Calculating reinforcement equivalencies??

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#1

I don’t even know what this would be called, so I’m hoping to adequately explain my predicament.

I’m developing a process for laying up some oddly shaped tubes of carbon fiber. To save $$$ on development, I’m using basalt fiber sleeves, which are about a third the price of carbon, by length.

Now, once I’ve figured out layup orientation and process to get a stiff enough tube, I want to substitute carbon for the basalt.

Because carbon fiber has better mechanical properties than basalt, I don’t need as much carbon to get the same properties. But is there a way to calculate just HOW much less carbon would be required?

I know full well that there is likely to be no direct, all-encompassing method that doesn’t involve FEA software, but what I’m looking for is a reasonable starting point.

#2

Yes. You could start calculating the equivalent amount of carbon with just their stiffness values and some assumptions. With stiffness (and not strength) it is fairly easy to find an equivalent.

Assume:
[ul]
[li]same fiber volume ratio between the two reinforcements. (Doesn’t matter what ratio it is, as long as it is the same).[/li][li]Same resin used, and same resin-dominated properties when cured.[/li][li]That the equivalent stiffness of carbon will be strong enough.[/li][li]That since you are making tubes, that we can approximate the tube walls as thin shells (in other words, that the tube shape is providing bending stiffness, not strictly the thickness, as in a flat plate).[/li][/ul]

I’m going to estimate that the carbon (dry carbon) is 3x stiffer and 2x stronger than the basalt (again, dry fibers). I estimated from this pageat the bottom:

Some additional numbers, first ones I found:
[ul]
[li]Basalt fibers:[/li]Elastic modulus: 89 GPa
Density: 2.7 gram/cubic centimeter
from: http://www.junantai.com/en/products/basalt/basalt_fiber.htm

[li]Carbon fibers (AS4):[/li]Elastic Modulus: 235 GPa
Density: 1.8 g/cubic centimeter
From (Engineering Mechanics of Composite Materials)
[/ul]
The short answer is, 3x less carbon (by cross-sectional surface area). Unfortunately, a fabric 1/3 the weight is not equivalent because the densities are different. You could however, choose a fabric that is 1/3 the thickness.

A another useful number would be how much less weight of fabric (in oz/yard or whatever you buy it in) or thickness per ply.

To figure out how much weight of carbon is equivalent, compare the specific stiffness of each material.

[Specific Stiffness] = [Stiffness]/[Density]
of carbon fibers:
235 GPA / 1.81 g/cm^3 = 130 kNm/g
of basalt fiber:
89 GPa / 2.7 g/cm^3 = 33 kNm/g

CF has 4x greater specific stiffness, so you can replace each ply of basalt with a ply of CF that has 1/4 of the fabric weight.

This does simplify a lot, as you noted. It might help to know which stiffness is important to spec (torsional, bending, axial), and to note that the strength of the equivalent stiffness of material is not the same. Some physical testing would be the safest, and easiest way to verify that.