Strain-based fracture assessment for an interface crack in clad pipes under complicated loading conditions

Ocean Engineering 198 (2020) 106992

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Strain-based fracture assessment for an interface crack in clad pipes under complicated loading conditions Haisheng Zhao a, b, Xin Li a, b, *, Seng Tjhen Lie c a

State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian, 116024, China School of Hydraulic Engineering, Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian, 116024, China c School of Civil and Environmental Engineering, Nanyang Technological University, 50 Nanyang Avenue, 639798, Singapore b

A R T I C L E I N F O

A B S T R A C T

Keywords: Welded clad pipeline Weld toe Surface crack Reference strain fracture assessment formulation

In welded clad pipelines, the weld toe is a critical failure position due to the combined effects of the potential weld defects and the stress concentration induced by weld reinforcement. The fracture risk in this position has seldom been assessed. Moreover, the pipelines are often exposed to complicated loading environments during the service period. Thus, the fracture responses of the pipelines with a crack at the weld toe and subjected to tension and internal pressure are considered in this study. A reference strain fracture assessment formulation is derived for the weld toe crack in welded clad pipelines. The formulation detailed expression form is determined by the extensive parametric finite element (FE) analyses and standard least square fitting method. The accuracy of the proposed formulation is validated by conducting a comparative study in J values attained from the formulation and FE analysis. Finally, a further study on extending the application range of the estimation formulation is carried out.

1. Introduction The increasing demand for recoverable corrosive hydrocarbons has motivated the introduction of a clad C–Mn steel pipe with an internal layer of corrosion resistant alloy (CRA). The clad pipe segments are welded together to construct the whole pipeline. During the welding procedure, some micro defects may be incorporated in the pipe welds, and these defects are not easily identified by non-destructive testing (NDT). During the service period, the welded pipelines can experience complicated loading conditions, e.g., longitudinal and transversal forces generated by ground movement, internal pressure exerted by trans­ ported gas or liquid, external pressure induced by sea water, giving rise to large plastic deformation in pipelines, up to the order of 3% (Yi et al., 2012a,b,c). The combined effects of these loads may trigger the growth and coalescence of micro defects to further propagate into a macro crack, which finally leads to the structural failure (Hoh et al., 2010). Therefore, it is important to perform the fracture assessment for the cracked pipelines subjected to large plastic deformation. Based on the GE/EPRI approach, Kim et al. (2002) performed engi­ neering estimates for J-integral in pipes with a part-through surface crack. Then, the obtained GE/EPRI J-estimation equation was re-derived by using the reference stress method (Anderson, 2005), which extends

its application range for all types of stress-strain behaviors, not only limited to the Ramberg-Osgood material constitutive model. Subse­ quently, the reference stress method was further developed by Tkaczyk et al. (2011) for a defect assessment in pipelines, and the proposed method for a parent material can also be safely applied to the case of over-matched welds. It is worth noting that the estimation methods mentioned above are all designed for the pipelines under the load-controlled conditions (Chiodo and Ruggieri, 2010; Paredes and Ruggieri, 2015; Souza and Ruggieri, 2015; Souza et al., 2016). However, the loading scheme of pipelines is controlled by the displacement or strain in some cases. Therefore, the strain-based method should be developed for the structural integrity assessment (Bastola et al., 2017; Budden, 2006; Jayadevan et al., 2004; Jia et al., 2016, 2017; Lie et al., 2017; Østby et al., 2005; Parise et al., 2015; Souza and Ruggieri, 2017; Zhao et al., 2017, 2019, 2018). A reference strain approach was estab­ lished by Nourpanah and Taheri (2010) to evaluate the fracture re­ sponses of a homogeneous pipeline subjected to large plastic strains. Yi et al. (2012a,b,c) conducted the fracture analyses of girth welded clad pipelines with a circumferential surface crack subjected to biaxial loading conditions, and it is concluded that BS 7910 (2013) gives an over-conservative prediction in the fracture assessment, especially for a large plastic strain loading case. However, the formulation proposed by

* Corresponding author. State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian, 116024, China. E-mail address: [email protected] (X. Li). https://doi.org/10.1016/j.oceaneng.2020.106992 Received 7 November 2019; Received in revised form 15 January 2020; Accepted 18 January 2020 Available online 28 January 2020 0029-8018/© 2020 Elsevier Ltd. All rights reserved.

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Ocean Engineering 198 (2020) 106992

Yi et al. (2012a,b,c) is only for a specific pipe geometric configuration. As seen in Fig. 1, the weld centerline (WCL) and weld toe are two main failure positions in welded pipelines. In comparison with the WCL, the weld toe is a more vulnerable position of crack initiation and propagation due to the stress concentration raised by weld reinforce­ ment (Fig. 1(b)) and the potential defects induced by incomplete fusion (Fig. 1(c)), slag inclusions, etc (Yi et al., 2012a,b,c). However, the aforementioned research works all aimed at the pipelines with surface cracks located at the WCL (Bastola et al., 2017; Budden, 2006; Chiodo and Ruggieri, 2010; Jayadevan et al., 2004; Jia et al., 2016, 2017; Lie et al., 2017; Østby et al., 2005; Paredes and Ruggieri, 2015; Parise et al., 2015; Souza and Ruggieri, 2015, 2017; Zhao et al., 2019), and seldom investigations can be found for the fracture analysis of a weld toe crack, i.e., a crack located at the interface of outer pipe and girth weld, in welded pipelines (Yi et al., 2012a,b,c; Zhao et al., 2018). Therefore, the fracture assessment for welded clad pipelines with an interface crack and subjected to complicated loading conditions is carried out in the present study.

where α is a dimensionless constant, εy and σy are the yield strain and yield stress of the material, respectively; a, θ, t, De are the crack depth, half central angle of crack length, pipe wall thickness and pipe outside diameter, respectively; b is the uncracked ligament length with b ¼ t – a, n is the material strain hardening exponent, h1 is the geometry factor depending on a/t, θ/π , De/t and n, P and PL are the applied load and the limit load of the structure, respectively. The above EPRI J-estimation procedure aiming at the tension case was developed by Chiodo and Ruggieri (2010) for the structural components subjected to a bending moment, � �nþ1 M Jp ¼ αεy σ y bh1 ða = t; θ = π; De = t; nÞ (4) ML

2. Fracture assessment strategies of welded clad pipes

where Rm is the pipe mean radius with Rm ¼ (De - t)/2, and β is defined as π h �θ ��a�i β¼ 1 (6) 2 π t

where M is the applied bending moment, ML is the limit bending moment and its expression is given as the following: � � a sinθ (5) ML ¼ 2σ y R2m t 2sinβ t

