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©NACE International. All rights reserved. Paper Number 02089 reproduced with permission from CORROSION/2002 Annual Conference and Exhibition, Denver, Colorado. See the NACE web site at http://www.nace.org for more information.

ASSESSMENT OF CRACK-LIKE FLAWS IN PIPELINES

C. E. Jaske, P. H. Vieth, and J. A. Beavers CC Technologies 6141 Avery Road

Dublin, OH 43016-8761 USA

ABSTRACT Inspection of pipelines may reveal crack-like anomalies. United States standards require that crack-like features by repaired or removed from pipelines. In contrast, Canadian standards permit an engineering critical assessment (ECA) of crack-like features. ECA utilizes pipeline dimensions, operating pressures, material properties, fracture mechanics, and inspection data to determine the disposition of crack-like anomalies. Methods for performing an ECA are reviewed. They include estimation of failure conditions for toughness-controlled fracture and the potential of crack growth by fatigue, stress-corrosion cracking, or corrosion fatigue. Application of the failure assessment diagram (FAD) as well as inelastic fracture mechanics is discussed. The importance of pressure cycle counting is pointed out. The rain flow cycle counting method is extended to incorporate cyclic frequency so time/cycle-dependent crack growth can be evaluated. Practical examples are presented to illustrate the application of ECA.

INTRODUCTION

Hazardous liquid pipeline operators with 500 or more miles of pipeline in the United States must have programs for integrity management in high consequence areas.1 Similar requirements are being developed for hazardous liquid operators with less than 500 miles of pipeline and for operators of gas pipelines. For this reason, there has recently been increased interest in pipeline integrity.

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An essential element of pipeline integrity management is inspection. Pipeline inspection typically reveals a number of anomalies in a pipeline system. These anomalies are evaluated to determine if they are likely to be flaws such as manufacturing defects, mechanical damage, corrosion wall loss, or cracking. These determinations are documented in an inspection report.

Once the probable flaw type has been determined, its effect on pipeline integrity must be evaluated. Methods such as ASME B31G2 and RSTRENG3 are available for evaluating pipe wall loss. However, when crack-like defects such as fatigue, stress-corrosion cracking (SCC), hook cracks, or lack-of-fusion defects are identified, current United States standards4, 5 require that they be repaired or removed. In contrast, the Canadian standard6 permits an engineering critical assessment (ECA) of crack-like defects.

ECA utilizes pipeline dimensions, operating pressures, other loads, material properties, fracture mechanics, and inspection data to evaluate the effect of crack-like flaws and determine their disposition. Even if crack-like flaws are repaired or removed, an ECA may be performed to evaluate the potential of undetected flaws causing a threat to pipeline integrity. Thus, ECA is a valuable tool for pipeline integrity management.

BACKGROUND

This section of the paper reviews methods that are typically employed in ECA of pipelines. ECA applies the well-known principles of engineering fracture mechanics7, 8 to evaluate the potential for failure of components with crack-like flaws. The linear elastic stress intensity factor (K) is used to characterize the behavior of components with cracks: K = Yσ (πa)1/2 (1) Y is a shape factor that can be found in handbooks and codes9–11 or computed using finite-element analysis (FEA), σ is the nominal stress, and a is the crack size.

For nonlinear elastic-plastic stress-strain behavior, both the J parameter and crack-tip opening displacement (δ) are used to characterize the behavior of components with cracks. J can be defined and calculated using a path-independent line integral. It also can be interpreted as the rate in change of potential energy of a component with respect to crack size as follows:

dadU

B1J −= (2)

B is wall thickness, and U is potential energy. J is related to δ by the following expression:12 J = mSYδ (3)

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SY is the yield strength, and m is the plastic stress intensification factor. The value of m is generally between 1.0 and 2.0. As reviewed by Jaske,13–14 values of J can be computed from solutions published in the literature or computed using FEA.15

The fracture toughness of material is used to assess the potential for sudden fracture. The applied value of K, J, or δ is computed for a cracked component under load and compared with the value of fracture toughness. Fracture toughness is a material property measured in the laboratory and is designated as Kc, Jc, or δc, depending upon which fracture-mechanics parameter is used. The c subscripts indicate that these are critical values of the parameters. When the value of the applied parameter equals or exceeds the fracture toughness, sudden fracture is predicted to occur. In actual applications, the maximum value of the applied parameter is kept below the minimum fracture toughness to provide a conservative assessment.

