Determination of SIFs and T-stress using an over-deterministic method based on stress fields: Static and dynamic

Abstract

An over-deterministic method based on crack-tip stress fields is proposed for evaluating stress intensity factors (SIFs) and T-stress at crack tip for mode I, mode II or mixed-mode I/II cracks under static or dynamic loading. In this method, the coordinates and stresses of the nodes around the crack tip, obtained from finite element method (FEM) or extended finite element method (XFEM), are brought into the expansion of Williams’ stress series when the cracked body is subjected to static or dynamic loading. Then, a set of over-deterministic equations can be obtained, and the optimal solution of SIFs as well as T-stress can be achieved by solving these equations using the least square method. Various cracked bodies are employed to verify the accuracy of the proposed method, and the effects of the number of terms in Williams’ series expansion, the number and location of the nodes selected around the crack tip, and the mesh around the crack tip on SIFs and T-stress are detailed discussed. Results show that the proposed method is quite simple and convenient to obtain SIFs and T-stress under static or dynamic loading, with being in good agreement with the solutions from previous works. Satisfactory results can be achieved only if the coordinates and stresses of the nodes around the crack tip are accurate enough. In addition, it can be found that the proposed method can also be used to calculate higher-order coefficients of Williams’ series expansion.