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Composite Structures

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Influence of fibre orientation on pultruded GFRP material properties

Shaohua Zhang, Colin Caprani⁎, Amin HeidarpourDepartment of Civil Engineering, Monash University, Melbourne, Australia

A R T I C L E I N F O

Keywords:Glass fibre reinforced polymer (GFRP)PultrusionFibre orientationOff-axis tensile strengthElastic modulusHankinson’s formula

A B S T R A C T

Pultruded glass fibre reinforced polymer (GFRP) has light weight, good strength, and excellent resistance tocorrosion. These features make GFRP a material well-suited for civil engineering applications. Considering thecomposite action of fibre and resin in pultruded GFRP, understanding the dependency of strength and stiffnesson its material constituents has gained interest amongst researchers. This paper studies the influence of fibreorientation on material properties of pultruded GFRP, namely tensile strength and elastic modulus. Eightycoupons with fibre orientations from 0° to 90° are tested under uniaxial tensile loadings. Based on the experi-mental results, a generalized Hankinson’s formula is proposed to predict the off-axis properties of pultrudedGFRP. To verify this proposed formula, off-axis strengths and elastic moduli of pultruded GFRP from previousstudies are compared with the predictions. This work should find use in structural design guidelines for pul-truded GFRP, and provides a complete understanding of fibre orientation effect.

1. Introduction

1.1. Background on FRP

The application of fibre reinforced polymer (FRP) composites incivil engineering is increasing as a high-performance structural elementor reinforcing material for rehabilitation purposes [1]. Its high strength-to-weight ratio and excellent durability make FRP an ideal material forconstruction. FRP composite consists of two material constituents: fibrereinforcement (e.g. glass, carbon, and aramid etc.) and polymer resinmatrix (e.g. epoxy, polyester and vinylester). To manufacture FRPprofiles, a highly automated and continuous manufacturing processknown as pultrusion is considered as the most economical method(Bank [2] and Meyer [3]). Normally, glass fibre embedded withpolyester or vinylester is used in the production of pultruded FRPcomposites. So far, pultruded GFRP has been used to construct com-posite structures or work as a reinforcing material with concrete or steel[4]. For example, in Switzerland, a five-storey building (the Eyecatcherbuilding) was built as an office and a 40m long cable-stayed Fibrelinebridge was constructed in Kolding, Denmark [1].

Extensive research has been conducted on GFRP composite to in-vestigate its material properties. Considering the orthotropic nature,fibre orientation has been found to have a significant influence on thematerial properties of laminated or pultruded GFRP (e.g. Kumar, Garg[5], Ninan, Tsai [6], Tsai and Sun [7], Haj-Ali and Kilic [8] and Kha-shaba [9]). Glass fibres typically have uniaxial tensile strengths of

2350–4830MPa and tensile modulus of 72–88 GPa, while the resin hasaround 65–90MPa and 3–4 GPa, although the exact values depend onthe specific materials adopted (Bank [2] and Gibson [10]). Therefore,generally, for materials with small off-axis angles (e.g. 0°, 10° and 15°),the majority of the load is taken along the fibre orientations. In con-trast, for high off-axis angles (higher than 30°), GFRP composite pre-sents similar behaviour to that of just the resin (matrix)—the fibre haslittle effect. Therefore, due to the higher strength of the fibre, a con-siderably higher strength or stiffness of GFRP composite can beachieved in small off-axis fibre orientations compared with high off-axisloading directions. In some relevant previous work, it has been foundthat the ratio between pultruded GFRP strengths at 0° and 90° is around70% [8].

To estimate the material strength at different fibre orientations,various criteria have been proposed to understand the mechanical be-haviour. In contrast, there are no criteria to predict the correspondingelastic modulus at off-axis angles. Tsai-Wu theory expressed in a poly-nomial form was used to estimate failure strength of anisotropic ma-terials [11]. Different studies have been carried out to develop othercriteria based on Tsai-Wu theory (e.g. Wu [12], Hashin [13], andClouston [14]). However, there is no general conclusion available onthe expression of interaction coefficient (F12) in this theory, even forfrequently-studied wood [15]. In addition, Norris [16] developed astrength criteria for orthotropic materials using the Maximum Distor-tion Energy Theory. It has been shown that the predicted results are tooconservative, since the isotropic material with regular voids were

https://doi.org/10.1016/j.compstruct.2018.07.104Received 20 February 2018; Received in revised form 25 June 2018; Accepted 29 July 2018

⁎ Corresponding author.E-mail address: colin.caprani@monash.edu (C. Caprani).

Composite Structures 204 (2018) 368–377

Available online 31 July 20180263-8223/ © 2018 Elsevier Ltd. All rights reserved.

T

applied to represent the orthotropic material [14]. Furthermore, thestrength criteria proposed by Hankinson [17] has been widely used topredict the off-axis strength of wood. In light of the accuracy of thiscriteria on wood, and its adoption in codes of practice, the applicationof Hankinson’s formula on composite materials has brought attentionfrom other research [18]. However, a poor agreement has been foundon pultruded GFRP between experimental results and Hankinson’spredictions. There are no other studies on pultruded GFRP.

