Weak interface in long fiber composites

The problem of the di€usion of load from a ®ber to an embedding matrix is considered in a three dimensional context. It is assumed that the ®ber-matrix interface allows sliding, which is assumed to be proportional to the interface tangential stress. The close-form solution is obtained for generic loads applied to the ®ber, and the case of a concentrated force is studied in detail. The main e€ects of the interface sti€ness, such as avoiding the stress singularities and increasing the length of the zone of in¯uence, are discussed and illustrated by some numerical examples. Successively, the problem of the broken ®ber is considered and solved with the same method as the previous case. Three di€erent situations are discussed: no interaction between ®bers, very close neighboring ®bers and an intermediate case. It is shown that both problems have the same equations apart from a given function which plays the role of the constitutive equation and which characterizes the considered model. The e€ect of the neighboring ®bers on the interfacial stress is discussed and it is shown that it has a non-monotonic dependence on the distance between the ®bers