Journal of Composite Materials

(1)

http://jcm.sagepub.com/

Journal of Composite Materials

http://jcm.sagepub.com/content/46/11/1345 The online version of this article can be found at:

DOI: 10.1177/0021998311418390

2012 46: 1345 originally published online 21 September 2011 Journal of Composite Materials

UA Khashaba, SM Aldousari and IMR Najjar

experimental and analytical

woven composites under combined bending and tension loading: part?-?I 8

Behavior of [0]

Published by:

http://www.sagepublications.com On behalf of:

American Society for Composites

can be found at:

Journal of Composite Materials Additional services and information for

http://jcm.sagepub.com/cgi/alerts Email Alerts:

http://jcm.sagepub.com/subscriptions Subscriptions:

http://www.sagepub.com/journalsReprints.nav Reprints:

http://www.sagepub.com/journalsPermissions.nav Permissions:

http://jcm.sagepub.com/content/46/11/1345.refs.html Citations:

What is This?

- Sep 21, 2011 OnlineFirst Version of Record

- Feb 20, 2012 OnlineFirst Version of Record

- May 29, 2012 Version of Record

>>

(2)

C O M P O S I T E M AT E R I A L S Article

Behavior of [0] ₈ woven composites under combined 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]8woven 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 their high speciﬁc strength, high fracture toughness, lower production costs, and better control over the thermo–

mechanical properties as compared to unidirectional composites. The study of the mechanical properties of such composites is an extremely important area from the scientiﬁc and industrial point of view and a better understanding of their behavior under combined loads will ensure the long life of the products.

In many engineering applications, structural mem- bers such as shafts, beams, and plates are subjected not only to uniaxial loading but also to multiaxial loading. Flexbeam is a good example that experienced four combined loads. Flexbeam is the link between the helicopter rotor-hub and the blade.^1–4 During flight, the rotor-hub and flexbeam are subjected to constant axial tension load from the centrifugal forces, bending out of the plane of rotation (flap), and bending in the plane of rotation attributable to the lead–lag motion.² In addition, the pitching moment applied to the blades result in twisting the flexbeam, Figure 1.¹

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

estimated from beam theory. Single lap joint⁵ and single-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 the joint, 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 the tension test. While maintaining this preload, a transverse bending load was then applied in displacement control until flange debonding occurred. Maximum specimen deflections at the top grip contact point were recorded using a spring loaded linear variable dif- ferential transformer (LVDT). Lee and Knauss⁸ carried-out their combined tension/bending tests using two different devices. One of these devices was designed to 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: [email protected]

Journal of Composite Materials 46(11) 1345–1355

!The Author(s) 2012 Reprints and permissions:

sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/0021998311418390 jcm.sagepub.com

(3)

testing machine. The tension is provided by the test machine in the standard fashion, but the torsional mode was translated through an appropriate linkage system into a lateral force for providing the lateral deflection. The accompanying lateral force was recorded by a compression load cell. This device allowed 3-point as well as 4-point bending. In the second technique the tension/bending loads were provided through mounting the specimen eccentrically and subjecting the grips to tension only. The range of the eccentricity ‘e’ varied from2.5 to 13 mm. By adjusting the off-set, a range of tension/bending combinations is achieved. Similarly, Palmer et al.⁹implement the combined tension/bending tests using special test fixture through it the axial loads not only implement the tensile stresses (strains) but also implement the bending stresses (strains) through using offset shims placed between the plane of the specimen and the loading axis to give various eccentricities ‘e’. The latter technique was used in the present work.

Several researchers found that bending strength was greater than tensile strength in polymeric composite materials.^9–12 Wisnom¹⁰ reported in his review that the ratios between 3-point bending strength and tensile strength of diﬀerent composite materials were in the range of 1.3–1.49. Khashaba and Seif¹² reported that the 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’s work on the mechanical behavior of woven composites under combined tension/bending loading.^11–13 The main objective of the present work is to investigate the mechanical properties of woven glass ﬁber reinforced polyester (GFRP) composites under monotonic and combined loads. The monotonic loads will be tension, 3-point bending, and 4-point bending, while the combined loads will be tension/bending. The woven composites were manfactured using hand lay-up technique with [0]8stacking sequence.

