Variability in, and property prediction for, natural fibre composites
John Summerscalesa, Amandeep Singh Virkb and Wayne Hallb
(a) Plymouth University – UK, (b) Griffith University – Australia
Presented at:
 21st Anniversary Conference of the Bio-Environmental Polymer Society,
Coventry, 18-20 September 2013, keynote paper.
 1st Intl. Conf.: Natural Fibers: sustainable materials for advanced applications
(ICNF2013), Guimarães – Portugal, 09-11 June 2013.
 9th International Conference on Composite Science and Technology (ICCST_9):
2020 scientific and industrial challenges, Sorrento – Italy, 24-26 April 2013 (this
text).
ABSTRACT
Natural fibres are perceived as a sustainable reinforcement for polymer matrix
composites but reported mechanical properties have high variability. The authors
have conducted experiments using a single batch of jute fibres and established that the
coefficient of variation (CoV) in strain-to-failure is lower than the CoV for modulus or
strength [1]. This characteristic appears to arise from the (incorrect) assumption of
circular fibre cross-section. Weibull statistics were used to compare the apparent
cross-sectional area derived from the diameter measured by optical microscopy
transverse to the fibre to the true cross-sectional area measured from sectioned fibres.
For the jute fibres studied, the above ratio can be used as a fibre area correction factor
(FACF) in the rule of mixtures to generate improved prediction of the composite
mechanical properties [2]. This paper will report comparisons between predictions
with, and without, the FACF and experimental values for the authors' quasiunidirectional natural fibre composites data. Further analysis considers results from
other research groups where sufficient data is available to make the comparison. The
modified rules-of-mixture generally result in significantly better predicted values for
the modulus and strength of natural fibre reinforced polymer matrix composites.
INTRODUCTION
In 1987, the World Commission on Environment and Development [1] served
notice that the time had come for a marriage of economy and ecology. Governments
and their people should take responsibility not just for environmental damage, but for
the policies that cause that damage. In the intervening years, there has been an
increasing interest in the adoption of technologies which could minimise the
environmental burdens on the planet. This will be especially important if the current
world leaders continue to seek economic growth fuelled by unrestrained growth in the
human population of the planet.
In the composites industry, natural fibres are seen as a “green” alternative to
reinforcements manufactured either at high temperatures (e.g. melting of glass or
pyrolysis of polymer fibres to produce carbon fibres) or using aggressive chemicals
(e.g. acid solvents for aramids). The authors of this paper have reviewed natural fibres
reinforcements [2], natural fibre reinforced polymer (NFRP) composites [3],
modelling of NFRP [4], manufacturing methods for NFRP [5] and life cycle
assessment of NFRP [6]. A more comprehensive list of books and review papers on
NFRP can be found at [7].
VARIABILITY
Natural fibres are perceived to have greater variability than man-made fibres,
due to the variety of sub-species within a particular plant family, their production in
open agricultural systems exposed to the weather, the harvesting and fibre separation
technologies and the dependence of properties on the moisture content of the fibre.
However, perhaps the most critical contributor to the reported variability of
mechanical properties lies in assumptions made in the determination of moduli and
strengths. It is common practice to measure the apparent fibre diameter under the
microscope and use the assumption of circular cross section to calculate a crosssectional area (CSA). In reality, natural fibres are normally polygonal in cross section
and when prepared for microscopy are expected to lie with their centres of gravity at
the lowest position which will mean the measurement is likely to indicate the length of
the greatest chord of the section. When the resulting over-estimate of the CSA is used
to calculate elastic moduli or strengths, it is inevitable that those mechanical property
values will be lower than would be obtained using the true CSA.
Virk et al [8] examined tensile test data from 785 individual tests on jute fibre
from a single batch using the “apparent” diameter as the basis for the calculation of
CSA. The coefficients of variation for failure strain were consistently lower than the
CoV for fracture stress (strength) as shown in Figure 1. The former is independent of
CSA whilst the latter is a dependent parameter.
Virk et al [9] measured the ‘true’ CSA of 106 jute fibres and made a comparison
with the ‘apparent’ CSA of 785 fibres from the same batch of jute fibres. Log normal
fits were used to represent the apparent and the true CSA distributions. The geometric
means of the log normal distributions were calculated and found to be 2697 μm2 for
the apparent CSA and 1896 μm2 for the true CSA. The ratio of apparent/true CSA is
designated κ and now known as the Fibre Area Correction Factor (FACF). In the case
of this batch of jute fibre, κ = 1.42. As a consequence of the method by which the
parameter was determined, variation along the fibre length is embedded in the data as
there was no selection of the analysed images for position within the plant stem. The
FACF may be specific to particular varieties within a species of plant, a function of the
conditions during plant growth and dependent on the age of the plant at harvest.
