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Modulus of Elasticity of Long Fibre Composites

In this calculation, a two-component material consisting of a matrix with a relative volume Vm and a modulus of elasticity Em, and reinforcing fibres with a relative volume Vf and a modulus of elasticity Ef is considered. The reinforcing fibres run continuously along the entire length of the material.

As a result of calculations, the total modulus of elasticity of the composite material El is determined in the direction of fibres, as well as modulus of elasticity Ec in the transverse direction.

When setting the load F along the direction of the fibres for a part with section area A, tensile stresses in the matrix σl and in the reinforcement σf, as well as the relative deformations of the composite material ε are calculated .

Modulus of elasticity of long fibre composites
Modulus of elasticity of long fibre composites

INITIAL DATA

Vm - Matrix volume;

Vf - Fibre volume;

Еm - Modulus of elasticity of the matrix;

Еf - Modulus of elasticity of the fibre;

Fl - Tensile force in the longitudinal direction;

A - Total cross-section area of composite.

RESULTS DATA

Еl - Modulus of elasticity of the composite in the longitudinal direction;

Ес - Modulus of elasticity of the composite in the lateral direction;

σl - Stress at matrix under load Fl;

σf - Stress at fibre under load Fl;

ε - Deformation under load Fl.

Matrix volume (Vm)

Fibre volume (Vf)

Modulus of elasticity (Еm)

Modulus of elasticity (Еf)

Longitudinal (Еl)

Lateral (Ес)

Tensile force (Fl)

Section area (A)

Stress at matrix (σl)

Stress at fibre (σf)

Deformation (ε)

BASIC FORMULAS

Relative matrix volume:

Vm% = Vm / (Vf + Vm);

Relative fibre volume:

Vf % = Vf / (Vf + Vm);

Longitudinal modulus of elasticity:

Еl = Еf*Vf % + Еm*Vm%;

Lateral modulus of elasticity:

Ес = Еm*Еf / (Vm%*Еf + Vf %*Еm).

INITIAL DATA

Vm - Matrix volume;

Vf - Fibre volume;

Еm - Modulus of elasticity of the matrix;

Еf - Modulus of elasticity of the fibre;

Fl - Tensile force in the longitudinal direction;

A - Total cross-section area of composite.

RESULTS DATA

Еl - Modulus of elasticity of the composite in the longitudinal direction;

Ес - Modulus of elasticity of the composite in the lateral direction;

σl - Stress at matrix under load Fl;

σf - Stress at fibre under load Fl;

ε - Deformation under load Fl.

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