Calculating minimum bend radius of Composite rod

[oneeyedwitchdoctor]

Hello

Is there a standard methodology for calculating the theoretical minimum bend radius of composite rod. I have a spoolable 10 mm dia rod and I want to know what the minimum drum diameter that i can spool it onto is.

Ultimately I want to use this formula to run a numerical optimization to find the best overall stiffness (changing the diameter of the rod, and composite mixture/material) when the rod is in a pipe bore, so any info on buckling calculations for composite is also very useful to me.

Thanks in advance

 

[RPstress]

It comes down to the allowable strain of the rod material. If it can take, say, 1000 microstrain (0.001 absolute strain) then it can be wrapped round an inside bend radius of 500 (well, 499.5) times the rod's diameter. The max surface strain is 1/(2*R) where R is radius to the centreline. For carbon fibre a strain of 2000 microstrain is probably very safe, and maybe 5000. It probably won't break until about 15000 microstrain. If it's E-glass then you can double those numbers.

It's probably safe to use Euler buckling for a composite rod. Stress for buckling = pi^2*E*I/L^2. (I for round rod is pi*D^4/64.)

For UD ordinary carbon at a fibre volume of 50% E is about 100000 MPa (14.5 Msi). UD glass is maybe 35000 MPa (5 Msi).

 

[RPstress]

Oops, E for UD HS carbon at 50% Vf is probably nearer 120000 MPa, 17 Msi or so. Sorry, disfunctional brain.

 

[oneeyedwitchdoctor]

Thanks for the info RP.

Maybe it's that Friday feeling, but i don't see where you get the 500 (well 499.5) ratio of rod diameter to bend radius. The manufacturer has quoted a minimum bend radius of 1.4m. perhaps this is empirical based on low cycle fatigue or something though. Your info has pointed me in the right direction though, as we want to be able to play around with the numbers ourself to find the youngs modulus (or carbon fill), rod diameter, and also the grade of carbon that we are using

 

[RPstress]

Oops again, surface strain = t/(2*R[sub]centreline[/sub]) so R/t for a strain of 0.001 is 500.

For a 10 mm rod and an IBR of 1.4 m I get 3560 microstrain and maybe 15 or 20 MPa in UD glass or 400 MPa in carbon, which sounds passably safe for repeated application with glass.

[What little data I've got for glass in fatigue gives a max tensile stress of 20 ksi (137 MPa) for a life of 10^8 cycles...however, that corresponds to a strain of 0.68% according to them (Sandia report for wind energy, SAND92–7005), which seems to give a bit of a low E for UD E-glass, though the claimed fibre volume fraction is also low (30%).]

For a sane number of winding on of 1000 times the Sandia stress was 45 ksi. Say a factor of one and a half for scatter (a guess) and another one and a half for 0+-P not P+-P loading (a real guess) gives an allowable bending stress of maybe 20 ksi again. 1.4 m doesn't look daft.

 

[RPstress]

I just realised that you've said it is carbon not glass.

I've got even less info on UD carbon in fatigue than glass. What I've got indicates fatigue strengths of at least 80% of the static strength, about 600+-600 MPa in compression. That's a maximum failure strain of about 8500 microstrain.

Say a strain of 4000 microstrain, that implies an inside bend radius of 1.2 m. As I said, their 1.4 m would give a strain of 3600 microstrain. It's possible that the limits for static strength in damaged carbon are more important than fatigue, even for a civil structure like this.

Someone else might have a more realistic estimate for bending fatigue allowables in carbon.