Dynamic response for functionally graded materials with penny-shaped cracks

This paper provides a method for studying the penny-shaped cracks configuration in functionally graded material (FGM) structures subjected to dynamic or steady loading. It is assumed that the FGMs are transversely isotropic and all the material properties only depend on the axial coordinate z. In the analysis, the elastic region is treated as a number of layers. The material properties are taken to be constants for each layer. By utilizing the Laplace transform and Wankel transform technique, the general solutions for the layers are derived. The dual integral equations are then obtained by introducing the mechanical boundary and layer interface conditions via the flexibility/stiffness matrix approach. The stress intensity factors are computed by solving dual integral equations numerically in Laplace transform domain. The solution in time domain is obtained by utilizing numerical Laplace inverse, The main advantage of the present model is its ability for treating multiple crack configurations in FGMs with arbitrarily distributed and continuously varied material properties by dividing the FGMs into a number of layers with the properties of each layer slightly different from one another.