Need formulas (longitudinal tensile/compressive strength) 1

[Laminator]

Hi all,

Does anybody know the equations to calculate Xt (fiber direction tensile strength) and Xc(fiber direction compressive strength)if stress and strain of the fibers and matrix are not provideed?

Your help is much appreciated. Thanks.

 

[Hansmeister]

If the fiber and matrix are not defined, then there is no way to determine these properties.

 

[Laminator]

The fiber and matrix are defined. The values of E1f, E2f, Xtf,Xcf,Vf etc are provided, but NOT the values for stress and strain, which means is it possible to solve Xt and Xc without knowing the stress and strain of the fiber/matrix?

Thanks.

 

[Laminator]

More information, I asked the programmer and he said it has to deal with 'Rule of Mixtures'. It's limited by the lower of the failure strains of the fiber or matrix. I have searched through some books and websites but still couldn't get the formulas for Xt, and Xc.

Please advise.

 

[SWComposites]

No, it is not possible. The "rule of mixtures" only applies to modulus values, not strength, and then only for fiber direction modulus. Even if you have strength values for the bare fiber and resin there is no accurate way to predict Xt and Xc; you can get approximate (+/- 20%) values for Xt by using the fiber strain times Ex; for Xc there are various published formulas that use the fiber stiffness, diameter and matrix shear modulus, but again these are not very accurate.

 

[Laminator]

These are the property that I input into the program,

Fiber property:
E1f
E2f
G12f
v12f
Xtf (fiber tensile strength)
Xcf (fiber compressive strength)
Sf (Shear Strength)
Vf (volume fraction)

Matrix property:
Em
Gm
vm (poisson)
Xtm (matrix tensile strength)
Xcm (matrix compressive strength)
Sm (Shear strength)

After inputting these properties, the results of the fiber direction tensile & compressive strength (Xt & Xc) are shown. For sure, some of the properties above were, or were not, be used for calculating Xt & Xc.

I tried Xt=Xtf*Vf+Xm*Vm, but it doesn't work. But in some circumstances, I think they used Xt=Xtf*Vf, Xc=Xcf*Vf. Not sure about it, but at least the answer came out to be the same.

I have tried looking for several books and websites, but I still couldn't get the equations to calculate this.

Please advise.

 

[Hansmeister]

There was a technical paper written by Chamis and published in the "Journal of Composite Materials" back in the 1980's, dealing with various forms of determining properties using micromechanics. With some searching, you may locate it.

 

[SkyD]

I would tend to agree with what SWComposite said. I would be extremely careful in trying to obtain values for strength of a composite laminate with just an equation. There are far too many parameters. If you are doing a very top level study then maybe it is worth it but if you are looking at sizing a component, even as a preliminary sizing, I would definitely not try to approximate the result.

The actual values can be influenced by lots of factors including volume fraction, manufacturing process, defects in the laminate, etc... Unless you have a fully defined combination resin/fibre and manufacturing process, it could be very dangerous to make any assumptions.

I'd say in your list of parameters you are missing at least one crucial: data on the resin fracture toughness... That will play a large part in the compressive strength...

May I ask what you are planning to do with these values... One way of doing it would be to get hold of test data for combination of resin and fibres that are similar to what you are using. This could be a first place to start... By applying a good safety margin and with some advice, you might be able to find what you need.

 

[SWComposites]

Laminator - are you trying to figure out what equations are used in a certain computer program? what program is this?

 

[Laminator]

First of all, thank you all the people who have provided their opinions and ideas on this forum.

Hansmeister: Yes, I was thinking of Chamis equation as well. I am still trying to find the paper you were talking about. And yes,it's deal with "MICROMECHANICS".

SkyD: Thank you for your long reply. I don't think the program wanted me to input the value for resin fracture toughness. Maybe it's already counted in the resin compressive strength (Xcm).

SWComposites: Yes, I am trying to figure how did the computer program come out with those results. The program is call "Laminator" (same as my user name ).

If anybody know anything about the program 'Laminator', please advise. Thanks.

