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 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.

The Combined Effect of Pressure and Autofrettage on Uniform Arrays of Three-Dimensional Unequal-Depth Cracks in Gun Barrels

2005 ◽  
Vol 127 (4) ◽  
pp. 464-470 ◽  
Author(s):  
M. Perl ◽  
B. Ostraich
Keyword(s):  
Residual Stress ◽  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Stress Field ◽  
Crack Depth ◽  
Three Dimensional ◽  
Favorable Effect ◽  
Residual Stress Field ◽  
Inner Surface

Due to the repeated firing of the gun, large uniform arrays of unequal-depth fatigue cracks develop from the inner surface of the barrel. The combined effect of pressure and autofrettage on the mode I stress intensity factor (SIF) distribution along the fronts of these three-dimensional, semi-elliptical, surface cracks is herein studied. Crack depth inequality is modeled using the “two-crack depth level model” previously proposed. The analysis is performed via the finite element (FE) method employing singular elements along the crack front. The autofrettage residual stress field is simulated using an equivalent thermal load. The distribution of the combined stress intensity factor due to pressurization and full autofrettage KIN=KIP+KIA, for numerous array configurations is evaluated for a barrel of outer to inner radii ratio of Ro/Ri=2. These configurations bear n=n1+n2=8 to 128 cracks, a wide range of crack depth to wall thickness ratios, a1/t=0.01 to 0.40, and various crack depth to half-length ratios (ellipticities) a1/c1=0.30 to 1.50. The results for KIN distributions clearly indicate that the level of effect of crack depth inequality depends on all three parameters: crack number in the array, crack depth and crack ellipticity. Furthermore, the results indicate that adjacent unequal-depth cracks influence each other only within a limited range of their depths, i.e., the “interaction range”. The range of influence between adjacent cracks on the maximal SIF KNmax depends on crack ellipticity and is found to be inversely proportional to the crack density of the array. The results re-emphasize the favorable effect the residual stress field has on the fracture endurance and the fatigue life of gun barrels bearing uniform arrays of three-dimensional unequal-depth cracks at their inner surface. This favorable effect is governed by the ratio of the gun’s material yield stress to its internal pressure—ψ=σ0/p. The higher ψ is, the more effective autofrettage becomes.

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 Influence of the Bauschinger Effect on the Stress Intensity Factors for a Radially Cracked Autofrettaged Thick-Walled Cylinder

2005 ◽  
Author(s):  
M. Perl ◽  
C. Levy ◽  
V. Rallabhandy
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Crack Front ◽  
Bauschinger Effect ◽  
Crack Depth ◽  
Crack Plane ◽  
Fe Method ◽  
Wide Range ◽  
Walled Cylinder

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 3-D analysis is performed via the finite element (FE) 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 (BE) 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 towards 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 less than 10% as compared to 60% BEDA, and on the average the difference is only about 2–4%.

The Favorable Effect of Autofrettage on Uniform Arrays of 3-D Unequal-Depth Cracks in a Thick-Walled Cylindrical Pressure Vessel

2003 ◽  
Author(s):  
M. Perl ◽  
B. Ostraich
Keyword(s):  
Residual Stress ◽  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Stress Field ◽  
Pressure Vessel ◽  
Crack Depth ◽  
Favorable Effect ◽  
Residual Stress Field ◽  
Cylindrical Pressure Vessel

The favorable effect of autofrettage on the mode I stress intensity factor (SIF) distributions along the fronts of radial, semi-elliptical surface cracks pertaining to large uniform arrays of unequal-depth cracks emanating at the bore of a pressurized thick-walled cylinder is studied. The analysis is based on the, previously proposed, “two-crack-depth level model”. SIF values are evaluated by the finite element method (FE) using the ANSYS 6.1 code. In the FE model singular elements are employed along the crack front and an equivalent temperature load simulates the autofrettage residual stress field. The distribution of KIN = KIP + KIA, the combined stress intensity factor due to pressurization and full autofrettage, 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. The accuracy of the evaluated SIFs is increased using an improved displacement extrapolation. The results clearly indicate the favorable effect of the residual stress field on the fracture endurance and the fatigue life of autofrettaged cylindrical pressure vessel bearing uniform arrays of 3-D unequal-depth cracks emanating from its inner bore. This favorable effect is governed by Ψ = σo/p — the ratio of the vessel’s material yield stress to its internal pressure. The higher ψ is the more effective autofrettage becomes. The “interaction range” for the various configurations of uneven crack arrays is evaluated. The range of influence between adjacent cracks on the maximal combined SIF, KNmax, 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’ ellipticity.

The Influence of Autofrettage With Bauschinger Effect on the SIFS of Multiple Longitudinal Coplanar Cracks in Pressurized Cylinders

2005 ◽  
Author(s):  
C. Levy ◽  
M. Perl ◽  
S. Kotagiri
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Crack Front ◽  
Bauschinger Effect ◽  
Crack Depth ◽  
Crack Density ◽  
Crack Plane ◽  
Fe Method ◽  
Wide Range

The influence of the Bauschinger Effect (BE) on the three dimensional, Mode I, Stress Intensity Factor (SIF) distributions for arrays of longitudinal coplanar, surface cracks emanating from the bore of a fully or partially autofrettaged thick-walled cylinder is investigated. The generation and comparison of the SIFs for a “realistic” - Bauschinger Effect Dependent Autofrettage (BEDA) and those for an “ideal” - Bauschinger Effect Independent Autofrettage (BEIA), which until now did not exist, is undertaken. The 3-D analysis is performed via the finite element (FE) 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 250 different crack configurations are analyzed. SIFs for various crack densities (2c/d = 0.25–0.75), a wide range of crack depth to wall thickness ratios (a/t = 0.01–0.25), various ellipticities (a/c = 0.5–1.5), and different levels of autofrettage (ε = 30%–100%) are evaluated. The Bauschinger Effect (BE) is found to significantly lower the beneficial stress intensity factor due to autofrettage, KIA, by up to 52%, as compared to the case of “ideal” autofrettage. The reduction in KIA varies along the crack front with the maximum determined by the crack ellipticity, crack depth and crack separation distance. In some cases the maximum occurs at the deepest point of the crack and in others the maximum is at the point of intersection between the crack plane and the inner surface of the cylinder. In certain situations, the maximum transitions from one to the other as crack density increases. The detrimental influence of the BE increases as the crack density decreases 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 less than 15–17% when compared to 60% BEDA, and on the average the difference is only about 6%. Furthermore, the results indicate that crack density, and, in some cases, crack depth and crack ellipticity have opposing effects on the SIF of longitudinally coplanar crack arrays.

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.

Sign in / Sign up

Export Citation Format

Share Document