We will start with Aggregate:

<B>Aggregate</B>
<UL>
<LI>Fracture Toughness of Aggregate Material Chosen
<LI>Aggregate Size Distribution Relative to Largest Aggregate in mixture
<LI>Size of Largest Aggregate in mixture
<LI>Solid Phase pH of Aggregate surface
</UL>

I notice that there are many folks who are looking at the Mohs Scale of Hardness values as an aggregate selection criteria. This is really only a rough estimate of surface hardness and has no guarantee of correlating with performance of the material under these circumstances.

Materials Science in the branch that studies fracture in hard materials gives us a different criterion called the "fracture toughness". Higher fracture toughnesses equates to materials that are harder to break. The value of fracture toughness is more important as best I can discern than the round or angular nature of the aggregate. The units for fracture toughness are either psi sqrt(inch) or MPa sqrt(meter)

Here's a quick rundown from a couple of sources on fracture toughness in MPa sqrt(m) so that we can compare these aggregates effectively:

Synthetic Fused Quartz 0.7
Spinel 1.3
Chalcedony 1.3
Chert 1.4
Flint 1.4
Agate, Banded 1.8
Sapphire 2.1
Aluminum Oxide 3.9
Silicon Carbide 4.0
Silicon Nitride 4.0

The above fracture toughness values are from the work of Wood and Weidlich in the following paper:
http://www.minsocam.org/ammin/AM67/AM67_1065.pdf

From the NIST cermaics webbook

Titanium Diboride 5.2
Zirconium Oxide Yttrium Oxide 10

For interest's sake,

Metallic aluminum is about 30
Polycarbonate (Lexan) is about 3.6

I expect that the values for garnet and some other materials would be very good but I haven't felt like spending the money to subscribe to <U>The American Minerologist</U> to get the data although it would be cheaper than the gas to get to the nearest library with a copy. They put their older issues up for free but they want you to join the society and pay for the new stuff. The have one of the most reasonable polices of any of the societies and some of the lowest journal costs however taxes are due in a few days for me so not this week . . . There's a paper in there from 2007 by a Margaret Broz with values for garnet as well as some other nice papers lately.

It needs to be pointed out that these numbers tend to improve as particle sizes go down although once you're into the micrometer sized particles, it may be a moot point.

Exactly how strong that the aggregate needs to be is dictated by the bond strength between the aggregate and the epoxy. If the aggregate is much much stronger than the epoxy, it will never reach anywhere near it's critical stress and if it was expensive to get aggregate that tough, you don't get good value for the money spent. Stronger in everything is generally good but there is a definite limit. The only certainty is that of almost all of the possible candidates for mineral aggregates that we can get cheaply as abrasives, quartz is the worst!

<B>Epoxy</B>
<UL>
<LI>Epoxide Equivalent Weight of Epoxy
<LI>Hardener family (amine etc.)
<LI>Reactive Dilutants
<LI>No Non-reactive dilutants
<LI>Fracture Toughness value of the epoxy
</UL>

Ideally, as strong an epoxy as one can find is optimal provided it's cost-effective and that it's possible to mix the stuff and get the aggregates dispersed. What is chosen for epoxy will be highly dependent on the mixing techniques we have available and the aggregate sizes involved. The chosen epoxy should contain no non-reactive dilutants although reactive dilutants that aren't ridiculously toxic are fine. Ultimately,the fracture toughness of the epoxy governs the ultimate strength of the part if the aggregate does not fracture. If anybody has experience with epoxy chemistry, please expand upon or correct this.


<B>Bonding Agents</B>
<UL>
<LI>Bonding Agent choice: Polysiloxane, Titanate, Zircoaluminate
</UL>

Bonding agents are chemicals that have affinities for both the chemistry of the aggregate and the matrix. The handbooks I saw suggested these 3 although practically speaking, an epoxide group siloxane like dow z6040 seems ideal. In general it appears that epoxy makes it easy to choose bonding agents and aggregates as its chemistry is very compatible with more than most adhesives.