2.1. Stress-based fracture assessment method

The material obeying the Ramberg-Osgood model is assumed in the EPRI J-estimation procedure. However, the flow behavior exists in many materials, deviating considerably from the power law. In this case, applying Eq. (3) or Eq. (4) for the fracture assessment causes a signifi­ cant error. In order to better characterize the flow behavior of materials, Ainsworth (Anderson, 2005) proposed a reference stress J-estimation approach by defining a reference stress σref as

For structures under load-controlled conditions, the stress-based evaluation procedures are usually used for the fracture assessment of cracked components. The EPRI J-estimation approach and the reference stress method (Anderson, 2005) are the two commonly used stress-based methods. By dividing the total J into the sum of the elastic component (Je) and the plastic component (Jp), the EPRI procedure provides a J-integral estimation approach of covering the full range of elastic-plastic regime as J ¼ Je þ Jp

σ ref P M ¼ or ML σ y PL

(1)

Substituting Eq. (7) into Eq. (3) or Eq. (4) gives the following equation � � σ ref εy Jp ¼ σref bh1 εref (8)

where Je is the elastic release rate, which can be determined through the following expression, Je ¼

K 2I E’

(7)

(2)

σy

where εref is the reference strain corresponding to the σ ref. For a material following the Ramberg-Osgood model, Eq. (8) can predict the same Jintegral value with Eq. (3) or Eq. (4). It is noted that Eq. (8) is equally applicable for other types of stress-strain relationship. In other words, the reference stress approach is a generalization of the conventional EPRI J-estimation procedure.

where KI is the Mode-I stress intensity factor, E’ ¼ E for plane stress condition and E’ ¼ E/(1-ν2) for plane strain condition with E and ν being the elastic modulus and the Poisson’s ratio, respectively. The second term of Eq. (1), fully plastic equation of J, is determined as follows: � �nþ1 P Jp ¼ αεy σy bh1 ða = t; θ = π; De = t; nÞ (3) PL

2.2. Strain-based fracture assessment method For the offshore pipelines under reeling installation, the pipelines are subjected to large plastic deformation, up to the order of 3% (Lie et al., 2017; Yi et al., 2012a,b,c). During this process, the strain-controlled or displacement-controlled boundary condition is dominant. Therefore, it is more appropriate and accurate to use the strain-based approach for the fracture assessment. Based on the reference stress approach under­ lying R6, a reference strain method is proposed as follows: � � � εref σref 2 J ¼ F πaσ nom εnom (9) εnom =σnom where F is the geometry factor depending on the structural geometry and loading mode, σnom and εnom are the nominal stress and strain, respec­ tively. The next step is to replace σnom and εnom in Eq. (9) by σ uc and εuc (Linkens et al., 2000), where σuc and εuc are the elastic-plastic uncracked-body equivalent stress and strain, respectively. Eq. (9) now becomes the following form by adding the safety factor of 2,

Fig. 1. (a) Crack placements in clad welds (Macdonald and Cheaitani, 2010); (b) A real weld profile with weld reinforcement in clad pipes (Yi et al., 2012a,b, c); (c) Crack propagation and structural failue induced by incomplete fusion at the interface of outer pipe and girth weld.

J ¼ 2F 2 πaσuc εuc 2

(10)

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Ocean Engineering 198 (2020) 106992

Fig. 2. Schematic of the welded clad pipe with an interface crack.

The strain formulation as indicated in Eq. (10) is not sufficiently accurate in a quantitative fracture assessment, which can qualitatively capture the fracture responses of the pipelines. The reason is that the difference between εnom and εuc becomes larger and larger with the increasing crack depth, violating the underlying assumption of small cracks in Eq. (10). On the basis of Eq. (10), Nourpanah and Taheri (2010) developed a more accurate strain-based J-estimation formulation by proposing a linear relationship between the normalized J and εuc. This formulation was originally established for a crack normal to the pipe surface. However, whether it is equally applicable for the case of an interface crack remains unknown. In this study, it is observed that the linear relationship between the J and εuc still holds true for the welded clad pipelines with an interface crack. Therefore, the reference strain evaluation formulation proposed by Nourpanah and Taheri (2010) is valid for the integrity assessment of an interface crack in welded clad pipelines subjected to tension and internal pressure by developing the new parameter expressions of f1 and f2 instead of original ones as J ¼ σ y tðf1 εuc þ f2 Þ

My ¼

σ wy σout y

(12)

out where σ w y and σ y are the yield stress of the weld metal and outer pipe

steel, respectively. Three mismatch levels, viz., My ¼ 0.8 (20% under­ match), My ¼ 1.0 (evenmatch) and My ¼ 1.25 (25% overmatch), are considered in the current analysis, covering a wide range of material types found in real application (Souza and Ruggieri, 2015). An API X60 pipeline grade steel is selected as the outer pipe material herein and its material properties are σ out ¼ 483 Mpa and nout ¼ 12 (Chiodo and y Ruggieri, 2010; Souza and Ruggieri, 2015); hence, the yield stress of weld metal can be calculated based on Eq. (12), which are summarized in Table 1. Table 2 tabulates the details of pipe geometry, girth weld and crack dimensions. Two different ratios of pipe outside diameter to pipe wall thickness (De/t) are adopted, viz., De/t ¼ 10 and 20, with a constant wall thickness t ¼ 20.6 mm and CRA layer thickness tCRA ¼ 3 mm. The crack size is characterized by the crack depth (a) and crack length (2s ¼ Deθ), and the crack depth ratio (a/t) and crack length ratio (θ/π ) used in this analysis are varying from 0.1 to 0.4 and from 0.05 to 0.20, respectively. The weld groove angle (ϕ), weld root opening width (h) and weld reinforcements (Ru and Rd) are employed to define the weld geometry. For the weld groove angle, ϕ ¼ 45� is considered, and the value of h/t adopted is 0.3, signifying the typical girth weld profile encountered in engineering practice. However, the girth welds with flushed surface are considered in this study, which means that Ru and Rd both tend to infinity. It is because the presence of the weld reinforce­ ment restrains the crack tip opening, inducing a smaller crack driving force. Therefore, neglecting the weld reinforcement can produce a slightly conservative prediction in the J values (please refer to Sub-section 5.2 for details).

