[ckelloug]

Hi Roman,

Thanks for posing the question about interlock. The question that remains is whether spherical or crushed particles are better and I think that that's been an age old argument.

I'm going to make an argument from the strict perspective of the theory below for the sake of argument even though I suspect there may be other mechanisms at work. I'm curious what others think of the quality of the argument.

From the perspective of the two models I work with*, it's much more difficult to get a high packing density with crushed particles. A given size of crushed particles tends to get Beta Packing Density Coefficients in the high 50's to low 60's. Round particles tend to be between the mid 60's and the theoretical max around 71%.

Looking at the graph representation of the Hashin-Shtrikman model I posted back in post 3119, it's fairly clear that a small change in packing density makes a large change in the modulus.

http://www.cnczone.com/forums/444339-post3119.html

Because spheres have a better packing density, the models would suggest spheres as the lower effort approach to obtain a given modulus. The reference aggregate design in Hexion's mineral casting epoxy flyer also bears this out. See attached reference originally posted on page 215 attached in post 2902: http://www.cnczone.com/forums/418868-post2902.html

I'd also posit that aspect ratio 1:1 particles uniformly covered in a thin layer of epoxy exactly satisfy the conditions for validity of the Hashin-Shtrikman equation which equates the elastic strain energy between a shell of epoxy and a contained particle. When every particle is covered in a thin layer of epoxy there is no direct particle-particle contact and no direct interlock can exist unlike in the dry case. Thus, from the model perspective, interlock isn't relevant to the obtained modulus.

Having given the model perspective, I'd have to say that I think that there may be some positive effects from interlock when a high enough packing density is achieved since in practice the epoxy layer might not be quite so uniform. I'll also say that I remember seeing an article in an academic journal pointing to the effects of interlock in arresting crack propagation.

On the other hand, fracture mechanics tells us crushed aggregates are more likely to create flaws in the epoxy matrix with a very small crack tip radius which provide stress concentrations and lower the critical stress for crack propagation. Along this line, One of the articles in Kinloch's book found an increase in strength at a given packing density when smaller particles were used.

*Note: I use the Compressible Packing Model for predicting packing density and the Hashin-Shtrikman equation for predicting modulus from packing density.

I've probably gone on long enough on this topic today.

Regards all,

Cameron

[RomanLini]

Ah, "there's the rub" - would that happen ?
I have a nasty feeling that if one takes "pointy" to mean longer in one axis, then vibration would tend to make the particles line up rather than randomize, and any possible interlocking might be reduced rather than increased.
What do you think ?
John

I think you are correct in theory, but only to a point (is that a pun?).

The garnet "shards" are not necessarily greatly elongated but are typical sharp fractured shapes (imagine lots of points and triangular flat sides like broken glass) and maybe up to 1:2 aspect ratios at the highest.

Also vibrating while in a fixed size container (like a mold) probably causes more interlocking than unmeshing if my "cup of nails analogy" holds true, which it may not with such tiny particles sizes compared to mold size, but at a glance it looks logical. Maybe Cameron could discuss?

...
When every particle is covered in a thin layer of epoxy there is no direct particle-particle contact and no direct interlock can exist unlike in the dry case. Thus, from the model perspective, interlock isn't relevant to the obtained modulus.
...

Yes and no. I would be concentrating on ways to reduce the epoxy layer thickness between particles as a priority, I have advocated use of physical compression and/or air vac/pressure to crush the particles together.

Also (as I'm sure you know) with shard shaped particles the high surface pressure and small area at the interlocking points means they are much more likely to dispel the epoxy layer at those interlocking points than round particles that are more likely to develop a slick epoxy boundary layer over their entire surface (and hence between them and all other particles).

...
On the other hand, fracture mechanics tells us crushed aggregates are more likely to create flaws in the epoxy matrix with a very small crack tip radius which provide stress concentrations...

I absolutely agree, but counter somewhat with the deliberate use of sharp particles of a very high (gem) strength like garnet as opposed to much weaker sharp particles like sand.

There has to be some generalisation, ie; some mixes are better for strength, some for flex modulus, some easier to mix or pour, some cheaper, etc etc.

