[ckelloug]

Where's Zumba's picture of the tumbleweed when you need it?

I just wanted to say that my copy of deLarrard's book on scientific aggregate designs arrived today and I am eagerly looking forward to diving into it.

Anybody out there got any new results?

Any lurkers have questions about what's going on on this thread?

--Cameron

[greybeard]

Hi Cameron.
Sounds like you need a little encouragement. How's the workshop progressing ?

I've now got the materials in hand to start some spin casting(or should that be "rotational casting" ?) experiments, so hope to have pics next week.
I want to find a transparent tube so that I can see what's going on, before I start, so that I can hit the panic button asap.

I plan to do a before and after cure shot of plain resin, just to demonstrate the migration of the air bubbles, and get a feel for the minimum speeds necessary. First trial will be in about 1" diam tube, and then work up to 4" diam as my target for a short gantry tube.
The final design will have a metal insert top and bottom, cast in situ, so lots of fun ahead.

I've been thinking about that vision you had of rapid spinning head dispensing the mix inside the tube, and wonder what might be the advantage in slowly feeding the dry mix into a spinning tube with the freshly mixed resin already in place.
( I've done the design based on an old lathe bed I have )
This could have been de-aired by high speed spinning in a separate set up previously.
I see the aggregate particles 'sinking' outward as it spins, and I wonder if this would minimize the amount of air being trapped in. Rather along the lines of vacuum impregnation by the resin from one end of a mold.

I can't see if there would be any appreciable stratification of the sizes of the mix, or indeed, if there might be anything to gain by introducing each component separately.
Any thoughts ?

The other approach would be to do the mix in a pot, spead it all inside the mold tube with some sort of 'doctor blade' along the axis, then spin up, first to a de-airing speed, then slow to a casting speed for the gel time.

It's beginning to sound like I need an old programmable spin drier.

John

[ckelloug]

After reading some of the pertinent chapters of <U>Concrete Mixture Proportioning, A Scientific Approach</U> by Fran&ccedil;ois de Larrard, I've learned that there is both very much and very little to know about aggregate design.

I'll start by citing my favorite paragraph of the book's conclusion and then get on with the aggregate answers:
<BLOCKQUOTE>
In the hypothesis in which fracture-mechanics-based methods will eventually find international acceptance for the design of concrete structures, it will be important to select real material properties (fracture toughness, fracture energy, brittleness, etc.) as inputs for these models. The the question of integrating fracture mechanics in the system will emerge, and there will be a need to model the related properties as functions of the mixture proportions.
</BLOCKQUOTE>

<h4>Intro to de Larrard's Theory</h4>
Chapter 1 of the book describes a mathematical model for predicting packing densities that was tested against hundreds of aggregate designs over a dozen years of work. Mr. de Larrard was also able to quantify the effects of different compaction techniques to the point that he could match the measured density of a given mix with his model if he were told how it was compacted. The steps used in validating this model were published in detail and it was then used to show the effects of the various aggregate design techniques used since ancient times.

The bad news in all this is that an Ancient Greek philosopher named Apollonius de Perga who died in 190 B.C. was the last person to have an aggregate design theory that actually produced maximum packing density. All commonly used aggregate designs since then have actually been steps backwards in terms of maximum packing desnsity from the technology available in 190 BC. Monsiuer de Larrard takes great pleasure in showing how this Ancient Greek Model is a special case of his very well validated model of aggregate packing.

<h4>Important Result 1: Fuller's Rule is not the answer</h4>
Without getting boring, de Larrard shows that Fuller's rule is the least effective aggregate grading strategy commonly used. It lags all other models by about 7%. This would be nothing but a footnote to history on this thread were it not for the rule of mixtures whose graph I posted back in <A href="http://www.cnczone.com/forums/showthread.php?p=291506?postnum=1082"> Post 1082</A> . The graph shows that (neglecting epoxy bond strength and focusing only on material moduli) that nearly a factor of 2 improvement in modulus can be had for that particular 7% improvement in packing density. The maximum simulated packing density for a Fuller mix was shown to be 86.9% while the optimum simulated packing density was 92.9%. These are not purely theoretical results: the model used here correlates with real data to within 1% and figures are shown for what is achievable by prolonged pressure and vibrocompaction of these mixes to the extent possible.