(11)

where f1 and f2 are the two new parameter expressions depending on the pipe geometry, crack size and material properties. 3. Numerical models and procedures 3.1. Material properties and geometrical details Fig. 2 shows the schematics of a welded clad pipe with a circum­ ferential part-through surface crack along the interface of girth weld and outer pipe, which is a critical location of crack initiation and growth. The welded clad pipe is composed of three different materials (Fig. 2): outer pipe steel, weld metal and internal CRA layer. It is noted that the heat affected zone (HAZ) is not incorporated in this study due to its narrow width in comparison with the weld width and uncracked liga­ ment length. Hence, ignoring the HAZ causes an ignorable effect on the fracture behaviors. Besides, the HAZ typically presents over-matched material properties compared to its surrounding constituents, i.e., outer pipe steel and weld metal, thus neglecting the HAZ results in a slightly conservative prediction for fracture responses, which is benefi­ cial for the engineering critical assessment of pipelines (Kim and Schwalbe, 2001). For the CRA material and weld metal, identical ma­ terial properties are adopted. It is because the filler material commonly used in the welding of clad pipe segments, such as nickel-chromium alloy 625 (UNS N06625), has almost the same mechanical properties as the CRA material (Souza et al., 2016; Souza and Ruggieri, 2017). In this study, it is assumed that the material properties of outer pipe steel and weld metal (or inner CRA material) follow the classical Ramberg-Osgood relationship. A weld strength mismatch factor (My) is introduced to characterize the mismatch effect between these two types of materials,

3.2. Model development and numerical procedures As mentioned in the above, various parameters, i.e., pipe diameter, weld geometry, crack size, yield stress and strain hardening exponent, are incorporated in this study to investigate the fracture responses of welded clad pipelines with an interface crack. A large number of FE Table 1 Yield stress and strain hardening exponent of pipeline materials (Souza and Ruggieri, 2015). My

3

Outer carbon steel

Weld metal

σout y (MPa)

nout

σw y (MPa)

nw

0.8

483

12

386.4

1.0 1.25

483 483

12 12

483 603.8

6 9 12 12 12 15 18

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Ocean Engineering 198 (2020) 106992

small geometry change (SCC) assumption are incorporated in the pre­ sent FE analysis. Fig. 6 shows the boundary conditions used in the present study for the welded clad pipeline. Due to symmetry, only half of the pipe needs to be considered; hence a symmetric boundary condition is applied to the surface of Y ¼ 0. At the left end of the pipe, the displacements in X-axis and Z-axis directions are constrained for preventing rigid motion. A tensile displacement loading (u) is applied to the right end of the pipe for providing the tension, and εuc can be expressed in the form of u as

Table 2 Table of analysis matrix. Parameter

Value

De/t a/t θ/π

10, 20 0.1, 0.15, 0.2, 0.3, 0.4 0.05, 0.1, 0.15, 0.2

models are required to be created. Therefore, a FE mesh generator is developed by using MATLAB code to simplify the cumbersome and timeconsuming task. The FE mesh generator can conveniently produce FE models of various pipeline types and crack locations, not limited to the pipe model of the present study. A detailed function list is depicted in Fig. 3(a) to better describe the function modules of the mesh generator. The generated FE models are processed by ABAQUS (2011) and post-processed by a self-developed Python script to extract the required results, e.g., displacement, stress, J-integral (Fig. 3(b)). In the generation of the FE models, the most pivotal part is to determine the position coordinates of the crack front line, which is the baseline of constructing the crack tube (Fig. 4(a)). The crack front line can be described by considering the constant crack depth part AB and varying depth part BC separately as follows: θarc ¼ arcsinð2a = De Þ

(13)

YD ¼

(14)

ðDe = 2

ZD ¼ ðDe = 2 YE ¼

a cosβE Þsinðθ

a cosβE Þcosðθ

θarc Þ þ a sinβE cosðθ

θarc Þ

a sinβE sinðθ

θarc Þ�

θarc Þ

u L

(18)

εuc is set up to 3% by allowing for the large plastic deformation of the pipeline during the reeling installation or in-service operation. Besides, an internal pressure (P) of 20 MPa is applied to the internal surface of the pipeline to realize the biaxial loading conditions. Based on the flow theory of plasticity, the J-integral value depends on the loading path. For the biaxial loading conditions of tension and internal pressure, three different loading paths are considered: applying P first and then εuc (load path 1), applying P and εuc simultaneously (load path 2), and applying εuc first and then P (load path 3). Fig. 7 shows the comparisons of the Jintegral values obtained from the three loading paths, and it is observed that the load path 1 induces the maximum value of J-integral, which produces the same conclusion with Yi et al. (2012a,b,c). Therefore, the biaxial loading path used in this study is to apply the internal pressure, P, first before the εuc acts on the pipeline segment. The validity of the generated FE model needs to be confirmed before it is used for the fracture analysis of the welded clad pipelines with an interface crack and subjected to biaxial loading conditions. At first, the FE mesh generator is employed to create the FE model of the homoge­ neous pipeline with a surface crack normal to the pipe surface by setting ϕ ¼ 0, and the J values obtained are compared with Nourpanah and Taheri (2010) results. A good agreement between one another is observed with the largest percentage difference being about 6% (Fig. 8), convincingly verifying the validity of the mesh refinement and FE modelling. Then, for the welded clad pipelines with an interface crack, convergent tests covering the range of various parameters tabulated in Tables 1 and 2 are conducted to determine the required number of el­ ements. It is noted that the number of elements ranging from 20,000 to 35,000 is adequate in this study depending on the pipe geometry and crack size. The above sensitivity analyses provide confidence in the accuracy of the subsequent parametric study for the welded clad pipe­ lines with an interface crack.

(15)

aÞcosβD

½ðDe = 2

ZE ¼ ðDe = 2

aÞsinβD

εuc ¼

(16) (17)

where D and E are any point in segment AB and BC, respectively, βD and βE denote the corresponding angle of AOD and BO’E (Fig. 4(b)). Based on the crack front line, a focused spider-web mesh pattern along the crack front is used with a small keyhole geometry at the crack tip to capture the high strain gradient and overcome the convergent issue induced by the large plastic deformation (Fig. 4(a)). The small radius of the keyhole in this study is set to 0.001 mm 12 circumferential layers surrounding the crack front are employed to provide the distance sufficiently far from the crack tip to ensure the path independence of the J-integral. Based on the mesh strategies described above, the crack tube can be generated (Fig. 4(a)). Finally, the welded clad pipe model is constructed step by step as shown in Fig. 5. The element type used is 20-node brick element with reduced integration (C3D20R). The deformation plasticity and the