1.2. Study objective

This paper investigates the effect of fibre orientation on the materialproperties of pultruded GFRP under quasi-static tension loading, spe-cifically the tensile strength and the elastic modulus. Pultruded GFRPcoupons are tested under tensile loading in a wide range of fibre or-ientations. Based on the experimental results, a generalizedHankinson’s formula is proposed and used as a basis to evaluate theconsidered off-axis properties of pultruded GFRP. Calibration of theexponential coefficient in the proposed generalized Hankinson’s for-mula is done. To verify the proposed criteria, further experimental re-sults obtained from other research works are also examined.Furthermore, various failure modes corresponding to the pultrudedGFRP coupons at different fibre orientations are presented in this study,showing the internal combined action of composite material. This re-search aims to facilitate the use of Hankinson’s formula for ready use inpractical engineering applications.

2. Current strength criteria

Hankinson’s formula was initially developed to estimate the off-axisstrength of wood. The generalized form (with exponent n) is:

=+

σ σ σσ θ σ θsin cosθ n n

0 90

0 90 (1)

where, σθ is the off-axis strength; σ0 is the longitudinal strength; n is thetransverse strength; n is an empirical coefficient; and the angle θ in-dicates the fibre orientation relative to the loading direction (Fig. 1).Interestingly, it has been found that the exponential coefficient n=2provides accurate estimation of compressive strength of wood, while nlocated in the range of 1.5–2 is more applicable for tensile strength[14]. Also, it is generally assumed that the strength is symmetricalin± θ, thus, the fibre orientation θ is only considered in the range of0°–90°. Furthermore, there are no shear strength properties involved inthis one-dimensional equation, making it easy to apply on orthotropicmaterials.

Some researchers have adopted other failure criteria to derive theHankinson’s formula. Tan [19] proposed a failure theory in the form ofFourier sine series:

∑= ⎡

⎣⎢ − ⎤

⎦⎥

=

−

σ A A nθsinθn

m

n01,2,3...

2

1

(2)

where, σθ is the off-axis strength; A0 and An (n=1, 2, 3…) are thestrength coefficients. For samples in the longitudinal direction (θ=0°),Eq. (2) becomes:

= =−σ A Aσ

[ ] , then 1 ,0 01

00 (3)

while for samples in the transverse direction (θ=90°) and n=1, itis:

= − −σ A A[ sin 90]90 0 12 1 (4)

Substituting Eq. (3) into (4) gives:

= − = −−σ σ A Aσ σ

[1/ sin 90] , then 1 1 ,90 0 12 1

10 90 (5)

Therefore, when n=1, Eq. (2) gives:

⎜ ⎟= ⎡⎣⎢

−⎛⎝

− ⎞⎠

⎤⎦⎥

−

σσ σ σ

θ1 1 1 sinθ0 0 90

21

(6)

and so at any angle,

= ⎡⎣⎢

− + ⎤⎦⎥

= ⎡⎣⎢

+ ⎤⎦⎥

=+

− −

σ θσ

θσ

θσ

θσ

σ σσ θ σ θ

1 sin sin cos sin

sin cos

θ2

0

2

90

1 2

0

2

90

1

0 90

02

902 (7)

Similarly, Tan and Cheng [20] found that this theory can be ex-pressed in the form of a Fourier cosine series, providing the same pre-dictions. However, it should be noted that there is no general expres-sion of strength coefficient and An will change for different fibreorientations [14].

Cowin [21] used Tsai-Wu theory to derive Hankinson’s formula as aspecial case. In his study, the linear term of Tsai-Wu theory was takeninto consideration. It was assumed that shear stress can be ignoredunder uniaxial loading. Therefore, the strength criteria for orthotropicmaterials is given by:

= + =F σ F σ F σ1, then 1,i i 1 1 2 2 (8)

where, Fi is the strength; σi is the normal stress; and in the notation ofthis paper, the index 1 and 2 are given by 0° and 90°, respectively.According to the coordinate transformation, normal stresses are givenby,

=σ σ θcosθ12 (9)

=σ σ θsinθ22 (10)

For uniaxial tensile load in the 0° direction (σ2= 0), Eq. (8) is:

= =F σ Fσ

1, then 11 1 1

0 (11)

Similarly, the strength F2 is 1/σ90. Therefore, Eq. (8) becomes:

+ =σ θσ

σ θσ

cos sin 1θ θ2

0

2

90 (12)

Giving,

=+

σ σ σσ θ σ θsin cosθ

0 90

02

902 (13)

This method has been validated against the experimental results,showing a good accuracy for wood materials. However, there is noapplication on other orthotropic materials. Furthermore, Liu [22] re-commended that the coefficient of interaction, F12, in Tsai-Wu theorycan be determined according to Hankinson’s formula, alluding thatHankinson’s formula more closely reflects the fundamental relation-ship.

Many studies have been carried out to show the reliability ofHankinson’s formula. Similar to the effect of grain angle in wood, fibreorientation plays a vital role in material properties of composites.Considering the orthotropic nature of FRP composite, the effect in itsthickness direction is generally ignored which is very small comparedwith the in-plane dimensions [2]. In this study, pultruded GFRP isreasonably regarded as a tetragonal material [23], which assumes thatits material properties in the thickness direction is the same as oneother direction.

