Modulus and Strength Prediction for Natural Fibre Composites

Transcription

1 Modulus and Strength Prediction for Natural Fibre Composites Amandeep Singh Virk a, Wayne Hall b and John Summerscales c, d a. School of Mechanical and Mining Engineering, University of Queensland, Brisbane, Queensland 4072, Australia b. Griffith School of Engineering, Gold Coast Campus, Griffith University, Queensland 4222, Australia c. Advanced Composites Manufacturing Centre, School of Marine Science and Engineering, Reynolds Building, University of Plymouth, Plymouth PL4 8AA, United Kingdom d. Corresponding author Keywords: Polymer-matrix composites (PMCs); natural fibres; mechanical properties, strength; micromechanics Abstract This paper presents a new micromechanical model for the prediction of the tensile modulus and strength of natural fibre reinforced polymer matrix composites. The model addresses issues linked to the statistical variation inherent in fibre reinforcements extracted from plants. The new model introduces a fibre area correction factor (FACF). Modulus and strength are estimated and compared to experimental data for a jute-epoxy composite. The predictions of tensile modulus and strength using the FACF show improvements over those from other micromechanical models presented in the literature. Nomenclature ASTM American Society for Testing and Materials (now ASTM International) CSA cross-sectional area CT computer tomography FACF fibre area correction factor FDDF fibre diameter distribution factor FLDF fibre length distribution factor FODF fibre orientation distribution factor GRP Glass fibre Reinforced Plastics MDS Multiple Data Set NLIM Natural Logarithm Interpolation RH relative humidity RoM rule of mixtures Page 1

2 WLS Weak-Link Scaling a n E cl E f E m V f V m η d η l η o θ f θ n κ σ c σ c σ f proportion of the fibres oriented at a fibre angle θ n composite modulus in the fibre direction fibre modulus matrix modulus fibre volume fractions matrix volume fractions fibre diameter distribution factor (FDDF) fibre length distribution factor (FLDF) fibre orientation distribution factor (FODF). angle between the fibre axes and the composite load direction fibre angle relative to the applied load direction fibre area correction factor (FACF) unidirectional composite tensile strength quasi-unidirectional composite strength tensile strength of the fibres σ m(max) matrix tensile strength (σ m ) εf matrix stress at a strain that is equal to the fibre failure strain 1. Introduction Natural fibres are increasingly being considered as the reinforcement for polymer matrix composites as they have the potential to play a significant role in sustainable product and infrastructure development. The use of natural fibres in this context has recently been reviewed by Hill et al [1], Summerscales et al [2, 3], Pandey et al [4], La Mantia and Morreale [5] and Ku et al [6]. Natural fibre composites have similar specific elastic moduli to Glass fibre Reinforced Plastics (GRP), and are perceived by the general public to be more environmentally friendly (i.e. natural fibres sequester carbon dioxide during the growth phase and dependent on the matrix may be biodegradable by composting). Despite the obvious benefits, their wide-spread use as reinforcements in structural composites has not materialised, at least, in part due to the high (batch-to-batch) variation in their mechanical properties. It is common practice in fibre reinforcement research to use fibre diameter (an average of several linear measurements) to compute the apparent fibre crosssectional area (CSA). Virk et al [7] have reported that significant variation in mechanical property measurements may arise from the use of this apparent CSA Page 2

