Structural stiffness related to material and scantling rules

[baeckmo]

Trying to get a better grip on the consequenses for structural behaviour from the differences in elasticity between various hull materials. First thing: what variation is there?

For the normally used materials steel, aluminium and grp the rules stipulate the critical mechanical properties like stress and modulus of elasticity, but when checking for info on carbon/epoxy as used for a single-skin panel, there is a very wide range coming up from the search.

When it comes to highly elastic materials, like LDPE, HDPE, ABS and the like, they are applied widely across industries and I think most of the info there can be used "straight off".

So, a question to our "high-strength lamination dudes": what would be realistic values for design yield stress (or corresponding) and E for a layup with a reasonable balance between strength in two main directions?

 

[jehardiman]

Every high strength composite design I've been involved in the lay-up was engineered for that specific case. This is because composite lay-ups are anisotropic.... it matters where in the depth of the lay-up the direction that the fibers are oriented, and the shape of those fibers. You choose the directions, and weave, of each individual layer to maximize needed strength...to the point of orienting individual strands in laid carbon items; as well as selecting the matrix for the needed elasticity (and rather than elasticity think flexural strength...every time you try to "stretch" a composite you damage it slightly). And yes, there are also "standard" "nominal" lay-ups that shoot for isotropic properties...at least in two axes...such as G-10.

Think of it as designing an I-beam made up of different materials. You have different loads in the top and bottom flanges (i.e. skins) than you do in the web (core). If you really want to get into this I suggest the text Theory of Composites Design by Stephen W. Tsai.

EDIT: See if you can download this. https://apps.dtic.mil/sti/tr/pdf/ADA157710.pdf
(and notice that the document was printed from a Mac...which was what the original design program was written in...see his Composites Design book. Amazon.com https://www.amazon.com/Composites-Design-Stephen-W-Tsai/dp/0961809027#:~:text=Composites%20Design:%20Tsai%2C%20Stephen%20W,Tsai )

 

[william stokes]

I never cease to be in awe of just how string carbon fibre layups are
you look at Comanche , 100ft of power with record breaking crossing of the Atlantic under sail
of course this is not a material for amatuer build.
as a builder of alu craft I can compare and one has to go up in hull skin thickness to have the strength and other properies of carbon, then when you do weight rules out for race yachts
nice post jehardiman

 

[baeckmo]

Thanx for the ref. download, JHM, it worked. Actually, I'm not getting too involved in composites. I'm looking into the dimensioning consequenses with odd (extreme ?) values of the ratio (design stress)/(Young's modulus) as input into scantling rules, and found E-values for orthotropic panels about 70 GPa and tensile stress 600 MPa.

And yes, I'm aware that the rules are not set up for these composites, I just wanted a reference at "the opposite end" re PE and the like. The rabbit hole I jumped into is about the influence of structural stiffness on effective slamming impact pressures in "real" seawater, with pressure wave celerity depending on both the liquid's gas content (including its dependence on natural foaming agents) and the "container stiffness", analog to the way internal waves (ie waterhammer) are treated in piping systems. Right now I'm only collecting info and digging backwards into the works of "the forefathers"..... Found my 1990 ABS draft of Guide for Building and Classing of High-Speed Craft in the sediments, and its design pressure calc method is still the base for DNV-GL, ISO 12215 etc etc.

 

[BlueBell]

Is epoxy the most elastic, then Kevlar, and carbon fiber the least elastic?

 

[baeckmo]

You must consider the complete matrix; fiber bundles won't make you any good.

 

[jehardiman]

The rabbit hole I jumped into is about the influence of structural stiffness on effective slamming impact pressures in "real" seawater, with pressure wave celerity depending on both the liquid's gas content (including its dependence on natural foaming agents) and the "container stiffness", analog to the way internal waves (ie waterhammer) are treated in piping systems. Right now I'm only collecting info and digging backwards into the works of "the forefathers"..... Found my 1990 ABS draft of Guide for Building and Classing of High-Speed Craft in the sediments, and its design pressure calc method is still the base for DNV-GL, ISO 12215 etc etc.

For that, see this 20 year old post and thread.
Hull Water Loads https://www.boatdesign.net/threads/hull-water-loads.4085/page-3#post-27687

 

[Ad Hoc]

.... what would be realistic values for design yield stress (or corresponding) ...

