In this paper, the asymptotic singular fields at cracks and sharp notches in isotropic and orthotropic media are numerically investigated. The Finite Element Iterative Method (FEIM) is used for evaluating the power of the singular field at the notch root under three different loading conditions: tension, shear, and a combination of tension and shear. The numerical results for the isotropic case, obtained by the FEIM, are in excellent agreement with the results from analytical solutions. In tension, the singularity at the notch root converges to the strong singularity lambda(a), while under shear, convergence is to the weak singularity lambda(b). When the loading is a combination of tension and shear, the singularity at the notch root always converges to lambda(a). The stress singularity results for orthotropic materials followed the same trend. However, the stress singularities lambda(a) and lambda(b), are strongly dependent on the elastic properties of the material. Under combined tension and shear loading, the number of iterations for convergence significantly increases, as the loading changes from tension-dominated to shear-dominated. This study has demonstrated the usefulness of the FEIM for the evaluation of asymptotic singular fields at sharp notches in orthotropic materials.