[greybeard]

I concede to your "point", given that aspect ratio.
Re the penetration of the points through the epoxy layer surrounding them.
I find it difficult to separate the macro experience of the way large particles would be expected to behave, and what would actually happen at this micro level, where the effects of what in my days was only referred to as "surface tension".
I think it's agreed that the better the epoxy wets the surface of the aggregate, the better the bond between epoxy and aggregate. But isn't this property the same as that which resists the penetration of the film by the particle ?
Not sure where that leaves us, but then what's new
John

[ckelloug]

Hi Roman and greybeard,

I'm still trying to figure out what happens in a lot of the cases you two are talking about. What I do know is this:

Vibrating in a container generally increases the packing density for all sizes. De Larrard says in his book that containers exert the same effect as large sized particles do on smaller ones: a local decrease in packing density. The effect of the container wall is negligible for the average packing density for particles away from the wall as long as the container dimensions are 5 times the size of the largest particle.

Particles smaller than 10 microns begin to have their behavior dominated by attractive Van der Waals forces between the particles and the trend is severe for particles less than 5 microns. This leads to agglomeration which prevents uniform distribution of the particles and adsorbed/entrapped air in a mixture otherwise containing only particles. It also probably leads to a layer of these tiny particles being attracted to the sides of the mold at least when dry. These forces appear to bind to the epoxy increasing the local viscosity and making it hard to disperse the remaining epoxy throughout the other particles.

As for reducing the layer of epoxy between particles, that's how you increase modulus. The problem is that if you decrease the layer to zero at contact points, then you have probably reduced the strength of the material as there is no longer any epoxy resisting forces on this portion of the particle surface. On the other hand, if you increase the epoxy content to 100% (maximum tensile strength) then your composite has the higher tensile strength and lower compressive strength of the base epoxy as well as it's underlying low modulus, high cost, and high thermal expansion. I would intuit based on this observation that there is a continuum of desirable epoxy amounts based on one's stated goal. I also agree that compression, vibration and vacuum are good things.

Because of the huge pieces of E/G generally used in machine parts for damping purposes and stiffness, I consider the strength to be much less important than the modulus. You can always add more material to a part to get the strength up but you can't always easily add material if you get effects like shear or compressive deformation due to low modulus. If the part is big enough not to deform significantly under the given load, it's also strong enough.

I'm attaching a graph of the Hashin-Shtrikman modulus predictions for Epoxy-Garnet. Garnet is twice as stiff as quartz and it should be relatively easy with garnet to get modulus equivalent to the commercial materials even neglecting interlock. Interlock can only help but modeling it isn't something I am sure how to do right now.

The only problem with non-quartz materials is that quartz provides a piezoelectric damping effect that is not provided by other materials. I would expect the damping to be lower for garnet based E/G materials as well as for other minerals.

Regards all,

Cameron

[brunog]

As for reducing the layer of epoxy between particles, that's how you increase modulus. The problem is that if you decrease the layer to zero at contact points, then you have probably reduced the strength of the material as there is no longer any epoxy resisting forces on this portion of the particle surface.

Cameron,
This effect is directly related to the type of epoxy and it's viscosity. a very low viscosity epoxy (100CPS or less) will reduce the probability of getting a zero layer at contact points, not only that but also less air entrapment and optimum compaction.

Best regards,

Bruno

[rusel]

Hi

Just thought you might be interested in this thread
Build Thread Phenolic Basalt head for our HM45 - CNCzone.com-The Largest Machinist Community on the net!

Russell

[ckelloug]

Bruno,

I agree. That sums it up nicely.

Russell,

That's pretty cool. Congrats on getting something made. :cheers:

Romanlini and greybeard,

Thanks for bringing up the point about interlock and bludgeoning me over the head with it for a while. I fully agree at this point that it is important and I am fairly certain that the commercial E/G mixtures owe some of their published moduli to interlock. I suspect the interlock effect may lead to something on the order of 1-3 percentage points lower packing density being required for a given modulus than the Hashin-Shtrikman equation would predict but this is just a guess at this point.

I've got a few books coming that may help me understand the relationship between the epoxy and the aggregate. Hopefully the 7 inches of unexpected snow we got here last night in Huntsville, AL don't slow the FedEx trucks.

Regards all,

Cameron

[brunog]

Hopefully the 7 inches of unexpected snow we got here last night in Huntsville, AL don't slow the FedEx trucks.

Regards all,

Cameron

Cameron,
ship that snow up here where it should be.

We've hardly had any snow since christmas.

Best regards

Bruno

[Nivea]

After casually following this thread from day one, I've gone back and re-read every post. Very interesting to read 4 years worth in 6 days!

Ok,

It seems the very fine aggregates are causing grief with wet-out and therefore compaction of the mix. What would happen if we calculate a set of aggregate sizes still optimized for maximum packing density but such that it's smallest particle is large enough for successful vacuum degassing and compaction of the mix. I know larger aggregates are not as fracture resistant as smaller but it may be worth a shot in the hope of at least achieving a higher modulus sample.

