Impacts of residual stresses on J-integral for clamped SE(T) specimens with weld centerline cracks

Journal Pre-proofs Impacts of residual stresses on J-integral for clamped SE(T) specimens with weld centerline cracks Yifan Huang, Wenxing Zhou PII: DOI: Reference:

S0167-8442(19)30451-3 https://doi.org/10.1016/j.tafmec.2020.102511 TAFMEC 102511

To appear in:

Theoretical and Applied Fracture Mechanics

Received Date: Revised Date: Accepted Date:

15 August 2019 26 January 2020 28 January 2020

Please cite this article as: Y. Huang, W. Zhou, Impacts of residual stresses on J-integral for clamped SE(T) specimens with weld centerline cracks, Theoretical and Applied Fracture Mechanics (2020), doi: https://doi.org/ 10.1016/j.tafmec.2020.102511

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Impacts of residual stresses on J-integral for clamped SE(T) specimens with weld centerline cracks

Yifan Huang, Wenxing Zhou Department of Civil and Environmental Engineering, The University of Western Ontario, 1151 Richmond Street, London, Ontario N6A 5B9, Canada Abstract: Three-dimensional (3D) finite element analyses (FEA) are performed on clamped single-edge notched tension (SE(T)) specimens to investigate the impact of residual stresses on the average J-integral (J) evaluated over the crack front. Both shallow- and deeply-cracked (i.e. a/W = 0.2 and 0.5) specimens are considered in the analysis. The residual stresses are introduced by different mechanical pre-loading techniques and consistent with those measured from pipeline girth welds and those specified in well-known structural integrity assessment standards. The analysis results indicate that the impact of the residual stress on J depends strongly on the preloading techniques employed for the generation of residual stresses and level of the primary loading applied to the SE(T) specimen.

Keywords: Residual stress, Single-edge notched tension (SE(T)), Three-dimensional finite element analysis (3D FEA), J-integral.



Corresponding author, Email: [email protected], [email protected]. Present address: SNC-Lavalin Nuclear Inc./Caudu Energy Inc., 2251 Speakman Drive, Mississauga, Ontario L5K 1B2, Canada.

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Nomenclature a a0 B C(T) d E f() eJ H J Jave 𝐽𝑁𝑅 𝑎𝑣𝑒 𝐽𝑖𝑙𝑜𝑐(𝑘) Jmid K, SIF Keff, Km and KRS LC m() MY P PR PY PY(W) PB PC PRB PT Q R RSP S L SE(B) SE(T) W δx, δy

0 u rm RS YS  YSBM

BM  UTS WM  YS Y yy(R)  

crack length reference crack length thickness of the specimen compact tension half of the strip weld width elastic modulus non-dimensional functions for calculation of SIF difference of Jave caused by residual stress daylight length (distance between grips) nonlinear energy release rate the average J value along the crack front average J obtained from the residual stress-free specimen the local J value at the ith layer obtained by using the kth domain the local J value in the mid-plane stress intensity factor effective SIF, SIFs caused by mechanical loading and residual stress local compression weight functions for calculation of SIF material strength mismatch ratio applied load reference load limit load for an SE(T) specimen made of the base metal only limit load for an SE(T) specimen containing both the base metal and weldment pre-bending pre-compression pre-reverse bend pre-tension welding heat input energy per unit length per unit thickness radius of the indenter residual stress profile, distribution of yy(R) along the pipe wall thickness the support span of the specimen the loading span of the specimen single-edge bend single-edge tension the width of the specimen distances between the center of the indenter and notch tip reference strain, ε0 = σYS/E BM true strain corresponding to  UTS remote external loading stress residual stress in the uncracked ligament with respect to a0 yield strength yield strength of base metal ultimate tensile strength of base metal yield strength of weldment flow stress opening residual stress Poisson’s ratio slenderness of the weld,  = (W - a)/d

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1. Introduction The fracture toughness resistance curve, such as the J-integral resistance (J-R) curve, is a key input to the structural integrity assessment of metallic structures. The J-R curve is typically obtained from the deeply-cracked single-edge bend (SE(B)) or compact tension (C(T)) specimen as standardized in ASTM E1820-13 [1], BS7448-4 [2] and ISO 12135 [3]. Recent years have witnessed the increasing interest [4-6] in using the SE(T) specimen to evaluate the J-R curve in the energy pipeline industry, because the crack-tip stress and strain fields of the SE(T) specimen are similar to those of the full-scale pipe containing surface cracks under longitudinal tension and/or internal pressure [7, 8]. Figure 1 schematically depicts the configuration of a typical SE(T) specimen including the width (W), thickness (B), crack length (a) and daylight distance (the distance between the clamped surfaces, H) of the specimen.

Pipe segment

Girth weld

W

Radial (x)

a

Clamped surfaces for tensile loading Figure 1 Schematics of SE(T) specimens. Many engineering fabrication and construction processes inevitably introduce residual stresses in structural components. A typical example is the residual stress caused by the thermal strain associated with the welding procedure [9]. In general engineering pratice, the residual stress is considered as a secondary load and has insignificant contribution to the crack driving force. The current J-R curve testing methodologies [1-3] were mainly developed for residual stress-free specimens.

In the case that specimens contain non-negliable levels of residual stresses, it is

acknowledged that residual stresses can impact the measured J-R curve by influencing the evaluation of the applied crack driving force (i.e. stress intensity factor (SIF or K) and J) in the test [10-16],

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crack-tip constraint [17-24] and crack front curvature [25-28]. The present study focuses on the first aspect, i.e. the impact of residual stresses on the evaluation of the applied J. Since solutions of the applied J included in the current J-R curve testing methods are developed without considering the residual stress, applying these solutions to specimens containing residual stresses may lead to error in the experimentally-determined J-R curve, i.e. fracture toughness resistance curve. Therefore, the present study is relevant to the fracture toughness determination. A great deal of studies are reported in the literature concerning the effects of residual stresses on stress intensity factor (K) and J [10-15]. Within the realm of the linear-elastic fracture mechanics and under the opening mode (i.e. Mode I) loading, J is related to K through the following equation:

K 2 (1  2 ) J E

(1)

with E and v being Young’s modulus and Poisson’s ratio respectively. For a two-dimensional (2D) cracked body containing near-tip residual stresses and simultaneously under mechanical loading, the effective SIF, Keff, is a superposition of two components, Km and KRS, namely the SIFs caused by the external mechanical loading and residual stresses, respectively [10, 11, 29]:   K eff  K m  K RS   a  K m  a   f    rm  a W   a  K a    RS a0 m  x, a   RS  x  dx 

(a) (b)

(2)

