ASYMPTOTIC ANALYSIS OF THE REINFORCEMENT OF A BRITTLE CRACK BY BRIDGING FIBERS

The subject of the paper is the cracking of a brittle matrix reinforce d by unidirectional fibres. A crack is introduced into the matrix, tra nsverse to the fibres, which bridge the crack and tend to tie the face s together. The fibres are treated in an 'averaged' manner: the uncrac ked composite material is modelled as homogeneous linearly elastic mat erial and the effect of the bridging fibres is modelled by a nonlinear law of cohesion between the crack faces. The problem is formulated as a nonlinear, highly singular, integral equation. The 'long-crack' lim it is addressed, which corresponds to the bridging fibres carrying mos t of the load across the crack. The equation then contains a small par ameter and is solved by a matched expansion technique. This has only r ecently been expressed in a form suitable for the singular perturbatio n of integral equations and is likely to have applicability beyond the specific example considered here.