Effects of pipe steel heterogeneity on the tensile strain capacity of a flawed pipeline girth weld

Engineering Fracture Mechanics 115 (2014) 172–189

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Effects of pipe steel heterogeneity on the tensile strain capacity of a flawed pipeline girth weld Stijn Hertelé a,⇑, Noel O’Dowd b, Koen Van Minnebruggen a, Rudi Denys a, Wim De Waele a a b

Ghent University, Soete Laboratory, Technologiepark Zwijnaarde 903, 9052 Zwijnaarde, Belgium University of Limerick, Department of Mechanical, Aeronautical and Biomedical Engineering, Materials and Surface Science Institute, Limerick, Ireland

a r t i c l e

i n f o

Article history: Received 13 March 2013 Received in revised form 2 September 2013 Accepted 1 November 2013 Available online 9 November 2013 Keywords: Girth weld Weld flaw Strain based design Strain capacity Heterogeneity

a b s t r a c t An accurate estimate of the tensile strain capacity of flawed girth welds is essential for the safe use of pipelines in harsh environments. Current strain-based flaw assessments neglect the unavoidable presence of strength heterogeneity between two connected pipes. This paper describes and quantifies the resulting effects on strain capacity. A theoretical framework predicts a remarkable sensitivity, which depends on the failure location (whether in the weld or base metal). A finite element study critically validates the predicted results. Probabilistic analysis reveals that pipe steel heterogeneity should be taken into account to allow for accurate evaluations of tensile strain capacity. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction The increasing energy demand and the depletion of existing fossil fuel resources have led to the installation and operation of transmission pipelines in increasingly hostile conditions. The nature of their installation (e.g. reeling of offshore pipelines) and/or environment (e.g. permafrost, seismic or land slide prone terrains) may impose large longitudinal strains on the pipeline. The girth welds that connect pipe sections unavoidably contain weld flaws, which makes them potential weakest links under severe longitudinal straining. Under these circumstances, the acceptability of detected girth weld flaws is judged in a strain based assessment which considers (plastic) deformation as the failure controlling parameter rather than the load. The last decade has seen the development of analytical procedures for the strain based assessment of girth weld flaws. A lack of consensus on key influence factors has led to a variety of approaches. So far, most attention has been devoted to influences of flaw dimensions [1,2], combined with weld strength mismatch [3–6], ductile tearing resistance [4–6], internal pressure [3–6], and weld misalignment [4–6]. From studies of weld strength mismatch effects, it is particularly known that the tensile strain capacity is to a great extent influenced by the actual (rather than the minimum specified) stress–strain properties of the base metal (i.e. the line pipe steel) and weld metal [7]. In this respect, of particular relevance to strain capacity is the weld flow stress overmatch OMFS (%), defined as

OMFS ¼

  FSWM  FSBM  100% FSBM

ð1Þ

where FSWM and FSBM represent the flow stress (average of yield strength Rp0.2 and ultimate tensile strength Rm) of weld metal and base metal respectively [8,9]. ⇑ Corresponding author. Tel.: +32 9 331 04 74; fax: +32 9 331 04 90. E-mail address: [email protected] (S. Hertelé). 0013-7944/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.engfracmech.2013.11.003

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Nomenclature a a0 BM CMOD CTOD CWP e E em emax er FS HAZ LVDT n1 n2 OMFS p P Pmax R Rm Rp0.2 s t u WM Y/T

a b Ds e

r r0.2 r1 r2

flaw depth (mm) initial flaw depth (mm) base metal crack mouth opening displacement (mm) crack tip opening displacement (mm) curved wide plate engineering strain (–) Young’s modulus (MPa) uniform elongation of the base metal (–) strain capacity (–) remote strain (–) flow stress (MPa) heat affected zone linear variable differential transformer first strain hardening exponent in UGent stress–strain model (–) second strain hardening exponent in UGent stress–strain model (–) weld flow stress overmatch (%) probability (%) tensile load (N) load bearing capacity (N) reduction in strain capacity due to base metal heterogeneity (%) ultimate tensile strength (MPa) 0.2% proof stress (MPa) engineering stress (MPa) wall thickness (mm) applied piston displacement during CWP test (mm) weld metal yield-to-tensile ratio Rp0.2/Rm (–) factor in CTOD resistance curve exponent in CTOD resistance curve base metal heterogeneity (MPa) true strain (–) true stress (MPa) true 0.2% proof stress in UGent stress–strain model (MPa) UGent stress–strain model parameter (MPa) UGent stress–strain model parameter (MPa)

Although the importance of material properties in a strain based assessment is widely recognized, current flaw assessment procedures assume that the base metals at both sides of a weld possess identical stress–strain properties. For welded pipelines this assumption may not hold since line pipe specifications allow for considerable variations in the constitutive properties of pipe steels. For instance, API 5L [10] has a tolerance band of 150 MPa on yield strength for common line pipe steel grades (X60 to X100). As a result, it is likely that a girth weld connects two pipes with different stress–strain properties. This phenomenon is here referred to as ‘base metal heterogeneity’. Fig. 1 shows the probability distribution of differences in yield strength between two pipes of nominally identical API 5L strength grade, based on extensive data sets reported in [11,12] and assuming a normal yield strength distribution. The reported data sets cover API 5L grades X42 to X100. Remarkably, the reported data indicate that the distribution of differences in yield strength is fairly grade independent, i.e. Fig. 1 applies to a large variety of strength grades. Base metal heterogeneity was identified as an influence on strain partitioning upon plastic deformation as early as 1994 by Denys [13]. His findings were based on the analysis of Curved Wide Plate (CWP) test results. A CWP test can be described as an intermediate scale uniaxial tensile test on a pipeline section (typically 200–400 mm wide) containing a girth weld, which is often deliberately notched to simulate a weld flaw [14,15]. The collection of CWP data investigated at Ghent University provides a strong experimental basis to confirm Denys’ hypothesis on the importance of base metal heterogeneity. For instance, Fig. 2 [16] shows the longitudinal strain distribution during a smaller scale (150 mm specimen width) notched CWP tension test, measured by means of digital image correlation as described in [17]. Although the difference in strength of the two connected pipe pieces is modest (DRp0.2 = 22 MPa; DRm = 37 MPa), the weaker pipe section (on the left) experiences significantly higher deformation than the stronger pipe. The ratio between the remote strain levels for the two pipes in Fig. 2