(c)

where a0 and a are the reference and actual crack lengths; W is the width of the specimen; rm is the remote external loading stress; RS is the residual stress in the uncracked ligament with respect to a0, and the non-dimensional function, f(), and weight function, m(), are well documented for various specimen configurations (e.g. [29, 30]). The integration in Eq. (2c) is performed over the crack length from a0 to a. Specially when a0 = 0, RS is the residual stress in the uncracked body. Within the realm of the elastic-plastic fracture mechanics, the impact of residual stresses on J is generally considered in terms of the domain-dependence of J. The J-integral [31] proposed by Rice (referred to as the standard J) can be expressed as a contour integral or domain (area) integral, with the latter being more conveniently implemented in the finite element analyses (FEA). For a cracked body characterized by the deformation theory of plasticity (i.e. small strain kinematics and nonlinear elastic constitutive model) under proportional loading, J is domain- (or path-) independent [31]. However, it has been reported that the standard J-integral shows domain-dependence if the cracked body contains near-tip residual stresses, and the level of the domain-dependence increases with the magnitude of the residual stress [12-15]. By eliminating the initial plastic strain and its

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contribution to the strain energy density within the domains, Lei et al. [12] proposed a modified Jintegral definition that leads to domain-independent J. In their study, the domain-dependence was studied based on 2D FEA of single-edge notched bending (SE(B)), single-edge notched tension (SE(T)) and centre cracked panel specimens containing residual stresses. Subsequent work by Meith and Hill [13] further investigated the domain-dependence of the modified J based on threedimensional (3D) FEA of SE(B) specimens. Farahani et al. [14] and Zhu [15] showed that for SE(B) specimens, the higher the tensile near-tip residual stress is, the larger modified J values are obtained at the same loading level. On the other hand, studies [12, 21, 22, 24] indicate that with the presence of residual stresses, the path-independence of standard J in the practical sense still exists if the following conditions are satisfied: (a) the zone of highly non-proportional loading is well engulfed within the domain used to calculate J (i.e. the far-field J) [21, 22]; (b) the small-strain formulation was employed in the FEA [24] and, (c) the primary loading level is sufficiently high [12, 21, 22], e.g. reaching the reference load corresponding to fully plastic deformation throughout the uncracked ligament. It should be noted that in the J-R curve test, J is typically evaluated based on the measured load-displacement response [1-3] since the standard J can be interpreted as the total strain energy release rate. In the test, it is difficult to define the initial plastic strain field and separate its contribution to the total strain energy from the global load-displacement response. This leads to difficulties in the experimental evaluation of the modified J. Despite the rich literature on the impact of residual stresses on J, there is a lack of a systematic study aimed at quantifying the impact of residual stresses on J for the SE(T) specimen. Furthermore, the impact of residual stresses on J for SE(T) specimens containing the weldment has not been investigated in previous studies. The objective of the present study is to address the above-mentioned knowledge gaps by quantifying the impact of residual stresses on J for clamped SE(T) specimens containing weld centerline cracks. We carry out 3D FEA of plane-sided clamped SE(T) specimens with two crack lengths (a/W= 0.2 and 0.5), one thickness-to-width ratio (B/W = 1), and three strength mismatch ratios (i.e., MY = 1.0, 1.2 and 1.5), where MY is the ratio between the yield strengths of the weldment and base metal. For a specimen with given a/W and MY, sixteen different residual stress states are introduced using different mechanical pre-loading techniques. At a given primary loading level, the average J obtained from a specimen containing residual stresses is compared with that obtained from the residual stress-free specimen with the same a/W and MY. Note that the standard J as opposed to modified J definition is adopted in this study because the latter is not amenable to implementation in the J-R curve test. The path-dependence of the standard J for the considered specimens is investigated.

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2. Review of Through-thickness Axial Residual Stress Profile for Pipeline Girth Weld The mode I (opening mode) fracture toughness of pipeline girth weld containing circumferential surface cracks is largely impacted by the axial (i.e. crack opening) residual stress, denoted as yy(R). The distribution of yy(R) along the pipe wall thickness is the focus of the present study and simply denoted as the “residual stress profile” (RSP) hereafter. The RSP in actual pipeline girth weld is very complex and dependent on many factors such as the pipe diameter (D) and thickness (t), yield strengths of the base metal (  YS ) and weldment (  YS ), configuration of the welds, and welding BM

WM

heat input energy per unit length per unit thickness (Q). The fracture mechanics-based structural integrity assessment procedures for metallic structures specified in well-known standards such as BS 7910:2005 [32], R6 Rev 4 [33], FITNET [34], API 579-1 [35] and SINTAP [36] typically recommend different RSPs corresponding to different assessment levels for ferritic steels.

For example,

Assessment Level 1 of BS7910 [32] provides the simplest and most conservative solution by assuming a uniform tensile RSP equal to the material yield strength. Assessment Level 2 provides a more detailed but still conservative RSP based on the upper bound of experimental and predicted data reported in the literature. Level 3 profiles represent a more realistic estimate of the specific welding RSP based on experimental measurements combined with detailed numerical analysis. Measurements of RSPs in pipeline girth welds have also been reported in the literature [37-47]. Table 1 summarizes 23 sets of RSP measurements obtained from the girth welds of 15 ferritic steel pipelines reported in the literature. Figure 2 compares RSPs (for ferritic steels) specified in BS 7910, API 579 and SINTAP (grey lines in the figure) with the RSP measurements summarized in Table 1 (coloured lines in the figure). The horizontal coordinate x/t denotes the normalized radial distance away from the pipe outside surface. Note that RSPs specified in R6 and FITNET are identical to those specified in BS 7910. Figure 2 indicates that there are large variations in the standard-prescribed as well as measured RSPs, even in the case of similar welding heat input. Directly inputting RSPs shown in Figure 2 into the FEA model for the SE(T) specimen is problematic for the following reasons. First, all the profiles shown in Figure 2 are one-dimensional, i.e. distributions of yy(R) over a line, whereas the 3D FEA models employed in this study require two-dimensional RSPs, i.e. distributions of yy(R) over a surface. Second, the profiles shown in Figure 2 are for the uncracked ligament, i.e. the full pipe wall thickness, whereas the RSP for the SE(T) specimen is for the remaining ligament after the introduction of the crack in the specimen. For the purpose of investigating the impact of residual stresses on the crack driving force, the present study employs a widely adopted practical approach, namely mechanical pre-loading techniques [12-16, 19, 23, 24, 48-50], to generate residual stresses in SE(T) specimens. The yellow

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curve presented in Figure 2(f) is the RSP caused by one of the mechanical pre-loading techniques. The figure suggests that mechanical method is a viable option to produce comparable RSP as the one resulted from welding. The advantage of this approach is that RSPs are introduced in the specimen in a controlled manner [50]. A variety of the pre-loading techniques can cover a wide range of RSPs and allow a systematic study of the influence of the residual stress field on the estimated J.

