Fiber Volume Fraction

What V_f does to every property of a ply, what you can actually manufacture, and how to read the sweep instead of guessing a number.

What fiber volume fraction is

Fiber volume fraction is the share of a cured ply's volume that is fiber rather than matrix, written V_f and quoted either as a fraction (0.60) or a percentage (60%). The rest is matrix, V_m = 1 - V_f, assuming no voids. Outside the US it is usually spelled fibre volume fraction, and it is the same quantity.

Every micromechanics model takes V_f as an input, and it is the strongest lever any of them has. Change the fiber and you change one set of constants. Change V_f and you move every predicted property at once, in different directions: stiffness and axial strength go up, transverse strength goes down, and thermal expansion can pass through zero. That is the case for looking at it as a curve rather than a number.

Fiber volume fraction vs fiber weight fraction

These are not the same number, and prepreg datasheets usually quote the weight one. Carbon is denser than epoxy, so for a carbon/epoxy ply the weight fraction is always the larger of the two: a 60% V_f laminate is around 68% fiber by weight. The conversion needs both densities:

W_f is the fiber weight fraction, ρ_f and ρ_m the fiber and matrix densities. The ply calculator does this both ways, and also derives V_f from fiber areal weight and cured ply thickness, which is how you get it from a process rather than from a datasheet.

Sweeping fiber volume fraction instead of guessing it

The UD lamina builder has a Vf Sweep tab that evaluates the models at 81 values of V_f from 10% to 90% and plots one curve per model. You pick a property group (elastic, strength, CTE/CME, or the general properties: density, fiber areal weight and total areal weight) and then a property within it, and the chart redraws. The dashed vertical line marks the V_f the builder is currently set to, so you can see where your own operating point sits on every curve.

Clicking anywhere in the plot sets the builder's V_f to the value you clicked, which makes the chart an input rather than a readout. Find the stiffness you need, click there, and the results table below updates to that V_f.

The range runs past what anyone can build on purpose. Fibers would have to touch above roughly 70%, leaving no resin to transfer load between them, so nothing above that is manufacturable. It is on the chart because the shape of a curve near its asymptote tells you what a model assumes, and because a model that misbehaves at 85% is often already drifting at 65%.

The sweep tab in the UD lamina builder, with the tooltip open at the marked V_f. The tooltip lists every model in the group, including the ones that do not predict the property on screen, so a missing curve reads as a stated fact instead of a gap.

How fiber volume fraction changes the elastic constants

Four plots, same fiber and matrix throughout: T300 carbon in 3501-6 epoxy, with all six elastic models drawn. Read them as a set. The first and the last say the choice of model hardly matters; the middle two say it matters a great deal.

E₁, axial modulus. All six models draw one straight line. Load along the fibers is carried at equal strain, every model reduces to the same volume average, and none of the refinements touch it. For axial stiffness the choice of model is not a decision you have to make.

E₂, transverse modulus. The same six models, and now they fan out. They stay within a few percent of each other up to about V_f = 40% and separate from there; by 90% the highest is more than twice the lowest. Puck climbs fastest, which is a semi-empirical fit doing what fits do outside the data they were calibrated on.

G₁₂, in-plane shear modulus. Same shape as E₂ and for the same reason: the load path runs through the matrix. Chamis is drawn heavier because it is the model selected in the builder, which changes emphasis only and leaves the other five curves exactly where they were.

ν₁₂, major Poisson ratio. Poisson contraction under axial load is strain-controlled, so a volume average captures it and five of the six models agree exactly. Only CCA sits a little below the rest. Watch the axis: this plot is scaled from zero, and the whole disagreement is a fraction of one tick.

The pattern behind all four: where load runs along the fibers, every model reduces to a volume average and they agree. Where load has to cross from fiber to fiber through the matrix, each model makes its own assumption about how the stress gets there, and that assumption is what you see fanning out. The micromechanics page covers what each of the six assumes and which to pick.

Fiber volume fraction and lamina strength

The strength models are not four competing answers to one question. Each predicts a different subset of the five lamina strengths, so half the plots below carry a single curve, and the legend names only the models that predict the property on screen. That is the honest picture: for three of these five strengths you have exactly one model, and knowing that is worth more than a chart that hides it.

S₁ₜ, axial tension. One curve, because ROM is the only model that predicts it. A straight line: the fibers carry the axial load, so the ply allowable scales with how many of them are in the section.

