Jaske-Beavers IPC2002 Paper 27027 by DNV Columbus

Integrity TOC Proceedings of IPC’02 Proceedings of IPC’02 International Pipeline Pipeline Conference 2002 Conference 4th International September 29 – October 3, 2002, Calgary, Alberta, Canada September 29-October 3, 2002, Calgary, Alberta, Canada

IPC2002-27027 IPC02-27027 DEVELOPMENT AND EVALUATION OF IMPROVED MODEL FOR ENGINEERING CRITICAL ASSESSMENT OF PIPELINES C. E. Jaske and J. A. Beavers CC Technologies 6141 Avery Road Dublin, OH 43016 USA Phone: (614) 761-1214; Fax: (614) 761-1633 cjaske@cctlabs.com or jbeavers@cctlabs.com

ABSTRACT In past work, the authors developed a very useful model for engineering critical assessment (ECA) of pipelines with stress corrosion cracking (SCC). That model uses the effective area method to characterize the crack-depth profile along with flow strength and fracture toughness failure criteria. In the current work, the model was improved in four areas. Tearing instability was added to the fracture toughness failure criteria, formulations for computing values of the J integral for surface cracks were improved, interaction criteria were developed for co-planar flaws, and relationships for estimating values of the strain-hardening exponent were developed. To help validate the improved model, J fracture toughness tests were conducted using compact-tension (CT) specimens, and burst tests were conducted on pipe samples with large flaw length-to-depth ratios. INTRODUCTION Pipelines may contain crack-like flaws from fabrication or exposure to service conditions. Lack of fusion, toe cracks, and hook cracks at welds are examples of typical crack-like flaws caused by fabrication. Stress corrosion cracking (SCC), fatigue, and corrosion fatigue are examples of service conditions that can cause cracks to develop in pipelines. When crack-like flaws are discovered or the possibility of their presence must be addressed, engineering critical assessment (ECA) is employed to evaluate the potential for crack growth and pipeline failure. ECA uses engineering fracture mechanics models to predict failure when crack-like flaws are present. ECA must include crack growth by SCC, fatigue, or corrosion fatigue during future service, as well as failure. For a pipeline under internal pressure, failure can occur either by a crack growing through the wall until a leak occurs or by sudden rupture of a critical

size crack. The sudden rupture can occur either because the crack grows to a size that is critical under the loading condition or because a loading condition increases to a level that causes a crack to become critical. Sudden rupture or crack instability can be governed either by the pipeline steel’s strength or by its fracture toughness, whichever results in the lower failure load or smaller critical crack size. Both surface cracks (non-leaks) and through-wall cracks (leaks) can reach a point of instability where sudden rupture occurs. All of these potential failure modes have to be considered in ECA. The authors developed the very useful CorLAS™ ECA failure model [1] and applied it to SCC of pipelines in past work [2-4]. It employs the effective-area method coupled with flow-strength and fracture-toughness failure criteria. Tensile yield and ultimate strengths are used to characterize flow strength, while a critical value of the J is used to characterize fracture toughness. Application of the original failure model revealed that improvements could be made in four areas. First, tearing instability could be incorporated into the fracture toughness failure criteria. Second, the formulations for computing values of the J could be improved. Third, interaction criteria could be developed for coplanar flaws. Fourth, relationships for estimating values of the strain-hardening exponent could be developed. As a result, the current work was undertaken to develop these improvements and incorporate them into the ECA failure model. NOMENCLATURE a = flaw size A = effective flaw area Ao = flaw length times wall thickness Acv = net cross-sectional area of Charpy specimen 1

CVN Cfl d da/dN da/dt E f3(n) Fsf J Jc Jp K Ks L M n Qf RSF SMYS Sfl t T Tmat TYS TUS ∆K εe εp εt σ σf

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

Charpy impact energy for full-size specimen flow strength coefficient flaw depth cyclic crack-growth rate time-dependent crack-growth rate elastic modulus function of strain-hardening exponent free-surface factor J integral J fracture toughness plastic component of J linear elastic stress intensity factor strength coefficient flaw length Folias factor strain-hardening exponent elliptical flaw shape factor remaining strength factor specified minimum yield strength material flow strength wall thickness crack tearing parameter tearing modulus of material tensile yield strength tensile ultimate strength linear elastic stress intensity factor range elastic strain plastic strain total strain stress applied nominal stress at failure