<B>Dispersion Hardeners</B>
<UL>
<LI>Dispersion hardener choice: Carbon Black, Silica fume, Epoxy Dispersed Colloidal Silica Sol
<LI>Dispersion hardener weight fraction
</UL>

Dispersion hardeners are a class of compounds used in advanced materials to pin dislocations in the crystal lattice. Dispersion hardeners are characterized by particle sizes below 1 um. The movement of dislocations tends to make a material flexible and ductile while a dispersion hardener tends to block these movements increasing the modulus and sometimes the strength. Dispersion hardeners are not very commonly used in concrete yet because the science behind them is relatively new. Silica Fume only became available after this microscopic nuisance dust was required by regulations to be collected for air pollution control. Eventually they figured out that it had some really helpful properties and it started gaining acceptance in concrete. Carbon black has been around for hundreds of years and is used as a dispersion hardeneing agent in rubber. It is used in epoxy as a colorant and to improve electrical properties and in theory should work well as a dispersion hardener although the large fractions that are necessary drastically increase the cure time due to adsorption of the hardener.


<B>Catalysts</B>
<UL>
<LI>Choose catalyst: None, Cobalt Acetyl Acetonate, Mica dust, Chromium Oxide, Cobalt silicate
</UL>

These substances increase the reaction rate in the epoxy hardening reaction. Cobalt Acetyl Acetonate is also known to improve the crosslinking which results in higher strength and which also raises the glass transition temperature of the epoxy and thus the temperature at which the cured item may be used.


<B>Mechanical Qualities of Mixture</B>
<UL>
<LI>Percentage and size of voids
<LI>Void location: Entrapped in matrix or surrounding aggregate
<LI>Voids smaller than Griffith flaw for part stress
<LI>Vaccum deairing
<LI>Effective compaction
<LI>No material seggregation
<LI>Epoxy setting temperature: higher is better
<LI>Avoidance of shear planes

</UL>
The biggest problem with the epoxy is voids. They are worse than with Portland Cement due to the fact that small aggregate is more convenient and stronger and epoxy is more viscous and less wetting than water. Brittle materials fail via crack propagation governed by the Griffith equations.

A simple void in the epoxy, which I will call a type 1 void is a bubble of air in the epoxy matrix that it adjacent to aggregate. From the griffith equations, a type one void will cause no appreciable problems as long as its size is smaller than that prescribed by the equations for the stress level that the void experiences in the completed part. If this type one void is larger than the critical flaw size for the stress level then the part is likely to fail suddenly and catastrophically when that stress is applied.

I hypothesize without having seen this in the literature that there exists another type of void. I call this a type 2 void. A type 2 void occurs when air that is adsorbed or otherwise held by an aggregate particle forms a shell around the particle. In this case, the particle has little or no mechanical connection to the matrix. A type 2 void both provides a griffith flaw for some stress level in the epoxy and it also causes that particle to provide no reinforcement. It is my belief that the presence of type 2 voids explains the failures that are associated with batches using the smallest aggregates. If an epoxy and micrometer aggregate mixture were produced without adequate deairing, the net result would be a bar of unreinforced epoxy filled with griffith voids and waiting for failure. Since the air bubbles around adjacent particles could coalesce, the effect might be to create griffith voids that would propogate to catastrophic failures at extraordinarily low stress levels.

It is my current belief that the liklihood of type 2 voids goes down as the aggregate gets bigger but the severity of the consequences of one occuring goes up. A piece riddled with type 2 voids will be useless.

The shear plane effect is caused when the aggregate is not distributed properly in the matrix. If the aggreate is not distributed randomly then it is possible for a crack to form which is not impeded by aggregate particles. Such a crack is blocked by the fracture toughness of the epoxy matrix alone and will likely propagate to failure. Other than the relatively unattainable nature of a close pack solution, preventing distinct shear planes is a prime reason for widely distributed aggregate sizes.


<h4>Please post missing factors so we don't miss anything!!!!</H4>[/QUOTE]