How to Calculate and Solve for Randomly Oriented Composite Modulus of Elasticity | Composites

The randomly oriented composite modulus of elasticity is illustrated by the image below.

To compute for randomly oriented composite modulus of elasticity, five essential parameters are needed and these parameters are Fibre Efficiency Parameter (K), Elastic Modulus of the Fibre (Ef), Elastic Modulus of the Matrix (Em), Volume Fraction of the Fibre (Vf) and Volume Fraction of the Matrix (Vm).

The formula for calculating randomly oriented composite modulus of elasticity:

E = KEfVf + EmVm

Where:

E = Randomly Oriented Composite Modulus of Elasticity
K = Fibre Efficiency Parameter
Ef = Elastic Modulus of the Fibre
Em = Elastic Modulus of the Matrix
Vf = Volume Fraction of the Fibre
Vm = Volume Fraction of the Matrix

Let’s solve an example;
Find the randomly oriented composite modulus of elasticity when the fibre efficiency parameter is 14, the elastic modulus of the fibre is 10, the elastic modulus of the matrix is 16, the volume fraction of the fibre is 12 and the volume fraction of the matrix is 8.

This implies that;

K = Fibre Efficiency Parameter = 14
Ef = Elastic Modulus of the Fibre = 10
Em = Elastic Modulus of the Matrix = 16
Vf = Volume Fraction of the Fibre = 12
Vm = Volume Fraction of the Matrix = 8

E = KEfVf + EmVm
E = (14)(10)(12) + (16)(8)
E = (1680) + (128)
E = 1808

Therefore, the randomly oriented composite modulus of elasticity is 1808 Pa.

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