Stress Intensity Factor Solutions for Narrow Plates

2014 ◽  
Vol 891-892 ◽  
pp. 784-790
Author(s):  
Matthew J. Hammond ◽  
Scott A. Fawaz
Keyword(s):  
Stress Intensity ◽  
Crack Depth ◽  
Three Dimensional ◽  
Sheet Thickness ◽  
Solution Space ◽  
Analytical Investigation ◽  
Crack Growth Behavior ◽  
Finite Width ◽  
Wide Range ◽  
Corner Cracks

Accurate quantification of crack tip stress intensity values is paramount in the analysis of damage tolerant structures. The present analytical investigation seeks to determine the stress intensity solutions for crack geometries outside the existing valid solution space and expand the analysts ability to capture representative crack growth behavior. The focus of this investigation is to calculate the stress intensity factors of single quarter-elliptical corner cracks emanating from centrally located holes in finite width plates under various loading conditions (remote tension, bending, and pin loading). Many of the available finite width corrections are singled valued and universally applied to all locations along the crack front. Early investigations into the validity of this application indicated that this correction procedure produces stress intensity values +/- 30% from new solutions. The crack depth to length ratio and depth to thickness ratio can also significantly influence the accuracy of historical finite width solutions and corrections. The analytical investigation utilizes the three dimensional virtual crack closure technique and well-structured, completely hexahedral, element meshes. Stress intensity values are generated for a wide range of ratios for crack depth to crack length, crack depth to sheet thickness, hole radius to sheet thickness, and sheet width to hole diameter. This effort is being executed under a US DoD Technical Corrosion Collaboration program.

3-D Stress Intensity Factors for Internal Cracks in an Overstrained Cylindrical Pressure Vessel—Part I: The Effect of Autofrettage Level

2000 ◽  
Vol 122 (4) ◽  
pp. 421-426 ◽  
Author(s):  
M. Perl ◽  
A. Nachum
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Crack Depth ◽  
Three Dimensional ◽  
Internal Surface ◽  
Favorable Effect ◽  
Residual Stress Field ◽  
Fe Method ◽  
Wide Range

Three-dimensional, mode I, stress intensity factor (SIF) distributions for arrays of internal surface cracks emanating from the bore of an autofrettaged thick-walled cylinder are evaluated in Part I of this paper. The 3-D analysis is performed via the finite element (FE) method and the submodeling technique, employing singular elements along the crack front. The autofrettage residual stress field is simulated using an equivalent temperature field. More than 200 different crack configurations were analyzed. SIFs for numerous crack arrays (n=1–180 cracks), a wide range of crack-depth-to-wall-thickness ratios a/t=0.05-0.6, various ellipticities a/c=0.2-1.5, and different levels of autofrettage (e=10–100 percent) were evaluated. The results clearly indicate the importance of autofrettage in reducing the effective stress intensity factor, and thus, slowing the crack growth rate. The sensitivity of this favorable effect to the number of cracks in the array as well as to the level of autofrettage are also discussed. The combined effect of pressure and autofrettage is discussed in detail in Part II of this paper. [S0094-9930(00)00604-1]

The Influence of the Bauschinger Effect on 3D Stress Intensity Factors for Internal Radial Cracks in a Fully or Partially Autofrettaged Gun Barrel

2005 ◽  
Vol 128 (2) ◽  
pp. 233-239 ◽  
Author(s):  
M. Perl ◽  
C. Levy ◽  
V. Rallabhandy
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Crack Front ◽  
Bauschinger Effect ◽  
Crack Depth ◽  
Three Dimensional ◽  
Crack Plane ◽  
3D Analysis ◽  
Wide Range

The influence of the Bauschinger effect (BE) on the three-dimensional, mode I, stress intensity factor (SIF) distributions for arrays of radial, internal, surface cracks emanating from the bore of a fully or partially autofrettaged thick-walled cylinder is investigated. A thorough comparison between the prevailing SIFs for a “realistic” (Bauschinger effect dependent autofrettage (BEDA)) and those for an “ideal” (Bauschinger effect independent autofrettage (BEIA)) is done. The three-dimensional (3D) analysis is performed via the finite element method and the submodeling technique, employing singular elements along the crack front. Both autofrettage residual stress fields, BEDA and BEIA, are simulated using an equivalent temperature field. More than 300 different crack configurations are analyzed. SIFs for numerous crack arrays (n=1-64 cracks), a wide range of crack depth to wall thickness ratios (a∕t=0.01-0.2), various ellipticities (a∕c=0.5-1.5), and different levels of autofrettage (ε=30-100%) are evaluated. The Bauschinger Effect is found to considerably lower the beneficial stress intensity factor due to autofrettage, KIA, by up to 56%, as compared to the case of ideal autofrettage. The reduction in KIA varies along the crack front with a maximum at the point of intersection between the crack plane and the inner surface of the cylinder, decreasing monotonically toward the deepest point of the crack. The detrimental influence of the BE increases as the number of cracks in the array increases and as crack depth decreases. For a partially autofrettaged cylinder, as the level of overstrain becomes smaller the influence of the BE is considerably reduced. As a result, the SIFs due to 100% BEDA differ by <10% as compared to 60% BEDA, and on the average the difference is only about 2–4%.