3 which exaggerates the variation in mechanical properties (modulus and strength) as the fibre cross-section is neither circular nor uniform along the fibre length. Alternative techniques to determine fibre CSA include weight per unit length divided by density (but density measurement is not trivial and the weight of individual test samples is very small) or non-destructive imaging (but x-ray CT resolution is limited). The mechanical properties of a composite can be predicted using micromechanical models. These models use the mechanical properties of the individual constituent materials, the relative volume fractions and the fibre-reinforcement characteristics. Micromechanical models are frequently employed to optimise composite properties for a specific application, but the irregular cross-sectional area of natural fibres presents a further complication. Facca et al [8] have considered elastic modulus prediction of natural fibre reinforced thermoplastics and suggested that further study should include fibre angle and length distribution factors to improve predictions. This paper seeks to validate a novel methodology for tensile modulus and strength estimation of natural fibre composites through careful consideration of each parameter in the rule of mixtures (RoM) combined with the introduction of a fibre area correction factor (FACF). Modulus and strength measurements for a jute-epoxy composite are compared to the FACF model predictions, as well as to other micromechanical models that are frequently employed throughout in the literature. 2. Materials and Methods This study considers jute-epoxy composites using one layer of 880 g/m 2 carded quasi-unidirectional technical jute fibres from a single source in South Asia. The fibre dimensions [7], modulus, strength and fracture strain data for these fibres, assuming circular fibre cross-section, have been reported elsewhere [9-12]. The composite plate was manufactured using fibres from the same batch by resin infusion with a flow medium/distribution mesh [13]. The fibres for one plate were dyed black with Procion MX cold fibre reactive dye and the epoxy-matrix was pigmented white (West System 501 White Pigment for epoxy) to improve the contrast ratio between the fibres and matrix for optical microscopy and image analysis enabling fibre-reinforcement characterisation (i.e. volume fraction and fibre orientation distribution factor using images similar to Figure 1). Three further plates were manufactured with un-dyed fibres and un-pigmented resin with otherwise identical conditions. Page 3

4 A flat glass plate treated with release agent was used as a mould. The reinforcement was laid directly on the mould surface. To attempt to achieve a uniform test plate thickness a pre-released Perspex sheet wrapped in flash-tape was placed on top of the fibres and spacers were inserted between the glass plate and Perspex sheet to control the plate thickness (in practice, some thickness variation does arise where the flash tape is overlapped). This resin infusion arrangement was bagged and a vacuum of mbar absolute drawn before the resin was infused along the fibre direction. The infusion system was Sicomin TM 8100 epoxy resin and SD8822 hardener mixed at 100/31 ratio by weight [14]. The infused plates were cured for 24 hours at ambient temperature and then post-cured at 60 C for 16 hours in accordance with the resin manufacturer s recommendation. Tensile test specimens were machined from the composite plates (parallel to the fibre direction) using a diamond slitting saw. The specimens from the dyed/pigmented plate were then used to characterise composite fibre volume fraction and fibre angle distribution. The specimen ends were reinforced by gluing ±45 glass fabric-epoxy end tabs to encourage sample failure within the gauge length [15-18]. The specimens (the dyed/pigmented samples are referred to from this point forward as S01 to S06) were machined and tested according to ASTM D3039 standards [17]. The test specimen dimensions were: overall length = 250 mm, gauge length = 150 mm, width =~25 mm and mean thickness = ~3.5 mm. Tensile tests were performed at ambient temperature (10 C 1 and 70% RH) on an Instron 5582 universal testing machine with an Instron 100kN load cell (serial number UK185) at a constant cross-head speed of 2 mm/min. The tensile strain in the specimen was measured with a 50 mm gauge length Instron extensometer (serial number 77). Samples S01 and S03-S06 failed within the gauge length, but S02 failed near the tab. All modulus results are included as this parameter only depends on the initial slope of the stress strain curve but strength and fracture strain results for S02 are discarded. The tensile modulus, strength and failure strain for each specimen were calculated in accordance with ASTM D3039 and the respective failure modes were recorded. The axial strain range of 1000 µε to 3000 µε was used to calculate tensile modulus [17]. 1 This is the correct temperature: there was a heating system failure on the days the tests were conducted. Page 4

