jaske fatigue crack growth paper ipc06-10155

1 Copyright © 2006 by ASME

Proceedings of IPC 2006 6th International Pipeline Conference

September 25-29, 2006, Calgary, Alberta, Canada

IPC06-10155

ASSESSMENT OF PIPELINE FATIGUE CRACK-GROWTH LIFE

Carl E. Jaske CC Technologies, Inc.

5777 Frantz Road Dublin, OH 43017 USA

Phone: (614) 761-1214 Fax: (614) 761-1633 [email protected]

ABSTRACT This paper describes an accepted approach for predicting

fatigue crack-growth life in pipelines. Fatigue life is computed as the number of cycles for a crack-like flaw to grow from an initial size to a final critical size. This computation is performed by integrating a fracture-mechanics model for fatigue crack growth. The initial flaw size is estimated either from inspection results or by using fracture mechanics to predict the largest flaw that would have survived a hydrostatic pressure test. The final flaw size is estimated using fracture mechanics. Fracture-mechanics models for computing fatigue crack growth and predicting flaw size are reviewed.

The anticipated cyclic loading must be characterized to perform the crack-growth calculations. Typically, cyclic loading histories, such as pressure cycle data, are analyzed and used to estimate future loadings. To utilize the crack-growth models, the cycles in the loading history must be counted. The rainflow cycle counting procedure is used to characterize the loading history and develop a histogram of load range versus number of cycles. This histogram is then used in the fatigue crack-growth analysis. Results of example calculations are discussed to illustrate the procedure and show the effects of periodic hydrostatic testing, threshold stress intensity factor range, and pressure ratio on predicted fatigue crack-growth life.

INTRODUCTION Operating pipelines are subjected to cyclic loadings. These

include both pressure fluctuations and varying external loads. The cyclic loadings may initiate and grow fatigue cracks at defects and stress concentrations. The most likely locations for fatigue cracking in pipelines are weld joints, dents, wrinkles, and similar areas of metallurgical discontinuity or stress concentration. As part of pipeline integrity management

programs, the potential of fatigue crack growth at such locations should be evaluated. The conservative engineering approach is to assume that a crack-like flaw exists at a location of interest and use fracture-mechanics models to predict fatigue life. This paper reviews the features of such an approach and discusses the results of example calculations to illustrate its application to pipelines.

NOMENCLATURE CVN = Charpy impact energy for full-size specimen C = Paris Law coefficient d = crack depth da/dN = cyclic crack-growth rate J = J integral Jc = J fracture toughness Kmax = maximum stress intensity factor L = crack length m = Paris Law exponent MOP = maximum operating pressure n = Walker parameter exponent OD = outside diameter Pmax = maximum pressure R = pressure or stress ratio; the ratio of minimum to maximum pressure or stress SMYS = specified minimum yield strength t = wall thickness ∆K = stress intensity factor range ∆Keff = Walker effective stress intensity factor range ∆Keff(th) = Walker effective threshold stress intensity factor ∆Kth = threshold stress intensity factor range ∆P = cyclic pressure range


TECHNICAL APPROACH Fatigue occurs in mechanical equipment and structures

because of cyclic loading. The primary source of fatigue in pipelines is pressure cycling. If cyclic loads are high enough, fatigue cracks can initiate and grow. When crack-like flaws, such as very sharp notches, lack of fusion in welds, etc., are present, the initiation phase of fatigue cracking can be quite short. In these cases, fatigue crack growth dominates the fatigue life. For this reason, it is often conservatively assumed that a crack-like flaw is present and that fatigue life consists of the growth of this flaw until failure occurs. This is the approach that is applied to pipelines in the current paper.

Fatigue cracking almost always propagates from either the internal or external surface of the pipe wall. Very rarely does fatigue cracking propagate from a flaw embedded within the pipe wall. As long as the dimension in the through-thickness direction is used as the crack depth, it is conservative to assume that the crack is surface connected. For this reason, only the fatigue growth of a crack at the external or internal surface is addressed in the current work.