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Table 1 Review of the axial residual stress profiles in 15 ferritic pipeline girthwelds Year

Authors

Zhang et al. [37] 2012 Law and Luzin [38] Ren et al. [39] Paddea et al. [40] He et al. [41] 2011

Neeraj et al. [42]

2010

Yaghi et al. [43]

1987

Ritchie and Leggatt [44]

1985

Scaramangas and Goff [45]

1982

Leggatt [46] Ueda et al. [47]

Residual Stress Profile ID RSP-1a RSP-1b RSP-1c RSP-2a RSP-2b RSP-3a + RSP-3b RSP-4a + RSP-4b RSP-5 RSP-6 RSP-7 RSP-8a RSP-8b RSP-9 RSP-10a RSP-10b RSP-10c RSP-11 RSP-12 RSP-13 RSP-14 RSP-15

Pipe Diameter (D, mm)

Pipe Thickness (t, mm)

D/t

Pipe Materials

Base Metal Yield Strength (σBMYS, Mpa)

Weldment Yield Strength (σWMYS, Mpa)

Mismatch Ratio (MY)

Measurement Techniques

406

19.1

21.3

X70 steel

519

728

1.40

DHD

508

22.9

22.2

X65 steel

539.2

653.7

1.21

BRSL

1067

24

44.5 X70 steel

483

\

\

ND

1067

30

35.6

1066.8 324 910

28 25.4 32

38.1 12.8 28.4

X80 steel P91 steel X52 steel

570 500 335

25.4

20.0

X65 steel

478

290

55

5.3

P91 steel

489

0.79 1.35 1.49 1.24 1.05 1.12

DHD ND DHD

508

448* 675 500 591 500 550

761

25.4

30.0

345*

430

1.25

BRSL

1000 1000 1000 610 1400

9.1 15 19.5 15.5 50

109.9 66.7 51.3 39.4 28.0

520 542 527 540 \

1.46 1.53 1.48 1.06 \

Notes: *: Minmum yield strength, no measured yield strength reported ND: Neutron Diffraction XD: X-way Diffraction DHD: Deep-hole drilling BRSL: Block removal, splitting and layering

50D steel 355* X65 steel HT80 steel

510 785

+ : Upper bound of a sets of data - : Lower bound of a sets of data

ND XD

BRSL BRSL BRSL

9

1.5

 yy R   YSBM

1.5

(a)

1

1

0.5

0.5

0.5

 yy R 

0

RSP-1a 7 RSP-1b 8a 8b RSP-1c

RSP-2a 7 RSP-2b 8a 8b RSP-3a RSP-3b 9

9 BS7910 [32], Q < 50 (J/mm/mm) BS7910 [32], 50< Q < 120 (J/mm/mm) BS7910 [32], Q > 120 (J/mm/mm) SINTAP [36], Q < 60 (J/mm/mm) API 597 [35], Q = 29.3 (J/mm/mm)

0.2

0.4

0.6

x/t

0.8

1

0

1.5

(d)

0.2

0.4

0.6

x/t

-1.5

0.8

0

1

1.5

(e)

1

0.5

0.5

0.5

1.5 1 0.5 0 -0.5 -1 -1.5 -2

1.5 1 0.5 0 -0.5 -1 -1.5

 YSBM

0

1.5 1 0.5 0 -0.5 -1 -1.5 -2

 yy R  1.5 1 0.5 0 -0.5 -1 -1.5

RSP-4a 7 RSP-4b 8a 8b RSP-5 9 RSP-6

BS7910 [32], Q < 50 (J/mm/mm) BS7910 [32], 50< Q < 120 (J/mm/mm) BS7910 [32], Q > 120 (J/mm/mm) SINTAP [36], Q < 60 (J/mm/mm) API 597 [35], Q = 29.3 (J/mm/mm)

1

 yy R 

0.2 00.4 0.6 0.8 1

-1

1

0

1.5 1 0.5 0 -0.5 -1 -1.5

-0.5

0.2 00.4 0.6 0.8 1

-1

(c)

0

 YSBM

1.5 1 0.5 0 -0.5 -1 -1.5

-1.5

0

Figure 2

 yy R 

0 -0.5

0.2 00.4 0.6 0.8 1

-1.5

1.5

 YSBM

1.5 1 0.5 0 -0.5 -1 -1.5

-1

 YSBM

(b)

1

-0.5

 yy R 

1.5

 YSBM 1.51 0.5 0 -0.5 -1 -1.5 -2

0

0.2

0.4

x/t

0.6

BS7910 [32], Q < 50 (J/mm/mm) BS7910 [32], 50< Q < 120 (J/mm/mm) BS7910 [32], Q > 120 (J/mm/mm) SINTAP [36], Q < 60 (J/mm/mm) API 597 [35], Q = 29.3 (J/mm/mm)

0.8

1

(f)

1.5 1 0.5 0 -0.5

-1 -1.5 0.2 0.4 00.6 0.8 1 1.5 1 0.2 00.4 0.6 0.8 1 -0.5 -0.5 -0.5 0.5 0.2 00.4 0.6 0.8 1 0 0.2 00.4 0.6 0.8 1 -0.5 -1 0.2 0.4 00.6 0.8 1 -1.5 -2 0.2 0.4 00.6 0.8 1 1.5 1 0.5 0 -0.5 RSP-12 7 -1 RSP-10a 7 -1.5 RSP-7 -2 7 0.2 0.4 00.6 0.8 1 RSP-13 8a RSP-10b 8a PB(I) on RSP-8a 8a -1 -1 -1 0.2 0.4 00.6 0.8 1 1a 8b RSP-14 RSP-10c 8b unnotched 8b RSP-8b 9 RSP-15 1a 9RSP-11 specimen 1b 9 1a RSP-9 BS7910 [32], Q < 50 (J/mm/mm) BS7910 [32], Q < 50 (J/mm/mm) BS7910 [32], Q < 50 (J/mm/mm) -1.5 1b -1.5 -1.5 1a 1c 1b BS7910 [32], 50< Q < 120 (J/mm/mm) BS7910 [32], 50< Q < 120 (J/mm/mm) BS7910 [32], 50< Q < 120 (J/mm/mm) BS7910 [32], (J/mm/mm) 1b BS7910 [32], Q0.6 < 50 (J/mm/mm) BS7910 [32], 1c 0.6 0.2 0.4 0.6Q > 1200.8 1 0 0.2 0.4 1a 0.8 1 Q > 120 (J/mm/mm) 0 0.2 0.4 0.8 1 Q > 120 (J/mm/mm)1c0 BS7910 [32], [36], Q < 60 (J/mm/mm) SINTAP [36], Q < 60 (J/mm/mm) BS7910 [32], Q < 50SINTAP SINTAP [36], Q < 60 (J/mm/mm) (J/mm/mm) 1b 1c BS7910 [32], 50< Q < 120 (J/mm/mm) BS7910 [32], Q < 50 (J/mm/mm) x /597t [35], Q = 29.3 (J/mm/mm) API x/t API 597 [35], Q = 29.3 (J/mm/mm) x /1ct API 597 [35], Q = 29.3 (J/mm/mm) BS7910 [32], 50< Q < 120 (J/mm/mm) 50 (J/mm/mm) BS7910 [32], Q >< 120 (J/mm/mm) BS7910 [32], 50< Q < 120 (J/mm/mm) BS7910 BS7910 Q 120 BS7910 [32], [32],QQ>>120 120(J/mm/mm) (J/mm/mm) [32],QQ Q≤><50 50(J/mm/mm) (J/mm/mm) BS7910 [32], [32],50 50< Q ≤<(J/mm/mm) 120(J/mm/mm) (J/mm/mm) SINTAP [36], Q << 60 BS7910 [32], [32], 120 (J/mm/mm) SINTAP [36], Q < 60 (J/mm/mm) BS7910 [32], 50< Q29.3 <(J/mm/mm) 120 (J/mm/mm) BS7910 Q ≤>= 120 (J/mm/mm) SINTAP [36], Q 60 (J/mm/mm) API 579[36], [35], Q Q<=60 (J/mm/mm) API 597 [32], [35], 29.3 (J/mm/mm) SINTAP API 597 [35], Q = 29.3 (J/mm/mm) BS7910 SINTAP [36], Q < 60 (J/mm/mm) API 597 [32], [35], Q Q >= 120 29.3(J/mm/mm) (J/mm/mm) 𝐵𝑀 SINTAP [36],of Q <60 (J/mm/mm) API 597 [35], Q = 29.3 (J/mm/mm) Through-thickness distribution / in ferritic pipeline girth weld: (a) RSP-1; (b) RSP-2 and RSP-3; (c) RSP-4, RSP-5 and RSP-6; 𝜎 yy(R) 𝑌𝑆 API 597 [35], Q = 29.3 (J/mm/mm)

