Calculating Crack Opening Area for the Limited Plasticity Situation

2003 ◽  
Author(s):  
E. Smith
Keyword(s):  
Plastic Deformation ◽  
Stress Distribution ◽  
Crack Opening ◽  
Two Dimensional ◽  
Flow Properties ◽  
General Applicability ◽  
Tensile Stresses ◽  
Normal Operating ◽  
Elastic Crack ◽  
Leak Before Break

When formulating a leak-before-break case for a component in a pressurized system, it is essential to quantify the opening area associated with a crack that is subjected to the tensile stresses that are appropriate to normal operating situations. In a paper presented at the 2002 PVP Conference, the author presented a simple and exact method, based on the strip yield representation of plastic deformation, for calculating the area. The method was validated against the known result for the case of an isolated two-dimensional crack in a uniformly stressed infinite solid, but the method has general applicability. Special consideration was given to the case where plastic deformation is limited, as is usually appropriate for normal operating situations, and the method then simplifies considerably. This paper shows that the method, as it is applied to the limited plastic deformation situation, gives results which are the same as those obtained by use of the equivalent crack procedure, where an actual crack is replaced by an effective elastic crack, which is longer than the actual crack by an amount which is related to the flow properties of the material and the applied loadings. To illustrate the usefulness of the author’s method, it is applied to a specific stress distribution as might arise from a combination of pressure induced and weld residual tensile stresses.

A Simplified Method for Calculating Crack Opening Area

2002 ◽  
Author(s):  
E. Smith
Keyword(s):  
Plastic Deformation ◽  
Stress Distribution ◽  
Crack Opening ◽  
Two Dimensional ◽  
Simple Method ◽  
Tensile Stresses ◽  
Normal Operating ◽  
General Stress ◽  
Simplified Method ◽  
Leak Before Break

In the context of the formulation of a leak-before-break case for a component in a pressurized system, this paper is concerned with the quantification of the crack opening area associated with a two-dimensional crack that is subjected to tensile stresses. We present a simple method, based on the strip yield representation of plastic deformation, for calculating the area. The method is validated against the known result for the ease of an isolated crack in a uniformly stressed infinite solid. It is then used for a general stress distribution, as might arise from a combination of pressure induced and weld residual tensile stresses, with the considerations being focussed on the case where plastic deformation is limited, as is usually appropriate for normal operating situations; application of the method is then especially simple.

Crack Opening Area for an Isolated Crack Subjected to a Symmetric Mode I Stress Distribution

2004 ◽  
Author(s):  
E. Smith
Keyword(s):  
Stress Distribution ◽  
Crack Opening ◽  
Operating Conditions ◽  
Mode I ◽  
Stress Distributions ◽  
Simple Derivation ◽  
Opening Displacement ◽  
System A ◽  
Simplified Procedure ◽  
Leak Before Break

In developing a leak-before-break case for a component in a pressurized system, a key element is an estimation of the size of through-thickness crack that will give a measurable leakage under normal operating conditions, and this requires a knowledge of the crack opening area. In this context, the paper presents a simple derivation of an expression for the crack opening area associated with an isolated crack that is subjected to a general Mode I symmetric tensile stress distribution which could arise from a combination of applied and residual stresses. The paper also presents a simple derivation of an expression for the crack opening displacement at the crack centre which, coupled with the assumption that the crack opening profile conforms to an elliptical shape, has been used as the basis for a simplified procedure for estimating the crack opening area. The resulting expressions are validated by comparing them with known results for specific stress distributions. They are also used to give new results for a cosine stress distribution.

Estimation of Elastic Crack Opening Displacement for Thin Elbows With Circumferential Through-Wall Cracks

2015 ◽  
Author(s):  
Min-Kyu Kim ◽  
Han-Bum Surh ◽  
Min-Gu Won ◽  
Nam-Su Huh ◽  
Moon-Ki Kim ◽  
...  
Keyword(s):  
Crack Opening Displacement ◽  
Nuclear Power ◽  
Crack Opening ◽  
Three Dimensional ◽  
Opening Displacement ◽  
Dimensional Finite Element ◽  
Elastic Crack ◽  
Thin Walled ◽  
Three Dimensional Finite Element ◽  
Leak Before Break

Leak-before-break (LBB) is an important concept that could confirm design and integrity evaluation of nuclear power plant piping. For the LBB analysis, the detective leakage rate should be calculated for a through-wall cracked pipes. For this calculation, the crack opening displacement (COD) calculation is essential. Recently, sodium faster reactor (SFR) which has thin-walled pipes with Rm/t ranged 30–40 was introduced and then the investigation of these thin walled pipes and elbows has received great attention in the LBB evaluation. In this context, the three-dimensional finite element (FE) analyses for thin elbows with circumferential crack under in-plane bending are carried out to investigate the elastic COD values. Finally, the solution for elastic COD which can cover sufficiently thin elbow is successfully addressed.