Figure 1: CoV for strength and fracture strain plotted against fibre diameter
In a separate study of fibres from the above batch, 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 CSA was calculated using the projected
width as the diameter of the 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 1.297 (geometric mean) with a median for the dataset of 1.303. The higher
calculated value of 1.42 above from measurements transverse to fibres mounted on
test cards.
Aslan et al [10] measured cottonised flax fibres to determine the apparent CSA
using optical microscopy transverse to the fibre axis (399 fibres) and the true CSA
using electron microscopy of polished embedded samples (585 samples). Their
reported data gives a fibre area correction factor κ of 1.39 (327 and 236 µm2
respectively). For the same fibre set, the mean lumen content was 1.6% with >85% of
fibres having a lumen content <1%.
Thomason et al [11] measured the CSA of individual flax and sisal fibres using
transverse optical microscopy of fibres mounted on cards and optical microscopy of
polished embedded cross-sections. CSA values obtained from the respective fibre
“diameter” measurements were on average more than double the values obtained from
direct observation of the fibre cross sections, although some fibres did have high
aspect ratios. Linear fits of data on plots of cross-section calculated from apparent
diameter against true cross-section had slopes of 2.55 (flax) and 1.99 (sisal) albeit with
R2 of 0.46 and 0.43 respectively. Twelve individual fibres from each plant were
measured at ten positions along a 21 mm length of each fibre. The variation along the
length of each individual fibre was significantly lower than the difference in average
CSA observed between fibres. The average CSA at the centre or at the ends of the
gauge length were greater than the overall respective means and within a range of
<15% CSA implying that CSA is independent of position along the fibre.
TABLE I: Fibre area correction factors (FACF) derived from various sources
Fibre
FACF
Reference
Jute (mounted on test cards)
1.42
[9]
Jute (arithmetic mean)
1.375±0.485
[9]
Jute (geometric mean)
1.297
[9]
Jute (median)
1.303
[9]
Flax
2.55
[11]
Cottonised flax
1.39
[10]
Sisal
1.99
[11]
PREDICTION OF MECHANICAL PROPERTIES
The mechanical properties of fibre-reinforced composites can be
estimated/predicted using the rules-of-mixture (RoM).
Virk et al [9] and
Summerscales [12] have recently proposed the addition of two new parameters into
the basic RoM as in Equations (1) and (2):
Ec = κ ƞd ƞl ƞo Vf Ef + Vm Em
(1)
σc' = κ σf' Vf + σm* Vm
(2)
where Ex = elastic modulus, Vx = component volume fraction, ƞd = (new) fibre
diameter distribution factor (FDDF) [12], ƞl = fibre length distribution factor (FLDF),
ƞo = fibre orientation distribution factor (FODF), κ = (new) fibre area correction factor
(FACF, see above), σx' is strength, σm* = stress in the matrix at the failure strain of the
fibre and the subscript x indicates composite (c), fibre (f), matrix (m) or voids (v) with
Vf + Vm + Vv = 1.
To verify the predictions from Equations (1) and (2), a set of experimental data
was used with fibre volume fractions and fibre orientation distribution factors for the
composite specimens (manufactured with the same batch of fibre as used for the fibre
area correction factor data above) calculated from micrographs. Further details of
these calculations are reported by Virk [13]. Fibre length distribution factors (FLDF)
were calculated using the geometric mean of the measured fibre length of the 785 jute
fibres (65.60 mm). The mean apparent diameter (60.16 μm) was used to calculate the
fibre CSA (assuming circular cross-section and uniform square packing). The well
characterised fibres enable the fibre diameter distribution factor (FDDF) to be taken
as 1. The full data set is presented in reference [9].
The RoM║, generalised RoM and FDDF models (all without FACF)
underestimated the jute/epoxy composite moduli. The Kelly–Tyson model (without
FACF) significantly underestimated the composite strength in all cases. The FACF
models proposed in Equations (1) and (2) offered the smallest error in the predicted
plate (mean) modulus and strength and typically offered better predictions on a sample
by sample basis. The improvement results from the FACF 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.
Data on jute fibre reinforced composites from publications by other authors were
analysed to triangulate these findings (Figure 2). In all but one case, it was observed
that the calculated modulus (without FACF) was lower than the experimental
modulus. Assuming that the FACF for the other authors’ jute fibres is similar to that
reported in the present paper and calculating the composite modulus using Equation
(1), it was observed that the error in the predicted composite modulus was reduced (for
all but two cases). The large scatter could arise from any of the factors above and
from the differences in experimental technique between research groups.