(d) RSP-7, RSP-8 and RSP-9; (e) RSP-10 and RSP-11; (f) RSP-12, RSP-13, RSP-14 and RSP-15.

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3. Mechanically Induced Residual Stresses 3.1 In-plane pre-loading Four in-plane pre-loading techniques including pre-tension (PT), pre-compression (PC), prebending (PB) and pre-reverse bending (PRB) are used in this study to generate residual stresses in the SE(T) specimen. Figure 3(a) through 3(d) schematically illustrate these techniques. PC and PRB lead to tensile near-tip yy(R), whereas PT and PB lead to compressive near-tip yy(R). As suggested in BS 7448-2 [51], PRB is adopted as a residual stress relaxation treatment for specimens containing compressive near-tip yy(R) non-uniformly distributed along the crack front. 3.2 Out-of-plane pre-loading A commonly used out-of-plane pre-loading technique for introducing residual stresses is the local compression (LC) technique proposed by Dawes [48], also known as the side punching. The LC technique is recommended in BS 7448-2 [51] and Annex C of ISO 15653 [52] (both are standards for the fracture toughness testing of welds) as a stress relaxation treatment to mitigate residual stresses that are non-uniformly distributed along the crack front, and has proven effective for the standard SE(B) and C(T) specimens based on a number of experimental investigations [25, 48, 49]. Figure 4(a) schmatically illustrates the typical LC technique, which involves a single pair of cylinder indenters being used to apply the out-of-plane (i.e., z direction) compression on the notched specimen. The indenter has a radius of R. The origin of the x-y-z coordinate system is the notch tip at the mid-thickness of the specimen. δx and δy denote the distances between the center of the indenter and notch tip in the x and y directions, respectively. For single pair of cylinder indenters, δy = 0. As specified in Annex C of ISO 15653 [52], 88% to 92% of the ligament in front of the machined notch shall be compressed (i.e., δx = (88% ~ 92%)(W – a) – R), and the indentation as measured by the plastic strain shall not exceed 0.5%B on each side. Mahmoudi et al. [50] improved the LC technique for the aluminium C(T) specimen with a/W = B/W = 0.5 by using double pairs of cylinder indenters (see Figure 4(b)). They showed that using such indenters can produce either tensile or compressive opening residual stress depending on δx and δy. Note that the initial plastic strain adjacent to the crack tip reduces the ductility of the specimen [50]. Compared with single pair of cylinder indenters, using double pairs of cylinders indenters generates smaller plastic strains near the crack tip at similar levels of the opening residual stress, and therefore reduces the impact of the plastic strain on toughness.

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P

a

W

P

P

P (a)

(b)

z

x

y

P/2 P/2

P (c)

(d)

Figure 3 The in-plane pre-loading techniques: (a) Pre-tension (PT); (b) Pre-compression (PC); (c) Pre-bending (PB); (d) Pre-reverse bending (PRB).

δx

W

a

Indenters

z

x

y

(a)

δx

Indenters

δy

(b) Figure 4 The local compression techniques: (a) Single pair of cylinder indenters; (b) Double pairs of cylinder indenters.

12

4. Finite Element Analysis 4.1 Specimens configurations and mesh Three-dimensional models of SE(T) specimens with clamped ends are prepared for FEA. All the specimens included in the present study have the same width and thickness (W = B = 20 mm) as well as the daylight length (H/W = 10). Two relative crack lengths corresponding to shallow and deep cracks respectively, i.e. a/W = 0.2 and 0.5, are adopted based on the recommendation in [53]. All the specimens contain weld centerline cracks, and the weldment is modeled as a strip shape with the width of the weld groove, 2d, equal to 0.35W [54] (see Figure 5(a)). Because of symmetry, only one quarter of the specimen with appropriate constraints imposed on the remaining ligament is modelled. A typical FE models with a/W = 0.2 is schematically shown in Figure 5(a) together with the fixation and loading conditions. Specimens with and without residual stresses are analyzed. To generate the near-tip residual stresses, pre-loadings are applied to the specimen prior to the primary tension loading, whereas the primary loading is directly applied to the residual stress-free specimens. The commercial software ABAQUS 6.13 [55] is employed to carry out the FEA. The 8-node 3D hexahedral elements with reduced integration (C3D8R) are used in the analysis. The accuracy of using such elements to calculate J has been shown to be adequate [24]. Stationary cracks are assumed in all the FE models. A sharp crack tip is incorporated and the surfaces of the hexahedral elements are collapsed to a line at the crack tip (see Figure 5(a)) to simulate the singularity condition. A spiderweb mesh around the crack tip is established with 40 concentric semicircles (i.e. domains) surrounding the crack tip. The radii of the smallest and largest domain around the crack-tip are 0.01 and 3 mm, respectively, as suggested in [24]. The model is equally divided into 20 layers over the half thickness (B/2) to ensure that the surface profiles of yy(R) introduced by both in-plane and outof-plane pre-loadings are sufficiently accurate. The total number of elements is approximately 12,000 in a typical quarter-symmetric specimen.