 

[PanelGuy]

Agarwal and Broutman wrote a Text in '90 called "Analysis and Performance of Fiber Composites". It is a standard text at Winona State (class of '93).

As above, I am always cautious using any calculated values as gospel BUT...as analysis people we must start somewhere...

Assuming good bonding, straight fibers yada yada yada...

The rule of mixtures partially applies but only in a max strain concept...consider that the strain in the composite is equal in both components at any time (not a 'stretch'

Then ( I hope I get this right..)

Xt=Vf*Xtf+(1-Vf)*Xtmfs
(where Xtmfs is the tensile in the matrix at the fiber fracture strain value)

This makes sense when you consider that as long there is plenty of fiber that is where the load will be carried. If you really want to back of the envelope it then consider the load to only be carried by the fibers and the matrix becomes "insurance" that your fibers are straight and well bonded.

The last assumption is a little bit "cowboy" but if you are using particularly high strength fibers, and a general epoxy the contribution is minimal. The whole real world v.s ideal can be discussed ad nauseum but we all know the "book value" is always high from the "real value" because many book values are calculated or tested under such tight controls as you may never replicate in production.

It always pays to have someone break a few to be sure and get real values.

Please note - For transverse stress, you will get in to Halpin-Tsai equations.

The Broutman text and the one by KK Chawla cover micromechanics fairly well, if not I know other people you could talk to.

Darin

Darin.jensen@bellcomb.com

Chief Engineer
Bellcomb.com

 

[Laminator]

Darin,

Thanks for your ideas. I guess the equation that you provided above ( Xt=Vf*Xtf+(1-Vf)*Xtmfs )is correct as like what the programmer said, we have to use rules of mixture. However, I wonder if you know the way to calculate "Xtmfs" by using the variables which listed in my previous mail?

I tried plotting some numbers into the program. In some circumstances, I realized that Xt=Vf+Xtf, which I asssumed that the program treats Xtmfs=0. Does anybody know why?

I have searched on the books that you recommended. I think that's pretty neat.

FYI, the programmer said we have to use rules of mixture as well to calculate Xc.

Darin, were you saying that you know someone whom I can talk to about my problem?

Onve again, thank you Darin for your information.

 

[PanelGuy]

Laminator -

Hooke's law...

Basically

Stress equals modulus times strain (elongation)...

so...Strain of fiber at max stress is E1f*Xtf

or E1f*Xtf=Xtmfs.

I think what you will find is that the contribution of the matrix to the overall capability in tension is small and perhaps your software is estimating it at 0 or it is too small to see.

What fiber and volume fraction are you using? You can check the above assumption by lowering your Vf way down and seeing if anything shows up OR lowering you fiber modulus and seeig if the contribution shows up.

Essentially, athe properties you have come from testing the components individually so make the software look at them individually.

Most fibers (not all) are pretty much a hgih tesion carrying thing and that is it. It really is the definition of composites that you put two distinctly differing materials together and get a new distinctly different material. In most cases, just the fact that the matrix sheaths the fibers and make them more that just strands is huge. Think of something like woven roving in Polyester and TwinTex which is woven roving in Polyester...Tensile strengths are close (fiber) but all of the other properties are very different impact, compression, bend radius, heat deformation and so on BUT the base strength should be relatively close.


There may be someone at CCM at the University of Delaware that could help, but they may be more esoteric. Anholt Technologies is very good with composite design, but you really need to let them do it..Dan Coppens or Dave Rabeno.

Let me know how it comes out.

Dairn

 

[RPstress]

There are some very rough rules of thumb for very preliminary strength estimations for strong and stiff fibres (glass and carbon) in polymer matrixes.

If you have the average tensile fibre strength and modulus as stresses (usually available from the fibre suppliers), then average tensile strength of an all-0 degree composite with Vf fibre volume fraction is (roughly, remember!) 0.8*Vf*fibre_strength and average stiffness is 0.9*Vf*fibre_stiffness. You may sometimes get 0.95 for stiffness.

For glass and high strength (standard modulus) carbon, the compression strength can be taken, with a large pinch of salt, as 2/3 the tension value. Compressive stiffness may often be 10% less than tensile stiffness for glass and HS carbon.

