Editing Composite material (section)

==Physical properties==
{{main|Rule of mixtures}}

[[File:Composite elastic modulus.svg|thumb|Plot of the overall strength of a composite material as a function of fiber volume fraction limited by the upper bound (rule of mixtures) and lower bound (inverse rule of mixtures) conditions.]]
Usually, the composite's physical properties are dependent on the direction of consideration, and so are [[Anisotropy|anisotropic]]. This applies to many properties including [[elastic modulus]],<ref name="PSD">{{cite book|last=Alger|first=Mark. S. M.|title=Polymer Science Dictionary|edition=2nd|year=1997|publisher=[[Springer Publishing]]|isbn=0412608707}}</ref> [[ultimate tensile strength]], [[thermal conductivity]], and [[electrical conductivity]].<ref name="SEM">{{cite book|last1=Askeland|first1=Donald R.|last2=Fulay|first2=Pradeep P.|last3=Wright|first3=Wendelin J.|title=The Science and Engineering of Materials|edition=6th|date=2010-06-21|publisher=[[Cengage Learning]]|isbn=9780495296027}}</ref> The ''rule of mixtures'' and ''inverse rule of mixtures'' give upper and lower bounds for these properties. The real value will lie somewhere between these values and can depend on many factors including:
* the orientation of interest
* the length of the fibres
* the accuracy of the fibre alignment
* the properties of the matrix and fibres
* delamination of the fibres and matrix
* the inclusion of any impurities

[[File:Isostress and isostrain conditions for composite materials.gif|thumb|Figure a) shows the isostress condition where the composite materials are perpendicular to the applied force and b) is the isostrain condition that has the layers parallel to the force.<ref>{{cite journal |last1=Kim |first1=Hyoung Seop |title=On the rule of mixtures for the hardness of particle reinforced composites |journal=Materials Science and Engineering: A |date=September 2000 |volume=289 |issue=1–2 |pages=30–33 |doi=10.1016/S0921-5093(00)00909-6}}</ref>]]

For some material property <math>E</math>, the rule of mixtures states that the overall property in the direction [[Parallel (geometry)|parallel]] to the fibers could be as high as
:<math> E_\parallel = fE_f + \left(1-f\right)E_m </math>

The inverse rule of mixtures states that in the direction [[perpendicular]] to the fibers, the elastic modulus of a composite could be as low as
:<math>E_\perp = \left(\frac{f}{E_f} + \frac{1-f}{E_m}\right)^{-1}.</math>

where
* <math>f = \frac{V_f}{V_f + V_m}</math> is the [[volume fraction]] of the fibers
* <math>E_\parallel</math> is the material property of the composite parallel to the fibers
* <math>E_\perp</math> is the material property of the composite perpendicular to the fibers
* <math>E_f</math> is the material property of the fibers
* <math>E_m</math> is the material property of the matrix

The majority of commercial composites are formed with random dispersion and orientation of the strengthening fibres, in which case the composite Young's modulus will fall between the isostrain and isostress bounds. However, in applications where the strength-to-weight ratio is engineered to be as high as possible (such as in the aerospace industry), fibre alignment may be tightly controlled.

In contrast to composites, isotropic materials (for example, aluminium or steel), in standard wrought forms, possess the same stiffness typically despite the directional orientation of the applied forces and/or moments. The relationship between forces/moments and strains/curvatures for an isotropic material can be described with the following material properties: Young's Modulus, the [[shear modulus]], and the [[Poisson's ratio]], in relatively simple mathematical relationships. For the anisotropic material, it needs the mathematics of a second-order tensor and up to 21 material property constants. For the special case of orthogonal isotropy, there are three distinct material property constants for each of Young's Modulus, Shear Modulus and Poisson's ratio—a total of 9 constants to express the relationship between forces/moments and strains/curvatures.

Techniques that take benefit of the materials' anisotropic properties involve [[mortise and tenon]] joints (in natural composites such as wood) and [[pi joint]]s in synthetic composites.