Effect of Vf on composite properties

General Composites Discussions Engineering Talk
#1

Hi,

Everyone says that a higher Vf, fiber/resin ratio means stiffer, stronger parts. But does anyone know the exactly how much the stiffness and strength depend on the Vf? Is there a linear correlation between Vf and compression stiffness? Meaning increasing Vf by 20% translates to 20% more stiffness? Or is it more complicated than that?

I have also heard that a Vf of around 60% translates to the best impact resistance. Is this true and how? The epoxy resin is pretty brittle and weak compared to the reinforcing carbon fibers. The only explanation would mean it would be more resistant to delamination.

Also, what’s the highest possible Vf you can achieve? Assuming all the fibers are aligned perfectly, are perfectly round, and as little resin as possible is used, I have calculated the highest Vf theoretically achievable is 90.69% by taking the area of 3 1/6ths of a circle (a semicircle) and dividing by the area of an equalateral triangle with the side length = diameter.

0.5^2 * π / 2 = 0.3927

√(3)/4 = 0.4330

0.3927 / 0.4330 = 0.9069

The highest Vf I have seen advertised for a finished part seems to be 71%
That’s much lower than the theoretical maximum.

#2

Hello geneiusxie,

the question how the strength of your part and the Vf correlates first depends at how you calculate. If you take the total mass of your finished part as fixed, then a higher Vf simply means more fibers and less resin and then the strength will be nearly linear to Vf in a certain range. If you take a fixed amount of fibers and then vary the Vf the influence on the strength is much smaller.
To be a little more precise you can’t simply speak of “strength” or “stiffness”. You have to deal with compression, shear and tensile strength and with elastic modulus. And then composites are engineered materials, so they are most often anisotropic.
There are many publications elaborating on the micro mechanics of the fiber matrix compound. Maybe this paper gives you a few answers without too much overhead: http://ningpan.net/publications/1-50/24.pdf

#3

A test that I participated in revealed that a Vf of 50 to 55% with 3K plain weave carbon yielded the highest impact strength.

Increasing the Vf for a given layup doesn’t necessarily increase it’s strength. The laminate will become thinner and lighter as the Vf increases. Most structures fail due to buckling. Thinner laminates, assuming equal fiber volume, will buckle earlier than thicker ones with a lower Vf.

If you want to increase the Vf and increase strength then you need to add more fiber. This increases material cost and typically increases the labor.

A laminate with 3 layers of 5.6 ounce carbon and a Vf 40% would weigh 32.9 ounces/yard^2 and be .031" thick. A laminate with 4 layers at 60% would weigh 31.95 ounces/yard^2 and be .028" thick. The second laminate would have a higher tensile and compression strength and have a slightly higher flexural modulus.

The theoretical maximum Vf is impossible because it requires that the fibers stack perfectly.

#4

Yes, I understand that adding more resin while keeping the amount of fiber constant will increase strength. But I want the maximum performance for the least amount of weight and thickness. I’m not really concerned with material costs and labor.

Yep, I got that. But will the laminate with 4 layers be 4/3 = 1.33 times as strong and stiff as the one with 3 layers?

#5

I have seen panels with 10% resin (single side coated aramide prepreg) or 20% (fully impregnated). These are for ballistic panels, where the panels NEED to delaminate at impact.

Indeed there are a couple of factors to consider:

Higher Vf means thinner laminate. Very true in daily composites. However, also higher bending modulus, which is not connected to thickness.

Bending stiffness is given as 1/3wh^3 (w=width, h=height) so 1,33 thicker, means some 2,35 times stiffer. This makes it painfully clear that thickness always wins, if it comes to stiffness. So much more than fiber properties.

But this was all about Vf. A very interesting discussion.

-how to influence Vf
-in different circumstances (specific stiffness, ILSS, etc) are there optimums?

#6

A laminate with 3 layers of 5.6 ounce carbon and a Vf 40% would weigh 32.9 ounces/yard^2 and be .031" thick. A laminate with 4 layers at 60% would weigh 31.95 ounces/yard^2 and be .028" thick. The second laminate would have a higher tensile and compression strength and have a slightly higher flexural modulus.

Wouldn’t 3 layers of 5.6oz at 60% Vf also have the same tensile and compression strength since strength is based on area (lbf/in^2, or MPa) as the 4 layer version? I realize the thinner 3 layer version would be more susceptible to buckling, but this is more a function of geometry than Vf, no?

