Application of the internal and external Williams functions for stress intensity factors assessment in plane stress problems

Abstract Existing analytical methods for calculating stress intensity factors are the application of the complex variables functions or solutions based on the potential theory. Nowadays, computer programs, most based on the finite element method, are widely used, and allow one to obtain the stress intensity factors of any geometry with any combinations of boundary conditions with an accuracy sufficient for most engineering applications. Thus the further contribution in the analytical methods is questionable. It’s preferable to use understandable and easy coding classical methods based on Williams functions, better known as Boundary Collocation Method. However, questions of the application of this method, its educational significance, determination of the real advantages and disadvantages of Williams’ functions remain open. The main purpose of this paper is to investigate the possibility of applying internal and external Williams functions to find the stress intensity factors in plane problems. Also applying the global equilibrium which considerably improve accuracy and convergence of the analysis.