A new weight function representation for one-dimensional edge cracks: application to mode I stress intensity factor evaluation for a radial edge-crack in a solid circular disk

Accurate evaluation of stress intensity factors (SIFs) is fundamental to many fatigue and fracture mechanics analyses. The weight function method (WFM) provides a simple and computationally efficient approach for evaluating SIFs under complex loading conditions. In this study, a new representation of the one-dimensional WF for edge cracks is proposed and applied to derive the Mode I WF for a radial edge-crack in a solid circular disk subjected to tensile loading. Given the availability of SIF solutions and several approximate WF formulations for this geometry, the primary objective is to assess the effectiveness of the proposed representation in constructing approximate WFs from reference SIFs. To this end, reference SIFs for three tensile stress distributions were calculated using finite element analysis (FEA) and used to determine the WF coefficients. Fitting expressions were then developed to represent these coefficients as continuous functions of the relative crack length, enabling efficient SIF evaluation within the investigated range. The derived WF was validated using three independent, complex nonlinear stress distributions, and its predictions showed good agreement with FE results. Furthermore, comparisons with previously published WF formulations for radial edge cracks demonstrated the capability of the proposed representation to construct accurate one-dimensional approximate weight functions from reference SIFs.