There in lies the rub.
I dont view these materials in terms of stress, or yield/design stress limits.
It is all deflection driven.

I decide, if not given, a deflection (in mm) that I would be comfortable with for whatever the structural element under consideration is....whether it is the whole hull or just local panels/girders, and then design to that deflection.
Invariably the stress ends up 'below' what one would consider acceptable. But it is not the stress that is the driver, it is the deflection with composites....always.

 

[fallguy]

There in lies the rub.
I dont view these materials in terms of stress, or yield/design stress limits.
It is all deflection driven.

I decide, if not given, a deflection (in mm) that I would be comfortable with for whatever the structural element under consideration is....whether it is the whole hull or just local panels/girders, and then design to that deflection.
Invariably the stress ends up 'below' what one would consider acceptable. But it is not the stress that is the driver, it is the deflection with composites....always.

I have nothing to contribute, but want to ask the basis. Is this because of the failure mode of composite versus steel or aluminum? A composite panel deflecting past a certain point results in total failure, but a metal hull can bend quite a lot before breaking. And so for the presented use case; the carbon epoxy layup in a single skin doesn’t take too much to fail (in crude builder analysis) because it won’t bend more than 1-2%?

I remain the student here.

 

[Ad Hoc]

... Is this because of the failure mode of composite versus steel or aluminum? ....

One needs to first understand what is structurual stiffness. Well, it is the product of E and I…where E = Young’s modulus and I is the second moment of area of the structure under investigation.

So, if we take say steel, with its E of roughly 210 GPa, and a flat bar say a 50x5mm, if we compare this to aluminium, which has an E of 70GPa, before we do any calculations, we can immediately see that steel has 3 times the value of aluminium for the same EI.

What does this mean?...well, it means that if we look at the equations for a simple deflection of a cantilever beam:

Deflection = Wl^3/3EI

If we assume all things equal between the steel and ally flat bar, i.e same span and same load etc,
The interesting part to note, is the denominator, the 3EI, or simply the EI part.

Thus, the deflection of a steel FB v an ally one will be…yup…3 times less, or the ally one is 3 times greater with all things being equal, except the choice of material. That increase in deflection may or may not be a problem., it depends upon the application.

So, knowing that composites, like carbon fibre, failure in a brittle manner, we need to look at the generic curve of strain limits, not the stress. Their characteristic stress – strain curve, generally shows a relatively straight line at a high gradient, and then sudden failure. And of course depending upon the orientation of the load.

That’s just for the fibre itself.
So when in a resin matrix, the values are altered:

So we can see that the strain limit is decreasing.
Thus, when a structure deflects, there is strain in the fibres, one needs to ensure that the strain encountered, by the deflection is not going to cause failure, is it within the 'safe limits'.

And then, not forgetting any structure that flexes, is subjected to – fatigue.

So, we then also need to look at the fatigue SN curve of CF:

In general fatigue limits are 2 x 10^6 (FAT Limits) or 1 x10^8 cycles.

So, after checking what strain is experienced in the structure, given the applied load, what stress does that give?...then is that stress below the limits for fatigue damage, in this case circa down to 45%.

But, and the point of deflection driven.
Deflection can either be a problem or not a problem, again it depends upon the application.

If you have a wing of an aircraft, deflection is not uncommon, in fact it is ‘designed in to keep the stresses lower. Whereas, if we take 2 box beams joining the hulls of a catamaran together….deflections or rather flexing is not wanted or welcomed, it is positively dangerous!! Thus, just because the stress is low, doesn’t mean it does the job!

This is the very very simple 2/c explanation.

 

[rxcomposite]

Think of it as designing an I-beam made up of different materials. You have different loads in the top and bottom flanges (i.e. skins) than you do in the web (core). If you really want to get into this I suggest the text Theory of Composites Design by Stephen W. Tsai.

EDIT: See if you can download this. https://apps.dtic.mil/sti/tr/pdf/ADA157710.pdf

Thank you JE. Seems this is relatively new as it is dated 1984. I have seen Tsai Hill and Tsai Wu theory but this one includes the Mohr's circle. It is the matrix algebra that I have seen in the older papers dated late 1970's.

 

[gonzo]

Mohr's circle is a theory from the late 1800's. In general, design is based on crack theory that accounts for fatigue failure.

 

[rxcomposite]

And yes, I'm aware that the rules are not set up for these composites, I just wanted a reference at "the opposite end" re PE and the like. The rabbit hole I jumped into is about the influence of structural stiffness on effective slamming impact pressures in "real" seawater, with pressure wave celerity depending on both the liquid's gas content (including its dependence on natural foaming agents) and the "container stiffness", analog to the way internal waves (ie waterhammer) are treated in piping systems. Right now I'm only collecting info and digging backwards into the works of "the forefathers"..... Found my 1990 ABS draft of Guide for Building and Classing of High-Speed Craft in the sediments, and its design pressure calc method is still the base for DNV-GL, ISO 12215 etc etc.

LR Class Rule requires a max bending criteria that must be complied with. This can be met if the Aspect Ratio of the panel, the modulus (or strength) of the laminate is met, the thickness is complied with. There is a limit however. Too stiff (too brittle, too high modulus) and the impact strength suffers. Please refer to to Marine Composites by E green an Associates, Chapter 4, Impact for some text.

As a guide, LR requires different bending limit for different structures. Example a crossbeam is a primary structure and the limit of bending is severely limited. So does an airplane wing.

 

[baeckmo]

Too stiff (too brittle, too high modulus) and the impact strength suffers.

This is in the direction I'm heading, thanx for that reference. My main issue right now is compliance with the ISO 12215 (with its workboat appendix), which is the de facto rule for design of small workboats within the EU.

In that norm, it is only in the dimensioning of composite sandwhich structures that I see a reference to the elasticity of the panel; which is why I specifically asked about isotropical/orthotropical single-skin panels (and, ok the norm has examples of the values I looked for, but I was interested to see what our qualified forum members would come up with). This indicates to me that the hydroelastic interaction with the water during a local pressure peak, as from a slamming impact, has not been taken into consideration. Consequently, the elasticity is only viewed as an "interlayer" factor for the laminate strength or endurance; the deflection work is not expected to influence the pressure peak, which I believe it should. As this norm is aiming at "Small Craft", the critical design zone is the local panel, not the global strength, which is also stated in the scoop of the norm. As long as we use materials with elasticity-strength ratios typical for those used in the empirical definition of slamming pressure, we are in "known waters", but if we use materials (or structures for that matter) which allow larger deflections or take up more of the pressure peak, we are lost.

As Jehardiman noticed, this has been up for discussion here before. With a bunch of additional threads on the use of Polyethene for hulls in later years, and with the present lack of design guidance, I think the amalgamated knowledge and experience in this forum is the perfect development scene.

As I see it, and with the experience with such materials in "landlocked" applications, we could benefit from their use in hull performance, both in terms of slamming loads and for operation with a demand for low hydroacoustic signature. But that requires improved understanding of the behaviour of "hyperelasticity" in the real marine environment (I recall some of the mistakes we saw in the early 1970:ies, when steelbuilders bought a MIG and suddenly became alu-specialists; no idea of the consequenses of local hard points f.i. ....).

Maybe it is indicative of the goals of the ISO norm, that there is only one (I may have missed some other.....) reference to the analysis of slamming events; the classical paper of Heller and Jasper: "On the structural design of planing craft"; RINA 1961. It should ring a few bells when one checks the speed of the registered pressure pulses traveling from initial impact at the keel and out to the chine.

 

[rxcomposite]

If you are leaning towards ISO, then 12215-5 has the formula for bending moment, deflection and minimum skin thickness. The min thickness requires you to give a notice that it is a "no step zone and prone to puncture". Marine Composites (MARINE COMPOSITES Acrobat file - Eric Greene Associates, Inc. https://www.yumpu.com/en/document/read/36992620/marine-composites-acrobat-file-eric-greene-associates-inc) gives you the formula for impact strength. You have to define the velocity and mass of the impactor.

For sandwich layup, note how they rate the various cores as it rates to impact. ISO choice for core materials is the same. Choice of core is critical for impact but ISO does not define it. The best study that was made was published in PBB a long time ago. That is high strength, high density core tends to transmit the impact to the other side causing delamination. Low modulus, high stretch core gives in quickly and will cause penetration or damage to the outer skin.

As a design approach, note that DNV Rules for High Speed Vessel does not allow sandwich construction for hull bottom. Composite aircraft wings have solid (single skin) laminate in the leading edge (where bird strike is most likely) and foam core only after the LE. The core is for rigidity so as not for the skin to sag.