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25%

Girth weld

Pipe 1

Pipe 2

Probability (%)

20%

Δ Rp0.2 = |Rp0.2,1 – Rp0.2,2| 15%

10%

> 100

90 - 100

80 - 90

70 - 80

60 - 70

40 - 50

50 - 60

30 - 40

20 - 30

10 - 20

0%

0 - 10

5%

Line pipe steel heterogeneity of yield strength, Δ Rp0.2 (MPa) Fig. 1. Distribution of difference in yield strength (DRp0.2) between pipes of the same grade, based upon extensive datasets reported in [11,12]. This distribution covers API 5L grades X42 to X100.

Girth weld

εxx = 0.053

‘Stronger’ pipe

0.016

150 mm

‘Weaker’ pipe

Tensile load P = 1.06 MN

Longitudinal direction

Longitudinal true strain εxx (-) 0.003

0.053

Fig. 2. Longitudinal strain distribution in a CWP specimen, measured using digital image correlation [16].

is approx. 3.3 (0.053 versus 0.016). Such a non-uniform strain distribution clearly alters the overall strain capacity as the weaker pipe, which experiences higher deformation, has a corresponding stronger tendency towards failure. This results in a lower overall strain capacity than would be obtained if the pipes had identical material properties. To address the deficiency in current assessment procedures, this paper investigates the effect of base metal heterogeneity on strain capacity. The paper is structured as follows. Section 2 explains a theoretical framework which provides the basis for further discussion. Section 3 is devoted to a finite element study for validation of the theoretical framework. Section 4 compares and discusses the obtained numerical and theoretical results. Conclusions are finally drawn in Section 5. 2. Theoretical framework This section focuses on a model to estimate the effect of base metal heterogeneity on strain capacity. The assumptions of the model are outlined in Section 2.1. Section 2.2 introduces the concepts of a reference weldment and a reference base metal. Then, effects are predicted in Sections 2.3 and 2.4, each section considering a different failure location (in the unflawed pipe body or in the flawed weld, respectively). Section 2.5 summarizes matters. 2.1. Assumptions Five assumptions which form the basis of the theoretical framework are discussed below. 2.1.1. The investigated problem is uniaxial This implies that the influence of in-plane transverse and shear stresses is not taken into account. As a consequence, the structural problem can be investigated using uniaxial stress–strain properties obtained from small scale tensile tests. It is recognized that a biaxial stress state, arising from the presence of a defect or from combined axial tension and internal

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pressure, will influence the strain capacity of pipes [18–21]. Therefore, the results obtained here should be seen as a first step towards a more advanced model which also accounts for stress biaxiality (or triaxiality). 2.1.2. Failure is governed by the region with the lowest load bearing capacity Three potential locations of failure are considered in the theoretical framework: either of the base metal pipes, denoted as ‘BM1’ and ‘BM2’, and the girth weld, denoted as ‘WM’. Note that failure in the heat-affected zone of the girth weld is considered to be associated with the presence of a weld flaw (e.g. lack of fusion) and is categorized here as failure in the girth weld. Three load bearing capacities are considered in the theoretical model: that of the weld (Pmax,WM) and those of the base metals (Pmax,BM1 and Pmax,BM2). The load bearing capacity Pmax of the entire weldment is then

Pmax ¼ minðPmax;WM ; Pmax;BM1 ; P max;BM2 Þ

ð2Þ

Note that the load bearing capacity of the weld, Pmax,WM, is assumed constant. This implies that stable ductile tearing of the weld flaw is not taken into account in the theoretical model. 2.1.3. Both girth welded pipes have an identical geometry The model examines girth welds between pipes with identical geometry. As a consequence, pipes with identical stress– strain properties are assumed to have an equal load bearing capacity. 2.1.4. Strain capacity is defined as the average of the remote strains at failure In this work the strain capacity emax is defined as

emax ¼

minðer;1 ; em;1 Þ þ minðer;2 ; em;2 Þ 2

at maximum load

ð3Þ

where er,1 and er,2 are the remote strains in the base metals and em,1 and em,2 their respective uniform elongations (strain corresponding with the ultimate tensile strength Rm as measured in a small scale tensile test). This definition allows the individual contributions of the two base metals to be taken into account. For conservatism, the strain capacity is not allowed to exceed the average of the uniform elongations. In this study, remote strains er,1 and er,2 are obtained in CWP specimens according to LVDT measurements as shown in Fig. 3. The setup shown in this figure (both geometry and instrumentation) is advised in the UGent guidelines for CWP testing [14]. 2.1.5. Base metal heterogeneity is constant over the entire stress–strain curve Base metal heterogeneity is characterized on the basis of a single value, Ds, the difference between the strength of the two base metals BM1 and BM2 (Fig. 4). As a result of this simplification, both base metals have the same uniform elongation, em. Note that Ds is defined based on the engineering stress–strain curve. For convenience and without loss of generality, it is further assumed that heterogeneity corresponds with BM2 being stronger than BM1 (Pmax,BM2 > Pmax,BM1), and this is translated into a positive value for Ds. Based on assumption 4, a ‘relative strain capacity’, is defined as emax/em. From Eq. (3), it follows that emax/em 6 1. 2.2. Definition of the reference weldment and reference base metal For convenience a hypothetical ‘reference weldment’ is introduced. The reference weldment is identical to the actual (heterogeneous) weldment, with the exception that the base metals have the same properties (Ds = 0). It is assumed that the base metal of the reference weldment has the stress–strain properties of the weaker base metal BM1; BM1 is further referred to as the ‘reference base metal’. Sections 2.3 and 2.4 compare the strain capacities of weldments with an identical reference weldment (i.e. identical base metal BM1 and weld metal) but different base metal heterogeneity Ds (i.e. different base metal BM2).

