young modulus and frequency 2

[fabiof]

I am using a numerical/experimental approach to determine the young modulus (E1 and E2) of carbon fiber/epoxi composite plates. The results are showing that E1 is frequency depedent: up to 2 kHz E1 = E2 = 52 GPa; from 2 to 4 kHz E1 = E2 = 55 GPa. These are the values that make the numerical acelerance match the experimental for all the spectra. I am wondering if this is correct? Can E have distinc values for different frequencies? Anyone had the same experience? Thanks in advance

 

[YoungTurk]

I believe that for most materials, the modulus of elasticity exhibits strain rate dependence. This is due to the visco part of the viscoelastic behavior of the material. Young's Modulus is implicity referring to the "static" modulus, in other words, the value that the MOE approaches as the strain rate goes to zero, or the purely elastic modulus.

I did some work at the FPL with this for fiberboard. Attempting to correlate static MOE with dynamic MOE from various test methods. Natural frequency vibration vs. forced vibration vs. stress wave testing all yielded different MOEs. We developed some interesting empirical correlations, but they required developing a constant associated to the specific material.

I suggest reading up on complex modulus of elasticity. I had some excellent papers by A.A. Moslemi pertaining to fiberboard, but alas I left them with the lab. I believe they appeared in the journal of wood and fiber science in the 60s.

 

[AXXX]

I concur with youngTurk but, it seems strange that you are getting E1=E2; their values should be considerably different, unless you are using a non-standard measurement methodology.

 

[YoungTurk]

Wouldn't E1=E2 for a plate with randomly oriented fibers (in the plane)?

 

[wes616]

Wouldn't E1=E2 for a plate with randomly oriented fibers (in the plane)?

E1=E2, in a laminate with equal number of fibers in the x-direction and the y-direct (a BID). Randomly oriented fibers would suggest E1.ne.E2 don't you think.

Wes C.
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No trees were killed in the sending of this message, but a large number of electrons were terribly inconvenienced.

 

[fabiof]

thanks for the responses. The plate I am testing has 90/90 orientation, made of prepeg carbon/expoxi. This might explain E1 = E2

 

[YoungTurk]

Wes,

You've got me scratching my head here. Though I don't work with fiber/matrix composites regularly, I don't see why randomly oriented fibers wouldn't yield E1=E2(=E in plane, any angle) on average for the material.

Are you making the assumption that we are talking about a single specimen in which case some incidental E1 ne E2 would be expected, with a magnitude dependent upon fiber length and specimen size? Or am I missing something more fundamental?

It is academic at this point, since fabiof tells us its a bi-directional plate; still curious, though.

 

[wes616]

Youngturk,

Fiber composites are, by nature, orthotropic. Inplane, the fiber is held in tension/compression along the length of a strand. The goal of composites are to carry (any) load in tension/compression along the lengh of a fiber. While it may be possible to get E1=E2 through a randomly oriented fibers, it would be highly unlikely (and accidental).

While you can approximate E1=E2=E with a "quasi-isotropic" laminate {0/45/90/-45/}, it will never be truely isotropic like you are suggesting.

Wes C.
------------------------------
No trees were killed in the sending of this message, but a large number of electrons were terribly inconvenienced.

 

[YoungTurk]

While it may be possible to get E1=E2 through a randomly oriented fibers, it would be highly unlikely (and accidental).

I don't think that is a fair statement. Having sat in front of testing machines for months running fiberboard specimens, the MOE I measured was equal for E1 and E2 (within a few percent) for the majority of board specimens. I don't see why this would be any different for other short (relative to specimen size) fiber composites.

On the other hand, if you're talking E1 vs E2 at a point (small area actually; measured with a strain guage, for example), I would agree you're more likely to measure a difference, though for a short fiber I still wouldn't expect a very large difference.

That being said, my experience is limited so I probably shouldn't debate the finer points of this topic. I guess its the YoungTurk way.

 

[AXXX]

I suspect fiberboard can be considered to be isotropic, therefore E1=E2.
Laminated composites are intentionally oriented at specific angles in order to attain directional strength; is not uncommon to see E2 values that are double digits lower than E1 in unidirectional composites. It is intentional to have E1 <> E2; when E1 = E2 is either accidental or pure weight reduction is sought, whereby one seeks to substitute metals by composites, completely disregarding component loads.

Since E = f (Hz), can the natural frequency of a composite component be calculated / predicted by numerical means?

Resonance induced by engines/pumps is an interesting composite problem.

 

[YoungTurk]

I suspect fiberboard can be considered to be isotropic, therefore E1=E2.

