An over-deterministic method for calculation of coefficients of crack tip asymptotic field from finite element analysis

• Published in: Fatigue & fracture of engineering materials & structures 2011-03, Vol.34 (3), p.159-176
• Main Authors: AYATOLLAHI, M. R., NEJATI, M.
• Format: Article
• Language: English
• Subjects: Applied sciences; Asymptotic properties; coefficients of the higher-order terms; crack; Crack propagation; Exact sciences and technology; Fatigue failure; Finite element analysis; Finite element method; Fracture mechanics; Mathematical analysis; Mechanical properties and methods of testing. Rheology. Fracture mechanics. Tribology; Metals. Metallurgy; over-deterministic method; Stress analysis; stress intensity factor (SIF); T-stress
• ISSN: 8756-758X; 1460-2695
• DOI: 10.1111/j.1460-2695.2010.01504.x

ABSTRACT An over‐deterministic method has been employed for calculating the stress intensity factors (SIFs) as well as the coefficients of the higher‐order terms in the Williams series expansions in cracked bodies, using the conventional finite element analysis. For a large number of nodes around the crack tip, an over‐determined set of simultaneous linear equations is obtained, and using the fundamental concepts of the least‐squares method, the coefficients of the Williams expansion can be calculated for pure mode I, pure mode II and mixed mode I/II conditions. A convergence study has been conducted to examine the effects of the number of nodes used, the number of terms in Williams expansion and the distance of the selected nodes from the crack tip, on the accuracy of the results. It is shown that the simple method presented in this paper, yields accurate results even for coarse finite element meshes or in the absence of singular elements. The accuracy of SIFs and the coefficients of higher‐order terms are validated by using the available results in the literature.