K and Kc strictly apply to only brittle materials where linear elastic behavior is a reasonable approximation. Pipeline steels are typically quite ductile. Therefore, they are assessed using J and Jc or δ and δc. Jc or δc is usually measured by a laboratory test of a small specimen. For evaluating a crack in a large structure, it is sometimes useful to predict Kc from Jc using the following relation: Kc = (Jc E)1/2 for plane stress or Kc = (Jc E/(1 – ν2))1/2 for plane strain (4) E is elastic modulus, and ν is elastic Poisson’s ratio. Values of Jc can be evaluated from values of δc or vice versa using Equation (3) with a value of m = 2 for carbon manganese steels.12

Fracture mechanics parameters are also used to assess the potential for growth of sub-critical cracks and to compute how long it would take a crack to grow to a critical size. Two mechanisms of crack growth are usually addressed: fatigue and stress corrosion cracking. The cycle-dependent fatigue crack growth rate (da/dN) is characterized using the range of the stress intensity factor (∆K).16 The most widely used relationship for characterizing the fatigue crack growth behavior of engineering materials is the well-known Paris Law:17, 18 da/dN = Cp (∆K)mp (5) Cp and mp are material dependent constants that are obtained by fitting experimental data from constant amplitude cyclic loading tests of pre-cracked specimens to Equation (5). In a similar fashion, the time-dependent SCC rate (da/dt) is often characterized as a function of K or J. When experiments show that there is a threshold for fatigue or SCC, the value of ∆K or K below which cracking is not observed in designated as ∆KTH or KSCC, respectively. For application to integrity assessment, fatigue life is calculated by integrating Equation (5) or SCC

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life is calculated by integrating the relation between da/dt and K. In some cases, SCC growth occurs at an approximately constant rate above the threshold level and SCC life is computed using this rate.

APPLICATION OF ECA TO PIPELINES

When crack-like flaws are found in pipelines, ECA is performed to evaluate their potential for fracture or to estimate the critical crack size. The critical crack size is defined as the minimum size of crack that is predicted to cause fracture under the maximum load. Pipeline steels are typically quite ductile, so an elastic-plastic fracture mechanics parameter (J or δ) must be employed directly or indirectly. Failure Assessment Diagram

The failure assessment diagram10, 11 (FAD) shown in Figure 1 was developed to indirectly incorporate elastic-plastic fracture mechanics in the failure curve. Thus, an engineer can use elastic stress analysis to compute values of K and predict whether failure is expected to occur. The y axis of the FAD is the toughness ratio (Kr), whereas the x axis is the load ratio (Lr). These are both normalized parameters. The toughness ratio is the ratio of the applied stress intensity factor to the minimum fracture toughness of the material, while the load ratio is the ratio of the reference stress (σref) to the minimum yield strength of the material. As the value of the load ratio increases, the amount of plasticity increases, so the diagram curves downward to take the plasticity into account.

Fracture toughness and yield strength are measured in laboratory tests of the pipeline material or conservative estimates of their values are made using data from handbooks or published literature. Stress analysis is performed to calculate values of K and σref for a specific component and crack configuration. Formulas for computing K were described in the previous section. Comparable formulas for σref are used to compute the stress related to the local or net section collapse of various configurations containing cracks. Examples of configurations considered in pipelines include longitudinal and circumferential semi-elliptical surface cracks, longitudinal and circumferential through-wall cracks, and longitudinal and circumferential embedded cracks.

Once K and σref are calculated, values of Kr and Lr are calculated and plotted on the FAD. If the point falls below the curve, no fracture is predicted. If the point falls on or above the curve, fracture is predicted. The crack size associated with a point that falls on the curve is the critical crack size. It can be determined by repeated calculations, until the point that falls on the curve is identified. Since plasticity is only indirectly incorporated into the FAD, its use becomes increasingly conservative as Lr increases, especially at values of Lr greater than 0.4.

