calculating laminate thickness

[dionysis]

Hi all,

I need to determine laminate thickness as a function of number of layers, ratio of fibre to matrix, and the areal weight of fibre. So far, I have two formulae, but they are giving different results. Anyone got a reliable method of calculating the thickness? It is for hand layup.

[Slowmo]

Originally Posted by dionysis

Hi all,

I need to determine laminate thickness as a function of number of layers, ratio of fibre to matrix, and the areal weight of fibre. So far, I have two formulae, but they are giving different results. Anyone got a reliable method of calculating the thickness? It is for hand layup.

The answer is more or less obvious.

For hand layup there are no formulas.

No one knows how much matrix your foam distance material will absorb. If unlucky (or stupid) the foam will absorb even more matrix then the fiber will.

In what manner will you do the work?

etc. etc.

You can do some aproximations but then you have to settle for more or less everything to really know.

IF... Choose the formula you like the most and make 3 scenario calculations.
1) ...with the theoretical best (litest) output.
2) ...with the practical worst (heaviest) output.
3) a middle, most likely outcome.

Then you choose yourself, which calc is the most likely to appear.

[sorenfdk]

Originally Posted by Slowmo

The answer is more or less obvious.

For hand layup there are no formulas.

No one knows how much matrix your foam distance material will absorb. If unlucky (or stupid) the foam will absorb even more matrix then the fiber will.

Oh yes - there are formulas! They're not 100% accurate (what is?), but they're quite OK for practical use, so designers all over the world use them every day.

See http://boatdesign.net/forums/showthread.php?t=4826

I've never heard of foam that absorbs more resin than the fibres - can you please tell me which foam you are referring to? I guess one has to be really, really unlucky (or really, really stupid!) for that to happen...

[guest12020101217]

I think the following is use the same as on the posts at http://boatdesign.net/forums/showthread.php?t=4826, but here goes

From Rule of Mixture Theory
t = {(n*W)/(1000*pf*pm)}*((pf/Wf)-(pf-pm))
t = ply thickness in mm
n = number of plys
W = weight in g per sq.m
pf = specific gravity of fibres
pm = specific gravity of matrix (resin)
Wf = Weight Fraction = Weight of Fibre:Weight of Lamina
If you have a laminate at resin ratio 2:1. Wf = 1/("2"+1) = 0.33 (2 s.f.)

Wf = (pf*Vf)/(pf*Vf+Pm*Vm)
Vm = Fibre Volume Fraction
Vf = Matrix Volume Fraction
Vm = 1 -Vf (in absence of voids (usually about 2%)
Wf = (Pf*Vf)/(pf.Vf+pm*Vm)

Overall Density of a Laminate = (pf.Vf+pm*Vm)/(Vf+Vm)
= Vf(pf-pm)+pm
SG valves
E-Glass = 2.56
Aramid = 1.45
Carbon = 1.8
Polyester Resin = 1.2
Vinylester = 1.1 to 1
Epoxy = 1 and below
For Polyester/Glass laminates thickness equation becomes.
t(mm) = {w/3072)*((2.56/Wf)-1.36))

Aramid WF
UD 0.4
WR 0.35
CSM 0.19
Carbon
UD 0.45
WR 0.4
CSM 0.23
E-Glass
UD 0.54
WR 0.45
CSM 0.35

Please take all typical valve given about with care and a pinch of salt as it is only theory.

cjdengate

[Dutch Peter]

Originally Posted by dionysis

Hi all,

I need to determine laminate thickness as a function of number of layers, ratio of fibre to matrix, and the areal weight of fibre. So far, I have two formulae, but they are giving different results. Anyone got a reliable method of calculating the thickness? It is for hand layup.

You have two formulae and you want a third or fourth???
With all the different approaches/views on what the major factors are and what the safety factor should be?
If you compaire 5 formulae from 5 Class Societies, I bet you'll get 5 different answers, it doesn't make them all wrong. (It doesn't make one of them right either!)
To understand what is happening you'd better post the formulae and your data, then someone can explain what the difference is, and why, and then you can decide what answer you liked best!


Good luck

[sorenfdk]

Originally Posted by Dutch Peter

You have two formulae and you want a third or fourth???
With all the different approaches/views on what the major factors are and what the safety factor should be?
If you compaire 5 formulae from 5 Class Societies, I bet you'll get 5 different answers, it doesn't make them all wrong. (It doesn't make one of them right either!)
To understand what is happening you'd better post the formulae and your data, then someone can explain what the difference is, and why, and then you can decide what answer you liked best!


Good luck

I think you have misunderstood what Dionysis is asking for. He's not asking for a formula to calculate the laminate thickness to achieve a certain strength or stiffness, but a formula to tell him how much material to use if he wants to achieve a given laminate thickness. At least that's how I read his posting.