LoadingDirection

FibreDirection

y

x xx

Fig. 1. Coordinates of off-axis material.

S. Zhang et al. Composite Structures 204 (2018) 368–377

369

Apart from investigations on wood (e.g. Mascia and Nicolas [15]and Suryoatmono and Pranata [24]), Hankinson’s formula has beenused on laminated FRP (Tan [19], Clouston [14], and Daniel, Werner[25]) and pultruded GFRP [18]. Interestingly, good agreement has beenfound between the estimated strength and experimental values forother orthotropic materials, except for pultruded GFRP. The compar-ison of pultruded GFRP by using original Hankinson’s formula is shownin Fig. 2. It is obvious that there is a poor relationship between thepredicted strength and experimental results, especially for small off-axisfibre orientations (< 45°). For one study, it was suggested that apolynomial of order six is required to establish the strength formula[18]. This proposal ignores knowledge of material behaviour and seemsto over-parametrize the empirical problem.

3. Experimental investigation

3.1. Material properties

The pultruded GFRP used in this study was manufactured by ExelComposites, Australia. The flat profiles consist of E-glass fibre (majorreinforcement) and polyester resin (matrix). The internal fibre archi-tecture is shown in Fig. 3, in which roving fibre layers alternate be-tween continuous strand mats (CSM). The thickness of pultruded GFRPsheets is around 6mm. The fibre volume fraction (FVF) of pultruded

GFRP materials is determined to be around 42.1 ± 0.3% from a burn-off test.

3.2. Test specimen and experimental procedure

Currently, there is no specific test standard for pultruded GFRP.Generally, researchers refer to ASTM D3039 [26] to conduct tensiletests on composite materials (Haj-Ali and Kilic [8], Gosling and Sar-ibiyik [27], Asprone, Cadoni [28], and Kawai and Saito [29]). There-fore, in this study, off-axis tests on pultruded GFRP were conducted inaccordance with the same standard. Rectangular coupons were cut fromthree pultruded GFRP flat plates via waterjet cutting to check platevariations. The tested off-axis angles, θ, are: 0°, 10°, 20°, 30°, 45°, 60°,75° and 90°. The sample dimensions are the same for all tests(250mm×25mm×6.21mm) (as shown in Fig. 3). Three plates areused to evaluate any inter-element variability due to the manufacturingprocess. It should be emphasised that no size effect has been observedon pultruded FRP composites unless variation exists in the character-istics of fibre or resin [30]. Furthermore, to avoid the effect of endconstraint on material properties, a 45mm griping distance is allocatedat two ends to ensure a proper aspect ratio (length (L)/width (W) > 6)[31]. Thus, the gauge length is 160mm.

Off-axis tension tests were performed at the Civil Engineering la-boratory, Monash University, using a Universal Instron 100 kN testingmachine. Axial tension load was applied in a displacement controlmode with a rate of 2mm/min. Two strain gauges were installed in themiddle section of coupon to measure longitudinal and transverse strainssimultaneously (Fig. 4). Linear foil strain gauges (LY41) with soldertabs are manufactured by HBM. The dimension of measuring grid is6 mm and nominal resistance is 120Ω±0.3%. The stiffness of a straingauge generates a significant reinforcing effect when installing onmaterials with low modulus (Little, Tocher [32] and Perry [33]). It hasbeen found that the sensitivity to the reinforcement effect for HBMstrain gauges increases with the decrease of the grid length, which isapproximately 1.08 at 6mm [34]. Therefore, a gauge factor 2 ± 1%has been applied via the dataTaker to account for the reinforcementeffect due to strain gauge. All coupons were tested until the samplefailed. For each plate, there are three repetitions of each off-axis angleand extra eight coupons were tested to account for unexpected ex-perimental error. Therefore, 80 off-axis tensile tests were conducted intotal, but results of 72 tests were effective and summarized in this study

Fig. 2. Comparison of off-axis tensile strengths on pultruded GFRP obtainedthrough experiments and Hankinson’s formula (after Zafari and Mottram [18]).

250

LoadingDirection Pultruded

FibreDirection

45

25

Gripped Zone

Gripped Zone

250

6,21

Fig. 3. Pultruded GFRP internal structure and sample geometry (units: mm). Fig. 4. Test sample and experimental apparatus.

S. Zhang et al. Composite Structures 204 (2018) 368–377

370

to assess the sample variability both within each plate (intra-platevariability) and between different plates (inter-plate variability).

3.3. Example results

The approach used to obtain the tensile properties of pultrudedGFRP is explained using two sets of results. The same steps are appliedthroughout. Generally, GFRP composites fail by brittle fracture withoutplastic deformation and yield point [35]. Therefore, the tensile strengthof pultruded GFRP is taken as the maximum stress, defined as:

≡ =F σ PAt maxmax

(14)

where, Ft is the tensile strength, σmax is the maximum stress, Pmax is themaximum load before failure, and A is the cross-sectional area. As notedin Section 3.2, the cross-sectional areas of pultruded GFRP coupons areuniform in this study, which are around 155mm2. The elastic modulusof pultruded GFRP (Eθ), is calculated based on the theory of elasticity[36], by taking the slope of stress-strain curves in the strain range of0.001–0.003. Axial tension load and longitudinal strain were measuredsimultaneously until the sample failed. Although material responses of0° and 45° coupons are different (Fig. 5), the corresponding tensilestrengths are taken as the maximum stresses (σmax), which are322.6MPa and 116.6MPa, respectively. A significant reduction isshown on the elastic modulus from 23 GPa at 0° to 11.1 GPa at 45°,which is similar to the strain energy decreasing from 3245.1 kJ/m3 to1199.1 kJ/m3 accordingly.

