A simple analytical crack tip opening displacement approximation under random variable loadings

• Published in: International journal of fracture Vol. 173; no. 2; pp. 189 - 201
• Main Authors: Liu, Yongming, Lu, Zizi, Xu, Jifeng
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.02.2012; Springer; Springer Nature B.V
• Subjects: Algorithms; Amplitudes; Approximation; Automotive Engineering; Characterization and Evaluation of Materials; Chemistry and Materials Science; Civil Engineering; Classical Mechanics; Computer simulation; Crack propagation; Crack tips; Displacement; Economic models; Exact sciences and technology; Fatigue failure; Finite element method; Fracture mechanics; Fracture mechanics (crack, fatigue, damage...); Fundamental areas of phenomenology (including applications); Hardening; Materials Science; Mathematical analysis; Mathematical models; Mechanical Engineering; Original Paper; Physics; Random variables; Solid mechanics; Structural and continuum mechanics; Cyclic loading; Variable loading; Random; Crack tip opening displacement; Probabilistic approach; Modeling; Fatigue crack; Crack propagation; Plasticity zone; Finite element method; Crack opening displacement; Cyclic load; Random load; Crack tip; Dynamic load
• ISSN: 0376-9429; 1573-2673
• DOI: 10.1007/s10704-012-9682-6

A simple analytical approximation is proposed in this paper to calculate the crack tip opening displacement under general random variable amplitude loadings. This approximation is based on a modified Dugdale model for cyclic loadings. The discussion is first given under constant amplitude loading and is extended to several simple cases under variable amplitude loadings. Following this, a general algorithm is proposed under general random variable loadings. Numerical examples are verified with finite element simulations. Following this, hardening effect is included by including a hardening correction function. The proposed analytical approximation is very efficient compared to the direct finite element simulation. The solution can be used for detailed fatigue crack growth analysis under random variable amplitude loadings.