Mechanics of high performance FRC

An extension of the approach outlined in Section 4.3, based on mechanics of composites, was presented by Naaman [1 ], to provide an overview of the conditions which need to be met to achieve strain and deflection hardening. The following outline is based on this paper. In the case of strain hardening (tensile loading). 

For strain hardening to occur, the post-cracking strength should be bigger than the cracking strength  

Substituting Eqs 12.1 and 12.2 into 12.3, and solving it for critical fibre volume for tensile strain hardening, yields the following relation  

It should be noted that Eq. 12.8 can be viewed as a general one, outlining the conditions for strain hardening as well as deflection hardening for Ar = 1 it is applicable for strain hardening and for 1/3 Ar 1 it is relevant for deflection hardening. 

1 Monofibre systems with normal strength matrix 

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