B. N. Leis, F. W. BrustBattelle Columbus Division

Columbus, Ohio

The crack-driving force in line-pipe steel material can be expected to increase as a consequence of cyclic load and hold-time effects. These effects are especially evident during hydrotesting.

In addition, repeated hydrotesting can cause cracks to grow at pressures less than achieved in a prior test.

These are only two of the major conclusions from fullscale tests of line pipe with patched through-wall flaws and part-through-wall flaws. These tests form the basis for judgments about the accuracy of flaw growth and failure-pressure predictions.

For these tests, an engineering model of ductile flaw growth in line-pipe steels based on J-tearing theory was developed to assess flaw growth during hydrotesting.

Part 1 of this two-part series will present that theory; the concluding article will discuss the tests conducted and elaborate on the significant conclusions.

### REVALIDATION

Hydrostatic testing is widely used to demonstrate pipeline integrity. The test has been used to validate the maximum allowable operating pressure (MAOP) of lines being commissioned.

As existing pipelines age, the test is used to revalidate integrity following repairs. Repeated hydrotesting over some interval of time is also being considered as a regulatory measure.

Both the initial hydrotest and subsequent repeated hydrotesting introduce the possibility for flaw growth, with low-cycle fatigue being an obvious concern. The objective of the work reported here was to assess the influence of the frequency of repeated testing and the test level on pipeline integrity.

Historically safe operation points to the adequacy of hydrotesting to operating pressure ratios that range in the U.S. from 125 to 150% MAOP. Federal regulations limit the peak MAOP to a value corresponding to 72% of the specified minimum yield stress (SMYS) of the material.

Therefore, at a test pressure (Pt) to service pressure (P,) ratio (Pt/Ps) of 1.25, the maximum stress is 1.25 x 0.72 x SMYS x 1 00% 90% SMYS. At Pt/P, = 1.5, the maximum stress is 108% SMYS.

It follows from these hydrotest stress levels that inelastic flow occurs in the material surrounding defects and may also occur throughout sections of pipe whose actual yield is close to the minimum yield stress.

Because the hydrotest develops stresses in excess of the yield stress in the region surrounding a defect, inelastic effects on defect growth, during as well as following a hydrotest, should be considered.

If the inelastic action is small compared to the length of the crack and the remaining (net section) ligament, linear elastic fracture mechanics (LEFM) is a valid basis for assessing flaw growth.

The crack-driving force is represented by the stress intensity factor (K) which represents the effects of stress, crack size, shape and orientation, and the dimensions of the pipe. The material's resistance is conservatively characterized by the plane strain fracture toughness (Kic).

In such cases, flaw growth initiates and continues until a leak or rupture occurs during the course of fracture.

### NLFM REQUIRED

For tough ductile materials, however, the inelastic field is not confined to the crack tip so that the material's resistance is not uniquely characterized by LEFM, Therefore, nonlinear elastic fracture mechanics (NLFM) must be used.

Because tough ductile materials can sustain a growing defect without it becoming unstable at initiation, a defect can grow stably during the course of service or overloading as in a hydrotest. Because of this growth, the presumed margin of safety that follows from the usual LEFM analysis of the hydrotest (e.g., see References 1 and 2 for discussion) may be lost to crack advance that is not accounted for.

Evidence of ductile flaw growth in line pipe can be found in pressure reversals which develop when a leak or a rupture occurs on repressurizing at a pressure less than just achieved.'

Assessing the extent of flaw growth after hydrotesting in tough ductile materials requires use of NLFM.

The purpose here is to present an NLFM model being developed to predict crack extension in ductile line pipes, emphazing its application to recent full-scale testing. This model is based on "J-tearing theory."

The theory, which includes the ductile nature of the material, expresses the balance between the material's resistance to cracking and the crack-propagating effects of the pressure.

The objective of this work was to provide the gas industry with an accurate and validated model for predicting growth of a flaw resulting from the effects of a hydrostatic test or hydrostatic retesting. The end product will be a validated model that predicts crack extension during the load-and-hold portion of a hydrotest and subsequent operation.

Development has progressed to crack-growth predictions for patched, through-wall flaws in line pipe and, by early last year, was validated for part-through-wall (PTW) flaws in line pipe .4

### MODELING CRACK GROWTH

For purposes of analysis, the hydrotest history has been idealized as shown in Fig. 1.

Defect growth is considered to occur because of plasticity effects during loading or time-dependent (creep) effects during the pressure hold for leak check.

Ductile crack growth in line-pipe materials is assumed to be J controlled. That is, a driving force for crack growth with a Hutchinson-Rice-Rosengren (HRR) singularity is assumed.5

Such a formulation may be argued to be valid if the change in crack length fails to advance the crack tip beyond the controlled field and only global proportional loading is considered .6 Moreover, the value of J must be determined such that crack closure is not a complicating factor.7

Other forms of crack-driving force could have been used in lieu of J. Use of such parameters, however, requires detailed application-specific numerical analyses.