4. Determination of the reference strain J-estimation formulation The necessity of developing a new reference strain J-estimation formulation for an interface crack in welded clad pipelines subjected to tension and internal pressure should be confirmed first. The engineering critical assessments of a cracked pipeline under uniaxial stress state (tension or bending) were carried out by some scholars (Chiodo and Ruggieri, 2010; Paredes and Ruggieri, 2015; Souza and Ruggieri, 2015, 2017; Souza et al., 2016). Even though Yi et al. (2012a,b,c) have established the estimation equation for a cracked clad pipeline under tension and internal pressure, their equation is only applicable to a specific pipe geometry and material property. In this study, the fracture analysis for a cracked clad pipeline under biaxial loading conditions is conducted by covering a wide range of geometric configurations and weld strength mismatch values. Fig. 9 shows the comparison of J values for the cracked clad pipeline subjected to uniaxial and biaxial stress state, respectively. It is clearly noted that the J values obtained from the biaxial stress state are always larger than those from the uniaxial stress state, and the largest percentage difference between one another is attained at the case of De/t ¼ 20, a/t ¼ 0.1, My ¼ 0.8 and nw ¼ 12 with the value being about 60%, verifying a remarkable influence of the

Fig. 3. (a) Function list of the FE mesh generator and (b) flowchart of the present FE analysis. 4

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Ocean Engineering 198 (2020) 106992

Fig. 4. Schematic of the crack tube.

loading condition cases, viz., tension þ internal pressure and bending moment þ internal pressure, respectively. The J values of the former case are always slightly larger than that of the latter case. Therefore, it is more significant by proposing the reference strain estimation formula­ tion for the combined tension and internal pressure case since it can be equally suitable for the bending moment and internal pressure case, but not vice versa. As indicated in Eq. (11), the key of proposing the reference strain Jestimation formulation is to confirm the expressions of f1 and f2. For convenience, Eq. (11) can be rewritten into the following form by replacing the original f1 and f2 as J

σ out y t

� � � � � � � � ¼ f1 De t; a t; θ π ; My ; nw εuc þ f2 De t; a t; θ π; My ; nw (20)

Parametric FE analyses totally including 280 models are performed to develop the factors f1 and f2 by covering a wide range of parameter values as tabulated in Tables 1 and 2, and Fig. 11 depicts the whole process of determining f1 and f2. A nonlinear evolution curve between J/ (σout y t) and εuc can be observed at the initial deformation stage, which is referred to as a short transient region prior to the fully plastic defor­ mation state (Zhao et al., 2018). Then, a linear dependence of J/(σ out y t) on εuc always holds true for the range of 0.5%–3.0%; hence, the factors f1 and f2 are ascertained by fitting the numerical data in this range. The factor f1 can be easily obtained by extracting the slope of this curve in Fig. 11, and the intercept at ordinate is employed to determine the f2. The same operation procedure is carried out for all the parameter combinations incorporated in this study, and a series of f1 and f2 values

Fig. 5. Construction of welded clad pipelines.

internal pressure induced by the transported liquid or gas on the structural integrity. Besides, in some working conditions, the pipelines undergo the combined action of bending moment and internal pressure, and the relationship between the global strain and bending moment is given as

εuc ¼

De γ 2L

(19)

where γ denotes the rotation angle of the pipeline. Fig. 10 presents a comparative study of J values for the pipeline under two different biaxial

Fig. 6. Boundary conditions of the welded clad pipe subjected to tension and internal pressure. 5

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Ocean Engineering 198 (2020) 106992

0.30

Load path 1 Load path 2 Load path 3

0.25

a/t = 0.3 / = 0.1 My = 0.8

0.20

t) y

h �θ �B2 i�a�B3 f2 ¼ B1 t π

nw = 9

0.15 0.10 0.05 0.00 0.000

0.005

0.010

0.015

0.020

0.025

0.030

uc

Fig. 7. Effect of load path on the J-integral.

0.35 0.30

uc

The objective of this section is to extend the application range of the

a/t = 0.3 / = 0.10 / = 0.659 (n = 10) y u

= 0.04

0.45

Tension and pressure, My = 0.8, nw = 9

0.40

Bending and pressure, My = 0.8, nw = 9

Tension and pressure, My = 1.25, nw = 15

0.35

0.20 uc

= 0.03

uc

= 0.02

uc

= 0.01

J/(

0.05

0.25

y

t)

0.15 0.10

Bending and pressure, My = 1.25, nw = 15

0.30 out

J/( yt)

0.25

5. Extension in application scope of the estimation formulation

Parameters used: De/t = 15

Present analysis Nourpanah and Taheri (2010)

(22)

where A1 to A4 and B1 to B3 are coefficients depending on De/t, My and nw as given in Tables 3 and 4. Substituting Eqs. (21) and (22) into Eq. (20) obtains the reference strain J-estimation formulation for an inter­ face crack in welded clad pipelines under biaxial loading conditions. The goodness of fit of the proposed formulation is required to be verified due to its complex form. Fig. 12 displays the comparisons of J values ob­ tained from the formulation and numerical data by considering effects of various parameters, and these two sets of values are well consistent with one another, signifying the J-estimation formulation being a good fit to the FE data.

J/(

out

evolution trends of f1 and f2, their concrete expression forms can be constructed by using multiple regression analysis as h � �A4 i h �θ �A2 i�a� A3 πθ (21) f1 ¼ A1 t π

Parameters used: De/t = 10

Parameters used: De/t = 10 / = 0.1 = 0.03

0.20

uc

0.15 0.10

0.00

400

450

500

y

0.05

550

(MPa)

0.00 0.05

Fig. 8. Comparisons of J values obtained from present analysis and Nourpanah and Taheri (2010) research work for varying yield stress and uncracked strain.

