SIFs for Radial Cracks in Annular Discs Under Internal and External Shrinkage Pressure and Constant Angular Velocity

2007 ◽  
Author(s):  
A. Sakhaee-Pour ◽  
A. R. Gowhari-Anaraki ◽  
S. J. Hardy
Keyword(s):  
Finite Element ◽  
Angular Velocity ◽  
Constant Angular Velocity ◽  
Coefficient Of Determination ◽  
Linear Elastic ◽  
Crack Configuration ◽  
Wide Range ◽  
Elastic Fracture ◽  
Radial Cracks

Finite element method has been implemented to predict stress intensity factors (SIFs) for radial cracks in annular discs under constant angular velocity. Effects of internal and external uniform pressure on the SIFs have also been considered. Linear elastic fracture mechanics finite element analyses have been performed and results are presented in the form of crack configuration factors for a wide range of components and crack geometry parameters. These parameters are chosen to be representative of typical practical situations. The extensive range of crack configuration factors obtained from the analyses is then used to develop equivalent prediction equations via a statistical multiple non-linear regression model. The accuracy of this model is measured using a multiple coefficient of determination, R2, where 0 ≤ R2 ≤ 1. This coefficient is found to be greater than or equal to 0.98 for all cases considered in this study, demonstrating the quality of the model fit to the data. These equations for the SIFs enable designers to predict fatigue life of the components easily.

Stress intensity factors for radial cracks in annular and solid discs under constant angular velocity

2005 ◽  
Vol 40 (2) ◽  
pp. 217-223 ◽  
Author(s):  
A. R Gowhari-Anaraki ◽  
S J Hardy ◽  
R Adibi-Asl
Keyword(s):  
Finite Element ◽  
Stress Intensity ◽  
Angular Velocity ◽  
Stress Intensity Factors ◽  
Constant Angular Velocity ◽  
Experimental Sample ◽  
Intensity Factors ◽  
Rotating Disc ◽  
Crack Configuration ◽  
Wide Range

The finite element method has been used to predict the stress intensity factors for single- and double-edge cracks in six annular and solid rotating discs under constant angular velocity. Linear elastic fracture mechanics finite element analyses have been performed and the results are presented in the form of crack configuration factors for a wide range of component and crack geometry parameters. These parameters are chosen to be representative of typical practical situations and have been determined from evidence presented in the open literature. The extensive range of crack configuration factors obtained from the analyses are then used to obtain equivalent prediction equations using a statistical multiple non-linear regression model. The accuracy of this model is measured using a multiple coefficient of determination, R2, where 0 ≤ R2 ≤ 1. This coefficient is found to be greater than or equal to 0.98 for all cases considered in this study, demonstrating the quality of the model fit to the data. Predictive equations for stress intensity factors enable designers to predict the fatigue life of these components easily. It is also suggested that one of the component configurations (i.e. the cracked slit rotating disc) can be selected as a suitable experimental sample to measure the real fracture toughness of rotating components, using the relevant predictive equation presented in this study. Finally a fracture criterion is also suggested graphically to determine the limit load value of angular velocity for similar rotating disc components.

Mixed-mode fatigue crack propagation in thin T-sections under plane stress

2003 ◽  
Vol 38 (6) ◽  
pp. 557-575 ◽  
Author(s):  
A. R Gowhari-Anaraki ◽  
S J Hardy ◽  
R Adibi-Asl
Keyword(s):  
Finite Element ◽  
Crack Propagation ◽  
Shear Crack ◽  
High Stress ◽  
Axial Loading ◽  
Coefficient Of Determination ◽  
Element Analysis ◽  
Predictive Equations ◽  
Crack Configuration ◽  
Wide Range

Data that can be used in the fatigue analysis of flat T-section bars subjected to axial loading and local restraint are presented. The paper describes how finite element analysis has been used to obtain stress fields in the vicinity of a crack or crack-like flaw introduced into the fillet (i.e. high-stress) region of the component. The effect of both the position and inclination of the crack has been investigated. The inclination of the crack to the transverse direction is varied in such a way that a combination of mode I (tension opening) and mode II (in-plane shear) crack tip conditions are created in the component when subjected to axial loading which is applied to the entire flat shoulder of the projection. Linear elastic fracture mechanics finite element analyses have been performed, and the results are presented in the form of J integrals and notch and crack configuration factors for a wide range of component and crack geometric parameters. These parameters are chosen to be representative of typical practical situations and have been determined from evidence presented in the open literature. The extensive range of notch and crack configuration factors obtained from the analyses are then used to obtain equivalent prediction equations using a statistical multiple non-linear regression model. The accuracy of this model is measured using a multiple coefficient of determination, R2, where 0 < R2 < 1. This coefficient is found to be greater than or equal to 0.98 for all cases considered in this study, demonstrating the quality of the model fit to the data. Predictive equations for stress intensity factors and J-integral values, which are based on the elastic stress concentration factor, are also developed. A crack propagation methodology, based on existing theory coupled with these predictive equations, is then presented for this type of component and loading.

