Advances in Materials Science and Engineering

Volume 2018 (2018), Article ID 2089514, 11 pages

https://doi.org/10.1155/2018/2089514

## Failure Assessment for the High-Strength Pipelines with Constant-Depth Circumferential Surface Cracks

Correspondence should be addressed to L. H. Dai

Received 22 September 2017; Revised 24 November 2017; Accepted 4 December 2017; Published 18 February 2018

Academic Editor: Philip Eisenlohr

Copyright © 2018 X. Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

In the oil and gas transportation system over long distance, application of high-strength pipeline steels can efficiently reduce construction and operation cost by increasing operational pressure and reducing the pipe wall thickness. Failure assessment is an important issue in the design, construction, and maintenance of the pipelines. The small circumferential surface cracks with constant depth in the welded pipelines are of practical interest. This work provides an engineering estimation procedure based upon the GE/EPRI method to determine the *J*-integral for the thin-walled pipelines with small constant-depth circumferential surface cracks subject to tension and bending loads. The values of elastic influence functions for stress intensity factor and plastic influence functions for fully plastic *J*-integral estimation are derived in tabulated forms through a series of three-dimensional finite element calculations for different crack geometries and material properties. To check confidence of the *J*-estimation solution in practical application, *J*-integral values obtained from detailed finite element (FE) analyses are compared with those estimated from the new influence functions. Excellent agreement of FE results with the proposed *J*-estimation solutions for both tension and bending loads indicates that the new solutions can be applied for accurate structural integrity assessment of high-strength pipelines with constant-depth circumferential surface cracks.

#### 1. Introduction

The growing demand for energy and natural resources has been pushing exploration and production activities of oil and natural gas. In particular, application of thin-walled high-strength steel has become a trend in the oil and gas transportation system over long distance, which can improve the transportation efficiency by high-pressure operation and reduce the pipe laying cost by reducing the wall thickness of pipes [1, 2]. Research projects have then been focused on the development of API grades X80 and X100 and more recently to grade X120 [1]. The high-grade pipeline steels have high yield-to-ultimate tensile strength ratio, which means they have relatively low strain-hardening ability. For the high-strength pipelines adopted in industries, the mean diameter-to-thickness ratio *D*/*t* generally ranges from 50 to 100, such as the grade API 5L X80 steel applied on TransCanada system.

The long-distance oil and gas pipes are joined by girth weld. Common failures in pipelines result primarily from the weld defects. The failure assessment of crack-like flaws is an important issue in design and maintenance of the pipeline systems. Specifically, the fracture parameter *J*-integral has been widely used in the structural integrity assessment of defective pipes. Full three-dimensional finite element (FE) analyses can provide accurate results for the fracture response. However, FE analyses require large computational time, expertise, and resources, which make the numerical computation quite expensive to be used routinely; hence, they are not suitable for engineering structural integrity assessment. Therefore, the simplified *J*-estimation scheme with much less computational cost is highly desired from the view of engineering application.

Based upon the fully plastic *J*-integral solution developed by Shih and Hutchinson [3], Kumar et al. [4] introduced the widely known GE/EPRI *J*-estimation approach for two-dimensional geometries. Afterwards, the original work was extended by various researchers [5–14] to include additional geometries and loading conditions. Another popular *J*-estimation method is the reference stress approach which adopts the plastic limit load as the reference stress [15]. Based upon the FE results for pipes with varying geometries under different loading conditions, it was proposed that the reference stress could be redefined by an “optimized reference load” (rather than the plastic limit load) [16–19]. This method is termed as an enhanced reference stress method and can improve the accuracy in *J* estimation. However, it should be noted that these works mainly cover the cases of cracked pipes having mean diameter-to-thickness ratio (*D*/*t*) not more than 40, while the values of *D*/*t* for high-strength pipelines are normally larger than 50.

To verify the applicability limit of the existing GE/EPRI method with regard to the diameter-to-thickness ratio *D*/*t*, Cho et al. [20] have explored the *J*-estimation schemes for semielliptical surface-cracked pipes with *D*/*t* ranging from 10 to 120. Park et al. [21] have performed several FE analyses for pipes with a short circumferential through-wall crack. As pointed by those previous works [20–22], an application of existing solutions would result in inaccurate structural integrity assessment results when thin-walled pipes with large diameter are considered. If existing GE/EPRI solution, whose applicability is *D*/*t* ≤ 40, is directly extrapolated to thin-walled pipes with *D*/*t* > 60, the *J*-integral would be nonconservative compared with the FE results [20, 21]. Underestimation of the crack-driving force might be very dangerous in the engineering failure assessment, which needs to be avoided. Therefore, extension of the estimation methods is urgently required for thin-walled pipes. Furthermore, in most of previous works, the surface cracks are usually modeled as elliptical configuration. The surface cracks with constant depth might represent well the weld defects commonly observed in pipelines [23]. Moreover, based upon the limits routinely adopted in design as well as nondestructive testing examination, such as API 1104 [24], small cracks are often a major concern for the welded pipes with large diameter. In this content, *J*-estimation solutions for thin-walled pipes with small constant-depth cracks need to be developed to overcome the limitations of the existing solutions.

