Dynamic stress on a partially bonded fiber

The dynamic stress on a partially bonded fiber is analyzed for shear wave incidence, with particular attention given to the stress intensity factor at the neck joining the fiber to the matrix. The problem is formulated in terms of the unknown stress across the neck and the remainder of the fiber-matrix interface is modeled as a curved interfacial crack. Explicit asymptotic expressions are derived for the near and far-fields that are valid in the frequency range in which the recently discussed resonance phenomenon occurs (Yang and Norris, 1991). This resonance is a rattling effect that is most prominent when the neck becomes very thin, and can occur at arbitrarily small values of the dimensionless frequency ka, where a is the radius of the fiber. The asymptotic results indicate that the dynamic stress intensity factor becomes unbounded as the neck vanishes, in contrast to the prediction of a purely quasi-static analysis that the stress intensity factor vanishes in the same limit.