No Agsco here however thanks to johnoharas suggestion, I've found a local supplier of reasonably high purity quartz but it is un graded so Im ordering a complete array of mesh sizes to sieve it. If anyone has some suggestions on making use of different sizes than the Agsco mixes I can make some samples. I have high vacuum and vibration too.

Regards,

Shae.

[greybeard]

.......... so Im ordering a complete array of mesh sizes to sieve it. ....
.

$$$ouch$$$

I was lucky to find a set in a country auction here, and with no one knowing what they were, I got a "steal".
Try modding your vibrator to take the seives. It'll save a lot of backache.

Regards, and good luck
John

[ckelloug]

After casually following this thread from day one, I've gone back and re-read every post. Very interesting to read 4 years worth in 6 days!

Ok,

It seems the very fine aggregates are causing grief with wet-out and therefore compaction of the mix. What would happen if we calculate a set of aggregate sizes still optimized for maximum packing density but such that it's smallest particle is large enough for successful vacuum degassing and compaction of the mix. I know larger aggregates are not as fracture resistant as smaller but it may be worth a shot in the hope of at least achieving a higher modulus sample.

No Agsco here however thanks to johnoharas suggestion, I've found a local supplier of reasonably high purity quartz but it is un graded so Im ordering a complete array of mesh sizes to sieve it. If anyone has some suggestions on making use of different sizes than the Agsco mixes I can make some samples. I have high vacuum and vibration too.

Regards,

Shae.

Shae,

You make a good suggestion with regards to using a larger minimum size. I plead insanity as to why I didn't go this way. Unless a significant breakthrough is achieved, 10 micron and below probably are worth avoiding. Due to my insanity however, I'm not ready to give up on them yet

More seriously, an experiment I've been doing back in the lab with some abrasives is predicting a need for 19mm as the largest aggregate size without increasing the minimum size. This veritable boulder makes it hard to cast any small parts without dominance by container wall effects. The aggregate I'm working with has very jagged edges and packing density is lowered appreciably by the shape of the particles in the largest sizes so I'm afraid how much bigger the top size could get if some of the smaller sizes have to be dropped.

Rereading my new copy of Kinloch's book Structural Adhesives Developments in Resins and Primers(Found a cheap copy on Amazon), it appears that modulus, strength and toughness decrease weakly as particle size increases. The effects probably aren't enough to worry about significantly but perhaps they are food for thought. See Chapter 7 around page 170 if you can get hold of the book.

The Hexion HCI556 mineral casting brochure suggests 90 micron as the smallest average size to use with only 5 to 10 percent smaller than this. My recent research both in the library and lab has shown that particles below 10 microns begin to behave badly in air and particles below 5 microns behave positively badly.

I've begun reading the third edition of Intermolecular and Surface Forces by Jacob N. Israelachvili. It's very deep and I'm only scratching the surface at this point. What I have gathered from it is that small and large particles may either repel or attract each other based on the exact circumstances. My current opinion is that we are probably in a large particles repel and small particles attract situation which means that the dense packing we want is not thermodynamically favorable.

I've come to the tentative deduction that coupling agents such as silanes and titanates reduce viscosity by inducing dipole moments in the particles they are coupling and that these dipole moments disrupt the short range attractive forces between small particles. I'll say more about this some day when I understand the interaction better than the current level of a guess.

One thing that was mentioned offhand in the book is that when solvent is added to epoxy that even a very small amount of solving evaporating during curing can cause massive effects on the strength of the resulting hardened epoxy.

One other observation the book mentions is that the van der Waals forces are decreased significantly in a solvent from those related to just the bulk particles. I ascribe to this saying that small particles which agglomerate in bulk or in air will tend to disperse better in a solvent and the higher the refractive index of the solvent, the larger the effect.

My final observation from the book up to chapter 11 is that when packing density exceeds approximately 55% for a single size of spheres, jamming occurs and the mixture will no longer flow. As a result, no form of low shear mixing like my rotating drum mixer is going to produce significant mixing. This leads back to the possibility of Stepper Monkey's and lgalla's suggestion of a bleed layer back on page 67 of the thread. If you can use enough enough epoxy to prevent jamming during mixing, you can get a thorough mixing and then let some epoxy drain off during compaction. Based on the desired and predicted compaction, I think this will work but at a large cost of wasted epoxy.