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The value of Lr is often well above 0.4 for many pipeline problems. To avoid excessive conservatism, elastic-plastic fracture mechanics is often directly applied to pipeline problems. Failure Model

The CorLAS™ computer program19–22 has been developed to evaluate longitudinal crack-like flaws in pipelines. Using either the maximum flaw depth and length or the effective area of the flaw-depth profile, the most severe semi-elliptical surface flaw is modeled and used to compute the effective stress and the applied value of J for internal pressure loading. The effective stress and applied J are then compared with the flow strength and fracture toughness, respectively, to predict the failure pressure. Whichever criterion, flow strength or fracture toughness, predicts the lower failure pressure governs. This model also can be used to predict the critical crack size at a specific internal pressure. As shown by the example in Figure 2, critical flaw depth can be computed as a function of flaw length. In this case, fracture toughness governs the predicted failure for a crack-like flaw. Estimating Fracture Toughness

A very conservative J fracture toughness value of 87.6 kJ/m2 (500 lb/in) was used for the example shown in Figure 2. If available, measured J fracture toughness data can used. However, these data are often not available for a specific pipeline steel, but Charpy impact energy (CVN) data are often available. For this reason, methods of estimating J fracture toughness from Charpy tests of full-size specimens have been developed. Two such relations that have been used in the past22 are given below: Jc (kJ/m2) = 1000 CVN (J) / Ac (mm2) (6) Jc (kJ/m2) = 1.03 CVN (J for full size specimen) (7) Ac is the net cross-sectional area of a Charpy specimen. Equation (6) gives a high value of fracture toughness that has been found to correlate reasonably well with pipe-burst test data,19–21, 23; whereas, Equation (7) gives a lower-bound value of fracture toughness22, 25 that has been shown to give very conservative failure predictions.19–21

The following expression is slightly less conservative than Equation (7) and was found to provide lower-bound estimates of fracture toughness of pipeline steels based on data from past25, 26 and current work: Jc (kJ/m2) = 1.29 CVN (J for full size specimen) (8) Equation (8) is used to estimate the lower-bound fracture toughness of pipeline steels. Instead of using Equation (8), it is usually more appropriate to use Equation (6) to estimate the typical fracture toughness and then apply an appropriate safety factor.

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Stress Corrosion Crack Growth

In laboratory work, it was found that the flaw growth rate (da/dt) for near-neutral pH SCC can be characterized as a power-law function of the J integral:27, 28 da/dt = G Jg (9) G and g are material/environment constants. Crack-growth rates ranging from 3 × 10-7 to 6 × 10-4 mm/s (0.37 to 745 in/year) were measured on rising load tests of compact-tension (CT) specimens. Under cyclic loading conditions, the cracking velocity was not a function of the applied J integral. During cyclic loading, maximum cracking velocities were about 2.0 × 10-8 mm/s (0.025 in/year). The cyclic loading is more representative of actual service conditions than the rising loading.

Field crack growth rate data have been obtained primarily from analysis of field SCC failures. One method of estimating the crack velocity is to divide the total crack depth by the life of the pipeline. This method would be expected to give non-conservative estimates since the cracks generally do not initiate when the pipe is first placed in the ground. An incubation time is required for the coating to disbond, for the potent cracking environment to develop, and for the cracks to initiate. Improved estimates of cracking velocities may be obtained where there are demarcations on the fracture surface associated with prior hydrostatic testing. This latter technique has yielded average and maximum values of approximately 1 × 10-8 and 2 × 10-8 mm/s (0.012 and 0.024 in/year), respectively, for the growth of near-neutral-pH stress corrosion cracks.

