Rule of mixture is the simples relation between the properties of a composite and those of its constitutents. The simplest is the linear mixture rule, e.g.

Ec = v1E1 +v2E2

for the modulus. Ec is the composite modulus v1 is the volume fraction of component 1 with modulus E1 (say the matrix) and v2, E2 are the corresponding quantities for component 2 (say, the reinforcement). This is true physically is you have parellel phases and the force is parallel with the phases. The other extreme is the reciprocal mixture rule:

1/Ec = v1/E1 + v2/E2

in this case the elements are in series. The real situation is somewhere in-between. Formally the two extermes can be combined (Takayanagi equation, see:

https://www.researchgate.net/publication/230344082_Effect_of_Dispersed_Phase_Composition_on_Morphological_and_Mechanical_Properties_of_PETEVAPP_Ternary_Blends).

In real short-fiber filled systems a good approximation given by

Ec= v1E1+ qv2E2 where q is a factor taking itno account the average orientation of the fibers.

For a more detaled introduction see:

http://www.tech.plym.ac.uk/sme/mats333/rules%20of%20mixture.pdf

For more sophisticated equations see:

http://cdn.intechweb.org/pdfs/16833.pdf

Article Effect of Dispersed Phase Composition on Morphological and M...

Rule of mixture is the simples relation between the properties of a composite and those of its constitutents. The simplest is the linear mixture rule, e.g.

Ec = v1E1 +v2E2

for the modulus. Ec is the composite modulus v1 is the volume fraction of component 1 with modulus E1 (say the matrix) and v2, E2 are the corresponding quantities for component 2 (say, the reinforcement). This is true physically is you have parellel phases and the force is parallel with the phases. The other extreme is the reciprocal mixture rule:

1/Ec = v1/E1 + v2/E2

in this case the elements are in series. The real situation is somewhere in-between. Formally the two extermes can be combined (Takayanagi equation, see:

https://www.researchgate.net/publication/230344082_Effect_of_Dispersed_Phase_Composition_on_Morphological_and_Mechanical_Properties_of_PETEVAPP_Ternary_Blends).

In real short-fiber filled systems a good approximation given by

Ec= v1E1+ qv2E2 where q is a factor taking itno account the average orientation of the fibers.

For a more detaled introduction see:

http://www.tech.plym.ac.uk/sme/mats333/rules%20of%20mixture.pdf

For more sophisticated equations see:

http://cdn.intechweb.org/pdfs/16833.pdf

Article Effect of Dispersed Phase Composition on Morphological and M...

The rule of mixture is one of the simple empirical methods permitting to estimate the properties of the "mixtures" composed by two (or more) different materials with different nature. In this rule, the only parameters taken account are the amount of each component in the mixture and the property (Young Modulus, ...) of each pure component. Then, the property of the mixture varies with the amount of components. Nevertheless, it is well known that other parameters (size, shape, distribution, orientation, interaction between phases,...) play an important role on the properties (mechanical or other) of composites.    

You can use this rule for particulate filled polymers as well as the fiber reinforced one as explained by Dr. Gyorgy Banhegyi. But you have to keep in mind that this is a very rough approximation.  

I agree with above comments. Also, be mindful that rule of mixture is generally used for modulus prediction as defined by the equations above. In my opinion modulus increase does not necessarily leads to automotive increase in yield strength or strength at break ( tensile or flexural).

Only to add some other details:

For long fiber unidirectional laminates

Eparallel =vf Ef + (1-vf) Em  ; f:fibre  m:matrix

In experimental data the result have deviation from this eq. because we have the presence of micro-voids (5-  20 micron), so, the eq. should be :

Eparallel =vf Ef + (1-vf -vv) Em  ;     vv is volume fraction of the voids

E transv =(Ef Em ‘ )/((vf Em ‘ + (1-vf - vv) Ef) ;   where  Em ‘ = Em/(1- nm 2 ) ,   nm : matrix poisson mod.  ; for plastic matrix generally  0,3 < nm

Emedium is Eaverage

Good response. I also suggest to look at more complex model developed in last 5 years to differentiate stiffness prediction vis-à-vis toughness prediction.

sorry for typing mistake

hq = 0 for aligned fibers -> is incorrect , the right one is : hq = 1 for aligned fibers

Dear Arbind,

To this point the answer I like most is the one by Dr Atli even though it is quite vague. Please allow me to expand a bit.

With particulate systems each case is unique and you may find your own empirical relationship for the particular property you're considering. But you need to be careful about extrapolations and be aware of the limitations.

There are many reasons why a specific relationship will collapse. Often the properties will not only depend on the materials mixed but also on the procedure/process utilised for its preparation. Unfortunately, these conditions are rarely described in the publications.

People not experienced in the art of formulation and compounding they may run into some shortcuts and pitfalls with such relationships.

Kind regards

Guy