5 3. Micromechanical Models There are numerous micromechanical models in the literature for modulus and strength prediction of fibre-reinforced composites. Each model has inbuilt limitations and assumptions. These include a perfect bond between fibres and matrix, fibres are homogenous, linear elastic and regularly spaced in the composite, and the matrix is homogenous, linear elastic and void free. This section provides an overview of some of the most common micromechanical models. Their predictions are compared (in Section 6) to the experimental data for the jute-epoxy composites described in Section Tensile Modulus Prediction RULE OF MIXTURES (RoM): The simplest micromechanical model used to predict the composite elastic modulus parallel to the principal axis is the Rule of Mixture (RoM ). It is a parallel spring model based on the assumption that fibres and matrix will experience equal strain under loading in the fibre direction. It is assumed that the fibres can be anisotropic with different mechanical properties in the axial and transverse (radial) directions, whilst the matrix is isotropic [19]. The RoM equation [19-20] for the modulus of a continuous unidirectional fibre composite in the fibre direction is: E cl = E f V f +E m V m Equation 1 where E cl is composite modulus in the fibre direction, E f and E m are the fibre and matrix modulus respectively and V f and V m are the fibre and matrix volume fractions. Equation (1) provides an upper bound estimate when matrix and fibre axial Poisson s ratios are equal [21]. A more generalised form of the RoM is given by: E c = η l η o E f V f +E m V m Equation 2 where η l is the fibre length distribution factor (FLDF) and η o is the fibre orientation distribution factor (FODF). The FLDF assumes that the matrix and fibre remain elastic and the interface bond is perfect, and the shear stress at the fibre ends is maximum and falls to zero after half the critical length. Tensile stress at the fibre ends is assumed to be zero rising to a maximum after half the critical length. The FLDF can be calculated using the Cox equation [22]. The FODF enables fibre orientation to be considered using the Krenchel equation [23]: Page 5

6 η o = n a n cos 4 n Equation 3 where a n is the proportion of the fibres oriented at a fibre angle θ n relative to the applied load direction. The modulus of natural fibres has been reported to decrease with increasing fibre diameter [9, 24-25] and hence Summerscales et al [3] proposed a modification to Equation (2). The modification solely focuses on modulus with respect to diameter and hence, does not take account of the fact that natural fibres are not circular. The authors suggest the modulus of a composite reinforced with natural fibres can be more accurately estimated if an additional fibre diameter distribution factor, η d is included: E c = η d η l η o E f V f +E m V m Equation 4 The fibre diameter distribution factor (FDDF) can be taken as 1 (and hence Equation 4 defaults to the usual generalised RoM in Equation 2) when the fibre reinforcements have been well characterised, i.e. the modulus of the batch of fibres used has been measured independently. A deeper discussion of FDDF can be found in [26]. 3.2 Tensile Strength Prediction A common method used to predict the strength of unidirectional (continuous fibre) composites is to assume all the reinforcing fibres have identical strength, and the strain in the fibres and the matrix is equal during loading. If the fibre failure strain is less than the matrix failure strain then the fibre-reinforced composite longitudinal tensile strength (parallel to the fibres) can be estimated using the Kelly-Tyson [27] equation: c = f V f + ( m ) f V m Equation 5a or, at low fibre volume fractions: c < m(max) V m Equation 5b where σ c is the unidirectional composite tensile strength, σ f is the tensile strength of the fibres, (σ m ) εf is the matrix stress at a strain that is equal to the fibre failure strain and σ m(max) is the matrix tensile strength. The composite strength is assumed to be the highest of the two values calculated from Equations (5a) and (5b). The tensile strength of quasi-unidirectional composite loaded slightly off-axis to the fibre direction is given by [28]: c = c sec 2 f Equation 6 Page 6

