Ultrasonic Energy Transfer and Stress Concentrations in a Single-Fiber Composite with Absorbing Interface Layer

Abstract

Elastic wave scattering from coated and layered cylindrical scatterers encased in an elastic matrix is reviewed. Interaction of time harmonic monochromatic longitudinal and shear ultrasonic waves with a single fiber coated by homogeneous dissipative (polymeric) materials and embedded in an unbounded elastic matrix is studied using the classical method of eigenfunction expansion. The novel features of Havriliak—Negami model is employed to include the effect of hysteresis-type of compressional and shear waves' absorption in the interphase material by introduction of proper frequency-dependent complex moduli. The pertinent integrals for the time-averaged total fiber energy induced by the elastic waves refracted along the fiber are derived and numerically evaluated. The numerical results reveal the important effects of the absorptive fiber—matrix bond as well as interphase thickness on fiber/matrix energy transfer and dynamic stress concentrations. The calculated results may be interpreted in the context of phenomena observed in acousto-ultrasonic (AU) experiments on fiber reinforced composite materials by correlating certain parameters in the frequency spectrum of the detected waveform to mechanical characteristics of the dissipative interface layer. Limiting cases are considered and good agreements with well-known solutions are established.