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 DOI: 10.1177/0021998311418390

2012 46: 1345 originally published online 21 September 2011Journal of Composite MaterialsUA Khashaba, SM Aldousari and IMR Najjar

experimental and analytical woven composites under combined bending and tension loading: part?-?I8Behavior of [0]

  

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JOURNAL OFC O M P O S I T EM AT E R I A L SArticle

Behavior of [0]8 woven composites undercombined bending and tension loading:part - I experimental and analytical

UA Khashaba, SM Aldousari and IMR Najjar

Abstract

The objective of this work is to investigate the mechanical properties of [0]8 woven glass fiber reinforced polyester

(GFRP) composites under monotonic and combined tension/bending loading. The results show that the failure of

combined test specimen was at its ends, which have zero deflection and maximum bending moment and stress. This

behavior agrees with the analytical stress distribution along the specimen length. Adding a tensile load at the ends of

woven composite beams that designed to carry pure bending loads, such as bridge decks, can duplicate bending capacity

of the beam. The relationship between combined bending moment and tensile load was constructed.

Keywords

Woven composites, tension, bending, combined tension/bending

Introduction

Woven carbon fiber is being extensively used in aero-space, automotive, and civil applications, owing to theirhigh specific strength, high fracture toughness, lowerproduction costs, and better control over the thermo–mechanical properties as compared to unidirectionalcomposites. The study of the mechanical properties ofsuch composites is an extremely important area fromthe scientific and industrial point of view and a betterunderstanding of their behavior under combined loadswill ensure the long life of the products.

In many engineering applications, structural mem-bers such as shafts, beams, and plates are subjectednot only to uniaxial loading but also to multiaxial load-ing. Flexbeam is a good example that experienced fourcombined loads. Flexbeam is the link between the heli-copter rotor-hub and the blade.1–4 During flight, therotor-hub and flexbeam are subjected to constantaxial tension load from the centrifugal forces, bendingout of the plane of rotation (flap), and bending in theplane of rotation attributable to the lead–lag motion.2

In addition, the pitching moment applied to the bladesresult in twisting the flexbeam, Figure 1.1

Specimens with non-uniform cross-section, in simpletension test, result in combined tension and bendingloads. The deflection and moment distribution can be

estimated from beam theory. Single lap joint5 andsingle-strap joint6 in tension are other examples,which exhibit a combined tension and bending loads.The latter is due to the eccentric load path through thejoint, Figure 2.

Krueger et al.7 performed the combined tension/bending tests in axial tension and bending using servo-hydraulic load frame. The specimens were initially pre-loaded in load control to an axial tension load of 85%the average damage initiation load determined for thetension test. While maintaining this preload, a trans-verse bending load was then applied in displacementcontrol until flange debonding occurred. Maximumspecimen deflections at the top grip contact pointwere recorded using a spring loaded linear variable dif-ferential transformer (LVDT). Lee and Knauss8 car-ried-out their combined tension/bending tests usingtwo different devices. One of these devices was designedto draw on the tension/torsion capability of a MTS

Mechanical Engineering Department, Faculty of Engineering, King

Abdulaziz University, Jeddah, Saudi Arabia

Corresponding author:

UA Khashaba, Mechanical Engineering Department, Faculty of

Engineering, King Abdulaziz University, P.O. Box 80200, Jeddah

21589, Saudi Arabia

Email: khashabu@hotmail.com

Journal of Composite Materials

46(11) 1345–1355

! The Author(s) 2012

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DOI: 10.1177/0021998311418390

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testing machine. The tension is provided by the testmachine in the standard fashion, but the torsionalmode was translated through an appropriate linkagesystem into a lateral force for providing the lateraldeflection. The accompanying lateral force wasrecorded by a compression load cell. This deviceallowed 3-point as well as 4-point bending. In thesecond technique the tension/bending loads were pro-vided through mounting the specimen eccentrically andsubjecting the grips to tension only. The range of theeccentricity ‘e’ varied from �2.5 to 13mm. By adjustingthe off-set, a range of tension/bending combinations isachieved. Similarly, Palmer et al.9 implement the com-bined tension/bending tests using special test fixturethrough it the axial loads not only implement the tensilestresses (strains) but also implement the bending stres-ses (strains) through using offset shims placed betweenthe plane of the specimen and the loading axis to givevarious eccentricities ‘e’. The latter technique was usedin the present work.

