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Research Papers: Pipeline Systems

# Effect of Lüders Plateau on Fracture Response and Toughness of Pipelines Subject to Extreme Plastic Bending

[+] Author and Article Information

Department of Civil and Resource Engineering, Dalhousie University, Halifax, NS, B3J 1Z1, Canada

Farid Taheri1

Department of Civil and Resource Engineering, Dalhousie University, Halifax, NS, B3J 1Z1, Canadafarid.taheri@dal.ca

1

Corresponding author.

J. Pressure Vessel Technol 133(5), 051701 (Jul 11, 2011) (9 pages) doi:10.1115/1.4002930 History: Received July 07, 2010; Revised September 21, 2010; Published July 11, 2011; Online July 11, 2011

## Abstract

The reeling technique presents an economical pipeline installation method for offshore oil and gas applications, especially for thick-wall (low $D/t$) pipelines. During reeling, the pipe is subjected to large plastic bending strains up to 3%. In thick-wall pipes, the tensile fracture response of the pipeline/girth weld would normally be the governing limit state. Seamless line pipes are preferred for the reeling applications in which the Lüders plateau is often exhibited in materials stress-strain response. In this paper, the fracture response of such pipelines is investigated from a continuum perspective using a nonlinear 3D finite element analysis. A typical pipeline with a hypothetical defect is considered, with the material having a range of Lüders strains and strain hardening indices. Results show that the Lüders plateau modifies the shape of the moment-strain response curves of the pipe, as well as the $J$-integral fracture response. It is observed that the response is always bounded between two limiting material models, which are (i) the elastic-perfectly plastic stress-strain response and (ii) the conventional elastic-strain hardening plasticity response, without a Lüders plateau. Also, the Lüders plateau was observed to decrease the crack opening stress ahead of the crack tip and thus the crack tip constraint. On the other hand, the presence of a Lüders plateau elevates the near tip plastic strain and stress triaxiality fields, thus promoting ductile fracture. A micromechanical damage integral model coupled with a modified boundary layer analysis was incorporated to study this aspect. Based on the findings of this study, it is believed that the presence of Lüders plateau could significantly alter the fracture response and toughness of pipes subject to relatively high strains.

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## Figures

Figure 1

The family of uniaxial true stress-strain curves considered for the high strain hardening (n=10) case

Figure 2

Schematic of the cracked pipeline cross section

Figure 3

(Left) The FE mesh with the applied boundary conditions and (right) the focused mesh of the crack tip showing the local r-θ-s coordinates utilized for result extraction

Figure 4

Moment-strain curves for the family of Lüders termination strains along with the two limiting cases for a material with (a) n=10 and (b) for n=25

Figure 5

Evolution of the normalized J-integral extracted at crack center (s/c=0) for the material with n=10, and the family of εL (a) as a function of applied moment and (b) as a function of applied global strain εg

Figure 6

Variation of Qave as a function of εg for the family of εL (material with n=10)

Figure 7

Distribution of the crack opening stress along the crack front extracted at the crack center, s/c=0, for materials with (a) n=10 and (b) n=25

Figure 8

Distribution of the crack opening stress along the crack front extracted at r/(J/σy)=5 for the family of εL and material with n=10

Figure 9

Effect of the Lüders plateau on the crack opening parameter, d=δt/(J/σy), for the n=10 material

Figure 10

Distribution of εp along the “crack surface path” for the n=10 material and the family of εL, extracted at the crack center (s/c=0) at εg=3%

Figure 11

Two parameter diagram of εp versus σh/σe for the family of εL and for the material with n=10. Results extracted at crack center s/c=0 and from the uncracked ligament at r=2.5×J/σy

Figure 12

Deformed near tip region at the crack center, s/c=0, for two cases (ΔεL=0 and εL=2.5%, material with n=10) showing contours of εp=0.05 and 0.07

Figure 13

Schematic illustration of the damage integral approach (22) utilized to assess the Lüders plateau effect on material toughness

Figure 14

(Left) FE mesh of the MBL model along with the relevant coordinate systems and boundary conditions; (right) crack tip mesh details showing the initial notch radius

Figure 15

Variation of ductile initiation toughness ratio as a function of εL for various values of n. The symbols represent the results obtained by the MBL models, and solid lines represent the power-law fits (Eq. 10).

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