Dear Rajorshi,

You can use the rule of mixtures, like suggested by Marco. However, I don't think you really need to know the elastic modulus of the matrix, given that you have both longitudinal and transverse moduli.

You can just use a two equations systems for the two unknowns (fibre and matrix modulus): as first equation you can use the rule of mixture for the longitudinal direction, as second equation the inverse rule of mixture for the perpendicular direction. Something like:

1) Ex = Vf * Ef + (1-Vf) * Em

2) Ey = 1 / [ Vf / Ef + (1-Vf) / Em ]

Where Ex and Ey are the parallel and perpendicular moduli of the composite, respectively and Vf is the volume fraction. Ef and Em are the moduli of fibres and matrix you are looking for.

Both equations are in Wikipedia:

https://en.wikipedia.org/wiki/Rule_of_mixtures

I hope this will help.

Luca

Dear Koyal,

The modulus of elasticity is essentially a measurement of the stiffness of a material.

The Young's modulus of the Composite is given by the 'rule of mixtures' i.e. EC = EF VF + EM VM , also ( VM + VF ) = 1 or VM = (1 - VF ). The elastic modulus along the fiber direction can be controlled by selecting the volume fraction of the fibers.

One of the examples you can refer to see your purpose. The Young’s modulus of the fiber matrix composites can compared to theoretical values generated by the rule of mixtures, Halpin–Tsai, Nairn’s generalized shear-lag analysis and Mendels et al. stress transfer (micromechanical) models is most useful in this regard. Homogenization method is also useful to calculate young modulus.

Refer this article; equation 5 can be used to calculate the young modula of fiber matric composites.

https://www.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252015000300583

Ashish