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Fiber volume ratio is an important mathematical element in composite engineering. Fiber volume ratio, or fiber volume fraction, is the percentage of fiber volume in the entire volume of a fiber-reinforced composite material. [1] When manufacturing polymer composites, fibers are impregnated with resin.
It is the same concept as volume percent (vol%) except that the latter is expressed with a denominator of 100, e.g., 18%. The volume fraction coincides with the volume concentration in ideal solutions where the volumes of the constituents are additive (the volume of the solution is equal to the sum of the volumes of its ingredients).
Schematic illustration of idealized fiber arrays and their corresponding unit cells. In the theory of composite materials, the representative elementary volume (REV) (also called the representative volume element (RVE) or the unit cell) is the smallest volume over which a measurement can be made that will yield a value representative of the whole. [1]
The amount of fibers added to a concrete mix is expressed as a percentage of the total volume of the composite (concrete and fibers), termed "volume fraction" (V f). V f typically ranges from 0.1 to 3%. The aspect ratio (l/d) is calculated by dividing fiber length (l) by its diameter (d).
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In other words, we assume that the volume of the solvent does not change, and we use the partial molar volume where the number of moles of the solute is exactly zero ("the molar volume"). Thus, in the defining expression for apparent molar volume ϕ V ~ 1 {\displaystyle {}^{\phi }{\tilde {V}}_{1}} ,
where is the volume fraction of the fibers in the composite (and is the volume fraction of the matrix).. If it is assumed that the composite material behaves as a linear-elastic material, i.e., abiding Hooke's law = for some elastic modulus of the composite and some strain of the composite , then equations 1 and 2 can be combined to give
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