Engineering Fracture Mechanics 242 (2021) 107455 Available online 7 December 2020 0013-7944/© 2020 Elsevier Ltd. All rights reserved. Determination of SIFs and T-stress using an over-deterministic method based on stress fields: Static and dynamic Cheng Hou a , Zhiyong Wang b , Xiaochao Jin a, * , Xinkuo Ji a , Xueling Fan a, * a State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace Engineering, Xi’an Jiaotong University, Xi’an 710049, China b Institute of Applied Mechanics, College of Mechanical and Vehicle Engineering, Taiyuan University of Technology, Taiyuan 030024, China A R T I C L E INFO Keywords: Dynamic stress intensity factor Dynamic T-stress Williams’ series expansion Over-deterministic method 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 ob- tained, 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 ac- curacy 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 re- sults 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. 1. Introduction In recent years, more and more attention has been paid to the safety of engineering structures. The existence of cracks changes the failure modes of materials and structures, the ability to make an accurate prediction for occurrence of brittle fracture is of great importance on safety service of engineering structures [1–4]. Determination of crack-tip fracture parameters, including stress intensity factors (SIFs), T-stress and the coefficients of the higher-order terms in the Williams’ series expansion at the crack tip, is the basic starting point for fracture analysis of engineering structures and the fundamental task of linear elastic fracture mechanic (LEFM) [5,6]. An accurate evaluation of these crack-tip fracture parameters will play an important role on understanding and predicting fracture behavior of a cracked body when subjected to a static or dynamic loading. Numerous efforts have been made before to develop new methods to evaluate SIFs and T-stress at crack tip, such as Weight Function method [7], Virtual Crack Closure Technique [8], Cohesive Zone Model [9,10], and path independent integrals like J-Integral [11], H- * Corresponding authors. E-mail addresses: [email protected] (X. Jin), [email protected] (X. Fan). Contents lists available at ScienceDirect Engineering Fracture Mechanics journal homepage: www.elsevier.com/locate/engfracmech https://doi.org/10.1016/j.engfracmech.2020.107455 Received 12 July 2020; Received in revised form 30 November 2020; Accepted 2 December 2020
Determination of SIFs and T-stress using an over-deterministic method based on stress fields: Static and dynamic
May 23, 2023
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