7 where σ c is the quasi-unidirectional composite strength, σ c is the unidirectional composite tensile strength and θ f is the angle between the fibre axes and the composite loading. Natural fibres show large scatter in the tensile strength and therefore a mean fibre strength needs to be calculated from the fibre strength distribution. The tensile strength distribution of the natural fibres can be described by two-parameter Weibull distributions [10-12, 29-30]. However as there is no factor in the standard Weibull model to account for different fibre lengths and natural fibre strengths are dependent on the fibre gauge length [10, 11], either a Multiple Data Set (MDS) Weak-Link Scaling model (WLS) [10] or a Natural Logarithm Interpolation Model (NLIM) [11, 12] were used to predict the fibre strength. The mean fibre strength used in Kelly-Tyson model was predicted at the geometric mean fibre length of mm [10] for this batch of jute fibres. The calculated mean fibre strength using the MDS and the NLIM statistical models were 275 MPa and 298 MPa respectively. 4. Fibre Area Correction Factor (FACF) model The tensile properties of natural fibre reinforcements are obviously critical to the resultant composite properties. A natural fibre has an irregular cross-section shape and the cross-sectional area (CSA) varies along the fibre length. All existing models (see Section 3) assume an uniform CSA, except where the CSA is determined from weight, length and density. Many authors determine the mean of multiple projected fibre widths measured along the fibre length and use this diameter to calculate the apparent CSA assuming a circular cross-section [10-12, 29-30]. This method results in an inaccurate CSA [7] and hence inaccurate mechanical (modulus and strength) properties. To improve tensile modulus and strength predictions for natural fibre composites, it is postulated that a natural fibre model needs to compensate for the irregularity in the fibre cross-section. This compensation is included here as a fibre area correction factor (FACF denoted by the symbol κ) and is used to modify Equations (7) and (8), viz: E c = κη d η l η o E f V f +E m V m Equation 7 and c = κ f V f + ( m ) f V m Equation 8 Page 7

8 The mechanical properties for 785 jute fibres from the batch used to manufacture the composite plates have been reported elsewhere based on the apparent CSA method [9-12]. The true CSA of 106 jute fibres from the same batch of fibres (but not the same sample) was measured by Virk et al [7]. A comparison of the apparent CSA for the 785 fibres and the true CSA for the 106 fibres is shown in Figure 2. Lognormal fits [31, 32] are used to represent apparent and true CSA distributions this is consistent with reference [7]. The geometric means of the log-normal distributions (see [33]) are calculated for the apparent and true fibre CSA to be 2697 µm 2 and 1896 µm 2 respectively. The apparent CSA is an overestimate and hence fibre modulus and strength calculations for the fibres will be underestimated. The FACF (designated κ) compensates for the overestimate in the apparent CSA and is calculated as the ratio of the apparent CSA to the true CSA (i.e. κ = 2697/1896 = 1.42). The value for FACF above is from data generated during microscopical characterisation of a sample of >100 fibres from a single batch and, by default, includes variation along the fibre length as there was no selection of the analysed images for position. FACF may be (a) specific to particular varieties within a species of plant, (b) a function of the conditions during plant growth and (c) dependent on the age of the plant at harvest. In a separate study of fibres from the batch used here, the projected width of the fibre was measured at 50 intervals (i.e. every 3.6 during rotation through 180 ) from transverse sections of the fibre. The apparent cross-sectional area was calculated using half the projected width as the radius for circular cross-section. The mean FACF calculated by dividing the apparent CSA by the true CSA was found to be 1.375±0.485 (arithmetic mean) or (geometric mean) with a median for the dataset of The higher calculated value of 1.42 above from measurements transverse to fibres mounted on test cards probably arises because pressure applied to the fibre during attachment to the card will move the centre of gravity lower and hence generate higher apparent CSA. 5. Modulus and Strength: Measurements and Predictions Typical stress strain curves for the jute fibres used in this study are presented in reference 11. A typical stress strain curve for the composite is presented in Figure 3. Mechanical properties for the epoxy-matrix and jute fibres are presented in Table 1. This table also shows jute fibre data from the literature [35-42] to confirm the Page 8