The parameter J is favored for the present "engineering analysis" because it can be evaluated for many materials and geometries with handbook information. Moreover, there is a wealth of current research being directed at the evaluation of J for pipe geometries.8

### TIME DEPENDENCE

To satisfy the assumption that the crack tip remains in the controlled field, the analysis updates the parameters used to define this problem prior to estimating J if crack extension occurs. The timedependent analysis has been formulated by time marching, a deformation theory of plasticity analysis.

Time dependence is accounted for in an otherwise time-independent model by incrementing time in steps and calculating J with material-deformation behavior which represents that time step. Likewise the material's resistance to crack growth (the J-resistance or R curve 9) could be updated based on laboratory test data as a discretized function of time.

As is the case for the choice of J, several parameters are advocated as a basis for characterizing creep crack. Again, reliance on a time-marching-based analysis is dictated in part by the availability of solutions.

But there are other reasons.

First, observations on timedependent defect growth suggest that the initial transient behavior may control the conditions under which subsequent cracking occurs and may also dominate the cracking process. This behavior cannot be modeled by alternative parameters which assume both a steady-state process and material-flow behavior which is time dependent everywhere within the cracked body.

Second, use of other approaches requires a shift in how the material-flow process is characterized in the transition from the loading phase to the hold-time (constant-load) phase. The analysis is "discontinuous" in such cases, a situation which may produce incompatible boundary conditions between the plasticity and the creep analysis.

In contrast, time-marching J uses the time-independent result as an initial condition and so avoids possible errors and incompatible boundary conditions.

In summary, there are definite uncertainties in the rigorous interpretation of J and in the time-marching J analysis. These drawbacks, however, are believed to be out weighed by the benefits of ease of evaluation and model formulation at least for present purposes.

### TYPICAL DATA

This study includes loading conditions that simulate the effects of repeated load (hydrotest) cycles. This cyclic plastic strain which may occur in repeated hydrotesting alters the constitutive response of a material.

For this reason "cyclic" rather than "monotonic" stress-strain behavior has been developed to assess the influence of repeated hydrotesting and the effect of a hydrotest on cracking during subsequent service.

Prior to yield in the net ligament at a part-through flaw, the crack tip plastic zone is "contained" by the elastic net section. This contained flow means that material deformation and fracture are effectively "displacement controlled" so that "strain controlled cyclic stress-strain data" are appropriate up to net section yield.

With the onset of net section yield, material at the crack tip reverts to the net section load-control condition because pipes are pressurized. Therefore, "load controlled cyclic stress-strain data" are appropriate after net section yield.

Previous work has shown control condition does not appreciably alter the cyclic stress-strain curve for one line pipe steel but does exert a significant effect on transient response in the transition from monotonic to stable cyclic behavior .4

The material stress-strain response is idealized by the Ramberg Osgood equation (Equation 1; see accompanying box).

In this equation, so, is taken as the proportional limit stress (at a plastic strain, ep, = 0.001), although the value of so, chosen is arbitrary as long as eo =so/E.

If monotonic stress-strain data are being fitted to Equation 1, so is found from tension test data. If cyclic stress-strain data are being fitted, so, is based on the cyclic proportional limit.

If time-dependent, stress-strain data are being fitted, so, is the proportional limit for the time step of interest. It follows then that so,eo,a and n are generic parameters in a fitting function.

The parameters a and n are found from the strain hardening exponent (m) and the strength coefficient (k) in the usual log form s = k(Ep)m. The value of n = 1 /m, and of a = k- n E so n-1

Specific data developed in support of this program are presented, for example, for an X52 steel4 in Figs. 2a and b on logarithmic coordinates which permit direct evaluation of k and m.

The results in Fig. 2a present the monotonic stressstrain curve obtained from strain-controlled longitudinal flattened strap specimens. Also shown in Fig. 2 are trends that represent the resistance of a specific X52 steel when subjected to cyclic stress such as would develop in the plastic zone at a defect or crack tip in a line pipe subjected to pressure cycles.

These curves represent strain rates, -&, of 2 sec-1, 0.016 sec-1, and 0.0016 sec

The difference in the stress needed to produce a given strain indicates the stressstrain behavior of this linepipe steel is rate dependent. Similar data for other line pipe steels show that this rate dependence is not unusual.

Fig. 2b presents results that characterize the loadcontrolled creep behavior of the steel whose strain-controlled monotonic tension curve was shown in Fig. 2a. Creep behavior is presented in Fig. 2b in terms of the total inelastic strain at a given stress-a format referred to as an isochronous (constant time) stress-strain curve.

Observe from this figure that both the slope (m) and the constant (k) are functions of time.

