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Graph 3 σ ε σfu εfu σf σmu σm εmu σfmu



This is how the stress on an
individual fibre varies with strain



This is how the stress on a matrix
on its own varies with strain
σ1



The composite stress is given by the rule of mixtures up to εfu \[ \sigma _{1} =f\sigma _{f}+(1-f)\sigma _{m}\]
Fibre fracture
σ1



On exceeding εfu the fibres
fracture into shorter lengths,
leading to an increase in strain at constant composite stress.
If the matrix fails before the entire load is transferred to the matrix, then this is the composite failure stress. \[ \sigma _{1u} =f\sigma _{fu}+(1-f)\sigma _{mfu}\]
Composite failure
σ1