A new rule of mixtures for
natural fibre composites
Amandeep Singh Virk a, Wayne Hall b, John Summerscales c
a. University of Queensland, Australia
b. Griffith School of Engineering, Australia
c. ACMC Plymouth, United Kingdom
Structure of talk
• jute fibres
– fibre tensile tests
– statistical modelling (no equations )
• composites
– characterisation
– new parameters
– new rule of mixtures
Jute fibres
• Corchorus capsularis. L. - white jute
• Corchorus olitorius L. - Tossa jute.
– second most common natural fibre, after cotton,
cultivated in the world
– grown in Bangladesh, Brazil, China, India, Indonesia
– our experiments use a well-characterised batch of fibres of
unknown provenance from a single source in South Asia
Fibre tensile tests
•
•
•
•
adapted Grafil Test Method 101.13
100 tests at each of 6, 10, 20, 30 and 50 mm long
50 tests at each of 100, 200, 300 mm
mean Young’s modulus in range 26-34 GPa
– assuming circular cross-section (for the moment – but wait!)
AS Virk, W Hall and J Summerscales,
The tensile properties of jute fibres,
Materials Science and Technology,
October 2009, 25(10), 1289-1295.
Fibre
strength
and
failure strain
Fibre modulus vs length
• mean Young’s modulus in range 26-34 GPa
Fibre strength vs length
• strength reduces with increasing length
Failure strain vs length
• failure strain reduces with increasing length
Weak-link scaling predictions
• reference data at single fibre length (point estimate).
• Weibull distribution parameters calculated
• maximum likelihood parameter estimation method
used to quantify the variation.
• single parameter (standard) and
Multiple Data Set (MDS) weak link scaling predictions
assessed using GOFN
(Anderson-Darling Goodness Of Fit Numbers).
• lowest GOFN total indicates ‘best fit’
AS 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), 1764-1771.
Weak-link scaling: strength
Standard-WLS
MDS-WLS
Weak-link scaling: strain ε’
Standard-WLS
MDS-WLS
Weak-link scaling predictions
• weak link scaling should be performed with
– at least two points, preferably three, and
– with fibre length at two extreme and
a third point near the mean fibre length.
MDS Weak-link Model
ΣGOFN strength
ΣGOFN ε’
6 and 300
41.4
58.3
6, 50 and 300
35.3
33.8
6, 100 and 300
34.8
48.2
All (6 mm … 300 mm)
33.0
32.1
Natural logarithm
interpolation model (NLIM)
• analysis for fibres up to 50 mm long
extended to include fibres of lengths ≤ 300 mm
• NLIM produces a significant improvement
in predicted properties cf MDS-WLS model.
• GOFN confirms this finding
• Anderson–Darling GOFN as MDS/NLIM
= 2.74 for strength and = 2.23 for strain.
AS Virk, W Hall and J Summerscales
Modelling tensile properties of jute fibres
Materials Science and Technology,
January 2011, 27(1), 458-460.
Effect of fibre diameter
Easy to select for length, but not for diameter:
Effect of fibre diameter
To permit comparisons, data is grouped:
Use ε’ for design (not σ’)
Coefficient of variation lower for failure strain than for strength
AS Virk, W Hall and J Summerscales
Strain as the key design criterion for failure of natural fibre
composites, Composites Science and Technology,
June 2010, 70(6), 995-999
… but the fibre CSA irregular
Confocal Laser Scanning
Microscope (CLSM) images
Rotated to max length on
horizontal axis and fitted by various shapes
True fibre cross-sectional area
• 106 individual
jute technical
fibres measured
• true fibre
cross-sectional
area distribution
plotted
True fibre cross-sectional area
• log-normal
plot of area
distributions
for 106 fibres
True fibre cross-sectional area
• Error in the area
measurement
based on
assumed shape
AS Virk, W Hall and J Summerscales
Physical characterisation of jute technical fibres:
fibre dimensions
Journal of Natural Fibres, 2010, 7(3), 216-228.
