Fracture Behavior of Finite Length Part Through Wall Flaws in Zirconium-Niobium Pressure Tubes

2006 ◽  
Author(s):  
Don R. Metzger ◽  
Gordon K. Shek ◽  
Ed T. C. Ho
Keyword(s):  
Finite Length ◽  
Process Zone ◽  
Three Dimensional ◽  
Analytical Techniques ◽  
Fracture Initiation ◽  
Zirconium Hydride ◽  
Experimental Program ◽  
Two Dimensional ◽  
Finite Element Program ◽  
Pressure Tubes

Flaws encountered in nuclear pressure tubes must be evaluated to ensure that a delayed hydride cracking (DHC) mechanism is not initiated where the stress concentration at a flaw tip causes diffusion of hydrogen and precipitation of zirconium hydride at the flaw tip. A fracture initiation model for DHC involves a process zone description for the interaction of hydride precipitation with the flaw tip stress distribution. Analytical techniques for this model are practical and accurate for two-dimensional geometry, but cannot be easily applied to the three-dimensional features of finite length surface flaws. Recently, a numerical rendition of the model has been incorporated into a finite element program so that arbitrary geometry and material properties can be managed. The three-dimensional finite length model is applied to specific flaw geometries used in an experimental program. Comparison with corresponding two-dimensional tests demonstrates that the finite length flaw has a significantly higher threshold load than that predicted on the basis of a two-dimensional model.

Contracting ducts of finite length

1951 ◽  
Vol 2 (4) ◽  
pp. 254-271 ◽  
Author(s):  
L. G. Whitehead ◽  
L. Y. Wu ◽  
M. H. L. Waters
Keyword(s):  
Stream Function ◽  
Finite Length ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Relaxation Method ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Hodograph Plane ◽  
Two Dimensional Flow ◽  
Working Section

SummmaryA method of design is given for wind tunnel contractions for two-dimensional flow and for flow with axial symmetry. The two-dimensional designs are based on a boundary chosen in the hodograph plane for which the flow is found by the method of images. The three-dimensional method uses the velocity potential and the stream function of the two-dimensional flow as independent variables and the equation for the three-dimensional stream function is solved approximately. The accuracy of the approximate method is checked by comparison with a solution obtained by Southwell's relaxation method.In both the two and the three-dimensional designs the curved wall is of finite length with parallel sections upstream and downstream. The effects of the parallel parts of the channel on the rise of pressure near the wall at the start of the contraction and on the velocity distribution across the working section can therefore be estimated.

Delayed Hydride Cracking Initiation at Simulated Secondary Flaws in Zr-2.5 Nb Pressure Tube Material

2004 ◽  
Author(s):  
Jun Cui ◽  
Gordon K. Shek ◽  
Douglas A. Scarth ◽  
William K. Lee
Keyword(s):  
Hydrogen Diffusion ◽  
Process Zone ◽  
Pressure Tube ◽  
Experimental Program ◽  
Small Surface ◽  
Integrity Assessment ◽  
Pressure Tubes ◽  
Delayed Hydride Cracking ◽  
The Impact ◽  
Hydride Cracking

Flaws in Zr-2.5 Nb alloy pressure tubes of CANDU nuclear reactors are susceptible to a crack initiation and growth mechanism called Delayed Hydride Cracking (DHC), which is a repetitive process that involves hydrogen diffusion, hydride precipitation, growth of the hydrided region and fracture of the hydrided region at the flaw-tip. The presence of small surface irregularities, or secondary flaws, at the bottom of service-induced fretting flaws in pressure tubes requires an integrity assessment in terms of DHC initiation. Experimental data and analytical modeling are required to predict whether DHC initiation can occur from the secondary flaws. In the present work, an experimental program was carried out to examine the impact of small secondary flaws with sharp radii on DHC initiation from simulated fretting flaws. Groups of cantilever beam specimens containing blunt notches with and without secondary flaws were prepared from unirradiated pressure tube materials hydrided to a nominal concentration of 50 wt ppm hydrogen. The specimens were subjected to multiple thermal cycles to form hydrides at the flaw-tip at different applied stress levels, which straddled the threshold value for DHC initiation. The threshold conditions for DHC initiation were established for different simulated fretting and secondary flaws. The experimental results are compared with predictions from the engineering process-zone DHC initiation model.