0.40

0.15

0.20

0.25

a/t

0.30

0.35

0.25

Tension Tension and internal pressure

Tension Tension and internal pressure

0.20

0.35 0.30

0.15

t out

y

0.20

J/

y

J/

out

t

0.25

0.10

0.15 0.10

0.05

0.05 0.00 0.05

0.10

0.15

0.20

0.25

0.30

0.35

a/t (a) De/t = 10, / = 0.1, My = 0.8, nw = 9

0.40

0.40

0.45

Fig. 10. Comparison of the J values obtained from two different biaxial loading conditions.

varying with De/t, a/t, θ/π, My and nw are attained. Based on the 0.45

0.10

0.45

0.00

(0.8, 6)

(0.8, 12)

(1.0, 12)

(My, nw)

(1.25, 12)

(b) De/t = 10, a/t = 0.2, / = 0.1

Fig. 9. Effect of internal pressure on the J values for εuc ¼ 0.03. 6

(1.25, 18)

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Ocean Engineering 198 (2020) 106992

0.30

Fitted line

0.25

y

J/(

out

t)

0.20 0.15

Parameters used: De/t = 20

0.10

f1

0.05

f20.000.000

a/t = 0.2 / = 0.1 My = 0.8

nw = 9 0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

uc Fig. 11. Determination procedure of factors f1 and f2. Table 3 Coefficients for the polynomial fitting of f1 and f2 shown in Eq. (20) for De/t ¼ 10. My

nw

A1

A2

A3

A4

0.8

6 9 12 12 12 15 18

6370 9344 6892 15850 15630 27390 36560

2.133 2.187 1.964 2.412 2.509 2.712 2.801

6.188 5.678 4.732 6.295 7.352 7.666 7.689

0.555 0.541 0.518 0.551 0.610 0.616 0.610

1.0 1.25

B1 7.543 7.359 4.566 7.079 6.709 10.053 12.221

B2

B3

1.266 1.308 1.155 1.329 1.337 1.418 1.456

3.838 2.866 1.988 2.631 2.918 2.934 2.892

Table 4 Coefficients for the polynomial fitting of f1 and f2 shown in Eq. (20) for De/t ¼ 20. My

nw

A1

A2

A3

A4

0.8

6 9 12 12 12 15 18

11220 19200 11740 33210 47200 60200 63890

1.906 2.021 1.739 2.207 2.485 2.468 2.421

5.237 5.164 4.058 5.563 6.248 6.526 6.367

0.407 0.438 0.410 0.429 0.451 0.457 0.443

1.0 1.25

B1 10.241 19.113 11.582 19.833 13.882 28.633 31.604

B2

B3

1.108 1.254 1.122 1.283 1.313 1.357 1.374

3.606 3.044 2.071 2.799 2.779 3.115 2.954

developed reference strain J-estimation formulation in Eq. (20) by considering the effects of yield strength, weld profile, potential material property difference, realistic stress-strain relation and temperature.

out of the σout y as part of the characteristic variable, σ y t. For the pipe wall

5.1. Effect of yield strength and pipe wall thickness on the J

largely reduces the dependence of Eq. (20) on the outer pipe yield strength and pipe wall thickness. In other words, the developed J-esti­ mation formulation can be available for a wide range of outer pipe yield strengths and pipe wall thickness, not just limited to the case of σ out ¼ y

thickness, three different t, viz., t ¼ 15 mm, t ¼ 20.6 mm and t ¼ 25 mm, are considered, and almost identical J/(σout y t) values are observed (Fig. 13(b)). Therefore, setting the σout y t as the characteristic variable

Even though the J-estimation formulation in Eq. (20) has been nondimensionalized by σ out y t, it is developed based on the outer pipe

483 MPa and t ¼ 20.6 mm.

made of an API X60 pipeline grade steel with the σout y and t being 483

MPa and 20.6 mm, respectively. Thus, the general applicability of Eq. (20) needs to be proved due to the variation in the material property and geometrical dimension of the pipelines encountered in practice. It is noted from Fig. 13(a) that the dimensionless J, i.e., J/(σout y t), obtained

5.2. Effect of weld profile on the J The estimation formulation is built up for the cracked clad pipelines with flushed weld surface, i.e., Ru -> ∞ or hu ¼ 0.0 mm (Fig. 2). How­ ever, the weld reinforcement more or less exists in some actual situa­ tions; hence, the availability of the proposed formulation for the girth

from σout ¼ 483 MPa and σ out ¼ 579.6 MPa (20% higher than 483 MPa) y y for an identical t are well consistent with one another, and the same is true for the case of the lower σout y value, which demonstrates the validity 7

H. Zhao et al.

Ocean Engineering 198 (2020) 106992

0.35

0.7

FE data, My = 0.8, nw = 9

Eq. (20), My = 0.8, nw = 9

0.30

Eq. (20), My = 0.8, nw = 9

0.6

FE data, My = 1.0, nw = 12

Eq. (20), My = 1.0, nw = 12

0.25

FE data, My = 0.8, nw = 9

FE data, My = 1.0, nw = 12

Eq. (20), My = 1.0, nw = 12

0.5

FE data, My = 1.25, nw = 15

FE data, My = 1.25, nw = 15

Eq. (20), My = 1.25, nw = 15

0.20 out

J/(

0.15

y

t)

0.4

y

J/(

out

t)

Eq. (20), My = 1.25, nw = 15

0.3

0.10

0.2

0.05

0.1

0.00

0.005

0.010

0.015

0.020 uc

(a) De/t = 10, a/t = 0.3,

0.025

0.0

0.030

0.005

0.010

0.015

0.020

0.025

uc

= 0.10

(b) De/t = 20, a/t = 0.3,

0.030

= 0.10

Fig. 12. Validation of the proposed estimation formulation. 0.30 out y

0.20

out

(= 483 MPa)

y

My = 0.8, nw = 6

0.25

My = 0.8, nw = 12 My = 1.0

0.15

0.05

0.00 0.000

t

t = 20.6 mm a/t = 0.2 / = 0.1

0.005

0.010

y

out

Parameters used: De/t = 10

0.15

Parameters used: De/t = 20

J/

t y

J/

out

0.20

My = 1.25, nw = 12

My = 1.25, nw = 18 0.10

t = 15 mm t = 20.6 mm t = 25 mm

(= 579.6 MPa, 20% higher)

out

0.10

y

0.05

0.015

0.020

0.025

0.030

0.035

0.00 0.000

nw = 9

0.005

0.010

0.015

uc

(a) Effect of

out y

on the J/

out y

= 483 MPa

a/t = 0.2 / = 0.1 My = 0.8 0.020

0.025

uc

(b) Effect of t on the J/

t

out y

0.030

0.035

t

out Fig. 13. Effect of (a) σ out y and (b) t on the J/(σ y t).

weld with face reinforcement should be investigated. Herein, three different cases, viz., hu ¼ 0.0 mm (case 1), hu ¼ 2.6 mm (case 2), and hu ¼ 4.0 mm (case 3), are considered. The hu value in case 2 is taken from a real weld reinforcement dimension as shown in the paper of Yi et al. (2012a,b,c), and the hu in case 3 is set to 4.0 mm in view of the AWS D1.1 (2000) recommendation of retaining minimum weld reinforcement (not exceeding 3 mm). Fig. 14 shows the comparative study of the J values obtained from the three cases by covering varying crack sizes, weld mismatch levels and strain hardening exponents, and it is clearly noted that the reduced hu causes an increase in the J. In a linear elastic fracture mechanics regime, the corresponding fracture parameter, i.e., stress intensity factor (SIF), can be magnified due to the stress concentration induced by the weld reinforcement, especially for a shallow crack. However, for the large plastic strain case of this study, the magnification effect can be negligible and the presence of weld reinforcement restrains the further opening of the crack tip, resulting in a decreased J value. Therefore, the reference strain J-estimation formulation in Eq. (20) can provide a reasonably conservative fracture assessment for the cracked clad pipelines with weld reinforcement. As stated previously, a typical girth weld profile with ϕ ¼ 45� and h/t ¼ 0.3 is adopted in the development of the J-estimation formulation. In

