Extraction of Stress Intensity Factors by Using the P-Version Finite Element Method and Contour Integral Method
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ISSN 1860-2134
Extraction of Stress Intensity Factors by Using the P-Version Finite Element Method and Contour Integral Method Jianming Zhang1
Jun Chen1
Liang Wu2
1
( Department of Engineering Mechanics, Kunming University of Science and Technology, Kunming 650500, China) (2 Department of Water Resources and Hydropower Engineering, Kunming University of Science and Technology, Kunming 650500, China)
Received 25 November 2019; revision received 8 August 2020; Accepted 24 August 2020 c The Chinese Society of Theoretical and Applied Mechanics 2020
ABSTRACT The stress intensity factors (SIFs) for two-dimensional cracks are extracted using the p-version finite element method (P-FEM) and the contour integral method. Several numerical experiments, e.g., crack initiating from the edge of a circular hole under an unidirectional uniform tension and two equal-length, unequal-length hole–edge cracks, respectively, at a rectangular plate, an inclined centered crack under uniaxial tension at a square plate and a pipeline crack model, are used to demonstrate the accuracy and effectiveness of the approaches. SIFs are presented for the effects of various crack lengths and length–width ratio. Numerical results are analyzed and compared with reference solutions and results obtained by the Voronoi cell finite element method, boundary element method, high-order extended finite element method (high-order XFEM) and commercial finite element software ABAQUS in the available literature. Numerical results are in good agreement with the benchmark problems and show faster convergence rate, higher accuracy and better numerical stability.
KEY WORDS Fracture mechanics, Stress intensity factors, P-version finite element method, Contour integral method
1. Introduction The analysis of crack behavior is one of the most important subjects in engineering structures such as aircrafts, trains, automobiles, ships, pressure vessels and pipelines. The stress intensity factors (SIFs) play a very important role in linear elastic fracture mechanics (LEFM) and are also used to describe the strength near crack tip displacements and strains. The crack originating from a hole is a classical problem in fracture mechanics. Due to stress concentration (SC), plates contain holes of different shapes. The hole–edge cracks and straight cracks, even very small, may probably lead to structural damage. Many numerical methods have been developed to simulate and research crack and crack propagation problems in complex structures and materials, for example the finite element method (FEM) [1–3], boundary element method (BEM) [4–6], meshless method (MLM) [7–9], generalized or extended finite element method (G/XFEM) [10–13] and high-order extended finite element method
Corresponding author. E-mail: [email protected]
ACTA MECHANICA SOLIDA SINICA
(high-order XFEM). Many researchers investigated the hole–edge crack problems through different approaches. Bowie [14] first obtained the solutions of a circular hole with a single edge crack and a pair of symmetrical edge cracks
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