# CLT (Classical Laminated Theory) Thermal & Moisture Coef

Discussion in 'Materials' started by Erwan, Mar 29, 2019.

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### ErwanSenior Member

Hi
Being a rookie in FEA or structural engineering, I guess the following question might look a bit candid, so please, be indulgent.

In the following link regarding (CLT); Thermal and moisture coefficients are part of the equations:

https://wstein.org/edu/2010/480b/pr.../A summary of Classical Lamination Theory.pdf

I wonder if it is the case, because of aeronautical applications, where airplanes fligh high altitude in very low temperatures ?

So if application is a carbon mast for beach cat, is it possible to make things simplier and easier, neglecting these 2 coefficients??

Erwan

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### DejaySenior Newbie

There are much smarter guys here who can help you, but looking at the formula and assuming that "delta T" stands for the temperature difference, it looks to me like this would turn all the MT and MM terms to zero so they can just be left out at step 7.

PS: Here you can see the moisture coefficient just being left out: https://courses.washington.edu/mengr450/CLT_Summary.pdf

Last edited: Mar 29, 2019
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### rxcompositeSenior Member

You don't need thermal and moisture content analysis if the laminate is not subject to extreme environmental changes. For a carbon mast analysis, you need stiffness analysis. FEA is good if you are analyzing shapes with compound or acute angles. For a simple round or elliptical design, the matrix form of CLT is good enough. CLT in matrix form can be arranged to analyze different ply behavior like strain, twist, shear stress, and modulus of elasticity.

For your need, a filament wound laminate is the best manufacturing method. This simplifies to a single layer of laminate of the same basic mechanical property but whose angle relative to its axis varies from layer to layer. This is an angle ply laminate and the biggest problem you will encounter is the internal stress influenced by shear strain. This is caused by rotation of the ply angle relative to each other.

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### ErwanSenior Member

Even if I attended mathematics university around 40 years ago, I am still very rookie with FEA or structural analysis, and looking carefully at this carbon tube project, I just realized that there is no much alternatives, just because if you want to use UD T700 , you can get 100g/sqm (the lightest available at "reasonnable" price). So may be a thorough FEA analysis would not be that important.

On the other hand, just by analogy with similar tubes, built some years ago, I have a little idea of the global weight and diameter. These similar tubes weights around 620 g/m for 91 mm diameter
So the 20 feet lenght was at around 4 kg, but it was built with the best technology available (prepeg + autoclave).

I might use prepeg no sure, but no autoclave because the mandrel is plastic and can bear only a little heat below 60°c during epoxy curing.
Later when the plastic mandrel will be removed and cooked again at a slightly higher temperature if it makes sense.

It will be mandrel wrapping more than filament winding, I think I will use from inside to outside
(1 ply @ 90°) + (8 plies @ 0°) + (3 plies @+45°) + (3 plies @ -45°) + (1 ply @90°)

Anyway, static loads are light for this 20 feet long tube, ie: It is only around
1- 1250/1400 Newtons for compression
2-500 /600 Newtons for flexion or 100 N/ m for evenly distributed load along the 20 feet lenght
3-Around 600 Newtons x meter for the torsion load.

So it might be cheaper to built one than to pay for FEA.

Thanks again and happy week-end

Erwan

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### ErwanSenior Member

If anybody knows a freeware a rookie can use to perform the appropriate calculations, please do not hesitate to post the link.
Cheers
Erwan

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### rxcompositeSenior Member

Erwan,

We used low temp prepreg and vacuum bagged method before. Oven was home built with electronic temp control. Female mold used is high temp resin laminate.

If you want it shiny on the outside, wrap it in a rubber tube with provision for air pressure, insert the laminate in a metal tube, and fire it in the oven.

You can easily program the CLT matrix format in Excel. Excel has the inverse command to build up the ABD-1 matrix. I have done it using textbook examples. I don't know of any FREE CLT program available but I bought mine some 15 years ago at SAMPE for \$200. Still works fine but I have to use an old computer. Generates report on ADB matrix format. The Newer programs available now cost \$2,000 above.

Just remember that CLT programming would require at least the material properties even for a single ply orientation. If it is rotated, the matrix will do it for you but the initial properties has to be right.

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### ErwanSenior Member

Thank you so much RX,

So if I cannot avoid matrix inversion , I will have to do it, and at least it will be a good intellectual exercice.
So I have to find the relevant inputs:
E(theta) =probably the Young Modulus
E2 = Transcerse Modulus
G = Shear Modulus of Elasticity
vega= Poisson's ratio

I guess I will have to calculate E(Theta) for the different wrapping angles (0° / +45° /- 45°/90°) ?

Please can you tell me if it is a correct approach ?

According to your comments, you are used to build these kind of carbone tubes, Too bad you are so far.
It would have made things easier.

Cheers and Thanks again.

Erwan

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### rxcompositeSenior Member

E, Poissons, at 0 and 90 degree. Shear modulus and thickness can be computed. These are minimum inputs for 1 laminate. The Etheta can be calculated by the CLT.

CLT models can be same laminate, one rotated to an angle, two laminate, different material, three laminate with same properties, three lam with different properties.

I have several models. The one downloaded from Wayne State university is the most complete as it has solved examples.

Should be easy for you. You have formal training. Me, I have to figure out everything.

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Last edited: Apr 3, 2019
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### rxcompositeSenior Member

Possible to do inversion in Excel

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### rxcompositeSenior Member

If you want CLT, long hand, and figuring out, E, strength, shear, poissons at different angles, try using engineering constant as discussed in Filament Winding Composite Structures by S.T. Peters et al. Here the induced stress by ply angle rotation is discussed. The matrix theory is also discussed but no solved examples. Very good book to review.

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### ErwanSenior Member

Thank you very much RX, and Dejay,I will pay attention to the document DEJAY has post, as there are many solved exemple and it will be a good way to learn.

I know Excel has a matrix inverter, but I never used it so far, but soon I will.

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### ErwanSenior Member

Thank you very much RXComposite and DEJAY,

I think I will pay a lot of attention to the document DEJAY has posted, as there are solved examples.

I will have a look at the Wayne State University too.

Thanks again best regards

Erwan

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