Elastic Modulous fo FRP

Discussion in 'Sailboats' started by messabout, Jul 8, 2013.

  1. messabout
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    messabout Senior Member

    I have used a windsurfer mast on my little skiff. It is too bendy for the sail that I have chosen.. I'm figuring to build a birdsmouth mast with a little larger diameter.

    Just for giggles I am trying to estimate the bending of the new mast to compare with the FRP one. I know what to expect from the wood, I know how to get in the ball park with the wooden one. I get "I" for the windsurfer alright but I have no clue what to use for "e"for the FRP pole.. I am going to assume that the windsurfer pole is epoxy/glass Any one got a SWAG estimate for the FRP Yes, I know that the word "assume" is a tried and proven fools trap. This is just a fun exercise but I would appreciate any wild assed guesses that you may offer.
     
  2. sharpii2
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    sharpii2 Senior Member

    Now that I've thought about it awhile, I think I can tell you exactly why.

    Fiberglass (GRP) is, by definition, a composite.

    It is made of two different materials, Glass fiber and polyester, combined in a matrix.

    Each of these materials has its own Modulus Of Elasticity (MOE).

    When the two are combined, you end up with an MOE that is somewhat of an average between the two. My guess is the glass has the highest and polyester has the lowest.

    Depending on how the two are combined, you get your composite MOE.

    If you have more glass fiber than polyester, I imagine the MOE will be higher than the other way around.

    But this too depends on several variables such as how the glass fibers are oriented, for example, as well as how much air, water, and other impurities got into the mix.
     
  3. messabout
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    messabout Senior Member

    Sharpie, I expect that you have described the situation with perfect reasoning. There are way too many variables to even make an educated guess. I think that I will make up a glass rich strip and do some deflection tests. Then I can arrive at a ball park idea of the MOE. That of course will not identify the real modulous of the material in the windsurfer mast. This is all for the purpose of satisfying my curiosity. Information not intended for an industry paper.

    Thanks for the reply.
     
  4. oldsailor7
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    oldsailor7 Senior Member

    I think you will find that windsurfer masts are made of glassfibre/polyester.
     
  5. gonzo
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    gonzo Senior Member

    There is an easy test. Put boat mast on sawhorses and hang a weight from the middle. Measure the bend. It will give you a comparison between the masts. That is how we used to tune-up wooden masts many years ago.
     
  6. Eric Sponberg
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    Eric Sponberg Senior Member

    Messabout--the modulus of elasticity for fiberglass will likely be between 1,000,000 and 2,000,000 psi. That is is the same realm as the wood, by and large, which varies by species and grain orientation. If the glass is fabric with a low glass content by weight, it will be in the lower end of the range. If the glass is primarily unidirectional (with a small amount of cloth) and a high glass content, it will be at the upper end of the range. It is possible to achieve moduli outside this range, but this is typical.

    I hope that helps.

    Eric
     
  7. messabout
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    messabout Senior Member

    Thanks Eric. That is about the range that I might have guessed.


    I am having senior moments Gonzo. A simple deflection test would have given me a close estimate of the number I was looking for. Why did I not think of that before? .......... Duuh!
     
  8. gggGuest
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    gggGuest ...

    You know, if you get get unidirectional glass cloth where you are, it might be easier just to make the glass mast stiffer (assuming it is glass of course) by gluing on more glass. If the wood is going to be more fun to do though (and who really likes working with glass?) then don't let me stop you. The other thing to be wary of is that wood won't like the sort of extreme bend board masts often have to assume.

    But board masts are made out of all sorts of materials from cheap glass/polyester through higher grades of glass up to carbon fibre, and equally of higher grades of resin.
     
  9. rxcomposite
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    rxcomposite Senior Member

    Chasing the “E” or Modulus of Elasticity is a little more difficult given that composite structure strength is highly directional.

    You can use the formula of LR, BV, ISO to find the “E” of a ply but you will be limited to minimum value required for the class rule, not the prediction of ply property with a fiber and resin of your choice.

    The Rule of Mixture formula as suggested by Sharpii2 is more versatile. It looks deceptively simple but it is more complex as it needs more input. The rule assumes the fibers are perfectly aligned. It goes like this Mod= (Modf x FVf) + (Modr x (1-FVf)). Modf is Fiber Modulus, Modr is resin Modulus, FVf is fiber volume fraction, and FVf+FVr=1. *Note it is Fiber Volume Fraction, not Glass Content by weight.

