Development of stress intensities for cracks in FGMs with orientation perpendicular and parallel to the gradation

Within this paper the development of stress intensities for cracks in functionally graded materials is addressed. Thereby crack orientations perpendicular as well as parallel to the gradation are under consideration. Those gradations basically produce two different types of changes with respect to a homogeneous and isotropic case, namely changes in the magnitude of the stress intensity (which impacts the lifetime of a structure) and changes in the mode mixity (which impacts the crack path). It will be quantified, in which way both changes depend on the mismatch ratio between the involved materials or on the slope of the gradient, respectively. Additionally the paper will focus on the issue of approximating a continuous gradient by means of sections with piecewise constant material behavior. It will be shown, that even a relatively small number of sections will be able to reasonably model a gradient region during a fatigue crack growth simulation.