Fig. 3. CWP geometry and positions of LVDTs were chosen in accordance with Ghent University’s guidelines for CWP testing [14].

S. Hertelé et al. / Engineering Fracture Mechanics 115 (2014) 172–189

Engineering stress s (MPa)

176

‘BM1’

Δs

‘BM2’

Uniform elongation

em

Δ s = 0: homogeneous (reference) weldment Δ s > 0: BM2 stronger than BM1 (the reference base metal) 0

0

Engineering strain e (-)

Fig. 4. Base metal heterogeneity is characterized on the basis of one offset value, Ds.

2.3. Reference weldment fails in base metal This section focuses on cases where the reference weldment necks in one of the base metal pipes rather than failing at the weld. This failure mode is also referred to as gross section collapse and mostly occurs for strength overmatching welds, whose potential weld flaws are shielded from remotely applied deformations [7]. Given that failure does not occur in the weld of the homogeneous reference weld, the following relations apply for Ds = 0 (assumption 2):

Pmax ¼ Pmax;BM1 < Pmax;WM

ð4Þ

Since Pmax,BM1 and Pmax,WM are independent of Ds for a constant reference weldment, the inequality in Eq. (4) remains unaltered and failure will never occur in the weld if Ds is varied. However, the introduction of base metal heterogeneity implies that the strongest base metal (i.e. BM2) will not achieve em upon maximum load, which is governed by the weakest base metal BM1 (Fig. 5). The resulting strain capacity is then expressed by the following equation:

  emax 1 eðRm  DsÞ 1þ ¼ 2 em em

ð5Þ

Engineering stress s (MPa)

where e(s) represents the stress–strain behavior (engineering strain as a function of engineering stress) of the reference base metal prior to necking (e 6 em) and Rm the ultimate tensile strength of the reference base metal.

‘BM1’

‘BM2’

Δ s (> 0)

Rm e(Rm – Δ s)

0

0

emax

em Failure (BM1 necks)

Engineering strain e (-)

Fig. 5. Graphical explanation of Eq. (5).

S. Hertelé et al. / Engineering Fracture Mechanics 115 (2014) 172–189

Relative strain capacity emax/em (-)

Stress

177

em

1.0

Strain Rotate 90°

0.5

0.0

0

Base metal heterogeneity Δ s (MPa) Fig. 6. Predicted effect of base metal heterogeneity on strain capacity in case of gross section collapse (Eq. (5)).

Eq. (5), illustrated in Fig. 6, reveals some important characteristics of the effect of base metal heterogeneity on strain capacity, when the reference weldment fails by gross section collapse. The shape of Fig. 6 reflects the stress strain curve of the reference base metal, as illustrated in the inset. It may be noted from Fig. 6 that the strain capacity can be reduced by a factor up to 2 due to base metal heterogeneity (emax/em is 1 for the homogeneous weldment and converges to 0.5 for large Ds). Eq. (5) is independent of weld material properties and flaw dimensions. This is based on the assumption that in the case of gross section collapse, failure occurs remote from the defect and the girth weld. Note that Eq. (5) does not depend on pipe geometry but, as will be seen, weld and flaw characteristics and pipe geometry partially govern the failure location of the reference weldment (base or weld metal). 2.4. Reference weldment fails in flawed weld section Given that failure occurs in the flawed weld for the reference weldment, the load bearing capacities are related as follows (assumption 2):

Pmax ¼ Pmax;WM < Pmax;BM1

ð6Þ

For the actual (heterogeneous) weldment, as BM2 is stronger than BM1, the location of failure is unaltered since Pmax,BM2 > Pmax,BM1 and, hence, the weld remains the weakest link. Compared with the reference weldment, however, the remote strain in base metal BM2 upon maximum load (Pmax,WM) is reduced due to its increased strength. In contrast with cases of gross section collapse (Section 2.3), the exact evolution of emax/em is more challenging to quantify since the failure load Pmax,WM is not a priori known (this value depends on weld and flaw characteristics). However, similar to Eq. (5), the resulting strain capacity reduction converges to a factor 2 for large Ds-values, compared with the homogeneous case Ds = 0. This follows from comparison between the following two limit cases (Fig. 7):  Ds = 0: both base metals deform equally (er,1 = er,2) and Eq. (3) reduces to emax = er,1 at P = Pmax,WM (note that er,1 and er,2 < em as failure occurs in the weld). This point is symbolized as A in Fig. 7.  Ds ? 1: in this situation, BM2 hypothetically becomes infinitely strong and merely deforms elastically. Hence er,2 is close to zero. Eq. (3) reduces to emax  er,1/2 at P = Pmax,WM, which is half of the strain capacity for Ds = 0, or A/2 (note that Pmax,WM is assumed constant). As seen in Fig. 7, A/2 provides the lower bound strain capacity emax/em for a heterogeneous weldment that fails in the weld. Eq. (5), which describes gross section collapse, provides an upper bound for emax/em. 2.5. Summary Summarizing matters, the following theoretical predictions are made:  The failure location of a heterogeneous weldment (either base metal or weld metal) is equal to the failure location of its homogeneous reference weldment.  Regardless of the failure location, strain capacity converges to 50% of its value for the reference weldment, for increasing base metal heterogeneity. This limit provides a lower bound strain capacity reduction.

