Determination of stress intensity factors for elements with sharp corner located on the interface of a bi-material structure or homogeneous material

This paper presents a new universal analytical and numerical method allowing for determination of stress intensity factors (SIFs) for notches and cracks located in both a homogeneous and a heterogeneous material. An advantage of the proposed method is that it does not require knowledge of an analytical description of singular stress/displacement fields or connection of SIFs to energy parameters such as energy release factor. In this method, a universal analytical function has been used, which in combination with data obtained using finite element method (FEM) allows for a direct determination of stress intensity factors. One parameter that is necessary to know when using the proposed method is the eigenvalue $$\lambda $$ λ . The characteristic equation allowing for determination of the eigenvalues for any corner has been given herein. What is more, also a criterion clearly defining the nodes is determined, from which FEM numerical results are implemented to the developed analytical function. In order to verify the proposed method, for a selected group of geometrical and material structures with sharp corner, values of stress intensity factors were determined and compared to data available in the literature. Satisfactory compliance of obtained results with literature ones was found.