Several researchers found that bending strength wasgreater than tensile strength in polymeric compositematerials.9–12 Wisnom10 reported in his review thatthe ratios between 3-point bending strength and tensilestrength of different composite materials were in therange of 1.3–1.49. Khashaba and Seif12 reported thatthe ratios between the 3-point/tension and 4-point/tension were 1.27 and 1.62, respectively.

The current paper is a continuation of the author’swork on the mechanical behavior of woven compositesunder combined tension/bending loading.11–13 Themain objective of the present work is to investigatethe mechanical properties of woven glass fiber rein-forced polyester (GFRP) composites under monotonicand combined loads. The monotonic loads will be ten-sion, 3-point bending, and 4-point bending, while thecombined loads will be tension/bending. The wovencomposites were manfactured using hand lay-up tech-nique with [0]8 stacking sequence.

Specimen manufacture

The polymeric composite material was fabricated frompolyester resin reinforced by woven glass fiber. TheStacking sequence of the composite laminate is [0]8.The details of the constituent materials are illustratedin Table 1. The composite material was made by Handlay-up technique as follows:

. Eight layers of woven glass fiber (500� 500mm)were cut along warp and weft threads to ensureright angle of all layers.

. A layer of resin was spread on a glass plate (700�700mm) that was treated by release agent (wax).

. The first layer of woven glass fiber was placed on theresin and consolidated using a suitable laminatingroller until the mat is fully impregnated and all vis-ible air inclusions were removed from the laminate.This procedure was repeated with alternate layers ofresin and woven glass fiber (which was carefullyplaced with all warp roving parallel) until thebuild-up is complete.

. After all layers are completely impregnated withoutinclusion of air voids, the last layer was covered by acellophane paper and rolled by a round aluminum

Figure 1. Combined tension, torsion, and bending (flap and lag)

loads in helicopter flexbeam.

σbending

σtensionσtension

GripGrip

Figure 2. Single-strap joint in tension.

Table 1. Material specification

Material Type

Reinforcement E-woven roving glass fiber

Yarn count (Yarns/Cm) : 3.9 (Warp)

& 3.2 (Weft)

Fabric weight: 0.324 Kg/m2

Fabric weave: Plain

Vf¼ 32.1%, No. of glass layers¼ 8

Matrix Orthophthalic polyester resin,

RESIPOL 9024 ST.

Catalyst: Methylethyl ketone peroxide

(0.8% of matrix volume)

Hardener: Cobalt naphthenate 0.8%

of matrix volume)

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pipe to remove all visible air bubbles and squeezeany excess resin.

. A glass plate was placed on the cellophane paper anda weight of 25 kg was distributed on the glass plate,BS 3496.

. The glass plate and the cellophane paper wereremoved after 24 h and the laminate was completelycured at room temperature for 21 days, ISO 1268.

. The margins of the laminate, up to at least 20mmfrom the edge, were cut and the working portion ofthe specimens was taken away from the edge byabout 30mm.

. The thickness of the composite laminates was3.5� 0.1mm.

. The fiber volume fraction (Vf) was determined experi-mentally using the ignition technique according toASTMD3171-99.TheaveragevalueofVfwas32.1%.

Mechanical tests

Tension, 3-point bending, 4-point bending, and com-bined tension/bending tests were carried out onwoven GFRP specimens using a universal testingmachine (Testometric 200 kN). The crosshead speedof the loading member was 2mm/min. Twenty-fourspecimens were used in this work. Twelve of themwere tested in tension and bending tests (four specimensfor each test). Twelve specimens were tested under com-bined tension/bending loads (three specimens for eacheccentric value). The strength values were determinedbased on the average values. The load displacementdiagrams were printed through the PC of the testingmachine. The strains were measured for each test typeusing strain gages that connected to Digital StrainMeter (Tc-21K model 232). The tensile and bendingproperties (strength and modulus) and their coefficientof variation (CV%) are illustrated in Table 2.

Tension test

The tensile properties of woven composites weredetermined experimentally according to the ASTM

D3039M-00. The dimensions of each test specimenare illustrated in Figure 3. The strain gage (S.G.) wasbonded longitudinally at the center of the test speci-mens to determine the actual value of the tensilemodulus.

