Determination of Fibre Volume Fraction

Rules-of-mixtures

The properties of fibre-reinforced composites can be estimated using rules-of-mixtures for

• modulus (or similar properties by substitution of the appropriate terms), or
• strength (e.g. Kelly-Tyson equation for unidirectional composites).

All these estimations rely on the fibre volume fraction (normally denoted as V_f or FVF).  The determination of fibre volume fraction for man-made fibre composites can be achieved by various means:

• Curtis [1] adopted as ISO14127 Procedure A1 [2] suggested thermal resin removal (burn-off).
• Moon et al [3] proposed the use of thermogravimetric analysis (TGA) to determine FVF of CFRP and GFRP at an isothermal temperature of 550 °C. The carbon fibre also loses mass at this temperature so a fibre weight loss fraction parameter should be considered, or the weight loss of raw fibres measured.
• Curtis [1] adopted as ISO14127 Procedure A2 [2] suggested chemical resin removal by nitric acid.
• Green [4] proposed the use of a 600W domestic microwave oven with a Parr 4782 microwave digestion bomb and concentrated nitric acid (SG 1.42) to determine the FVF of CF/Ep composites.
• Curtis [1] adopted as ISO14127 Procedure A3 [2] suggested chemical resin removal by sulphuric acid/hydrogen peroxide,
• Curtis [1] adopted as ISO14127 Procedure B [2] suggested thickness measurement where V_f = n A_F / ρ_f t,
  where n = number of plies, A_F = areal weight of each reinforcement layer, ρ_f = fibre density, and t = laminate thickness.
• Curtis [1] also suggested density measurement.
• mesoscopic image acquisition, processing and analysis [5].  Thébault et al [6] have compared composites FVF measurements by five methods:
• Otsu's thresholding method is the most widely used image analsis technique for FVF.  The image is thresholded to separate fibres from the matrix, then the FVF is the ratio of fibre pixels to the total number of pixels (i.e. the area fraction) in the image,
• watershed method treats the segmented input as a tpographic surface with pixel intensity values representing elevation.  The algorithm simulates a flooding process where basins are filled until it reached a watershed level at high-intensity ridges,
• fiber counting assumes the fibre cross-sections are perfect ellipses with the mean area being the product (π a b) of the total number of fibres times the area computed from the average major (a) and minor (b) semi-axes of the detected elliptial shapes,
• machine learning segmentation model, and
• machine learning regression model.

Thébault et al concluded that "Otsu's thresholding proved reliable and efficient for most practical applications", except when FVF <5%.

For natural fibre reinforced composites, Jang et al [7] have proposed a modified burn-off method which selectively combusts natural fibres and quantifies the remaining resin mass.

References

1. PT Curtis, CRAG Test Methods for the Measurement of the Engineering Properties of Fibre Reinforced Plastics, Royal Aerospace Establishment Technical Report RAE-TR-88-012, February 1988  MooDLE.
2. Anon., Carbon-fibre-reinforced composites — Determination of the resin, fibre and void contents, BS ISO 14127:2008, International Organization for Standards, Geneva ~ Switzerland, 1988.
3. C-R Moon, B-R Bang, W-J Choi, G-H Kang and S-Y Park, A technique for determining fiber content in FRP by thermogravimetric analyzer, Polyer Testing, May 2005, 24(3), 376-380.
4. P Green, Fibre volume fraction determination of carbon-epoxy composites using an acid digestion bomb, Journal of Materials Science, 1 October 1991, 1(19), 1162–1164.
5. FJ Guild and J Summerscales, Microstructural image analysis applied to fibre composite materials: a review, Composites, 1993, 24(5), 383-393.
6. F Thébault, A Clément, S Fréour, G Le Moal and P Casari, Comparison of fiber volume fraction measurement methods from composite micrographs, Composites Science and Technology, 26 July 2026, 282, 111689.
7. J Jang, J-BRG Souppez and D Oh, Modified burn-off method for fiber content assessment in hemp and flax reinforced composites for marine structural applications, Polymer Testing, 2026, 157, 109139.

Determination of moisture content of composites

The Standard Test Method for moisture absorption properties and equilibrium conditioning of polymer matrix composite materials is ASTM D5229/D5229M-20 [1].

Arnold et al [2] consider the methods for determination of the directional moisture diffusion coefficients of composite materials.  They identify full Fickian 3-D as the most rigorous and having the lowest error.  The Starink, Starink and Chambers approximation [3] was found to be in good agrrement with the full 3-D case, while the Shen and Springer model [4] gave systematically low values for diffusion across and normal to the fibres.

Link for a discussion of (non-)Fickian Diffusion.

References

1. Anon., Standard Test Method for Moisture Absorption Properties and Equilibrium Conditioning of Polymer Matrix Composite Materials, ASTM D5229/D5229M-20, ASTM International, ~ United States of America, 07 April 2020.
2. JC Arnold, SM Alston and F Korkees, An assessment of methods to determine the directional moisture diffusion coefficients of composite materials , Composites Part A: Applied Science and Manufacturing, December 2013, 55, 120-128.
3. MJ Starink, LMP Starink and AR Chambers, Moisture uptake in monolithic and composite materials: edge correction for rectanguloid samples, Journal of Materials Science, January 2002, 37(.), 287-294.
4. C-H Shen and GS Springer, Moisture absorption and desorption of composite materials, Journal of Composite Materials, January 1976, 10(1), 2-20.