scholarly journals A closed form for the Stress Intensity Factor of a small embedded square-like flaw

2020 ◽  
Vol 14 (54) ◽  
pp. 182-191
Author(s):  
Paolo Livieri ◽  
Fausto Segala
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Closed Form ◽  
Numerical Results ◽  
Explicit Equation ◽  
Minimum Value ◽  
Axes Of Symmetry

In the present work, the stress intensity factor (SIF) of a small embedded square-like flaw is calculated by means of a procedure based on the Oore-Burns integral. An explicit equation is given to evaluate the SIF along the two axes of symmetry that correspond to the points where the SIF takes its maximum and minimum value on the contour crack. The SIF is calculated in accordance with FE numerical results.

scholarly journals Numerical solution of an integral equation arising in the problem of cruciform crack using Daubechies scale function

2019 ◽  
Vol 14 (1) ◽  
pp. 21-27
Author(s):  
Jyotirmoy Mouley ◽  
M. M. Panja ◽  
B. N. Mandal
Keyword(s):  
Stress Intensity Factor ◽  
Integral Equation ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Numerical Solution ◽  
Present Method ◽  
Numerical Results ◽  
Scale Function ◽  
Forcing Term ◽  
Classical Integral

Abstract This paper is concerned with obtaining approximate numerical solution of a classical integral equation of some special type arising in the problem of cruciform crack. This integral equation has been solved earlier by various methods in the literature. Here, approximation in terms of Daubechies scale function is employed. The numerical results for stress intensity factor obtained by this method for a specific forcing term are compared to those obtained by various methods available in the literature, and the present method appears to be quite accurate.

Closed-Form Stress Intensity Factor Solutions for Surface Cracks With Large Aspect Ratios in Plates

2019 ◽  
Vol 142 (2) ◽  
Author(s):  
Kisaburo Azuma ◽  
Yinsheng Li ◽  
Steven Xu
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Closed Form ◽  
Influence Coefficient ◽  
Maximum Point ◽  
Surface Cracks ◽  
Fourth Degree ◽  
Aspect Ratios ◽  
Influence Coefficients

Abstract Alloy 82/182/600, which is used in light-water reactors, is known to be susceptible to stress-corrosion cracking. The depth of some of these cracks may exceed the value of half-length on the surface. Although the stress intensity factor (SIF) for cracks plays an important role in predicting crack propagation and failure, Section XI of the ASME Boiler and Pressure Vessel Code does not provide SIF solutions for such deep cracks. In this study, closed-form SIF solutions for deep surface cracks in plates are discussed using an influence coefficient approach. The stress distribution at the crack location is represented by a fourth-degree-polynomial equation. Tables for influence coefficients obtained by finite element analysis in the previous studies are used for curve fitting. The closed-form solutions for the influence coefficients were developed at the surface point, the deepest point, and the maximum point of a crack with an aspect ratio a/c ranging from 1.0 to 8.0, where a is the crack depth and c is one-half of the crack length. The maximum point of a crack refers to the location on the crack front where the SIF reaches a maximum value.

Stress Intensity Factor Coefficients for Circumferential ID Surface Flaws in Cylinders for Appendix A of ASME Section XI

2013 ◽  
Author(s):  
Russell C. Cipolla ◽  
Darrell R. Lee
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Flat Plate ◽  
Closed Form ◽  
Fourth Order ◽  
Surface Crack ◽  
Crack Size ◽  
Plate Geometry

The stress intensity factor (KI) equations for a surface crack in ASME Section XI, Appendix A are based on non-dimensional coefficients (Gi) that allow for the calculation of stress intensity factors for a cubic varying stress field. Currently, the coefficients are in tabular format for the case of a surface crack in a flat plate geometry. The tabular form makes the computation of KI tedious when determination of KI for various crack sizes is required and a flat plate geometry is conservative when applied to a cylindrical geometry. In this paper, closed-form equations are developed based on tabular data from API 579 (2007 Edition) [1] for circumferential cracks on the ID surface of cylinders. The equations presented, represent a complete set of Ri/t, a/t, and a/l ratios and include those presented in the 2012 PVP paper [8]. The closed-form equations provide G0 and G1 coefficients while G2 through G4 are obtained using a weight function representation for the KI solutions for a surface crack. These equations permit the calculation of the Gi coefficients without the need to perform tabular interpolation. The equations are complete up to a fourth order polynomial representation of applied stress, so that the procedures in Appendix A have been expanded. The fourth-order representation for stress will allow for more accurate fitting of highly non-linear stress distributions, such as those depicting high thermal gradients and weld residual stress fields. The equations developed in this paper will be added to the Appendix A procedures in the next major revision to ASME Section XI. With the inclusion of equations to represent Gi, the procedures of Appendix A for the determination of KI can be performed more efficiently without the conservatism of using flat plate solutions. This is especially useful when performing flaw growth evaluations where repetitive calculations are required in the computations of crack size versus time. The equations are relatively simple in format so that the KI computations can be performed by either spreadsheet analysis or by simple computer programming. The format of the equations is generic in that KI solutions for other geometries can be added to Appendix A relatively easily.