0.7

My = 0.8, nw = 12:

hu = 0.0 mm

0.6

y

t) out

J/(

0.3

hu = 0.0 mm

hu = 2.6 mm

0.5 0.4

My = 1.25, nw = 12:

hu = 2.6 mm

hu = 4.0 mm

hu = 4.0 mm

Parameters used: De/t = 10

0.2

/ = 0.1 = 0.03

uc

0.1 0.0 0.05

0.10

0.15

0.20

0.25

a/t

0.30

0.35

0.40

Fig. 14. Effect of weld reinforcement on the J values.

8

0.45

H. Zhao et al.

Ocean Engineering 198 (2020) 106992

order to extend the application scope of the formulation in the weld profile, the ϕ and h/t values ranging from 30� to 60� and from 0.2 to 0.4, respectively, are employed in this analysis, incorporating the commonly-used weld shape found in welded pipelines. It is observed from Fig. 15(a) that, for a constant h/t, a larger ϕ results in a decrease in the J value by considering various weld mismatch levels and strain hardening exponents. As the ϕ increases, the angle (90o-ϕ/2) between the crack face and the applied tensile loading becomes smaller and smaller, reducing the effective loading in opening the crack (Fig. 2), and then decreasing the corresponding J. Hence, the reference strain Jestimation formulation for ϕ ¼ 45� can reliably predict the fracture re­ sponses for the cracked clad pipelines including ϕ varying from 45� to 60� with the largest over-estimation percentage difference being only 6.4% in the case of Fig. 15(a). For the weld root opening width, the change of h/t with a constant ϕ exerts relatively little effect on the J by noticing the percentage difference between one another in Fig. 15(b) within 2% except the case of My ¼ 0.8 and nw ¼ 12, in which the J decreases with the reduced h/t. Therefore, the J-estimation formulation initially developed for h/t ¼ 0.3 can make a slightly conservation pre­ diction in the J for the cracked clad pipelines with h/t being smaller than 0.3. However, the formulation mentioned above should be used with caution in the fracture assessment when the h/t of the girth weld is larger than 0.3.

1 will undergo a larger deformation and then a smaller deformation occurs in the pipe-2, inducing a decrease in the J value. Therefore, the reference strain J-estimation formulation in Eq. (20) can predict a reasonably conservative result in the J for a smaller yield strength or a larger strain hardening exponent in pipe-1 in comparison with that in pipe-2, and the largest over-estimation percentage difference is about 14% in the case of Fig. 16. However, as the potential material property difference between adjacent pipes further enlarges, the proposed formulation will produce an over-conservative prediction in the J. For example, if the yield strength of pipe-1 is 20% lower than that of pipe-2, the percentage difference of the J value given by the formulation and FE analysis becomes almost 60%. In general, the adjacent pipes made of the same material do not exhibit distinct property difference; hence, the above J-estimation formulation can still be well applied to the fracture assessment of welded clad pipelines with potential material property difference between adjacent outer pipes. 5.4. Effect of Lüders plateau and temperature on the J In this study, the Ramberg-Osgood model is employed to charac­ terize the stress-strain relation of the clad pipeline. However, the ma­ terial of the outer pipe in clad pipelines is usually low carbon steel, which exhibits a Lüders plateau after initial yielding (Wang et al., 2019). In addition, more and more pipelines are exposed to low temperature conditions due to the exploitation of oil and gas resources continuously moving into harsher environments, e.g., the Arctic (Dahl et al., 2018). Yield strength and ductile-to-brittle transition (DBT) are two parameters apparently affected by the low temperature, while the latter one is not the scope of this analysis. Østby et al. (2013) and Ren et al. (2015) investigated the tensile properties of a 420 MPa steel with the temper­ ature varying from 0 � C to 90 � C, and the dependent relationships of yield strength (σy,T) and Lüders strain (εL) on the temperature are given as � � 105 σ y;T ¼ 420 þ 0:73 137 (23) 491 þ 1:8T

5.3. Effect of potential material property difference between adjacent pipes on the J The clad pipelines are composed of a series of pipe segments by welding. Even though these pipe segments are made of an identical material, the adjacent pipes welded together may exist difference in material properties due to the effect of pressing process. Hence, it is necessary and significant to investigate the influence of potential ma­ terial property difference between adjacent pipes on the J. Fig. 16 pre­ sents the comparative study of the J values calculated for varying yield strengths and strain hardening exponents of outer pipe. In this analysis, the welded clad pipeline is divided into two parts, viz., pipe-1 and pipe2, and the material property difference is implemented by changing the properties (σ out y and nout) of pipe-1 and keep these of pipe-2 constant as

indicated in Fig. 16. It is noted that a smaller

σ out y

in pipe-1 relative to

The engineering stress-strain curves of the steel at different tem­ peratures are shown in Fig. 17. The σ y,T and εL values are 470 MPa and 1.42% at T ¼ 0 � C and gradually increased to 542 MPa and 2.23%, respectively, at T ¼ 90 � C. In a word, a lower temperature brings about an increase in the yield strength and Lüders strain for the steel. Hence,

pipe-2 always causes a downward shift in the J values, and a reverse trend is observed for the nout. A smaller yield strength and a larger strain hardening exponent both imply a “softer” pipe; thus, when a same displacement loading is applied to the welded pipeline, the “softer” pipe-

0.22

0.20

o

h/t = 0.3, = 45 o h/t = 0.3, = 30 o h/t = 0.3, = 60

0.18

0.18

0.12

t) out

a/t = 0.2 / = 0.1 = 0.03 uc

y

0.14

Parameters used: De/t = 10

0.16

J/(

out

o

= 45 , h/t = 0.3 o = 45 , h/t = 0.2 o = 45 , h/t = 0.4

0.20

Parameters used: De/t = 10

y

t)

0.16

J/(

(24)

εL ¼ 0:0142expð 0:005TÞ

0.10

a/t = 0.2 / = 0.1 = 0.03 uc

0.14 0.12 0.10

0.08

0.08

0.06 (0.8, 6)