<h4>Important Result 2: Optimal Mix Design</h4>
For a mixture where the particle sizes vary by four orders of magnitude (with a range of 1 - 10 000) broken into a smallest diameter range and 9 larger diameter ranges according to the logarithm of diameter in a geometric progression, the optimum mixture is 13.6% by volume of the smallest range, 13.6% of the largest range, and 9.09% of each of the remaining 8 ranges.

Duplicating exactly what was in de Larrard's Simulated Grading Curves Graph:
<Table>
<TR><TH>Size (arbitrary units)</TH> <TH>Percentage</TH><TR><TD>0 - 1 <TD>13.6 </TR><TR><TD>1 - 2.78 <TD>9.09</TR><TR><TD>2.78-7.74 <TD>9.09</TR><TR><TD>7.74-21.54 <TD>9.09</TR><TR><TD>21.54-59.94 <TD>9.09</TR><TR><TD>59.94-166.8 <TD>9.09</TR><TR><TD>166.8-464.1 <TD>9.09</TR><TR><TD>464.8-1291 <TD>9.09</TR><TR><TD>1291-3593 <TD>9.09</TR><TR><TD>3593-10000
<TD>13.6</TR>
</TABLE>

This is the best one sized fits all approximation for a grading curve. Monsieur de Larrard does point out however that such a mix design is dependent on the amount of compaction that occurs but the value predicted by this formula has been achieved in the laboratory. Such a wide aggregate size difference is probably not necessary in practice.

<h4>Important Result 3: Most Foolproof Mix Design</h4>
One of the largest problems in mix design is that the aggregates of different sizes can separate during mixing and end up in different parts of the batch. This is called segregation by de Larrard and the literature. The best mix design to prevent segregation shown here where particles vary over 4 orders of magnitude and are broken into 10 ranges by logarithm of particle diameter in a geometric progression is <B>Get This</B> 10% of each of the 10 size ranges! What is fascinating is that the mix has only 0.3% difference in packing density from the optimal mix.

<Table>
<TR><TH>Size (arbitrary units)</TH> <TH>Percentage</TH><TR><TD>0 - 1 <TD>10 </TR><TR><TD>1 - 2.78 <TD>10</TR><TR><TD>2.78-7.74 <TD>10</TR><TR><TD>7.74-21.54 <TD>10</TR><TR><TD>21.54-59.94 <TD>10</TR><TR><TD>59.94-166.8 <TD>10</TR><TR><TD>166.8-464.1 <TD>10</TR><TR><TD>464.8-1291 <TD>10</TR><TR><TD>1291-3593 <TD>10</TR><TR><TD>3593-10000
<TD>10</TR>
</TABLE>



<h4>Implications</h4>
Unfortunately de Larrard's chapter on Rheology (flow characteristics) is based on data that involves wet concrete and admixtures. The techniques would be applicable to E/G but I don't think any of us have the 12 years de Larrard spent studying this to recalibrate all of the models for epoxy.

In absence of firm guidance, I will go out on a limb and suspect from what was in the book about packing density that the 92.9% solids mix created from the optimal packing density aggregate won't be too hard to deal with because the amount of epoxy remaining will be just enough to fill the space that is left. In the experiments many folks have reported here, I believe the bad behavior of a "dry mix" has been due to the fact that the epoxy present was not filling the voids in the mixture. We all know that you can't stir a bucket of sand easily and a bucket of sand with only half enough epoxy to fill the space not taken up by the sand and lubricate it will likely be even worse. . .

<h4>Importance of Graded Aggregate</h4>
Without going into detail here, 2 component mixtures tend to achieve optimal packing densities of about 65%. For three component optimal mixtures, the value is about 78%.