Four rectangular aluminum end tabs were bonded,for each specimen, at the gripping portions. Theseend tabs reduces the stress concentration owing tothe lateral compressive stresses of grips serration andprevent the slipping of the test specimen from thegrip, where the serration of the grip indented the alu-minum tabs and engaged with it. End-tabs alsosmoothly transfer the lateral compressive load owingthe grips of the testing machine to the specimen andprevent the crushing of the test specimens between thegrips.14

Bending tests

The 3-point and 4-point bending tests were imple-mented on woven specimens, with 26mm width,according to JIS K 7055. The dimensions of 3-pointbending test were: 80mm total length, 60mm distancebetween the supporting points, and the loading point atthe center of the specimen. The dimensions of 4-pointbending test were: 130mm total length, 105mm dis-tance between the supporting points, and 35mm dis-tance between the loading points. Two strain gageswere bonded back to back on the 4-point bending speci-men to monitor the surface strains on both sides duringthe bending test. The fracture strengths for 3-point (�b3)

Table 2. Tensile and bending properties of woven composite laminate

Composite

configurations

Tensile properties Bending properties

Tensile strength Tensile modulus 3-Point bending strength 4-Point bending strength Bending modulus

(MPa) CV% (GPa) CV% (MPa) CV% (MPa) CV% (GPa) CV%

[0]8 250.71 10.5 22.0 3.2 244.43 7.2 258.79 8.3 10.90 4.1

[0/� 45/90]s12 201.1 18.1 255.73 326.4 12.11

Tab

210

390

27

3.5

S.G .

Figure 3. Dimension of tension specimen.

Khashaba et al. 1347

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and 4-point (�b4) bending tests were determined fromEquations (1) and (2), respectively,

�b3 ¼Mb3c

I¼

Pmaxðb3ÞL

4

� �t2

� �112wt

3¼

3Pmaxðb3Þ:L

2w:t2, ð1Þ

�b4 ¼Mb4c

I¼

Pmaxðb4ÞL

6

� �t2

� �112wt

3¼

Pmaxðb4Þ:L

w:t2, ð2Þ

where Mb3 and Mb4 is the bending moment in 3-pointand 4-point bending tests, respectively, c is the perpen-dicular distance between specimen surface and neutralaxis, Pmax(b3) and Pmax(b4) are, respectively, the maxi-mum load (fracture load) in 3-point and 4-point bend-ing tests, L is the specimen length between the outersupports, w is the specimen width, and t specimenthickness. The bending modulus of elasticity, E, isdetermined from the initial inclination of the load–deflection curve of the 3-point bending specimenusing the following equation:

Eb3 ¼1

4:L3

w:t3:P

�, ð3Þ

where P/D represents the slope of the initial portion ofthe load–deflection curve (N/mm).

Combined tension/bending test

Special test fixtures, Figure 4, were designed andmanufactured by Khashaba et al.11–13 according tothe specifications illustrated in NASA report numberTM-1999-209511.9 Eccentric tension load was imple-mented to the test specimens through using offsetshims. The eccentric load result in axial tension andbending stresses and strains, where their values stronglydepend on initial eccentricity (ei¼ thickness of offset-steel-shimsþ half thickness of test specimen, Figure4). The thicknesses of the offset-steel-shims were 10,15, 20, and 30mm. The dimensions of combined ten-sion/bending test specimens are illustrated in Figure 5.Two strain gages were mounted back to back on thecenter of one specimen for each offset value, while twospecimens were tested without using strain gages. Thegages were longitudinally centered at the specimenwaist. During the combined tension/bending test, thestrain gage on one side was under compression, whilethe gage on the other side was under tension. The outof plane displacements (yout) at the specimen centerwere measured using dial indicator with 0.002mmresolution.

Results and discussions

The following subsections show the results and discus-sions on the mechanical properties of [0]8 woven com-posites. Fruitful comparison between the previouslypublished result11–13 on quasi-isotropic woven GFRPlaminate [0/� 45/90]s and the current experimentalresults on [0]8 woven composites will be discussed.

Tension results

Figure 6 illustrates the load–displacement diagram ofwoven composite in tension test. The actual modulus ofelasticity was determined from the initial linear portionof the stress–strain diagram that was drawn using thestrain gage results, Figure 7. The ultimate tensile

Figure 4. Combined tension/bending fixture.

