[ckelloug]

According to Callister pg 517, the rule of mixtures governs the strength of a large particle composite such as E/G or E/Q. Running the rule of mixtures for our US Composites #635 19000psi epoxy and some 10.5e6psi glass spheres, once can see that the mixture is not assured to achieve a strength more than several times that of the epoxy itself until well over 80% fill rate is achieved.

According to http://mathworld.wolfram.com/SpherePacking.html the packing density of glass spheres like zeospheres varies from between approximately 5% and 75%. At 5% spheres, the mix would be almost all epoxy and thus perform badly. The smaller spheres seem to fight this effect and pack in more uniform and dense arrangements.

Regardless of size, getting better than a 75% fill rate on glass spheres of a single size is mathematically impossible. This indicates that we need either multiple sizes of spheres or spheres and fibers as our macro reinforcements.

The variance in strength for a given ratio is huge. We can see from the graph that the most effective way of minimizing the variance and maximizing strength is to minimize the epoxy fraction as walter correctly predicted from his experiments. It seems to me that one of the other posters mentioned the second aggregate should be 1/5 the size of the first but I couldn't find the post with that reference.

What this says to me is that the correct aggregate mix is going to be something like 75% G800 zeospheres and 25% of something like G200 zeospheres. Zeospheres are nice if they aren't too expensive since they are quality controlled and thus likely to produce similar results each time.

This writeup neglects the effects of the exotic additives in my previous posts and just focuses on materials science that has been known for the last 50 years. In short, we first need to get the epoxy fraction down by using multiple aggregate sizes and then we can focus on the special property improving additives.

[lgalla]

NO more MSDS searching for me.Judging from 2 beers and a couple of smokes every day,I died 20 years ago, not to mention exposure to cobalt,polyesters,fumed silicas,polyurethanes,cyinide curing agents etc.I have always taken precautions such as air supplied respriator or body suit if required.If the chemical was in question,simply don't use it.

[walter]

Regardless of size, getting better than a 75% fill rate on glass spheres of a single size is mathematically impossible.

See, that's why I threw out my calculator... I find math very limiting and and it's best not to use it if a good alternative is available.

just kidding.

btw, my place starts to look like Frankenstein's lab.
_

[ckelloug]

So Walter,

Wherever you live, there must be a market for E/G paving stones eh? I don't think you have to worry about testing those, they're big enough to break the plastics testing machines I've read about. I expect you'd have to use the big machines they use to test core samples of highway and bridge concrete!

Having looked over at
http://www.ptli.com/testlopedia/tests/Flex-D790.asp

The standard ASTM D690 test specimen for flexural modulus is .125in thick, .5in wide, and 2.5in long.

Do you have any feeling for the length of beam you want, how large the forces placed on it are, and what the acceptable deflections are? Talking to Larry, it sounds like the rule he's using is that .001in per foot static deflection is acceptable for a beam length of up to 4 feet. I was thinking in terms of metal work where one wants to be able to hold less than .0001 static deflection (which can be nulled with post tensioning) over that distance and less than .0001 over the expected axis loads.

Designing the uber epoxy mix is fun and in a way people off this board might find a bit sick... On the other hand, referring back to one of your earlier summary posts, it would be easy to incorporate a lot of materials and engineering that make the beam much stiffer than required both mechanically and in cost.

The reichhold 635 epoxy and hardener is good. The sands that you have and zeospheres are good and by using a mixture of them, you should be able to get a marked increase in strength with what you have got.

I'd assume a factor of 4 improvement if you can mix your sands to get a volume of sand in the mixture from what I predict to be 75% up to about 92%. I'd also predict that adding a few percent carbon black and 10% nanosand should be able to get between 1.5 and 10 times as strong as the best sand only mix.

The important thing to note is that the strength vs. sand content is not linear, an 18% change in sand content works out to a factor of 4 increase in minimum predicted strength.

For a stronger composite, we could always do the exercise again with inch long carbon fibers and some kind of ploy to directionally orient them . . . Of course to take this to a level far beyond reality and into just plain fun we could always build a beam reinforced with aluminum oxide whiskers. . . only $2.39 a gram or $1082 a pound. . .


Depending on luck and the exact density of your current samples (which I would like to know once you get your scale), I would expect from the rule of mixtures graph I posted that between a factor of 6 and a factor of 40 strength improvement can be had without resorting to carbon fiber or exotic accelerators (just mixed sand and nanosand).

Cheers Guys.