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Relative strain capacity emax/em (-) 1.0

Eq. (5): upper bound for emax/em A

A 2

0.0

0

Base metal heterogeneity Δ s (MPa)

Fig. 7. Predicted effect of base metal heterogeneity on strain capacity in case of failure in the flawed weld.

 For cases of gross section collapse, strain capacity is predicted by means of Eq. (5). emax is equal to em for the reference weldment and converges to 0.5em for increasing heterogeneity.  For cases of failure at the weld, the exact evolution of emax is challenging to quantify. Next to the lower bound (see the second point above), Eq. (5) provides an upper bound for emax. 3. Finite element analysis To evaluate the theoretical framework, flawed curved wide plate (CWP) specimens have been examined through parametric finite element analysis using the software package ABAQUSÒ (version 6.10). The details of the finite element models are outlined in [22]. Experimental validations of the model are provided in [9,16]. Section 3.1 highlights model characteristics that apply to all analyzed simulations. Section 3.2 focuses on the parametric study performed. 3.1. Finite element model The finite element model, shown in Fig. 8, represents a CWP specimen with a girth weld containing a semi-elliptical surface flaw. Transverse symmetry is assumed and implemented by means of a longitudinally oriented symmetry plane. Two rigid end blocks are tied to the specimen ends. A tensile deformation is applied by keeping one block fixed in space and translating the other block in displacement control; rotations are suppressed for both rigid ends. The model is constructed of three-dimensional solid linear brick elements with reduced integration (element type C3D8R in ABAQUSÒ). The mesh was sufficiently fine to avoid inaccuracies due to unwanted phenomena related to this element type, such as hourglassing. For the present study, the finite element models contained between 13,402 and 18,578 nodes (between 10,772 and 15,370 elements). A focused mesh ensures accurate calculations of crack driving force. A flaw with an initial tip radius of 75 lm was chosen following in-house experimental practice [14]. A finite deformation formulation of strain was implemented. All materials were assumed to harden isotropically according to the Von Mises yield criterion. Constitutive properties of the base metals were modelled by means of the ‘UGent’ stress–strain model [23], an enhanced form of the classical Ramberg–Osgood (RO) model [24]. The UGent model has been found to accurately represent contemporary line pipe steels, which often show two distinct stages of strain hardening [25]. Defined on the basis of true stress (r, MPa) and true strain (e, dimensionless), the model is characterized by six parameters (Young’s modulus E, yield strength r0.2, strain hardening exponents n1 and n2, transition stresses r1 and r2) as follows:

8 > < RO1 ðrÞ e ¼ RO1!2 ðrÞ > : RO2 ðrÞ

r 6 r1 r1 < r 6 r2 r2 < r

ð7Þ

with

RO1 ðrÞ ¼

r E

 þ 0:002

r r0:2

n1 ð8Þ

S. Hertelé et al. / Engineering Fracture Mechanics 115 (2014) 172–189

179

Fig. 8. Finite element model: boundary conditions and mesh of an example configuration.

RO2 ðrÞ ¼

r E

RO1!2 ðrÞ ¼

 þ 0:002

r r0:2

n2

 De

ð9Þ

       r n1 r  r1 r n2 r n1 þ 0:002 þ 0:002  r0:2 r0:2 E r2  r1 r0:2 " # n2 þ1 n1 þ1 n2 þ1 n1 þ1  r1 r  r1 0:002 r   1 r2  r1 ðn2 þ 1Þrn0:22 ðn1 þ 1Þrn0:2

r

ð10Þ

where De in Eq. (9) is defined as follows:

De ¼

0:002 r2  r1

"

r2n2 þ1  r1n2 þ1 r2n1 þ1  r1n1 þ1  2 1 ðn2 þ 1Þrn0:2 ðn1 þ 1Þrn0:2

# ð11Þ

The ‘UGent’ model was preferred over other, less elaborate, constitutive laws for the base metals since their stress–strain behavior is a key factor to the theoretical framework and, particularly, Eq. (5). Weld metal was modelled using the more common Ramberg–Osgood model. Note that the Ramberg–Osgood model may be represented by the ‘UGent’ model, by equalizing n1 with n2. In this case, Eq. (7) reduces to e = RO1(r). The response of all materials beyond necking (engineering strain > em) was modelled by a power law extrapolation as explained in [26]. The following outputs were extracted from all simulation results:  Remote strains at both base metals (er,1 and er,2). These strains were obtained from ‘virtual LVDT’ measurements in agreement with experimental practice.  Crack mouth opening displacement CMOD.  Crack tip opening displacement CTOD, obtained according to Rice’s 90° intercept definition [27]. CTOD is considered as an expression of crack driving force.  Tensile load P. Given the implementation of a finite strain formulation, this output allows for an identification of plastic collapse corresponding to a drop in tensile load.

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Ductile tearing was not explicitly modelled within the simulations. Instead, simulations with different (but fixed) flaw depths, a, were performed for each configuration. Starting from its initial value, a0, the flaw depth was increased to a0 + 2 mm in discrete steps of 0.5 mm, resulting in five simulations for each configuration. Fourth-degree polynomial curve fitting between these five simulation results led to crack driving force curves in terms of crack tip opening displacement, CTOD(a,er), where er represents the average remote strain. The flaw depth corresponding to a remote strain eri then corresponds with the intersection between CTOD(a,eri) and the crack growth resistance curve CTODR(a), represented by the following two-parameter (a and b) power law fit [6],

CTODR ¼ aða  a0 Þb ¼ aðDaÞb

ð12Þ

Failure by unstable tearing is then identified by means of the tangency criterion, i.e.