Effect of Flaw Orientation on Delayed Hydride Crack Initiation in Zr-2.5Nb Pressure Tubes

2013 ◽  
Author(s):  
Gordon K. Shek ◽  
Jun Cui ◽  
Douglas A. Scarth ◽  
Steven Xu
Keyword(s):  
Stress Concentrator ◽  
Hydrogen Diffusion ◽  
Process Zone ◽  
Axial Direction ◽  
Pressure Tube ◽  
Experimental Program ◽  
Evaluation Procedure ◽  
Oblique Angle ◽  
Repetitive Process ◽  
Pressure Tubes

The Zr-2.5Nb pressure tubes of CANDU reactor are susceptible to a cracking mechanism known as Delayed Hydride Cracking (DHC), which is a repetitive process that involves hydrogen diffusion, hydride precipitation and fracture at a stress concentrator such as a flaw or a crack. Service-induced flaws are present in some pressure tubes and they need to be assessed for susceptibility to DHC initiation. An engineering procedure based on the process-zone methodology has been developed and incorporated into the Canadian standard to determine the susceptibility of flaws in pressure tubes to DHC initiation. The engineering procedure was validated against experiments on flaws which were oriented in the axial direction of the pressure tube. However, many of the service-induced flaws are oriented at some oblique angle with respect to the axial direction of the tube and they may have higher threshold stresses for DHC initiation than those of the axial flaws. It would be advantageous to apply the process-zone evaluation procedure to such angled blunt flaws. For this purpose, an experimental study was carried out to measure the threshold stresses for DHC initiation from machined V-notches with different orientations (0°, 15°, 30° and 45°) with respect to the axial direction of an unirradiated pressure tube. The experimental results were used to support the development of the evaluation procedure for angled blunt flaws. The experimental program and the validation of the engineering procedure for angled blunt flaws are described in this paper.

A Three-Dimensional Theory for Calculating Circulation in Axial Turbomachines (Direct Problems)

1974 ◽  
Vol 96 (4) ◽  
pp. 365-371
Author(s):  
E. Lumsdaine ◽  
A. Fathy
Keyword(s):  
Finite Length ◽  
Three Dimensional ◽  
Tip Clearance ◽  
Two Dimensional ◽  
Line Theory ◽  
Large Length ◽  
Circulation Distribution ◽  
Direct Problems ◽  
Lifting Line ◽  
Lifting Line Theory

In this work the steady-state spanwise circulation distribution of thin, slightly cambered radial blades of finite length is calculated using the method of singularities. The analysis extends the method of Scholz [1] for two-dimensional cascades to the three-dimensional case of radial blades of finite length. The effect of the casing enclosing the cascade is introduced by the method of images. The present analysis uses the generalized cylindrical coordinates without the restriction of the Prandtl lifting line theory. Comparisons show that for large hub-tip ratios, the use of the lifting line approximation will result in large errors. For small tip clearance or large length-chord ratio the present results reduce to the two-dimensional cascade solution.

scholarly journals Mixed Boundary-Value Problems in Potential Theory

1979 ◽  
Vol 22 (2) ◽  
pp. 91-98 ◽  
Author(s):  
A. H. England
Keyword(s):  
Boundary Value Problems ◽  
Potential Theory ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Three Dimensional ◽  
Analytical Techniques ◽  
Mixed Boundary Conditions ◽  
Two Dimensional ◽  
Axially Symmetric ◽  
Mixed Boundary Value Problems

The problems associated with finding solutions of Laplace's equation subject to mixed boundary conditions have attracted much attention and, as a consequence, a variety of analytical techniques have been developed for the solution of such problems. Sneddon (1) has given a comprehensive account of these techniques. The object of this note is to draw attention to some simple orthogonal polynomial solutions to the most basic mixed boundary-value problems in two and threedimensional potential theory. These solutions have the advantage that most quantities of physical interest are easily evaluated in terms of known functions. Two-dimensional problems are considered in §2 and axially-symmetric three-dimensional problems in §3.