[lgalla]

Cameron, has it been determined that sand,micro fillers and nano particulate will give better properties than the sand,1/4",3/8" aggregates?If so the only disadvantage would be the cost.
I copied a blurb on what is considered Nano:Nano particles are those which are less than 100 nanometers or 0.1 microns in size. To help judge what this means: a human hair is between 40 to 120 microns thick. To give you an idea of how small this is you would have to line up 40,000 nano PCC particles, side by side, to make a line of particles the width of the finest human hair. Very small, indeed!
Larry

[ckelloug]

Larry,

The rule of mixtures calculation I did only shows that getting better than 80% aggregate of the hardness of quartz in the mixture is essential for getting strength a lot better than the epoxy. The sphere packing problem shows that multiple sizes of aggregate are needed to get better than 75% fill.

Walter's test data indicate that smaller aggregate worked better period which is backed up by my Materials engineering book by Callister who says on pg 516 that "For effective reinforcement, the particles should be small and evenly distributed throughout the matrix."

Other than Walter's data which I am quite thankful for, I don't have any other hard evidence about the exact effect of aggregate size although several posters much earlier in the thread suggested they had some expertise in the area. Intuitively, it seems to me that smaller aggregates will be likely to fill the space better leaving less room for epoxy. I am also in favor of the smaller aggregates as it will be much easier to get the mixture to mix uniformly under our imperfect shop conditions. The smaller aggregates will also lead to nicer surface finishes.

Given the rule of mixtures numbers, your sand,1/4",3/8" aggregate should work fine if you get it mixed up in such a way that you get an aggregate percent volume above 80% and hopefully about 92% just like any other target aggregate mix. Given Walter's data and intuition, I'm a touch skeptical but have no more data to support my skepticism.

The only material whose size actually matters specifically is the true nanoparticles which walter and I have been calling nanosand in our discussions. The stuff that we're looking at from Nanoresins Inc. has a diameter of 20 nanometers (much smaller than silica fume) and comes packed in low viscosity epoxy resin as an epoxy additive. The nano-particles are a dispersion hardener and not an aggregate so the rules of mixtures stuff I used on the aggregates does not apply as they interact on the molecular level rather than on the easy to imagine physical scale. The nanosand should improve by a reasonable margin any but the most horrible of sand mixtures.

My current belief is that there is no reason to make parts with the wrong aggregate size ratios since these ratios can be adjusted very cheaply to make the strongest cost effective parts. Parts that need only to be heavy and vibration damping but don't need perfect finish can use as large of aggregates as one can mix effectively with epoxy. It's parts that need to be as strong as reasonably possible with nice surface finish where the work is. I'd personally like to come up with a sufficiently cheap easy to way to make all parts have nice surface finish and be as strong as possible but I don't have price data on all the components to make this calculation easy.

Walter, can you post a list of materials and prices for the purposes of optimizing the cost/quality of the mix design?

[walter]

`
I had a chat with a lab technician and he says the price of quartz is based on availability, not the size. So, by definition, pool sand should be the most expensive (he says.)

It doesn’t seem to work that way though.. Have a look:


Pool Sand - $5.99 - 50lbs (typically 99% Quartz, 400-700 micron, from retail outlet)
Fine Quartz - $12.50 - 50lbs (size 40, average particle size of 2.8 micron, from distributor)
Zeeospheres - $24 - 50lbs (type 850, 200 micron, from distributor)


I wonder how much the coarser Quartz sells for. US Silica didn't have it but I remember seeing someone advertise the '0.25" Pure Quartz'. I would love to test that...

Do you have any feeling for the length of beam you want, how large the forces placed on it are, and what the acceptable deflections are?

My current project is 36" x 36" fixed gantry hybrid (E/Q with aluminum guts). The beam will probably be in the 4"x6" area, carrying 50lbs max.

I didn't really get to the point where I could worry about sagging gantry, I'm still working on E/Q uniformity & density...

Below are my latest and if they fail, then I'm back in square one.
_

[ckelloug]

Walter,

If you are having trouble with the parts you are making hardening, they probably need to be post cured. According to the Reichhold data sheet, this epoxy needs 24 hours at room temperature and 2 hours at 250F on the standard curing schedule for cast parts.

As for the gantry you are building, If you have the length, the loading (which you have given at 50 lbs) and the allowable deflection under this loading, it can be calculated how big a beam you need. Since you have said you want a 4x6 beam, alternately, you can calculate the fill ratio in the E/G required to achieve it.

Unfortunately the HR department says I have to work this week so I probably ought to get to it. Good luck and if you decide on the acceptable deflections we can figure out how good the E/G needs to be and perhaps even what needs to be in it with math!

[walter]

Heh, good stuff!

But.. I think I have to make it as good as it can be.

What if I change my mind and go for a 16 footer?
What if someone else wants to use it in their project? I can't just tell them not to go over 36"

Thanks for the curing info!

[ckelloug]

Walter,

What the math can answer for you is if what you want to do is possible or cost effective. If you want a 4x6 beam to be strong enough but calculations show that you have to get the epoxy fraction down to 2% for it to be strong enough, the math would serve as advance warning to pick a new strategy. This is just an example, no bearing on your current application.

