| The dynamically accelerating, mode III problem for a semi-infinite interfacial crack between two linear elastic functionally graded material is considered. Using perturbation analysis, an estimate of the Dirichlet-to-Neumann map is constructed for each half plane. An asymptotic expansion of the Stress Intensity Factor (SIF) as a function of time for some given applied crack face loading is constructed to determine its dependence upon the material properties. Using this construction, a numerical simulation of an interfacial, non-uniform motion crack between a homogenous substrate and functionally graded material is performed. From the model, it was seen that the role of material density in determining the dynamic SIF is smaller than the shear modulus. Also observed was that certain grading patterns induce oscillatory behavior in the stress field near the crack tip. |
