Macrocrack-Microdefect Interaction

1986 ◽  
Vol 53 (3) ◽  
pp. 505-510 ◽  
Author(s):  
A. A. Rubinstein
Keyword(s):  
Stress Intensity Factor ◽  
Integral Equation ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Numerical Technique ◽  
Finite Size ◽  
Numerical Procedure ◽  
Complex Stress ◽  
Elastic Interactions ◽  
Crack Tip Geometry

Elastic interactions (in terms of the stress intensity factor variation) of the macrocrack (represented as semi-infinite crack) with microdefects such as finite size, arbitrarily positioned crack, circular hole or inclusion are considered. A solution for the problem of the interaction with dilational inclusion is also given. The influence of the crack tip geometry on the surrounding stress field is studied by analyzing the case of crack-hole coalescence. Problems are considered in terms of complex stress potentials for linear elasticity and formulated as a singular integral equation on the semi-infinite interval. A stable numerical technique is developed for the solution of such equations. In a particular case, in order to evaluate the accuracy of the numerical procedure, results obtained through the numerical procedure are compared with the available analytical solution and found to be in excellent agreement.

A Numerical Procedure for Estimating the Stress Intensity Factor of a Crack in a Finite Plate

1964 ◽  
Vol 86 (4) ◽  
pp. 681-684 ◽  
Author(s):  
A. S. Kobayashi ◽  
R. D. Cherepy ◽  
W. C. Kinsel
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
High Speed ◽  
Linear Equations ◽  
Infinite Plate ◽  
Numerical Procedure ◽  
Complex Stress ◽  
Theory Of Elasticity ◽  
Finite Plate

The advantages of the complex variable method are combined with the numerical procedure of collocation for estimating the stress intensity factors in finite, cracked plates subjected to in-plane loadings. In this approach, the complex stress functions for an infinite plate problem are modified to meet the boundary conditions for a finite plate with identical crack configuration. This procedure produces a system of linear equations which can be programmed readily on high-speed computers. The procedure is used to find the elastic stress intensity factor at the crack tip in a centrally notched plate in uniaxial tension. The resulting values are nearly identical to the stress intensity values determined analytically by the theory of elasticity. This numerical procedure should be useful for designers and analysts working in the fields of fracture mechanics and fail-safe concepts.

Edge Crack in an Elastic Strip on a Liquid Foundation

1989 ◽  
Vol 33 (03) ◽  
pp. 214-220
Author(s):  
Paul C. Xirouchakis ◽  
George N. Makrakis
Keyword(s):  
Stress Intensity Factor ◽  
Integral Equation ◽  
Fourier Transform ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Edge Crack ◽  
Applied Pressure ◽  
Theory Of Elasticity ◽  
Elastic Strip ◽  
Pressure Loading

The behavior of a long elastic strip with an edge crack resting on a liquid foundation is investigated. The faces of the crack are opened by an applied pressure loading. The deformation of the strip is considered within the framework of the linear theory of elasticity assuming plane-stress conditions. Fourier transform techniques are employed to obtain integral expressions for the stresses and displacements. The boundary-value problem is reduced to the solution of a Fredholm integral equation of the second kind. For the particular case of linear pressure loading, the stress-intensity factor is calculated and its dependence is shown on the depth of the crack relative to the thickness of the strip. Application of the present results to the problem of flexure of floating ice strips is discussed.

Stress Intensity Factor Calculation Using a Weight Function Method

2007 ◽  
Author(s):  
Rui Sun ◽  
Zongwen An ◽  
Hong-Zhong Huang ◽  
Qiming Ma
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Crack Propagation ◽  
Weight Function ◽  
Function Method ◽  
Method Comparison ◽  
Finite Size ◽  
Unstable Crack ◽  
Weight Function Method

Propagation of a critical unstable crack under the action of static or varying stresses is determined by the intensity of strain field at tips of the crack. Stress intensity factor (SIF) is an important parameter in fracture mechanics, which is used as a criterion to judge the unstable propagation of a crack and plays an important role in calculating crack propagation life. SIF is related to both geometrical form and loading condition of a structure. In the paper, a weight function method is introduced to study crack propagation of center through cracks and edge cracks in a finite-size plate. In addition, finite element method, linear regression, and polynomial interpolating technique are used to simulate and verify the proposed method. Comparison studies among the proposed and current methods are performed as well. The results show that the weight function method can be used to calculate SIF easily.

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.

