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Research Papers: Design and Analysis

On the Calculation of Stress Intensity Factors and J-Integrals Using the Submodeling Technique

[+] Author and Article Information
Eduard Marenić, Ivica Skozrit

Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Ivana Lučića 5, 10000 Zagreb, Croatia

Zdenko Tonković

Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Ivana Lučića 5, 10000 Zagreb, Croatiaztonkov@fsb.hr

J. Pressure Vessel Technol 132(4), 041203 (Aug 05, 2010) (12 pages) doi:10.1115/1.4001267 History: Received July 09, 2009; Revised February 10, 2010; Published August 05, 2010; Online August 05, 2010

In the present paper, calculations of the stress intensity factor (SIF) in the linear-elastic range and the J-integral in the elastoplastic domain of cracked structural components are performed by using the shell-to-solid submodeling technique to improve both the computational efficiency and accuracy. In order to validate the submodeling technique, several numerical examples are analyzed. The influence of the choice of the submodel size on the SIF and the J-integral results is investigated. Detailed finite element solutions for elastic and fully plastic J-integral values are obtained for an axially cracked thick-walled pipe under internal pressure. These values are then combined, using the General Electric/Electric Power Research Institute method and the reference stress method, to obtain approximate values of the J-integral at all load levels up to the limit load. The newly developed analytical approximation of the reference pressure for thick-walled pipes with external axial surface cracks is applicable to a wide range of crack dimensions.

Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

A membrane with a semi-elliptical crack subjected to tension: (a) geometry, dimensions, and loading of the membrane; and (b) geometry of a submodel

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Figure 2

Meshes for a semi-elliptical surface crack in a rectangular membrane: (a) one-quarter of the global (shell) model mesh without a crack, and (b) one-quarter of the submodel mesh with a semi-elliptical crack

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Figure 3

A solid reference model of the cracked membrane

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Figure 4

A pipe with an external axial surface crack subjected to internal pressure: (a) geometry, dimensions, and loading of the pipe; (b) geometry of the submodel; and (c) geometry of the crack

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Figure 5

Typical FE meshes for a pipe: (a) global (shell) model mesh without a crack, and (b) submodel mesh with a semi-elliptical crack (Ri/t=10, c/a=10, a/t=0.4, s/c=2)

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Figure 6

Overlay plot of the global model and the submodel (Ri/t=10, c/a=10, a/t=0.4, s/c=2)

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Figure 7

A solid reference model of the cracked pipe (Ri/t=4, c/a=10, a/t=0.8)

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Figure 8

Dependence of the stress intensity factor on the submodel size: (a) Ri/t=10, c/a=10, a/t=0.4 and (b) Ri/t=4, c/a=5, a/t=0.4

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Figure 9

Radial displacement distribution of the inner surface of the pipe along a longitudinal cross section

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Figure 10

Radial displacement distribution of the inner surface of the pipe along a circumferential cross section

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Figure 11

Hoop stress distribution of the inner surface of the pipe along a longitudinal cross section

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Figure 12

Hoop stress distribution of the inner surface of the pipe along a circumferential cross section

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Figure 13

Submodel and full 3D model without a crack under the same pressure: (a) schematic representation of deformed configurations, and (b) deformed configuration of the submodel

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Figure 14

(a) Hoop stress distribution of the inner surface of the pipe along a longitudinal cross section (Ri/t=4, c/a=5, a/t=0.4, t=1.625 mm, and s/c=3 and 4); ((b) and (c)) details A and B

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Figure 15

A comparison of the dimensionless function F for the stress intensity factor between the present work and the published solutions obtained by Raju and Newman (21)

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Figure 16

Computational model of the vessel-nozzle junction with a crack in the weld toe (type D according to Ref. 20)

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Figure 17

Typical FE meshes for a vessel-nozzle junction: (a) global (shell) model mesh without a crack, (b) a junction detail of the global model, (c) the submodel mesh with a semi-elliptical crack in the weld toe, and (d) 3D model mesh without a crack

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Figure 18

Variations of the difference in radial displacement distribution of the midsurface along a longitudinal and a circumferential cross section of the pressure vessel obtained from the shell model and the full 3D solid FEA

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Figure 19

Dependence of the Jep-integral results on the submodel size: (a) Ri/t=10, c/a=10, a/t=0.4 and (b) Ri/t=4, c/a=5, a/t=0.4

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Figure 20

Dependence of the plastic influence h1-function on the load magnitude (Ri/t=4, c/a=5): (a) a/t=0.2 and (b) a/t=0.6

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Figure 21

Engineering stress-strain curves of the 08X18H10T steel at 300°C(31)

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Figure 22

Comparison of the FE and GE/EPRI J results with the proposed reference stress-based J estimations (Rm/t=4.8, c/a=2.08, a/t=0.8)

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