calculating torsional stiffness hull

I see more epoxies having a specific gravity of just above 1 (West Epoxy)?

 

Hi RX, I have been reading your forum contributions. I think this one Carbon Fiber Chainplates https://www.boatdesign.net/threads/carbon-fiber-chainplates.49724/page-2#post-680622 explains what your were mentioning before? So maybe I have to find another epoxy. The epoxy I mentioned before L+ 15%GL1 +15% GL2 does: tensile str: 79 MPa, elong: 4,8%, tensile mod: 3450 MPa. What kind of epoxies should I try to find? Are this professional epoxies? Aviation kind of epoxies? The ones I could find on webshops have a lower spec.

 

Coupon testing: a friend very experienced in workshop machinery told me the press I proposed couldn't handle the backlash from breakage. He proposes using a canting press pressing a hinged triangular construction with the test sample as the base (for tension). Applied force is a little more difficult to measure (triangular height) but will work.

My question is about coupons: I read: 7 samples, tension/ compression/ bending. For the individual fabrics I want to use. At specified fibre/epoxy ratio. With/without vaccuum (with vacuum: maybe not for all combinations). A total of 63-126 tests.
Interlaminar shear tests?
For compression tests: can I use foam to keep the fibres oriented?
For bending tests: also use foam? Or making a thick laminate?
For tests on +-45 degree fabrics: making long samples let the fibres end in air which is not very realistic. Can I make a (flattened) circulair sample around foam for this?

 

There are test specimen configuration for tensile, compression, shear test. I suggest you find out about the test specimen shape.

Attached is a DIY test jig that I remember. Since we are looking at around 1,000 N/mm2 (MPa), it is doable. Because pressure is Force/Area you do not make the width of the test specimen 25 mm wide (standard). and you can do single skin laminate that ranges from 0.5 to 1 mm thick.

So calculating 4000 N/4mm2 (1 mm thick x 4 mm wide) area will yield 1000 N/mm2 (1 megapascal). Most of the time the laminate is less than a mm thick. Worst come to worst, you don't need to see the ultimate strength, just the point where it will yield or where the specimen starts to crack. That will be about 60% of ultimate.

For coupon test, of the 7 samples, the lowest is thrown out and only 6 are computed to give you a certain level of confidence in accordance with Standard Deviation formula. I can give you the formula if you are interested.

For practical use, only 3 is needed and averaged to compare with baseline and a corresponding factor of adjustment is inserted into the standard formula.

 

I have been working on the spar design based on standard material strength published by LR/ISO so the derivation of material strength of other material is taking the back burner at the moment.

Basically the mast load is as shown by calculation is a concentrated load imposed on the simply supported beam. That is not weight, just force, and the shear and moment diagram suggest a beam thick at the center and tapering at the ends. The beam bends upward. When one hull is out of the water, it becomes a cantelever with a concentrated load (one hull flying) at the free end and another load (pod) in the center. The beam now bends into an S curve. The shear and moment diagram now suggest the base is the thickest part. Now to combine the two. That is what I am working on. Will post later when completed.

 

Thanks RX! I know how to calculate standard deviation.

 

Pammie
This is the simplified method of the post you have cited. The original post is very complex as I have to show the differing resin curve. This one uses the standards of Lloyd's and shows what happens when you use a different type of resin. I chose the DER epoxy resin and the Epoxy L + GL1 hardener for comparison. Inset shows how the DNV method uses the limiting strain method instead of the limiting stress method used by Lloyd's.

 

thanks RX, I'm learning every day!

DER 354 slightly better. I asked my supplier for alternatives but no answer yet.

I suppose its no problem to use LR for laminates and DNV for calculating global loads.

Have been reading about material tests. Now understand the relation with CLT. Have to work out how to do the specific test setups in practice. A few questions:
1. for beamconstruction I want to use carbon. I have got 100 sqm uni 320 carbon from a friend. Are there other carbon ply's you think sensible to test?
2. How important is compressive modulus? Difficulter to measure because of sample size.
3. I have found copies of ASTM D3039 and D3410, but not on D7078 or D4255. Do you have them?

 

Your Epoxy L +GL1 is class approved also. very little difference with DER which I remember is also class approved.

I have finished my material analysis and just need to polish up the presentation. It seems best to use E glass WR for the web and unidirectional carbon for caps. WR is more stable. Biax (or cross plied has initial high strength but degrades quickly when rotated to 45 degree). We need high shear for the web which the WR fits nicely. Note that I am designing with rectangular beams, not ellipse. To do the ellipse would mean an entirely new spreadsheet and use filament winding calculation technique.

Composites properties has lower compressive modulus than tensile. About 3% difference for carbon and Eglass. Not for Kevlar though as it is very poor in compression. For all practical purposes, designers use tensile but I use both as it is more accurate.

