Analysis of stresses and displacements in the vicinity of blunt V-notches by considering higher order terms

Mode I asymptotic stress and displacement fields of blunt V-notches are calculated based on the Muskhelishvili's approach. First, by using appropriate complex potential functions, the stress and displacement components in the polar coordinate system are determined. By applying proper mapping, the notch profile is built up, and then by utilizing the near-field boundary conditions, free parameters are specified. Afterwards, the solution procedure available for the singular term is extended for higher order terms leading to asymptotic relations for stress and displacement fields. Subsequently, the coefficients of the asymptotic stress fields are computed by using a numerical procedure named overdeterministic technique. It is shown that the proposed method that considers the higher order terms yields very good results, whereas the methods based only on the singular term have significant errors. Finally, some parameters affecting the convergence of the numerical results are studied and discussed.