Would someone please explain resin fiber ratio. I’m not a complete idiot here. I just would like to hear more about vf wf. How they are calculated. Whats ideal for each time of fabric ETC. I have a scale and I weigh how much fabric goes in. Then I weigh the final part to see how much resin I have put in. I’m trying to see how good of a part I am making.
First off Wf is fiber weight fraction and Vf is fiber volume fraction. The weight fraction is the percentage of the laminate weight that is fiber. Volume fraction is the percentage of the laminate volume that is fiber.
Here are some interesting differences between the two:
A Vf of 50% with carbon would be 61% by weight
A Vf of 50% with e-glass would be 69% by weight
A Vf of 50% with s-glass would be 68% by weight
A Vf of 50% with Kevlar49 would be 56% by weight
The difference between the Wf and the Vf has to do with the differing densities of the fibers. This means that lower density fibers like Kevlar (1.44 g/cc) have a higher volume of fiber for a given weight compared to a higher density material like e-glass (2.55 g/cc).
The standard of 50:50 by weight, which is often broadcasted over the internet, is often done with total disregard for the chosen fiber. A 50:50 by weight with e-glass is only a Vf of 31%.
Calculation Scenario:
Weight of carbon fabric: 200 grams
Weight after layup: 333 grams
Weight of resin in part: 133 grams
Divide the weight of fiber (200 grams) by the final weight (333 grams) = .60 or 60%
This would be a Wf of 60% or a ratio by weight of 60:40
You can use these figures to convert to Vf but you need the density of the fiber and the density of your resin (aka specific gravity).
Pan-based carbon: 1.8 g/cc
E-glass: 2.55 g/cc
S-glass: 2.49 g/cc
Kevlar 49: 1.44 g/cc
Resin: 1.1 to 1.2 g/cc
So, using the above stats we would use the density of our components to calculate the volume.
200 grams of carbon / 1.8 g/cc = 111 cc
113 grams of resin / 1.15 g/cc = 116 cc
Total volume = 111cc of carbon + 116 cc of resin = 227 cc total volume
111 cc of carbon / 227 total volume = .49 or 49%
This would equal a Vf of 49% or have a ratio by volume of 49:51
The above is theoretical and assumes that there are no voids within the laminate. Most unassisted hand layup range in the Vf 35 to 45%. Infusion and one atmosphere bagging can get you to Vf 50 to 60% (some claim higher). Bladder molding can get Vf 50 to 70% depending on the pressure. High pressure autoclave can range from 50% to 70%. Personally I think anything above 60% Vf gets pretty brittle. I typically shoot for 55% to 60% for all around durability. There is certainly nothing the matter with Vf 50%. I’ve seen some unassisted hand layups with a Vf of 40% perform well.
It’s important to remember that the only way to improve the Vf is eliminate unnecessary surface resin and compact the fiber close together. You can create some laminates that have impressive Wf but perform very poorly. If the fibers are not fully saturate then the Wf can look great but in reality the fiber are inadequate supported by the matrix (resin). This is why it’s very important to calculate the theoretical thickness and compare it to the real part. If the real part is thicker than the theoretical thickness then you could have inadequate fiber saturation.
Later today I’ll post the math for calculating theoretical thickness and estimated laminate porosity. It’s also possible to estimate the Vf based of the laminate thickness.
I once posted an excelsheet which had all the calculations within, and asking for Vf achieved for different materials. Did not get too much reaction, though. Will look it up.
Scenario Two:
Layup: 3 layers of 5.7 oz/yard2 (193 g/m2) 3k Toray T700s (1.8 g/cc) carbon fabric
Fabric Weight Before Layup: 8.55 ounces (242 grams)
Weight After Layup: 13.15 ounces ( 373 grams)
Weight of the Resin (Layup weight - fabric weight): 4.6 ounces (130 grams)
Epoxy resin: 1.15 g/cc density
Measured Laminate Thickness: .027 (.69 mm)
Lets calculate the theoretical Vf of the actual laminate:
242 grams of carbon / Density of 1.8 g/cc = 134 cc of carbon
130 grams of resin / Density of 1.15 g/cc = 113 cc of resin
134 cc of carbon + 113 cc of resin = 247 cc total volume
134 cc of carbon / 247 cc total volume = .54 or 54% Vf, 54:46 volume ratio
Now lets calculate the theoretical thickness using 54% Vf for our 3 layer 3K layup:
To calculate thickness we have to know the volume of the fiber, the volume of the resin, and the area. Calculating the area for a given layup can be a little intense. Fortunately, we don’t have know the area of part. We just have to know an accurate areal weight of the fiber (ounce/yard or grams/meter).
NOTE: To calculate a theoretical thickness you need a Fiber Volume Fraction (Vf).
3 layers of 193 g/m2 carbon would yeild a total weight of 579 g/m2 (193 x 3)
579 grams / density of carbon 1.8 g/cc = 322 cc of carbon
Now we need to figure out the volume of resin for 322 cc of carbon with a Vf of 54 % (54:46).
