3 224 3!2 mm A

270A 6.75 20.8 375 384 K2 284 5!3 mm A

270B 6.75 18.3 330 386 K15 363 None A270C 6.75 18.8 339 405 K16 – 3!2 mm A

290 7.25 17.1 331 699 K51 510 None A

300 7.50 17.9 359 358 !1 – 5!3 mm A

310 7.75 19.1 396 425 K7 336 3!2 mm A

330A 8.25 20.5 452 516 K12 438 5!3 mm A and B

330B 8.25 17.7 390 400 K3 270 None A

360 9.00 16.0 385 411 K6 338 None A

370A 9.25 17.5 433 548 K21 468 None A

370B 9.25 14.2a 351a 358 K2 280 3!2 mm –

390 9.75 15.1 394 437 K10 216 None A

Strain gauge broke before the maximum load. A-type failure mode, Extensive fracture in the compressive flange and the web; B-type failure mode, Structural

delamination in the tensile or compressive flange.a Specimen had premature failure at one support.




bending stresses might be less reliable as they may have

been affected by the local deformation of varying degree.

Nevertheless, this relatively low load-bearing capacity isexpected to some extent in considering small L / hs used and

several aforementioned manufacturing limitations (ply

discontinuity and voids at the flange-web joints) in addition

to the neglected potential effect of couplings. In nine out of

seventeen I-beams, no attempt was made to fill up cavities at

the flange-web joints. The overestimation of the moments of

inertia in those beams could also contribute to the under-

estimation of the bending stresses. Consequently, the

respective overestimated moments of inertia in those

beams may have also contributed to the discrepancy.

The central region underneath the loader and in its

immediate vicinity is also expected to carry other significantstress components such as the TTT normal stress, in

addition to the maximum compressive bending stress. As

the L / hs of the I-beams are relatively short, the critical

conditions in the I-beams are likely to be influenced by

shear stresses as well. At the flange-web joints, both shear

stresses tyz and tzx could be substantial and the normal stress

sx may also be near its largest value. Thus the central region

is in a very complicated state of stress. This is demonstrated

by Fig. 9 in which the web shear at the mid-span was

significantly skewed by the TTT normal stress when

compared to Fig. 7.

The TTT shear stress tzx f

at the mid-plane of the flanges

can be calculated by

tzxf Z1

a11

Pmax

4Dx

hKt f

2

(8)

as this is where delamination in the flanges is most likely to

occur (see Fig. 12). The examination of the experimental

data in Fig. 8 seems to show such indication. The TTT shear

stresses for the web are given by

tzxw maxZ1

t wa11

Pmax

16Dx

4bt f ðhK t f Þ

t wC ðhK2t f Þ

2

(9a)

at the mid-plane of the web (thereby the cross section) and

by

tzxw minZ1

t 2wa11

Pmaxbt f

4Dx

ðhK t f Þ (9b)

at the flange inner surfaces. In-plane shear stresses

estimated via Eq. (9a) are compared with experimental

values in Table 3, and agreement between the two is less

than 8%. It is also clear from this table (and Fig. 7) that the

maximum in-plane shear strain of less than 5000 m3 atfailure for the web seems low, as expected.

It was known [6] that a small tilting of the loader off the

bending plane could also contribute to the local shear stress

tyz at the ‘compressive’ flange-web joint in the y–z plane.

Since the web thickness is relatively small and potential

void could be present, this transverse shear could be one of

the local operating deformation mechanisms, which was

previously observed [6,8]. The transverse shear stress can be

estimated by

tyzZG23g0yzZ

2b13z

hK2t f

G23 (10)

in which 3z denotes the strain experienced by one half free

flange. Using the measured strain of 4608 m3 from the

transverse strain gauge bonded on the under surface of one

half free flange (right under the loader) from Table 4, the

transverse shear stress of 14.3 MPa could be reached.

9. Damage and failure analysis

The ultimate failure or load-bearing capacity of the

I-beams in bending depends on five major factors, namely,

I-section forming approach, combination of the cross-

sectional dimensions (including the fillet radius), lay-up

0

2

4

6

8

10

12

14

16

18

20

22

24

-2000 -1500 -1000 -500 0 500 1000 1500 2000

Microstrain

Load, kN

+45 Degree

-45 Degree

Fig. 9. Web strain response curves from a rosette located at the mid-span of

an I-beam.

