Density of composite materials

• ρEpoxy-resin = 1.1 g/cm³
• ρCarbon-fiber = 1.78 g/cm³
• ρE-glass-fiber = 2.54 g/cm³
• ρAramide-fiber = 1.45 g/cm³

Fiber volume fraction Vf

Vf at different manufacturing methods

The norm for specifying the fiber / resin ratio is the ratio of fiber versus total volume. So, in practice, weight has to be converted into volume. The fiber volume fraction [Vf] that can be achieved, depends on the manufacturing method:

• 50%. Hand lay-up, without vacuum.
• 60-70%. Vacuum infusion / hand lay-up with vacuum bagging.
• 80%. Advanced autoclave technology, used in aviation.

Fiber volume fraction Vf calculation

V=volume, M=mass, ρ=density

• Vf = Vfiber / Vtotal
• Vtotal = Vresin + Vfiber
• Vf = 1/(1 + Vresin / Vfiber))
• V = M/ρ
• Vf = 1 / (1 + (Mresin / ρresin) / (Mfiber / ρfiber))
• For a carbon fiber / epoxy laminate: Vf = 1 / (1+ 1.6 * Mepoxy / Mcarbon)

For hybrid laminates:

• Vf = 1 / (1 + (Mresin / ρresin) / (Mfiber1 / ρfiber1 + Mfiber2 / ρfiber2))

Example of fiber volume fraction Vf calculation

Here is an example of a 5x10cm carbon sheet, made with my DIY vacuum pump, 4 carbon-fiber layers and epoxy resin.

• Total: 6.29g
• Carbon: 4.24g
• Mepoxy = total – Mcarbon = 2.05g
• Vf = 1 / (1+ 1.6 * Mepoxy / Mcarbon) = 0.56

Calculation of the required amount of resin for a laminate

If Vf is known, the required amount of resin can be calculated:

• Mresin = Mfiber * (1 / Vf – 1) * ρresin / ρfiber, (M = mass)
• For a carbon fiber / epoxy laminate: Mepoxy = Mcarbon * (1 / Vf – 1) / 1.6
 Vf Mepoxy/Mcarbon 30% 1.46 35% 1.16 40% 0.94 45% 0.76 50% 0.63 55% 0.51 60% 0.42 65% 0.34 70% 0.27

Will be continued...