Influence of FGM coating on the dynamic fracture behavior of multiple cracks in a homogeneous half-plane under in-plane loading

This study investigates the stationary interacting of multiple cracks within both the interface and the embedded layer of a homogeneous half-plane coated with a functionally graded material (FGM) under elastodynamic in-plane loading. Leveraging the distributed dislocation technique, this research provides a novel framework for exploring the intricate fracture mechanics of this specific material configuration. To accurately quantify dynamic stress intensity factors (DSIFs) within this complex medium, the study employs the method of integral transformations. This approach involves strategically positioning Volterra-type climb and glide edge dislocations at the critical interface between the half-plane and the FG coating. To characterize the traction vector along the surfaces of multiple cracks, we construct systems of Cauchy singular integral equations using dislocation solutions. By numerically solving these equations, we precisely determine the dislocation density along the crack surfaces. This critical information then enables exceptionally accurate computation of DSIFs at the crack tips. This study's numerical findings reveal how material gradient characteristics, Poisson's ratio, excitation frequency, coating thickness, crack length and crack interactions collectively govern the DSIFs of graded coatings. These results clarify the complex mechanics of these materials under elastodynamic loading.