Rule_of_mixtures
In materials science, a general rule of mixtures is a weighted mean used to predict various properties of a composite material .[1][2][3] It provides a theoretical upper- and lower-bound on properties such as the elastic modulus, ultimate tensile strength, thermal conductivity, and electrical conductivity.[3] In general there are two models, one for axial loading (Voigt model),[2][4] and one for transverse loading (Reuss model).[2][5]
In general, for some material property (often the elastic modulus[1]), the rule of mixtures states that the overall property in the direction parallel to the fibers may be as high as
where
- is the volume fraction of the fibers
- is the material property of the fibers
- is the material property of the matrix
In the case of the elastic modulus, this is known as the upper-bound modulus, and corresponds to loading parallel to the fibers. The inverse rule of mixtures states that in the direction perpendicular to the fibers, the elastic modulus of a composite can be as low as
If the property under study is the elastic modulus, this quantity is called the lower-bound modulus, and corresponds to a transverse loading.[2]