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.

Analysis of Uniform Arrays of Three-Dimensional Unequal-Depth Cracks in a Thick-Walled Cylindrical Pressure Vessel

2003 ◽  
Vol 125 (4) ◽  
pp. 425-431 ◽  
Author(s):  
M. Perl ◽  
B. Ostraich
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Crack Depth ◽  
Three Dimensional ◽  
Fe Method ◽  
Depth Level ◽  
Interaction Range ◽  
Wide Range ◽  
Displacement Extrapolation Method

The effect of crack depth unevenness on the mode I stress intensity factor (SIF) distributions along the fronts of semi-elliptical surface cracks is studied. These three-dimensional radial cracks pertain to large uniform arrays of unequal-depth cracks emanating from the bore of a pressurized thick-walled cylinder. The analysis is based on the “two crack depth level model,” previously proposed, and is performed via the finite element (FE) method employing singular elements along the crack front. The distribution of KIP-the stress intensity factor due to pressurization, for numerous uneven array configurations bearing n=n1+n2=8 to 128 cracks, a wide range of crack depth to wall thickness ratios, a1/t=0.01 to 0.4, and various crack ellipticities, a1/c1=0.3 to 1.5, are evaluated for a cylinder of radii ratio Ro/Ri=2. To increase the accuracy of the evaluated SIFs an existing improved version of the displacement extrapolation method is used. The results clearly indicate that unevenness, as reflected in KIP distributions, depends on both the number of cracks in the array as well as on the cracks’ depths and ellipticities. The “interaction range” for the various configurations of uneven crack arrays is evaluated. The range of influence between adjacent cracks on the maximal SIF, KPmax, is found to be dependent on the density of the array, as reflected in the inter-crack aspect-ratio, as well as on the cracks’ elipticity.

Three-Dimensional Interaction Effects in an Internally Multicracked Pressurized Thick-Walled Cylinder— Part I: Radial Crack Arrays

1996 ◽  
Vol 118 (3) ◽  
pp. 357-363 ◽  
Author(s):  
M. Perl ◽  
C. Levy ◽  
J. Pierola
Keyword(s):  
Radial Crack ◽  
Crack Depth ◽  
Three Dimensional ◽  
Internal Surface ◽  
Interaction Effects ◽  
Life Assessment ◽  
Fatigue Life Assessment ◽  
Dimensional Interaction ◽  
Least Squares Fit ◽  
Wide Range

Under certain conditions, numerous internal surface cracks develop in pressurized thick-walled cylinders, both in the radial and longitudinal directions. For fatigue life assessment of such vessels, the 3-D interaction effects among these cracks on the prevailing stress intensity factors (SIFs) need evaluation. In Part I of this paper, radial crack arrays are considered exclusively. The mode I SIF distribution for a wide range of semi-circular and semi-elliptical cracks are evaluated. The 3-D analysis is performed via the finite element method with the submodeling technique, employing singular elements along the crack front. SIFs are evaluated for arrays of up to n = 180 cracks; for a wide range of crack depth to wall thickness ratios, a/t, from 0.05 to 0.6; and, for various ellipticities of the crack, i.e., the ratio of crack depth to semicrack length, a/c, from 0.2 to 2. Using a least-squares fit, two simple expressions for the most critical (n = 2) SIFs are obtained for sparse and dense crack arrays. The formulas, which are functions of a/t and a/c, are of very good engineering accuracy. The results clearly indicate that the SIFs are considerably affected by the interaction among the cracks in the array as well as the three-dimensionality of the problem. In Part II of this paper, the interaction effects between longitudinal coplanar cracks will be analyzed.