9 reported values are consistent with the work of others. Table 2 shows typical experimental data (the six dyed/pigmented unidirectional jute-epoxy composite specimens) from the composite plates. The mean moduli and strengths were 8.19±0.6 GPa and 100.0±5.7 MPa respectively for the dyed/pigmented plate and 8.47±1.18 GPa and 101.0±17.2 MPa for the undyed/unpigmented plates respectively (i.e. the difference between the respective mean values is less than 50% of the lower standard deviation). In the model predictions, the fibre volume fractions and FODFs of the composite specimens were calculated from micrographs. Further details of these calculations are reported in Virk [34]. The FLDFs were calculated using the geometric mean of the measured fibre length of the 785 jute fibres (65.60 mm), and the mean apparent diameter (60.16 µm) was used to calculate the fibre cross-sectional area (assuming circular cross-section and uniform square packing). The well characterised fibres enable the FDDF to be taken as 1. Table 3 shows the modelling parameters for each specimen, the predicted modulus associated with each of the micromechanical models and the model error when compared to the empirical measurements. The Kelly-Tyson model [27] and FACF predictions for tensile strength are compared to the experimental measurements in Table 4. Equation 6 has not been used as the average angle of 7.4 increases the composite strength by just 1.7%, i.e. sec 2 (7.4 ) is The RoM, RoM, generalised RoM and FDDF models all underestimated the juteepoxy composite moduli. The Kelly-Tyson model significantly underestimates the composite strength in all cases. The FACF models proposed in Equations (7) and (8) offer the smallest error in the predicted plate (mean) modulus and strength and typically offer better predictions on a sample-by-sample basis. The improvement results from the FACF correction factor which takes account of the true fibre area to correct for the under-calculation of mechanical properties due to the apparent fibre CSA being larger than the true value. 6. Triangulation In order to triangulate these findings, data from other authors has been analysed. The jute fibre reinforced composite properties reported by different authors are presented in Table 5. The generalised RoM with Krenchel equation (Equations 2 and 3) was used to predict the elastic modulus of the composite using the reported fibre Page 9

10 volume fraction, fibre orientation factor and the form of reinforcement used. The jute fibre modulus used in the model was 27.8 GPa taken as the average of all the experimentally measured readings given in Table 1 (excluding 55.5 and 45 GPa as they are estimated from the composites). The calculated composite moduli are reported in Table 6. In each case (except one) it is observed the calculated modulus is lower than the experimental modulus. Assuming that the Fibre Area Correction Factor (FACF) for the other batches of the jute fibres used in [37, 41-46] is similar to that reported here (1.42) and calculating the composite modulus using Equation 7 (Table 6), it was observed that the error in the predicted composite modulus is reduced (for all but two cases [44]). The large scatter could arise from any of the factors listed in the penultimate paragraph of 4 and from differences in experimental technique between research groups. The authors of this paper propose that the value of FACF should be determined independently in other locations to establish whether it can be used as a constant for all batches of jute fibre. Page 10

11 7. Conclusion It is common practice in the composite sector to measure fibre cross-sectional area using linear measurements of fibre diameter and an assumption of circular crosssection. This method overestimates the CSA and hence results in low values of key mechanical properties (i.e. modulus and strength) of natural fibres. A fibre area correction factor (FACF) is proposed and used in the rules-of-mixture to predict the tensile modulus and strength of experimental jute fibre reinforced composites manufactured from well characterised fibres. The FACF has been shown to improve the prediction of tensile modulus and strength for both the authors samples and for other experiments reported in the scientific literature. Acknowledgements ASV is grateful to the University of Plymouth for a scholarship to pursue his doctorate. The authors would like to thank a former colleague Joe Ellison for obtaining the fibres from IJIRA/IJSG. This paper was presented at (a) International Seminar on Strengthening of Collaboration for Jute, Kenaf and Allied Fibres Research and Development, Secretariat of the International Jute Study Group (IJSG) and the Common Fund for Commodities (CFC), Dhaka Bangladesh, June 2011 and (b). 4th International Conference on Sustainable Materials, Polymers and Composites (EcoComp), Birmingham England, July Page 11

