Scattering of plane wave by an elastic fiber with partially debonded interface - boundary element analysis for shear wave polarized parallel with fiber
Biwa Shiro; Miyamura Harunori; Shibata Toshinobu
Abstract:Scattering of transverse elastic wave by an elastic fiber embedded in an infinite matrix with partially debonded interface is studied for time-harmonic steady cases by the boundary element method. The fiber is presently assumed to be of a right cylindrical shape, and the incident wave polarized parallel with the fiber axis and propagating in the plane normal to the fiber. In this circumstance the problem to be analyzed is two-dimensional and the governing equations reduce to a scalar Helmholtz equation for anti-plane displacements. Two kinds of boundary conditions are employed to describe the partially debonded fiber-matrix interface. In the first case, both the stress and the displacement are assumed to be continuous across certain parts of the interface, while on the rest of the interface the stress is supposed to vanish to simulate partial separation of the interface. In the second case, the notion of equivalent spring is introduced to take into account the presence of interface phase, thus resulting in the analysis of the case where the fiber is bonded to the matrix via an equivalent spring on partial areas of the interface while it is debonded on the rest. As an illustrative example, the total and differential scattering cross sections are computed for a circular cylindrical silicon-carbide fiber in a titanium alloy matrix for various frequencies. The influence of the extent of interface debonding as well as its orientation relative to the incident plane wave on the scattering behavior is discussed in detail. Key Words:elastic wave, scattering, elastic fiber, interface debonding, longitudinal shear, interphase, Helmholz equation, boundary element method, fiber-reinforced composite