Carbon fiber grades and elastic modulus

[Sleighai]

Howdy,

I'm a little confused about the correlation between carbon fiber grades and the elastic modulus of the final product. This article from Rock West indicates that standard modulus starts at 33 Msi, with ultra-high modulus at 65 Msi. However, the tubes I'm seeing all seem to have elastic modulus well below 33 Msi, such as this ultra-high modulus tube listed at 26.64 Msi. I thought this might be a matter of the fibers vs. the final product or the type of loading the tube undergoes, but I haven't found any information to that effect. Could y'all shed some light on this for me?

[John Kimball]

On 5/5/2023 at 5:07 PM, Sleighai said:

Howdy,

I'm a little confused about the correlation between carbon fiber grades and the elastic modulus of the final product. This article from Rock West indicates that standard modulus starts at 33 Msi, with ultra-high modulus at 65 Msi. However, the tubes I'm seeing all seem to have elastic modulus well below 33 Msi, such as this ultra-high modulus tube listed at 26.64 Msi. I thought this might be a matter of the fibers vs. the final product or the type of loading the tube undergoes, but I haven't found any information to that effect. Could y'all shed some light on this for me?

Welcome to the forum! We get your question somewhat regularly. The answer is quite simple, but the math behind is a lot more complicated, as it all depends on the particular tube and how its made.

While it's true that the fiber used in each tube may have a particular modulus, carbon fiber is considered anisotropic (as opposed to metals that are isotropic), so it only has strength properties in one direction, the direction of the fibers. When we make tubes, the fibers are oriented in a way that optimizes stiffness and reduces buckling. Because of this, the overall modulus of the tube is reduced. We call this a knockdown in performance. Most of the fibers are in the 0° orientation to create stiffness, but then the rest of the fibers are oriented in the 90° direction to decrease buckling (but these plies add nothing for the overall modulus of the tube). In some cases we may use +/-45° fibers to help with torsional requirements. In this case we should see a little bit higher tube modulus than with the 90° plies, but buckling is slightly increased. 

So, in a nutshell, if all the fibers ran in the 0° direction, you'd see a comparable tube / fiber modulus. But, when about 1/2 the fibers are not in the 0° orientation, but the tube tube dimensions are the same, you remove modulus from the tube as the 90° fibers add nothing, but they do take up space, so the tube modulus is reduced accordingly. Buckling (crushing, kinked garden hose affect, etc.) is high without the 90° fibers.

[Jeremy Senne]

One more update to John's answer.  The layup definitely contributes significantly to the overall aggregate modulus of the tube, but if you were expecting an all unidirectional tube to have the same modulus as the fiber you'll probably be disappointed to find its 40-50% low.  The other factor to consider is fiber volume compared to matrix volume, where the matrix is the resin the fiber is set in (usually epoxy or cyanate ester).  This boils down to a rule of mixture combination of the fiber contribution to modulus and the resin contribution to modulus at the volumetric level where the two usually add up to 100%.  The easy calculation is E_Total = Vf*E_fiber + Vm*E_matrix, where E_Total = Combined modulus, Vf = Fiber Volume, Vm = Matrix Volume, E_fiber = Fiber modulus, and E_matrix = Matrix modulus.

Most composite laminas (and laminates) are in the range of 40% to 60% fiber volume, which the higher performance structures closer to 60% fiber volume.  Since the fiber modulus is usually 10x or more the modulus of the matrix, you'll see the modulus of laminate at about 60% of the fiber modulus.

If you're thinking that becomes a huge knockdown when you do a multi-angle layup like [0/45/90/-45/-45/90/45/0] and then also go with 60% fiber volume you're right.  Usually this has you around 30-40% of the fiber modulus.