@CTODða; er Þ dCTODR ¼ @a da

ð13Þ

Østby et al. have shown that this pragmatic approach leads to conservative strain capacity predictions [28], provided that the crack growth resistance curve represents crack tip constraint conditions similar to those in a curved wide plate or (pressurized) pipe. Note that crack growth in the length direction of the flaw has not been incorporated, since there is numerical evidence that long shallow surface flaws under tension mostly extend in the through-thickness direction [29]. This observation is also confirmed by a large fraction of all experimental CWP tests performed at Ghent University. It may be noted that weld residual stresses are not included in the numerical model. However, its effect is limited under the occurrence of gross plasticity [30] (and overestimated by stress-based flaw assessment procedures [31]). It has been suggested to account for residual stresses by means of a small correction on strain capacity (namely Rp0.2,WM/E, which is less than 0.005 for common pipeline applications) [32,33].

3.2. Parametric study A parametric study was performed to evaluate the previously described theoretical framework. As mentioned in Section 2.1 (assumption 4), the geometry of the CWP specimens and positions of LVDTs for remote strain measurements were chosen in accordance with Ghent University’s guidelines for CWP testing [14], Fig. 3. In the simulation, the applied displacement is increased until either (a) unstable crack extension is deemed to occur due to fulfilment of the tangency criterion, Eq. (13), or (b) the tensile load drops upon increasing deformation. In the latter case, failure occurs in the weld metal if the remote strain level of the weakest base metal does not reach em (b1), or in the weakest base metal in the other case (b2). Criteria (a) and (b1) correspond to failure in the weld metal and criterion (b2) corresponds to failure by gross section collapse.

3.2.1. Fixed parameters The following parameters were kept fixed in all simulations:  Pipe outer diameter = 1067 mm (4200 ). This value, not uncommon for pipelines, was arbitrarily chosen, bearing in mind that pipe diameter is of secondary importance to the tensile strain capacity of a flawed girth weld [34].  Initial flaw depth, a0 = 3 mm; flaw length = 50 mm. The flaw shape is semi-elliptical and its location is in the centre of the weld. These flaw parameters have been kept constant since they do not influence Eq. (5). If the theoretical model holds for this arbitrarily chosen (and common in practice) flaw geometry, it can be assumed to equally hold for other flaw configurations.  Flow stress of the base metal of the reference weldment (600 MPa). This value was arbitrarily chosen as the numerical results depend on flow stress overmatch (i.e. weld flow stress relative to base metal flow stress) rather than magnitudes of flow stresses.  As described in Section 3.1, weld metal stress–strain behavior was described by the Ramberg–Osgood model [24] applied to true stress-true strain quantities. The yield-to-tensile ratio Y/T (=Rp0.2/Rm) of the corresponding engineering stress– strain curve was chosen to be 0.90. The ductile tearing resistance of the weld metal was defined according to Eq. (12), with a = 1.1 and b = 0.6. These values represent weld metals with a moderate resistance against ductile crack extension [35]. Weld metal Y/T and tearing resistance have been kept fixed since the emphasis of this study is on base metal rather than weld metal properties.  Stress–strain properties of the heat-affected zones (HAZs). These were based upon the properties of their corresponding base metal, assuming a softening level of 10%. This degree of HAZ softening is not uncommon for girth welded highstrength line pipe steels (API 5L grade X70 and above). HAZ softening was assumed constant over the entire stress–strain curve, i.e. base metals and their corresponding HAZ have the same stress–strain curve shape. The width of the HAZ was taken to be 2 mm either side of the weld.

181

S. Hertelé et al. / Engineering Fracture Mechanics 115 (2014) 172–189 Table 1 Geometrical wall thickness – weld combinations considered in this study. Geometry type

Wall thickness (mm)

Root opening (mm)

Bevel angle (°)

Weld cap reinforcement (mm)

Shown in Fig. . . .

A B C

15 15 25

5 5 5

10 30 10

1 1 1

9(a) 9(b)

10.3 mm

22.3 mm 1.0 mm

15.0 mm

1.0 mm

30°

10°

5.0 mm

5.0 mm

(a)

(b)

Fig. 9. Assumed weld geometries for pipes with 15 mm wall thickness: (a) bevel angle 10° (geometry A), (b) bevel angle 30° (geometry B).

Table 2 Characteristics and UGent stress–strain model [23] parameters chosen for the base metal of the reference weldments. Tensile test characteristics

UGent stress–strain model [23] parameters

Flow stress (MPa)

Y/T ratio (–)

Uniform elongation em (–)

E (MPa)

r0.2 (MPa)

r1 (MPa)

r2 (MPa)

n1 (–)

n2 (–)

600 600

0.85 0.90

0.09 0.07

206,900 206,900

551.4 568.4

578.0 580.0

640.0 652.3

22.2 26.0

14.3 18.9

3.2.2. Varied parameters Three combinations of pipe wall thickness t and weld fusion line profile were chosen and are summarized in Table 1. The weld fusion line profiles were defined on the basis of their bevel angle, assuming a V shaped weld as illustrated in Fig. 9 for two configurations. The weld flow stress overmatch OMFS of the reference weldments has been varied between 0% and 30% in steps of 10%. This range of overmatch levels provides for conditions of failure within the weld (likely for low OMFS) and failure in the base metal (likely for high OMFS). Two different yield-to-tensile ratios (Y/T = 0.85, 0.90) were considered for the reference base metal. Corresponding stress– strain curves (shown using engineering quantities in Table 2 and Fig. 10) were obtained by adopting model parameters shown in Table 2.

Engineering stress s (MPa)

700

em = 0.09

Y/T = 0.90

em = 0.07 600

Y/T = 0.85

500

400 0.00

0.05

0.10

Engineering strain e (-) Fig. 10. Two stress–strain curves considered for the base metal of the reference weldments.

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Finally, four different levels of base metal heterogeneity Ds were considered for each reference weldment described above: 0, 10, 20 and 50 MPa. Note that, for heterogeneous connections (Ds – 0), OMFS refers to the weaker (reference) base metal. Summarizing the above, 96 configurations were investigated (3 geometry combinations, 4 levels of weld strength overmatch, 2 reference base metal Y/T ratios, 4 levels of base metal heterogeneity), and 480 finite element simulations were performed in total (5 simulations per configuration to incorporate ductile tearing as described in Section 3.1).