S₁ᴄ, axial compression. Two models, more than a factor of three apart at V_f = 60%, because they predict different failure modes. ROM scales the fiber's own compressive allowable. Hopkins-Chamis predicts microbuckling, the shear-driven instability of a fiber in its matrix support, and climbs steeply because that support stiffens with V_f. Both modes are available to the real ply, so the governing number is the lower one.

S₂ₜ, transverse tension. Falling, not rising, which is the plot most worth showing someone new to composites. Chamis and Tsai-Hahn agree at low V_f and part company above roughly 20%; by 90% Tsai-Hahn is about a quarter of Chamis, so the disagreement is far larger than anything on the elastic plots.

S₁₂, in-plane shear. Chamis alone, and falling again. Same mechanism as transverse tension: the matrix carries the load, and raising V_f leaves less of it doing more work.

Note which way the transverse and shear curves run. Packing in more fiber buys axial strength and costs transverse strength, because the matrix is what carries load across the fibers and there is progressively less of it, under progressively sharper stress concentrations. A layup design that leans on high V_f for its 0° plies is quietly making its 90° plies weaker.

Fiber volume fraction, thermal and moisture expansion

Carbon fiber has a slightly negative coefficient of thermal expansion along its axis and epoxy a strongly positive one, so a carbon/epoxy ply contains a competition that V_f decides. The first plot is the clearest thing on this page.

CTE₁, axial expansion. All four models agree, and the feature is not the spread but the crossing. The fiber pulls the coefficient down and the matrix pushes it up, and near V_f = 67% for this pair they cancel: the ply has no axial thermal expansion at all. Above that it contracts on heating.

CTE₂, transverse expansion. Across the fibers the models split: Chamis lowest, ROM in the middle, Schapery highest. CCA is on the chart but invisible, drawn underneath Schapery because the two agree almost exactly here. Unlike CTE₁ this never approaches zero, so a ply that is thermally stable along the fibers still moves across them.

CME₁, axial swelling. Schapery is the only model that predicts moisture expansion, so both CME plots carry one curve. Along the fibers the coefficient decays quickly: carbon absorbs no moisture, the swelling is entirely the matrix's, and the fibers restrain it.

CME₂, transverse swelling. Across the fibers nothing restrains the swelling, so the curve falls close to linearly and stays far higher. Compare the two axis scales rather than the two curve shapes: at V_f = 60% this coefficient is around forty times CME₁.

The zero crossing in CTE₁ is the reason dimensionally stable structures (optical benches, satellite booms, metrology frames) are built from carbon/epoxy at a specified V_f rather than whatever the process happens to give. It is also why they are laid up to balance the transverse expansion, which never approaches zero. See hygrothermal effects for what these coefficients do once they are assembled into a laminate.

Typical fiber volume fraction by process: hand layup, infusion, prepreg

Read the sweep at the V_f your process gives you, not at the one that makes the numbers look best. Typical cured ranges:

• Hand layup, roughly 0.40 to 0.50. Consolidation is whatever the laminator's roller achieves.
• Vacuum infusion and wet filament winding, roughly 0.50 to 0.60.
• Prepreg with autoclave cure, roughly 0.55 to 0.65. The resin content is set at the prepreg line rather than on the bench, which is most of why it is higher and far more repeatable.
• Above roughly 0.70, not achievable with round fibers. They would have to touch, leaving nothing to transfer load between them.

If a supplier's lamina datasheet does not state V_f, the sweep is the fastest way to infer it. Enter the fiber and the matrix, find the quoted E₂ on the chart, and read off the V_f it implies. When that number is nowhere near what the datasheet claims, either the constituent properties or the lamina properties are not what they say they are, and it is worth finding out which before the value reaches a stress report.

References

1. Daniel, I.M. & Ishai, O., Engineering Mechanics of Composite Materials, 2nd Ed., Oxford University Press, 2006.
2. Barbero, E.J., Introduction to Composite Materials Design, 3rd Ed., CRC Press, 2018.
3. Chamis, C.C., "Simplified Composite Micromechanics Equations for Hygral, Thermal and Mechanical Properties", NASA TM-83320, 1983.
4. Hopkins, D.A. & Chamis, C.C., "A Unique Set of Micromechanics Equations for High Temperature Metal Matrix Composites", NASA TM-87154, 1985.
5. Tsai, S.W. & Hahn, H.T., Introduction to Composite Materials, Technomic Publishing, 1980.
6. Schapery, R.A., "Thermal Expansion Coefficients of Composite Materials Based on Energy Principles", Journal of Composite Materials, Vol. 2, No. 3, 1968, pp. 380-404. doi:10.1177/002199836800200308

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