How do I use the rule of mixture for calculating the elastic modulus of a particle composite with volume fraction more than 50 percents?
I think using Mori-Tanaka homogenization principle gives you more accurate results.
Hi Atefeh,
you can use the lower bound approach, namely
1/Ec=(Ef X EM)/(Vf x Em+ Vm x Em) (1)
where Ec, Ef , Em are the moduli of composite, reinforcement and matrix respectively ,and Vf and Vm are the the volume fraction of particles and matrix, respectively.
THe Halpin-Tsai equation can be also used , provided the particles' geometry is approximately defined. Both approaches give quite similar results. However, the approaches are based on the concept of "isolated particles". That is not your case, I suppose. At such high volume fraction several particles clusters may be formed even in well dispersed systems. You may check experimentally the consistency of both approaches suggested above.
In any case, fixing the particle content , the experimental elastic modulus cannot be lower than that the "lower bound" predicted by eq. (1)
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