4. Results and analysis

4.1. Failure modes

Brittle failure occurred at the end of each test on pultruded GFRPcomposites. Similar failure modes were observed from all coupons(Fig. 6), including debonding between the fibre and matrix, fibre pull-out and matrix cracking (Cantwell and Morton [37] and Richardson andWisheart [38]). The interaction effect due to the strain gauge installa-tion is negligible since large gauge length and proper gauge factor havebeen applied in the experiments [39]. It is noticeable that damage waslimited to the middle region of the specimen through the strain gauges,especially for pultruded GFRP specimens with off-axis angle higher than30°. The continuous filament mat has been found to be the weakestelement of pultruded GFRP [40], which can influence the failure me-chanism of composites with off- axis fibre orientations [41]. However,for coupons with off-axis direction lower than 30°, delamination alongthe roving fibre was clearly shown in each test due to the fibre-domi-nant behaviour. Besides, it should be mentioned that for all pultruded

GFRP specimens, the failure crack was along the off-axis fibre direction,although relatively similar cracks occurred on the surface of couponswith off-axis angles 60° and 75°.

4.2. Off-axis properties of pultruded GFRP

Some typical stress-strain curves of pultruded GFRP with differentfibre orientations are shown in Fig. 7. It should be noted that each curveis taken as the average of nine datasets at the specific orientation. Basedon the stress-strain relationships, material properties of pultruded GFRPare calculated using the methods mentioned in Section 3.3. Due to theinfluence of fibre orientation on pultruded GFRP, the stress-strain re-sponses are considerably different for off-axis samples. It is clear thatthe longitudinal coupon (0°) shows a linear elastic behaviour untilreaching its maximum stress, followed by a sharp decrease of stress. Bycontrast, the off-axis coupon presents a linear response at relatively lowstrain and changes in the nonlinear behaviour at higher strains until thecoupon completely fails. Also, this nonlinearity increases with in-creasing fibre orientations, which is significant at fibre orientations lessthan 45°. For samples with fibre orientations higher than 45°, the stress-strain behaviours are relatively similar presenting small increments ofnonlinearity. This nonlinearity is a well-known consequence of the in-creasing influence of the matrix at higher orientations.

The observed tensile strengths of pultruded GFRP with differentfibre orientation are summarized in Table 1. Results of each plate aretaken as the average value obtained from three repetitions for each off-axis angle. It is noticeable that there are small differences in materialstrength among the plates. The coefficient of variation (CoV) is between3.4% and 8.1% regardless of fibre orientations, indicating consistencyin the pultrusion process. Clearly, the results show that the materialstrength of pultruded GFRP significantly decreases with increasing fibreorientation under quasi-static tensile loads. Comparing the tensilestrength of samples with smaller off-axis angles (< 45°), a clearstrength reduction is observed (Fig. 8). The longitudinal samples havethe highest tensile strength, almost three times higher than the strengthof the 30° specimen. Owing to the fibre reinforcement, 10° off-axiscoupons present complete fracture, leading to significantly higherstresses at failure than others. However, for composites with off-axisangles larger than 45°, the tensile strength presents a relatively smallreduction (less than 9%) when fibre orientation increases beyond 45°,especially for 75° and 90°. Overall, there is a 73% reduction of averagetensile strength between the longitudinal (0°) and transverse (90°)samples. This significant decrease was also found by Haj-Ali and Kilic[8] on pultruded GFRP with 12.7 mm thickness. All these results in-dicate that the matrix rather than fibre plays a more dominant role inpultruded GFRP with fibre orientation higher than 45°, showing littlesensitivity of tensile strength, elastic modulus and strain energy withincreasing off-axis angles. Although the matrix-dominant behaviourmay vary significantly, this variation does not significantly affect thematerial properties. Therefore, conducting off-axis tensile experimentsat higher fibre orientation is insufficient to illustrate the materialproperties of pultruded GFRP.

Similar to the tensile strength, fibre orientation also has an effect onthe elastic modulus (Eθ) of pultruded GFRP, respectively. Consideringthe consistency of pultruded GFRP plates, Table 2 summarizes theaverage results of pultruded GFRP at different fibre orientations andeach result is taken as the average of nine coupons. Overall, the elasticmodulus decreases significantly from 0° to 90°, presenting a 54% re-duction. The sensitivity of fibre orientation decreases with increasingfibre orientations, especially for samples with higher off-axis angles(> 45°) for which material properties are quite similar.

4.3. Calibration of Hankinson’s formula

4.3.1. Off-axis tensile strengthBased on the results, a generalized Hankinson’s formula to predict

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.020

50

100

150

200

250

300

350

400

Strain

Stre

ss(M

Pa)

Experiment - 0

Experiment - 45

Fig. 5. Stress-strain curves of 0° and 45° pultruded GFRP coupons.