Specimen manufacture

The polymeric composite material was fabricated from polyester resin reinforced by woven glass ﬁber. The Stacking sequence of the composite laminate is [0]8. The details of the constituent materials are illustrated in Table 1. The composite material was made by Hand lay-up technique as follows:

. Eight layers of woven glass ﬁber (500500 mm) were cut along warp and weft threads to ensure right angle of all layers.

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

. The ﬁrst layer of woven glass ﬁber was placed on the resin and consolidated using a suitable laminating roller until the mat is fully impregnated and all visible air inclusions were removed from the laminate.

This procedure was repeated with alternate layers of resin and woven glass ﬁber (which was carefully placed with all warp roving parallel) until the build-up is complete.

. After all layers are completely impregnated without inclusion of air voids, the last layer was covered by a cellophane paper and rolled by a round aluminum

Figure 1. Combined tension, torsion, and bending (flap and lag) loads in helicopter flexbeam.

σ_bending

σtension

Grip Grip

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

Vf¼32.1%, No. of glass layers¼8 Matrix Orthophthalic polyester resin,

RESIPOL 9024 ST.

Catalyst: Methylethyl ketone peroxide (0.8% of matrix volume)

Hardener: Cobalt naphthenate 0.8%

of matrix volume)

(4)

pipe to remove all visible air bubbles and squeeze any excess resin.

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

. The glass plate and the cellophane paper were removed after 24 h and the laminate was completely cured at room temperature for 21 days, ISO 1268.

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

. The thickness of the composite laminates was 3.50.1 mm.

. The ﬁber volume fraction (Vf) was determined experimentally using the ignition technique according to ASTM D3171-99. The average value ofVfwas 32.1%.

Mechanical tests

Tension, 3-point bending, 4-point bending, and combined tension/bending tests were carried out on woven GFRP specimens using a universal testing machine (Testometric 200 kN). The crosshead speed of the loading member was 2 mm/min. Twenty-four specimens were used in this work. Twelve of them were tested in tension and bending tests (four specimens for each test). Twelve specimens were tested under combined tension/bending loads (three specimens for each eccentric value). The strength values were determined based on the average values. The load displacement diagrams were printed through the PC of the testing machine. The strains were measured for each test type using strain gages that connected to Digital Strain Meter (Tc-21 K model 232). The tensile and bending properties (strength and modulus) and their coeﬃcient of variation (CV%) are illustrated in Table 2.

Tension test

The tensile properties of woven composites were determined experimentally according to the ASTM

D3039M-00. The dimensions of each test specimen are illustrated in Figure 3. The strain gage (S.G.) was bonded longitudinally at the center of the test specimens to determine the actual value of the tensile modulus.

Four rectangular aluminum end tabs were bonded, for each specimen, at the gripping portions. These end tabs reduces the stress concentration owing to the lateral compressive stresses of grips serration and prevent the slipping of the test specimen from the grip, where the serration of the grip indented the aluminum tabs and engaged with it. End-tabs also smoothly transfer the lateral compressive load owing the grips of the testing machine to the specimen and prevent the crushing of the test specimens between the grips.¹⁴

Bending tests

The 3-point and 4-point bending tests were imple- mented on woven specimens, with 26 mm width, according to JIS K 7055. The dimensions of 3-point bending test were: 80 mm total length, 60 mm distance between the supporting points, and the loading point at the center of the specimen. The dimensions of 4-point bending test were: 130 mm total length, 105 mm distance between the supporting points, and 35 mm distance between the loading points. Two strain gages were bonded back to back on the 4-point bending specimen to monitor the surface strains on both sides during the 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

3 90

27 3.5

S.G.

Figure 3. Dimension of tension specimen.

(5)

and 4-point (b4) bending tests were determined from Equations (1) and (2), respectively,

_b3¼M_b3c I ¼

Pmaxðb3ÞL 4

t 2

1

12wt³ ¼3P_maxðb3Þ:L

2w:t² , ð1Þ

_b4¼M_b4c I ¼

Pmaxðb4ÞL 6

t 2

1

12wt³ ¼Pmaxðb4Þ:L

w:t² , ð2Þ

where Mb3andMb4is the bending moment in 3-point and 4-point bending tests, respectively,cis the perpen- dicular distance between specimen surface and neutral axis, Pmax(b3) and Pmax(b4) are, respectively, the maximum load (fracture load) in 3-point and 4-point bending tests, L is the specimen length between the outer supports, w is the specimen width, and t specimen thickness. The bending modulus of elasticity, E, is determined from the initial inclination of the load–

deﬂection curve of the 3-point bending specimen using the following equation:

E_b3¼1 4: L³

w:t³:P

, ð3Þ

whereP/Drepresents the slope of the initial portion of the load–deﬂection curve (N/mm).

