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A new rule of mixtures for natural fibre composites

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

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A new rule of mixtures for natural fibre composites

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  1. 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

  2. Structure of talk • jute fibres • fibre tensile tests • statistical modelling (no equations ) • composites • characterisation • new parameters • new rule of mixtures

  3. 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

  4. 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.

  5. Fibrestrengthand failure strain

  6. Fibre modulus vs length • mean Young’s modulus in range 26-34 GPa

  7. Fibre strength vs length • strength reduces with increasing length

  8. Failure strain vs length • failure strain reduces with increasing length

  9. Weak-link scaling predictions • reference data at single fibre length (point estimate). • Weibull distribution parameters calculated • maximum likelihood parameter estimation methodused to quantify the variation. • single parameter (standard) andMultiple 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.

  10. Weak-link scaling: strength Standard-WLS MDS-WLS

  11. Weak-link scaling: strain ε’ Standard-WLS MDS-WLS

  12. Weak-link scaling predictions • weak link scaling should be performed with • at least two points, preferably three, and • with fibre length at two extreme anda third point near the mean fibre length.

  13. Natural logarithm interpolation model (NLIM) • analysis for fibres up to 50 mm longextended 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.

  14. Effect of fibre diameter Easy to select for length, but not for diameter:

  15. Effect of fibre diameter To permit comparisons, data is grouped:

  16. 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

  17. … but the fibre CSA irregular Confocal Laser Scanning Microscope (CLSM) images

  18. Rotated to max length onhorizontal axis and fitted by various shapes

  19. True fibre cross-sectional area • 106 individual jute technical fibres measured • true fibrecross-sectional area distribution plotted

  20. True fibre cross-sectional area • log-normal plot of area distributions for 106 fibres

  21. 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.

  22. 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)

  23. Fibre area correction factor, κ • geometric means forthe 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 composite in submission for publication

  24. so now composites … • jute fibres dyed black withProcion MX cold fibre reactive dye • fibre tensile tests confirmno significant change in moduli or strengths • quasi-UD composite plates made byresin infusion with a flow medium • Three plates with natural fibre and no pigment • One plate dyed fibres and white pigment in resin

  25. Microscopy • samples fromtensile 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)

  26. 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

  27. < S3: secondary wallinner layer, θ =60-90° < S2: secondary wallmiddle layer, θ =10-30° < S1: secondary wallouter layer, θ =50-70° < primary wall Fibre diameter distribution factor • ηd = complex function of fibre structure • well-characterised fibres used in our study, so ηd = 1 J Summerscales, W Hall and AS VirkA fibre diameter distribution factor (FDDF) for natural fibre compositesJournal of Materials Science, 2011, 46(17), 5876-5880.

  28. 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

  29. New equations: • modulus • Ec = κηd ηl ηo Vf Ef + Vm Em • strength • σ’c = κηd 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)

  30. 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

  31. RoM predictions

  32. Triangulation (external data) bar length  percentage error

  33. Conclusions • use of the apparent fibre diameterfrom 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

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