Fiber volume ratio is an important mathematical element in composite engineering.
[1] When manufacturing polymer composites, fibers are impregnated with resin.
The fraction of fiber reinforcement is very important in determining the overall mechanical properties of a composite.
A higher fiber volume fraction typically results in better mechanical properties of the composite.
[2] Calculating the volume of fiber ratio in a composite is relatively simple.
The volume fiber fraction can be calculated using a combination of weights, densities, elastic moduli, stresses in respective directions, Poisson's ratios, and volumes of the matrix (resin system), fibers, and voids.
[3] where: and This procedure involves the digestion of the polymer matrix using an acid which does not attack the fibers.
Following digestion, the remaining fibers are washed, dried, and weighed.
Knowing the initial weight of the composite specimen as well as the densities of the fiber and resin, the volume fraction of both the fiber and matrix in the original laminate may be determined.
This method is generally used for composites composed of carbon fiber reinforcement.
[4] Optical microscopy-based techniques involve potting sectioned samples of the laminate, polished using standard metallographic techniques, and obtaining digital cross-sectional photomicrographs using an optical microscope and magnifications between 100 and 2500.
[5] Digital images may be recorded at a number of locations along the length and through-the-thickness of the laminate.
Computer programs aid in the analysis of fiber ratio in the photomicrograph of the polished composite specimen.
This method is preferred as a non-destructive approach to determining fiber volume fraction.
Realistically the highest fiber volume ratio is around 70% due to manufacturing parameters and is usually in the range of 50% to 65%.
[4] Adding too little fiber reinforcement in the composite will actually deteriorate the properties of the material.
[7] Given the fiber volume fraction, the theoretical elastic properties of a composite can be determined.
In practical cases there can be variation in fiber diameter and irregular packing.
In practice, it's hard to achieve a volume fraction greater than 0.7 and this must be regarded as the realistic limit for commercial materials.
In the production process, using different fiber architecture methods can obtain different volume fractions.
There are many ways to determine if a composite part contains voids, such as industrial CT scanning or ultrasound.
where: and There are many methods of evaluating the void content of materials (including composites).
The first is to exam a polished section, identifying the voids in the section, either manually or using computer-aid analysis and determining the area fraction which corresponds to the volume fraction of the composite.
Application of Archimedes’ principle leads to the following expression for the measured density of the sample in terms of measured weight, where subscripts “a” and “L” refer to water and liquid, respectively:[5]
[1] Where: and The liquid used in this method should have a high density and chemical stability and low vapour pressure and surface tension.