The rule of mixtures graph shows that replacing an optimal 2 component mixture with an optimal 3 component mixture will have negligible effect on the modulus : about 10% increase in minimum predicted modulus and about 33% increase in maximum modulus.

The rule of mixtures graph also shows that replacing a 2 component mixture with a continuously graded mixture like the optimum one described above will raise the minimum possible modulus by 50% and the maximum possible modulus by at least 300%.

Properly graded aggregate will make E/G cheaper since aggregate is cheaper than epoxy. It should also make it much stiffer when dry and may actually make it easier to mix.

<h4>Footnote</h4>
De Larrard's book also has much data about the use of Silica Fume to strengthen ordinary concrete. I believe strongly but state without proof that either it or another nanoscale material (like Nanopox or carbon black) will have an incredible effect at such a high packing density.

Finally, we are indebted to the brilliant Mr. de Larrard who spent 12 years pouring rocks in boxes to generate a math model that removed the trial and error portion of aggregate design for us on this thread. There are still oodles of questions about admixtures, the perfect epoxy, how to mix it all up, whether it can be spin cast and above all, how to make it look sporty. I look forward to us solving those empirical questions here now that I know that we can do so rather than repeating the last 2000 years of aggregate design mistakes.

Cheers all,
Getting the aggregate design from the book is a heck of a lot more fun than reinventing the wheel.

--Cameron

Thanks to Ken and John for pointing out the misstatements in the first version of this post

[greybeard]

Quote ...The maximum simulated packing density for a Fuller mix was shown to be 86.9% while the optimum simulated packing density was 92.9%. These are not theoretical results: these are validated model results of what is achievable by prolonged pressure and vibrocompaction of these mixes.

Great info. I've underlined what I immediately spotted in your summary. I wonder how much the combination of pressure and vibration in fact modifies(re-shapes) the aggregate particles so they can then fit together better, in order to achieve those higher packing values ?

That's an amazing range of sizes. I'd better start finding a range of sieves.

John

Edit Was the size proportion measured before compaction or after ?

[lerman]

Am I correct that the distribution of sizes over four orders of magnitude is logarithmic; not linear.

Also, I assume that the proportions by weight assumes that the components have the same density. That is to say, we are actually talking about the distribution by volume of the solid material.

Ken

[greybeard]

Ken - I can't get my head round how you divide a logrithmic scale "uniformly" into 10 equal parts.
Could you expand that a bit ?
Thanks
John

[lerman]

Ken - I can't get my head round how you divide a logrithmic scale "uniformly" into 10 equal parts.
Could you expand that a bit ?
Thanks
John

I take the word uniformly to mean that within each of the ten sizes, all particles are the same size.

There are nine intervals over the range of 1 to 10,000. Take the ninth root of 10,000/1 = 2.7825594022071245976627481026572

Then, the sizes are:
1
2.7825594022071245976627481026572
7.7426368268112705972667945153697
21.544346900318837217592935665194
59.948425031894101481155956305342
166.81005372000587535997911490887
464.15888336127788924100763509194
1291.5496650148838754100755464721
3593.8136638046273021881672290384
10000

Ken

[greybeard]

Thanks Ken.
I think we have a semantic difference here.
Is it 10 uniform size ranges, or 10 uniform size ranges ?

Call up the referee

Regards
John

[ckelloug]

Ken and John,

Thanks for the corrections. (The article referred to here and this post have been edited)
I think I get extreme bonus points for rusty brain misreading a semilog plot!

De Larrard gives a log size vs. sieve passage chart and he has divided the log axis that represents particle diameter into 9 intervals covered by 10 points with a range of 1 to 10000 on the log axis. He called the grading range 10e-4. His sample curve would covers between 3um and 3cm not
3um and 3mm as the bogus original version of my post had it.

His motivation may be that French Standard Sieves which are tenth root of 10 apart although these curves are all computed from models.

