Composites theory
Published: 24 June 2012
Last updated: 04 July 2012
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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
How to use the Google's built-in calculator function
How to use the Google's built-in calculator function
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...