Combined tension/bending test

Special test fixtures, Figure 4, were designed and manufactured by Khashaba et al.^11–13 according to the specifications illustrated in NASA report number TM-1999-209511.⁹ Eccentric tension load was imple- mented to the test specimens through using offset shims. The eccentric load result in axial tension and bending stresses and strains, where their values strongly depend on initial eccentricity (ei¼thickness of offset- steel-shimsþhalf thickness of test specimen, Figure 4). The thicknesses of the offset-steel-shims were 10, 15, 20, and 30 mm. The dimensions of combined tension/bending test specimens are illustrated in Figure 5.

Two strain gages were mounted back to back on the center of one specimen for each oﬀset value, while two specimens were tested without using strain gages. The gages were longitudinally centered at the specimen waist. During the combined tension/bending test, the strain gage on one side was under compression, while the gage on the other side was under tension. The out of plane displacements (yout) at the specimen center were measured using dial indicator with 0.002 mm resolution.

Results and discussions

The following subsections show the results and discussions on the mechanical properties of [0]8woven composites. Fruitful comparison between the previously published result^11–13 on quasi-isotropic woven GFRP laminate [0/45/90]s and the current experimental results on [0]8woven composites will be discussed.

Tension results

Figure 6 illustrates the load–displacement diagram of woven composite in tension test. The actual modulus of elasticity was determined from the initial linear portion of the stress–strain diagram that was drawn using the strain gage results, Figure 7. The ultimate tensile Figure 4. Combined tension/bending fixture.

(6)

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

strain behavior was observed by Khashaba and Seif¹² woven GFRP specimens [0/45/90]s. They attributed this behavior to the fact that ﬁber-reinforced plastic materials are not only anisotropic, but, on the macro scale, they are also inhomogeneous.

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

(warp) direction is higher than that in the transverse (weft) direction. This result was due to the higher number of yarns in the warp direction than that in the weft direction, Table 1. The values of the actual modulus of elasticity were determined from the initial linear portion of the actual stress–strain diagrams, Figure 7, and illustrated in Table 2. The results in this table indicate that the actual modulus is about 3.1 times higher than the apparent modulus of elasticity of woven GFRP specimen. The lower value of apparent modulus was due to the compliance (deformation) of the testing machine. In addition, the shear deformation of the adhesive material between the tabs and the specimens, and the micro slip between the tabs and the test specimen may contribute in decreasing the apparent modulus.

Figure 7 shows that at the same stress level the [0]8

specimens exhibit higher stiffness (lower strains) than [0/45/90]s specimens under tensile loads. This is attributed to the presence of high volume of warp fibers in [0]8specimens that simulate the unidirectional fibers. The high volume of warp fibers not only increases the stiffness but also increases the tensile strength of [0]8 specimens than the quasi-isotropic woven 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]s

and [0]8specimens. The load–deﬂection diagram of [0]8

specimen has two knees. The ﬁrst at the same load level of the knee in the load–deﬂection diagram of [0/45/

90]sspecimen (0.35 kN) that owing to the initiation and propagation 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)

Load (kN)

0 1 2 3 4 5 6 7

0 5 10 15 20 25 30

Longitudinal

Transverse

Initial microcracks of the matrix

Catastrophic failure Apparent

modulus = 7.143 GPa

Figure 6. Load–displacement diagram in tension test, printed from PC of testing machine.

[0]8

Strain (%)

Stress (MPa)

0 0.2 0.4 0.6 0.8 1

0 20 40 60 80 100 120

[0/±45/90]s; [12]

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

(7)

(independent to the fiber configuration). The second knee was observed at 0.7 kN that may be owing to the weft fiber–matrix debonding and progressive breaks in the warp fibers. Further increase in the load–deflection curve up to the final failure was observed due to the redistribution of the load between the warp fiber and the matrix. The final failure was nearly catastrophic.

Figure 9 shows a comparison between the load–

deﬂection diagrams in 4-point bending tests for [0/

45/90]sand [0]8specimens. The results in this figure indicate that at the same load level the [0]8specimens exhibits lower stiffness (high deflection) than [0/45/

90]s specimens under bending loads. This attributed to the presence of45 layers that increases the stiﬀness of the specimens and the resistance to the shear stresses owing to bending loads and consequently the bending strength of [0/45/90]s. This behavior was contrary with the results under tensile loads. These results are of considerable value to the designer with woven composite materials.

