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]
- ^ a b Alger, Mark. S. M. (1997). Polymer Science Dictionary (2nd ed.). Springer Publishing. ISBN 0412608707.
- ^ a b c d "Stiffness of long fibre composites". University of Cambridge. Retrieved 1 January 2013.
- ^ a b Askeland, Donald R.; Fulay, Pradeep P.; Wright, Wendelin J. (2010-06-21). The Science and Engineering of Materials (6th ed.). Cengage Learning. ISBN 9780495296027.
- ^ Voigt, W. (1889). "Ueber die Beziehung zwischen den beiden Elasticitätsconstanten isotroper Körper". Annalen der Physik. 274 (12): 573–587. Bibcode:1889AnP...274..573V. doi:10.1002/andp.18892741206.
- ^ Reuss, A. (1929). "Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle". Zeitschrift für Angewandte Mathematik und Mechanik. 9 (1): 49–58. Bibcode:1929ZaMM....9...49R. doi:10.1002/zamm.19290090104.