The initial crack size is either one that is measured by means of nondestructive examination (NDE) or the largest size that may have not been detected by NDE. The final crack size is either that at which the remaining ligament ahead of the crack suddenly ruptures through the wall of the pipe to cause a leak or that at which the crack penetrates the pipe wall by stable growth and causes a leak. The type of failure that occurs depends on the crack size, the crack driving force, the fracture toughness of the pipe steel, and the tensile strength of the pipe steel. In the current work, the CorLAS™ model [1-5] predicts the final or critical flaw size. The J integral is the crack driving force, Jc is the fracture-toughness failure criterion, and SMYS + 68.95 MPa (10 ksi) is the flow-strength criterion. When a measured value of Jc is not available, its value is estimated from the CVN value.

As shown in Figure 1, fatigue loading of equipment and structures is typically variable. The basic parameters that are used to characterize variable fatigue loading [6] are illustrated in Figure 1. In contrast, laboratory specimens are typically tested under constant-amplitude loading as illustrated in Figure 2. The results of constant-amplitude fatigue crack-growth tests are then analyzed to develop a logarithmic plot of da/dN versus ∆K as illustrated in Figure 3. As indicated, the fatigue crack growth resistance is usually well characterized by the Paris Law above a threshold for fatigue crack growth. No significant crack growth is observed below the threshold. To predict minimum fatigue crack-growth life, the upper bound crack-growth rate relationship is integrated from the initial to the final crack depth.

Because the crack-growth data are developed for constant-amplitude loading but need to be applied to variable-amplitude loading, a method of relating these differing loading conditions is required in order to make fatigue crack-growth life calculations. This is accomplished by applying a cycle counting procedure to the variable-amplitude loading history. Common

methods of cycle counting include level crossing, peak counting, simple-range counting, and rainflow and related counting methods [6]. The rainflow and related methods include range-pair counting, rainflow counting, and simplified rainflow counting for repeating histories. For practical purposes, the three rainflow methods produce the same results. In pipeline applications, most fatigue-life predictions are based upon a representative block (e.g., one year) of pressure cycling history that is repeatedly applied until failure is predicted. For this reason, the simplified rainflow counting procedure is applied in the current work.

The simplified rainflow cycle counting method is applied to a representative period of operating pressure history. The count is started and stopped at the same cyclic peak or valley in the pressure history. Each full pressure cycle is then counted following a set of prescribed rules [6]. Once a cycle is counted, its range and mean value are recorded, and it is removed from the history. This process is repeated until all cycles have been counted. Then, the counted cycles are sorted and assigned to various ranges to develop a pressure cycle histogram.

Other, less frequent pressure cycling events may have to be added to the applied load history. The most common would be a periodic hydrostatic pressure test (hydrotest). Whereas, the representative block length of pressure cycling is frequently one year, the interval between hydrotests is typically five years or more. During a hydrotest, at least two pressure cycles are applied. More than two may be applied if retests are required. A provision for including a periodic hydrotest is included in the approach.

When a pressure cycle is counted, the maximum pressure and the pressure ratio (R) are recorded for that cycle. For a given range of pressure ratio, each cycle is grouped into a range of maximum pressure. This process is repeated to construct a histogram of pressure ratios with each pressure ratio in turn containing a histogram of maximum pressure values. For example, the cycles may grouped into ten pressure ratio ranges of 0 to 0.1, greater than 0.1 to 0.2, greater than 0.2 to 0.3, … and greater than 0.9 to 1.0. Within each range of pressure ratios the cycles then could be grouped in ten ranges of maximum pressure from 0 to 0.1 MOP, greater than 0.1 to 0.2 MOP, greater than 0.2 to 0.3 MOP, … greater than 0.9 to 1.0 MOP. Sometimes, it is deemed that pressure ratio does not have a significant effect on fatigue, so the data are grouped simply by ranges of pressure range, which equals (1-R) times the maximum pressure.

