Effect of Inter-Fibre Distance on Energy Transfer in Unidirectional Composites Containing Ultrasonic Waves

Abstract

Interaction of time harmonic monochromatic anti-plane (SH) waves with a pair of parallel unidirected elastic cylindrical fibres embedded in an unbounded elastic matrix is considered. The classical method of separation of variables along with the appropriate wave field expansions, the pertinent boundary conditions, and the translational addition theorems for cylindrical wave functions are employed to obtain a series solution in terms of Fourier coefficients. The presented development is illustrated with numerical examples in which the fibres are insonified at end-on/broadside incidence for a relatively wide range of nondimensional frequencies. Particular attention has been focused on the effects of lateral fibre spacing on energy transfer between the fibres and matrix. The numerical results reveal that, while inter-fibre scattering (interference) has a small influence on the normalized fibre energies for broadside incidence at all frequencies, it has a considerable impact on the energy distribution for end-on incidence (fibres positioned in the eclipse configuration) at intermediate and high frequencies. The proposed model can complement acousto-ultrasonic (AU) techniques in non-destructive evaluation of unidirectional fibre-reinforced composite materials which is generally hampered by the highly dense concentration of the fibres. Limiting case is considered and fair agreement with a well-known solution is established.