Analytical and 3D Finite Element Study of the Deflection of an Elastic Cantilever Bilayer Plate

2010 ◽  
Vol 78 (1) ◽  
Author(s):  
M. Chekchaki ◽  
V. Lazarus ◽  
J. Frelat
Keyword(s):  
Thin Films ◽  
Finite Element ◽  
Three Dimensional ◽  
Analytical Formula ◽  
Mechanical Stresses ◽  
Linear Elastic ◽  
Wide Range ◽  
Finite Element Calculations ◽  
Analytical Formulas ◽  
Three Dimensional Elasticity

The mechanical system considered is a bilayer cantilever plate. The substrate and the film are linear elastic. The film is subjected to isotropic uniform prestresses due for instance to volume variation associated with cooling, heating, or drying. This loading yields deflection of the plate. We recall Stoney’s analytical formula linking the total mechanical stresses to this deflection. We also derive a relationship between the prestresses and the deflection. We relax Stoney’s assumption of very thin films. The analytical formulas are derived by assuming that the stress and curvature states are uniform and biaxial. To quantify the validity of these assumptions, finite element calculations of the three-dimensional elasticity problem are performed for a wide range of plate geometries, Young’s and Poisson’s moduli. One purpose is to help any user of the formulas to estimate their accuracy. In particular, we show that for very thin films, both formulas written either on the total mechanical stresses or on the prestresses, are equivalent and accurate. The error associated with the misfit between our theorical study and numerical results are also presented. For thicker films, the observed deflection is satisfactorily reproduced by the expression involving the prestresses and not the total mechanical stresses.

The Damage Tolerance of a Sandwich Panel Containing a Cracked Honeycomb Core

2009 ◽  
Vol 76 (6) ◽  
Author(s):  
I. Quintana Alonso ◽  
N. A. Fleck
Keyword(s):  
Finite Element ◽  
Sandwich Panel ◽  
Finite Element Simulations ◽  
Analytical Models ◽  
Tensile Fracture ◽  
Linear Elastic ◽  
Statistical Variation ◽  
Wall Strength ◽  
Elastic Fracture ◽  
Weibull Theory

The tensile fracture strength of a sandwich panel, with a center-cracked core made from an elastic-brittle diamond-celled honeycomb, is explored by analytical models and finite element simulations. The crack is on the midplane of the core and loading is normal to the faces of the sandwich panel. Both the analytical models and finite element simulations indicate that linear elastic fracture mechanics applies when a K-field exists on a scale larger than the cell size. However, there is a regime of geometries for which no K-field exists; in this regime, the stress concentration at the crack tip is negligible and the net strength of the cracked specimen is comparable to the unnotched strength. A fracture map is developed for the sandwich panel with axes given by the sandwich geometry. The effect of a statistical variation in the cell-wall strength is explored using Weibull theory, and the consequences of a stochastic strength upon the fracture map are outlined.

Fractal crushing of ice and brittle solids

1991 ◽  
Vol 433 (1889) ◽  
pp. 469-477 ◽  
Keyword(s):  
Fractal Dimension ◽  
Fragment Size ◽  
Special Role ◽  
Field Observations ◽  
Linear Elastic ◽  
Brittle Solids ◽  
Wide Range ◽  
Elastic Fracture ◽  
Ice Forces ◽  
Fractal Size

A significant ‘scale effect’ is observed when sea ice forces on structures are measured at field scale: the force per unit contact area is not independent of area, but decreases with increasing area. Fragments of broken materials are found to have a fractal size distribution, with a fractal dimension close to 2.5 over a remarkably wide range of fragment size. The research described in this paper brings these two observations together, and shows that they can be explained by a simple model of crushing, which incorporates the relation between fragment size and splitting force predicted by linear elastic fracture mechanics. The model indicates a special role for the fractal dimension of 2.5, and predicts a relation between force and area, consistent with field observations.