I believe you've got that backwords. Fiberboard can be considered isotropic (in certain circumstances) only because E1=E2, which is acheived through random fiber orientation. Not the other way around. And, for some applications (mainly those which involve out of plane loading) assuming isotropy of fiberboard will yield wildly incorrect results. Also, saying something is isotropic and saying E1=E2 are two very different statements.

As to whether the natural frequency of composites can be calculated, it certainly can be for simple geometries and load conditions, but I suspect the math would become increasingly cumbersome for as the part/load became more complex. I'm sure someone will hate this statement, but I'd think some FEA packages could do a decent job at it.

 

[wes616]

OK - I think there has been some confusion here, so I'll try to clear it up with my last post on this topic.

Young Turk has been talking about short fiber composites. Short fiber (or discontinuous) composites (l/d~100) require very nearly perfectly random placement in the matrix in order to achieve full mechanical properties. As YT stated, this will typically yeild (in plane) isotropy regarding specific properties (read elastic modulus E1=E2). Much of the properties are dependant to the resin mixture, because there is no continuous loadpath through the fiber.

---------------------------------
|\-/\-|\|-\-/\-|\|-\-/\-|\|-/|-|
P<--- |-|\|-/|--|\|-\-/\-/\-|\|-\-/\-| --->P
|\-/\-|\|-\-/\-|\|-\-/\-|\|-/|-|
---------------------------------

Out of plane properties are very dependant on environment (Hot/Wet), and processing; thus allowables should be developed through testing. Short fiber composites have many applications, but are typically not used in structural application (some secondary structure).

Long fiber (structural) composites (l/d --> OO), however, are by nature, anisotropic. Inplane, the fiber is held in tension/compression along the length of a strand.

===============
P <--- =============== --->P
===============

Across the weave, the only componet of the matrix carying load is the resin.

P
^
|
==============
==============
==============
^
|
-P

The goal of structural composites are to carry (any) load in tension/compression along the lengh of a fiber (continuous loadpath).

BID (woven) Fabrics will yeild E1=E2, due to the fact that there are 2 sets of fiber strands running 90 deg offset, and woven together. I'm sure that the OP was testing some type of woven fabric or a laminate of 0/90 uni.

+++++++++++++
+++++++++++++
+++++++++++++
+++++++++++++

In most cases, FEA is the best way to perform analysis on these composites due to the high number of elastic constants (may be as many as 21). Remember, isotropy is a special case.


Wes C.
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No trees were killed in the sending of this message, but a large number of electrons were terribly inconvenienced.

 

[YoungTurk]

Nice post Wes.

 

[PanelGuy]

Wow, great series of posts!

I think Wes hit it on where there are some very short fiber composite and long fiber composite construciton going on. YoungTurk may also find some research where inducing flow in the forming of fiberboards or the clever use of Eddy currents is giving anisotropic results...

To get back to the beginning...The variance in your numbers is small, perhaps a sample or system variance is causing it. As well, it depends on how you have tested your samples whether you are starting fresh at each frequency. The biggest issue I have always had with straight numerical issues is that there are so many variables in manufacture of the samples (even in the lab) that you can cause significant variance.

One effect that blows by lots of folks (especially non-lab) is the micro-cracking at the interphase of the resin and fiber. I have seen things such as a sudden temperature drop (take from press to room temp), dropping the test sample, tapping the sample (you know, nervous habit of drumming on the plate), half cycling and then resetting the sample in the tester, small voids, etc cause up to 30% variance...tough to account for.

My guess would be that a frequency change would have a different value. It would depend on the ability to process, but also on the crystallinity of the fiber and the matrix. Perhaps it would be more interesting to vary these...set up a test matrix using no fiber, glass, carbon and a paper? with an epoxy, phenolic and flex modified Polyester and see where the different materials take you.

In some ways, the frequency testing can have the effect of an artificial hardening as well. Kind of a break in where the defects in the laminae are resolved in reptitive loading. Higher frequency would increase this effect.

Please share any further results if possible. Kind of cool.

 

[jorisbracke]

To go back to the beginning: as far as i know E and natural frequency are related:

E=0,9465(mf^2/b)(L^3/t^3)(1+6,858(t/L))

So if geometrie (b,t,L) and mass (m) stays the same natural frequency (f) can only change whene there has changed someting inside the test-piece (micro cracks, ...), and if natural frequency changes so does Young's modulus.

In the past we used the RFDA MF system 23 (

http://www.imce.cit.be/)

in our lab to measure this. This system uses the impulse excitation technique (

http://en.wikipedia.org/wiki/Impulse_excitation_technique)

to measure dynamic Young's modulus.