The value of bending strength determined from 4-point bending test of [0]8 specimens is higher than that from the 3-point bending test. Similar observation was reported for [0/45/90]sspecimens, Khashaba and Seif.^12,13They attributed their results to the stress concentration owing to the center load in 3-point bending test that result in early micro cracking of the matrix and ﬁber breakage under the loading point. In 4-point bending the specimens were sbjected to constant bending moments between the two loading points and its failure was due to pure bending stress.

Figure 10 illustrates the stress–strain diagram of 4-point bending specimen. The results in this ﬁgure indicate that the strains at the bottom (tension) side is

lower than that for the strain of the top (compression) side for [0]8specimen. In contrast for the strains in the quasi-isotropic woven GFRP specimens [0/45/90]s

where the compression side exhibit strains lower than that for tension side. The failure of the [0]8 specimen was started at the tension side for the 3-point and 4-point bending tests. In 4-point bending test the failure was initiated at one of the loading points and the delaminations were propagated toward the other point. It is interesting to note that the value of tensile strength (250.71 MPa) is approximately equal to the bending strength (3-point and 4-point), Table 2, which conﬁrms the responsibility of the tension side on the ﬁnal failure of the test specimen. This behavior is contrary to the failure of quasi-isotropic woven GFRP specimens [0/45/90]s where the compression

Load (kN)

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.

Load (kN)

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 1.5

0 50 100 150 200 250

Surface strain, ε (%)

Stress (MPa)

[0]8

[0/±45/90]_s;[12]

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

(8)

side is responsible to the ﬁnal failure of the test specimens.¹²

It interesting to note that the scatter in strength values (CV%) is higher than that of the modulus values in both tension and bending tests. This result was due to the fact that the scatter in the modulus is related to the material variation, while the scatter in the strength is influenced by the surface flaws of the fiber glass and the complex failure mechanisms specially at the warp and weft fibers interlacing.

Combined tension/bending results

Figure 11 shows the load–displacement diagrams of woven composites under combined tension/bending loads at diﬀerent initial eccentricities ‘ei’. The main characteristic of the load–displacement curve is the non-linear behavior, at the start of the test, associated with large displacement especially at high initial eccentricity. The large initial displacement was due to the fast rotation of the ﬁxtures at the start of loading process.

The slope of load–displacement diagrams was increased with further increase in the applied load. The non-linear portion is followed by an approximately linear behavior up to the ﬁnal catastrophic failure. The results in Figure 11 also show that the slope of load–displacement diagrams (stiﬀness) and failure loads decreases with increasing the initial eccentricity.

Figures 12(a)–(d) show load–strain diagrams at midpoint of combined tension/bending GFRP specimens tested with diﬀerent values of initial eccentricities.

The main characteristic of these ﬁgures is the presences of bending strains (the diﬀerence between the negative

compressive strain and positive tensile strain) at the beginning of loading process. This means that at low loads, the bending stress is more dominant than the tensile stress.

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

Increasing the applied load result in zero bending strains at specimen midpoint and the tensile stress becomes more dominant. This was clearly illustrated by the positive strains of the compression and tension sides of the specimen, Figure 12(a)–(d). This result was due to the maximum deﬂection of the specimen at midpoint reduces the bending arm (ea-) and consequently the bending moment and stress. Recalling the load-yout

relationship, Figure 13, the initial portion (increasing theyoutat very low loads) is responsible for the bending strains shown in Figure 12(a)–(d). With advance the loading process the load in the load-yout relationship become dominant tension resulting in zero bending strains, Figures 12(a)–(d).

The variation of specimen deﬂection (y) from zero at specimen ends (x¼0 andx¼L) to maximum at midpoint (x¼L/2) plays an important role in the distribution of the bending moment (M), Equation (4), along the test specimen and consequently the combined stress:

M¼ F eð _ayÞ, ð4Þ

where F is the applied load indicated by the testing machine. The deﬂection of the beam subjected to eccentric tension load was derived from the integration of the second order diﬀerential equation of the moment–

curvature relationship, Equation (5).^12,13

EI@²y

@x² ¼ Fðe_ayÞ ð5Þ

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

y¼ea coshkL1 sinhkL

sinhkxeacoshkxþea, ð6Þ

wherek²¼F/EIandeais the actual eccentricity of the specimen plane from the loading plane after applying tension load, and L is the length of the specimen between the ﬁxtures. The value ofeais less than the initial eccentricity (ei) due to the rotation of the ﬁxture as a rigid body towardeiby angle equal,f, Figure 14.