Table 3

In-plane and interlaminar shear stresses through the depth of carbon/epoxy I-beams

Support span (mm) Shear force (kN) Shear strain (%) In-plane shear at the mid-plane of web (MPa) Interlaminar shear at

the mid-plane of flange

(MPa)

Predicted Measured Predicted

250 17.7 0.461 78.0 82.5 6.2

310 19.1 0.463 85.2 82.9 6.7

370 12.6 0.287 55.5 51.4 4.4

In-plane and interlaminar shear strengths are 204 MPa and 34 MPa, respectively, [21].




design, manufacturing quality and L / h. Loads associated

with damage initiation and ultimate failure are

clearly affected by the way with which the I-sections are

formed [1,8]. In the meanwhile, different combinations of

the cross-sectional dimensions could lead to different

consequences of failure event. For example, I-beams with

the wide and/or thin flanges could initiate compressive

flange buckling, which precipitates the ultimate failure [5–7,

9]. The effect of the lay-up designs as discussed in Section 3

could be significant if the segment laminates are very thin,

but otherwise could be small if the number of plies in the

segment laminates is relatively high as in the current case.

Nevertheless, whatever I-section forming concept the I-

beams were made with, their ultimate failure and thereby

load-bearing capacity are likely to be dominated by integrity

of the compressive flange-web joint due to a complicated

state of local stress. With the fixed cross-sectional

dimensions of composite segments assembled via the co-

curing approach in the present investigation, focus is thus on

the latter two factors.

A general manufacturing quality of the present I-beams

is good, though fibre wetting on the web surfaces is a little

poor on some specimen. The latter could be due to the factthat a relatively high viscosity of the current resin system

did not promote sufficient resin flow under the mould

closing pressure and for the given time. Nevertheless, this

may not affect the mechanical behaviour of these I-beams,

as it was observed earlier that the web in-plane shear was

not extensive. To minimise cost of the investigation, a

testing for manufacturing repeatability was very limited

(only between 210B and 210C). Two major inter-related

manufacturing issues thus are incomplete consolidation,

especially at the flange-web joints, and cross-sectional

dimension control. Taking dimensional measurements of

the I-beams before testing indicated that the average flangeor web thickness varied slightly within 7% whereas the

overall dimensions (i.e. depth and flange width) were very

accurate. This seems to suggest that pressure via the two

press plates during cure could have forced two side mould

pieces ajar. Consequently, segment laminate consolidation

may not have been complete, in agreement with the

measured final flange and web thickness. On the other

hand, the presence of unfilled void in some of the selected

specimens led to a slight sagging of plies from the flat stack

at the joint of one flange as the worst sample shows in

Fig. 10. This could be due to that the full pressure of

the press plates was applied before the two channel

sublaminate stacks were completely closed.

Post-mortem inspection shows that most I-beams failed

with severe damage on the compressive flange but with

limited web in-plane shear, categorised as type A in Table 2.

The flange failure seemed to have propagated into the web.

A typical photograph of such failure mode is shown in

Fig. 11. In most tests, a clear cracking sound was heard at

the load ranging from 11.7 to 13.9 kN. It originated most

likely from the compressive joint around the bent fillet

regions. Nevertheless, there was no sign of stiffness

degradation corresponding to that in either the load-

displacement or load-strain curves. An exception to this

A-type failure mode is flange delamination at the mid-plane

of one flange for three I-beams with small L / hs (180, 210A

and 210C), as the front view of the failed specimen (210C)

shows in Fig. 12. Interestingly, such flange delamination

Table 4

Transverse strains underneath the compressive flange of carbon/epoxy I-

beams

Support span (mm) Transverse strain (%) Note

210B K0.0512 Initially tensile

290 0.4608 –

370A 0.2480 –

Fig. 10. Cross-sectional view of a composite I-beam in a quasi-isotropic

lay-up.

