The Effect of Crack Length Unevenness on Stress Intensity Factors Due to Autofrettage in Thick-Walled Cylinders

1997 ◽  
Vol 119 (3) ◽  
pp. 274-278 ◽  
Author(s):  
M. Perl ◽  
D. Alperowitz
Keyword(s):  
Stress Intensity ◽  
Crack Length ◽  
Stress Intensity Factors ◽  
Relative Length ◽  
Intensity Factors ◽  
Residual Stress Field ◽  
Interaction Range ◽  
Wide Range ◽  
Level Model ◽  
Radial Cracks

The effect of crack length unevenness on the mode I stress intensity factors (SIFs) for large uniform arrays of radial cracks of unequal depth in fully or partially autofrettaged thick-walled cylinders is investigated. The analysis is based on the previously proposed “two-crack-length level model.” Values for KIA—the SIF due to the compressive residual stress field—for various crack arrays bearing n1 = n2 = 2−512 cracks, a wide range of nondimensional crack lengths l1/a=0.01−0.1, and numerous levels of autofrettage ε = 30−100 percent are evaluated by the finite element method for a cylinder of radii ratio of b/a = 2. The interaction range for different combinations of crack arrays and crack length is then determined. The obtained results show that the unevenness in the SIFs depends on all three parameters, i.e., the number of cracks in the array, the cracks’ lengths, and the level of autofrettage, while the interaction range between adjacent cracks is determined only by the relative length of the cracks and the density of the array.

Uniform Arrays of Unequal-Depth Cracks in Thick-Walled Cylindrical Pressure Vessels—Part I: Stress Intensity Factors Evaluation

1990 ◽  
Vol 112 (4) ◽  
pp. 340-345 ◽  
Author(s):  
M. Perl ◽  
K. H. Wu ◽  
R. Arone´
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Initial Crack ◽  
Pressure Vessels ◽  
Intensity Factors ◽  
Interaction Range ◽  
Sequence Of Events ◽  
Wide Range ◽  
Final Failure ◽  
Level Model

The influence of the unevenness of crack lengths on the mode I stress intensity factors (SIF) for large uniform arrays of radial cracks of unequal depth in thick-walled pressurized cylinders is investigated applying the previously proposed “two-crack-length level model.” Using the finite element method, SIFs are evaluated for numerous configurations of crack arrays bearing a wide range of crack lengths. The interaction range for various combinations of crack arrays and crack lengths is then determined. The numerical results anticipate that any statistical unevenness of the initial crack lengths, prevailing in the pressurized cylinder, will be amplified during the process of fatigue crack growth. Thus, while the fatigue life of the vessel is determined by a large number of cracks, its final failure, which is governed by a small number of the largest cracks, is likely to be caused by one major crack, as is usually the case. This sequence of events results from the particular nature of the inter-crack stress field, which is analyzed and discussed in detail in Part II of the paper.

Stress Intensity Factors for a Radially Multicracked Partially Autofrettaged Pressurized Thick-Walled Cylinder

1988 ◽  
Vol 110 (2) ◽  
pp. 147-154 ◽  
Author(s):  
M. Perl ◽  
R. Arone´
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Favorable Effect ◽  
The Finite Element Method ◽  
Intensity Factors ◽  
Slowing Down ◽  
Wide Range ◽  
Radial Cracks ◽  
Compressive Residual Stresses ◽  
Walled Cylinder

Mode I stress intensity factors for crack arrays of up to 1024 equal radial cracks originating at the inner surface of a partially autofrettaged, pressurized thick-walled cylinder are evaluated. Both stress intensity factors i.e., KIp due to the pressurization, and the negative KIA due to the compressive residual stresses, are calculated for numerous crack arrays (n = 2–1024), a wide range of nondimensional crack lengths (1/a = 0.005–0.625), and various levels of autofrettage (ε = 30, 60, 100 percent) via the finite element method. The obtained results emphasize the notable significance of the number of cracks in the array, as well as the importance of the level of autofrettage, on the stress intensity factor prevailing at the tip of these cracks. The sensitivity of the favorable effect of the overstrain in slowing down fatigue crack growth to any decrease in the level of autofreggate is also discussed.

The Effect of Autofrettage on Uniform Arrays of Three-Dimensional Unequal-Depth Cracks in a Thick-Walled Cylindrical Vessel

2004 ◽  
Vol 127 (4) ◽  
pp. 423-429 ◽  
Author(s):  
M. Perl ◽  
B. Ostraich
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Crack Depth ◽  
Three Dimensional ◽  
Residual Stress Field ◽  
Depth Level ◽  
Interaction Range ◽  
Wide Range ◽  
Level Model

The distribution of the mode I stress intensity factor (SIF), resulting from autofrettage, along the fronts of radial, semi-elliptical surface cracks pertaining to large uniform arrays of unequal-depth cracks emanating at the bore of an overstrained thick-walled cylinder is studied. The three-dimensional analysis is based on the “two-crack depth level model” previously proposed and is performed via the finite element method employing singular elements along the crack front. The autofrettage residual stress field is simulated using an equivalent thermal load. The distribution of KIA, the stress intensity factor due to autofrettage, for numerous uneven array configurations bearing n=n1+n2=8-128 cracks, a wide range of crack depth-to-wall thickness ratios, a1∕t=0.01-0.4, and various crack ellipticities, a1∕c1=0.3-1.5, are evaluated for a cylinder of radii ratio Ro∕Ri=2. The results clearly indicate that unevenness, as reflected in KIA distribution, depends on all three parameters (i.e., the number of cracks in the array, cracks’ depth, and cracks’ ellipticity). The “interaction range” for the different combinations of crack arrays and crack depths is then evaluated. The range of influence between adjacent cracks on the maximal SIF, KAmax, is found to be dependent on the density of the array, as reflected in the intercrack aspect ratio, as well as on the cracks’ ellipticity.