I we are talking about strength and stiffness, then you're absolutely right. There are different approaches, and one should be careful when choosing among these. Software with reliable results is available - The Laminator and CompositePro are just two of them - but they are all more or less based on theory. To be on the safe side, one should test pieces of laminate built of the same materials and in the same way as if it was the actual boat being built.

BTW: One should see and treat formulas from Classification Societies as parts of a complex of formulas. Never use one formula alone - it's either all or nothing!

And just out of pure curiosity, I would like to see Dionysis' two formulas, too!

[Dutch Peter]

Dionsys, sorenfdk,

Sorry if I misunderstood, still like to know the formulae anyway!

[dionysis]

I am sorry I have not replied earlier, the forum's email that this thread had got replies, never got to me. Must have been a glitch.

He's not asking for a formula to calculate the laminate thickness to achieve a certain strength or stiffness, but a formula to tell him how much material to use if he wants to achieve a given laminate thickness. At least that's how I read his posting.

yup, thanks sorenfdk

Anyway, here are the two formulae I had to begin with.

I cannot remember where I got the first two from. For the first formula:

d = laminate thickness
n = number of plies
A(w) = areal weight of fabric
rho(f) = density of fabric
V(f) = volume fraction

The table is informative. The last one is from SP Systems "Guide to Composites"

I have gained some understanding in calculating laminate thicknesses. In many ways it is a headache because unless you can build up the laminate under controled conditions, you have no guarantee that your thickness will give you the predicted laminate strength. Oh well, that is what safety factors are all about.

Thanks very much for your help. I will put it to good use.

[guest12020101217]

Dear sorenfdk

I think you rasied a very important point about using formula from Classification Societies when you are not working to a Classification Societies.

Quote "BTW: One should see and treat formulas from Classification Societies as parts of a complex of formulas. Never use one formula alone - it's either all or nothing!"

Most formulas in Classification Societies (i.e. Lloyds SSC etc) can be worked backward to first princples like simple beam theory, rule of mixtures or classical laminate theory, but the Societies formula may well have "fudge factors" or factors of safety or offer things added. There factors work well then used with the rest of the classification method.
What ever formula you use, it is always useful to sit down and try and work out it origin. I bet most will be from simple beam theory, rule of mixtures or classical laminate theory unless it is a Statistical (sorry if spelling is wrong) approach. If it is a statistical approach based formula it will only be useful if what you are working on falls with the data limits of the formula's base.

[sorenfdk]

Often, the problem is to find out where the fudge/safety factors are hidden. Furthermore, different Classification Societies may have different opinions as to where the critical stresses will occure. According to the ABS Guide, for instance, the critical stress in a sandwich hull panel will be compression in the inner skin along the stiffener. Others say otherwise.

[Dutch Peter]

Originally Posted by sorenfdk

Often, the problem is to find out where the fudge/safety factors are hidden. Furthermore, different Classification Societies may have different opinions as to where the critical stresses will occure. According to the ABS Guide, for instance, the critical stress in a sandwich hull panel will be compression in the inner skin along the stiffener. Others say otherwise.

That's what I was aiming at with my comments, it's not always a good idea to try to get to the answer fast. Sometimes you need thew background info to determine weather you're going the right way.

[dionysis]

You are right Dutch Peter, especially with fiber laminates. Good old steel and aluminium can guarantee predictable behaviour since they have uniform properties. Fudge or safety factors need only take into account above average loads and fatigue etc., for these materials, but fiber reinforced laminates are critically dependent on layup. You just have to test samples to destruction.

[Slowmo]

Originally Posted by sorenfdk

Oh yes - there are formulas! They're not 100% accurate (what is?),

In reality the "formula" will prove to give somthing like + /- 30% accuracy in this area.

That's an aproximation.

One may also take the given likely ply thickness from the glass supplier, add up the plies and then add 30% ...or retract 30% and voila!

Everything can have formulas... but that doesn't say that they are true or realistic.

[sorenfdk]

Originally Posted by Slowmo

In reality the "formula" will prove to give somthing like + /- 30% accuracy in this area.

That's an aproximation.

One may also take the given likely ply thickness from the glass supplier, add up the plies and then add 30% ...or retract 30% and voila!

Everything can have formulas... but that doesn't say that they are true or realistic.

That sounds interesting! Could you please tell me where (URLs, books, papers) you have the +/- 30% accuracy from?
The formula I referred to (and which is the same formula as the one from SP Systems) is from a book by C.S. Smith of The Admiralty Research Establishment in Scotland. The title is "Design of Marine Structures in Composite Materials".

[dionysis]

That 30% figure looks too high to me. I would not like to have so much leeway in calculating laminate thickness. Imagine what effect this variation would have on laminate strength. Talk about safety factors.