Analysis of Three-Dimensional Clamped Single Edge Notched Tension (SENT) Specimens

2018 ◽  
Author(s):  
Zheng Liu ◽  
Xu Chen ◽  
Xin Wang
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Crack Depth ◽  
Plate Thickness ◽  
Three Dimensional ◽  
Width Ratio ◽  
Element Analysis ◽  
Out Of Plane ◽  
T Stress

In the present paper, three-dimensional clamped SENT specimens, which is one of the most widely used low-constraint and less-conservative specimen, are analyzed by using a crack compliance analysis approach and extensive finite element analysis. Considering the test standard (BS8571) recommended specimen sizes, the daylight to width ratio, H/W, is 10.0, the relative crack depth, a/W, is varied by 0.2, 0.3, 0.4, 0.5 or 0.6 and the relative plate thickness, B/W, is chosen by 1.0, 2.0 or 4.0, respectively. Complete solutions of fracture mechanics parameters, including stress intensity factor (K), in-plane T-stress (T11) and out-of-plane T-stress (T33) are calculated, and the results obtained from above two methods have a good agreement. Moreover, the combination of the effects of a/W and B/W on the stress intensity factor K, T11 and T33 stress are thus illustrated.

Comparison of the Stress Intensity Factor Influence Coefficients for Axial ID Surface Cracks in Cylinders of RSE-M and API 579-1

2015 ◽  
Author(s):  
Patrick Le Delliou ◽  
Stéphane Chapuliot
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Nuclear Power ◽  
Crack Depth ◽  
Wall Stress ◽  
Surface Point ◽  
Evaluation Procedures ◽  
Influence Coefficients ◽  
Wide Range

Analytical evaluation procedures for determining the acceptability of flaw detected during in-service inspection of nuclear power plant components are provided in Appendix 5.4 of the French RSE-M Code. Linear elastic fracture mechanics based evaluation procedures require calculation of the stress intensity factor (SIF). In Appendix 5.4 of the RSE-M Code, influence coefficients needed to compute the SIF are provided for a wide range of surface axial or circumferential flaws in cylinders, the through-wall stress field being represented by a cubic equation. On the other hand, Appendix C of API 579-1 FFS procedure provides also a very complete set of influence coefficients. The paper presents the comparison of the influence coefficients from both documents, focused on axial ID semi-elliptical surface flaws in cylinders. The cylinder and crack geometries are represented by three ratios: Ri/t, a/t, and a/c, where Ri, t, a, and c are respectively the inner radius, the wall thickness, the crack depth and one-half of the crack length. The solutions for the coefficients G0 and G1 at the deepest point and at the surface point are investigated. At the deepest point, the agreement between the solutions is good, the relative difference being lower than 2 %, except for the plate (Ri/t = ∞) at a/c = 0.125 and 0.0625 and a/t = 0.8 (around 5 %). At the surface point, the agreement between both solutions is not so good. At this point, the relative differences depend strongly on the a/c ratio, being larger for elongated cracks (with low a/c ratios). However, it must be recalled that the absolute values of the coefficients are low at the surface point for elongated cracks, and that for these cracks the critical point regarding the stress intensity factor is the deepest point.

Stress Intensity Factors for Cracks in Conventional S-N Fatigue Specimens

1996 ◽  
Vol 118 (2) ◽  
pp. 203-207
Author(s):  
T. P. O’Donnell
Keyword(s):  
Stress Intensity ◽  
Crack Growth ◽  
Fatigue Testing ◽  
Axial Stress ◽  
Crack Depth ◽  
Three Dimensional ◽  
Axial Displacement ◽  
Element Analysis ◽  
Displacement Boundary ◽  
Specimen Diameter

Stress intensity values for cracks growing in conventional fatigue specimens are determined, with emphasis on the end constraint conditions associated with S-N fatigue testing. Three-dimensional finite element analysis methods are used to analyze thumbnail-shaped cracks in cylindrical geometries. Crack front straightening due to the increased bending introduced as crack growth progresses is included in the models. Because relatively stiff fatigue test machines prevent rotation at the clamped ends of test specimens, uniform axial displacement boundary conditions are imposed. Results for uniformly applied axial stress end conditions are also obtained for comparison. For crack-depth-to-specimen-diameter ratios over one-third, bending restraint induced in the specimens under applied axial displacement significantly reduces the resulting stress intensity relative to values computed for uniform end tension. The results are useful for evaluating crack growth in fatigue specimens within the limits of linear elastic fracture mechanics.

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