REVIEW OF ORIGINAL MODEL This section reviews the original ECA failure model. Fig. 1 illustrates the general approach used for ECA of crack-like flaws. The first step is characterization of the initial flaw type and size. This includes determining if the flaw is crack-like. Next, the critical or final flaw size at failure under operating or upset conditions is predicted. Remaining life is computed based on growth from the initial to the final flaw size. If the final flaw size is not greater than the initial one, no remaining life is predicted. If the flaw growth rate cannot be estimated, remaining life cannot be predicted, and monitoring is recommended to assure safe pipeline operation. The size of the flaw is characterized by means of in-service inspection or hydrostatic pressure testing. In-service inspection may yield a detailed profile or contour of the flaw depth as a function of its length or only the flaw length and depth. When a detailed flaw-depth profile is available, an effective surface flaw is determined from this profile using the procedures described in detail by Kiefner and Vieth [5]. The effective flaw area is defined by its effective length and actual cross-sectional depth. The effective flaw depth is then defined based on a semielliptical flaw shape and equivalent flaw area.

When a detailed flaw profile is not available, the effective flaw is characterized as having a semi-elliptical shape with the maximum measured depth and length. When hydrostatic pressure testing is used to characterize the surface flaw, the effective flaw size is estimated to be the largest flaw that would have survived the test. In practice, these effective flaw sizes are estimated as a function of L/d, because this ratio affects the critical flaw depth. It must be determine if the flaw is crack-like. Inspection data usually provide this information. If the inspection cannot clearly identify the flaw type, it is conservative to assume a crack-like flaw of the measured size for ECA. However, when hydrostatic testing is employed, the flaw type must be inferred from other data. If this cannot be done with confidence, then a non-crack-like flaw should be use for computing the initial size from the hydrostatic testing data and a crack-like flaw should be used to predict failure conditions to yield a conservative ECA. The critical flaw size is computed for two different failure criteria: flow strength and Jc. Jc is an elastic-plastic fracture mechanics parameter and is used because typical pipeline steels are quite ductile and tough. Both flow strength and fracture toughness must be considered as possible failure criteria for crack-like flaws. The smaller of the two calculated critical flaw sizes is the one predicted to result in failure. Remaining life is the time required for the flaw to grow from its initial to final size. It is computed by integrating a flawgrowth relationship from the initial to final flaw size. For SCC, da/dt is characterized as a function of J or K. For fatigue or corrosion-fatigue, da/dN is characterized as a function of ∆K. These crack growth rates depend on the material-environment combination and are measured by means of laboratory testing or estimated based on field experience. The critical flaw size for the flow-strength failure criterion is determined by solving the following equation for A: σf = Sfl RSF = Sfl [(1 - A/Ao)/(1 - A/(MAo))]

(1)

Values of M are computed using the relationship given by Kiefner and Vieth [5]. For a specific relation among A, L, and d, such as a semi-elliptical shape with a constant L/d, L and d are uniquely defined by the value of A obtained from solving Eq. (1). Because M is a function of L, Eq. (1) is solved iteratively. The value of Sfl is determined from TYS or from a combination of TYS and TUS using one of the following two expressions:

Sfl = TYS + 68.95 MPa (10,000 psi)

(2a)

Sfl = TYS + Cfl (TUS - TYS)

(2b)

Characterize Flaw Type and Size

In-Service Inspection

Hydrotesting

Crack-Like?

Yes

Is There a Detailed Flaw Profile?

Compute Effective Flaws and Define Equivalent SemiElliptical Flaws

Define Effective SemiElliptical Flaws Based on Their Length and Depth

Compute Critical Flaw Size for Operating Conditions

J Fracture Toughness Criterion

Compute Remaining Life Based on Toughness Limit

Estimate Critical Effective Semi-Elliptical Flaws for Hydrotest Conditions

Yes

Is Flaw Crack-Like and Does Toughness Control?

Flow Strength Criterion

Compute Remaining Life Based on FlowStrength Limit

Fig. 1 General approach for engineering critical assessment (ECA) of crack-like flaws in pipelines.