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strength was determined at the maximum tensile load(fracture), Table 2. The main characteristic of Figures 6and 7 was the non-linearity of the load–displacementand stress–strain diagrams. Similar non-linear stress–strain behavior was observed by Khashaba and Seif12

woven GFRP specimens [0/� 45/90]s. They attributedthis behavior to the fact that fiber-reinforced plasticmaterials are not only anisotropic, but, on the macroscale, they are also inhomogeneous.

The results in Figure 6 show that the ultimate tensilestrength of the GFRP specimens in the longitudinal

(warp) direction is higher than that in the transverse(weft) direction. This result was due to the highernumber of yarns in the warp direction than that inthe weft direction, Table 1. The values of the actualmodulus of elasticity were determined from the initiallinear portion of the actual stress–strain diagrams,Figure 7, and illustrated in Table 2. The results in thistable indicate that the actual modulus is about 3.1 timeshigher than the apparent modulus of elasticity of wovenGFRP specimen. The lower value of apparent moduluswas due to the compliance (deformation) of the testingmachine. In addition, the shear deformation of theadhesive material between the tabs and the specimens,and the micro slip between the tabs and the test speci-men may contribute in decreasing the apparentmodulus.

Figure 7 shows that at the same stress level the [0]8specimens exhibit higher stiffness (lower strains) than[0/� 45/90]s specimens under tensile loads. This isattributed to the presence of high volume of warpfibers in [0]8 specimens that simulate the unidirectionalfibers. The high volume of warp fibers not onlyincreases the stiffness but also increases the tensilestrength of [0]8 specimens than the quasi-isotropicwoven GFRP specimens [0/� 45/90]s.

Bending results

Figure 8 shows a comparison between the load–deflec-tion diagrams in 3-point bending tests for [0/� 45/90]sand [0]8 specimens. The load–deflection diagram of [0]8specimen has two knees. The first at the same load levelof the knee in the load–deflection diagram of [0/� 45/90]s specimen (0.35 kN) that owing to the initiation andpropagation of matrix cracks in the woven composite

300

27

35

100

40

67

80

φ7

S.G.

Figure 5. Dimensions of combined tension/bending specimen.

Displacement (mm)

Loa

d (k

N)

0 1 2 3 4 5 6 70

5

10

15

20

25

30

Longitudinal

Transverse

Initial microcracks of the matrix

Catastrophicfailure

Apparent modulus =7.143 GPa

Figure 6. Load–displacement diagram in tension test, printed

from PC of testing machine.

[0]8

Strain (%)

Stre

ss (

MPa

)

0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120

[0/±45/90]s; [12]

Figure 7. Actual stress–strain diagram in tension test.

Khashaba et al. 1349

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(independent to the fiber configuration). The secondknee was observed at 0.7 kN that may be owing tothe weft fiber–matrix debonding and progressivebreaks in the warp fibers. Further increase in theload–deflection curve up to the final failure wasobserved due to the redistribution of the load betweenthe warp fiber and the matrix. The final failure wasnearly catastrophic.

Figure 9 shows a comparison between the load–deflection diagrams in 4-point bending tests for [0/� 45/90]s and [0]8 specimens. The results in this figureindicate that at the same load level the [0]8 specimensexhibits lower stiffness (high deflection) than [0/� 45/90]s specimens under bending loads. This attributed tothe presence of�45 layers that increases the stiffness ofthe specimens and the resistance to the shear stressesowing to bending loads and consequently the bendingstrength of [0/� 45/90]s. This behavior was contrarywith the results under tensile loads. These results areof considerable value to the designer with woven com-posite materials.

The value of bending strength determined from4-point bending test of [0]8 specimens is higher thanthat from the 3-point bending test. Similar observationwas reported for [0/� 45/90]s specimens, Khashaba andSeif.12,13 They attributed their results to the stress con-centration owing to the center load in 3-point bendingtest that result in early micro cracking of the matrix andfiber breakage under the loading point. In 4-pointbending the specimens were sbjected to constant bend-ing moments between the two loading points and itsfailure was due to pure bending stress.

