Benchmark of Finite Elements and Extended-Finite Elements Methods for Stress Intensity Factors and Crack Propagation

2018 ◽  
Author(s):  
Rémi Lacroix ◽  
Axelle Caron ◽  
Sandrine Dischert ◽  
Hubert Deschanels ◽  
Moïse Pignol
Keyword(s):  
Finite Element ◽  
Stress Intensity ◽  
Finite Elements ◽  
Crack Propagation ◽  
Stress Intensity Factors ◽  
Power Plants ◽  
Classical Case ◽  
Finite Elements Method ◽  
Intensity Factors ◽  
Numerical Predictions

Stress intensity factors (SIFs) are a major feature in regulatory analyses of Nuclear Power Plants (NPP) components, as they allow to rule on the acceptability of defects when compared to a critical experimental value (K1c). Simplified and robust evaluations of SIFs have been provided in major regulations standards for cracks having usual geometries and locations in major components. However, their evaluations still require a significant effort in the case of important deviations of the geometry of cracks regarding the usual semi-elliptical shape, or in the case of specific geometries of components, and specific locations of cracks in components. In these cases, time-consuming Finite Element meshes must be constructed, either manually or using semi-automatical tools, to represent the components and its defect(s). This method can become particularly costly, especially in the case of fatigue crack propagation. The eXtended-Finite Elements Method (X-FEM) has been proposed to overcome this issue. The representation of the defect is carried out by the level-set method, and specific enrichment functions are used to represent the solution near the crack surface and the crack front. This paper proposes a benchmark of numerical predictions of stress intensity factors using SYSTUS software [5]. It will be based on: a) Available analytical solutions; b) Classical Finite Element method; c) EXtended-Finite Elements Method. The classical case of a circular and elliptical crack in a semiinfinite body is first presented. Then the case of a circumferential crack in a valve under a thermo-mechanical loading is analyzed. The accuracy of the different methods is then compared and discussed.

Fully Automated Mixed Mode Crack Propagation Analyses Using VCCM (Virtual Crack Closure-Integral Method) for Tetrahedral Finite Element

2011 ◽  
Vol 462-463 ◽  
pp. 900-905 ◽  
Author(s):  
Hiroshi Okada ◽  
Hiroshi Kawai ◽  
Takashi Tokuda ◽  
Yasuyoshi Fukui
Keyword(s):  
Finite Element ◽  
Stress Intensity ◽  
Fracture Mechanics ◽  
Crack Propagation ◽  
Crack Closure ◽  
Stress Intensity Factors ◽  
Integral Method ◽  
Large Scale ◽  
Intensity Factors ◽  
Element Analysis

The authors have been developing a crack propagation analysis system that can deal with arbitrary shaped cracks in three-dimensional solids. The system is consisting of mesh generation software, a large-scale finite element analysis program and a fracture mechanics module. To evaluate the stress intensity factors, a Virtual Crack Closure-Integral Method (VCCM) for the second-order tetrahedral finite element is adopted and is included in the fracture mechanics module. The rate and direction of crack propagation are predicted using appropriate formulae based on the stress intensity factors.

Stress Intensity Factors for Unequal Longitudinal-Radial Cracks in Thick-Walled Cylinders

1991 ◽  
Vol 113 (1) ◽  
pp. 22-27 ◽  
Author(s):  
J. L. Desjardins ◽  
D. J. Burns ◽  
R. Bell ◽  
J. C. Thompson
Keyword(s):  
Stress Intensity Factor ◽  
Finite Element ◽  
Stress Intensity ◽  
Finite Elements ◽  
Intensity Factor ◽  
Stress Intensity Factors ◽  
Two Dimensional ◽  
Intensity Factors ◽  
Radial Cracks ◽  
Good Agreement

Finite elements and two-dimensional photoelasticity have been used to analyze thick-walled cylinders which contain arrays of straight-fronted, longitudinal-radial cracks of unequal depth. The stress intensity factor K1 has been computed for the dominant crack and for some of the surrounding cracks. Cylinders with 2, 4, 6, 8, 16, 36 and 40 cracks have been considered. Good agreement has been obtained between the experimental and the numerical results and, for cylinders with 2 or 4 cracks, with previously published predictions. The results for all of the foregoing cases are used to develop simple, approximate techniques for estimating K1 for the dominant crack, when the total number of cracks is different from those that have been considered herein. Estimates of K1 obtained by these techniques agree well with corresponding finite element results.

On the Crack Propagation Trajectory of Central Cracked Plates under Mixed Mode Loading Conditions

2011 ◽  
Vol 462-463 ◽  
pp. 154-159
Author(s):  
Miloud Souiyah ◽  
Andanastuti Muchtar ◽  
Ahmad Kamal Ariffin
Keyword(s):  
Finite Element ◽  
Stress Intensity ◽  
Crack Propagation ◽  
Stress Intensity Factors ◽  
Mixed Mode ◽  
Loading Conditions ◽  
Intensity Factors ◽  
Element Analysis ◽  
Cracked Plates ◽  
Fortran Language

A Finite Element (FE) programme for crack propagation was developed by using a source code written in the FORTRAN language to evaluate the Stress Intensity Factors (SIFs) and to predict the crack propagation trajectory. In this study, a Central Cracked Plate (CCP) with two holes under mixed mode (I & II) loading conditions is considered. Finite Element Analysis (FEA) combined with the concepts of Linear Elastic Fracture Mechanics (LEFM) provides a practical and convenient means to study the fracture and crack growth of the solid materials. The Displacement Extrapolation Technique (DET) is performed on this work in order to compute the stress intensity factors (SIFs) during the crack propagation. Additionally, to validate the capability and the reliability of this developed FE programme, the results of the current study are compared with experimental results from the literature.