13

W

z y

a

x

b

3 mm

(a)

14

(b)

(c)

(d)

Figure 5 Configuration and meshing of typical finite element models: (a) Quarter model for specimen with a/W = 0.2; (b) Pre-bending; (c) Pre-reverse bending; (d) Local Compression using double pairs of cylinders. 4.2 Material model An elastic-plastic constitutive model based on the incremental theory of plasticity as well as the small-strain formulation [55] is adopted in FEA. The true stress () and true strain () relationship of the material is characterized by the following equation:     YS  n  0         YS 

,   0

(3) ,  0

where σYS is the yield strength; ε0 = σYS/E, and n is the strain hardening exponent. A bi-material system is adopted to account for the strength mismatch for specimens made of heterogeneous materials. The mismatch ratio, MY, is defined as MY 

WM  YS  YSBM

(4)

The elastic modulus, Poisson’s ratio and strain hardening exponent for both the base metal and weldment are assumed to be 207 GPa, 0.3 and 13 respectively. The value of

 YSBM is selected to be

15

510 MPa to simulate the X80 grade pipeline steel [56], whereas

WM  YS = 510, 612 and 765 MPa are

adopted to simulate evenmatching, 20%-overmatching and 50%-overmatching weldment, respectively, (i.e., MY = 1.0, 1.2 and 1.5). These mismatch ratios are similar to those reported in the literature [37-47] (see Table 1). The limit load, PY, for an SE(T) specimen made of the base metal only can be evaluated as PY = B(W - a)Y [8], where Y is the flow stress and determined as ( YS + BM

BM BM UTS )/2. The quantity UTS

is the ultimate tensile strength of the base metal and can be estimated as [27, 28]: 

BM UTS



E 1/ n  YSBM

( n 1) / n

exp   u 

where u is the (true) strain corresponding to = 207 GPa,



 u1/ n

(5)

BM UTS and assumed to equal 1/n [57]. For n = 13 and E

BM  UTS is about 615MPa. The limit load, PY(W), for an SE(T) specimen containing both the

base metal and weldment is calculated using the following equation proposed by Paredes [58] PY W    PY M Y      1  M Y  9   M Y  1     10   

(6) for 0     1

(a)

for    1

(b)

(7)

where  = (W - a)/d characterizes the slenderness of the weld, and 1 is given by

1  e

 M Y 1 2

(8)

The values of , 1 and  for the specimens considered in the present study are summarized in Table 2. Table 2 , 1 and  for various a/W and MY values a/W = 0.2 a/W = 0.5 MY

1.0

1.2

1.5

1.0

1.2

1.5



4.571

4.571

4.571

2.857

2.857

2.857

1

1.000

0.905

0.779

1.000

0.905

0.779



1.000

1.060

1.135

1.000

1.083

1.186

4.3 Pre-loading and notching The pre-loading is applied to the specimens prior to the application of the primary loading to introduce residual stresses. The load is applied in a displacement-controlled manner. For PT and PC, uniform displacements are applied on the two lateral surfaces that are considered the clamped surfaces with a length of 4W (see Figure 5(a)) along the negative and positive y directions. For PB and PRB,

16

rigid rollers are modeled for loadings and supports (see Figure 5(b) and 5(c)). The support span (S) equals 4W for PB and PRB, whereas the loading span (L) equals 2W for PRB. Vertical displacement is applied to the loading roller while the supporting roller is fixed. The load P is calculated as the total reactions of the nodes on the clamped surface for PT and PC, and the reactions of the loading rollers for PB and PRB. The loading levels of the in-plane pre-loading are defined in terms of P/PR, where the reference load (PR) for the in-plane pre-loadings is given as:  B W  a   Y  2 1.456 B W  a   Y  S  PR   2  2 B W  a   Y  3 S  L   

, for PT, PC

(a)

, for PB

(b)

(9) , for PRB

(c)

Three levels of pre-loadings are defined and denoted as (I), (II) and (III), respectively. For PT and PC, (I), (II) and (III) correspond to P/PR ≈ 0.3, 0.5 and 0.8 respectively, while only (I) and (II) corresponding to P/PR ≈ 0.5 and 0.8, respectively, are considered for PB and PRB. Figure 5(d) illustrates a typical quarter-symmetric FE model with a/W = 0.2, for which the double pairs of cylinders technique is used to introduce residual stresses. Three types of the LC technique, denoted as LC-A, LC-B and LC-C respectively, are considered. LC-A involves single pair of cylinder indenters with δx = 0; LC-B involves single pair of cylinder indenters with δx = R, and LC-C involves double pairs of cylinders with δx = 0 and δy = 1.5R, where the radius of the indenter R equals 4 mm. A rigid and frictionless contact between the specimen and indenter is assumed. The displacement is applied to the indenter to introduce indentation (h) on the specimen. Two pre-loading levels, (I) and (II), corresponding to h = 0.5% and 1%B (i.e. the total indentations on both sides of the specimens are 1% and 2%B), are adopted for each type of the LC technique. Note that the largestrain formulation [55] is adopted in FEA for cases with PB, PRB, LC-A, LC-B and LC-C in order to achieve more acuurate results in the contact analyses. Once the target pre-loading level for a given specimen is achieved, the internal forces throughout the specimen are recorded and then input as the initial stresses to a new model that has the same meshing but without the external loading. A subsequent step is created to allow the internal forces to self balance, which is equivelent to the unloading process. Once this step is completed, the self-balenced stress state is the residual stress state caused by the pre-loading. To this end, for a specimen with given a/W and MY, sixteen different residual stress states are generated from various combinations of the pre-loading technique and magnitude of the pre-loading. Each of the 16 residual stress states is assigned an ID in the format of ‘Pre-loading technique(loading magnitude)’: 

Pre-tension: PT(I), PT(II), PT(III);

17



Pre-compression: PC(I), PC(II), PC(III);



Pre-bending: PB(I), PB(II);



Pre-reverse bending: PRB(I), PRB(II)



Local compression: LC-A(I), LC-A(II), LC-B(I), LC-B(II), LC-C(I), LC-C(II).

For example, PT(I) refers to the residual stress state generated by PT with a pre-loading magnitude of Level I. The above-described pre-loading procedure is applied to notched specimens. To compare the residual stresses generated by the pre-loading with the standard-recommended and measured RSPs, residual stresses for three evenmatched uncracked specimens are generated by applying LC-A(I), LCC(I) and PB(I), respectively, to these specimens. Note that for uncracked specimens, x = 0 and x = W denote the two free surfaces of the specimen that are perpendicular to the direction of the crack propagation, and the nominal notch tip is located at x = y = 0. In such cases, δx = W/2 and δy = 0 is adopted for LC-A(I), and δx = W/2 and δy = 1.5R is chosen for LC-C(I). These positions are identical to those corresponding to LC-A(I) and LC-C(I) on notched specimens with a/W = 0.5. To further investigate the effects of the notching and pre-cracking processes on the residual stress redistribution, the two uncracked specimens that have been subjected to LC-A(I) and LC-C(I), respectively, further undergo a two-step notching process by removing the corresponding boundary condition on the x-z symmetric plane. The first notching step creates a crack length of a/W = 0.35, and the second step creates a crack length of a/W = 0.5. The corresponding re-distributed residual stresses at the end of each notching steps are retrieved from the FEA models.

J 0 J loc k 

1 2 J loc  k  J loc k  J 3 4 loc  k  J loc  k 

Jave(k) 19 J loc k 

20 J loc k 

0

0.025

0.05

0.075

0.1

0.475

0.5

z/B

Figure 6 Schematic of the calculation of the weighted average J along the crack front.