Figure 10 illustrates the stress–strain diagram of4-point bending specimen. The results in this figureindicate that the strains at the bottom (tension) side is

lower than that for the strain of the top (compression)side for [0]8 specimen. In contrast for the strains in thequasi-isotropic woven GFRP specimens [0/� 45/90]swhere the compression side exhibit strains lower thanthat for tension side. The failure of the [0]8 specimenwas started at the tension side for the 3-point and4-point bending tests. In 4-point bending test the failurewas initiated at one of the loading points and thedelaminations were propagated toward the otherpoint. It is interesting to note that the value of tensilestrength (250.71MPa) is approximately equal to thebending strength (3-point and 4-point), Table 2,which confirms the responsibility of the tension sideon the final failure of the test specimen. This behavioris contrary to the failure of quasi-isotropic wovenGFRP specimens [0/� 45/90]s where the compression

Loa

d (k

N)

Deflection (mm)0 1 2 3 4 5 6 7 8

0

0.2

0.4

0.6

0.8

1

[0]8

[0/±45/90]s; [12]

Figure 8. Load–deflection diagram in 3-bending test, printed

from PC of testing machine.

Loa

d (k

N)

Deflection (mm)0 2 4 6 8 10 12 14 16

0

0.2

0.4

0.6

0.8

1

[0/±45/90]s; [12]

[0]8

Figure 9. Load–deflection diagram in 4-bending test, printed

from PC of testing machine.

-1.5 -1 -0.5 0 0.5 1 1.50

50

100

150

200

250

Surface strain, ε (%)

Str

ess

(MP

a)[0]8[0/±45/90]s;[12]

Figure 10. Actual stress–surface strain diagram in 4-point

bending test.

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side is responsible to the final failure of the testspecimens.12

It interesting to note that the scatter in strengthvalues (CV%) is higher than that of the modulusvalues in both tension and bending tests. This resultwas due to the fact that the scatter in the modulus isrelated to the material variation, while the scatter in thestrength is influenced by the surface flaws of the fiberglass and the complex failure mechanisms specially atthe warp and weft fibers interlacing.

Combined tension/bending results

Figure 11 shows the load–displacement diagrams ofwoven composites under combined tension/bendingloads at different initial eccentricities ‘ei’. The maincharacteristic of the load–displacement curve is thenon-linear behavior, at the start of the test, associatedwith large displacement especially at high initial eccen-tricity. The large initial displacement was due to the fastrotation of the fixtures at the start of loading process.The slope of load–displacement diagrams was increasedwith further increase in the applied load. The non-linearportion is followed by an approximately linear behav-ior up to the final catastrophic failure. The results inFigure 11 also show that the slope of load–displace-ment diagrams (stiffness) and failure loads decreaseswith increasing the initial eccentricity.

Figures 12(a)–(d) show load–strain diagrams at mid-point of combined tension/bending GFRP specimenstested with different values of initial eccentricities.The main characteristic of these figures is the presencesof bending strains (the difference between the negative

compressive strain and positive tensile strain) at thebeginning of loading process. This means that at lowloads, the bending stress is more dominant than thetensile stress.

The fast rotation of the fixtures at the start of theloading process leads to high out of plane displace-ment (yout) that was measured at specimen midpoint,Figure 13, which is the main reason for the presence ofbending strains (negative and positive strains) and thelarge displacements of load–displacement diagrams atthe initial loading process.

Increasing the applied load result in zero bendingstrains at specimen midpoint and the tensile stressbecomes more dominant. This was clearly illustratedby the positive strains of the compression and tensionsides of the specimen, Figure 12(a)–(d). This result wasdue to the maximum deflection of the specimen at mid-point reduces the bending arm (ea-�) and consequentlythe bending moment and stress. Recalling the load-youtrelationship, Figure 13, the initial portion (increasingthe yout at very low loads) is responsible for the bendingstrains shown in Figure 12(a)–(d). With advance theloading process the load in the load-yout relationshipbecome dominant tension resulting in zero bendingstrains, Figures 12(a)–(d).

