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rule of mixtures : ウィキペディア英語版
rule of mixtures

In materials science, a general rule of mixtures is a weighted mean used to predict various properties of a composite material made up of continuous and unidirectional fibers.〔(【引用サイトリンク】title=Stiffness of long fibre composites )〕 It provides a theoretical upper- and lower-bound on properties such as the elastic modulus, mass density, ultimate tensile strength, thermal conductivity, and electrical conductivity.〔 In general there are two models, one for axial loading (Voigt model),〔 and one for transverse loading (Reuss model).〔
In general, for some material property E (often the elastic modulus〔), the rule of mixtures states that the overall property in the direction parallel to the fibers may be as high as
: E_c = fE_f + \left(1-f\right)E_m
where
* f = \frac is the volume fraction of the fibers
* E_f is the material property of the fibers
* E_m 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
:E_c = \left(\frac + \frac\right)^.
If the property under study is the elastic modulus, this quantity is called the lower-bound modulus, and corresponds to a transverse loading.〔
== Derivation for elastic modulus ==


抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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