I think you're on a great track and I agree with optimizing an inexpensive design to the extent that it can be optimized for everyone's use. Knowing the design parameters for your machine however helps optimize the design for everyone by making sure that realistic choices get made. Even with the best basic E/G sand/epoxy formulation possible, there comes a size of part where it's probably not the appropriate formulation.

If you want to build a 16 ft gantry, I'd probably be looking at continuous carbon fiber or rebar in the bottom half of the beam.

Likewise, you saw my comment about aluminum oxide nano-whiskers. They cost over $1000 a pound and are really really strong but the math shows that they aren't effective with a matrix as weak as epoxy. They'd probably have to be embedded in liquid Aluminum to be effective!

Summarizing my theoretical results:
<OL>
<LI> Multiple sizes of sand are needed for maximum strength.
<LI> Two or three types of small sand are probably better than two or 3 types of large sand.
<LI> 2 Hours at between 250F and 320F will likely be needed to achieve full cure.
<LI> A single sand type can yield a fill rate of no higher than 75%.
<LI> The Minimum Strength of the E/G is not much better than epoxy until 80% fill rate is achived.
<LI> Nanoparticles will provide extra strength above that of any fill percentage of ordinary "large" aggregates by providing dispersion hardening.
</OL>

[brunog]

Summarizing my theoretical results:

1. Multiple sizes of sand are needed for maximum strength.
   
2. Two or three types of small sand are probably better than two or 3 types of large sand.
   
3. 2 Hours at between 250F and 320F will likely be needed to achieve full cure.
   
4. A single sand type can yield a fill rate of no higher than 75%.
   
5. The Minimum Strength of the E/G is not much better than epoxy until 80% fill rate is achived.
   
6. Nanoparticles will provide extra strength above that of any fill percentage of ordinary "large" aggregates by providing dispersion hardening.
   

Cameroun,
Larger size aggregates are preferable, approx 20% increase in compressive strength and split-tensile strength. Also % by weight of epoxy resin looks at its optimum strength at 16%.

Addition of Silane to the aggregate surface will boost compressive strength by an additional 50%

please see attached article from "Journal of Reinforced Plastics and Composites"

Best regards

Bruno

[brunog]

Cameroun,
Please download the pdf file and take a look through this report, I have a bit of a problem with 3 dimension graphs

http://fire.nist.gov/bfrlpubs/build99/art032.html

Best regards

Bruno

[ckelloug]

brunog,

Is there anything specific you want me to notice in the the NIST report? The other article you just posted was quite interesting. I'm still analyzing them.

--Cameron

[brunog]

Cameron,
You'll probably find the NIST as interesting as the other article, greater number of variable, epoxy vs polyester resin, sand vs aggregate ratios, aggregate types, fumed silica .... However this report is as obvious to decypher.

I have a few more articles attached I want to share with all members.

Best regards

Bruno

[ckelloug]

Thanks brunog for bringing all of these articles to everybody's attention. I have now read the article by Gupta et. al. from the Journal of Reinforced plastics and composites. I have not had a chance to pull reference 1, the article by Gamski and find out what the binder skin theory states. What does jump out at me is the fact that there were six different aggregate sizes in Composition I while there were 4 different aggregate sizes in composition II.

By my best visualization of the geometry involved and accepting that the rule of mixtures model is considered accurate enough to be in my text book; I think that Gupta et. al. ignore the fact that the ratio between the multiple aggregate sizes is critical. Furthermore, given the wrong ratio of multiple aggregate sizes, it would be easy to make a formulation of worse packing density than single sized aggregate. Gupta may also have found effects that relate to the epoxy aggregate interface which are second order.

I do not believe Gupta et. al.'s theory on aggregate sizing but in carefully reading the data from NIST jointly done with the Polish Team, I believe it correlates with the belief I and others seem to hold that's borne out in Walter's data that the smaller particle composites are working better.

The second graph on pg 16 of the NIST report says that the strength given the ratio of sand to 2 mm crushed quartz aggregate has a distinct maxima at a ratio of approximately 1:1 and that the aggregate percentage also has a distinct maxima. The second graph on page 17 shows that the strength given the ratio of sand to 4mm aggregate increases uniformly with respect to the percentage of sand in the mixture and also increases uniformly with the percentage of aggregate to resin in the mixture.

Both pages 16 and 17 follow well though not perfectly with the rule of mixtures predicting the moduli to be the highest as the percentage of aggregate goes towards 100%.

I agree with the Gupta paper that a silane based promoter could greatly increase the epoxy aggregate bond but I don't think that their finding about 14% to 16% epoxy is applicable to anything but the case that they studied as they were not very careful about their aggregate size ratios. lgalla has already posted about the commerical E/G machines getting down into the 8% epoxy range.