4. Results and discussion 4.1. General observations Of all 96 simulated configurations, 60 (62.5%) failed due to gross section collapse (criterion (b2) in Section 3.2) and 36 (37.5%) failed in the weld by means of unstable crack extension (criterion (a)). None of the simulated configurations failed by means of collapse in the weld (criterion (b1)). Fig. 11 confirms that, as expected, failure in the weld and in the base metal are promoted by low and high OMFS-values respectively. To illustrate the approach adopted in the tearing analysis an example configuration with failure in the weld is illustrated in Fig. 12 (geometry A, base metal Y/T = 0.90, reference weldment with OMFS = 10%, Ds = 20 MPa). Unstable crack extension occurs when the average remote strain, er = 0.0415. This strain is also the strain capacity according to Eq. (3), given that the remote strains in the base metals do not exceed the uniform elongation of 0.07 (Fig. 13). It may be seen in Fig. 13 that within the range of base metal heterogeneity levels examined (0 MPa 6 Ds 6 50 MPa), strongly different remote strains can be achieved between both connected pipes. Defined as the ratio between er of the weakest base metal to that of the strongest base metal, the remote strain ratio at failure in Fig. 13 is 2.7. Fig. 14 plots the remote

100%

100%

100%

Weld failure

Base metal failure 0%

0%

0%

0%

10%

20%

30%

0%

10%

20%

0%

30%

OMFS reference weldment (%)

OMFS reference weldment (%)

(a) Geometry A

(b) Geometry B

10%

20%

30%

OMFS reference weldment (%)

(c) Geometry C

Fig. 11. Proportion of simulations failing by gross section collapse and weld failure (unstable crack extension). The different geometry types (A, B, C) are specified in Table 1.

2.0

2.0 Unstable crack extension (tangency criterion met)

1.5

Tangency (Eq. (13))

1.5 Average remote strain 0.0415

CTOD 1.0 (mm)

CTOD 1.0 (mm) 0.729 mm

0.729 mm Average remote strain 0.0335

0.5

0.5

0.0 0.00

a = 3.0, 3.5, 4.0, 4.5, 5.0 mm

0.01

0.02

0.0335

0.03

Average remote strain (-)

(a)

0.04

CTODR, Eq. (12) 0.0

3.0

3.5

4.0

4.5

5.0

Flaw depth a (mm)

(b)

Fig. 12. Analysis of an example configuration with failure in the weld: (a) CTOD response interpolated from five simulations with fixed flaw depths, (b) ductile tearing analysis.

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em = 0.07

Failure (unstable crack extension)

Remote strain BM1, er,1 (-)

0.06

1

2.7

1

1

0.04

183

0.02

0.00 0.00

0.02

0.04

0.06

Remote strain BM2, er,2 (-) Fig. 13. Evolution of remote strains for the configuration analyzed in Fig. 12.

10

Remote strain ratio at failure (-)

Base metal with Y/T = 0.85 Base metal with Y/T = 0.90

1 0

10

20

50

Base metal heterogeneity Δ s (MPa) Fig. 14. Effect of base metal heterogeneity on remote strain ratio (vertical axis is on a logarithmic scale).

strain ratios at failure for all simulated configurations as a function of the base metal heterogeneity level Ds. The highest observed remote strain ratio is 9.2. From Fig. 14, the non-uniformity of remote strain appears to be strongly sensitive not only to base metal heterogeneity, but also to the Y/T ratio of the base metal. In this respect, higher Y/T values promote higher remote strain ratios. This can be understood from the increased sensitivity of strain to stress beyond yield for an increasing Y/T ratio (or decreasing work hardening, e.g. Fig. 10). Given a certain stress offset Ds in the plastic region, this increased sensitivity leads to stronger differences in strain and, hence, higher remote strain ratios. 4.2. Strain capacity versus base metal heterogeneity Fig. 15 plots all obtained results in terms of relative strain capacity emax/em as a function of base metal heterogeneity, Ds, along with the curves for gross section collapse predicted by Eq. (5), indicated by the solid line in each figure. Fig. 15(a)–(c) provide results for base metals with Y/T = 0.85, Fig. 15(d)–(f) for base metals with Y/T = 0.90. Fig. 15(a) and (d) correspond to geometry A; Fig. 15(b) and (e) correspond to geometry B; Fig. 15(c) and (f) correspond to geometry C. In each figure, filled symbols indicate failure due to gross section collapse; open symbols represent configurations that failed at the weld. Different levels of overmatch are indicated by different symbols, as described by the legend in Fig. 15(a). The point corresponding to the case study illustrated in Figs. 12 and 13 is indicated in Fig. 15(d). Each subfigure has an equal number of data points. However, some results coincide, which at first sight makes some subfigures appear to have fewer points than actually plotted (compare e.g. Fig. 15(f) with Fig. 15(a)). A number of important results are evident from Fig. 15. It is seen that Eq. (5) serves as a near upper bound for emax/em for all weldments, regardless of the failure mode of the reference weldment (gross section collapse or failure in the weld). The

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(a) Y/T = 0.85, geometry A

1.0

(d) Y/T = 0.90, geometry A 1.0

Eq. (5) Relative strain 0.5 capacity emax/em (-)

Relative strain 0.5 capacity emax/em (-)

OMFS = 0

10

20

Figs 12, 13

Failure at… weld base metal 30% 0.0

0.0 0

10

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0

Base metal heterogeneity Δ s (MPa)

(b) Y/T = 0.85, geometry B

1.0

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Base metal heterogeneity Δ s (MPa)

(e) Y/T = 0.90, geometry B

1.0

Relative strain 0.5 capacity emax/em (-)

Relative strain 0.5 capacity emax/em (-)