18

4.4 Primary loading The primary loading in FEA is identical to that for PT as described in the previous section. The final applied displacement corresponding to P/PY(W) = 1.0 – 1.3 is reached in about 30 to 60 steps in each simulation. At a given loading step, the values of J in each of the 20 layers along the thickness i direction, i.e. the local J values, are calculated using the domain integral method [55]. Let J loc  k  (i

=1, 2, ..., 20; k = 1, 2, ..., 40) denote the local J at the ith layer obtained by using the kth domain in the 0 domain integral method. Note that the local J value at the mid-plane, Jmid, equals J loc  k  . The

average J value over the entire crack front, Jave(k), is then calculated following the trapezoidal rule (Figure 6): J ave  k  

0 20  J loc 1  J loc  k  19 i k    J loc  k     20  2 2  i 1

(10)

In this study, Jave as opposed to the local J values is used because the plastic-work method specified in fracture testing standards [1-3] typically corresponds to Jave.

Domain number, k 10

1.1

20

Domain number, k

30

40

1.1

J ave 40

20

30

40

P / PY  0.54 0.537017658 0.85 0.846329849 0.91 0.913105609 1.10 1.096730509 1.20 1.197350009

1.05

1.05

J ave k 

10

J ave k 

1

J ave 40

P / PY 

0.67 0.537017658 0.81 0.846329849 0.98 0.913105609 1.06 1.096730509 1.19 1.197350009

0.95

0.9 0

0.5

1

1.5

2

Domain radius (mm) (a)

2.5

1

1.1 1.05 1 0.95 0.9

0.95

0

0.9 0

3

0.5

1

1.5

2

2.5

3

Domain radius (mm)

1.1 1.05 1 0.95 0.9 0

(b)

Figure 7 Domain-dependence of the computed Jave for specimens with MY = 1.0, PC(III) and: (a) a/W = 0.2; (b) a/W = 0.5. The domain dependence of the calculated average J values is investigated for specimens with a/W = 0.2 and 0.5, and MY = 1.0, and a representative residual stress state designated by PC(III). Figure 7 shows the variation of Jave(k) (normalized by Jave(40)) with the size of the corresponding domain. The lower horizontal coordinate represents the radius of domain that is used to calculate the local and average J. The vertical coordinate represents the average J value calculated based on the kth (k is the domain number as indicated by the upper horizontal coordinate, k = 1, 2, …, 40) domain

19

and normalized by the average J calculated from the outmost domain (see Figure 5(a)). The figure suggests that with the presence of residual stress, the calculated average J is mildly path-dependent if the load ratio P/PY is less than 0.8. The Jave(k) shows less domain dependence as the loading level increases; for P/PY ≥ 0.8, the calculated Jave is pratically path independent. These observations agree with the findings reported in [12, 21, 22]. For example, the difference between Jave(20) (correspondign to the domain size of 0.53 mm) and Jave(40) (correspondign to the domain size of 3 mm, see Figure 5(a)) is about 3 to 6%, and the difference between Jave(35) (correspondign to the domain size of 2 mm) and Jave(40) is about 2% at the loading level of P/PY = 0.8. In this study, Jave corresponds to Jave(40) unless noted otherwise.

20

5. Residual Stresses Caused by Pre-loading 5.1 Pre-loading on uncracked specimens The RSPs generated by LC-A(I), LC-C(I) and PB(I) on the evenmatched uncracked specimens are shown in Figure 8. These RSPs are obtained at the mid-planes of the specimens Note that two RSPs corresponding to PB(I) applied in opposite directions, respectively, are shown in Figure 8, one with compressive residual stress at x = 0 and the other with tensile residual stress at x = 0. One finding is that the RSPs caused by the LC technique is symmetric about x/t = 0.5 whereas the RSPs generated by PB and reverse PB are anti-symmetric. It is expected that more complex and non-symmetrical RSPs can be generated if the locations of the indenters (or rollers) are not symmetric about the crack plane. It can also be deduced that a combination of LC and PB can result in diversities of RSPs. In Figure 2(f), the RSP corresponding to PB is compared with those specified in the standards and obtained from measurements. It is observed that the residual stresses generated by the preloadings are in general consistent with those obtained from measurements. Both Figure 2(f) and Figure 8 suggest that the mechanical pre-loading can be a viable option to simulate residual stresses in girth welds of ferritic pipelines.

1.5 1 0.5 0 -0.5 -1 -1.5

1 0.5

 YSBM

0.2 00.4 0.6 0.8 1

0.2 00.4 0.6 0.8 1

1.5

 yy R 

1.5 1 0.5 0 -0.5 -1 -1.5

0

7 8a 8b LC-C(I) Reversed PB(I) 7 9 LC-A(I) PB(I) 8a BS7910 [32], Q < 50 (J/mm/mm) 8b BS7910 [32], 50< Q < 120 (J/mm/mm) 9 BS7910 [32], Q > 120 (J/mm/mm) BS7910 [32], Q < 50 (J/mm/mm) [36], Q < 60 (J/mm/mm) < 120 (J/mm/mm) BS7910 [32], 50< QSINTAP API(J/mm/mm) 597 [35], Q = 29.3 (J/mm/mm) BS7910 [32], Q > 120 SINTAP [36], Q < 60 (J/mm/mm) API 597 [35], Q = 29.3 (J/mm/mm)

-0.5 -1 -1.5 0

0.2

0.4

0.6

0.8

1

x/t Figure 8 Residual stress profiles generated by mechanical pre-loading on evenmatched uncracked specimens.

21

5.2 Pre-loading on notched specimens Figure 9(a) through 9(g) show the distributions of yy(R) (normalized by

YSBM ) over the

remaining ligament surface of the specimen with a/W = 0.5 and MY = 1.0 corresponding to seven representative residual stress states. Note that x = 0 denotes the crack tip, and z = 0 and ±B/2 denote the mid-plane and free surfaces of the specimen, respectively. Positive and negative values of yy(R)/

YSBM represent tensile and compressive stresses, respectively. High stress gradients along the x axis are observed at the region x/(W - a) ≤ 0.2 for all the cases. PT(I), PC(I) and PB(I) yields relative uniform distribution of yy(R) along the crack front, whereas PRB(I) and LC lead to non-uniform distributions of yy(R) along the crack front. Figure 10(a) through 10(d) show the distribution of yy(R)/ YS for 0 ≤ x/(W - a) ≤ 0.2 at the BM

mid-plane for specimens with a/W = 0.2 and 0.5, and MY = 1.0. These figures indicate that PT and PB lead to compressive yy(R) at the crack tip whereas PC, PRB, LC-A and LC-B yield tensile neartip yy(R). It is interesting to observe that LC-C causes compressive near-tip yy(R) for the specimen with a/W = 0.2, but tensile near-tip yy(R) for the specimen with a/W = 0.5. The absolute value of

yy(R)/ YS at the crack tip increases with the pre-loading level. Figure 10(a) and 10(c) indicate that BM

absolute value of yy(R)/ YS corresponding to the in-plane pre-loading rapidly decreases from within BM

the range of 1.5 to 3 to within the range of 0 to 0.5 as x increases from 0 to 0.05(W – a), and then remains stable as x further increases. On the other hand, Figure 10(b) and 10(d) show that as x increases from 0 to 0.01(W – a), yy(R)/ YS corresponding to LC rapidly increases from within the BM

range of 0 to 0.5 to within the range of 1.5 to 2.0 followed by a stable decrease. The variation of

yy(R)/ YS corresponding to LC-C for specimens with a/W = 0.2 is an exception as it follows the BM

similar trend shown in Figure 10(a) and 10(c). The variations of yy(R)/ YS within 0 ≤ x/(W - a) ≤ BM

0.2 for specimens with MY = 1.2 and 1.5 generally follow the same trend and therefore are not presented here to save space.