The variation of specimen deflection (y) from zeroat specimen ends (x¼ 0 and x¼L) to maximum at mid-point (x¼L/2) plays an important role in the distribu-tion of the bending moment (M), Equation (4),along the test specimen and consequently the combinedstress:

M ¼ �F ea � yð Þ, ð4Þ

where F is the applied load indicated by the testingmachine. The deflection of the beam subjected to eccen-tric tension load was derived from the integration ofthe second order differential equation of the moment–curvature relationship, Equation (5).12,13

EI@2y

@x2¼ �Fðea � yÞ ð5Þ

The integration of Equation (5) leads to Equation(6):

y ¼ eacoshkL� 1

sinhkL

� �sinh kx� eacosh kxþea, ð6Þ

where k2¼F/EI and ea is the actual eccentricity of thespecimen plane from the loading plane after applyingtension load, and L is the length of the specimenbetween the fixtures. The value of ea is less than the ini-tial eccentricity (ei) due to the rotation of the fixture asa rigid body toward ei by angle equal, �f, Figure 14.

Displacement (mm)

Loa

d (k

N)

0 2 4 6 8 10 12 14 16 18

0

4

8

12

16

20

ei = 31.75

ei = 16.75

ei = 21.75 ei = 11.75

Figure 11. Load–displacement diagram of woven specimens

tested in combined tension/bending, printed from PC of testing

machine.

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The calculation procedure of the stresses distribu-tion for combined tension/bending specimen with11.75mm initial eccentricity (as example) was as follows:

The value of ea was calculated from Equation (7),Figure 15:

ea ¼ ei cos �f � Lf sin �f ¼ 1:26 mm, ð7Þ

where Lf is the fixture length¼ 150mm, �f¼ 4o,Figure 16.

Therefore, the value of y can be calculated at anypoint (x) along the specimen, Equation (6), and conse-quently the bending moment, Equation (4).

The combined stress was calculated from Equation (8):

�Comb: ¼ �t þ �b ¼F

AþMc

I, ð8Þ

where F is the ultimate load (19 kN), and A and I are,respectively, the actual cross-section area and areamoment of inertia.

Tensile, bending, and combined stress distributionalong the specimen length are illustrated in Figure 17.The variation in tensile stress was due to the variationin specimen cross-section (A), while the variation inbending stress was due to the variation in the areamoment of inertia (I) and bending arm (ea – y). Thelatter was varied from maximum at specimen ends(y¼ 0 at x¼ 0 and x¼L) to minimum at specimen mid-point (y¼ ymax¼ �). Therefore, the maximum bendingstress occurred at the specimen ends, which have max-imum bending arms (ea – 0¼ ea). On the other hand,the minimum bending stress occurred at specimen mid-point, which has minimum bending arm (ea–�). Theresults in Figure 17 and the photograph of the fracturedspecimen confirm that the analytical stress distribution

ε %

0

4

8

12

16

20L

oad

(kN

)

Tension side

Compression side

(a)

ei = 11.75 mm

ε %

0

4

8

12

16

20

Loa

d (k

N)

Tension side

Compression side

(b)

ei = 16.75 mm

ε %

0

4

8

12

16

20

Loa

d (k

N)

Tension side

Compression side

(c)

ei = 21.75 mm

-0.3 0 0.3 0.6 0.9 1.2 1.5 -0.3 0 0.3 0.6 0.9 1.2 1.5

-0.3 0 0.3 0.6 0.9 1.2 1.5 -0.3 0 0.3 0.6 0.9 1.2 1.5

ε %

0

4

8

12

16

20

Loa

d (k

N)

Tension side

Compression side

(d)

ei = 31.75 mm

Figure 12. Actual load-strain diagrams at midpoint of combined tension/bending GFRP specimen, (a) ei¼ 11.75 mm, (b)

ei¼ 16.75 mm, (c) ei¼ 21.75 mm, and (d) ei¼ 31.75 mm.

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predict well the failure position of the specimen undercombined load.

The experimental results show that the ratios ofthe maximum bending moments under combined and3-point loading were: 1.85, 1.89, 1.91, and 1.97 for

Bending load with bending strains

Tension load with zero bending strains

0 2 4 6 8 10 12 14 16

Load (kN)

0

2

4

6

8

10

12

14

Out

of

plan

e di

spla

cem

ent (

mm

)

e = 11.75 mm

Figure 13. Out of plane displacement (yout) vs. tensile load in

combined tension/bending test.

θf

Pin/clevisconnection

Offset

Lower spindle of testing machine

Steelshims

Pin/clevisconnection

Specimen

Figure 14. Specimen under combined tension/bending loading;

� is the inclination of the upper and lower fixtures.

