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 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 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),

Fibre strength and failure strain

Fibre modulus vs length mean Young’s modulus in range 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),

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 Σ GOFN strength Σ GOFN ε’ 6 and , 50 and , 100 and All (6 mm … 300 mm)

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),

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),

… 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),

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 µm 2 and the measured true fibre area 1896 µm 2 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 V f : 5 micrographs from each specimen 7.81 mm x 2.95 mm (11440 x 4324 pixels) η o : 46 micrographs from 6 tensile test specimens mm x 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 V f from thresholded intensity histogram η o uses mask rotated at seed points seeking minimum intensity at each angle

Fibre diameter distribution factor η d = complex function of fibre structure well-characterised fibres used in our study, so η d = 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),

equations: modulus  E c = η l η o V f E f + V m E m strength  σ’ c = η l η o V f σ’ f + V m σ m* where: σ m* is failure stress in matrix at failure of the fibres other parameters as per normal usage

New equations: modulus  E c = κ η d η l η o V f E f + V m E m strength  σ’ c = κ η d η l η o V f σ’ f + V m σ m* where: κ is a fibre area correction factor η d is a fibre diameter distribution factor (assumed = 1 here)

Composite parameters (dyed plate) Κ (FACF)1.42 η d and η l 1 η o (FODF = cos 4 θ)0.967 mean fibre angle 7.4° ± 18° fibre volume fraction18.9 % ± 3.9 % tensile modulus 8.18 ± 0.6 GPa tensile strength100.0 ± 5.7 MPa

RoM predictions RoM without κ RoM with κ ExperimentalRoM/xptl Modulus (GPa) % Strength (MPa) %

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