(0.8, 12)

(1.0, 12)

(1.25, 12)

0.06

(1.25, 18)

(My, nw)

(0.8, 6)

(0.8, 12)

(1.0, 12)

(1.25, 12)

(1.25, 18)

(My, nw) (b) Effect of weld root opening width on J

(a) Effect of weld groove angle on J

Fig. 15. Effects of weld groove angle and weld root opening width on the J values. 9

H. Zhao et al.

Ocean Engineering 198 (2020) 106992

Pipe-2

Pipe-1

Pipe-1:

out y out y out y

= 483 MPa

0.20

= 458.9 MPa (-5%) = 507.2 MPa (+5%)

out

0.16

0.24

Parameters used: De/t = 10

Pipe-2: nout = 12

a/t = 0.2 / = 0.1 = 0.03 uc

Pipe-1:

nout = 12

nout = 9

nout = 15

0.16

J/(

out

J/(

y

t)

0.20

a/t = 0.2 / = 0.1 = 0.03 uc

0.28 Pipe-2: out = 483 MPa y

t)

0.24

Parameters used: De/t = 10

y

0.28

0.12

0.12

0.08

0.08

0.04

(0.8, 6)

(0.8, 12)

(1.0, 12)

(1.25, 12)

0.04

(1.25, 18)

(My, nw)

(0.8, 6)

(0.8, 12)

(1.0, 12)

(1.25, 12)

(1.25, 18)

(My, nw) (b) Effect of strain hardening exponent

(a) Effect of yield strength difference

Fig. 16. Effect of potential material property difference between adjacent pipes.

the effect of Lüders plateau on the stress-strain relation should be considered, especially for a pipeline operated in low temperature envi­ ronment. Wang et al. (2019) carried out the fracture analysis of a cracked X65 pipe with Lüders plateau, and it is concluded that properly selecting the softening modulus of an “up-down-up” constitutive model contributes to the fracture assessment of cracked pipes in the presence of Lüders plateau. In the present analysis, a Ramberg-Osgood fitting of realistic stress-strain curves with Lüders plateau is applied for evaluating the fracture responses of an interface crack in welded clad pipelines under tension and internal pressure0. Fig. 18(a) displays three different fitting strategies for the stress-strain curve with Lüders plateau, i.e., a best fit to the elastic part of the curve (red line), a best fit to the strain hardening part of the curve (dark cyan line), and an average fit (blue line). The evolution curves of J with εuc obtained from the realistic stress-strain curve and the three Ramberg-Osgood fits are depicted in Fig. 18(b). The J values given by the three fitting approaches can reasonably trace the realistic J-εuc curve well within a certain range of εuc; however, the elastic fitting method is recommended for use since it

can conservatively predict the fracture responses for most of the strain range relative to the other two methods. Therefore, the reference strain J-estimation formulation can be employed for the fracture assessment of cracked pipelines with a realistic stress-strain relation based on the elastic fitting method. 6. Conclusions The fracture responses for an interface crack in welded clad pipelines subjected to tension and internal pressure are analyzed. A FE mesh generator is developed to create the corresponding FE models, and the accuracy of the models is verified by observing a consistent result in the J values extracted from the present analysis and Nourpanah and Taheri (2010) paper. Then, the necessity of proposing a reference strain eval­ uation scheme for the cracked clad pipelines under biaxial loading conditions is elucidated by considering the particularity of the interface crack and the significant influence of internal pressure on the final J. Therefore, based on the research work of Nourpanah and Taheri (2010), a reference strain J-estimation formulation is established for the inter­ face crack and biaxial loading case, and a linear dependence of the J on the global strain is observed. The detailed expression forms of the formulation are determined by using the extensive parametric FE ana­ lyses, which incorporate the various pipe diameters, crack sizes, weld mismatch levels and strain hardening exponents. The accuracy of the proposed formulation is confirmed by comparing the J results from the formulation with those from FE analysis. Finally, the application scope of the developed formulation is largely extended by taking into account the effects of yield strength, weld profile, potential material property difference, realistic stress-strain relation and temperature.

700

Engineering stress (MPa)

600 500 400 300 200

Declaration of competing interest o

0 C,

y

100

= 470 MPa

o

-30 C,

y

= 487 MPa

y

= 511 MPa

y

= 542 MPa

o

-60 C, o

-90 C,

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. CRediT authorship contribution statement

0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20

Haisheng Zhao: Conceptualization, Writing - original draft. Xin Li: Conceptualization, Writing - review & editing. Seng Tjhen Lie: Writing review & editing.

Engineering strain (mm/mm) Fig. 17. Engineering stress-strain relations of a steel for different temperature (Ren et al., 2015). 10

H. Zhao et al.

Ocean Engineering 198 (2020) 106992

1000

700

800 700

400

-1

J (N mm )

True stress (MPa)

500

300 200

Luders plateau, Elastic,

100 0 0.00

Luders plateau Elastic Average Post yield

900

600

out y y

Post yield,

0.02

0.04

0.06

0.08

y

= 487 MPa

y

0.10

0.14

nw = 12

100

= 390 MPa, nout = 9

0.12

400

a/t = 0.2 / = 0.1 w = 483 MPa y

200

= 440 MPa, nout = 11.7

out

500

300

= 483 MPa, nout = 15.2

out

Average,

out

600

Parameters used: De/t = 10

0.16

True strain (mm/mm) (a) A realistic stress-strain curve and three Ramberg-Osgood fits

0 0.000

0.005

0.010

0.015

0.020

0.025

0.030

uc

(b) Evolution curves of J with

uc

Fig. 18. (a) Three Ramberg-Osgood fits to a realistic stress-strain curve with a Lüders plateau and (b) the corresponding evolution curves of J with εuc.

