Impact of interfacial imperfections on the Reflection and Transmission phenomenon of plane waves in a Porous-Piezoelectric model

Abstract

Reflection and transmission of plane waves are extensively used to conduct non-destructive testing(NDT) or non-destructive evaluation(NDE) of composites for characterizing/mapping subsurface defects and assessing the in-situ condition of structural components without reforming the original features of the composites in a non-tarnish way. These materials composed of more than one base material are the major components in the construction and modelling of air-crafts, space-crafts, military & defense applications, and nuclear industry. Thus, the present work deals with a mathematical model focused on the phenomenon of reflection and transmission of an incident plane wave at an imperfect interface between two different Porous-Piezoelectric(PP) half-spaces. According to the nature of the PP material, an incident plane wave (I-qP1 wave) results in five reflected and transmitted waves, namely reflected and transmitted quasi-longitudinal and quasi-transverse waves in the solid phase(qP1 and qSV, respectively), quasi-longitudinal wave in the fluid phase(qP2), and electro-acoustic waves in solid and fluid phases(EA1 and EA2, respectively). Due to reasons like the presence of interfacial defects owing to accumulative damages, half-spaces are generally not perfectly bonded. Mechanical and electrical interfacial defects fundamentally affect the performances of structural components that are utilized in several fields. Thus, reflection and transmission of different waves are studied for six distinct interfaces, viz. normally stiff interface, transversely stiff interface, electrical imperfection, slip interface, complete debonding, and welded interface. With the aid of secular equations and boundary conditions, a system of algebraic equations is obtained, from which the amplitude ratios are derived. Furthermore, the energy ratios of these waves are obtained, along with the interaction energy among various waves, using the energy flux relations and amplitude ratios. The conservation of total energy at the interface of the two media and some exclusive cases of this problem validate the study. For graphically illustrating the effects of these interface conditions on the reflection and transmission phenomenon, numerical data of PP BaTiO3 and PZT−7H materials are adopted. The energy ratios of various reflected and transmitted waves are plotted against the angle of incidence as well as against wave number.