Displacement (mm)

Load (kN)

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 e_i = 11.75

Figure 11. Load–displacement diagram of woven specimens tested in combined tension/bending, printed from PC of testing machine.

(9)

The calculation procedure of the stresses distribution for combined tension/bending specimen with 11.75 mm initial eccentricity (as example) was as follows:

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

ea¼ei cos fLfsin f¼1:26 mm, ð7Þ

where Lf is the ﬁxture length¼150 mm, f¼4^o, Figure 16.

Therefore, the value of y can be calculated at any point (x) along the specimen, Equation (6), and consequently the bending moment, Equation (4).

The combined stress was calculated from Equation (8):

_Comb:¼_tþ_b ¼F AþMc

I , ð8Þ

whereFis the ultimate load (19 kN), and AandIare, respectively, the actual cross-section area and area moment of inertia.

Tensile, bending, and combined stress distribution along the specimen length are illustrated in Figure 17.

The variation in tensile stress was due to the variation in specimen cross-section (A), while the variation in bending stress was due to the variation in the area moment of inertia (I) and bending arm (ea – y). The latter was varied from maximum at specimen ends (y¼0 atx¼0 andx¼L) to minimum at specimen midpoint (y¼ymax¼). Therefore, the maximum bending stress occurred at the specimen ends, which have maximum bending arms (ea – 0¼ea). On the other hand, the minimum bending stress occurred at specimen midpoint, which has minimum bending arm (ea–). The results in Figure 17 and the photograph of the fractured specimen conﬁrm that the analytical stress distribution ε %

0 4 8 12 16 20

Load (kN)

Tension side Compression side (a)

ei= 11.75 mm

ε %

0 4 8 12 16 20

Load (kN)

Tension side Compression side

(b)

ei= 16.75 mm

ε %

0 4 8 12 16 20

Load (kN)

(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

ε %

0 4 8 12 16 20

Load (kN)

(d)

ei= 31.75 mm

Figure 12. Actual load-strain diagrams at midpoint of combined tension/bending GFRP specimen, (a)ei¼11.75 mm, (b) e_i¼16.75 mm, (c)e_i¼21.75 mm, and (d)e_i¼31.75 mm.

(10)

predict well the failure position of the specimen under combined load.

The experimental results show that the ratios of the maximum bending moments under combined and 3-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 plane displacement (mm)

e = 11.75 mm

Figure 13. Out of plane displacement (yout) vs. tensile load in combined tension/bending test.

θf

Pin/clevis connection

Offset

Lower spindle of testing machine

Steel shims

Pin/clevis connection 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.

θ

^f

Figure 16. Inclination angle of the fixture (f) atei¼11.75 mm.

(11)

ei¼11.75, 16.75, 21.75, and 31.75, respectively.

Therefore, it can be concluded that adding a tensile load at the ends of woven composite beams that designed to carry pure bending loads, such as bridge decks, will improve the bending capacity of the beam. In this case the problem can be approximated as ﬁxed–

ﬁxed beam with load Pmax(F-F) at the midpoint. The bending moment of such beam was calculated from Equation (9):

M_FF¼pmaxðFFÞL

8 ð9Þ

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

Pmax(b3)¼2), which approximately equal the ratio of the improvement in the bending capacity due to the eccentric loads.

Figure 18 shows the variation of normalized combined tension/bending moment with the initial eccentricity. The results in this figure indicate that increasing the initial eccentricity leads to increasing the maximum bending moment at fracture of woven GFRE specimens and vice versa for maximum tensile loads. The results in this figure also show that the initial eccentricity has more significant effect on the decreasing the ultimate combined tensile load for [0]8 specimens than the quasi-isotropic woven GFRP laminate [0/45/90]s. The interaction between moment and tension at fracture of [0]8 specimen is presented in Figure 19. Such interaction relationship is very important for the designer with composite materials subjected to eccentric tension loads.

Conclusions

The results show that the [0]8 composites have higher tensile strength and stiﬀness than [0/45/90]scomposites and vice versa for bending. The value bending strength determined from 4-point bending test is higher than that from the 3-point bending test.