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0.0 0

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0

Base metal heterogeneity Δ s (MPa)

(c) Y/T = 0.85, geometry C

1.0

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Base metal heterogeneity Δ s (MPa)

(f) Y/T = 0.90, geometry C 1.0

Relative strain 0.5 capacity emax/em (-)

Relative strain 0.5 capacity emax/em (-)

0.0

0.0 0

10

20

50

Base metal heterogeneity Δ s (MPa)

0

10

20

50

Base metal heterogeneity Δ s (MPa)

Fig. 15. Overview of obtained relative strain capacities as a function of base metal heterogeneity.

relative strain capacity tends to increase towards this upper bound as weld strength overmatch increases, leading to gross section collapse for higher weld strength overmatch values (shaded circles). Fig. 15 demonstrates that Eq. (5) provides a good prediction of the influence of base metal heterogeneity on strain capacity for all observed situations of gross section collapse. In particular, for joints experiencing gross section collapse, emax/em is 1 for reference weldments and converges to 0.5 for high levels of base metal heterogeneity. In these cases, it is confirmed that base metal heterogeneity may reduce strain capacity up to a factor two. Simulated strain capacities in cases of a reference weldment that fails in the weld are not in complete agreement with the theoretical predictions of Fig. 7, since emax/em does not monotonically decrease to half its level observed for Ds = 0. Indeed, emax/em appears fairly insensitive to Ds and may even increase as heterogeneity increases. The reason for this discrepancy is a violation of the assumption of a constant load bearing capacity Pmax for Ds > 0. Instead, the maximum tensile force increases as Ds increases. This is illustrated in Fig. 16 for an example configuration from Fig. 15(d) (geometry A, reference base metal with Y/T = 0.90, OMFS = 0%).

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185

3.0

Tensile force (MN)

Failure at ‘BM1’ Failure at weld Δ s = 0, 10, 20, 50 MPa 2.5

2.0 0.0

1.0

2.0

CTOD (mm) Fig. 16. Dependence of tensile force-CTOD curve on base metal heterogeneity, Ds.

The increasing maximum tensile force in Fig. 16 results from a violation of assumption 1 (Section 2.1). Indeed, the stress state in vicinity of the flawed weld is far from uniaxial and strongly influenced by the constraint of the surrounding material. An increased Ds introduces a hoop tension stress in the weld, necessary to fulfil deformation compatibility with the stronger BM2 which shows less lateral contraction. Recalling the assumption of isotropic hardening obeying the Von Mises yield criterion, the resulting increase in stress biaxiality is understood to reduce plasticity in the weld. This is confirmed in Fig. 17, comparing the configurations of Fig. 16 with Ds = 0 and 50 MPa. The top contour plots depict the equivalent plastic strain distribution in and around the weld at an equal force (namely, the load bearing capacity of the homogeneous connection from Fig. 17(a)). Simulations with fixed flaw depth 3 mm were selected for this illustration. The reduced plasticity in the weld for Ds = 50 MPa is translated into a strongly reduced CTOD for equal tensile force (detail plots at bottom in Fig. 17) and hence, provided that failure occurs in the weld, an increased strain capacity. Note that the weld flaw opens fairly symmetrical even for Ds = 50 MPa (Fig. 17(b), section view and detail at bottom), i.e. contributions to CTOD are similar at either sides of the flaw. Hence, the influence of Ds on CTOD results from a change of global plasticity in the weld (as discussed above) rather than local effects near the flaw tip. Finally, note that the assumption of a constant load bearing capacity is only violated for cases of failure in the weld. For cases of gross section collapse, Pmax is fairly constant as Ds is varied (e.g. Fig. 18). This results from the highly uniaxial stress state in most of the base metal, as opposed to the strongly multiaxial distributions near the weld observed and discussed in Fig. 17. Fig. 18 explains why theoretical predictions are in much stronger agreement with numerical results for gross section collapse, compared with cases of failure in the weld.

4.3. Experimental validation An experimental validation of the proposed framework introduces new challenges. In particular, the definition of a unique value for Ds and em is far from straightforward for actual welded pipes, which most likely have different stress–strain curve shapes and uniform elongations. The treatment of such cases is outside the scope of this paper. Instead, the reader is referred to reference [36], which presents a practical approach to do so. In this reference, ‘‘equivalent’’ values are estimated for base metal heterogeneity (Dseq) and uniform elongation (em,eq), based on DRp0.2, DRm, em,1 and em,2. Using these equivalent values to construct diagrams of emax/em,eq versus Dseq (similar to Figs. 6, 7 and 15) have confirmed Eq. (5) as an upper bound for strain capacity, for a total of 56 CWP tests performed at Ghent University.

4.4. Implications for strain based design The observations of this study have practical implications for strain based assessments of pipeline girth welds. It has been shown from numerical analysis and supported by a theoretical framework that base metal heterogeneity may reduce the strain capacity of a curved wide plate specimen by a factor of up to 2. In this respect, Eq. (5) provides an upper bound which is independent of weld or flaw properties. Small variations from ideal homogeneity can have a pronounced effect on strain capacity (see Figs. 6 and 15). Cases of gross section collapse are most sensitive, since Eq. (5) becomes an accurate relationship rather than an upper bound. The heterogeneity induced reduction in strain capacity can be examined from a probabilistic point of view. To this end, Eq. (5) has been combined with the yield strength heterogeneity distributions derived from [11,12] (and translated into the

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Load bearing capacity Pmax (MN)

Fig. 17. Equivalent plastic strain at an equal load for (a) Ds = 0 MPa; (b) Ds = 50 MPa. Case analyzed is geometry A, reference base metal with Y/T = 0.90, reference weldment with OMFS = 0%. Contour plots taken at a load equal to Pmax of the homogeneous connection (2.806 MN).

