The shear modulus G and Bulk modulus B can be calculated using the Voigt-Reuss-Hill approximation which is the arithmetic average of
Voigt and Reuss bounds that represent the upper and lower limit of the actual effective modulus.
How can this Voigt-Reuss be applied to metallic binary alloy?
Using Al-Nb as an example, are we to find BV, GV and BR, GR for both Al and Nb separately or ?
Dear Taiwo Akande, I am sorry but I think that the Voigt-Reuss-Hill approximation should not be used for an alloy. It can be used for the calculation of the properties of composite materials or multi-materials for which you can measure the mechanical properties of each constituent, not for an alloy for which the properties can be very different. The properties for an alloy do not depend only on the properties of each pure material which are combined. It is an other material with other chemical, physical and mechanical properties.
In an other hand, the boundaries given by different approximations like Voigt-Reuss-Hill or other, are not very precise and underestimate often the role of interfaces. There are different sophisticated homogenization theories which can give better results, but not for alloys. For instance, you can read the papers from Dr. Samuel Forest, the last solid mechanics Fellow of Euromech.
http://matperso.mines-paristech.fr/People/samuel.forest/
The Young’s moduli (E) of the polycrystals for these mettalic alloys or Zr binary alloys can be calculated from the calculated elastic constants of the single crystal by using the Voigt-Reuss-Hill averaging scheme.
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