22

 yy R 

 yy R 



 YSBM

BM YS

2z B

x W a

x W a

(a)

(b)

 yy R 

 yy R 



 YSBM

BM YS

x W a

2z B

(c)

2z B

x W a

2z B

(d)

23

 yy R 

 yy R 



 YSBM

BM YS

2z B

x W a

x W a

(e)

2z B

(f)

 yy R   YSBM

x W a

2z B

(g) Figure 9 Area distribution of yy(R)/𝜎𝐵𝑀 𝑌𝑆 in the uncracked ligament for specimen with a/W = 0.5, MY = 1.0 and: (a) PT(I); (b) PC(I); (c) PB(I); (d) PRB(I); (e) LC-A(I); (f) LC-B(I); (g) LC-C(I).

24

 yy R  

BM YS

3

3

2

2

1

1

 yy R 

0



-1

PT (I) PT (III) PC (II) PB (I) PRB (I)

-2 -3

BM YS

PT (II) PC (I) PC (III) PB (II) PRB (II)

0 -1

LC-A (I) LC-A (II) LC-B (I) LC-B (II) LC-C (I) LC-C (II)

-2 -3

-4

-4

0

0.05

0.1

x / W  a 

0.15

0.2

0

0.05



BM YS

3

3

2

2

1

1

 yy R 

0



-1

PT (I) PT (III) PC (II) PB (I) PRB (I)

-2 -3

0.15

0.2

(b)

(a)

 yy R 

0.1

x / W  a 

PT (II) PC (I) PC (III) PB (II) PRB (II)

BM YS

0 -1

LC-A (I) LC-A (II) LC-B (I) LC-B (II) LC-C (I) LC-C (II)

-2 -3 -4

-4 0

0.05

0.1

x / W  a 

0.15

(c)

0.2

0

0.05

0.1

x / W  a 

0.15

0.2

(d)

Figure 10 Distribution of yy(R)/𝜎𝐵𝑀 𝑌𝑆 ahead of crack tip at specimen mid-thickness (z = 0) for specimens with: (a) a/W = 0.2 and in-plane pre-loadings; (b) a/W = 0.2 and out-of-plane preloadings; (c) a/W = 0.5 and in-plane pre-loadings; (d) a/W = 0.5 and out-of-plane pre-loadings. 5.3 Effects of the notching process Figure 11(a) and 11(b) depict the redistribution of yy(R) for 0 ≤ x/(W - a) ≤ 0.1 at the midplane as the notching process is applied to the two uncracked specimens that have been subjected to LC-A(I) and LC-C(I), respectively. The figures indicate that yy(R) in the uncracked specimen is as low as (0.2 ~ 0.3) YS after the local compression. As a crack length of a/W = 0.35 is introduced in BM

the specimens, the redistribution of yy(R) for 0 ≤ x/(W - a) ≤ 0.1 is significant, which is expected.

25 4

4 a/W=0

a/W=0 a/W=0.35

3

a/W=0.35

3

a/W=0.5

a/W=0.5

 yy R  

BM YS

 yy R 

2

 YSBM

1

2

1

0

0

0

0.02

0.04

0.06

x / W  a 

0.08

0.1

0

0.02

0.04

0.06

x / W  a 

0.08

0.1

(b)

(a)

Figure 11 Distribution of yy(R)/𝜎𝐵𝑀 𝑌𝑆 ahead of crack tip at specimen mid-thickness (z = 0) during the notching process for specimens with: (a) LC-A(I); (b) LC-C(I). 4

4 LC before notching LC after notching

3

 yy R   YSBM

LC before notching LC after notching

3

 yy R 

2

 YSBM

1

2

1

0

0 0

0.02

0.04

0.06

x / W  a  (a)

0.08

0.1

0

0.02

0.04

0.06

x / W  a 

0.08

0.1

(b)

Figure 12 Impact of the sequence of the LC technique and notching process on the distribution of of yy(R)/𝜎𝐵𝑀 𝑌𝑆 at specimen mid-thickness (z = 0) for specimens with a/W = 0.5, MY = 1 and: (a) LCA(I); (b) LC-C(I). However, as the crack length further increases to a/W = 0.5 through the notching process, the redistribution of yy(R) is significant only within the region very close to the crack tip, i.e. 0 ≤ x/(W a) ≤ 0.02; there is little change in yy(R) for x/(W - a) > 0.02. Similar observations have also been reported in the literature [14, 24]. Figure 12(a) and 12(b) show the impact of the sequence of the LC technique and notching process on the distribution of yy(R). The figures suggest that in the region of

26

0 ≤ x/(W - a) ≤ 0.01, values of yy(R) corresponding to the cases that the LC technique is applied before notching are markedly higher than those when the LC technique is applied after notching. In the region of x/(W - a) > 0.02, values of yy(R) is not sensitive to the sequence of the LC technique and notching process, especially if LC-A(I) is considered.

27

6. Effect of Residual Stress on Estimated J At each level of the primary loading characterized by P/PY(W), the difference between the average J obtained from a specimen containing residual stress (Jave) and the average J (𝐽𝑁𝑅 𝑎𝑣𝑒) obtained from the corresponding residual stress-free specimen with the same a/W and MY is defined as eJ 

NR J ave  J ave NR J ave

(11)