As for the highest Vf that is practical, this will depend on your fabrication process. Generally, there is a law of diminishing returns after a certain Vf (about 53% for glass fiber, maybe higher for carbon due to lower density) where voids begin to form in the matrix, reducing the strength and stiffness.

Strength and modulus properties are fairly linear (within a certain range) with Vf and can be estimated using rule of mixtures equations.

#7

No. The Vf is important because it tells you how much fiber is within the cross-sectional area. If the Vf is higher then there is more fiber within the area.

#8

If you want to increase the Vf and increase strength then you need to add more fiber.

Then by increasing the amount (percentage) of fiber within the cross sectional area aren’t you increasing the strength (I am referencing in-plane strength)? A rule of mixtures equation would estimate the strength and modulus would increase with increasing Vf. i.e. Composite Strength = VmMatrix Strength + Vf Fiber Strength (same for modulus)

Of course, a thinner laminate will be more suseptable to buckling, but this is failure due to unstable conditions forcing the laminate to fail below it’s actual strength.

#9

Geneiusxie,

Getting back to your original question of how material properties (strength, modulus) vary with Vf, please reference the 'Data Normalization" section of the MIL Handbook 17 (http://www.lib.ucdavis.edu/dept/pse/resources/fulltext/HDBK17-1F.pdf, pgs 140-141). Normalization is the method used to estimate fiber dominated properties at different Vf values.

#10

You are correct in terms of uniaxial stress and pressure (force/area), but increasing the Vf of a given layup in a structure does not enable the structure to handle a greater force. In fact, it almost always decreases the load bearing ability of the structure. If have tested and witnessed this time and time again. I recently consulted on the boom fabrication for a UAV. The designed team went from a hand layup to a high pressure bladder with an identical volume of fiber (fiber usage constant). The Vf of the layup went from 42% to 60%. The 42% boom passed their testing while the 60% failed. In the end we were lighter by using the pressure bladder but had to add more fiber than the 42% hand layup contained.

Buckling is the most common failure mode of thin walled composite structures and beams. The flexural modulus of a skin or flange is a crucial arena of design because it is the predominate factor in preventing buckling.

#11

Yes, I understand that less resin and same amount of fiber = weaker structure due to buckling failure.

But what about more resin and less fiber, keeping the weight constant? Because fiber has a higher density than resin, increasing the Vf for the same weight would mean a slightly thinner laminate. Because bending stiffness of a infinitely long plate is inversely proportional to the density cubed, I came up with an equation:

total bending stiffness = Vf/(1.2+0.6Vf)^3

where 1.2 is the density of the resin and
0.6 = fiber density of 1.8 - resin density of 1.2
This assumes that the resin itself does not directly contribute to the stiffness of the part. Realistically, epoxy has about 1% of the stiffness of carbon fiber - 2.4GPa vs 230Gpa.

Then I graphed the result to find the Vf that would give me the maximum bending stiffness. I got 0.99999526

Obviously a Vf of 0.99999 isn’t even theoretically possible, so according to my calculations, having the highest Vf possible (without voids) should produce the highest bending stiffness, keeping weight constant.

However, when I used a similar equation for an ideal S-glass epoxy composite:

Vf/(1.2+1.28Vf)^3

I got 0.46875223 for the maximum Vf for the maximum stiffness for a given weight. The ideal Vf is lower for fiberglass because of its higher density. So achieving a higher Vf may actually decrease the stiffness to weight ratio of a fiberglass laminate.

#12

You are correct in terms of uniaxial stress and pressure (force/area), but increasing the Vf of a given layup in a structure does not enable the structure to handle a greater force. In fact, it almost always decreases the load bearing ability of the structure.

Total load bearing and strength are two different things. Strength is a material property and is independent of thickness, width, & length and has units of force/area (psi, MPa, etc.). The maximum load is determined by the strength (tensile, compression, shear, etc.) and the cross sectional area over which the load is applied.

I would assume that the UAV boom did fail via buckling of some sort. Same loading conditions, same amount of reinforcement layers, thinner laminate cross section. I am also assuming that the added fiber laminate had the same Vf (60%) as the thinner version. The strength of the laminate didn’t change, but the geometry did (thickness). I bet if the panel sizes were changed (stiffeners were added, etc.) instead of adding more fiber layers the critical buckling load would have changed. The laminate strength would not have changed, only the geometry.

#13

True enough, but at a greater cost. The challenge with any real world project is that there are deadlines to meet, budgets to stay within, and tooling to build and maintain.

Regardless of what the design engineer designs the structure has to fabricated and be functional. There are many significant and well funded projects that never made it because a process could not be developed to meet the engineers specification in a timely manner.