I've also skimmed a few chapters in my new copy of Epoxy Polymers: New Materials and Innovations Ed. Jean-Pierre Pascault and Roberto J.J. Williams. It mentions the use of small amounts of benzylamine to increase toughness in the epoxy by its role as a chain extender. There are two amine hydrogens in benzylamine and when a small amount is used with excess epoxy, it will create a large number of E-E-BA-E-E configuration molecules such that an epoxy molecule with 2 epoxy groups is now joined by a benzylamine to another epoxy molecule with two groups consuming one epoxy group from each molecule. As a result, a longer molecule which retains two epoxy groups is formed.

Time to go hit the books.

Regards all,

Cameron

[bagherdn]

i've used epoxy but not for complete building , just filled tubes of structure for rigidity and reinforcements u can see at
:http://www.cnczone.com/forums/diy-cn...00*1100mm.html
be glad

[Nivea]

Are we satisfied with the material that the big guys are using? The way I see it now we have already achieved perhaps better packing than them and have available the same epoxy/additives. We don't have an easy successful method for mixing with 7% epoxy but we know already that we can simply add more epoxy to mix then drain, I should probably just shut up and start making samples but until my mesh arrives there's not much I can do but wonder just what it is that I need to be trying to fix.

Cameron,

You made a terrific statement earlier in the thread regarding an un-optimized pour requires the same time/money/effort as an optimized pour. Im curious on the 'degree' of optimization at this stage. Are you focusing on superceding the current material the pros are using , or arrive at a method to mix 7% easier in the garage?

Shae

[veteq]

Im curious on the 'degree' of optimization at this stage. Are you focusing on superceding the current material the pros are using , or arrive at a method to mix 7% easier in the garage?

200% the first one....!!!
the second one has been done before by Thomas zietz and friends.
It not the goal to get there the fastest way, but the best way...

keep up the good works..!!

[Nivea]

200% the first one....!!!
the second one has been done before by Thomas zietz and friends.
It not the goal to get there the fastest way, but the best way...

keep up the good works..!!

That's my point, Thomas's formula as I understand was not considered to be optimal, but he has a machine. I wonder how his machines go with substantial cuts in steel.

[veteq]

That's my point, Thomas's formula as I understand was not considered to be optimal, but he has a machine. I wonder how his machines go with substantial cuts in steel.

His machine works, but that aint the goal here, then your missing the point off this thread, the goal is to make a perfect mixture.
If you want you cann make a machine with Thomas his mixture, of you know what that is...

[ckelloug]

Hi Shae,

I've been optimizing. Perhaps over optimizing. I'm also getting the chance to teach myself numerous kinds of science and math that I didn't get in engineering school. I'd like to master the science behind this type of composite in cooperation with all those who comment here. I'd like to hope our postings here are of interest to others who want to think about this hard problem. In short, I personally am looking for both a duplicate of the commercial products and some improved versions.

So far, I've done a lot of modeling and made a few samples based on graded crushed abrasive with drastically worse performance than I would expect based on the models.

It has been my experience that E/G with very high aggregate to epoxy ratios is quite difficult to mix adequately. Something like the industrial equivalent of a kitchenaid mixer is probably going to be required if we don't come up with a better way.

Seeing the problems viscosity causes, so far E/G appears to require epoxy with reactive dilutants to get the viscosity down. Lowering viscosity with the addition of solvents like acetone destroys epoxy performance because of molecule sized voids created by the evaporation of solvents (as Israelachvili's book tells us).

In short, I am no way happy with the mixing of extremely low epoxy E/G and the batches I've made or the performance of those batches. My batches have had epoxy amounts close to 1-aggregate percentage by volume and have not worked as desired. I'm starting to investigate the literature on particle and surface interactions in hopes that a better understanding will make obvious what a good solution is.

I'm also not that happy with what's going on with aggregate. Number 6 and larger of the abrasive I've been using pack around 55%. The smaller ones get up to around 62% and then getting down to micron sizes, anomalous results with much lower than desired packings crop up. At least in air, small spherical particles appear to be effected by short range Van der Waal forces of attraction which causes them to form agglomerations which don't pack in the way that spheres pack in the absence of attractive forces. The comments that have come up here recently and been mentioned in the literature about jamming also portend issues with mixing high density mixtures.

Running my measured packing data through the compressible packing model, it looks like 8mm and 19mm aggregate are going to be required with crushed filler. I guess I shouldn't be surprised as roach told us this and the Hexion HCI 556 datasheet also tells us this.