Equation (9) is integrated from the initial to the final flaw size to calculate remaining SCC life. If the growth rate is constant and independent of J, the difference between the final and initial flaw size is simply divided by that rate to calculate remaining SCC life. Some constraints must be placed on flaw shape as it grows. One of three options is used to constrain the flaw shape during growth: (1) growth with a constant length to depth (L/d) ratio, (2) growth with a constant length, or (3) constant growth all along the flaw boundary. The first criterion, constant L/d ratio is applied to small SCC cracks where significant crack inter-linking within the colony is expected to occur during growth. For large SCC cracks that are likely to consist of small cracks that have already linked, the constant L/d criterion is much too conservative. In this case, it is reasonable to model the crack as growing constantly. In some cases, it is observed that large cracks increase only in depth but not in length during growth. The constant length criterion is used for these cases. In practice, the difference between the constant length criterion and the constant growth criterion is often negligible.

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Fatigue Crack Growth

Fatigue crack growth can occur at crack-like flaws subjected to cyclic loading. Typically, the fatigue crack growth behavior is characterized using Equation (5), the Paris Law. Figure 3 shows some fatigue crack growth curves for API X52 steels compared with a reference curve for carbon steel given in API 579.10 The data were developed for three types of welded pipe and agree well with the reference curve for carbon steel, which is defined by the following equation: da/dN (mm/cycle) = 6.89x10-9 ∆K3.00 (MPa-m0.5) (10) Equation (10) can be applied to fatigue crack growth assessment of this type of steel when there is no environmental effect. However, for corrosion fatigue, the Paris-Law constants given in Equation (10) need to be developed by fatigue crack growth testing in an environment that simulates that to which the pipe steel is exposed in service.

As pointed out previously, integrating Equation (10) from an initial crack size (ao) to final crack size (af) gives the fatigue crack growth life (Nf). The value of ao is determined by the pipeline inspection, while the value of af is equal to the critical crack size. The integration is straightforward for constant amplitude cyclic loading, such as repeated pressure cycling of a pipeline from a minimum to a maximum pressure, because the experimental data are developed using this type of loading. In most cases, however, the cyclic loading is of variable amplitude, such as the variable pressure fluctuations on an operating pipeline. For variable amplitude fatigue loading, cycle counting is used to convert the actual loading history into a series of discrete events that can be related to the data for constant amplitude loading.18

Rainflow counting methods29, 30 have been developed and are widely used to relate variable amplitude fatigue loading to constant amplitude fatigue data. In typical pipeline applications, rainflow counting is applied to a representative pressure fluctuation history to produce cycle counts for series of pressure ranges. This history is usually for a discrete period of operation, such as one month or one year. Based on the number of cycles and crack size, the amount of crack growth is computed at each pressure range and repeatedly added to the crack size. To compute fatigue life, this numerical integration procedure is repeated until the computed crack size reaches the final value.

The standard cycle counting methods18, 29, 30 assume that the progression of fatigue damage is independent of frequency. This assumption causes a problem for corrosion fatigue conditions that occur when the crack-like flaw is exposed to a corrosive environment. As illustrated in Figure 4, the corrosion fatigue crack growth rate typically increases as the cyclic frequency decreases. In the current work, a standard rainflow cycle counting method29 was modified to incorporate the tracking of cyclic frequency. The average rise time associated with each pressure range is tracked during the cycle counting operation. Once the series of cycle

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counts as a function of pressure range are established, the rise time for each pressure range is used to compute the average frequency for that range and the corresponding cycles. Then, during the numerical integration, the Paris-Law equation corresponding to the frequency of a given pressure cycle is used to compute the crack advance for that cycle. This modification to standard rainflow cycle counting is necessary when there is a significant effect of cyclic frequency on the fatigue crack growth rate, as illustrated in Figure 4.

EXAMPLES OF ECA

Two examples of ECA are presented in this section. The first one illustrates the calculation of critical flaw size. The second one illustrates the calculation of fatigue crack growth life. Critical Flaw Size

A pipeline has the following material properties, dimensions, and operating parameters: API X52 steel Specified minimum yield strength (SMYS) = 359 MPa (52 ksi) Specified minimum tensile strength (SMTS) = 455 MPa (66 ksi) Minimum Charpy impact strength at operating temperature = 20.3 J (15 ft-lb) Outside diameter = 0.762 m (30 in.) Wall thickness = 7.62 mm (0.30 in.) Maximum operating pressure (MOP) = 5163 kPa (749 psig) No other significant loads

