3: Modulus of Elasticity - Isostress Loading

The isostress condition is different to the isostrain condition but can also be represented as an equation where σ = stress.

This equation can then be rewritten using the definition of Young's modulus to incorporate strain, ε, and modulus, E, terms.

In the isostress condition the rule of mixtures can be applied where v = volume fraction.

We can then substitute for strain using stress, σ, and modulus, E, terms.

We have isostress conditions where the stresses in both the matrix and fibres are the same. So σc = σf = σm. We can therefore cancel the stress terms.

We now rearrange the equation to make modulus, E, the subject.

Ultimately, we have:

In the isostress condition the composite modulus is not simply a weighted average of the modulus of the fibres and matrix. For isostress loading, the modulus is usually low except for high concentrations of fibres.