We need tensile, compressive, and shear. Shear test, I remember is just a notched sample. If you can measure the elongation (stretch) as load is applied, then we can plot the modulus. The laminate modulus curve is just a stress/strain relationship as shown in the graph provided earlier.

 

Hi RX,

do you allways work with rectangular beams? As I understood it the 2nd moment of inertia of a D form is much higher? Please also see my PM.

Testing: yes we will measure load and elongation both. Planning for a simple automated instrumentation setup (I have some experience wih pure data). Appointment with my workshop friend tomorrow to sort things out.

 

Not all....

Compression strength is very important on these beams. Since on the upper surface you have...tension...but what is on the lower surface...compression!

Thus one must check the whole structure not just tensile strength but compressive too.....since we don't want the beam to fail in compression, or, in buckling too.
Then, we can address the deflections...owing to its low E.

 

That is correct. It is very important but in most example calculation samples I have seen, the compressive stress is not factored in. Maybe the reason is there is generally a small difference in composites between the tension and compression properties say from 3 to 5%. When you are working on a safety factor of 3, that would provide a large margin of safety to err. Only in cases like Kevlar where there is a loss of about 60% in strength in the compression. For those who work with metals, generally (alloy for instance), the compression properties is much higher than tensile properties. So designing on the lower end of the properties is safe.

 

Pammie- Sorry for the long delay but in trying to pin down the behavior of laminate, I got bogged down.

With Lloyd's, It has enough formulas to predict a property(ies) if other parameters are missing or not available. Problem is the LR/ISO formula is in conflict with other known method of calculations and produces results which has a wide variance with others who has done independent testing.

I have prepared a material property table using mostly LR formula but have introduced other method of deriving result as well. It is a little bit detailed for your use but for me, it does matter.

The spreadsheet attached shows you the general behavior of the beam in concentrated load and the associated laminate thicknesses. Just change the data in the yellow boxes. Just a note of caution, don't mess with cells with formulas as I have not protected them. It is not user friendly and not for the faint hearted. It is also in the unfinished stage as the other method of a full blown analysis is not finished. But that is design. For the purpose of the discussion, the spreadsheet should suffice to give you an idea of what we are doing.

The first iteration shows the laminate layup at center. The second iteration shows the layup at ends. The next analysis would be to test if the ends would be sufficient if the load model changes from the concentrated load to cantelever load with one hull flying. After this, we can explore using oval beams and using the Bredt-Batho equation which I admit I am not familiar with. AdHoc is the master in this.

 

Is it? Lying on its side or at the ends. Using a homogenous material, the NA, and the second moment of inertia is easy to predict. In using different material properties (modulus) the neutral axis is very sensitive to the modulus at the ends. I just work on rectangular beams because the elements are easy to isolate.

 

I may have to expound more on this. There are two popular failure criteria. The Maximum Stress Theory and the Maximum Strain Theory. The Max Stress is the most popular and the Max Strain is the least understood.

LR uses the Maximum Stress Theory because it divides the ultimate stress by the factor of safety. DNV divides the maximum strain by the factor of safety. Fortunately, both uses the same method of using the Representative E modulus. In order for the equation (Hook's law) to be valid, the modulus must be a straight line. The elongation (strain) used is where it crosses the ultimate strength line. In other data sheets, the ultimate strength is shown at the breaking point way longer than the crosspoint of the modulus and UTs. While it is good to see the behavioral curve of the laminate, it only shows at what elongation the laminate ruptures. We seek only the yield point, the point where the laminate cracks (fail) which is about 50-60% of the UTs.

In the first sheet of the spreadsheet attached, It shows the LR divides the UTs by the FoS. DNV divides the strain by the FoS. That would be the "Allowable stress" or "Limiting Strain" criteria and cannot be exceeded. For all practical purpose LR and DNV uses the same method.

Sometimes, materials of differing material properties have to be mixed. LR cautions the user on mixing materials of different strain and discusses this method in the latter part of composite design, thus using the Limiting Strain Theory.

In the second page of the spreadsheet, it shows when a high modulus fiber (carbon fiber) is mixed with a low modulus one. The worst fabric is Eglass biax ( a cross plied Uni laminated at +45-45 degree angle). Though it gains in shear strength and shear modulus (good for web as it is shear defined), it loses strength quickly when loaded off axis. About 10-12% of the UTs remains at 45 degree angle. Placing the low modulus fiber on the uppermost layer (away from the neutral axis) means it would crack before the high modulus fiber is stressed. In theory at least with standard engineering formula, the outermost fibers receive the highest stress. Fortunately, the beauty of the LR and ISO formula relies on the stiffness (EI) in the neutral axis. It mitigates the stress on the outermost fibers.

The Limiting Strain is more popular in the aerospace industry as it easily shows which element receives the lowest strain. It is either eliminated or located elsewhere, saving weight.