A simple, robust novel Williams series-based FE-analytical hybrid technique for evaluation of SIFs and higher order coefficients

Abstract

To evaluate crack-tip parameters, various hybrid methods (HMs) amalgamating experimental domain data with multi-parameter field-variable expressions have been extensively employed. On the other hand, simpler HMs leveraging boundary contour data and demonstrating the robustness of the HMs for input data errors have been scarcely reported. In this regard, the present work addresses these gaps by proposing and illustrating a novel HM coupling coarse-mesh FE boundary displacement data on the crack lips, but not limited to it, with Williams’s series. Additionally, the HM’s robustness for simulated Gaussian error distribution in the input data is demonstrated. Comparison of HM-computed SIF values with converged FE values shows rapid convergence after 2–3 terms in the series and a certain number of retrieving points. Histogram analyses quantifying the deviations of HM-computed SIFs in the sample set indicate error tolerance within a reasonable limit for the fracture modes. These observations demonstrate the efficacy of the HM; In addition, the HM yields higher-order coefficients — accuracy of which are corroborated by comparing reconstructed field variables in the vicinity of the crack-tip with converged FEA. On the other hand, robustness analyses demonstrate that ±1σ of the data is within about 10% of error for all the modes. Thus, the proposed simple and robust HM offers a potential practical approach for evaluation of SIFs and higher order coefficients.