Fracture Analysis in an Imperfect FGM Orthotropic Strip Bonded Between Two Magneto-Electro-Elastic Layers

In this study, a functionally graded orthotropic layer sandwiched between two magneto-electro-elastic layers under anti-plane time-harmonic mechanic and in-plane electromagnetic loadings is studied. This paper examines the modeling of cracks by distribution of strain nuclei along crack lines. During this investigation, the Volterra-type screw dislocation is employed in the FGM orthotropic layer and the magneto-electro-elastic coating. The material properties of the strip are considered to obey exponential variations. To solve the dislocation problem, the complex Fourier transform is applied. One merit of this technique is the possibility of determination of the stress intensity factors for multiple smooth cracks. The system of equations is derived by considering the distribution of line dislocation on the crack. These equations are of Cauchy singular type in the location of dislocation, which can be solved numerically to obtain the dislocation density on the faces of the cracks. Various examples are solved, and the dynamic stress intensity factors are obtained. The effect of the cracks configuration, bonding constant, angular frequency and material properties on the mode III stress intensity factor is studied, and the validity of the analysis is checked.