I suppose it also tells us that round fillers will be more appropriate for homebuild machines since from the Hexion data only 10mm spheres are required for max density. The 10 mm spheres make for a minimum part dimension of around 50mm instead of 100mm with approximately 20mm max size. I think the packing density problems with crushed aggregate also tell us that the highest modulus mixture is going to be achieved with round rather than crushed aggregates.

My current wish would be to get a thin epoxy coating on all of the aggregate pieces individually. Rather than in the liquid state at room temperature, I would like the epoxy to to be in the vitrified partially hardened state like the coating on candy. This would allow the particles to be mixed as a solid rather than a liquid. Heating the vitrified epoxy during vibrational compaction would cause it to liquify and attractive intermolecular forces would ideally draw the material together assisting in the removal of air. This process might be possible using an engrosser like is used to coat candy but it would involve doing enough chemistry to get an epoxy that behaves appropriately.

In short, in the end game, using a near-optimum mixture will probably be just as easy and cheaper than an unoptimized picture. Developing such a mixture however may cause a teeny tiny delay in getting machines made. One day at a time. . .

Regards all,

Cameron

[veteq]

That was a nice write up Cameron,
cann imagine that other people will think the guys in this thread have lost it....lol:cheers:
It is taking ages and almost nobody understands it anymore, besides you.
Really like the trip that you are making and have to say: Respect..!
Very nice to share it here, dont read it all, because i mis the knowledge...

Still i like the idea off EG, my machine is almost ready...just like your mixture.
Got all the parts and even a cnc`ed wooden mould to cast the EG in.
Now there are only 2 problems to think about...lol:
-How will i make all the aluminum parts that form the mill? (dont have a mill etc..)
- will i cast the EG on my own, with a vibration table, or go to a German company that offered me a fill for 1 euro/Kg.....

Cann go the easy way to the German, but that wouldn`t be fun...I just always tell mysef, when i finish my study on manual doing the FEA calculations and FEA non-linear studies on the pc....then i will go into EG like overhere...lol. Hope i will make it... enjoying it for sure.

Here a nice little movie off my small machine, dubbeltab the screen and put it on 1080p for a better look:
[nomedia="http://www.youtube.com/watch?v=Q0BTHGUXlXk"]YouTube - CNC Mill[/nomedia]

Regards,

Roy

[greybeard]

Hi Roy.
Now I know what they mean by reverse engineering

A really neat explosion.
John

[Kevin_Johnson]

My emphasis :

Hi Roman,

Thanks for posing the question about interlock. The question that remains is whether spherical or crushed particles are better and I think that that's been an age old argument.

I'm going to make an argument from the strict perspective of the theory below for the sake of argument even though I suspect there may be other mechanisms at work. I'm curious what others think of the quality of the argument.

From the perspective of the two models I work with*, it's much more difficult to get a high packing density with crushed particles. A given size of crushed particles tends to get Beta Packing Density Coefficients in the high 50's to low 60's. Round particles tend to be between the mid 60's and the theoretical max around 71%.

Looking at the graph representation of the Hashin-Shtrikman model I posted back in post 3119, it's fairly clear that a small change in packing density makes a large change in the modulus.

http://www.cnczone.com/forums/444339-post3119.html

Because spheres have a better packing density, the models would suggest spheres as the lower effort approach to obtain a given modulus. The reference aggregate design in Hexion's mineral casting epoxy flyer also bears this out. See attached reference originally posted on page 215 attached in post 2902: http://www.cnczone.com/forums/418868-post2902.html

I'd also posit that aspect ratio 1:1 particles uniformly covered in a thin layer of epoxy exactly satisfy the conditions for validity of the Hashin-Shtrikman equation which equates the elastic strain energy between a shell of epoxy and a contained particle. When every particle is covered in a thin layer of epoxy there is no direct particle-particle contact and no direct interlock can exist unlike in the dry case. Thus, from the model perspective, interlock isn't relevant to the obtained modulus.

No, the question still remains. With the above argument you are simply encrypting into the model of the epoxy component the ability to have point contact everywhere (direct particle-particle contact) whilst removing that quality from the component class known formally as particles. So you are, in effect, arguing that it, simultaneously, is and is not the case. A safe position, perhaps.

Sorry to others about being a bit abstract.

Edit: Speaking as a novice looking at the discussion/argument from outside the field I am wondering why the Superpave gyratory compactor has not been looked at for comparative compaction of crushed and spherical particles over time? If this has been discussed, I sincerely apologize. Search parameters did not reveal it in the thread.