The authors of the present paper propose that the value of FACF should be determined
independently in other locations to establish whether the value above can be used as a
constant for all batches of jute fibre.
160.0
%
140.0
Old RoM
RoM + κ
120.0
100.0
Experimental reference data point
80.0
60.0
40.0
20.0
0.0
82a 82c 82b 82d 82e
83
84
85
86b 86a
55
87b 87a 88a 88b
Figure 2: Comparison of predicted moduli from rule of mixtures without (left/light
grey) and with (right/dark grey) the fibre area correction factor. The x-axis numbers
are the respective references from [3] from which the data was extracted for analysis
with the letters indicating individual data sets. Set 55 is from the authors of this paper).
CONCLUSIONS
The commercial use of natural fibres as reinforcement for composites is
constrained by a perceived high variability in strength. An examination of tensile test
data from 785 individual tests reveals that the coefficient of variation (CoV) for failure
strain is consistently lower than the CoV for fracture stress (strength). Hence, failure
strain is the more consistent failure criterion. The use of optical microscopy to
determine fibre “diameter” and hence cross-sectional area may explain this difference
as the strength is normally calculated from an assumed CSA area. The authors
recommend the use of failure strain as the key design criterion for natural fibre
composites in order to improve reliability in the design of natural fibre-reinforced
composites.
Further the assumption of a circular cross-section for natural fibres overestimates
the CSA and hence results in low values of key mechanical properties (i.e. modulus
and strength) of natural fibres. A FACF is proposed and used in the RoM 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 the
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 J. Ellison for obtaining
the fibres from IJIRA/IJSG. Data in the present paper was presented at the
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, 8–9 June
2011 and the 4th International Conference on Sustainable Materials, Polymers and
Composites (EcoComp), Birmingham, UK, 6–7 July 2011.
REFERENCES
1. World Commission on Environment and Development. 1987. Our Common Future.
Oxford Paperbacks, ISBN: 978-0-19-282080-8.
2. Summerscales, J., N. Dissanayake, W. Hall and A.S. Virk. 2010. “A review of bast fibres
and their composites. Part 1: fibres as reinforcements”, Composites Part A: Applied
Science and Manufacturing, 41(10):1329-1335.
3. Summerscales J., N. Dissanayake, W. Hall and A.S. Virk. 2010. “A review of bast fibres
and their composites. Part 2: composites”, Composites Part A: Applied Science and
Manufacturing, 41(10):1336-1344.
4. Summerscales, J., A.S. Virk and W. Hall. 20103. “A review of bast fibres and their
composites. Part 3: modeling”, Composites Part A: Applied Science and Manufacturing,
44(1):132-139.
5. Summerscales, J. and S. Grove. 2013. “Manufacturing methods for natural fibre
composites”, Chapter 16 in Handbook of Natural Fibre Composites: properties,
processes, failure and applications, A. Hodzic and R. Shanks, eds., Woodhead Publishing,
Cambridge, in press.
6. Dissanayake, N.P.J. and J Summerscales, Life Cycle Assessment for natural fibre
composites, Chapter 8 in Green Composites from Natural Resources, V.K. Thakur, ed.,
Taylor and Francis Group LLC, USA, ISBN 978-1-4665-7069-6, in press.
7. Summerscales, J. 2013. Virtual book on bast fibres and their composites,
http://www.tech.plym.ac.uk/sme/mats324/bast_book.htm.
8. Virk, A.S., W. Hall and J. Summerscales. 2010. “'Failure strain as the key design criterion
for fracture of natural fibre composites”,' Composites Science and Technology, 2010,
70(6): 995 – 999.
9. Virk, A.S., W. Hall and J. Summerscales. 2012. “Modulus and strength prediction for
natural fibre composites”, Materials Science and Technology, 28(7): 864-871
10. Aslan, M., G. Chinga-Carrasco, B.F. Sørensen and B. Madsen. 2011. “Strength
variability of single flax fibres”, Journal of Materials Science, 2011, 46(19), 6344-6354.
11. Thomason, J.L., J. Carruthers, J. Kelly and G. Johnson. 2011. “Fibre cross section
determination and variability in sisal and flax and its effects on fibre performance
characterisation”, Composites Science and Technology, 71(7):1008-1015.
12. Summerscales, J., W Hall and AS Virk. 2011. “A fibre diameter distribution factor
(FDDF) for natural fibre composites”. Journal of Materials Science, 46(17):5876-5880.
13. Virk, A.S. 2010. Numerical models for natural fibre composites with stochastic
properties, PhD thesis, University of Plymouth.