Longitudinal wave scattering from a partially bonded fiber

Analytical and numerical results are presented for in-plane longitudinal wave pulse scattering from a partially bonded circular fiber. The debonding is assumed to be a curved interface crack with non-contacting faces. The problem is cast in terms of the unknown stresses on the neck joining the fiber and matrix, which are found by solving a truncated set of equations in the frequency domain. Computations for both the scattering cross-sections and the dynamic stress intensity factors on the crack tips show that a strong rattling resonance occurs at a very low frequency when the neck becomes sufficiently small in extent. Transient responses are obtained for pulse incidence through the use of an inverse Fourier transform on the corresponding time harmonic solutions. Based upon the numerical results, it is suggested that the presence of the low frequency resonance may provide a feasible way to experimentally determine the extent of fiber debonding.