This paper focuses on extending *J*-estimation solutions for high-strength pipelines with small constant-depth cracks. A series of elastic and elastic-plastic FE analyses for the thin-walled pipes with *D*/*t* ranging from 50 to 100 under tension and bending loads are conducted in this paper. The analyses involve small constant-depth cracks with crack depth-to-thickness ratio *a*/*t* ranging 0.1–0.4 and normalized crack length *θ*/*π* ranging 0.01–0.08 for pipes with different strain-hardening properties. By analyzing the FE results, the values of elastic influence functions for elastic stress intensity factor *K* and plastic influence functions for fully plastic *J*-integral are proposed in tabulated forms based upon GE/EPRI estimation method. To show the efficiency of the estimation method for idealized Ramberg–Osgood material, *J*-integral values obtained from the new elastic and plastic influence functions are compared with those from detailed three-dimensional FE analyses. Moreover, to check confidence of the *J*-estimation solution in practical application, elastic-plastic FE analyses are also conducted using experimental stress-strain data for three typical grade pipeline steels.

#### 2. The GE/EPRI Method for Estimation

##### 2.1. The EPRI Methodology

To estimate elastic-plastic *J*-values for a cracked body, the GE/EPRI engineering method [3, 4] was developed based on FE solutions using deformation plasticity theory. The method assumes that the constitutive law for the materials can be characterized by the Ramberg–Osgood model:where *σ* is the true stress, *ε* is the true strain, *σ*_{0} is the yield stress, *E* is the elastic modulus, *ε*_{0} = *σ*_{0}/*E* is the corresponding reference strain, *α* is a dimensionless constant, and *n* defines the strain-hardening exponent.

The GE/EPRI estimation method evolved from the two limiting cases of elastic and fully plastic conditions. The elastic-plastic *J*-integral is split into elastic and plastic components aswhere the subscript “*e*” denotes the elastic part of *J*, adjusted by a plastic zone correction using the effective crack length *a*_{e}, and “*p*” refers to plastic contributions. The elastic component *J*_{e} can be expressed via the stress intensity factor *K* bywhere = *E* for plane stress condition and = *E*/(1 − *ν*^{2}) for plane strain condition, with *ν* representing the Poisson ratio. Irwin [25] proposed that the plastic zone corrected crack length *a*_{e} can be obtained bywhere *a* is the crack length, *β* = 2 for plane stress, and *β* = 6 for plane strain conditions.

In 1976, Shih and Hutchinson [3] developed a new method for fully plastic *J*-integral solutions. Upon consideration of a fully plastic cracked structure in which the elastic strains *ε*_{e} are vanishingly small compared with the plastic strains *ε*_{p}, the material defined by (1) follows a pure power-law stress-strain curve:

Under such assumption and close to the crack tip, the crack tip stress fields are given by the HRR singularity [26]where (*r*, *φ*) are polar coordinates centered at the crack tip, *I*_{n} is an integration constant, and are dimensionless stress functions. The HRR equation can be rewritten in the form of *J*-integral:

With the application of Ilyushin’s theorem [27] that the fully plastic stresses are simply proportional to the applied load *P*, the fully plastic *J* given by (7) can be expressed in terms of the applied load aswhere *W* is the component width, *b* = *W* − *a* defines the uncracked ligament, represents additional characteristic length for the component, and *h*_{1} is the plastic influence function dependent on crack size, specimen geometry, and strain-hardening exponent. In (8), the generalized load is normalized by a reference load *P*_{ref} which may be freely chosen provided it is proportional to *σ*_{0} but is often identified with the plastic limit load of the cracked component *P*_{L}.

##### 2.2. Extension to Circumferentially Cracked Pipes

Figure 1 shows the relevant pipe and crack dimensions for circumferentially cracked pipes subjected to tensile load *T* and bending moment *M*. The circumferential surface crack in this work is assumed to be of constant depth *a* and length 2*c* with an end radius equal to the crack depth (as displayed in Figure 1). For the thin-walled pipes with large diameter, the circumferential crack angle 2*θ* is related to the crack length by