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Estimations of composite materials properties

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

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:

Density

dc = dm*Vm + df*Vf

Where

dc,dm,df – densities of the composite, matrix and dispersed phase respectively;

Vm,Vf – volume fraction of the matrix and dispersed phase respectively.

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Coefficient of Thermal Expansion

αcl = (αm*Em*Vm + αf*Ef*Vf)/(m*Vm + Ef*Vf)

Where

αcl, αm, αfCTE of composite in longitudinal direction, matrix and dispersed phase (fiber) respectively;

Em,Efmodulus of elasticity of matrix and dispersed phase (fiber) respectively.

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

αct = (1+μm) αm *Vm + αf* Vf

Where

μm – 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.

Modulus of Elasticity

Long align fibers

  • Modulus of Elasticity in longitudinal direction (Ecl)

Ecl = Em*Vm + Ef*Vf

  • Modulus of Elasticity in transverse direction (Ect)

1/Ect = Vm/Em + Vf/Ef

Short fibers

Ecl = η0ηLVf Ef + VmEm

ηL = 1 - 2/βL*tanh(βL /2)
β = [8 Gm/(EfD²ln(2R/D))]½

where:

Ef – modulus of elasticity of fiber material;
Em – modulus of elasticity of matrix material;
Gm - shear modulus of matrix material;
ηL – length correction factor;
L – fibers length;
D – fibers diameter;
2R – distance between fibers;
η0 - fiber orientation distribution factor.
η0 = 0.0 align fibers in transverse direction
η0 = 1/5 random orientation in any direction (3D)
η0 = 3/8 random orientation in plane (2D)
η0 = 1/2 biaxial parallel to the fibers
η0 = 1.0 unidirectional parallel to the fibers

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Shear modulus

Gct = Gf Gm/(Vf Gm + VmGf)

Where:

Gf – shear modulus of elasticity of fiber material;
Gm – shear modulus of elasticity of matrix material;

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Poisson's ratio

μ12 = vf μf + Vmμm

Where:

μf – Poisson’s ratio of fiber material;
μm – Poisson’s ratio of matrix material;

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Tensile Strength

σc = σm*Vm + σf*Vf

Where

σc, σm, σf – tensile strength of the composite, matrix and dispersed phase (fiber) respectively.

  • Tensile strength of short-fiber composite in longitudinal direction

(fiber length is less than critical value Lc)

Lc = σf*d/τc

Where

d – diameter of the fiber;

τc –shear strength of the bond between the matrix and dispersed phase (fiber).

σc = σm*Vm + σf*Vf*(1 – Lc/2L)

Where

L – length of the fiber

  • Tensile strength of short-fiber composite in longitudinal direction

(fiber length is greater than critical value Lc)

σc = σm*Vm + L* τc*Vf/d

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estimations_of_composite_materials_properties.txt · Last modified: 2012/06/02 by dmitri_kopeliovich
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