What I had been trying to convey was that the percentage of aggregate retained on a given sieve with the 9th (was 10 here but wrong) root of ten as the interval between sieves should be the percentage I gave. So I meant that the particles in the continuous material distribution falling into a specific sieve fraction for ten ranges of particles in sieve fractions, not ten individual diameters. Further review shows that the book claims the optimum values for either ranges or individual diameters are the same but that the properties of the material with the ranges are better.

Other than making the numbers come out neatly I think the only point to going through 4 orders of magnitude is to suggest you need a continuous distribution or one with a relatively large number of fractions as distributions with a small number of fractions behave differently.

The original post has been corrected. If any other errors are spotted, please post so they can be corrected as I'd hate to be the one who posted bad info from a relatively authoritative and well written book.

--Cameron

[greybeard]

Great - now I have to find French sieves (chair)

There used to be a set at the local school when I was lab tech there.
Mind you, that was 32 years ago, so they may have got a bit of dust on them by now.

Night all.
John

[walter]

Thanks for the great info Cameron! That is truly hard core stuff.

[lgalla]

Walter In reply to hardcore stuff,confucius say:
Man who stands on toilet,high on pot.
Man who puts rouster in frezzer get stiff cock,or higher modulus.
I wonder what brand of epoxy Apohonius de perogie used?

[greybeard]

Re the 10% volume of each "fraction" - I guess that is measured as bulk volume, so each fraction could be taken with the same measuring pot.

I'm now wondering which would be the simpler path - using a crushed mix of one material, which one could check for size distribution, and adjust with a segregated portion, or track down a range of sizes of materials, which may or not be the same(?), and make up a known mix from scratch.

There are some interesting sites on "self-compacting concretes" with ideas and data that may be transferable to E/G. Does de Larrard mention them ?

Quote....De Larrard's book also has much data about the use of Silica Fume to strengthen ordinary concrete. I believe strongly but state without proof that either it or another nanoscale material (like Nanopox or carbon black) will have an incredible effect at such a high packing density....unquote

I've just done some background reading on Si fume and find that in dry mixes it is a great aid in improving the flow of the particles in pouring, yet reduces the effects of seggregation. Magic stuff !

John

[walter]

·
"Coupling agents are used to provide a stable bond between two otherwise nonbonding and incompatible surfaces. In reinforced and filled plastics, the improved bond between the fibrous or particulate inorganic component and the organic matrix polymer results in greater composite strength and longer service life.
Silane coupling agents are often used to treat silica (both fumed and precipitated) treatment with great effectiveness in filled polymer systems. The silane treatment can improve processing, performance, and durability of silica-modifed product by:
* Improving adhesion between the silica and the polymer
* Improving wet-out of the silica by the polymer
* Improving dispersion of the silica in the polymer
* Improving electrical properties
* Increasing mechanical properties
* Reducing viscosity of the silica/polymer mix.."


Someone suggested just washing the aggregate in 91% Isoprolyl wound wash solution (and not messing with toxic chemicals). I tested the Isopropyl idea, and it works. I bought a bottle at Walgreen's, poured into the container and thoroughly wetted the aggregate. 7 days later it was used in a mix. Jig test shows 10% performance increase (which makes me even more inclined to use real coupling agent!)


Don't mind the pictures, poor surface finish is due to my sloppy work. I developed affection for careless, sloppy joe mixes where I just dump things into container, mix vigorously for 3 minutes then dump it into the mold :nono: No vibrocompaction either... But these mixes are as strong as my "1ksi" mix from post #1597, so why not. Top surface picture shows "peanut butter" effect, not sure if it's good or bad, I'll talk about it in a moment.

Now, there's something special about this particular mix. It's brutal (and not plasticky), with tough surface and awesome awesome sound - it really gives me chills. Like metal but without the ringing. And I'm not talking about alcohol "treatment", that has nothing to do with it. The mix itself is interesting and I would love to see it on my machine. No, I want to see it on my machine - I am not kidding. So here's the plan:


1. Start work on the mold; plan on attaching a decent vibrating motor or two. Vibrating will take care of the voids and surface finish - I don't think I would recommend going without it.