Failure at base metal

2.90

2.85

2.80 0

10

20

50

Base metal heterogeneity Δ s (MPa) Fig. 18. The assumption of a constant load bearing capacity as Ds varies is only violated for cases of failure at the weld. Case analyzed is geometry A, reference base metal with Y/T = 0.90, different OMFS-levels. Legend is adopted from Fig. 15.

Probability p of having a greater reduction according to Eq. (14) (%)

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187

100

Y/T = 0.90

80

Y/T = 0.85 60

66%

40

45%

20

0 0

10

20

30

40

50

Reduction of strain capacity R (%) Fig. 19. Probability analysis of reduction of strain capacity due to base metal heterogeneity, for CWP specimens that fail by means of gross section collapse.

histogram of Fig. 1). Since Eq. (5) is adopted, the following discussion (up to Eq. (14)) is confined to cases of gross section collapse. The distribution of Ds derived from literature can be closely approximated by a normal distribution with average lDs = 0 and standard deviation rDs = 33.8 MPa. Note that this distribution allows for negative Ds-values, which at first sight conflicts with assumption 5 (Section 2.1). However, Ds can be turned into a positive value by changing the choice of reference base metal. It can be easily shown that, for gross section collapse, the sign of Ds does not affect emax/em. From this, it follows that a normal distribution centred around zero can be allowed for in the current analysis. Fig. 19 shows the resulting cumulative probability distributions of strain capacity reduction for both base metals investigated (Y/T = 0.85 and Y/T = 0.90). The figure is to be interpreted as follows. The reduction in strain capacity is defined as (1  emax/em) and expressed as a percentage. The ordinate of Fig. 19 represents the probability p (%) of having a reduction in strain capacity greater than a given value R (%), shown in the abscissa. The monotonously increasing nature of (1  emax/em) as a function of Ds (following from a simple reformulation of Eq. (5)) allows to calculate this probability p by:

   DsðRÞ  lDs  100% p½ð1  emax =em Þ  100% P R ¼ 1  U

rDs

ð14Þ

where U represents the standard cumulative normal distribution, and Ds(R) the base metal heterogeneity level Ds corresponding with 1  emax/em = R. Ds(R) is an implicit solution of Eq. (5), considering Ds as a function of emax/em (rather than emax/em as a function of Ds). Eq. (14) results in material specific probability curves. For instance, Fig. 19 shows that the probability of having 30% or more reduction of strain capacity due to base metal heterogeneity is 45% for Y/T = 0.85 and 66% for Y/T = 0.90. It should be emphasized that the predicted strong effect of base metal heterogeneity on failure probability (Fig. 19) is limited to cases of gross section collapse (favoured for high values of weld overmatch such as 20% and above, see Fig. 11). As observed in Fig. 15, the effect of base metal heterogeneity on strain capacity is significantly less pronounced if failure occurs in the weld (it may even be beneficial in some cases). The strongest observed reduction of strain capacity in the presence of weld failure is 10.6% (relative to the strain capacity of the reference weldment), for the configuration in Fig. 15(b) with OMFS = 0%. This study suggests that effects of base metal heterogeneity in the case of weld failure can be safely accounted for by means of a small correction factor on the strain capacity of the reference weldment. For instance, a reduction by a factor 1.2 would be safe for the simulated set of results. The results of this paper apply to curved wide plate specimens. More work is required to evaluate their transferability to actual pipelines, which may show a different loading (e.g. internal pressure) and/or different boundary conditions (e.g. pipesoil interaction effects for buried onshore pipelines versus displacement of CWP specimen ends). This study shows that three key properties should be taken into account when it comes to producing line pipe steel for strain based applications. First, the distribution of stress–strain properties such as yield strength should be kept as narrow as possible, since this positively influences the probability plot of Fig. 19. It is proposed that the specified minimum strength properties of the steel grade (provided in standards such as API 5L [10] and required to avoid pipeline burst due to the operational pressure) should be targeted since this promotes a higher weld strength overmatch and, hence, a higher strain capacity (Fig. 15). Second, a small Y/T ratio should be aimed at, given the larger sensitivity of strain capacity reduction to base metal heterogeneity for increased Y/T ratios. Finally, a large uniform elongation em is to be designed for, since this creates a higher margin for the relative strain capacity emax/em given a required strain capacity emax to withstand the strain demand of the application. The design for a small Y/T ratio and high uniform elongation em has been previously recognized (e.g. [37]).

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The aim for narrow distributions, however, has not been addressed yet to the authors’ knowledge. A probabilistic study may be required to find a trade-off between these desires, which are potentially conflicting and challenging to realize [38]. 5. Conclusions Although not explicitly accounted for in current strain based flaw assessment procedures, the unavoidable presence of heterogeneous strength properties of pipe steels has a substantial influence on the tensile strain capacity of a flawed girth weld. The following conclusions are drawn from the presented study, which adopted CWP specimens as a research tool.  When quantifying weld mismatch it is important to account for the variability in base metal strength or the strain capacity of the joint may be significantly overestimated.  Pipe steel heterogeneity exhibits different influences on strain capacity, depending on the failure mode of a ‘reference weldment’ where both pipes adopt the same properties as one of the actual welded pipes.  If the reference weldment collapses in the pipe material, strength heterogeneity always results in a decrease of strain capacity. The magnitude of the decrease is related to the strain hardening behavior of the pipes and can be up to a factor of two.  The effect of base metal heterogeneity on strain capacity is less pronounced for CWP specimens that fail in the weld. For the weld failures in this study, reductions in strain capacity due to base metal heterogeneity were limited to approximately 10% of the strain capacity of the reference weldment.  Eq. (5) serves as an upper bound for strain capacity, regardless of the failure mode. This equation is independent of weld or flaw properties.  A probabilistic analysis has revealed the potential significance of the addressed issue with respect to the strain based design of pipelines.  The transferability of the results (valid for CWP specimens) to actual pipelines deserves further investigation.

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