Examples

Example 7.2: For AS4 fibre and 3501-6 Epoxy material with 0.6 fibre volume fraction calculate all effective engineering constants of the composite using a) Voigt and b) Reuss approximations. The properties are given in Table 7.1 and Table 7.2.

Solution:

a) Voigt Approximation:
According to this approximation the effective stiffness tensor for composite is given as

The stiffness matrices for fibre and matrix are calculated using the respective engineering constants and are given below.

For this purpose it is better to calculate first the compliance matrices for fibre and matrix materials and invert them to get the stiffness matrices. We know that getting stiffness from compliance can be easier than remembering individual stiffness entries in terms of engineering constants. The compliance matrices for fibre and matrix material are calculated as below.

Now the stiffness matrices of fibre and matrix are:

Thus, the effective stiffness matrix according to Voigt approximation for fibre volume fraction of 0.6 is

The inverse of this effective stiffness matrix is

Effective engineering constants:

b) Reuss Approximation:
According to this approximation the effective compliance tensor for composite is given as

Using the compliance matrices for fibre and matrix we get the effective compliance for composite as

Effective engineering constants: