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Modulus of Elasticity of Short 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. Short reinforcing fibres are located in the volume of the matrix in three versions:

  • Fibres are parallel to each other. The elastic modulus of the composite Ec is calculated both in the fibre and transverse directions;
  • Reinforcing fibres are randomly arranged in parallel planes. The elastic modulus of the composite is calculated in an arbitrary direction parallel to the reinforcement plane;
  • Reinforcing fibres are located in random order throughout the volume of the matrix. The elastic modulus of the composite is calculated in an arbitrary direction.
Modulus of elasticity of short fibre composites
Calculation of modulus of elasticity of short fibre composites

INITIAL DATA

Vm - Matrix volume;


Vf - Fibre volume;


Еm - Modulus of elasticity of the matrix;


Еf - Modulus of elasticity of the fibre;

RESULTS DATA

Еc - Modulus of elasticity of the composite.

Matrix volume (Vm)

Fibre volume (Vf)

Modulus of elasticity (Еm)

Modulus of elasticity (Еf)

TYPES OF REINFORCEMENT

Parallel
(Ec at longitudinal direction)

Parallel
(Ec at lateral direction)

Randomly at parallel planes
(Ec at any direction of plane)

Randomly at any direction
(Ec at any direction)

Modulus of elasticity (Еc)

BASIC FORMULAS

Relative matrix volume:

Vm% = Vm / (Vf + Vm);

Relative fibre volume:

Vf % = Vf / (Vf + Vm);

Modulus of elasticity in the longitudinal direction (parallel reinforcement):

Ec = Еf*Vf % + Еm*Vm % ;

Modulus of elasticity in the lateral direction (parallel reinforcement):

Ec = Еm*Vm % ;

Modulus of elasticity at planes of fibre (reinforcement at parallel planes):

Ec = 0.375*Еf*Vf % + Еm*Vm % ;

Modulus of elasticity in any direction (fibres randomly distributed at three directions in space):

Ec = 0.2*Еf*Vf % + Еm*Vm % .

INITIAL DATA

Vm - Matrix volume;


Vf - Fibre volume;


Еm - Modulus of elasticity of the matrix;


Еf - Modulus of elasticity of the fibre;

RESULTS DATA

Еc - Modulus of elasticity of the composite.

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