Analysis of a Caisson Retained Island

1988 ◽  
Vol 110 (2) ◽  
pp. 68-76
Author(s):  
E. Evgin ◽  
S. Lord ◽  
I. Konuk
Keyword(s):  
Finite Element ◽  
Dimensional Analysis ◽  
Three Dimensional ◽  
General Purpose ◽  
Two Dimensional ◽  
Nonlinear Analyses ◽  
Stress Strain ◽  
Finite Element Program ◽  
Stress Strain Relation ◽  
Element Program

The results of the two and three-dimensional, nonlinear analyses of a caisson retained island in the Beaufort Sea are presented. A hyperbolic stress-strain relation for soils has been implemented in a general purpose finite element program, ADINA, to carry out the analysis. Based on the comparisons of the results, conclusions were drawn about whether a two-dimensional analysis can be safely used to replace a three-dimensional analysis.

High Resolution Microscopy of Multi-Layered Biological Crystals

1982 ◽  
Vol 40 ◽  
pp. 80-83
Author(s):  
H.A. Cohen ◽  
T.W. Jeng ◽  
W. Chiu
Keyword(s):  
High Resolution ◽  
Low Dose ◽  
Three Dimensional ◽  
Data Interpretation ◽  
Two Dimensional ◽  
Biological Objects ◽  
Density Maps ◽  
Density Map ◽  
Complex Crystal ◽  
High Resolution Microscopy

This tutorial will discuss the methodology of low dose electron diffraction and imaging of crystalline biological objects, the problems of data interpretation for two-dimensional projected density maps of glucose embedded protein crystals, the factors to be considered in combining tilt data from three-dimensional crystals, and finally, the prospects of achieving a high resolution three-dimensional density map of a biological crystal. This methodology will be illustrated using two proteins under investigation in our laboratory, the T4 DNA helix destabilizing protein gp32*I and the crotoxin complex crystal.

Instrumentation For Quantitative Microscopy

1977 ◽  
Vol 35 ◽  
pp. 206-209
Author(s):  
B. Ralph ◽  
A.R. Jones
Keyword(s):  
Volume Fraction ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Automatic Data ◽  
Phase Volume Fraction ◽  
Statistical Confidence ◽  
Resultant Data ◽  
Automatic Data Collection ◽  
Third Dimension ◽  
Evolution Of Microstructure

In all fields of microscopy there is an increasing interest in the quantification of microstructure. This interest may stem from a desire to establish quality control parameters or may have a more fundamental requirement involving the derivation of parameters which partially or completely define the three dimensional nature of the microstructure. This latter categorey of study may arise from an interest in the evolution of microstructure or from a desire to generate detailed property/microstructure relationships. In the more fundamental studies some convolution of two-dimensional data into the third dimension (stereological analysis) will be necessary.In some cases the two-dimensional data may be acquired relatively easily without recourse to automatic data collection and further, it may prove possible to perform the data reduction and analysis relatively easily. In such cases the only recourse to machines may well be in establishing the statistical confidence of the resultant data. Such relatively straightforward studies tend to result from acquiring data on the whole assemblage of features making up the microstructure. In this field data mode, when parameters such as phase volume fraction, mean size etc. are sought, the main case for resorting to automation is in order to perform repetitive analyses since each analysis is relatively easily performed.

A linearity test for thick specimens imaged by HVEM over a 180° angular range

1991 ◽  
Vol 49 ◽  
pp. 552-553
Author(s):  
Yu Liu
Keyword(s):  
Phase Contrast ◽  
Three Dimensional ◽  
Angular Range ◽  
Two Dimensional ◽  
Back Projection ◽  
Line Integral ◽  
Exponential Law ◽  
Transmission Electron ◽  
Absorption Law ◽  
Linearity Test

The image obtained in a transmission electron microscope is the two-dimensional projection of a three-dimensional (3D) object. The 3D reconstruction of the object can be calculated from a series of projections by back-projection, but this algorithm assumes that the image is linearly related to a line integral of the object function. However, there are two kinds of contrast in electron microscopy, scattering and phase contrast, of which only the latter is linear with the optical density (OD) in the micrograph. Therefore the OD can be used as a measure of the projection only for thin specimens where phase contrast dominates the image. For thick specimens, where scattering contrast predominates, an exponential absorption law holds, and a logarithm of OD must be used. However, for large thicknesses, the simple exponential law might break down due to multiple and inelastic scattering.

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