Closed-Form Calculation of Stress Intensity Factor for an Axial ID Surface Flaw in Cylinder Subjected to Weld Residual Stresses

2013 ◽  
Author(s):  
Douglas A. Scarth ◽  
Steven X. Xu
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Weight Function ◽  
Closed Form ◽  
Function Method ◽  
Current Method ◽  
Surface Flaw ◽  
Weight Function Method ◽  
Influence Coefficients

A method for calculating the stress intensity factor for linear elastic fracture mechanics based flaw evaluation is provided in Appendix A-3000 of ASME Section XI. In the 2010 Edition of ASME Section XI, the calculation of stress intensity factor for a surface crack is based on characterization of stress field with a cubic equation and use of influence coefficients. The influence coefficients are currently only provided for flat plate geometry in tabular format. The ASME Section XI Working Group on Flaw Evaluation is in the process of rewriting Appendix A-3000. Proposed major updates include the implementation of explicit use of Universal Weight Function Method for calculation of the stress intensity factor for a surface flaw and the inclusion of closed-form influence coefficients for cylinder geometry. The explicit use of weight function method eliminates the need for fitting polynomial equations to the actual through-thickness stress distributions at crack location. In this paper, the proposed Appendix A procedure is applied to calculate the stress intensity factors in closed-form for an axial ID surface flaw in a cylinder subjected to a set of nonlinear hoop weld residual stress profiles. The calculated stress intensity factor results are compared with the results calculated based on the current method in Appendix A using cubic equations to represent the stress distribution. Three-dimensional finite element analyses were performed to verify the accuracy of the stress intensity factor results calculated based on the current and proposed Appendix A procedures. The results in this paper support the implementation of the proposed stress intensity factor calculation procedure into ASME Code.

Closed-Form Relations for Stress Intensity Factor Influence Coefficients for Axial Outside Surface Flaws in Cylinders for Appendix A of ASME Section XI

2016 ◽  
Author(s):  
Steven X. Xu ◽  
Darrell R. Lee ◽  
Douglas A. Scarth ◽  
Russell C. Cipolla
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Closed Form ◽  
Inside Surface ◽  
Linear Elastic ◽  
Evaluation Procedures ◽  
Influence Coefficients ◽  
Elastic Fracture ◽  
Flaw Location

Linear elastic fracture mechanics based flaw evaluation procedures in Section XI of the ASME Boiler and Pressure Vessel Code require calculation of the stress intensity factor. Article A-3000 of Appendix A in ASME Section XI prescribes a method to calculate the stress intensity factor for a surface or subsurface flaw by making use of the flaw location stress distribution obtained in the absence of the flaw. The 2015 Edition of ASME Section XI implemented a number of significant improvements in Article A-3000, including closed-form equations for calculating stress intensity factor influence coefficients for circumferential flaws on the inside surface of cylinders. Closed-form equations for stress intensity factor influence coefficients for axial flaws on the inside surface of cylinders have also been developed. Ongoing improvement efforts for Article A-3000 include development of closed-form relations for the stress intensity factor coefficients for flaws on the outside surface of cylinders. The development of closed-form relations for stress intensity factor coefficients for axial flaws on the outside surface of cylinders is described in this paper.

