FEM and BEM analyses of notch stress intensity factors in anisotropic materials

The asymptotic stress field at sharp notches in orthotropic materials can be described as the sum of one or two singularity terms, where the first term corresponds to symmetric and the second term to antisymmetric loading of the notch. Following Stroh's formalism, the stress exponents and angular functions have been calculated analytically for a notch in monocrystalline silicon between two (111) lattice planes. To calculate the notch stress intensity factors (NSIFs), which are a measure for the magnitude of the stress terms, the Finite Element method (FEM) and the Boundary Element Method (BEM) have been employed. Using FEM, the NSIFs were extracted from the nodal stresses ahead of the notch trip. Using BEM, the NSIFs can be obtained directly by incorporating singular notch tip elements into the BEM code. Very good agreement was achieved for the NSIFs calculated by the two numerical techniques.