12 References [1] C Hill and M Hughes, Natural fibre reinforced composites opportunities and challenges, Journal of Biobased Materials and Bioenergy, 2010, 4, [2] J Summerscales, N Dissanayake, A Virk and W Hall, A review of bast fibres and their composites. Part 1 Fibres as reinforcements, Composites Part A: Applied Science and Manufacturing, 2010, 41(10), [3] J Summerscales, N Dissanayake, A Virk and W Hall, A review of bast fibres and their composites. Part 2 Composites, Composites Part A: Applied Science and Manufacturing, 2010, 41(10), [4] JK Pandey, SH Ahn, CS Lee, AK Mohanty and M Misra, Recent advances in the application of natural fiber-reinforced composites, Macromolecular Materials and Engineering, 2010, 295, [5] FP La Mantia and M Morreale, Green composites: a brief review, Composites Part A: Applied Science and Manufacturing, June 2011, 42(6), [6] H Ku, H Wang, N Pattarachaiyakoop and M Trada, A review on the tensile properties of natural fiber reinforced polymer composites, Composites Part B: Engineering, June 2011, 42(4), [7] A S Virk, W Hall and J Summerscales, Physical characterisation of jute technical fibres: fibre dimensions, Journal of Natural Fibres, 2010, 7(3) [8] A G Facca, M T Kortschot and N Yan, Predicting the elastic modulus of natural fibre reinforced thermoplastics, Composites Part A: Applied Science and Manufacturing, 2006, 37(10), [9] A S Virk, W Hall and J Summerscales, Failure strain as the key design criterion for fracture of natural fibre composites, Composites Science and Technology, June 2010, 70(6), [10] A S Virk, W Hall and J Summerscales, Multiple Data Set (MDS) weak-link scaling analysis of jute fibres, Composites Part A: Applied Science and Manufacturing, November 2009, 40(11), [11] A S Virk, W Hall and J Summerscales, Tensile properties of jute fibres, Materials Science and Technology, October 2009, 25(10), Page 12

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16 List of captions for figures Figure 1: Typical cross-section (above: used to determine fibre volume fraction) and plan-view (below: used to determine fibre orientation distribution factor) for the dyed/pigmented plate. Figure 2: Apparent and true fibre area distributions. Figure 3: (a) Typical jute-fibre reinforced composite stress-strain curve; (b) Typical axial and transverse strain gauge measurements from paired strain gauges on opposite sides of the specimen. List of captions for tables Table 1: Matrix and Fibre mechanical properties Table 2: Jute-epoxy composite: mechanical properties (measured) Table 3: Jute-epoxy composite: modulus prediction (and error [%]) Table 4: Jute-epoxy composite: tensile strength prediction (and error [%]) Table 5: Reported elastic properties of jute fibre reinforced composite Table 6: Estimated composite modulus using Equation 2 and Equation 7 with the error in the estimated modulus Page 16

17 Table 1. Matrix and fibre mechanical properties Density Modulus Strength Failure Poisson's [kg/m 3 ] [GPa] [MPa] Strain [%] Ratio Reference Matrix % 0.35 [14] Jute ~ %-1.8% - [9-12] % - [35] % - [36] Jute %-1.8% - [37] Modulus % - [38] from %-1.6% - [39] literature [40] [41] # [42]* ~ The modulus is calculated as the mean of all the moduli for the 785 jute fibres assuming the fibres have circular cross-section. Fibre properties calculated assuming circular cross-sectional area from multiple linear measurements. # Composite experimental properties (tested at different fibre volume fraction) used to estimate modulus and strength by extrapolating the respective properties to a fibre volume fraction of unity. * Composite experimental properties used to estimate modulus and strength by back calculating using rule of mixture and respective fibre volume fraction and fibre orientation factor. Page 17

18 Table 2: Jute-epoxy composite: mechanical properties (measured) Width Thickness Modulus Strength Sample [mm] [mm] [GPa] [MPa] Failure Strain [%] S % S S % S % S % S % PLATE % Page 18

19 Sample Table 3: Jute-epoxy composite: modulus prediction (and error [%]) relative to the mean experimental value of 8.18 GPa from Table 2 V f [%] RoM_PARALLEL RoM_GEN FACF κ η l η o η d Equation (1) Equation (2)* Equation (7) [GPa] [GPa] [GPa] S % (-21.2%) 6.39 (-28.9%) 8.15 (-9.2%) S % (-10.2%) 5.70 (-29.2%) 7.18 (-10.7%) S % (-5.9%) 6.51 (-21.4%) 8.35 (+0.9%) S % (-1.9%) 7.05 (-9.45%) 9.14 (+17.3%) S % (-1.5%) 6.45 (-11.9%) 8.25 (+12.6%) S % (-15.9%) 6.54 (-24.8%) 8.38 (-3.7%) PLATE 18.9% (-9.3%) 6.44 (-21.3%) 8.24 (+0.7%) * The ROM-GEN from Equation (2) and FDDF from Equation (4) are identical as η d = 1 for the well-characterised fibres used in this study. Page 19

