Crack tip asymptotic field coefficients analyses based on extended finite element method using over-deterministic displacement field fitting method

Abstract

The evaluation of the stress intensity factors (SIFs), T-stress, and higher-order coefficients in the crack tip asymptotic field in the extended finite element method (XFEM) is investigated based on the over-deterministic displacement field fitting method. Numerical examples of central cracked and edge cracked plate under uniaxial tension exhibit the accuracy of the evaluated coefficients. A convergence study is conducted to explore the influence of fitting parameters: the number of nodes used for fitting, the number of terms in the asymptotic field series used for fitting, and the distance from selected nodes to the crack tip. It indicates that the distance of selected nodes affects the accuracy of coefficients above 3rd order. Besides, the study of enrichment function and strategy demonstrates that adopting higher-order enrichment terms or more enriched layers of elements can improve the accuracy of coefficient evaluation. Particularly, the higher-order coefficients can be evaluated without the enrichment terms of the corresponding order. The analyses verify that the crack tip asymptotic field coefficients can be accurately evaluated in XFEM using this over-deterministic displacement field fitting method with the appropriate setting of enrichment and fitting parameters.