Increasing the initial eccentricity leads to increasing the initial displacement in the load–displacement diagram at the start of loading process, decreasing the tensile load at fracture, and increasing the combined bending moment at fracture. At the start of the combined test the bending strains (stress) is more dominant at the specimen midpoint than the tensile stress.

0 40 80 120 160

Specimen length (mm) 0

50 100 150 200 250 300

Stress (MPa)

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,e_i¼11.75 mm.

0 5 10 15 20 25 30 35

Initial eccentricity (mm)

0 0.5 1 1.5 2

Normalized mechanical units

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]8and [0/45/90]scomposites under combined loads.

16 17 18 19 20

Tensile Load (kN)

23 24 25 26

Bending Moment (N.m)

(ei = 11.75) (ei = 16.75) (ei = 21.75)

(ei = 31.75)

Figure 19. Moment–tension interaction for fractured specimens under combined loads.

(12)

Increasing the applied load result in zero bending strains and the tensile stress becomes more dominant.

The failure of combined test specimen was at its ends, which have zero deflection and consequently maximum bending moment and stress. This behavior agrees with the analytical stress distribution along the specimen length. The experimental results show that the ratio of the maximum bending moments under combined and 3-point loading ranged from 1.85 to 1.97 for the initial eccentricity ranged from 11.75 to 31.75, respectively. Therefore, it can be concluded that adding a tensile load at the ends of woven composite beams that is designed to carry pure bending loads, such as bridge decks, will improve the bending capacity of the beam. The initial eccentricity has more significant effect on decreasing the ultimate combined tensile load for [0]8 specimens than the quasi-isotropic woven GFRP laminate [0/45/90]s. The constructed relationship between combined bending moment and tensile load of [0]8 specimen tested at different eccentricity values is very important for the designer with woven composite materials subjected to combined loads.

References

1. Peretz PF. Rotary-wing aeroelasticity: current status and future trends.AIAA J2004; 42: 1953–1972.

2. Ogasawara T, Onta K, Ogihara S, Yokozeki T and Hara E.

Torsion fatigue behavior of unidirectional carbon/epoxy and glass/epoxy composites.Compos Struct2009; 90: 482–489.

3. Lim I and Lee I. Aeroelastic analysis of bearingless rotors with a composite flexbeam. Compos Struct 2009; 88:

570–578.

4. Murri GB and Schaff JR. Fatigue life methodology for tapered hybrid composite flexbeams.Compos Sci Technol 2006; 66: 499–508.

5. Ouinas D, Bouiadjra B, Achour T and Benderdouche N.

Influence of disbond on notch crack behaviour in single bonded lap joints.Mater Des2010; 31: 4356–4362.

6. Fawaz SA and de Rijck JJM. A thin-sheet, combined tension and bending specimen. Exper Mech 1999; 39:

171–176.

7. Krueger R, Cvitkovich MK, O⁰Brien TK and Minguet PJ. Testing and analysis of composite skin/stringer debonding under multiaxial loading. J Comp Mater 2000; 34: 1263–300.

8. Lee S and Knauss WG. Failure of laminated composites at thickness discontinuities under complex loading and elevated temperatures. Int J Sol Struct 2000; 37:

3479–3501.

9. Palmer SO, Nettles AT and Poe Jr, CC. An experimental study of a stitched composite with a notch subjected to combined bending and tension loading. NASA Report No. NASA/TM-1999-209511, National Technical Information Service, 1999.

10. Wisnom MR. The relationship between tensile and flex- ural strength of unidirectional composites.J Comp Mater 1992; 26: 1173–1180.

11. Khashaba UA. On the mechanical behavior of [0/45/

90]s woven composites subjected to combined bending and tension loading, In: Proceedings of the 4th International Engineering Conference, Mansoure University, Egypt, Vol. 1, pp.527–539.

12. Khashaba UA and Seif MA. Effect of different loading conditions on the mechanical behavior of [0/45/

90]_s woven composites. J Compos Struct 2006; 74:

440–448.

13. Khoshbakht M, Chowdhury SJ, Seif MA and Khashaba UA. Failure of woven composites under combined tension-bending loading. J. Compos Struct 2009; 90:

279–286.

14. Khashaba UA. In-plane shear properties of cross-ply laminates with different off-axis angles. J Compos Struct2004; 65: 167–177.

Journal of Composite Materials

http://jcm.sagepub.com/