Amandeep obtained a  BEng (honours) Mechanical Engineering  with Composites (first class) degree in 2007.  His group assignment for module MATS320 on the design of an asymmetric crossbow limb was published [1].  He was awarded a PhD for the study reported in his thesis entitled "Numerical models for natural fibre composites with stochastic properties" in December 2010 for data obtained from a single batch of jute fibres from South Asia.  The literature review was published in two parts [2, 3].

In [4], the jute fibre cross-sectional area was analysed using digital images and modelled using different geometrical shapes (major circle, minor circle, ellipse, superellipse, and convex hull).   The area distribution for each case was determined and it was observed that, for all the assumed shapes (except for the minor circle), the area distribution showed a negative skew (the distribution peak shifts toward right) and the maximum peak drops when compared with true area distribution. This negative skew indicates that the method overestimates the fibre area. The drop in distribution peak indicates an increase in the range of the data. The fibre cross-sectional area calculated assuming an elliptical cross-section gives a lower variation in the fibre area compared with the circular cross-section. The minimum elliptical area is calculated from the two orthogonal projection widths and gives the area closest to the true fibre area.  Any fibre area calculated using a method that overestimates the fibre area will always underestimate the modulus and strength of the fibre. Using the ellipse will yield an underestimate of both modulus and strength and hence will result in a safer mechanical design when the fibres are used as reinforcement in a composite.

In [5], an examination of tensile test data from 785 individual tests revealed 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 cross-sectional area (CSA).  Thus, it is recommended that failure strain is used as the key design criterion for natural fibre composites in order to improve reliability in the design of natural fibre-reinforced composites.

In [6], results of one hundred tensile tests at each of five distinct fibre lengths (6, 10, 20, 30 and 50 mm) were reported.  The jute fibres were found to have a Young’s modulus of ~30 GPa with ultimate strength and fracture strain falling from ~558 to ~336 MPa and ~1.79% to ~1.11% respectively as the length increased from 6 to 50 mm.  Weibull parameters for the jute fibres were estimated for each fibre length using a maximum likelihood estimate (MLE), i.e. point estimates.   Two empirical models (a linear and a natural logarithmic interpolation model) were successfully developed to characterise the ultimate strength and fracture strain across the entire range of the fibre lengths tested (i.e. 6–50 mm).   The logarithmic interpolation model for ultimate strength and fracture strain was found to produce a better fit to the experimental data (i.e. at the five distinct fibre lengths) than the linear model, but both models produce a better estimation for ultimate strength than for fracture strain.  In [7], the previously reported NLIM analysis was extended to include fibres with lengths up to 300 mm.  The NLIM produces a significant improvement in predicted properties over the MDS model. Use of Anderson–Darling goodness of fit number (GOFN) confirms this finding and reveals a reduction factor (Multiple Data Set (MDS) model GOFN/logarithmic model GOFN) for this measurement of 2.74 for strength and 2.23 for strain.

In [8], Weibull distribution parameters calculated for gauge lengths between 6 mm and 300 mm using the maximum likelihood parameter estimation method to quantify the variation.   Single parameter (standard) and MDS weak-link scaling predictions were assessed using Anderson–Darling Goodness of Fit Numbers.   The MDS weak-link scaling is recommended for this problem.  The MDS weak-link scaling should be performed with at least two points, and preferably three, and with fibre lengths at the two extreme cases and the third point near the mean fibre length.

In [9], it is proposed that a fibre diameter distribution factor (FDDF) should be included in the rule-of-mixtures. An equation for the FDDF gives a value between 0-1 to reflect the decrease in fibre modulus with increasing fibre diameter.  For fibres where the modulus is independent of diameter, the FDDF will be 1 and hence the new equation reduces to the traditional form.

Further, after comparison of the true cross-sectional area of the irregular cross-section fibre and the apparent area based on a "diameter" measured by optical microscopy, a fibre area correction factor (FACF) was determined [10].  The two new parameters above can now be incorporated into the rules of mixture to estimate the elastic modulus of all and the strength of quasi-unidirectional natural fibre composites:

E_c = κ η_d η_l η_o V_f E_f + V_m E_m

σ'_c = κ V_f σ'_f + V_m σ^*_m

where the parameters are:

• E = elastic modulus
• σ' = strength (stress at failure)
• σ^*_m = stress in the matrix at the fibre failure stress
• κ = fibre area correction factor
• η_d = fibre diameter distribution factor
• η_l = fibre length distribution factor
• η_o = fibre orientation distribution factor

and subscripts "f" and "m" refer to the fibre and matrix components respectively.  The inclusion of the FACF (value 1.42 for jute) to account for the non-circular cross-section of the natural fibres resulted in improved predictions of both the elastic modulus and the strength of jute fibre composites.   Data from other authors was analysed in order to triangulate these findings for elastic modulus and twelve of the fourteen cases returned an error of significantly reduced magnitude when the above FACF was used.

The e-thesis (4.612 MB PDF) is one of the first five research theses in the Plymouth Electronic Archive and Research Library (PEARL).

References

1. AS Virk, J Summerscales, W Hall, SM Grove and ME Miles
   The design, manufacture, mechanical testing and numerical modelling of an asymmetric composite crossbow limb
   Composites Part B: Engineering, 2009, 40(3), 249-257.
2. J Summerscales, N Dissanayake, W Hall and AS Virk
   A review of bast fibres and their composites. Part 1: fibres as reinforcements
   Composites Part A: Applied Science and Manufacturing, October 2010, 41(10), 1329-1335.
3. J Summerscales, N Dissanayake, W Hall and AS Virk
   A review of bast fibres and their composites. Part 2: composites
   Composites Part A: Applied Science and Manufacturing, October 2010, 41(10), 1336-1344.
4. AS Virk, W Hall and J Summerscales
   Physical characterisation of jute technical fibres: fibre dimensions
   Journal of Natural Fibres, 2010, 7(3), 216-228.
5. 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.
6. AS Virk, W Hall and J Summerscales
   The tensile properties of jute fibres
   Materials Science and Technology, October 2009, 25(10), 1289-1295.
7. AS Virk, W Hall and J Summerscales
   Modelling tensile properties of jute fibres
   Materials Science and Technology, January 2011, 27(1), 458-460.
8. 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.
9. J Summerscales, W Hall and AS Virk
   A fibre diameter distribution factor (FDDF) for natural fibre composites
   Journal of Materials Science, September 2011, 46(17), 5876-5880.
10. AS Virk, W Hall and J Summerscales, Modulus and strength prediction for natural fibre composites, Materials Science and Technology, published online 10 April 2012.