2. Use some kind of coupling agent, either BYK C-8000 or Cameron's Dow product. These things alone should be good for 10-40% in strength improvement. (Not that I really need it, I can already kill an elephant).

3. Figure out the peanut butter thing. Or just use vacuum..


The peanut butter thing is probably due to (improper) use of small aggregate. What it does it basically creates peanut butter like consistency and reduces flow. It's different from honey effect -you dump it on the surface and it just stays there. It looks puffy and lightweight, and not very serious. It does not reduce strength so it's no big deal, just a little annoyance. It may require vacuum though.
My smallest aggregate was in 0.05-0.12mm range and I read that you shouldn't just dump these tiny particles into the mix- some are using special blenders to control the process, it's some kind of rocket science. Whatever

Ok, here's the mix:

16% Epoxy
64% Quartz Aggregate
20% Zeeospheres

I mixed the epoxy with hardener, left in the pot for 10min, then added random pile of aggregate, 5 different sizes from 0.05mm to15mm (pictured below). I dumped it into the epoxy, all at once (I know you shouldn't do that). Good mixing ensued and finally Zeeospheres were added. These things are pure magic and I don't recommend going without it.

I immediately realized I had dialed the wrong "number"- my epoxy disappeared and there was not enough to wet the mix! I felt pretty stupid, but continued on with the mixing. Then, surprise.. My mix turned into cool flowy slurry. And then into peanut butter.

Conclusion: I should probably change my mixing "technique" and work on the air voids.. But the point is, I totally like the results. I would be thrilled to have it on my machine!
_

[walter]

Here's more:

The lure of this particular mix is so strong that I'm willing to encapsulate my THK rails in it.

http://www.cnczone.com/forums/showpo...75&postcount=3

[lgalla]

Walter, methyl hydrate is a form of alcohol and very good cleaner of uncured epoxy.If you must wash aggregates this is much cheaper than walgreens.Never try to thin epoxy with this as it is reactive as a catylist and you will get hot epoxy foam.
Your mix changed over time probably due to heat of cure,thus lowering viscosity before gel.Glad to see Zeospheres are useful.The 5 aggregate sizes allow higher packing density.Good progress Walter.
Larry

[walter]

Thanks Larry. And thanks for bringing in the Zeeospheres!

I have the 850's which are 10-200 microns and seriously thinking about getting bag of 800's which are 0.3-200 microns.

btw, Isopropyl was used as a coupling agent, not cleaner. My aggregate is lab clean.

[walter]

This latest mix got me pumped so I tried one more.
Results will be tested next week and here's the info:

16% Epoxy
59% Quartz Aggregate
25% Zeeospheres

I upped the Zeeospheres to 25% and got rid of large rocks. The largest component is now 5mm. The 59% Quartz Aggregate portion consist of:

1 part #5 quartz (up to 5mm)
1 part #4 quartz (0.6-1.68mm)
1 part #2 quartz (0.2-0.6mm)
1 part #1/2 quartz (0.6-0.25mm)
1 part #2/0 quartz (0.04-0.15mm)

I prepared epoxy and added the rest one by one, starting with 5mm stuff. Smallest aggregate was slowly poured in during mixing and there was no peanut butter effect. Of course something else went wrong. 25% Zeeospheres content made the mix drier than I would have liked, and there was no time for another batch of epoxy. But I went with it and took the pictures. The mix is pretty dry but started rolling like dough when placed on a shaker. Pretty interesting.

I forgot to mention Carbon Black. I added one-half of spoon to the epoxy. There will be slight change in color.
_

[greybeard]

Walter, sorry to ask, as I'm sure you've posted somewhere, but do you quote your recipes in part by weight or volume ? I'd guess it's volume.

John

[walter]

Hi John,

I own a small scale accurate to 1g and everything is in weight. My samples are 600g or more.
The one thing that is missing is a mixer..
_