Cfl is a constant between 0 and 1.0 and is usually taken to be 0.5. Equation (2a) is based on burst tests of steel pipe specimens [6], while Eq. (2b) with Cfl = 0.5 is usually used in plastic collapse analysis. The following formulation for a semi-elliptical surface flaw is used to compute values of applied J as a function of a and σ:

Value of J Integral

J = Qf Fsf a [σ2π/E + f3(n)εpσ]

Applied J

(3)

The function f3(n) is from stress analyses performed by Shih and Hutchinson [7]. A power law with the exponent n characterizes σ as a function of εp. Values of TYS and n are used to determine the power-law coefficient. DEVELOPMENT OF IMPROVED MODEL The original model gave good predictions of burst-test results and field failures governed by flow strength. However, it gave very conservative predictions for crack-like flaws when J fracture toughness data were used or cracks with L/d ratios of 20 or greater were evaluated. Adding a tearing instability criterion to the model addressed the former problem, while improving the formulas for computing values of J addressed the latter problem. The original model applied to only single flaws; flaw interaction criteria were added to deal with this problem. The strain-hardening exponent is used in Eq. (3). The original model uses a method of estimating these values that was based on handbook data for carbon and low-alloy steels. To improve the model, the method was extended to data for pipeline steels. This section describes the four main improvements that were made to the failure model. These improvements were not developed to improve the predictions of existing burst pressure data but rather to extend the general applicability of the model. Tearing Instability In the original model, fracture was predicted to occur when applied J reached Jc. For tough pipeline steels, this approach is conservative because a significant amount of stable crack tearing occurs before fracture instability is reached. For this reason, the tearing instability criterion of Paris, et al. [8] was incorporated into the failure model. Tearing instability, illustrated in Fig. 2, is predicted to occur when applied T equals or exceeds Tmat of the pipeline steel. Tmat is defined by the following equation: Tmat = dJ/da E/(Sfl)2

(4)

Tmat is determined from a standard laboratory fracture toughness test. The applied dJ/da is a function of applied load, pipeline configuration, crack size, and crack shape and is determined by stress analysis. Applied T is calculated in the same manner as Tmat is calculated in Eq. (4).

Material J-R Curve

Ductile Tearing Instability Applied dJ/da => Material dJ/da J Ic at ∆ a = 0.2 m m Crack Growth, ∆ a

Fig. 2 Illustration of tearing instability criterion. Formulations for Computing J The formulations for computing J values for semi-elliptical surface flaws were improved by modifying those in the original model. The new formulas for computing the terms in Eq. (3) are given in reference [9]. Modifications were evaluated by comparing them with the results of extensive finite-element stress analyses [10]. The Folias factor that is used to account for the stress increase caused by the local bulging of a flawed pipe under pressure was modified to be consistent with that used for the flow-strength failure criterion. These modifications removed the overly conservative predictions of the original model for flaws with large L/d values. Figure 3 shows a typical comparison of calculations made using the new formulations with the results of Yagawa, et al.’s [10] finite-element stress analysis. The comparisons show plastic J, which is the right-hand term of Eq. (3), as a function of L/d and at three a/t values. The elastic J, which is the lefthand term of Eq. (3), is a well-established formulation and was not modified. Overall, the new formulations provide reasonable approximations of the results of the stress analysis. In addition, they are smooth, continuous functions that can be reasonably extrapolated beyond as well as interpolated within the results of the stress analyses. Interaction Criteria When two or more surface flaws are present in the same region, one must decide if they are expected to interact and fail as one flaw or if only one of the flaws is expected to fail. If interaction occurs, the failure pressure will decrease. For this reason, flaw interaction needs to be incorporated into failure prediction. Interaction guidelines that have been developed for pressure vessels, piping, tanks, and other welded structures [1113] were reviewed. It was concluded that the effective area

method [5] used in the original model could be applied to flaw interaction. 9.53-mm Thick API X52 Steel at RT and 72% SMYS a/t = Ratio of Crack Depth to Wall Thickness