For intermediate modulus carbon fibres the compression may actually be quite good, but can come out low, so that 0.5 of the tension value should be used. Compression stiffness can be a good deal lower than tensile stiffness; as a lower bound I use IM_compressive_stiffness = 0.75*tensile_stiffness, but it's pretty rough.

For more realistic allowables, these averages should be knocked down by a further factor. In aerospace situations another 0.8 times is safe-ish, provided you've got a good test program lined up for characterising the material.

As a lower bound for 2-direction strength and stiffness and shear strength and stiffness the bulk resin properties can be used, provided it is a good epoxy or BMI.

Once the all-0 direction properties are estimated, then either classical laminate theory or Hart-Smith's 10% rule can be used to estimate multi-axial laminate properties.

NB: this is only for PAN-based carbon; if the fibres are pitch-based, then lower strengths are more than possible.

Non-glass/carbon fibres, especially polymers such as Kevlar, may just about be ok with this method for tension, but for compression all bets are off, and very low laminate strengths are possible.

Just to reiterate: use this sort of thing for preliminary work only, and be CAREFUL.

I would be very wary of inexperienced analysts and designers using numbers arrived at in this way (that's inexperienced in either knowledge of real-world results or composites).

 

[Laminator]

RPstress, thanks for your helpful information.

Darin, the Xtmfs equation that you provided didn't come out right. Below is the input values:

E1f=12
E2f=55
Em=100
Xtf=99
Xcf=85
Xtm=86
Xcm=45
Vf=0.6

I think these are all the variables for calculating Xt and Xc. The value of Xt and Xc come out to be 59.4 and -21.24 respectively.

P/S: The input values are just a rough one.

By the way, have a nice weekend and Happy Father's Day to everybody .

 

[Laminator]

I just received a reply from the programmer. Below is the formula which the programmer use to calculate Xt and Xc,

// Xt (fabs is the absolute value function)
if(fabs(Xtf/E1f) < fabs(Xtm/Em)) Xt = Xtf*Vf + Em*Xtf*Vm/E1f;
else Xt = Xtf*Vf; // assume the fibers alone carry the load

// Xc
if(fabs(Xcf/E1f) < fabs(Xcm/Em)) Xc = Xcf*Vf + Em*Xcf*Vm/E1f;
else Xc = E1f*Xcm*Vf/Em + Xcm*Vm; // assume matrix-governed failure

Are these formulas make any sense?

 

[glevans]

"The Laminator" can be found at

http://www.thelaminator.net.

 

[PanelGuy]

Yah!!

Basically it is what we all guessed...

It assumes the fiber bears all of the load in tension --

Statistically true when you look at the numbers.

in the first equation...Em*Xtf*Vm/E1f ==>
Xtf/E1f is the Xtmfs (stress tensile of Matrix at Fiber failure strain) we discussed...the tensile value in the modulus is Em*strain...or Xtmfs

As well, I had not thought about the compression portion of your problem. The compression is the opposite, it is totally matrix reliant.

That is exactly what the equation shows, it assume the matrix volume is carrying the compression load and will be the failure mode.

The second equation basically does the same thing only looking at the fiber contribution at the strain failure value of the matrix...



I do side with RPStress on much of this...PLEASE KEEP IN MIND...
A little knowledge is dangerous. Technology has come a long way in that it is very easy for people to get hands on systems designed for very knowledgable operators. I am sure RP knows systems like I do...The first laminate/laminae analysis program I wrote was in FORTRAN...the various spreadsheet programs available were not powerful enough. Now you can pick a few materials and BAM! answers fall out. I am not saying people do not know what they are doing BUT I do believe that at somepoint you need to test materials to ensure your calculations are correct.

I also believe that you should never use more than you really need...that is why we use composites. When the first DCX successfully tested, but had a situations that 1/3 of its fuselage was damaged, NASA congratulated itself on the design. Industry professionals thought it a failure that 1/3 of the structure was gone and it still acted perfect...It should have fallen apart, too much material was wasted.

Hey, enough soapbox. The equations make sense! yah!

Darin