With the above information, the previously described failure model was used to predict the critical crack depth as a function of length as shown in Figure 5. Equation (6) was used to estimate the J fracture toughness of 254 kJ/m2 (1452 lb/in.) from the minimum Charpy impact strength of 20.3 J (15 ft-lb). For crack lengths less than or equal to approximately 800 mm, the failure was predicted to be controlled by fracture toughness. For crack lengths longer than approximately 800 mm, the failure was predicted to be controlled by flow strength. This type of information is used to assess the severity of possible crack-like flaws identified during pipeline inspection or to establish the flaw detection criteria for inspection. It also is used to establish the final crack size for crack growth life calculations as discussed in the next example. Fatigue Crack Growth Life

The same pipeline that was evaluated in the first example is subject to periodic pressure fluctuations. A review of the pressure history reveals that 2 cycles per day from 20% to 100% of MOP is a conservative approximation. This amounts to a cyclic pressure range of 4131 kPa (599 psig) and a cyclic frequency of 0.0833 per hour. Alternatively, the rainflow cycle counting method could have been used to analyze the pressure history as discussed previously.

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Inspection reveals an anomaly that may be a crack-like flaw. The anomaly is located on the inside surface along the seam weld and is judged to have a maximum length of 130 mm (5.10 in.) and a maximum depth of 2.54 mm (0.100 in.). The pipeline operator wishes to predict how long a crack-like flaw of this size would grow under above operating conditions. The critical crack depth for this length is 3.81 mm (0.150 in.) as shown in Figure 5. Thus, the fatigue crack growth life from 2.54 to 3.81 mm needs to be calculated. For such a long shallow flaw, it is reasonable to neglect the change in crack length as it grows and just compute the change in crack depth.

The flaw is modeled as a semi-elliptical surface crack, so the following expression can be employed to compute ∆K:13, 14

∆K = Qf Fsf ∆σ (πa)0.5 (11) Qf is a flaw shape factor, Fsf is a free surface factor, and ∆σ is the local stress range. The value of ∆σ is computed from the nominal stress range using the Folias factor3 to account for local stress magnification. The operating environment is not corrosive, so Equation (10) can be used to characterize the fatigue crack growth behavior of the steel. Separating variables and integrating gives the following expression:

∫ ∆×= −fa

oa

00.38f daK1045.1N (12)

Equation (11) was substituted into Equation (12), and the integral was evaluated numerically to compute a value of Nf = 7408 cycles or 10.2 years of life at 2 cycles per day. This prediction provides quantitative guidance on how quickly the anomaly should be addressed by additional inspection, future inspection, or repair.

To provide information on remaining fatigue crack growth life for anomalies that may not have been detected, a series of similar calculations was made using an initial crack depth of 20% of the wall thickness and critical crack depths for various crack lengths shown in Figure 5. Figure 6 shows the computed fatigue crack growth life as a function of crack length. Predicted lives approach 90 years for very short cracks and 15 years for very long cracks. This type of information is used to establish inspection intervals and flaw detection criteria.

CONCLUSION

This paper showed that engineering critical assessment (ECA) provides a sound engineering approach for assessing crack-like flaws in pipelines. ECA is employed to predict failure conditions for crack-like flaws and to predict their possible growth by fatigue cycling or stress corrosion cracking. Methods, data, and software are available for application of ECA to

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pipelines as part of an integrity management program. The applicable ECA methods were reviewed and two examples were presented to illustrate their use.

ACKNOWLEDGEMENTS

The authors acknowledge the support of Pipeline Research Council International, Inc. (PRCI), under Contract PR 186-9709, for supporting the development of latest version of the software for the failure model.

REFERENCES 1. Part 195.452, Pipeline Integrity Management in High Consequence Areas, 49 Code of

Federal Regulations (CFR) 195, 2001. 2. ASME B31G, Manual: Determining Remaining Strength of Corroded Pipelines:

Supplement To B31 Code-Pressure Piping, ASME International, New York, 1991. 3. J. F. Kiefner and P. H. Vieth, “The Remaining Strength of Corroded Pipe,” Paper 29,

Proceedings of the Eighth Symposium on Line Pipe Research, A.G.A. Catalog No. L51680, American Gas Association, Inc., Washington, D.C., 1993.