S. Zhang et al. Composite Structures 204 (2018) 368–377

371

the off-axis material strength of GFRP is determined. From Table 1, thestrength coefficients, σ0 and σ90 are determined as the average value oftensile strength in longitudinal and transverse directions, respectively.The exponential coefficient, n, in the generalized Hankinson’s formulais then estimated as 1.284 ± 0.045 for the best fit line within a 95%confidence interval, using nonlinear least-squares optimization fitting

across all 72 samples. The coefficient of determination for this fit, R2, is0.9773 and the result is shown in Fig. 9. With this empirical value forthe exponent, n, Eq. (1), used to predict the off-axis tensile strength (σθ)of pultruded GFRP, becomes

=+

σ σ σσ θ σ θsin cos

,θ0 90

01.284

901.284 (15)

Fig. 6. Failure modes of off-axis pultruded GFRP under tension.

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.020

50

100

150

200

250

300

350

400

Strain

Stre

ss(M

Pa)

0

10

20

3045

60 , 75 , 90

Fig. 7. Typical stress-strain curves of pultruded GFRP at different fibre or-ientations.

Table 1Summary of pultruded GFRP tensile strengths (unit: MPa); the results for each plate are an average of three coupons.

Off-axis angle (θ) 0° 10° 20° 30° 45° 60° 75° 90° CoV-intra

Plate 1 360.0 244.9 164.2 138.6 115.4 104.1 90.5 92.2 3.9%Plate 2 341.1 286.1 155.9 131.9 111.7 99.2 97.5 93.0 4.9%Plate 3 328.0 254.6 177.1 138.1 116.3 101.5 99.2 93.2 3.7%Average 341.5 257.6 166.9 136.0 112.0 101.6 95.9 92.8 4.2%CoV 5.1% 7.9% 8.1% 3.4% 6.2% 3.7% 5.5% 3.8% –

0 10 20 30 40 50 60 70 80 900

50

100

150

200

250

300

350

400

Fibre orientation (Degree)

Stre

ss(M

Pa)

Experiment - Plate 1Experiment - Plate 2Experiment - Plate 3Experiment - Average

Fig. 8. Summary of pultruded GFRP tensile strength (6mm) showing averagesof three coupons for three plates and overall average.

S. Zhang et al. Composite Structures 204 (2018) 368–377

372

where, σθ is 341.5MPa; σ90 is 92.8MPa.As discussed in Section 2, the exponential coefficient, n, in the

generalized Hankinson’s formula used to predict the tensile strength oforthotropic material was found to be 1.5 and 2. The exponential coef-ficient n=1.25 is also applied as a comparison and the reason for thiswill be discussed in later Section 4.5.

Fig. 10 presents the comparison of off-axis tensile strength (σθ)obtained from experiments and prediction using n=1.25, 1.5 and 2.0;n clearly has a significant influence. Compared with the experimentalresults, n=1.5 and 2 provide higher estimated values for all off-axisangles, worsening with increasing n. In contrast, the tensile strengthcalculated with n=1.25 at various orientations is much closer to theexperimental data, with an exception for 20° off-axis samples.

Interestingly, test results for both 10° and 20° samples are found to havehigher coefficient of variance than others (as shown in Table 1), around7.9% for 10° samples and 8.1% for 20° samples. Similar variability ofHankinson’s formula for 20° samples has also been found in other stu-dies and is discussed in Section 4.4.

4.3.2. Off-axis elastic modulusThe same method has been applied to the calibration of Hankinson’s

formula to provide an estimation of the elastic modulus at differentfibre orientations. Based on Eq. (1), the elastic modulus of pultrudedGFRP is calculated in the same form (Radcliffe [42], Hu, Nakao [43],and Xu and Suchsland [44]). The exponential coefficient, n is found tobe 1.386 ± 0.05 for the elastic modulus with a 95% confidence in-terval and the corresponding R2, is 0.9612 (Fig. 11).

=+

E E EE θ E θsin cosθ

0 90

01.386

901.386 (16)

where, E0 and E90 are 23.0 GPa and 10.5 GPa, respectively.The comparisons of the predicted modulus and experimental results

based on different exponential coefficients are shown in Fig. 12. It isclear that the elastic modulus calculated with n=2 are considerablyhigher than the experimental results. By contrast, n=1.5 provides agood estimation of elastic modulus at different fibre orientations, whichare slightly higher (less than 10%) than the experimental results. Ad-ditionally, it is worth mentioning that the strength coefficient

Table 2Average values of elastic modulus of pultruded GFRP (each result is the averageof nine coupons).

Off-axisangle (θ)

0° 10° 20° 30° 45° 60° 75° 90° CoV –intra

Plate 1 23.7 19.8 16.4 14.2 10.9 11.0 10.8 10.6 3.4%Plate 2 22.6 21.0 16.4 12.9 11.2 10.5 10.8 10.3 3.1%Plate 3 22.5 20.6 17.2 13.3 11.1 10.6 10.3 10.5 3.0%Eθ (GPa) 23.0 20.5 16.7 13.5 11.1 10.7 10.6 10.5 3.2%CoV 5.2% 5.9% 3.8% 5.2% 5.6% 6.6% 4.0% 2.9% –

0 10 20 30 40 50 60 70 80 900

50

100

150

200

250

300

350

Fibre orientation (Degree)

Stre

ss (M

Pa)

Experiments (6 mm pultruded GFRP)Calibrated Hankinson's Formula95% confidence interval

Fig. 9. Calibration of the generalized Hankinson’s formula for off-axis uniaxialtensile strength, showing individual experimental results and the 95% con-fidence intervals for the fit.

