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*to *Composites

**Dr. Dmitri Kopeliovich**

Composite materials may be either **isotropic** or **anisotropic**, which is determined by the Structure of composites.

* Isotropic material* is a material, properties of which do not depend on a direction of measuring.

* Anisotropic* material is a material, properties of which along a particular axis or parallel to a particular plane are different from the properties measured along other directions.

* Rule of Mixtures* is a method of approach to approximate estimation of composite material properties, based on an assumption that a composite property is the volume weighed average of the phases (matrix and dispersed phase) properties.

According to Rule of Mixtures properties of composite materials are estimated as follows:

**d _{c} = d_{m}*V_{m} + d_{f}*V_{f}**

Where

**d _{c}**,

**V _{m}**,

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*Coefficient of Thermal Expansion (***CTE**) in longitudinal direction (along the fibers)

**α _{cl} = (α_{m}*E_{m}*V_{m} + α_{f}*E_{f}*V_{f})/(_{m}*V_{m} + E_{f}*V_{f})**

Where

**α _{cl}**,

**E _{m}**,

*Coefficient of Thermal Expansion (***CTE**) in transverse direction (perpendicular to the fibers)

**α _{ct} = (1+μ_{m}) α_{m} *V_{m} + α_{f}* V_{f}**

Where

**μ _{m}** – Poisson’s ratio of matrix.

* Poisson’s ratio* is the ratio of transverse contraction strain to longitudinal extension strain in the direction of applied force.

**Long align fibers**

*Modulus of Elasticity in longitudinal direction (***E**)_{cl}

**E _{cl} = E_{m}*V_{m} + E_{f}*V_{f}**

*Modulus of Elasticity in transverse direction (***E**)_{ct}

**1/E _{ct} = V_{m}/E_{m} + V_{f}/E_{f}**

**Short fibers**

**E _{cl} = η_{0}η_{L}V_{f} E_{f} + V_{m}E_{m}**

where:

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**G _{ct} = G_{f} G_{m}/(V_{f} G_{m} + V_{m}G_{f})**

Where:

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**μ _{12} = v_{f} μ_{f} + V_{m}μ_{m}**

Where:

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*Tensile strength of long-fiber reinforced composite in longitudinal direction*

**σ _{c} = σ_{m}*V_{m} + σ_{f}*V_{f}**

Where

**σ _{c}**,

*Tensile strength of short-fiber composite in longitudinal direction*

(fiber length is less than critical value **L _{c}**)

**L _{c} = σ_{f}*d/τ_{c}**

Where

**d** – diameter of the fiber;

**τ _{c}** –shear strength of the bond between the matrix and dispersed phase (fiber).

**σ _{c} = σ_{m}*V_{m} + σ_{f}*V_{f}*(1 – L_{c}/2L)**

Where

**L** – length of the fiber

*Tensile strength of short-fiber composite in longitudinal direction*

(fiber length is greater than critical value **L _{c}**)

**σ _{c} = σ_{m}*V_{m} + L* τ_{c}*V_{f}/d**

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http://www.virginia.edu/bohr/mse209/chapter17.htm

http://www.engineer.tamuk.edu/departments/meen/Upward_Bound/presentations/Presentation.ppt

http://webpages.charter.net/ericbeaton/powerpt/Chapter_16.pdf

http://www.tech.plym.ac.uk/sme/MATS324/MATS324B%20powerpoint/laminate%20thickness%20and%
20Vf.ppt

http://www.eng.wayne.edu/legacy/forms/10/ME5720Chap3Handouts1.pdf

http://www.eng.uwo.ca/es021/ES021a_2006/Lecture%20Notes/Chap%2016%20-%20Composites.pdf

www.materialsknowledge.org/index.php?option=com_docman&task=doc_download&gid=152

*to *Composites

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