Grouping by pressure (stress) ratio is important because the both the maximum pressure and pressure range affect the rate of fatigue crack growth. As pointed out in Appendix F of API RP 579 [7], one common method of accounting for the effect of stress ratio is the Walker effective stress intensity factor range parameter:

∆Keff = ∆K(1-n) (Kmax)n= (1-R)(1-n) Kmax (1)


For pressure cycle fatigue of pipelines, one can define a corresponding effective pressure range as follows: ∆Peff = (1-R)(1-n) Pmax (2) Equation (2) holds because Kmax is proportional to Pmax for thin-walled piping. The cyclic counting can be simplified by assigning each counted cycle to a range of ∆Peff values in a manner similar to that described previously for assigning a cycle to a range of pressure ranges values. This is the approach used to account for the effect of pressure ratio in the current work.

The value of n in Equations (1) and (2) is a material parameter that is determined by curve fitting fatigue crack-growth data obtained by testing at various values of R. Often, the value of n is approximately 0.5. For this case, the values of ∆Keff and ∆Peff at the R = 0.1, which is commonly used in testing, are as follows: ∆Keff = (1-0.1)0.5 Kmax = 0.949 Kmax (3) ∆Peff = (1-0.1)0.5 Pmax = 0.949 Pmax (4) In this case, the corresponding values of ∆K and ∆P are ∆K = (1-0.1) Kmax = 0.9 Kmax (5) ∆P = (1-0.1) Pmax = 0.9 Pmax (6) Therefore, ∆K / ∆Keff = ∆P / ∆Peff = 0.9/0.949 = 0.948 (7) Then, for R = 0.1 and n = 0.5, the Paris Law (see Figure 3) would become da/dN = C (0.948 ∆Keff)m (8) For other values of R and n, the Paris Law would have to be modified in a similar fashion. Alternatively to the above approach, the Paris Law could be developed by curve fitting a plot of da/dN versus ∆Keff for the material.

The Walker effective threshold stress intensity factor for R = 0.1 would be ∆Keff(th) = 1.054 ∆K (9) Of course, the constant in Equation (9) would be different for threshold stress intensity factor values developed at other stress ranges.

APPLICATION OF APPROACH To illustrate the application of the previously described

technical approach, the information on cyclic pressures shown

in Table 1 was created. These data represent the results of one-year of pressure cycle data for an operating pipeline to which simplified rainflow counting has been applied. They are not for any specific pipeline, so similarity to an existing pipeline is purely coincidental. They do indicate the type of results that might be expected for an operating pipeline. The values shown in Table 1 are the number of cycles for various combinations of maximum pressure ranges in %MOP and pressure ratio ranges.

To apply the data in Table 1 to fatigue crack-growth life analysis, they were analyzed and tabulated to determine the number of cycles as a function of ∆P and ∆Peff. Values of ∆P were computed using the lowest value of R for each range of pressure ratio from the following relationship: ∆P = (1-R) Pmax (10) Values of ∆Peff were computed in a similar fashion using Equation (2) with n = 0.5. The results of these calculations are summarized in Table 2 and plotted as histograms in Figure 4. Most of the values of ∆P are less than or equal to 30% MOP, and none are greater than 60% MOP. In contrast, the values of ∆Peff are in ranges from 10% to 80% MOP. In other words, when pressure ratio (or mean pressure) is taken into account, the histogram is shifted to increased values.

A value of ∆Peff gives a pressure range at R = 0 that is predicted to be effectively equivalent in terms of fatigue crack growth behavior to the value of ∆P at the specific value of R. For example, consider a value of ∆P = 10% MOP at R = 0.9. In this case, Pmax = ∆P/(1-R) = 10% MOP/0.1 = 100% MOP. (11) Therefore, for n = 0.5, ∆Peff = (1-R)0.5 Pmax = (0.1)0.5 100% MOP = 31.6% MOP (12) This means the pressure cycle of ∆P = 10% MOP at R = 0.9 is effectively equivalent to the pressure cycle of ∆P = 31.6% MOP at R = 0 from the viewpoint of fatigue crack growth behavior.