Figure 13 and Figure 14 show eJ values plotted against P/PY(W) for specimens with different a/W, MY and residual stress states. Loading levels in terms of 𝐽𝑁𝑅 𝑎𝑣𝑒 are also indicated in the figures. Only values of eJ corresponding to 0.7 ≤ P/PY(W) ≤ 1.0 to 1.25 (or 𝐽𝑁𝑅 𝑎𝑣𝑒 approximately between 10 and 1200 N/mm) are shown in these figures. This is because the absolute values of 𝐽𝑁𝑅 𝑎𝑣𝑒 corresponding to P/PY(W) ≤ 0.7 are small and therefore have little impact on the entire J-R curve. Moreover, the elastic component of Jave is significant (can be more than 50% of the total Jave) for P/PY(W) < 0.7; therefore, the impact of residual stresses on Jave for P/PY(W) < 0.7 is largely governed by the impact of residual stresses on K, which has been well studied (see Eqs. (1) and (2)). Finally, Jave is relatively strong domain-dependent for P/PY < 0.7 as discussed in Section 3.4, and P = 1.25PY(W) is representative of the maximum loading level in SE(T)-based J-R curve tests [8]. These figures suggest that eJ depends strongly on the pre-loading technique and level of the primary loading. For example, the maximum absolute values of eJ corresponding to P/PY(W) = 1.0 for specimens subjected to PRB(II) are around 30 – 60%, whereas these values are less than 20% for specimens subjected to PT(III). Pre-loading techniques that generate tensile near-tip residual stresses in general lead to positive eJ (i.e. J values greater than those of residual stress-free specimens), whereas preloading techniques that generate compressive near-tip residual stresses in general lead to negative eJ. For a specimen with given configuration and material properties, |eJ| generally decreases as the load increases and |eJ| approachs to 0 ~ 10% at P/PY(W) = 1.1 ~ 1.2. At small loading levels (described by the load ratio P/PY(W)), the residual stress has a relatively large contribution to the applied J compared with the primary loading, which causes relatively large eJ. As the loading level increases, the residual stresses start to relax with the local plastic flow, and totally relax if there is net-section yielding in the vicinity of the crack, resulting in small eJ. Figure 15(a) and 15(b) show eJ values plotted against P/PY(W) for specimens with a/W = 0.5 and MY = 1, where two LC techniques, i.e. LC-A(I) and LC-C(I), are applied before and after the notching process, respectively. These figures suggest that eJ values corresponding to "LC before notching" are always higher than those corresponding to "LC after notching" for 0.7 ≤ P/PY(W) ≤ 1.0; this observation is consistent with the results shown in Figure 12. On the other hand, the sequence of the LC technique and notching process has little impact on eJ for P ≥ PY(W).

28 150%

12.4

16.8

21.7

48.3

190

674

NR J ave (N / mm)

100% 50%

eJ

0%

PT(I) PC(I) PB(I) PRB(II) LC-B(I) LC-C(II)

-50% -100% -150% 0.7

0.8

0.9

PT(II) PC(II) PB(II) LC-A(I) LC-B(II)

PT(III) PC(III) PRB(I) LC-A(II) LC-C(I)

1

1.1

1.2

66.5

248

811

1

1.1

1.2

97.2

335

1080

1

1.1

1.2

P / PY W 

(a) 150%

14.5

18.1

24.4

0.7

0.8

0.9

NR (N / mm) J ave

100% 50%

eJ

0% -50% -100% -150%

P / PY W 

(b)

150%

14.3

30.9

47.4

0.7

0.8

0.9

NR J ave (N / mm)

100% 50%

eJ

0% -50% -100% -150%

P / PY W 

(c)

Figure 13 Variation of eJ with P/PY(W) and 𝐽𝑁𝑅 𝑎𝑣𝑒 for specimens with a/W = 0.2 and: (a) MY =1.0; (b) MY =1.2; (c) MY =1.5.

29 100%

39.2

60.6

89.9

PT(I) PC(I) PB(I) PRB(II) LC-B(I) LC-C(II)

50%

eJ

137

239 PT(II) PC(II) PB(II) LC-A(I) LC-B(II)

509 PT(III) PC(III) PRB(I) LC-A(II) LC-C(I)

NR (N / mm) J ave

0%

-50%

-100% 0.7

0.8

0.9

1

1.1

1.2

P / PY W 

(a) 100%

43.8

67.5

102

161

313

735

0.7

0.8

0.9

1

1.1

1.2

NR (N / mm) J ave

50%

eJ

0%

-50%

-100%

P / PY W 

(b) 58.1

79.9

113

202

454

1160

0.7

0.8

0.9

1

1.1

1.2

100%

NR (N / mm) J ave

50%

eJ

0%

-50%

-100%

P / PY W 

(c)

Figure 14 Variation of eJ with P/PY(W) and 𝐽𝑁𝑅 𝑎𝑣𝑒 for specimens with a/W = 0.5 and: (a) MY =1.0; (b) MY =1.2; (c) MY =1.5.

30 20%

20%

LC before notching LC after notching

10%

eJ

LC before notching

eJ

0%

-10%

LC after notching

10%

0%

-10%

-20%

-20%

0.7

0.8

0.9

1

P / PY W  (a)

1.1

1.2

0.7

0.8

0.9

1

1.1

1.2

P / PY W  (b)

Figure 15 Variation of eJ with P/PY(W) for specimens with a/W = 0.5, MY = 1 and: (a) LC-A(I); (b) LC-C(I).

31

7. Conclusions Three-dimensional finite element analyses are carried out to investigate the effects of residual stresses on the standard J-integral for the clamped SE(T) specimen consisting of the base metal and weldment. Specimens with H/W = 10, B/W = 1, a/W = 0.2 and 0.5 and MY = 1.0, 1.2 and 1.5 are analyzed. All specimens contain stationary straight cracks located at the weld centerline. For a given specimen, sixteen different residual stress states are generated by applying seven different mechanical pre-loading techniques (i.e. tension, compression, bending, reverse bending, local compression with a single pair of indenters and local compression with double pair of indenters) and three loading levels. A review of RSPs measured from girth welds of ferritic steel pipelines and specified in wellknown structural integrity assessment standards indicates that there are large variations in the measured and standard-prescribed RSPs.

The residual stresses generated by the pre-loading

techniques are in general consistent with those recommended in the standards and obtained from measurements, and are therefore a viable option to simulate residual stresses in pipelines. It is observed that PT, PC and PB yield relatively uniform distributions of yy(R) along the crack front, whereas PRB and LC lead to non-uniform distributions of yy(R) along the crack front. The impact of the residual stress on J depends strongly on the pre-loading technique and P/PY(W). Pre-loading techniques that generate tensile (compressive) near-tip residual stresses in general lead to positive (negative) eJ. For a agiven specimen, the absolute values of eJ generally decrease to 0 ~ 10% as P/PY(W) increases to 1.1 ~ 1.2. The sequence of the pre-loading and notching process has a large impact on the near-tip (0 ≤ x/(W - a) ≤ 0.01) residual stresses but a small impact on residual stresses at locations relatively far from the crack tip (x/(W - a) > 0.02) for specimens subjected to the LC technique. Furthermore, the sequence of the pre-loading and notching process has a large impact on eJ for 0.7 ≤ P/PY(W) ≤ 1.0 but little impact on eJ when P ≥ PY(W).

Acknowledgments We gratefully acknowledge the financial support provided by the Natural Sciences and Engineering Research Council of Canada (NSERC) through the Discovery Grant program and by the Faculty of Engineering at the University of Western Ontario.

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Author Statement Yifan Huang: Conceptualization, Methodology, Software, Data curation, Investigation, WritingOriginal draft preparation. Wenxing Zhou: Supervision, Writing- Reviewing and Editing, Funding acquisition.

37

Highlights 

Review the RSPs specified in the standards and measured from pipeline girth welds



Generate the residual stress states using pre-loading techniques based on 3D FEA



Evaluate the J integral for SE(T) specimens with/without residual stresses



Quantify the impact of residual stresses on J evaluated from SE(T) specimens