Prediction of Fatigue Crack Propagation of Rail Material Using 2D Finite Element Modeling

2012 ◽  
Vol 165 ◽  
pp. 16-20
Author(s):  
N.A. Akeel ◽  
Z. Sajuri ◽  
Ahmad Kamal Ariffin
Keyword(s):  
Finite Element ◽  
Fatigue Crack ◽  
Stress Intensity ◽  
Crack Propagation ◽  
Fatigue Crack Propagation ◽  
Stress Intensity Factors ◽  
Intensity Factors ◽  
Rail Track ◽  
Rail Head ◽  
Head Surface

Fatigue crack propagation in two-dimensional rail track model under constant amplitude loading was analyzed using finite element method. The stress intensity factor was predicted using the displacement correlation method that was written in FORTRAN code and exported to Post2D to run the program and utilizing the singular elements around the crack tip area with automatic remeshing model. The fatigue crack propagation is modeled through the successive linear extensions under the linear elastic assumption. To simulate the propagation a single edge angled-crack was introduced to calculate the accurate values of stress intensity factors. The fatigue crack propagation for rail track under four point bend loading model was successfully simulated. The crack was initially propagated in direction inclined to the rail head surface but changed its direction 90° to rail head surface after certain crack length. The mix mode stress intensity factors were also successfully determined through the proposed model.

Applications of the Fractal-Like Finite Element Method to Sharp Notched Plates

2007 ◽  
Author(s):  
Muhammad Treifi ◽  
Derek K. L. Tsang ◽  
S. Olutunde Oyadiji
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Intensity ◽  
Finite Elements ◽  
Stress Intensity Factors ◽  
Stress Singularity ◽  
Intensity Factors ◽  
Singular Region ◽  
Interpolation Functions ◽  
Element Method

The fractal-like finite element method (FFEM) has been proved to be an accurate and efficient method to analyse the stress singularity of crack tips. The FFEM is a semi-analytical method. It divides the cracked body into singular and regular regions. Conventional finite elements are used to model both near field and far field regions. However, a very fine mesh of conventional finite elements is used within the singular regions. This mesh is generated layer by layer in a self-similar fractal process. The corresponding large number of degrees of freedom in the singular region is reduced extremely to a small set of global variables, called generalised co-ordinates, after performing a global transformation. The global transformation is performed using global interpolation functions. The Concept of these functions is similar to that of local interpolation functions (i.e. element shape functions.) The stress intensity factors are directly related to the generalised co-ordinates, and therefore no post-processing is necessary to extract them. In this paper, we apply this method to analyse the singularity problems of sharp notched plates. Following the work of Williams, the exact stress and displacement fields of a plate with a notch of general angle are derived for plane stress and plane strain conditions. These exact solutions which are eigenfunction expansion series are used as the global interpolation functions to perform the global transformation of the large number of local variables in the singular region around the notch tip to a few set of global co-ordinates and in the determination of the stress intensity factors. The numerical examples demonstrate the accuracy and efficiency of the FFEM for sharp notched problems.

Stress intensity factors in novel specimens for crack propagation under loading conditions II+III in polymers

2020 ◽  
Author(s):  
Ondrej Slávik ◽  
Pavel Hutař ◽  
Michael Berer ◽  
Anja Gosch ◽  
Tomáš Vojtek ◽  
...  
Keyword(s):  
Stress Intensity ◽  
Crack Propagation ◽  
Stress Intensity Factors ◽  
Loading Conditions ◽  
Intensity Factors

A Coupled SBFEM-FEM Approach for Evaluating Stress Intensity Factors

2013 ◽  
Vol 353-356 ◽  
pp. 3369-3377 ◽  
Author(s):  
Ming Guang Shi ◽  
Chong Ming Song ◽  
Hong Zhong ◽  
Yan Jie Xu ◽  
Chu Han Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Complex Geometry ◽  
Stress Singularity ◽  
Intensity Factors ◽  
Finite Element Software ◽  
Scaled Boundary Finite Element ◽  
Element Method

A coupled method between the Scaled Boundary Finite Element Method (SBFEM) and Finite Element Method (FEM) for evaluating the Stress Intensity Factors (SIFs) is presented and achieved on the platform of the commercial finite element software ABAQUS by using Python as the programming language. Automatic transformation of the finite elements around a singular point to a scaled boundary finite element subdomain is realized. This method combines the high accuracy of the SBFEM in computing the SIFs with the ability to handle material nonlinearity as well as powerful mesh generation and post processing ability of commercial FEM software. The validity and accuracy of the method is verified by analysis of several benchmark problems. The coupled algorithm shows a good converging performance, and with minimum additional treatment can be able to handle more problems that cannot be solved by either SBFEM or FEM itself. For fracture problems, it proposes an efficient way to represent stress singularity for problems with complex geometry, loading condition or certain nonlinearity.

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