Integral transform technique for determining stress intensity factor in wave propagation through functionally graded piezoelectric-viscoelastic structure

Abstract

This study employs an integral transform approach for Love wave propagation in a rotating composite structure having an interfacial crack. The structure comprises an initially stressed functionally graded piezoelectric-viscoelastic half-space bonded to a piezoelectric-viscoelastic half-space, and is subjected to anti-plane mechanical loading and in-plane electrical loading. The study focuses on two material systems: the first material system consists of Epoxy-BNKLBT and Epoxy-KNLNTS, where BNKLBT stands for $0.885\left({\text{Bi}}_{0.5}{\text{Na}}_{0.5}\right){\text{TiO}}_3-0.05\left({\text{Bi}}_{0.5}{\text{K}}_{0.5}\right){\text{TiO}}_3-0.015\left({\text{Bi}}_{0.5}{\text{Li}}_{0.5}\right){\text{TiO}}_3-0.05{\text{BaTiO}}_3$, and KNLNTS represents $\left({\text{K}}_{0.475}{\text{Na}}_{0.475}{\text{Li}}_{0.05}\right)\left({\text{Nb}}_{0.92}{\text{Ta}}_{0.05}{\text{Sb}}_{0.03}\right){\text{O}}_3$, doped with $0.4\text{wt\%}{\text{CeO}}_2$ and $0.4\text{wt\%}{\text{MnO}}_2$. The second material system has Epoxy-BNKLBT and Epoxy-PZT7A, where PZT7A denotes Lead Zirconate Titanate. The viscoelastic materials are modeled to reflect their complex behavior under rotational and stress conditions. The Galilean transformation is applied to convert the Cartesian coordinate system into a moving reference frame aligned with the Love wave's propagation. Employing Bessel function properties, the system is converted into a set of double integral equations and subsequently reformulated into simultaneous Fredholm integral equations. Numerical solutions to these Fredholm integral equations are employed to compute the electric displacement intensity factor and the stress intensity factor near the interfacial crack. These factors are also used to derive the expression for the energy density factor, thereby demonstrating the intrinsic coupling between the stress intensity factor and the electric displacement intensity factor. The key objective of this study is to visualize the impact of different material parameters, including piezoelectric constants, dielectric constants, initial stress, electric displacement at the interface, as well as interface stress and rotation on the stress intensity, electric displacement intensity, and energy density factors. The investigations of this study will be helpful for advanced technologies like surface acoustic wave sensors and piezoelectric actuators, as well as to enhance surface acoustic wave bio-sensor sensitivity and stability for early cancer detection and biomedical implants.