Analysis of Residual Stresses and Assessment of Postulated Cracks in a Core Shroud Weld

2002 ◽  
Author(s):  
Igor Varfolomeyev ◽  
Dieter Siegele ◽  
Dieter Beukelmann
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Residual Stresses ◽  
Crack Depth ◽  
Numerical Procedure ◽  
Welding Process ◽  
Material Model ◽  
Finite Element Program ◽  
Core Shroud

In order to assess postulated cracks in weldments of a BWR core shroud residual stresses are calculated by simulating the welding process. In the numerical analysis, weld metal deposition and the sequence of weld passes follow the manufacture protocol. The calculations are performed using the finite element program ABAQUS and a material model with kinematic nonlinear hardening. Calculations of the crack driving parameter, the stress intensity factor, are carried out for postulated circumferential cracks using a numerical procedure, as well as by applying a weight function solution specially developed for cracks in a thin-walled cylinder. The results give rise to a discussion on the validity of linear elastic fracture mechanics for assessing defects in weldments. Additionally, for a complete circumferential crack the trend in the stress intensity factor is studied when the crack depth approaches the full wall thickness.

scholarly journals Stress Intensity Factor for Interface Cracks in Bimaterials Using Complex Variable Meshless Manifold Method

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Hongfen Gao ◽  
Gaofeng Wei
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Complex Variable ◽  
Interfacial Crack ◽  
Dissimilar Materials ◽  
Complex Stress ◽  
Interface Cracks ◽  
Interfacial Cracks ◽  
Crack Problems

This paper describes the application of the complex variable meshless manifold method (CVMMM) to stress intensity factor analyses of structures containing interface cracks between dissimilar materials. A discontinuous function and the near-tip asymptotic displacement functions are added to the CVMMM approximation using the framework of complex variable moving least-squares (CVMLS) approximation. This enables the domain to be modeled by CVMMM without explicitly meshing the crack surfaces. The enriched crack-tip functions are chosen as those that span the asymptotic displacement fields for an interfacial crack. The complex stress intensity factors for bimaterial interfacial cracks were numerically evaluated using the method. Good agreement between the numerical results and the reference solutions for benchmark interfacial crack problems is realized.

Analytical Solutions and Tools for Assessment of Surface Cracks in Cylindrical Components

2008 ◽  
Author(s):  
Igor Varfolomeyev ◽  
Dieter Beukelmann
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Fatigue Loading ◽  
Complex Stress ◽  
Radial Coordinate ◽  
Cylinder Wall ◽  
Crack Plane ◽  
Surface Cracks ◽  
Inner Radius

The paper reviews some advanced stress intensity factor solutions derived for analyses of axial and circumferential surface cracks in cylindrical components subjected to variable stress fields. The solutions are examined considering their validity ranges with respect to the crack and cylinder geometry, ability to account for a complex stress distribution in the pipe wall, as well as their accuracy. A method for estimating errors in numerical stress intensity factor solutions is introduced and applied to a particular set of data. Examples of a leak-before-break assessment and crack growth calculations under thermal fatigue loading are included to demonstrate the solutions performance. The considered analytical stress intensity factor solutions yield close results provided that the stress field in the prospective crack plane is described by a smooth function of the radial coordinate. For two-dimensional stress profiles as well as for variable ratios of the cylinder wall thickness to the inner radius, a selective use of the solutions is recommended considering their specific features and validity ranges.

Stress-Intensity Factor for a Short Edge-Notched Specimen Subjected to Three-Point Loading

1967 ◽  
Vol 89 (1) ◽  
pp. 7-12 ◽  
Author(s):  
H. T. Akao ◽  
A. S. Kobayashi
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Aspect Ratio ◽  
Intensity Factor ◽  
Numerical Technique ◽  
Bending Moment ◽  
Mapping Function ◽  
Notched Specimen ◽  
Short Edge ◽  
Aspect Ratios

Stress-intensity factors for a short edge-notched specimen with an aspect ratio of appoximately 2.7:1 and subjected to three-point loading were obtained by using Bowie’s numerical technique of expanding a mapping function. Numerical relations between the mapping function, aspect ratios, and crack depths of different specimens as well as numerical difficulty in convergence of the procedure are discussed. The results are compared with the nondimensionalized experimental results obtained by Kies, et al., for a larger aspect ratio of 8:1. The proportionality factor between bending moment and stress-intensity factor was approximately 10 percent lower than the corresponding factor for Kies’ specimen and is in substantial agreement with Gross’ results.

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