Investigation of the scattering of harmonic elastic waves by two collinear symmetric cracks using the non-local theory

The scattering of harmonic waves by two collinear symmetric cracks is studied using the non-local theory. A one-dimensional non-local kernel was used to replace a two-dimensional one for the dynamic problem to obtain the stress occurring at the crack tips. The Fourier transform was applied and a mixed boundary value problem was formulated. Then a set of triple integral equations was solved by using Schmidt's method. This method is more exact and more reasonable than Eringen's for solving this problem. Contrary to the classical elasticity solution, it is found that no stress singularity is present at the crack tip. The non-local dynamic elastic solutions yield a finite hoop stress at the crack tip, thus allowing for a fracture criterion based on the maximum dynamic stress hypothesis. The finite hoop stress at the crack tip depends on the crack length, the lattice parameter and the circular frequency of incident wave.