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RESEARCH PAPERS

# Application of Constraint Corrected $J$-$R$ Curves to Fracture Analysis of Pipelines

[+] Author and Article Information
Xian-Kui Zhu

Battelle Memorial Institute, 505 King Avenue, Columbus, OH 43201zhux@battelle.org

Brian N. Leis

Battelle Memorial Institute, 505 King Avenue, Columbus, OH 43201

J. Pressure Vessel Technol 128(4), 581-589 (Dec 06, 2005) (9 pages) doi:10.1115/1.2349571 History: Received July 26, 2005; Revised December 06, 2005

## Abstract

Fracture properties of an API X80 pipeline steel have been developed using a set of single edge notched bend (SENB) and single edge notched tension (SENT) specimens with shallow and deep cracks to generate different crack-tip constraint levels. The test data show that the $J$-$R$ curves for the X80 pipeline steel are strongly constraint dependent. To facilitate transfer of the experimental $J$-$R$ curves to those for actual cracked components, like flawed pipeline, constraint corrected $J$-$R$ curves are developed. The two-parameter $J$-$A2$ formulation is adopted to quantify constraint effect on the crack-tip fields and the $J$-$R$ curves. The constraint parameter $A2$ is extracted by matching the $J$-$A2$ solution with finite element results for a specific crack configuration. A constraint corrected $J$-$R$ curve is then formulated as a function of the constraint parameter $A2$ and crack extension $Δa$. A general method and procedure to transfer the experimental$J$-$R$ curves from laboratory to actual cracked components are proposed. Using the test data of $J$-$R$ curves for the SENB specimens, a mathematical expression representing a family of the $J$-$R$ curves is constructed for the X80. It is shown that the predicted $J$-$R$ curves developed in this paper agree well with experimental data for both SENB and SENT specimens. To demonstrate its application in assessing flaw instability, a pipeline with an axial surface crack is considered. For a crack depth of 50% of the wall thickness, the predicted $J$-$R$ curve is found to be higher than that for the SENB specimen with the same crack length to width ratio. From this predicted $J$-$R$ curve and crack driving force obtained by finite element analysis, the failure pressures of the pipeline at the crack initiation and instability are determined and discussed.

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## Figures

Figure 1

True stress-strain curve of X80 pipeline steel

Figure 2

Experimental J-R curves for SENB specimens

Figure 3

Experimental J-R curves for SENT specimens

Figure 4

Typical finite element mesh for test specimens

Figure 5

Distribution of opening stress σθθ along the distance from the crack tip. Symbols are FEA results, lines are asymptotic solutions. (a)a∕W=0.24, (b)a∕W=0.42.

Figure 6

Variation of A2 with J for SENB specimens by (a) the J-A2 solution and (b) the modified J-A2 solution

Figure 7

Variations of J0.2mm and J1.0mm with constraint parameter A2 for SENB specimens

Figure 8

Comparison of predicted and experimental J-R curves for SENB specimens

Figure 9

Comparison of predicted and experimental J-R curves for SENT specimens

Figure 10

Finite element mesh for 762×23mm2 pipe with an axial surface crack of a∕t=0.5

Figure 11

Distribution of the opening stress determined from the FEA and J-A2 solution along the distance from the crack tip

Figure 12

Predicted J-R curve for X80 pipe with a surface crack and compared with those for SENB specimens

Figure 13

Variation of J integral with internal pressure for the cracked pipe

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