350

Value of Jp, kJ/m2

300

n = 0.0936 + 0.685(TYS/TUS) - 0.774(TYS/TUS)2

Equation (6) is based on handbook data for carbon and lowalloy steels and was obtained by curve-fitting those data, as shown in Fig. 4. In the current project, data were obtained from past studies of pipeline steels [30,31] and correlated in the same fashion to develop the following expression:

a/t = 0.8

n = -0.00546 + 0.556(TYS/TUS) - 0.547(TYS/TUS)2

250

150

a/t = 0.5

100 a/t = 0.2

50 0

100

120

0.3 Carbon and HSLA Steels API Pipeline Steels

Fig. 3 Calculated values of plastic J for API X52 steel at stress of 72% SMYS. The effective area method predicts flow-strength failure based on Eq. (1). Multiple flaws are assessed by repeatedly applying it to all possible combinations of the flaws. The flaw or combination of flaws with the lowest RSF is predicted to cause failure. If the evaluation reveals that a single flaw has the lowest RSF, no interaction is predicted. If the evaluation reveals that some combination of the flaws has the lowest RSF, then interaction is predicted. Interaction is also assessed for the Jc failure criterion. J is computed for each possible flaw combination; the flaw or flaw combination that yields the largest J is predicted to cause failure. The critical flaw or flaw combination may be different for each of the two failure criteria. The one that predicts failure to occur at the lowest stress is then predicted to actually govern failure and determine the applicable failure criterion – flow strength or Jc. The interaction calculations are performed using the complete depth profile of the combined flaw. The flaw depth between individual flaws taken as a small value of 0.03 mm to avoid numerical problems in computing J. Strain-Hardening Approximations Evaluation of plastic J requires modeling of the pipeline steel’s stress-strain behavior. The following relationship is used for this purpose: (5)

Because Ks and n are not widely available for pipeline steels, methods for calculating them from known tensile properties were developed. Jaske [1] developed the following correlation for use with the original model:

Strain Hardening Exponent, n

Ratio of Crack Length to Depth (L/d)

εt = εe + εp = σ/E + Ks σn

(7)

As shown in Fig. 4, the curve represented by Eq. (7) falls below that represented by Eq. (6). Thus, the pipeline steels have lower strain-hardening exponents than other comparable steels. The data for pipeline steels are quite limited and that for API X42 steel fell lower than expected. Additional data should be developed for other pipeline steels to improve the current correlation.

Yagawa, et al. CorLAS™ 1.0 CorLAS™ 2.0

200

(6)

0.25 n = 0.0936 + 0.685(T YS/TUS) - 0.774(T YS/TUS)2

0.2 0.15 X42

X52

0.1

X70 X80

0.05 0 0.5

n = -0.00546 + 0.556(TYS/TUS) - 0.547(TYS/TUS)2

0.6

0.7

0.8

0.9

Ratio of Yield to Ultimate Strength (TYS/TUS)

Fig. 4 Strain-hardening exponent versus yield-toultimate tensile strength ratio. APPLICATION OF MODEL In order to use the failure model or similar models that employ elastic-plastic fracture mechanics, one must know the fracture-toughness behavior of the material being evaluated. Pipeline operators usually do not have Jc data for their pipeline steels, but they often have Charpy impact data. For this reason, empirical relations [1] have been developed for estimating fracture toughness from CVN: Jc (kJ/m2) = 1000 CVN (J) / Acv (mm2) 2

Jc (kJ/m ) = 1.03 CVN (J)

(8) (9)

Equation (8) gives a high value of fracture toughness that has been found to correlate reasonably well with pipe-burst test data [2-4,6], whereas Eq. (9) gives a lower-bound value of fracture toughness [16,17] that results in very conservative failure predictions [2-4]. The following expression is slightly less conservative than Equation (9) and provides lower-bound estimates of fracture

toughness for pipeline steels based on data from past [15,17] and current work: Jc (kJ/m ) = 1.29 CVN (J)

(10)

Leis and Brust [17] showed that the following expression provides a lower-bound estimate of Tmat: Tmat = 635.5 CVN (J) / Sfl (MPa)

(11)

Equation (11) is based on data for both pipeline steels and other low-alloy steels. When only the pipeline steels are evaluated, as in Fig. 5, it appears that Equation (11) is too conservative. However, additional tearing modulus data need to be developed for pipeline steels before a less conservative correlation for estimating values from Charpy data can be recommended. 500