The distributions of cyclic pressure ranges shown in Table 2 and Figure 4 were used to make fatigue crack-growth life predictions based on the following parameters:

• API X52 steel pipe • MOP = 6,454 kPag (936 psig) • OD = 762 mm (30 in.) • t = 9.53 mm (0.375 in.) • SMYS = 359 MPa (52 ksi) • Flow strength = 427 MPa (62 ksi) • Jc = 87.6 kJ/m2 (500 lb/in.) • C = 6.89 x 10-9 (mm/cycle; MPa m0.5) • C = 3.60 x 10-10 (in./cycle; ksi in.0.5) • m = 3.0


• ∆Kth = 2.0 MPa m0.5 (1.8 ksi in.0.5) • d = 2.54 mm (0.1 in.) • L = 25.4 mm (1.0 in.)

The value of Jc is a lower bound for pipeline steels. The Paris Law constants (C and m) are for the upper-bound curve for ferritic-pearlitic steels in Appendix F of API RP 579 [7], and the value of ∆Kth is a lower bound value from Appendix F of API RP 579 [7]. The values of d and L are the initial depth and length of a semi-elliptically shaped surface crack used in the fatigue-crack growth life calculations.

Results of the fatigue crack-growth life calculations for eight cases are summarized in Table 3. All of the predicted lives are minimum values. Cases 1 through 4 were based on use of only the pressure ranges, while Cases 5 through 8 were based on the corresponding effective pressure ranges, respectively. The Paris Law constants and the value of ∆Kth were adjusted from R = 0.1 to R = 0 for use with the effective pressure ranges. No hydrotest was used for Cases 1, 3, 5, and 7. A hydrotest at five-year intervals was used for Cases 2, 4, 6, and 8. No retardation of crack growth was included in the modeling the hydrotest; only the effect of a high cyclic pressure range was taken into account. A threshold value of stress intensity factor range was used for Cases 1, 2, 5, and 6 but not for Cases 3, 4, 7, and 8.

For the pressure cycling history and initial crack size used in the current work, there was no effect of modeling the crack-growth threshold on the predicted fatigue lives. The periodic hydrotest was predicted to lower fatigue life from 100 to 49 years in Cases 1 and 3 versus Cases 2 and 4 and from 11.2 to 9.0 years in Cases 5 and 7 versus Cases 6 and 8. Accounting for pressure ratio had a large effect on predicted fatigue life. It reduced the predicted life from 100 to only 11.2 years when there was no periodic hydrotest and from 11.2 to 9.0 years when there was a period hydrotest.

The results show that it is important to include the effects of pressure ratio in fatigue crack-growth life calculations. Such calculations for pipelines are frequently made using only the pressure ranges and assuming that the effect of pressure ratio is not significant. The results of this work indicate that such an approach could be very optimistic and greatly over predict fatigue life. It is also possible that, in other cases, the effect of pressure ratio could be much less than in this particular example. However, comparative calculations must be performed to quantify the effect of pressure ratio. Thus, the recommended approach is simply to include the effects of pressure ratio in fatigue life calculations.

CONCLUSIONS A straight-forward approach for computing fatigue crack-

growth life has been developed using J integral fracture mechanics to compute critical crack size and the Paris Law to compute crack growth as a function of applied pressure cycles. A threshold for fatigue crack growth can be included in the approach. The Walker parameter is used to account for the

effect of pressure ratio of fatigue life. The effect of pressure ratio should be accounted for because excluding it can lead to excessively non-conservative predictions of fatigue life.

REFERENCES [1] Jaske, C. E., and Beavers, J. A., 2002, “Development and

Evaluation of Improved Model for Engineering Critical Assessment of Pipelines,” Paper IPC02-27027, Proceedings of IPC 2002, The American Society of Mechanical Engineers, New York.

[2] Jaske, C. E., 1996, “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.

[3] Jaske, C. E., and Beavers, J. A., 1996, “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, pp. 287-297.

[4] Jaske, C. E., Beavers, J. A., and Harle, B. A., 1996 “Effect of Stress Corrosion Cracking on Integrity and Remaining Life of Natural Gas Pipelines,” Paper No. 255, Corrosion 96, NACE International, Houston.

[5] Jaske, C. E., and Beavers, J. A., 1997, “Fitness-For-Service Evaluation of Pipelines in Ground-Water Environments,” Paper No. 12, Proceedings for the PRCI/EPRG 11th Biennial Joint Technical Meeting on Line Pipe Research, Arlington, VA.

