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, Australiac. 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.

Fibrestrength

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 predictionsassessed using GOFN(Anderson-Darling Goodness Of Fit Numbers).

• lowest GOFN total indicates ‘best fit’

AS Virk, W Hall and J SummerscalesMultiple data set (MDS) weak-link scaling analysis of jute fibresComposites Part A: Applied Science and Manufacturing, November 2009, 40(11), 1764-1771.

Weak-link scaling: strengthStandard-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 improvementin 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 SummerscalesModelling tensile properties of jute fibresMaterials Science and Technology,January 2011, 27(1), 458-460.

Effect of fibre diameterEasy to select for length, but not for diameter:

Effect of fibre diameterTo 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 SummerscalesStrain 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 onhorizontal axis and fitted by various shapes

True fibre cross-sectional area

• 106 individual jute technical fibres measured

• true fibrecross-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 SummerscalesPhysical characterisation of jute technical fibres:fibre dimensionsJournal 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 andthe measured true fibre area 1896 µm2

• fibre area correction factor = 1.42

AS Virk, W Hall and J SummerscalesThe tensile properties of Jute/Epoxy UD compositein 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 specimen7.81 mm x 2.95 mm (11440 x 4324 pixels)

• ηo: 46 micrographs from 6 tensile test specimens27.60 mm x 12.16 mm (19900 x 8764 pixels)

Image analysis• Matlab R2008a digital environment:

– micrograph images were converted to8-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 pointsseeking 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 wallinner layer, θ =60-90°

< S2: secondary wallmiddle layer, θ =10-30°

< S1: secondary wallouter layer, θ =50-70°

< primary wall

J Summerscales, W Hall and AS VirkA fibre diameter distribution factor (FDDF) for natural fibre compositesJournal 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 factorηd is a fibre diameter distribution factor (assumed = 1 here)

Composite parameters (dyed plate)• Κ (FACF) 1.42

• ηd and ηl 1

• ηo (FODF = cos4θ) 0.967mean 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 predictionsRoM without

κRoM 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 BledzkiUD/epoxy 9.5 (-37%) 12.7 (-16%) 15

Shah and LakkadUD/epoxy 11.7 (-22%) 15.6 (+4%) 15

Shah and LakkadUD/UPE 9.6 (-21%) 12.4 (+1%) 12.2

Clark and AnsellCSM/polyester 4.2 (-20%) 4.9 (-7%) 5.2

Ahmed et alfabric/polyester 7.2 (-20%) 9.0 (+0.2%) 9.0

Ahmed et alfabric/polyester 5.2 (-20%) 6.2 (-5%) 6.5

bar length percentage error

Conclusions• use of the apparent fibre diameter

from linear measurementsunderestimates fibre properties

• a fibre area correction factor κin rules-of-mixture significantly improves prediction of mechanical properties

• References and hyperlinks athttp://www.tech.plym.ac.uk/sme/acmc/Jute.htm