Re-use of this resource is governed by a Creative Commons Attribution-
Noncommercial-Share Alike 2.0 Licence UK: England & Wales
https://creativecommons.org/licenses/by-nc-sa/2.0/uk/
creative commons DoITPoMS logo
Graph 1 σ ε σfu εfu σf σmu εmu σm σfmu f



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 εmu \[ \sigma _{1} =f\sigma _{f}+(1-f)\sigma _{m}\]
Onset of matrix cracking
σ1



On exceeding εmu matrix
crack growths lead to an
increase in strain at constant
composite stress.
If the fibres fracture before the entire load is transferred to the fibres, then this is the composite failure stress. \[ \sigma _{1u} =f\sigma _{fmu}+(1-f)\sigma _{mu}\]
Composite failure
σ1
But if the entire load is
transferred to the fibres
before fibre fracture, then σ1u = fu