Figure 15. Specimen dimensions for combined tension/bending

test.

θf

Figure 16. Inclination angle of the fixture (�f) at ei¼ 11.75 mm.

Khashaba et al. 1353

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ei¼ 11.75, 16.75, 21.75, and 31.75, respectively.Therefore, it can be concluded that adding a tensileload at the ends of woven composite beams that designedto carry pure bending loads, such as bridge decks,will improve the bending capacity of the beam. Inthis case the problem can be approximated as fixed–fixed beam with load Pmax(F-F) at the midpoint. Thebending moment of such beam was calculated fromEquation (9):

MF�F ¼pmax ðF�FÞL

8ð9Þ

Recall Equation (1), the ratio of load capacityrequired to produce the same bending moment values(MF-F¼Mb3), in fixed–fixed and simply supportedspecimens with the same lengths, is twice (Pmax(F-F)/

Pmax(b3)¼ 2), which approximately equal the ratio ofthe improvement in the bending capacity due to theeccentric loads.

Figure 18 shows the variation of normalized com-bined tension/bending moment with the initial eccentric-ity. The results in this figure indicate that increasing theinitial eccentricity leads to increasing the maximumbending moment at fracture of woven GFRE specimensand vice versa for maximum tensile loads. The resultsin this figure also show that the initial eccentricity hasmore significant effect on the decreasing the ultimatecombined tensile load for [0]8 specimens than thequasi-isotropic woven GFRP laminate [0/� 45/90]s.The interaction between moment and tension at frac-ture of [0]8 specimen is presented in Figure 19. Suchinteraction relationship is very important for thedesigner with composite materials subjected to eccentrictension loads.

Conclusions

The results show that the [0]8 composites have highertensile strength and stiffness than [0/� 45/90]s compos-ites and vice versa for bending. The value bendingstrength determined from 4-point bending test ishigher than that from the 3-point bending test.Increasing the initial eccentricity leads to increasingthe initial displacement in the load–displacement dia-gram at the start of loading process, decreasing the ten-sile load at fracture, and increasing the combinedbending moment at fracture. At the start of the com-bined test the bending strains (stress) is more dominantat the specimen midpoint than the tensile stress.

0 40 80 120 160Specimen length (mm)

0

50

100

150

200

250

300

Str

ess

(MP

a)

Bending stress

Tensile stress

Combined stress

Specimen fracture ahead of the fixture (max. bending)

Figure 17. Distribution of bending, tensile, and combined

tensile/bending stresses along the test specimen, ei¼ 11.75 mm.

0 5 10 15 20 25 30 35Initial eccentricity (mm)

0

0.5

1

1.5

2

Nor

mal

ized

mec

hani

cal u

nits

Combined bending moment for [0]8

Combined tensile load for [0]8

Combined tensile load for [0/±45/90]S

Figure 18. Normalized bending moment and tensile loads for

[0]8 and [0/� 45/90]s composites under combined loads.

16 17 18 19 20

Tensile Load (kN)

23

24

25

26B

endi

ng M

omen

t (N

.m)

(ei = 11.75)

(ei = 16.75)(ei = 21.75)

(ei = 31.75)

Figure 19. Moment–tension interaction for fractured speci-

mens under combined loads.

1354 Journal of Composite Materials 46(11)

at Zagazig University on September 30, 2012jcm.sagepub.comDownloaded from

Increasing the applied load result in zero bendingstrains and the tensile stress becomes more dominant.The failure of combined test specimen was at its ends,which have zero deflection and consequently maximumbending moment and stress. This behavior agrees withthe analytical stress distribution along the specimenlength. The experimental results show that the ratioof the maximum bending moments under combinedand 3-point loading ranged from 1.85 to 1.97 for theinitial eccentricity ranged from 11.75 to 31.75, respec-tively. Therefore, it can be concluded that adding atensile load at the ends of woven composite beamsthat is designed to carry pure bending loads, such asbridge decks, will improve the bending capacity of thebeam. The initial eccentricity has more significant effecton decreasing the ultimate combined tensile load for[0]8 specimens than the quasi-isotropic woven GFRPlaminate [0/� 45/90]s. The constructed relationshipbetween combined bending moment and tensile loadof [0]8 specimen tested at different eccentricity valuesis very important for the designer with woven compos-ite materials subjected to combined loads.

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