4. ANSI/ASME B31.4, Pipeline Transportation Systems for Liquid Hydrocarbons and Other

Liquids, ASME International, New York, 1998. 5. ANSI/ASME B31.8, Gas Transmission and Distribution Piping Systems, ASME

International, New York, 2000. 6. CSA Z662-99, Oil and Gas Pipeline Systems, Canadian Standards Association, Toronto,

1999. 7. D. Broek, Elementary Engineering Fracture Mechanics, Sijthoff & Noordhoff, Alphen aan

den Rijn, The Netherlands, 1978. 8. A. Saxena, Nonlinear Fracture Mechanics for Engineers, CRC Press, Boca Raton,

Florida, 1998. 9. H. Tada, P. Paris, and G.Irwin, The Stress Analysis of Cracks Handbook, Paris

Productions Inc., St. Louis, 1985. 10. Fitness-for-Service, API Recommended Practice 579, American Petroleum Institute,

Washington, D.C., 2000. 11. Guide on methods for assessing the acceptability of flaws in metallic structures, BS 7910,

British Standards Institution, London, 1999. 12. M. G. Dawes, “Elastic-Plastic Fracture Toughness Based on the COD and J-Contour

Integral Concepts,” Elastic-Plastic Fracture, ASTM STP 668, American Society for Testing and Materials, Philadelphia, 1979, pp. 307-333.

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13. C. E. Jaske, “Damage Accumulation by Crack Growth Under Combined Creep and Fatigue,” Ph.D. Dissertation, The Ohio State University, Columbus, OH, 1984.

14. C. E. Jaske, “Estimation of the C* Integral for Creep-Crack-Growth Test Specimens,” The

Mechanism of Fracture, ASM International, Materials Park, OH, 1986, pp. 577-586. 15. G. Yagawa, Y. Kitajima, and H. Ueda, “Three-Dimensional Fully Plastic Solutions for

Semi-elliptical Surface Cracks,” International Journal of Pressure Vessels and Piping, Vol. 53, 1993, pp. 457-510.

16. S. Suresh, Fatigue of Materials, Cambridge University Press, Cambridge, UK, 1998. 17. P. C. Paris, M. P. Gomez, and W. E. Anderson, “A Rational Analytic Theory of Fatigue,”

The Trend in Engineering, Vol. 13, No. 1, 1961, pp. 9-14. 18. P. C. Paris, “The Growth of Cracks Due to Variations in Load,” Ph.D. Dissertation, Lehigh

University, 1962. 19. C. E. Jaske and J. A. Beavers, “Effect of Corrosion and Stress-Corrosion Cracking on

Pipe Integrity and Remaining Life,” Proceedings of the Second International Symposium on the Mechanical Integrity of Process Piping, MTI Publication No. 48, Materials Technology Institute of the Chemical Process Industries, Inc., St. Louis, 1996, pp. 287-297.

20. C. E. Jaske, J. A. Beavers, and B. A. Harle, “Effect of Stress Corrosion Cracking on

Integrity and Remaining Life of Natural Gas Pipelines,” Paper No. 255, CORROSION 96, NACE International, Houston, 1996.

21. C. E. Jaske and J. A. Beavers, “Fitness-For-Service Evaluation of Pipelines in Ground-

Water Environments,” Paper 12, Proceedings for the PRCI/EPRG 11th Biennial Joint Technical Meeting on Line Pipe Research, Arlington, VA, 1997.

22. C. E. Jaske, “CorLAS 1.0 User Manual: Computer Program for Corrosion-Life

Assessment of Piping and Pressure Vessels,” Version 1.0, CC Technologies Systems, Inc., Dublin, OH, 1996.

23. J. F. Kiefner, W. A. Maxey, R. J. Eiber, and A. R. Duffy, “Failure Stress Levels of Flaws in

Pressurized Cylinders”, Progress in Flaw Growth and Fracture Toughness Testing, ASTM STP 536, American Society for Testing and Materials, Philadelphia, 1973, pp. 461-481.

