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.

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.

scholarly journals Stress Intensity Factor of an Edge Interface Crack in a Bonded Semi-Infinite Plate

2010 ◽  
Vol 76 (770) ◽  
pp. 1270-1277 ◽  
Author(s):  
Nao-Aki NODA ◽  
Xin LAN ◽  
Kengo MICHINAKA ◽  
Yu ZHANG ◽  
Kazuhiro ODA
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Interface Crack ◽  
Infinite Plate

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.

An Infinite Plate Weakened by Periodic Cracks

2002 ◽  
Vol 69 (4) ◽  
pp. 552-555 ◽  
Author(s):  
Y. Z. Chen ◽  
K. Y. Lee
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Eigenfunction Expansion ◽  
Infinite Plate ◽  
Elastic Response ◽  
Shear Stresses ◽  
Orthotropic Medium ◽  
T Stress ◽  
Periodic Cracks

An infinite plate weakened by doubly distributing cracks is studied in this paper. Two loading cases, the remote tension and the remote shear stresses, are assumed. Analysis is performed for a cracked cell cut from the infinite plate. It is found that the eigenfunction expansion variational method is efficient to solve the problem. The stress intensity factor, the T-stress, and the elastic response are evaluated. The cracked plate can be equivalent to an orthotropic medium without cracks. The equivalent elastic constants are presented.

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.

Modified Analytical Method for Stress Intensity Factor Calculation of Infinite MSD Plate Containing Multiple Holes

2010 ◽  
Vol 118-120 ◽  
pp. 269-273
Author(s):  
Jin Fang Zhao ◽  
Li Yang Xie ◽  
Jian Zhong Liu ◽  
Qun Zhao
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Analytical Method ◽  
Fatigue Cracks ◽  
Infinite Plate ◽  
Superposition Method ◽  
Typical Structure ◽  
Two Circular Holes ◽  
Multiple Holes

Multiple site damage (MSD) is the occurrence of small fatigue cracks at several sites within aging aircraft structures. Focusing on this typical structure, an analytical method for calculating the stress intensity factor (SIF) of an infinite plate containing multiple holes was introduced in this paper. The properties of complex variable functions are used to evaluate the stress function. The approximate superposition method is applied to solve SIF problems on multiple holes. Some numerical examples of radial cracks appearing at the boundary of two circular holes are examined by this method. By comparing the analytical and finite analysis results it was realized that the analytical results are accurate and reliable. This modified analytical method is easier to apply than traditional analytical method and can provide SIF solutions for an infinite plate containing multiple holes.

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