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How to create a DOE for observing percolation behavior in composites

craigwb

Community Trekker

Joined:

Feb 25, 2015


This is an unusual DOE situation, and I'm out of my depth on this...

A colleague wants to look at the action of reinforcing fillers and some of the associated chemistry (two other major components) in rubber compounds. The experiment seems to be straightforward except that reinforcing fillers undergo percolation transitions at the critical volume fraction of the filler.  This volume fraction is a function of the 'reinforcing power' of the filler. The responses are the critical volume fraction of the filler and the resultant power-law exponents of the percolation behavior.  These responses require the observation of a physical behavior (for example, mechanical properties) which is typically logarithmic (see below).

We have two things working simultaneously to compound the complexity:

  • Percolation phenomena are typically power-law behaviors, such that y(volume fraction) -->  (volume fraction)^exponent, so it is intrinsically nonlinear (though linear on a log scale);
  • At the critical volume fraction the mechanical behavior undergoes a nonreinforcing-to-reinforcing transition, which is demonstrated as a slope change on a log(mechanical value) vs. volume fraction plot.

In addition, we have a selection of components from two chemical classes which interact with the percolation behavior:

  • Rubber class: 2 rubbers, chosen exclusively (meaning, if one rubber is selected, the other is not present), and then the concentration is changed
  • Additive class: 2 additives, chosen exclusively, in a like manner as the rubbers, and their concentrations changed;
  • The rubber class and additive class are independent of one another.

How to build a DOE that handles the percolation phenomena (as a function filler volume fraction), and the categorical selection of each chemical entity in each chemical class, along with their concentration selection?

1 ACCEPTED SOLUTION

Accepted Solutions
louv

Staff

Joined:

Jun 23, 2011

Solution

Craig,

I would use the Custom Design platform and treat your filler as a discrete numeric factor and chose the number of levels that seem reasonable to delineate your known domain knowledge of the percolation phenomena. The two categorical factors to capture the rubber and additive choices and two continuous factors to capture the amounts of the rubber and additive employed. Not sure if you have disallowed combinations but you can handle this as well. If your budget allows it try the RSM model and see if the design generated suits your needs.

Lou V

2 REPLIES
louv

Staff

Joined:

Jun 23, 2011

Solution

Craig,

I would use the Custom Design platform and treat your filler as a discrete numeric factor and chose the number of levels that seem reasonable to delineate your known domain knowledge of the percolation phenomena. The two categorical factors to capture the rubber and additive choices and two continuous factors to capture the amounts of the rubber and additive employed. Not sure if you have disallowed combinations but you can handle this as well. If your budget allows it try the RSM model and see if the design generated suits your needs.

Lou V

craigwb

Community Trekker

Joined:

Feb 25, 2015

This makes sense.

Thanks Lou!