[6] ASTM E1049-85, 1990, “Standard Practices for Cycle Counting in Fatigue Analysis,” ASTM International, West Conshohocken, PA.

[7] American Petroleum Institute, 2000, “Fitness-For-Service,” API Recommended Practice 579, Washington, D.C.


Table 1. Example of data that might be obtained from simplified rainflow counting of pressure cycle data for one year (365 days) of pipeline operation.

Number of cycles rainflow counted at various maximum pressures and pressure ratios for one year of operationPmax,

%MOP 0 to < 0.1 0.1 to < 0.2 0.2 to < 0.3 0.3 to < 0.4 0.4 to < 0.5 0.5 to < 0.6 0.6 to < 0.7 0.7 to < 0.8 0.8 to < 0.9 0.9 to < 1.0> 0 to 10 0 0 0 0 0 0 0 0 0 0> 10 to 20 0 0 0 0 0 0 0 0 0 0> 20 to 30 0 0 0 0 0 0 0 0 1 0> 30 to 40 0 0 0 0 0 3 2 1 0 0> 40 to 50 0 0 0 0 0 0 0 2 3 5> 50 to 60 0 0 0 0 0 0 2 1 0 0> 60 to 70 0 0 0 0 0 0 15 23 14 23> 70 to 80 0 0 0 0 11 27 34 249 375 938> 80 to 90 0 0 0 0 12 35 25 567 4635 3444> 90 to 100 0 0 0 0 0 5 156 2001 3555 135

Pressure Ratio

Table 2. Distributions of cyclic pressure ranges.

∆P, Number of ∆Peff, Number of%MOP Cycles %MOP Cycles

> 0 to 10 4,549 > 0 to 10 0> 10 to 20 8,588 > 10 to 20 6> 20 to 30 2,857 > 20 to 30 4,416> 30 to 40 242 > 30 to 40 550> 40 to 50 51 > 40 to 50 9,021> 50 to 60 12 > 50 to 60 2,087> 60 to 70 0 > 60 to 70 214> 70 to 80 0 > 70 to 80 5> 80 to 90 0 > 80 to 90 0> 90 to 100 0 > 90 to 100 0Total 16,299 Total 16,299

Table 3. Results of fatigue crack growth life calculations.

Fatigue Life,Case Hydrotest ∆Kth d L d L years

1 No Yes 8.79 37.9 0.346 1.49 1002 Yes Yes 3.94 28.2 0.155 1.11 493 No No 8.79 37.9 0.346 1.49 1004 Yes No 3.94 28.2 0.155 1.11 49

5 No Yes 8.79 37.9 0.346 1.49 11.26 Yes Yes 5.56 31.4 0.219 1.24 9.07 No No 8.79 37.9 0.346 1.49 11.28 Yes No 5.56 31.4 0.219 1.24 9.0

Final Crack Size, mm Final Crack Size, in.

Based on Pressure Range, ∆ P

Based on Effective Pressure Range, ∆ P eff


Load

(+) Range

Ref. Load

Peak

Reversal

ReversalValley Mean Crossing

Time

(-) Range

Load

(+) Range

Ref. Load

Peak

Reversal

ReversalValley Mean Crossing

Time

(-) Range

Fig. 1 Illustration of basic fatigue loading parameters as defined in ASTM E 1049 [6].

Load

Time

Range

Maximum

Minimum

Mean

Load

Time

Range

Maximum

Minimum

Mean

Amplitude = Range/2Load Ratio = Minimum/Maximum

Fig. 2 Illustration of basic parameters for constant-amplitude fatigue loading.


Log

da/d

N

Log ∆K

Paris Law:da/dN = C (∆K)m

Threshold: ∆Kth

Fig. 3 Schematic illustration of a typical fatigue-crack growth curve for pipeline steels.

Pressure Cycle Distribution

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

10,000

1 2 3 4 5 6 7 8 9 10

%MOP/10

Num

ber

of C

ycle

s

Pressure RangeEffective Pressure Range

Fig. 4 Histograms of one year of pressure cycle data plotted in terms of ∆P and ∆Peff.

jaske fatigue crack growth paper ipc06-10155

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