    In Macromechanics theory (where you can still see the direction of the fibers) a fiber directionality factor (FD) is inserted to fine tune the formula for every fabric type. This becomes Mod= (Modf x FVf)*FD + (Modr x (1-FVf)).

    A UD fiber direction is not perfect. There is some 5 to 8 degrees of misalignment. FD factor is 0.88 to 0.91

    In a WR, half of the fibers are as aligned as a UD but due to undulations of the weave, the fibers go up and down by 38-45 degrees. FD ratio is about 0.481-0.487.

    A CSM with the fibers running randomly in all directions. FD is about 0.306

    In a Biax configuration, all the fibers are off axis by +-45 degrees. FD ratio is about 0.114

    All FD values are for Tensile Modulus. There is a different value for Compressive and Flexural modulus.

    In Micromechanics theory, the load is applied parallel to the fibers. If the load is not parallel to the fibers, an engineering constant is used to reduce the modulus derived when the applied load is normal to the fibers. LR, BV, ISO uses this formula but only for UD fabric. Biax and WR use a different formula.

    In short, as you rotate the load from the “normal” axis, the modulus is reduced. At 45 degree “off axis” load for a UD, the modulus is just almost equal to the modulus of the resin. This degradation continuous all the way up to 90 degree (transverse) load. (Violet)

    Biax is lowest at 0 degrees, reaches maximum at 45 then goes down again at 90 degree. (BLUE)

    WR is highest at 0 degrees, goes nearly to its lowest (transverse) modulus at 45 degree and goes back up again. (Red)

    CSM does not need any correction as its modulus is equal in all directions.

    Whew. Confusing!
     

    Attached Files:

  10. oldsailor7
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    oldsailor7 Senior Member

    It's good to see that things like a windsurfers mast is mathematically designed
    and not just constructed by TLAR.
    I was in the windsurfer business for five years, and some of the masts that I experienced must have been designed and constructed BG&BG. :eek:
     
  11. messabout
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    messabout Senior Member

    RXcomposite, thank you much for that erudite reply. This forum is characterized by the presence of very learned contributors. It is a resource of considerable interest and immeasureable value. The generosity of the respondents should be a source of great pride for its members.

    There are a lot of you out there. If I name just a few of you the list weill be much too long and much too incomplete.....some who spring to mind briefly,,,,...Leo, Guillermo, Eric, Par, Willoughby, Speer. Tom, Gonzo the practical one, and a lot more. Thanks to all including the many not named here.
     

  12. rxcomposite
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    rxcomposite Senior Member

    You’re welcome Messabout. Your head must still be spinning absorbing all the information. Given the variables, you can do preliminary sizing of the mast in a simplified way. Not spot on but will do for a start.

    A stayed mast works like a screwdriver. It is forced down (compressive) by the tension on the stays. A rotating force is generated by the sail emanating from the centroid of its area. It is a defined as a “couple” by engineering terms. There is also horizontal force exerted by the sail whose distance from the base (mast step) is measured from its centroid of area. Basically there are three loads you will be analyzing. Bending, compression, and tortional.

    Using only two basic materials (UD and Biax), this can be approximated using the Netting Analysis and the Rule of Mixture. This is where the angle theory comes in. It can be used for strength and modulus.

    Initially, I would use a UD for vertical compressive force and overall stiffness and a Biax to take care of rotational force. Adding the two properties of strength/modulus, I can find the result I need.



    I have attached the angle theory graph of several materials. It shows at what angle of fiber alignment will be optimum. So it seems that the optimum angle for UD is at 22 degree. A loss of some vertical strength but is reinforced by a gain from the Biax.

    For bending, we have to find the “E”. We need the Compressive E and the Tensile E.
    Unfortunately, I cannot find the said properties of said material from published data. Tensile modulus are easy to come by but not compressive. I will have to extract using the ROM rule. I will try to develop something for you.

    P.S.

    Sorry wrong word. The UD should be vertical (0 degree oriented) and the Biax is not a biax but a UD wound at +22-22 degree helix angle.
     

    Attached Files:

    Last edited: Jul 14, 2013
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