Ply Moment

[midsidenode]

I need help from someone here. Let's say i have a multi-ply laminate subject to plane stress that is loaded in some way (Nx, Ny, Nxy, Mx, My, Mxy). For one particular ply that I'm Interested in, i happen to know the global stresses at the top and bottom of the ply as well as its thickness. I also know the thicknesses of all the other plies. I would like to try and find out how much moment (let's say Mx) is carried by this one ply. I know i need to integrate the stress distibution across the ply, but can anyone provide me some specifics on how to do this? thanks...msn

 

[ESPcomposites]

Curious, what would be the point determining the moment in an individual ply?

Classical Laminate Theory usually considers the moment in the total laminate and then based on strain compatibility, you can deduce in-plane stress/strain of a ply. I have never seen a ply moment used for anything (off the top of my head). The thinking is that for practical applications, it is not relevant.

That said, I think your answer is to just use sigma=P/A + Mc/I of the individual ply. You would subtract the axial component and be left with the stresses that cause bending (i.e. a zero delta top and bottom stress indicates no bending). From there, back calculate out the moment (I=(1/12)bt^3) and c=t/2.

Brian

http://www.espcomposites.com

 

[midsidenode]

ESP - that technique will not work here especailly when trying to determine applied moments. my approach here is a little unique in that i really need to find the forces and moments that each ply carries. I kinda-sorta now how to approach this. It's just that i don't know how to carry out the integration of the global stress distribution across the ply (from top to bottom). Any help on this would be appreciated. msn

 

[ESPcomposites]

You said it would not work, but did not say why. If I understand you correctly, it should work ok for an linear strain distribution through the thickness. This would be valid only for a single ply. Where it would not work is if you were to consider the total laminate top and bottom surfaces since the varying modulii would affect the calculation.

Consider this, the strain distribution through the thickness of a laminate is linear (for typical laminates). Stress is not, due to varying modulii. At each ply, you also have a linear distribution of strain. A single ply has a single modulus in a given direction (through the thickness). Therefore, if you already have the ply outer fiber stresses you can back calculate the equivalent ply moment. Perhaps you can try a lamination program to verify this, but it should work ( I have not tried myself).

But again, Is there a practical reason or is it just to observe/understand something better?

Brian

http://www.espcomposites.com

 

[ESPcomposites]

I ran a few test cases (isotropic and laminated plates) and they performed as expected. The other way to check (or to think about) is to realize that k (curvature) = (M/EI) = constant for a laminate. The moment in each ply yields a curvature based upon its own I. That will match the other plies as well as the overall curvature. Strain compatibility leads to curvature compatibility.

Perhaps you think you need to integrate as one might when calculating the [D] matrix? However, don't forget that by the time you have the ply stresses, that has already been done. In other words, all the "work" has been done for you already.

The moment that actually remains in the ply should be relatively low, by design, and the overall moment is largely reacted by the plies farthest from the neutral axis. Think of the caps of an I-beam. The cap axial loads react the moment, with very little moment in the cap itself.

Hopefully that makes more sense now. If not, perhaps you can give an actual problem. There are quite a few resources about CLT as well. Have a look at the [D] matrix formulation process and how the integral is used. But remember that is different than the question you are asking. You asking about individual ply moments (as I understand) as opposed to overall moments.

Brian

http://www.espcomposites.com

 

[midsidenode]

For those that may be interested, I found a great way to solve this problem. You can integrate the global stress across the ply (from top to bottom) using a first order newton's divided difference ploynomial. The units will be (lbf-in)/in or (N-m)/m. A good check is to perform this across each ply and add the moment carried by each. They should obviously add up to the applied moment.