0 10 20 30 40 50 60 70 80 900

50

100

150

200

250

300

350

400

Fibre orientation (Degree)

Stre

ss(M

Pa)

Experiments (average)Hankinson n = 1.284Hankinson n = 1.25Hankinson n = 1.5Hankinson n = 2

Fig. 10. Off-axis tensile strength of pultruded GFRP for various Hankinsoncoefficients.

0 10 20 30 40 50 60 70 80 905

10

15

20

25

30

Fibre orientation (Degree)

Ela

stic

mod

ulus

(GP

a)

Experiments (6 mm pultruded GFRP)Calibrated Hankinson's formula95% confidence interval

Fig. 11. Calibration of the generalized Hankinson’s formula for off-axis uniaxialelastic modulus.

0 10 20 30 40 50 60 70 80 908

10

12

14

16

18

20

22

24

Fibre orientation (Degree)

Ela

stic

mod

ulus

(GP

a)

Experiments (average)Hankinson n = 1.284Hankinson n = 1.386Hankinson n = 1.5Hankinson n = 2

Fig. 12. Off-axis elastic modulus of pultruded GFRP with various Hankinsoncoefficients.

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(n=1.284 or 1.25 is also suitable for estimating the elastic modulus atoff-axis angles, giving a prediction that is less than 7% lower than itsactual value.

4.4. Comparison with previous studies

The generalized Hankinson’s formula has also been validatedagainst experimental results of pultruded GFRP obtained by a few otherresearchers. Table 3 and Table 4 present the strength and elasticmodulus parameters obtained in the longitudinal and transverse di-rections, respectively. Each parameter is taken as the average valuefrom repeated coupon tests. The group number indicates the number ofdatasets and each group of data is taken as the average value of three orfour repetitions. It should be noted that two groups tested by Satasivam,Bai et al. [45] and Satasivam and Bai [46] were manufactured byXingya FRP, China (Group 1) and Exel Composites, Australia (Group 2),respectively. Samples with different thicknesses were tested by Haj-Aliand Kilic [8], which are 6.35mm for Group 1 and 12.7 mm for Group 2.Regarding samples in the study of Zafari [47], four groups were cutfrom different plates. Based on all parameters, the off-axis tensilestrength and elastic modulus of pultruded GFRP calculated with theproposed exponential coefficients are shown in Figs. 13–17.

Fig. 13 presents the results of 10° off-axis pultruded GFRP manu-factured by Xingya FRP, China and Exel Composites, Australia. Theexponent n=1.284 provides a very good estimation for Exel Compositepultruded GFRP, differing by only 2.8%. This is unsurprising given thismanufacturer made the samples upon which the exponent n=1.284was derived. For the material supplied by Xingya FRP, there is a 12%difference between the predicted and experimental strengths at 10° off-axis angle. Although the thickness and fibre volume fraction of twomaterials are relatively similar, a significant difference in the 0° and 90°material strengths exists, mainly due to different fibre architecture[45]. Due to the random orientation of fibres within the plane, CSM isregarded as an extra reinforcement in multi-direction loading [2]. It hasbeen found that CFM layer has no influence on the failure mechanism ofpultruded GFRP with fibre orientation less than 15° [41]. PultrudedGFRP manufactured by Exel Composites consists of 11 fibre layers al-ternating with CSM, while the material supplied by Xingya FRP is madeof two CSM layers separated by one roving layer. Furthermore, thedifference in the internal structure also affects the predictions of theelastic modulus (Fig. 14): when using the same coefficient n=1.284,there is a 14.3% difference observed on pultruded GFRP provided byXingya FRP, whereas n=1.386 and 1.5 provide better predictions, 9%

Table 3Strength coefficients of pultruded GFRP from different researchers.

Reference Group number σ0 (MPa) σ90 (MPa)

Satasivam, Bai [45]Satasivam and Bai [46]

Group 1 393.1 22.0Group 2 305.7 88.7

Haj-Ali and Kilic [8] Group 1 260.9 69.0Group 2 244.9 77.1

Zafari [47] Group 1 188.0 166.0Group 2 170.0 146.0Group 3 154.0 120.0Group 4 136.0 110.0

Table 4Stiffness coefficients of pultruded GFRP from different researchers.

Reference Group number E0 (MPa) E90 (MPa)

Satasivam, Bai [45] Group 1 31.7 5.2Haj-Ali and Kilic [8] Group 1 18.0 10.3

Group 2 18.3 10.1

Fig. 13. Comparison of off-axis tensile strength on pultruded GFRP with 6mmthickness (data taken from Satasivam, Bai [45] and Satasivam and Bai [46]).

Fig. 14. Comparison of off-axis elastic modulus on pultruded GFRP with 6mmthickness (data taken from Satasivam, Bai [45]).