The paper posted by brunog on packing density from the INTERNATIONAL JOURNAL OF INFORMATION TECHNOLOGY VOLUME 3 NUMBER 3 2006 ISSN 1305-2403 was fascinating and I believe it represents the way forward in determining what aggregate to actually use.

I wasn't really able to make anything from the Sahmenko Ph.D. thesis.

My conclusion from all these papers of late given the packing density paper is that the strength of the composite is primarily a function of the packing density. Given Walter's data, it appears that for a single component, that strength qualitatively goes up as particle size goes down. The NIST and Gupta papers have provided evidence that this is usually true but in some cases there are anomalies which may relate to the aggregate size ratios.


<h4>Conclusion</h4>
My theory on aggregate distribution is that one should design the aggregate so that it can theoretically achieve a body centered cubic structure which is very very close to optimal. Filling in the big spaces in the BCC latice from simple geometry with spheres, I predict the ratio of 1.0: 0.414 : .086 for the diameters of the first three aggregates. As mentioned above, the paper by Gupta cited by brunog points out that treating the large aggregates with a silane promoter is good for a 50% strength increase due to the improved bonding of the epoxy to the aggregates.

If the big aggregate is picked so that the remaining space is only a few microns wide then a few percent silane treated silica fume like Cabot Cabosil TS-530 should fill in the remaining space along perhaps with some silane treated carbon black. Add a few percent of the Nanoresins Nanopox and presto you have a dispersion hardened near maximally filled composite in theory. Finally, I think I would add a surfactant like 3M Novec and a de-airing agent like BYK®-A 530 for Epoxy. (Thanks to the misc Reichhold datasheet for the de airing agent suggestion in a self leveling floor finish epoxy recipe). Seeing the problems Walter has been having with setting the epoxy, depending on the consensus of whether it is dangerous or not, I might also suggest some Cobalt III acetyl acetonate based on lgalla's description and the suggestion in Klaus's book.

This is my current best theory as to a universal formula but until I test it, I have no idea whether it is good or not. Any victims er I mean volunteers?

I'm glad to see such enthusiasm on the forum with so many participants and so much good information changing hands! I can't wait to finish my workshop!

[lgalla]

Silane coupling agents are cool,but I doubt Dow or any supplier will sell a pound.My info is from 1985 possibly out of date.All fiberglass is silane treated and as I remember some fillers are silane treated.Have no idea as to the cost.
Repeat,repeat,I have a habbit of repeating.
A box of spheres occupies 52% of the box, leaving 48% voids to be filled with resin or smaller spheres or irregulars.From web searches micropacking is not a well defined science.Spheres are isotropic not providing re inforcement.Irregular fibers,flakes,etc have aspect ratios providing re inforcement,but concentrate stresses to the ends of the fiber or flakes.An guess would be to use smooth aggregates or a mix of sphere sizes with a small%fiber to lock the micro structures to gether.Makes sence?I don't know.I am just a backyard epoxy formulator.
Question for Cameron.Being in the professional audio business,when we fly or rig loudspeakers from the roof of a stadium,all hardware is 4 times the rated load.Is this over rating or saftey factor applictable to beam calcs?
Larry
Addium,I emailed BYK about air release additives 2 weeks ago.No responce.

[lgalla]

Exodic additives enhance properties but may be hazard in bulk.Low %age in formulas are safe but best added by the formulator:
"Accidental releases of silane present potentially serious consequences, since silane can ignite spontaneously, and under certain conditions explode, when released into the air. Silane related risks are illustrated by the number of incidents recorded in the semiconductor industry. A survey of 12 semiconductor manufacturers showed 36 silane incidents between 1997 and 1982. These included 15 fires in ducts and process tools; 6 fires from silane leaks in cabinets or gas supply systems; 5 explosions in ducts; and 3 explosions in cabinets or gas supply systems. Another survey reports 38 incidents during the period 1988-1993, and a further survey recorded 53 incidents between 1985 to 1993. These incidents involved different parts of a silane system from cylinder changing to emission control [1].

[brunog]

I just finished reading on Silane, this gas autoignites at 21deg C.

That's room temperature!!

Larry is right, this product is too dangerous to use in a DYI workshop.

I wonder if soaking aggregate in a hydrochloric acid solution would do the same. This method is often used to clean masonry work.

Any suggestions?

Bruno

[brunog]

Here is more info on Silane coupling agents.

Best regards

Bruno

[brunog]

And the MSDS sheets for methacryloxypropyltrimethoxysilane (try to say this word 10 times in a row without fumbling)

http://www.harwickstandard.com/web/MSDS/0650114.pdf

Sorry it was too large a file too large to upload

Still not good

Bruno