J c (lb/in ) = 12 CVN (ft-lb) / Ac (in 2 ) P redicted Critical Flaw Depth, mm

2 Kiefner et al. D ata

NG-18 Report No. 183 Current Project Lower Bound Average Trend

400

S f = (S y + S u)/2

0 0

Actual Flaw Depth, mm

300

Fig. 6 Predicted versus actual flaw size for full-scale burst tests of Kiefner, et al. [6]

T mat = 1322 CVN/Sfl

200 120 2

J (kJ/m ) =1000 CVN (J) / A (mm )

Tmat = 635.5 CVN/Sfl

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

CVN/Sfl (J/MPa)

Fig. 5 Tearing modulus versus Charpy V-notch impact energy for pipeline steels. As shown in Figs. 6 and 7, the improved failure model was used to predict the results of previous full-scale burst tests [6], field failures [18], and full-scale burst tests from the current work. Measured tensile properties and CVN values that were available for each test or field failure were used in the calculations. Equation (2a) with Cfl = 0.5 was used to compute Sfl, and Eq. (8) was used to estimate Jc from CVN. Good, but somewhat conservative predictions were made for both the past burst tests and field failures, while excellent predictions were made for the current burst tests. Comparable predictions made using the original model gave similar results [1-4]. The correlation coefficient was 0.87 for the past burst tests (Fig. 6), 0.77 for the field failures (Fig. 7), and 0.99 for the current burst tests (Fig. 7). Thus, the improvements extended the model while not significantly compromising it.

Predicted Failure Stress (%SMYS)

100

S = (TYS + T US)/2

100

40 CEPA Data Current Data & Interaction Model Current Data & No Interaction Model

0 0

100

120

Actual Failure Stress (%SMYS)

Fig. 7 Predicted versus actual failure stress for field failures reported by CEPA [18] and full-scale burst tests of current work. In the current work, the burst tests were performed on 0.324-m diameter by 9.53-mm wall API X52 steel pipe samples with very long, deep surface flaws with L/d values in the range of 50 to 100. This diameter (0.324 m) was selected to facilitate

handling and laboratory testing, while this wall thickness (9.53 mm) was selected to facilitate removal of compact-tension specimens for J fracture toughness testing. Even though this pipe size is not similar to typical line pipe, the burst-test results can be used to validate the model because both pipe diameter (or radius) and wall thickness are parameters in the model. Future work should be done on larger diameter pipe to further validate the model. Two of the burst-test samples had only one long flaw, but the third sample had two co-planar flaws separated by a short gap of full-wall-thickness material. The fact that no interaction occurred and only one of the two flaws failed was correctly predicted. Also, if flaw interaction had not been modeled but had been assumed to occur, the failure stress would have been over predicted, as shown by the open square symbol in Fig. 7. At stress levels equal to 110% of SMYS, the predictions were somewhat conservative. We believe that the standard definition for flow strength underestimates the actual strength once some yielding of the pipe body occurs. In evaluating pipeline integrity, minimum properties and applicable safety factors are employed. This approach gives predicted failure pressures or critical flaw sizes that are well below the corresponding actual values, and it provides adequate margins for safe and reliable pipeline operation. SUMMARY The major accomplishment of this work was the development of an improved model for predicting the failure of pipelines with crack-like flaws. Four main tasks were undertaken and completed. A tearing instability criterion was incorporated into the model for predicting fracture-toughness dependent failures. Improved formulations for calculating J values for semi-elliptical surface flaws were developed and added to the failure model. A flaw interaction model for both flow-strength and fracture-toughness failure was developed and incorporated into the failure model. Finally, a relation for estimating the strain-hardening exponent of pipeline steels from tensile yield and ultimate strength was developed and added to the software. Full-scale burst tests, tensile tests, Charpy impact tests, and J fracture-toughness tests were conducted on specimens taken from 0.324-m diameter by 9.53-mm wall API X52 steel pipe. The results of these tests were used to help validate the tearing instability criterion, the improved J formulations, and the flaw interaction model. Two full-scale tests were performed on specimens with very long flaws. One burst test was performed on a specimen with two long flaws that did not interact, as predicted by the model. The model also gave good predictions of failure pressure and critical crack size for data reported in the literature. ACKNOWLEDGMENTS The Line Pipe Research Supervisory Committee of PRC International supported this work through their project number PR-186-9709.

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