0 10 20 30 40 50 60 70 80 900

50

100

150

200

250

300

350

Fibre orientation (Degree)

Stre

ss(M

Pa)

Hankinson - 6.35 mmHankinson - 12.7 mmPultruded 6.35 mm - Haj-AliPultruded 12.7 mm - Haj-Ali

Fig. 15. Comparison of off-axis tensile strength on pultruded GFRPwith 6.35mm and 12.7mm thickness (n=1.284) (data taken from Haj-Ali andKilic [8]).

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and 3.1% different from the corresponding experimental results, re-spectively.

To consider pultruded GFRP with different thickness, sample di-mensions, and FVFs, Hankinson’s formula with proposed coefficients is

applied to specimens tested by Haj-Ali and Kilic [8]. In this work,6.35mm and 12.7mm thick materials were tested under quasi-statictension load and the average FVF of two materials is 34%. All couponshave the same sample dimension, 304.8 mm by 31.75mm, with63.5 mm grip zones at the ends. The fibre architecture consists of 4roving layers alternating with 5 layers of CSM. The experimental resultsof off-axis coupons with different fibre orientations (0°, 15°, 30°, 45°,60° and 90°) are presented in Fig. 15 and Fig. 16 along with the pre-dictions of Hankinson’s formula.

From Fig. 15, good agreements can be seen for both thicknesses atall orientations for tensile strength. The coefficients of variation areapproximately 3.2%, 0.8%, and 0.2% for 30°, 45°, and 60°, respectively.An exception is noted for the 15° samples in which case the experi-mental results are 6.9% and 11.8% higher than predicted for the12.7 mm and 6.35mm materials, respectively. The difference may bedue to material variability, but n=1.284 still provides a conservativeestimate. At least from these results, it is seen that Hankinson’s formulacan be used to determine the tensile strength of off-axis pultruded GFRPwithout considering the size effect and FVFs.

For the elastic modulus, the Hankinson’s formula with exponentialcoefficients (1.284, 1.386 and 1.5) provides similar results at variousfibre orientations (Fig. 16). However, better agreements can be seen onsamples with 6.35mm rather than 12.7 mm, especially for samples withoff-axis angles (below 45°). For 6.35mm pultruded GFRP, the predictedmodulus calculated based on either n=1.284, 1.386 or 1.5 are rela-tively close to the corresponding experimental results with less than 4%difference and this good agreement is particularly noticeable inn=1.386. The obvious variation at 30° (approximately 10%) can beattributed to the material or experimental variability. By contrast, theelastic modulus of 12.7mm samples is generally underestimated usingthe generalized Hankinson’s formula with proposed coefficients. Thedifferences between predictions and experimental values are around10% at 15°, 30° and 45°. Also, when the value of n decreases, the dif-ference increases. However, there are no other experimental resultsavailable showing that the thickness of pultruded GFRP may have aninfluence the elastic modulus prediction. Consequently, it can be saidthat Hankinson’s formula is sufficient to estimate the elastic modulus ofpultruded GFRP regardless of the FVFs, while further study is requiredto investigate the size effect.

The exponential coefficient is next validated against experimentalresults obtained by Zafari and Mottram [18]. In this study, the pul-truded GFRP is manufactured by Creative Pultrusions Inc., which hasthe multiple layers of fibre reinforcement alternating with CSM. Thematerial thickness was 9.53mm and six off-axis angles (0°, 5°, 10°, 20°,45°, and 90°) were tested to investigate the fibre orientation effect.Fig. 17 shows the experimental results and the predictions of Hankin-son’s formula using n=1.284. The similarity of the 0° and 90° samplestrength is striking compared to the previous studies.

Nevertheless, the values predicted from Hankinson’s formula pre-sent reasonable agreement with the experimental data at different fibreorientations. A particular exception is at 45°, where the experimentalresults are always higher than the predicted values. Comparison of theresults across the four groups shows there is less than an 11% differencebetween estimated and experimental values. Interestingly, the pre-dicted strengths are almost the same as the test results at smaller off-axis angles, e.g. 5° and 10°. Unusually, for test results obtained fromGroup 3 and 4, the tensile strengths at 45° are higher than the values at20° but this is not explained in the paper. Overall then, it can be con-cluded that applying the generalized Hankinson’s formula (n=1.284)provides a reasonable fit to the test results from this study.

4.5. Recommendation

For tensile strength, the generalized Hankinson’s formula with anexponential coefficient of n=1.284 is found to correspond well withexperimental results from across the literature, as well as the

(a)

(b)

0 10 20 30 40 50 60 70 80 908

10

12

14

16

18

20

22

24

Fibre orientation (Degree)

Ela

stic

mod

ulus

(GP

a)

Pultruded 6.35 mm - Haj-AliHankinson - n = 1.284 - 6.35 mmHankinson - n = 1.386 - 6.35 mmHankinson - n = 1.5 - 6.35 mm

0 10 20 30 40 50 60 70 80 908

10

12

14

16

18

20

22

24

Fibre orientation (Degree)

Ela

stic

mod

ulus

(GP

a)

Pultruded 12.7 mm - Haj-AliHankinson - n = 1.284 - 12.7 mmHankinson - n = 1.386 - 12.7 mmHankinson - n = 1.5 - 12.7 mm

Fig. 16. Comparison of off-axis elastic modulus on pultruded GFRP: a) with6.35 mm thickness; b) with 12.7 mm thickness (data taken from Haj-Ali andKilic [8]).

