Spring and Asymptotic Boundary Condition Models for Study of Scattering by Thin Cylindrical Interphases

Specially designed fiber-matrix interphases are created in modern composites to improve fracture toughness, chemical compatibility and matching of thermal expansion coefficients between composite constituents [1, 2, 3]. Since the interphase transfers the load from matrix to fiber, the interphase elastic moduli, thickness and the quality of bonding with the surrounding fiber and matrix are essential in determining composite mechanical performance. Such interphase conditions can be sensed by ultrasonic waves due to strong interphase effects on wave scattering from fibers. However the interphase properties (elastic modulus and thickness) are in-situ parameters and are often difficult to define. One way to get around this is to introduce simplified boundary condition (B.C.) models to describe the displacement and stress fields across the interphase directly. In this paper we will address this problem with emphasis on spring and asymptotic B.C. models as a representation of a thin fiber-matrix interphase when studying wave scattering from fibers.