322 cc of carbon times 46 divided by 54 = 274 cc of resin.
So for our thickness calculation we have 322 cc of resin + 274 cc of resin for total volume of 596 cc.
Now we divide 594 cc by the area which is 1 square meter (100 cm x 100 cm):
596 / 10,000 = .0596 cm or .596mm. We will just round up to .60mm
Out theoretical laminate thickness is .60 mm (.236")
Estimating Porosity
No we can compare our theoretical thickness with the actual laminate thickness. We immediately see a problem. Our measured thickness is .69 mm while our theoretical thickness is .60. There is a discrepancy of .09 mm. This means that our layup could be light on resin (or we have thick area with a lower Vf and thin areas with a higher Vf)
So, based on our theoretical thickness calculation for 3 layers of carbon at Vf 54% we multiply our actual measured thickness (.69 mm) by 1 meter to find the new volume.
.069 cm x 10,000 cm = 690 cc.
So we had:
322 cc of fiber from our theoretical thickness calculation
274 cc of resin from our theoretical thickness calculation
94 cc of air (690 - 322 - 274=94)
So in reality our actual laminate had:
47% fiber (322 / 690)
40% resin (274 / 690)
13% air (porosity)
It’s not helpful to just measure the thickness of one area. Infused parts can have thicker resin rich areas and thinner more compacted areas. Often test parts need to be cut apart so you can measure the thickness is many areas to get an average thickness. This average thickness can be used to estimate porosity.
FUN WITH MATH!! 
Also keep in mind that on one side the surface is a bit wavy. So you always measure the thickest value (mountain) and never the thinest (valley). Try and measure both, and take the average. The thicker the laminate, the smaller the error made.
Thanks. That helps a lot.
Do you know the density of basalt?
doing a google search on “basalt fiber density” gives you the answer within the first 3 hits.
Moved to engineering talk. It’s a better fit over here
Hello,
Following this useful post on fiber volume fraction calculations, I would be very helpful if assistance could be provided to determine the same parameter for a laminate involving different fabrics.
In this post, calculations are based on the fact that the composite is made of one/several layer(s) of the same material in a resin matrix.
How would you calculate Vf when more than one fabric of different materials are used?
E.g.
Layer 1: Biaxial Carbon Fibre – 300 gsm
Layer 2: Biaxial Carbon Fibre – 100 gsm
Layer 3: Biaxial Carbon Fibre – 100 gsm
Layer 4: Biaxial Carbon Fibre – 300 gsm
Total fabric weight (4 layers) = 800g
Resin weight: 400g
Key question for the Vf determination:
How is the resin weight distributed across the layers for calculation purposes? Equally across the 4 layers (i.e. 100g for every layer) leading therefore to the determination of two different Vfs for the two type of Carbon Fibres (or whichever material)? Not equally depending on the fibre areal weight? Or simply considering the entire laminate as a whole and finding out a single Vf?
Thanks in advance for your help!
Cheers,
In your scenario you would just use the total fabric weight since they are all carbon. Vf is based on VOLUME. The volume of fiber in the laminate never changes. It is constant. The thing that changes is the volume of resin. Another way to think about it is the amount of space between the carbon filaments. Some processes will squeeze the fibers closer together leaving less space for resin. The thickness may change but the volume of fiber never does. The volume of fiber is easy to calculate if you know its weight and fiber density (specific gravity).
Thank you for your prompt response.
I completely agree with you that the volumen of resin does not change but, correct me if I am wrong, the volumen of carbon is not the same for both layers described in the example.
As you well say and, if I am right, the amount of space between the carbon filaments cannot be the same for two carbon fabrics of differet areal weight.
Using a numerical example and assuming 1,8g/cc for the Carbon Fibre density:
Layer 1: Carbon Fibre (300 gsm Areal weight), 300g -> Volume: 166,7 cc
Layer 2: Carbon Fibre (100 gsm Areal weight), 100g -> Volume: 55,6 cc
Layer 3: As Layer 2
Layer 4: As Layer 1
Resin: 400g @ 1,25g/cc -> Volume: 320 cc
Total Volume: (166,7x2) + (55,6x2) + 320 = 764,6 cc
How would Vf be calculated?
[(166,7x2) + (55,6x2)] / (746,6) = 0,58 … would be the usual approach …
However, volumen of fibre in Layers 1/4 and 2/3 is different as shown before … Should another different approach be adopted?
Help would be sincerely appreciated,
Thanks,
Your calculation is correct. If you know the volume of fiber and the volume of resin then you can simply calculate the Vf for the laminate. Volume is volume regardless of the format. 30 cc of 300 gsm fabric has the same volume as 30 cc of 100 gsm fabric. The Vf through the laminate may vary due to differing fiber formats. To get a more accurate understanding of how the processing is effecting the different fiber formats then you would have to run some batch samples for each fiber format separately. This data could then be used as a predictor for future laminates using the same processing perimeters.
Ouch, I would think that total uniformity would be something to strive for? Is this something that can be helped via process, or is that much thickness variation (.06 to .069, a difference of 15%) considered acceptable?