Semi-analytical solutions for the scattering of plane SH Waves by a Finite Crack - Fuqing Chu; Hui Qi; Shaoqiang Liu; Jing Guo (Results in Engineering)
In this study, we employ the wave function expansion method, integrated with the region-matching technique and the employment of half-integer order Bessel functions, to derive a semi-analytical solution for the scattering of plane SH waves by a finite crack. This approach elegantly transforms the traction-free boundary conditions at the crack edge into continuity conditions at circular auxiliary boundaries, thereby translating the boundary value problem into a solvable system of linear algebraic equations. Direct extraction of the dynamic stress intensity factor (DSIF) expressions, which satisfy the stress singularity at the crack tips, is achieved from the displacement expressions. The computed results of the wavefield and DSIF are found to be in good agreement with both the exact analytical solutions and the computational outcomes present in the existing literature. Our analysis reveals significant displacement amplitude amplification and DSIF variations at the crack tips, which are highly sensitive to the frequency and angle of incidence of the waves. The findings not only validate the accuracy of our methodology but also provide a computationally efficient and precise tool for understanding the behavior of elastic waves in the presence of discontinuities, with potential applications in non-destructive testing, fracture mechanics, and geophysics.