Estimates of Elastic Crack Opening Displacements of Slanted Through-Wall Cracks in Plate and Cylinder

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
Nam-Su Huh ◽  
Do-Jun Shim ◽  
Yeon-Sik Yoo ◽  
Suhn Choi ◽  
Keun-Bae Park
Keyword(s):  
Finite Element ◽  
Crack Opening ◽  
Three Dimensional ◽  
Bending Moment ◽  
Element Model ◽  
Finite Element Analyses ◽  
Opening Displacement ◽  
Elastic Crack ◽  
Leak Before Break ◽  
The Finite Element Model

This paper provides tractable solutions for elastic crack opening displacement (COD) of slanted through-wall cracks in plates and cylinders. The solutions were developed via detailed three dimensional elastic finite element analyses. The COD values were calculated along the thickness at the center of the crack. As for the loading conditions, only remote tension was considered for the plates, whereas remote tension, global bending moment, and internal pressure were considered for the cylinders. The finite element model employed in the present analysis was verified by using existing solutions for a cylinder with an idealized circumferential through-wall crack. The present results can be used to evaluate leak rates of slanted through-wall cracks, which can be used as a part of a detailed leak-before-break analysis considering more realistic crack shape development.

The Departure from Equilibrium of Turbulent Boundary Layers

1968 ◽  
Vol 19 (1) ◽  
pp. 1-19 ◽  
Author(s):  
H. McDonald
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Kinetic Energy ◽  
Stress Distribution ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Two Dimensional ◽  
Pressure Distributions ◽  
Momentum Integral ◽  
State Examination

SummaryRecently two authors, Nash and Goldberg, have suggested, intuitively, that the rate at which the shear stress distribution in an incompressible, two-dimensional, turbulent boundary layer would return to its equilibrium value is directly proportional to the extent of the departure from the equilibrium state. Examination of the behaviour of the integral properties of the boundary layer supports this hypothesis. In the present paper a relationship similar to the suggestion of Nash and Goldberg is derived from the local balance of the kinetic energy of the turbulence. Coupling this simple derived relationship to the boundary layer momentum and moment-of-momentum integral equations results in quite accurate predictions of the behaviour of non-equilibrium turbulent boundary layers in arbitrary adverse (given) pressure distributions.

Numerical Solution of Elastoplastic Torsion of a Shaft of Rotational Symmetry

1949 ◽  
Vol 16 (2) ◽  
pp. 139-148
Author(s):  
R. P. Eddy ◽  
F. S. Shaw
Keyword(s):  
Plastic Deformation ◽  
Stress Distribution ◽  
Numerical Solution ◽  
Rotational Symmetry ◽  
Relaxation Methods ◽  
Elastoplastic Boundary ◽  
Sufficient Magnitude ◽  
Elastoplastic Torsion ◽  
Von Mises

Abstract Using relaxation methods, an approximate numerical solution is found of the stress distribution in a shaft of rotational symmetry, which is subjected to a torque of sufficient magnitude to cause portions of the material to yield. It is assumed that the material of which the shaft is composed is isotropic and yields according to the condition of von Mises. The particular problem investigated is a shaft with a collar; results are presented showing the elastoplastic boundary, and the stress distribution, for two different amounts of plastic deformation.

Prediction of the Initial Crack Tip Microstructure in a Single Crystal of CuAlNi

1999 ◽  
Author(s):  
Galyna M. Vasko ◽  
Perry H. Leo ◽  
Thomas W. Shield
Keyword(s):  
Stress Field ◽  
Single Crystal ◽  
Crack Opening ◽  
Crack Tip ◽  
Initial Crack ◽  
Single Edge ◽  
Opening Displacement ◽  
Elastic Crack ◽  
Maximum Work ◽  
Anisotropic Elastic

Abstract The austenite to martensite pseudoelastic transformation induced by the anisotropic elastic crack tip stress field in a single crystal of shape memory alloy is considered. It is proposed that the orientation of the initial austenite-martensite interface that forms can be predicted based on knowledge of the stress field, the crystallography of the transformation and one of two selection criteria. These criteria are based on the work of formation of the martensite in stress field and the crack opening displacement the martensite causes at the crack. Predictions of the criteria are compared to experiments on three single edge notched CuAlNi single crystal specimens. Results indicate that the maximum work criterion accurately predicts the orientation of the austenite-martensite interfaces that initially form near a crack.

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