Acknowledgements

Nourpanah, N., Taheri, F., 2010. Development of a reference strain approach for assessment of fracture response of reeled pipelines. Eng. Fract. Mech. 77, 2337–2353. Østby, E., Akselsen, O.M., Hauge, M., Horn, A.M., 2013. Fracture mechanics design criteria for low temperature applications of steel weldments. In: The Twenty-Third International Offshore and Polar Engineering Conference. International Society of Offshore and Polar Engineers, pp. 315–321. Østby, E., Jayadevan, K.R., Thaulow, C., 2005. Fracture response of pipelines subject to large plastic deformation under bending. Int. J. Pres. Ves. Pip. 82, 201–215. Paredes, M., Ruggieri, C., 2015. Engineering approach for circumferential flaws in girth weld pipes subjected to bending load. Int. J. Pres. Ves. Pip. 12, 49–65. Parise, L.F.S., Ruggieri, C., O’Dowd, N.P., 2015. Fully-plastic strain-based J estimation scheme for circumferential surface cracks in pipes subjected to reeling. J. Pressure Vessel Technol. 137, 041204. Ren, X., Nordhagen, H.O., Zhang, Z., Akselsen, O.M., 2015. Tensile properties of 420 Mpa steel at low temperature. In: The Twenty-Fifth International Offshore and Polar Engineering Conference. International Society of Offshore and Polar Engineers, pp. 346–352. Souza, R.F., Ruggieri, C., 2015. Fracture assessments of clad pipe girth welds incorporating improved crack driving force solutions. Eng. Fract. Mech. 148, 383–405. Souza, R.F., Ruggieri, C., Zhang, Z., 2016. A framework for fracture assessments of dissimilar girth welds in offshore pipelines under bending. Eng. Fract. Mech. 163, 66–88. Souza, R.F., Ruggieri, C., 2017. Development of a strain based fracture assessment procedure for undermatched pipe girth welds subjected to bending. Theor. Appl. Fract. Mech. 92, 381–393. Tkaczyk, T., Pepin, A., Denniel, S., 2011. Integrity of mechanically lined pipes subjected to multi-cycle plastic bending. In: Proceedings of 30th International Conference on Ocean, Offshore and Arctic Engineering (OMAE 2011), pp. 255–265. Rotterdam, The Netherlands. Wang, L., Wu, G., Wang, B., Pisarski, H., 2019. Fracture response of X65 pipes containing circumferential flaws in the presence of Lüders plateau. Int. J. Solid Struct. 156–157, 29–48. Yi, D., Idapalapati, S., Xiao, Z.M., Kumar, S.B., 2012a. Fracture capacity of girth welded pipelines with 3D surface cracks subjected to biaxial loading conditions. Int. J. Pres. Ves. Pip. 92, 115–126. Yi, D., Xiao, Z.M., Idapalapati, S., Kumar, S.B., 2012b. Fracture analysis of girth welded pipelines with 3D embedded cracks subjected to biaxial loading conditions. Eng. Fract. Mech. 96, 570–587. Yi, D., Xiao, Z.M., Tan, S.K., 2012c. On the plastic zone size and the crack tip opening displacement of an interface crack between two dissimilar materials. Int. J. Fract. 176, 97–104. Zhao, H.S., Lie, S.T., Zhang, Y., 2017. Elastic-plastic fracture analyses for misaligned clad pipeline containing a canoe shape surface crack subjected to large plastic deformation. Ocean. Eng. 146, 87–100. Zhao, H.S., Lie, S.T., Zhang, Y., 2018. Strain-based J-estimation scheme for fracture assessment of misaligned clad pipelines with an interface crack. Mar. Struct. 61, 238–255. Zhao, X., Xu, L., Jing, H., Han, Y., Zhao, L., 2019. A strain-based fracture assessment for offshore clad pipes with ultra undermatched V groove weld joints and circumferential surface cracks under large-scale plastic strain. Eur. J. Mech. Solid. 74, 403–416.

The authors wish to acknowledge the financial support provided by the Fundamental Research Funds for the Central Universities (No. DUT19RC(3)056). References ABAQUS, 2011. Standard User’s Manual, Version 6.11. Hibbett, Karlsson & Sorensen Inc, USA. Anderson, T.L., 2005. Fracture Mechanics: Fundamentals and Applications. CRC Press. AWS D1.1-00, 2000. Structural Welding Code: Steel. American Welding Society (AWS), USA. Bastola, A., Wang, J., Shitamoto, H., Mirzaee-Sisan, A., Hamada, M., Hisamune, N., 2017. Investigation on the strain capacity of girth welds of X80 seamless pipes with defects. Eng. Fract. Mech. 180, 348–365. BS7910-Amendment 1, 2013. Guide to Methods for Assessing the Acceptability of Flaws in Metallic Structures. British Standards Institution, UK. Budden, P.J., 2006. Failure assessment diagram methods for strain-based fracture. Eng. Fract. Mech. 73, 537–552. Chiodo, M.S.G., Ruggieri, C., 2010. J and CTOD estimation procedure for circumferential surface cracks in pipes under bending. Eng. Fract. Mech. 77, 415–436. Dahl, B.A., Ren, X.B., Akselsen, O.M., Nyhus, B., Zhang, Z.L., 2018. Effect of low temperature tensile properties on crack driving force for Arctic applications. Theor. Appl. Fract. Mech. 93, 88–96. Hoh, H.J., Xiao, Z.M., Luo, J., 2010. On the plastic zone size and crack tip opening displacement of a Dugdale crack interacting with a circular inclusion. Acta Mech. 210, 305–314. Jayadevan, K.R., Østby, E., Thaulow, C., 2004. Fracture response of pipelines subjected to large plastic deformation under tension. Int. J. Pres. Ves. Pip. 81, 771–783. Jia, P., Jing, H., Xu, L., Han, Y., Zhao, L., 2016. A modified reference strain method for engineering critical assessment of reeled pipelines. Int. J. Mech. Sci. 105, 23–31. Jia, P., Jing, H., Xu, L., Han, Y., Zhao, L., 2017. A modified fracture assessment method for pipelines under combined inner pressure and large-scale axial plastic strain. Theor. Appl. Fract. Mech. 87, 91–98. Kim, Y.J., Kim, J.S., Lee, Y.Z., Kim, Y.J., 2002. Non-linear fracture mechanics analyses of part circumferential surface cracked pipes. Int. J. Fract. 116, 347–375. Kim, Y.J., Schwalbe, K.H., 2001. Mismatch effect on plastic yield loads in idealised weldments: part II-HAZ cracks. Eng. Fract. Mech. 68, 183–199. Lie, S.T., Zhang, Y., Zhao, H.S., 2017. Fracture response of girth-welded pipeline with canoe shape embedded crack subjected to large plastic deformation. J. Pressure Vessel Technol. 139, 021406. Linkens, D., Formby, C.L., Ainsworth, R.A., 2000. A strain-based approach to fracture assessment-example applications. In: Proceedings of the 5th International Conference on Engineering Structural Integrity Assessment. Churchill College, Cambridge, UK. Macdonald, K.A., Cheaitani, M., 2010. Engineering critical assessment in the complex girth welds of clad and lined linepipe materials. In: Proceedings of the 8th International Pipeline Conference (IPC 2010), pp. 823–843. Calgary, Alberta, Canada.

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