Closed Form Solutions for Stress Intensity Factor Coefficients for Circumferential ID Surface Flaws in Cylinders in ASME Section XI Appendix A

2012 ◽  
Author(s):  
Russell C. Cipolla ◽  
Darrell R. Lee
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Flat Plate ◽  
Closed Form ◽  
Fourth Order ◽  
Surface Crack ◽  
Crack Size ◽  
Plate Geometry

The stress intensity factor (KI) equations for a surface crack in ASME Section XI, Appendix A are based on non-dimensional coefficients (Gi) that allow for the calculation of stress intensity factors for a cubic varying stress field. Currently, the coefficients are in tabular format for the case of a surface crack in a flat plate geometry. The tabular form makes the computation of KI tedious when determination of KI for various crack sizes is pursued and a flat plate geometry is conservative when applied to a cylindrical geometry. In this paper, closed-form equations are developed based on tabular data from API 579 (2007 Edition) [1] for circumferential cracks on the ID surface of cylinders. The closed-form equations provide G0 and G1 coefficients while G2 through G4 are obtained using a weight function representation for the KI solutions for a surface crack. These equations permit the calculation of the Gi coefficients without the need to perform tabular interpolation. The equations are complete up to a fourth order polynomial representation of applied stress, so that the procedures in Appendix A have been expanded. The fourth-order representation for stress will allow for more accurate fitting of highly non-linear stress distributions, such as those depicting high thermal gradients and weld residual stress fields. It is expected that the equations developed in this paper will be added to the Appendix A procedures. With the inclusion of equations to represent Gi, the procedures of Appendix A for the determination of KI can be performed more efficiently without the conservatism of using flat plate solutions. This is especially useful in performing flaw growth calculations where repetitive calculations are required in the computations of crack size versus time. The equations are relatively simple in format so that the KI computations can be performed by either spreadsheet analysis or by simple computer programming. The format of the equations is generic in that KI solutions for other geometries can be added to Appendix A relatively easily.

An Closed Form Solution for Antiplane Problem of Doubly Periodic Non-Uniform Cracks

2006 ◽  
Vol 324-325 ◽  
pp. 311-314
Author(s):  
Yao Ling Xu ◽  
Wen Feng Tan
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Mapping Technique ◽  
Inhomogeneous Materials ◽  
Antiplane Problem ◽  
Microstructure Parameters

Inhomogeneous materials with doubly periodic non-uniform cracks under antiplane shear is dealt with. By using conformal mapping technique and elliptic function theory, the stress field and stress intensity factor at the tip of each crack are derived in closed form. Numerical examples show the influences of some microstructure parameters of crack distribution on stress intensity factor.

scholarly journals A Continuum Theory of Crack Shielding in Ceramics

1987 ◽  
Vol 54 (1) ◽  
pp. 54-58 ◽  
Author(s):  
M. Ortiz
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Constitutive Model ◽  
Closed Form ◽  
Applied Stress ◽  
Continuum Theory ◽  
Displacement Fields ◽  
Stress Strain ◽  
Macroscopic Crack

A phenomenological constitutive model is proposed which aims at describing the overall effect of microfracture in ceramics. Based on this model, the asymptotic stress, strain, and displacement fields at the tip of a stationary macroscopic crack are determined in closed form. The near-tip stress-intensity factor is computed and observed to be significantly smaller than the applied stress-intensity factor even for moderate amounts of damage.

Investigation of Calculating Stress Intensity Factor at Surface Point and its Inclusion in Engineering Standards

2018 ◽  
Author(s):  
Steven X. Xu ◽  
Greg Thorwald ◽  
Patrick Le Delliou ◽  
Russell C. Cipolla
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Closed Form ◽  
Working Group ◽  
Surface Point ◽  
Evaluation Procedures ◽  
Influence Coefficients ◽  
Engineering Standards ◽  
Point G

Article A-3000 of Appendix A in ASME Section XI provides methods to calculate stress intensity factors that are used in Section XI linear elastic fracture mechanics based flaw evaluation procedures. The ASME Section XI Working Group on Flaw Evaluation has been in the process of rewriting Article A-3000 of Appendix A. The rewrite of Article A-3000 includes implementation of closed-form equations for stress intensity factor influence coefficients for cylinder geometries. Closed-form relations for stress influence coefficients G0 and G1 for axial flaws on the outside surface in cylinders were recently developed and implemented into the 2017 Edition of ASME Section XI Appendix A. The closed-form equations were implemented with one restriction on the application related to very long flaws. This restriction was taken as an interim approach to addressing a technical concern from the US NRC staff. NRC staff had technical concern on the large percentage fitting errors for the G1 influence coefficients at surface point for some very long flaws. An action was assigned within the ASME Section XI Working Group on Flaw Evaluation to investigate the accuracy of surface point G values for very long flaws. The intent of the investigation is to provide technical justification for using the closed-form equations with no restriction and to identify any issues in the source data or during the fitting process. This paper describes current results from this ongoing investigation.

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