0 10 20 30 40 50 60 70 80 900

50

100

150

200

250

300

350

Fibre orientation (Degree)

Stre

ss(M

Pa)

Hankinson - Group 1Hankinson - Group 2Hankinson - Group 3Hankinson - Group 4Experiment - Group 1Experiment - Group 2Experiment - Group 3Experiment - Group 4

Fig. 17. Comparison of off-axis tensile strength on pultruded GFRP with9.35 mm thickness (n=1.284) (data taken from Zafari [47]).

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comprehensive suite of results in this work. Different lay-ups, FVFs, andmanufacturers are considered, and so the exponent seems to have quitegeneral applicability. Where there is a larger difference, the predictionsare conservative. Nevertheless, it is prudent to propose an exponentthat further underestimates strengths somewhat. Therefore, consideringthe 95% confidence intervals (± 0.045) of the generalized coefficient,an exponent n=1.25 would seem suitable for design purposes, oncematerial factors of safety are appropriately calibrated. For the elasticmodulus, the generalized Hankinson’s formula is also applicable with arange of exponential coefficients (1.284–1.5). The testing in this workindicates n=1.386. However, it is found that the thickness of the FRPhas an influence and there are yet insufficient experimental results toprovide a final recommendation considering this size effect. Since FRPmembers are mainly subjected to bending, axial force and shear, futureresearch should focus on the influence of fibre orientation on thesefundamental actions.

Given the very wide range of possible lay-ups in pultruded GFRP, agenerally-applicable Hankinson’s formula exponent of n=1.25 forboth tensile strength and elastic modulus will be necessarily con-servative, perhaps overly so. Therefore, it is also recommended thatmanufacturers report the exponent value for their material, as part oftheir product statement of material properties. However, since this re-quires testing, it is beneficial to rationalize the quantity of tests re-quired. Considering the foregoing analysis of material strengths andbehaviour of Hankinson’s formula, in addition to 0° and 90° tests, thereis generally less variation at 10° between the experimental results andestimated values of pultruded GFRP according to the comparisons ofdifferent studies. Therefore, it is recommended that 10° off-axis fibreorientation tests are conducted to calibrate the material exponent.When this approach is used for the 0°, 10°, and 90° tensile strengthresults in this study, the exponent is found to be n=1.289, very closeto the exponent obtained for the complete suite of tests (n=1.284),giving credence to this recommendation. Furthermore, considering thebiaxial stresses (longitudinal, transverse and in-plane shear stresses)induced simultaneously at off-axis angles, the 10° coupon generates thecloser strength to critical value based on force equilibrium, making itpreferable to estimate the material strength (Chamis and Sinclair [48]and Pindera and Herakovich [49]). To summarize, the 10° off-axiscoupons (in addition to the usual longitudinal and transverse tests) aresufficient to investigate the exponent of pultruded GFRP.

5. Summary

This paper investigates the effect of fibre orientation on the materialproperties of pultruded GFRP. A generalized form of Hankinson’s for-mula is proposed, and the exponent validated against experimentalresults for tensile strength and elastic modulus. Pultruded GFRP withdifferent fibre orientations (0°, 10°, 20°, 30°, 45°, 60°, 75° and 90°) weretested under uniaxial tensile loading. Following the presentation ofexperimental results, the proposed exponential coefficients are verifiedagainst results for pultruded GFRP reported across other studies. Theobservations are summarized below:

• Fibre orientation of pultruded GFRP presents a significant influenceon material. Generally, for the tests conducted in this work, thematerial properties increase as off-axis fibre orientation decreases.The properties in the longitudinal direction are always the highestvalue, and are approximately two or three times higher than that of30°. In contrast, there is less than 10% reduction of material prop-erties for samples with off-axis angle higher than 45°, indicating arelatively low sensitivity of fibre orientations.

• The observed failure modes are similar for all off-axis pultrudedGFRP coupons. The failure crack is always along the fibre orienta-tion although the loading is uniaxial.

• The generalized form of Hankinson’s formula with exponentialcoefficient n=1.284 can be used to predict the off-axis tensile

strength of pultruded GFRP. More specifically, the variation be-tween the estimated and experimental off-axis strength on pultrudedGFRP is normally less than 5% but roughly 12% for special cases.

• There is no size effect (e.g. thickness, sample dimensions and FVFs)existing on predicting the off-axis tensile strength of pultruded GFRPby using the generalized Hankinson’s formula.

• The Hankinson’s formula with a range of exponential coefficientfrom 1.284 to 1.5 is applicable to predict the elastic modulus ofpultruded GFRP at various fibre orientations, especially forn=1.386.

• There is a noticeable size effect of pultruded GFRP coupons onelastic modulus and so further study is needed to recommend agenerally-applicable exponential coefficient that is not very con-servative.

Finally, it is recommended that the generalized form of Hankinson’sformula with exponent n=1.25 is suited for design application ofpultruded GFRP and is conservative. However, should manufacturerswish to offer an exponent more reflective of their product, it is re-commended that in addition to longitudinal and transverse tests, 10°off-axis tests are used to calibrate the exponent.

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