24. G. M. Wilkowski, et al., “Degraded Piping Program - Phase II, Semiannual Report, April

1986 - September 1986”, NUREG/CR-4082, Vol. 5, Battelle’s Columbus Division, Columbus, OH, April, 1987.

25. B. N. Leis and F. W. Brust, “Ductile Fracture Properties of Selected Line-Pipe Steels,”

NG-18 Report No. 183, Pipeline Research Committee of the American Gas Association, Inc., Washington, D.C., 1990.

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26. B. N. Leis, “Ductile Fracture and Mechanical Behavior of Typical X42 and X80 Line-Pipe Steels,” NG-18 Report No. 204, Pipeline Research Committee of the American Gas Association, Inc., Washington, D.C., 1992.

27. B. A. Harle, J. A. Beavers, and C. E. Jaske, “Low-pH Stress Corrosion Cracking of Natural

Gas Pipelines,” Paper No. 242, CORROSION 94, NACE International, Houston, 1994. 28. B. A. Harle, J. A Beavers, and C. E. Jaske, “Mechanical and Metallurgical Effects on Low-

pH Stress-Corrosion Cracking of Natural Gas Pipelines,” Paper No. 646, CORROSION 95, NACE International, Houston, 1995.

29. ASTM Designation: E 1049 - 85, “Standard Practices for Cycle Counting in Fatigue

Analysis,” American Society for Testing and Materials, West Conshohocken, PA, 1995. 30. Fatigue Design Handbook, AE-10, Second Edition, The Society of Automotive Engineers,

Warrendale, PA, 1988.

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Failure AssessmentDiagram Envelope

PlasticCollapse

Load Ratio, Lr

Toug

hnes

sR

atio

, Kr

Brittle Fracture

Mixed Mode - Brittle Fractureand Plastic Collapse

AssessmentPoint

Kr = KI/KMAT

Stress IntensityFactor, KI

Flaw Dimensions

Stress Analysis

MaterialToughness,

KMAT

Lr = σref/σys Yield Strength, σys

ReferenceStress, σref

Flaw Dimensions

Stress Analysis

Overview of FFS Analysis forCrack-Like Flaws Using Failure

Assessment Diagram

FIGURE 1 – Use of general failure assessment diagram (FAD) for crack-like flaws. (Reference 10)

14

0

2

4

6

8

10

0 200 400 600 800 1000 1200 1400

Fla

w D

epth

, mm

Flaw Length, mm

X52 Steel, Jc = 87.6 kJ/m2 and T

mat = 150

MAOP = 6454 kPaOD = 0.762 m and WT = 9.53 mm

Flow Strength

Fracture Toughness

FIGURE 2 – Example of calculated critical flaw depth as a function of length.

10-7

10-6

10-5

10-4

10-3

10-2

100 101 102

Carbon Steel (Reference 10)API X52 W eld 1API X52 W eld 2API X52 W eld 3

da/

dN (m

m/c

ycle

)

∆K (MPa-m 0.5) FIGURE 3 – Fatigue crack growth curves for pipeline steels in air at room temperature.

15

10-6

10-5

10-4

10-3

10-2

100 101 102

da/

dN (m

m/c

ycle

)

∆K (MPa-m 0.5)

Decreasing CyclicFrequency

FIGURE 4 – Illustration of the effect of cyclic frequency on corrosion fatigue crack growth behavior of pipeline steels.

0

1

2

3

4

5

6

7

0 500 1000 1500

Cra

ck D

epth

(mm

)

Crack Length (mm)

Flow StrengthFracture Toughness

API X52 Steel PipelineMOP = 5163 kPa

0.762-m OD x 7.62-mm WT

J Toughness = 254 kJ/m2

FIGURE 5 – Calculated critical crack depth as a function of length for Example 1.

16

0

20

40

60

80

100

0 500 1000 1500

Fati

gue

Cra

ck G

row

th L

ife (y

ears

)

Crack Length (mm)

API X52 Steel Pipeline∆P = 4131 kPa and f = 2/day

ao = 1.52 mm (0.060 in.)

af is critical depth in Figure 5

FIGURE 6 – Calculated remaining fatigue crack growth life as a function of length for Example 2.