Fatigue analysis of groove weld with steel bar backing by fracture mechanics finite elements

1988 ◽  
Vol 15 (4) ◽  
pp. 524-533 ◽  
Author(s):  
Farid Taheri ◽  
Aftab A. Mufti
Keyword(s):  
Finite Element ◽  
Fracture Mechanics ◽  
Stress Ratio ◽  
Stress Range ◽  
Cyclic Life ◽  
Linear Elastic ◽  
Steel Bar ◽  
Elastic Fracture ◽  
Number Of Cycles ◽  
Cycles To Failure

The purpose of this paper is to analyze the fatigue crack growth rate in groove weld with backing steel bar. The linear elastic fracture mechanics approach is used. This approach is coded in a special purpose fracture mechanics package FAST. By using FAST, the structure is modeled and analyzed by its finite element module FAST-I, and the cyclic life is estimated by its crack propagation module FAST-II.An example recently studied by Baker and Kulak is investigated by the FAST program. The S–N curve (stress range versus number of cycles to failure) obtained by FAST is compared with the curve presented by Baker and Kulak. Key words: Engineering, finite element, fracture mechanics, fatigue, steel, stress intensity factor, numerical, computer analysis, weld, stress ratio, enriched element.

Validation of a Finite Element Toolbox for Studying Flaw Interaction

2020 ◽  
Author(s):  
Harry E. Coules
Keyword(s):  
Finite Element ◽  
Fracture Mechanics ◽  
Large Scale ◽  
Structural Integrity ◽  
Three Dimensional ◽  
Integrity Assessment ◽  
Linear Elastic ◽  
Wide Range ◽  
Parametric Studies ◽  
Elastic Crack

Abstract Structural integrity assessment often requires the interaction of multiple closely-spaced cracks or flaws in a structure to be considered. Although many procedures for structural integrity assessment include rules for determining the significance of flaw interaction, and for re-characterising interacting flaws, these rules can be difficult to validate in a fracture mechanics framework. int_defects is an open-source MATLAB toolbox which uses the Abaqus finite element suite to perform large-scale parametric studies in cracked-body analysis. It is designed to allow developers of assessment codes to check the accuracy of simplified interaction criteria under a wide range of conditions, e.g. for different interacting flaw geometries, material models and loading cases. int_defects can help analysts perform parametric studies to determine linear elastic crack tip stress field parameters, elastic-plastic parameters and plastic limit loads for simple three-dimensional cracked bodies relevant to assessment codes. This article focusses on the validation of int_defects using existing fracture mechanics results. Through a set of validation examples, int_defects is shown to produce accurate results for a very wide range of cases in both linear and non-linear cracked-body analysis. Nevertheless, it is emphasised that users of this software should be conscious of the inherent limitations of LEFM and EPFM theory when applied to real fracture processes, and effects such as constraint loss should be considered when formulating interaction criteria.

Application of the Finite Element Method to Linear Elastic Fracture Mechanics

1991 ◽  
Vol 44 (10) ◽  
pp. 447-461 ◽  
Author(s):  
Leslie Banks-Sills
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Intensity ◽  
Fracture Mechanics ◽  
Displacement Field ◽  
Three Dimensional ◽  
Linear Elastic Fracture Mechanics ◽  
The Finite Element Method ◽  
Linear Elastic ◽  
Elastic Fracture

Use of the finite element method to treat two and three-dimensional linear elastic fracture mechanics problems is becoming common place. In general, the behavior of the displacement field in ordinary elements is at most quadratic or cubic, so that the stress field is at most linear or quadratic. On the other hand, the stresses in the neighborhood of a crack tip in a linear elastic material have been shown to be square root singular. Hence, the problem begins by properly modeling the stresses in the region adjacent to the crack tip with finite elements. To this end, quarter-point, singular, isoparametric elements may be employed; these will be discussed in detail. After that difficulty has been overcome, the stress intensity factor must be extracted from either the stress or displacement field or by an energy based method. Three methods are described here: displacement extrapolation, the stiffness derivative and the area and volume J-integrals. Special attention will be given to the virtual crack extension which is employed by the latter two methods. A methodology for calculating stress intensity factors in two and three-dimensional bodies will be recommended.

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