Determination of Stress Intensity Factors for Gradient Stress Fields

1977 ◽  
Vol 99 (3) ◽  
pp. 477-484 ◽  
Author(s):  
J. M. Bloom ◽  
W. A. Van Der Sluys
Keyword(s):  
Stress Intensity ◽  
Crack Length ◽  
Stress Intensity Factors ◽  
Maximum Stress ◽  
Nuclear Industry ◽  
Stress Fields ◽  
Polynomial Method ◽  
Intensity Factors ◽  
Asme Code ◽  
Linear Envelope

This paper evaluates eight different analytical procedures used in determining elastic stress intensity factors for gradient or nonlinear stress fields. From a fracture viewpoint, the main interest in this problem comes from the nuclear industry where the safety of the nuclear system is of concern. A fracture mechanics analysis is then required to demonstrate the vessel integrity under these postulated accident conditions. The geometry chosen for his study is that of a 10-in. thick flawed plate with nonuniform stress distribution through the thickness. Two loading conditions are evaluated, both nonlinear and both defined by polynomials. The assumed cracks are infinitely long surface defects. Eight methods are used to find the stress intensity factor: 1–maximum stress, 2–linear envelope, 3–linearization over the crack length from ASME Code, Section XI, 4–equivalent linear moment from ASME Code, Section III, Appendix G for thermal loadings, 5–integration method from WRC 175, Appendix 4 for thermal loadings, 6–8-node singularity (quarter-point) isoparametric element in conjunction with the displacement method, 7–polynomial method, and 8–semi-infinite edge crack linear distribution over crack. Comparisons are made between all eight procedures with the finding that the methods can be ranked in order of decreasing conservatism and ease of application as follows: 1–maximum stress, 2–linear envelope, 3–linearization over the crack length, 4–polynomial method, and 5–singularity element method. Good agreement is found between the last three of these methods. The remaining three methods produce nonconservative results.

Experimental Determination of Side Boundary Effects on Stress Intensity Factors in Surface Flaws

1975 ◽  
Vol 97 (1) ◽  
pp. 45-51 ◽  
Author(s):  
M. Jolles ◽  
J. J. McGowan ◽  
C. W. Smith
Keyword(s):  
Stress Intensity ◽  
Crack Length ◽  
Taylor Series ◽  
Stress Intensity Factors ◽  
Taylor Series Expansion ◽  
Correction Method ◽  
Intensity Factors ◽  
Surface Flaws ◽  
Plate Width

A technique consisting of stress-freezing photoelasticity coupled with a Taylor Series Expansion of the maximum local in-plane shearing stress known as the Taylor Series Correction Method (TSCM) is applied to the determination of stress intensity factors (SIF’s) in flat bottomed surface flaws of flaw depth/length ratios of approximately 0.033. Flaw depth/thickness ratios of approximately 0.20 and 0.40 were studied as were plate width/crack length ratios of approximately 2.33 and 1.25, the former of which corresponded to a nearly infinite width. Agreement to well within 10 percent was found with the Rice-Levy and Newman theories using a depth-modified secant correction and equivalent flaw depth/length ratios. The Shah-Kobayashi Theory, when compared on the same basis, was lower than the experimental results. Using a modified net section stress correction suggested by Shah, agreement with the Shah-Kobayashi Theory was greatly improved but agreement with the other theories was poorer. On the basis of the experiments alone, it was found that the SIF was intensified by about 10 percent by decreasing the plate width/crack length from 2.33 to 1.25.

scholarly journals Influence Coefficients to Calculate Stress Intensity Factors for an Elliptical Crack in a Plate

2002 ◽  
Author(s):  
Patrick Le Delliou ◽  
Bruno Barthelet
Keyword(s):  
Finite Element ◽  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Atomic Energy Commission ◽  
Finite Thickness ◽  
Elliptical Crack ◽  
Intensity Factors ◽  
Normal Loading ◽  
Influence Coefficients ◽  
Wide Range

Crack assessment in engineering structures relies first on accurate evaluation of the stress intensity factors. In recent years, a large work has been conducted in France by the Atomic Energy Commission to develop influence coefficients for surface cracks in pipes. However, the problem of embedded cracks in plates (and pipes) which is also of practical importance has not received so much attention. Presently, solutions for elliptical cracks are available either in infinite solid with a polynomial distribution of normal loading or in plate, but restricted to constant or linearly varying tension. This paper presents the work conducted at EDF R&D to obtain influence coefficients for plates containing an elliptical crack with a wide range of the parameters: relative size (2a/t ratio), shape (a/c ratio) and crack eccentricity (2e/t ratio where e is the distance from the center of the ellipse to the plate mid plane). These coefficients were developed through extensive 3D finite element calculations: 200 geometrical configurations were modeled, each containing from 18000 to 26000 nodes. The limiting case of the tunnel crack (a/c = 0) was also analyzed with 2D finite element calculation (50 geometrical configurations). The accuracy of the results was checked by comparison with analytical solutions for infinite solids and, when possible, with solutions for finite-thickness plates (generally loaded in constant tension). These solutions will be introduced in the RSE-M Code that provides rules and requirements for in-service inspection of French PWR components.

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