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Research Papers: Materials and Fabrication

# Interaction of Hydrogen Transport and Material Elastoplasticity in Pipeline Steels

[+] Author and Article Information

Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, 1206 West Green Street, Urbana, IL 61801

Brian P. Somerday

Sandia National Laboratories, P.O. Box 969, MS 9403, Livermore, CA 94551

Petros Sofronis1

Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, 1206 West Green Street, Urbana, IL 61801sofronis@uiuc.edu

Ian M. Robertson

Department of Material Science and Engineering, University of Illinois at Urbana-Champaign, 1304 West Green Street, Urbana, IL 61801

Douglas Stalheim

DGS Metallurgical Solutions, Inc., 16110 NE 4th Street, Vancouver, WA 98684

1

Corresponding author.

J. Pressure Vessel Technol 131(4), 041404 (Jul 01, 2009) (13 pages) doi:10.1115/1.3027497 History: Received June 27, 2007; Revised June 24, 2008; Published July 01, 2009

## Abstract

The technology of large scale hydrogen transmission from central production facilities to refueling stations and stationary power sites is at present undeveloped. Among the problems that confront the implementation of this technology is the deleterious effect of hydrogen on structural material properties, in particular, at gas pressures of the order of $15MPa$, which are the suggested magnitudes by economic studies for efficient transport. In order to understand the hydrogen embrittlement conditions of the pipeline materials, we simulate hydrogen diffusion through the surfaces of an axial crack on the internal wall of a vessel coupled with material deformation under plane strain small scale yielding conditions. The calculation of the hydrogen accumulation ahead of the crack tip accounts for stress-driven transient diffusion of hydrogen and trapping at microstructural defects whose density evolves dynamically with deformation. The results are analyzed to correlate for a given material system the time after which hydrogen transport takes place under steady state conditions with the level of load in terms of the applied stress intensity factor at the crack tip and the size of the domain used for the simulation of the diffusion.

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Copyright © 2009 by American Society of Mechanical Engineers
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## Figures

Figure 1

Schematic of an axial crack on the ID surface of a pipeline and the crack tip region under consideration. The parameter L denotes the size of the analysis domain.

Figure 8

Evolution of normalized hydrogen concentration CL∕C0 in NILS versus normalized distance R∕b ahead of the crack tip at KI=30MPam with a domain size L=9.79mm. The parameter b=4.62μm denotes the crack tip opening displacement and C0=2.084×1021 H atoms/m3 (=2.46×10−8 H atoms per solvent atoms) is the enforced NILS hydrogen concentration at the crack face in equilibrium with a hydrogen-gas pressure of 1atm.

Figure 12

Plot of peak values of the normalized hydrogen concentration CL∕C0 in NILS at t=tss (effective time to steady state) versus domain size L at KI=80MPam. The parameter C0=2.084×1021 H atoms/m3 (=2.46×10−8 H atoms per solvent atoms) is the enforced NILS hydrogen concentration at the crack face in equilibrium with a hydrogen-gas pressure of 1atm.

Figure 13

Plot of effective time to steady state tss versus domain size L at KI=80MPam. The crack face is in equilibrium with hydrogen gas at 1atm pressure.

Figure 14

Plot of peak values of the normalized hydrogen concentration CL∕C0 in NILS at t=tss (effective time to steady state) versus the normalized domain size L∕b at different applied stress intensity factors. The parameter C0=2.084×1021 H atoms/m3 (=2.46×10−8 H atoms per solvent atoms) is the enforced NILS hydrogen concentration at the crack face in equilibrium with a hydrogen-gas pressure of 1atm.

Figure 15

Plot of the normalized effective time to steady state τss=Dtss∕b2 versus normalized domain size L∕b at different applied stress intensity factors. The crack face is in equilibrium with hydrogen gas at 1atm pressure.

Figure 16

Normalized hydrogen concentration CL∕C0′ in NILS at t=tss (effective time to steady state) versus normalized distance R∕b ahead of the crack tip for various domain sizes. The parameter C0′=12.77C0 is the enforced initial/boundary NILS hydrogen concentration at the crack face in equilibrium hydrogen gas at 15MPa.

Figure 17

Plot of peak values of the normalized hydrogen concentration in NILS at t=tss (effective time to steady state) against normalized domain size L∕b. The parameter C0′=12.77C0 is the enforced initial/boundary NILS hydrogen concentration at the crack face in equilibrium with hydrogen gas at 15MPa.

Figure 18

Plot of the normalized effective time to steady state τss=Dtss∕b2 against normalized domain size L∕b with the crack face being in equilibrium with hydrogen gas at 1atm and 15MPa.

Figure 2

Description of (a) boundary conditions for the elastoplastic problem and (b) initial and boundary conditions for the diffusion problem at the blunting crack tip. The parameter b0 denotes the crack tip opening displacement at the undeformed state, and u1elastic and u2elastic are the asymptotic displacements of Irwin’s singular field (24) in 1- and 2-directions, respectively. The parameter C0 is the NILS hydrogen concentration at the crack face in equilibrium with the hydrogen gas inside the crack and j is the hydrogen flux.

Figure 3

Contour plots of normalized hydrostatic stress σkk∕3σ0 at applied stress intensity factor KI=30MPam. The parameter σ0 denotes the yield stress of the material, and the inset shows the hydrostatic stress near the notch root. Dimensions are in millimeters.

Figure 4

Contour plots of equivalent plastic strain εp at applied stress intensity factor KI=30MPam. The inset shows the equivalent plastic strain near the notch root and dimensions are in millimeters.

Figure 5

Contour plots of normalized NILS hydrogen concentration CL∕C0 at steady state under KI=30MPam. The inset shows the concentration near the notch root. The parameter C0=2.084×1021 H atoms/m3 (=2.46×10−8 H atoms per solvent atoms) is the enforced NILS hydrogen concentration at the crack face in equilibrium with a hydrogen-gas pressure of 1atm.

Figure 6

Contour plots of normalized trapping site hydrogen concentration CT∕C0 at steady state under KI=30MPam. The inset shows the concentration at the notch root. The parameter C0=2.084×1021 H atoms/m3 (=2.46×10−8 H atoms per solvent atoms) is the enforced NILS hydrogen concentration at the crack face in equilibrium with a hydrogen-gas pressure of 1atm.

Figure 7

Contour plots of total hydrogen concentration (CL+CT)∕C0 at steady state under KI=30MPam. The inset shows the hydrogen concentration at the notch root. The parameter C0=2.084×1021 H atoms/m3 (=2.46×10−8 H atoms per solvent atoms) is the enforced NILS hydrogen concentration at the crack face in equilibrium with a hydrogen-gas pressure of 1atm.

Figure 9

Normalized NILS hydrogen concentration CL∕C0 at t=tss (effective time to steady state) versus normalized distance R∕b ahead of the crack tip at KI=30MPam for various domain sizes. The parameter C0=2.084×1021 H atoms/m3 (=2.46×10−8 H atoms per solvent atoms) is the enforced NILS hydrogen concentration at the crack face in equilibrium with a hydrogen-gas pressure of 1atm.

Figure 10

Plot of peak values of the normalized hydrogen concentration CL∕C0 in NILS at t=tss (effective time to steady state) versus domain size L at KI=30MPam. The parameter C0=2.084×1021 H atoms/m3 (=2.46×10−8 H atoms per solvent atoms) is the enforced NILS hydrogen concentration at the crack face in equilibrium with a hydrogen-gas pressure of 1atm.

Figure 11

Plot of effective time to steady state tss versus domain size L at KI=30MPam. The crack face is in equilibrium with hydrogen gas at 1atm pressure.

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