20 * Table 4: Jute-epoxy composite: tensile strength prediction (and error [%]) Kelly-Tyson Kelly-Tyson FACF FACF Sample (NLIM) (MDS) (NLIM) (MDS) Equation (5) Equation (5) Equation (8) Equation (8) [MPa] [MPa] [MPa] [MPa] S (-28.1%) 69.7(-33.6%) 97.4(-7.2%) 89.9(-14.3%) S (-) 71.1(-) 99.7(-) 92.0(-) S (-16.6%) 76.7(-23.0%) 108.5(+9.0%) 100.2(+0.6%) S (-20.7%) 78.2(-26.8%) 110.8(+3.8%) 102.3(-4.2%) S (-18.9%) 71.1(-25.0%) 99.6(+5.0%) 91.9(-3.0%) S (-17.1%) 72.1(-23.5%) 101.2(+7.4%) 93.4(-0.8%) PLATE 79.2(-20.8%) 73.1(-26.9%) 102.9(+2.8%) 95.0(-5.1%) Page 20

21 Table 5: Reported elastic properties of jute fibre reinforced composite Matrix Volume Weight Reinforcement Orientation Modulus Strength Failure Strain Poisson's Reference Fraction Fraction form Factor [GPa] [MPa] [%] Ratio Epoxy* 40% - Fibre yarn # 1* [37] Epoxy 35% 33% ± ± % - [43] Polyester 24% 22% ± ± % - [43] Polyester 13% - Sliver [41] Polyester 27% - Sliver [41] Polyester 31% - Sliver [41] Polyester 37% - Sliver [41] Polyester 43% - Sliver [41] Polyester 16% - Chopped Strand ± ± % ± 0.11% - [42] Polyester 45% - Fabric (20x12)^ ± ± [44] Polyester 45% - Fabric (20x12)^ ± ± [44] Polyester 36% - Fabric (22x12)^ $ [45] Polyester 36% - Fabric (22x12)^ $ [45] Polyester 29.5% [46] * Quasi-unidirectional $ Notched samples Page 21

22 Table 6: Estimated composite modulus using Equation 2 and Equation 7 with the error in the estimated modulus Matrix Matrix Modulus Volume Fraction Reinforcement Form Orientation Factor (OF) Twist Angle Twist - OF Final OF Modulus [GPa] Equation 2 [GPa] Eq. 2 Error Equation 7 [GPa] Eq.7 Error Reference Epoxy 3.3* 40% Fibre yarn # % % [37] Epoxy % % % [43] Polyester % % % [43] Polyester % Sliver % % [41] Polyester % Sliver % % [41] Polyester % Sliver % % [41] Polyester % Sliver % % [41] Polyester % Sliver % % [41] Polyester % Chopped Strand % % [42] Polyester % Fabric (20x12) ^ Polyester % Fabric (20x12) ^ Polyester % Fabric (22x12) ^ Polyester % Fabric (22x12) ^ % % [44] % % [44] % % [45] % % [45] Polyester % % % [46] * Resin properties taken from Rudd et al [47] for the specific resin / hardener system quoted by Gassan et al [37]. # Yarn twist angle (23.7 ) was calculated from the specified twist per meter and tex assuming a circular cross-section for the yarn and an average density of 1350 kg/m 3. ^ The yarn twist angle is assumed to be similar to that of yarn used by Gassan et al [37]. Page 22

23 Figure 1: Typical cross-section (above: used to determine fibre volume fraction) and plan-view (below: used to determine fibre orientation distribution factor) for the dyed/pigmented plate. Page 23

24 Figure 2: Apparent and true fibre area distributions. Page 24

25 Figure 3: (a) Typical jute-fibre reinforced composite stress-strain curve; (b) Typical axial and transverse strain gauge measurements from paired strain gauges on opposite sides of the specimen. Page 25