Fig. 11. A photograph showing a front view of a failed I-beam with

extensive compressive flange and web failures.




resulted in the catastrophic failure, just like solid rectangular

composite beams [17]. Although the predicted interlaminar

shear (ILS) stresses in Table 3 are very low, incomplete

laminate consolidation and the presence of void at the joints

could likely degrade the ILS strength of this composite

system. More significantly, there is little difference in

failure load for the I-beams with and without the joint

reinforcement as could be observed in Table 2. This lack of

noticeable improvement suggests that the ultimate failurewas dominated by the transverse bending failure of the fillet

regions rather than any maximum compressive bending

stress-related mechanism. Thus a smaller bend radius could

improve the load-bearing capability. Equally, if such I-

beams were subjected to a uniformly distributed load in the

aforementioned applications such as helicopter rotor blades,

stiffeners and aircraft wing spars, their loading-bearing

capacity would be likely to be greater. Although voids or

any other manufacturing defects at the joints would

definitively affect fatigue performance, they did not seem

to have made a direct substantial contribution to the quasi-

static failure process of the present I-beams.

The damage characteristics and ultimate failure of the I-

beams depend on a variation of L / h, just like solid

rectangular laminated beams [16,17,20]. At small L / hs, the

I-beams (180, 210A and 210C) failed with a huge flange

delamination as seen earlier. Obviously, their bending load-

bearing capacity would be underestimated because of that.

As the L / h was increased, the ultimate failure seemed to

have occurred first in the compressive flange shown in

Fig. 11, and then propagated into the web section. For the

L / hs of more than 6.75, all the tensile flanges remained

intact. However, the initiation of the failure manifested

itself with an audible cracking sound and it started much

earlier than that at the ultimate loads, though the load-displacement and load-strain curves in Figs. 6 and 7 did

show the nearly linear behaviour up to the ultimate failure. It

may be speculated that matrix cracks and delaminations

around the fillet regions, rather than voids, initiated the

ultimate failure due to the presence of high local stresses, as

also discussed in [4]. And delaminations around the bends

and fracture of fibres, especially 908 plies, led to the ultimate

failure of the compressive flange-web joints. In addition,

although few I-beams with the same physical conditions

were tested with the same L / h, at least it could be observed

from Table 1 that the lay-up related symmetrical

characteristics did not have an over-riding influence over

the mechanical performance in terms of bending strength.

10. Conclusions

Composite I-beams of different lengths were fabricated

by using a low-cost hot press with a purpose-made open

mould. They contained varying physical conditions at the

flange-web joints and with or without flange laminate

symmetry. The bending behaviour of these I-beams was

evaluated both experimentally and analytically in terms of

bending stiffness, strength and manufacturing quality.

Major manufacturing-related issues were segment laminate

consolidation, flange-web joint reinforcement and ply

discontinuity in the inner halves of the flanges. It was

found that these manufacturing features did not affect the

sectional flexural modulus of the I-beams and the latter was

in good agreement with the predicted. Although the I-beams

had the relatively small L / hs, the sectional shear modulus

could not be properly estimated experimentally due tolimited in-plane shear induced in the web. The joint

reinforcement and/or segment laminate symmetry did not

seem to have any significant effect on the flexural strength,

due likely to the substantial laminate thickness and as well

as to small L / hs. It was found that the ultimate failure was

most likely initiated at the bent fillet regions in the inner

halves of the flange laminates, which were in a complicated

state of high local stress. The presence of ply discontinuity

could be the most significant contributing factor. The

substantial variation of L/h led to the change of the damage

characteristics.

It was demonstrated that the present manufacturingmethod was viable for fabricating composite I-beams and

that an established engineering analytical methodology

paved the way for the examination of degradation of the

flexural stiffness and strength through the cross-sectional

dimensions and lay-up designs in future investigations.

Acknowledgements

The authors acknowledge that former students,

Ms T. Winterbone and Mr A.R. Giles, assisted some tests.

Fig. 12. A photograph showing a front view of a failed I-beam with extensive flange delamination.




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design, manufacture and evaluation of laminated carbon-epoxyi-beams in bending

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