True fibre cross-sectional area
• true cross-sectional area distribution overlaid
on the apparent fibre area distribution (left)
• location parameter of the apparent fibre area distribution, 7.90,
replaced with that of true fibre area distribution, 7.55 (right)
Fibre area correction factor, κ
• geometric means for
the apparent fibre area 2697 µm2 and
the measured true fibre area 1896 µm2
• fibre area correction factor = 1.42
AS Virk, W Hall and J Summerscales
The tensile properties of Jute/Epoxy UD composite
in submission for publication
so now composites …
• jute fibres dyed black with
Procion MX cold fibre reactive dye
• fibre tensile tests confirm
no significant change in moduli or strengths
• quasi-UD composite plates made by
resin infusion with a flow medium
– Three plates with natural fibre and no pigment
– One plate dyed fibres and white pigment in resin
Microscopy
• samples from
tensile specimens
• Vf: 5 micrographs
from each specimen
7.81 mm x 2.95 mm
(11440 x 4324 pixels)
• ηo: 46 micrographs
from 6 tensile test
specimens
27.60 mm x 12.16 mm
(19900 x 8764 pixels)
Image analysis
• Matlab R2008a digital environment:
– micrograph images were converted to
8-bit (0-255) greyscale images
– contrast of the greyscale images enhanced by
scaling intensities to cover full dynamic range
• Vf from thresholded intensity histogram
• ηo uses mask rotated at 22000 seed points
seeking minimum intensity at each angle
Fibre diameter distribution factor
• ηd = complex function of
fibre structure
• well-characterised fibres used
in our study, so ηd = 1
< S3: secondary wall
inner layer, θ =60-90°
< S2: secondary wall
middle layer, θ =10-30°
< S1: secondary wall
outer layer, θ =50-70°
< primary wall
J Summerscales, W Hall and AS Virk
A fibre diameter distribution factor (FDDF) for natural fibre composites
Journal of Materials Science, 2011, 46(17), 5876-5880.
equations:
• modulus
 Ec =
ηl ηo Vf Ef + Vm Em
• strength
 σ’c =
ηl ηo Vf σ’f + Vm σm*
where:
σm* is failure stress in matrix at failure of the fibres
other parameters as per normal usage
New equations:
• modulus
 Ec = κ ηd ηl ηo Vf Ef + Vm Em
• strength
 σ’c = κ ηd ηl ηo Vf σ’f + Vm σm*
where:
κ is a fibre area correction factor
ηd is a fibre diameter distribution factor (assumed = 1 here)
Composite parameters (dyed plate)
• Κ (FACF)
1.42
• ηd and ηl
1
• ηo (FODF = cos4θ)
0.967
mean fibre angle 7.4° ± 18°
• fibre volume fraction 18.9 % ± 3.9 %
• tensile modulus
8.18 ± 0.6 GPa
• tensile strength
100.0 ± 5.7 MPa
RoM predictions
RoM without κ
RoM with κ
Experimental
RoM/xptl
Modulus (GPa)
7.43
8.24
8.18
+7%
Strength (MPa)
75.2
95.0
100.0
-5%
Triangulation (external data)
MODULUS (GPa)
RoM without κ
RoM with κ
Experimental
Gassan and Bledzki
UD/epoxy
9.5 (-37%)
12.7 (-16%)
15
Shah and Lakkad
UD/epoxy
11.7 (-22%)
15.6 (+4%)
15
Shah and Lakkad
UD/UPE
9.6 (-21%)
12.4 (+1%)
12.2
Clark and Ansell
CSM/polyester
4.2 (-20%)
4.9 (-7%)
5.2
Ahmed et al
fabric/polyester
7.2 (-20%)
9.0 (+0.2%)
9.0
Ahmed et al
fabric/polyester
5.2 (-20%)
6.2 (-5%)
6.5
bar length  percentage error
Conclusions
• use of the apparent fibre diameter
from linear measurements
underestimates fibre properties
• a fibre area correction factor κ
in rules-of-mixture significantly improves
prediction of mechanical properties
• References and hyperlinks at
http://www.tech.plym.ac.uk/sme/acmc/Jute.htm