Deflection Calculations of a special CFRP "Beam" 1

[Roserio]

Dear all,

I will ask you to first have a look on the files in attachment with the part that I will refer to by "alveolus".

This alveoli parts is a square profile beam that has roughly 100x100x300mm with max 16 24x24mm square hallows inside. When I started designing this composite part I used conservative values and conventional beam theory to get an idea about its max deflection under max working load. The part has been tested and with good results but I would like to know how to do it using composite formulations (not FEM).

The part is made by using a simple idea of joining each small square profile all together, preheat to get the prepreg "softer", and then add an extra outer overlap to add extra strength but also to ensure that the resin wets the fabric everywhere without dry regions. The mold to press the prepreg is somehow unconventional and turned out difficult to achieve good results using only one layer.

Given this lengthy (hopefully helpful introduction I would like to ask if someone could give me some references on how to compute load deflections in such a beam (it works in cantilever conf.) for different wrapping configurations f.e. inner +-45 outer 0/90 or inner +-45 outer +-20 f.e.

Any hint would be great.

Thanks,
Roserio

PS: The project I am working on is a particles detector and is a public project that can be found by gooling f.e "PANDA at GSI"

 

[rb1957]

i'd model the beam as the upper and lower surfaces only, as a beam in bending ...
bending stress = M*y/(2*Ay^2) = M/(2*Ay) at the mid-thickness of the surface
(peak stress at surface, M*(y+t/2)/(2*A*y^2)

second model would add the three vertical webs (middle one is twice as thick as the outer ones) ...
bending stress = M*y/(2*Ay^2 + (2*t+2t)*(2y)^3)
more exact M*(y+t/2)/(2*A*y^2 + (2*t+2t)*(2*(y-t/2))^3)

Quando Omni Flunkus Moritati

 

[RPstress]

I have now looked at your pictures with my phone—I can't see 'dropbox' through my company's firewall.

How accurate do you want the results? Simply using the various layers with appropriate EA and simple cantilever bending of the vertical webs would normally be ok, much as rb suggests. However, at 300 mm long and 100 deep and wide there will probably also be significant shear deflection compared with the bending. If you decide to worry about that you need to check GA for vertical webs.

At 300 mm long and 100 wide and deep you might also be concerned by shear lag effects. If you have a fairly concentrated load it will take about 100 mm length before it reasonably approximates engineer's theory distribution, and possibly more if E vs. G is a high ratio cf. isotropic. It can take a longer distance than might be expected for load in a composite to shear over the full section. I would normally ignore this sort of thing but it depends on the accuracy you need.

Putting plies in at 45 will make the material more quasi-isotropic and give it a lower effective E of course. I'm not quite sure what areas you're suggesting might be made with layers at +-20°.

[I would just use simple laminate analysis software to assess the E and G of different layups. It won't be bad for stiffnesses (as opposed to strengths).]

 

[Roserio]

Hi guys,

The link below has a picture that gives a better idea about the outer (2nd) layer. This smaller config. was used to test the molding concept. A similar one with 4 hallows was loaded with 20Kg (5x the actual working load) and has a deflection of 0.450mm. (the photo with dial gauges in the 1st link).

How accurate? When I made the design I left a clearance of 0.550mm for bending and this should be fine. Now I have 7 different types of alveoli and I would like to know exactly how much each cofig. bends (deflection+shear bending) and rotates due to torsion. Knowing that I will be able to know the exact position of the detectors that goes inside each cavity (2nd link)

 

[Roserio]

guys could provide some links that I can use to get more familiar with composite beam theory.

rb1957 I somehow did what you mention, I computed the moment of inertia for each configuration and then used properties of two different laminates I tested with 60%fv and 40%mv but I think that in this parts the % of resin is even smaller than 40%.

RPstress: could you explain better what is "shear lag". Has it something to do with the bending due shear stresses? And which FE software do you recommend? Any freeware by change?

Thanks a lot, is really nice to have you help.

Roserio

 

[rb1957]

"shear lag" is a standard term ... look up google, wiki, or mechanics of solids textbook; it is a more precise calculation of how sher loads distribute themselves through structures.

with the simple I's suggested you can calc the deflection of the beam. use a % resin that gets you your results, then ask yourself "how reasonable is this result ?"

Quando Omni Flunkus Moritati

 

[RPstress]

It takes distance for loads applied over a small area to distribute themselves into a structure. Saint Venant's principal. This is behind what is often called shear lag, where a bending stress takes some distance to distribute across a thinnish-walled rectangular section. A wingbox is the classical example. True shear lag mainly applies to how distributed load doesn't build up endload which is constant across the width. This is also true close to small ("point") loads.

Composite beam theory is really just beam theory with small modifications (well, usually they're small) as discussed for things like a low shear modulus compared with Young's modulus, which increases the distance a load takes to distribute itself across a section in accordance with ETB. This can also worsen secondary effects like flanges bending at right angles to a longitudinal web. You usually also need to check things like through-thickness stresses with sharply curved beams more than you do with isotropics.

The cheapware for classical lamination theory (CLT is the sort of thing that can be put in a spreadsheet, and doesn't need finite element analysis) is usually something like The Laminator ($30; used to be free

http://www.thelaminator.net/).

There's some free actual FE as well, but I don't have any recommendations; often a pain to get working. The Laminator will give serviceable estimates of the equivalent E and G for different layups of unidirectional or woven composite. There should be some truly free classical lamination theory.

For the fundamentals of how composite structures differ from isotropic ones I would recommend getting a reference like Barbero or Kaw but there's lots online these days.

http://www.compositecarbonfiberprop.com/carbon_fiber.pdf

Introduction to Composites doesn't look too bad.

Will look at the new dropbox stuff later. Can't see through firewall at the moment.

 

[Roserio]

Dear RPStress,

Sorry for the late answer. I have used keywords I learn from you and got to something interesting:

http://www.isfk.at/en/1428/

and

http://wm.unileoben.ac.at:8080/webMathematica/ISFK/Laminate_Theory_webApp.jsp

which is what I was looking for.

I have learned a lot about composites since I started this one project with the carbon fibers alveoli, mainly with the "JEC Magazine COMPOSITES". I have come across complains about slow transition on the way the composite design still follows aluminium alloys rules and I would like to use CLT to avoid exactly this. I was interested in knowing more about the theory and I purchased the "Composites Materials 2Ed" from Daniel Gay/Suong V.Hoa though I found it difficult to follow specially if one is not fully dedicated to composite design.
Now I am making baking tests to see if it is possible to add a layer of Graphite in between two layers of carbon fiber to increase the overall thermal conductivity of the composite. I have tried to go for ultra high modulus carbon prepreg but the offer I got for min quant. of 50sqm of this material would cost more than €100K so graphite would be it if delamination is not a problem.

Hope to find some time in the following months to learn more about the formulations in the links above and post some results here.

Many thanks,
Roserio

 

[RPstress]

€100+k for 50 sqm...pricey stuff. I don't have any appropriate comparison costs. But then UHM is costly; the stiffest artificial material there is and not much used so I guess we can expect a premium, especially for such a limited quantity.

That ISFK stuff looks useful. Thanks. I look forward to any more information about your usage.

Graphite should be a better conductor than UHM composite through-the-thickness (UHM seems to be quite a poor thermal conductor through-thickness). (In the fiber direction UHM should be very good; better than copper.) How do you plan on joining the graphite and the composite?