As detailed in Reference 4, results developed at 175 F. show trends similar to those in Fig. 2b except that primary creep occurs somewhat faster.

It follows from Fig. 2 that the material's resistance to deformation is both time and cycle dependent. When cyclic load is imposed at high mean stress, as occurs in service following a hydrotest, creep occurs under cyclic load. This so-called cyclic creep has been observed in several line pipe steels at maximum stresses below SMYS.

### LOAD, GEOMETRY, CRACK SIZE

As noted, the value of J also depends on the geometry, the load, and the crack size.

Shih and others have developed a means to estimate J in terms of these variables, for materials whose deformation behavior is described by Equation 1.10

The estimation procedure of Shih represents J as the sum of an elastic and a fully plastic contribution (Equation 2).

The elastic contribution (Je) can be calculated from the linear elastic fracture mechanics (LEFM) stress intensity factor (K). The value of J, is shown in the accompanying equations box.

There, F1(a/b) is a tabulated function for the geometry of interest. It is defined by the ratio of the stress intensity factor (K) for that geometry divided by the stress intensity factor for an infinite center cracked panel.

The function F1 (a/b) can be found in handbooks (for example, Reference 11). The symbol E' is the plane strain corrected modulus, b is the width, and P is the load per unit thickness (t).

The symbol ae is an effective crack length. It is the sum of the physical crack length (a) and the length of the plastic zone along the crack line: ae = a + F ry, Here ry = ry(n, K/so.).

(This plastic-zone correction to the elastic J is suggested in Reference 10 for interpolation purposes between elastic and fully plastic conditions. However, its use is seemingly redundant and often leads to far too conservative estimates.)

Defining x = P/Po where Po = the limit load as defined in Reference 12 and c(a) = remaining ligament, then: Po = Po, [uv c(a), a/c(a)] and F = F(x). Specific functional forms can be found in Reference 12.

For line pipe with through-wall axial flaws, the value of J, is based on LEFM solutions and includes the effects of bulging through modification of F.

Because of the nature of these solutions, the formulation is valid only for flaw (crack) lengths less than the diameter of the pipe in applications to large diameter thin-walled pipe.

Provision for part-through-wall flaws is being achieved through further modification of F, based on the work of Newman and Raju.13 The value of J is currently calculated in the form of Equation 3.

The fully plastic contribution of J can be evaluated in the manner of Shih and others 10 from an equation of the form Equation 4.

There, the function h(a, b, is tabulated in Reference 12 for various geometries. In lieu of tabulated results, Jp could be numerically or otherwise calculated for fully plastic conditions.

Detailed inelastic analyses of axial flaws in pipes are not available even for a limited range of geometries and flaw sizes.

Thus, the function h(a, b, n) cannot be found for the exact problem of interest. However, recognizing that large-diameter, thin-wall pipe with a through-wall flaw can be reasonably represented by a center cracked panel (CCP) of some effective width allows use of tabulated solutions for the CCP.

For present purposes the effective width is determined such that the rupture pressure based on time-independent cracking calculated with the J-tearing theory as adapted in this article matches that based on the work of Maxey. 14

Setting the effective width in this manner makes use of the experience-proven solution which ignores crack growth as the starting point for this engineering analysis that includes the effects of crack extension.

Combining Equations 3 and 4 leads to the value of i for fixed values of a, b, x for a given material described by do, a, and n. Note that a = a(n,.,.,.). Thus, changes in n produce changes in a:a is not an independent variable. Details on practical applications of this estimation procedure can be found elsewhere, as for example Reference 15 which deals with cyclic stress corrosion crack growth.

### FRACTURE RESISTANCE

Use of the J-tearing theory characterizes the continued cracking process from initiation, through stable tearing, to instability.

The fracture resistance, therefore, can no longer be characterized by a single parameter such as Kic or a Charpy energy. Fracture resistance is instead represented by a J-resistance (J-R) curve.

For this work, the J-R curve has been obtained from deeply cracked compact-tension (CT) specimens with ASTM standard procedures for testing and data analysis (ASTM E813). A study of possible time and cycle dependence of the J-R curve is continuing.4

Ductile fracture resistance characterized by the J-R behavior is illustrated in Fig. 3. The J-R behavior shown here is presented in terms of a modification of J that includes crack growth in the test16- the so-called J-modification, denoted as Jm.

These samples represent crack growth in the long transverse (LT) direction in samples of flattened pipe and are therefore best suited for predicting the growth of axial through wall flaws. Results developed indicate some dependence of line-pipe J-R behavior on prior mechanical history, including the rate of loading. 17 18

Thus far, this dependence is manifested primarily in a reduction in initiation resistance.

Orientational effects give rise to a reduction in J-R behavior for both initiation and growth for short transverse applications (part-through-wall growth) as compared to LT (through-wall) properties.

### REFERENCES

- Kiefner, J. F., "Evaluating Pipeline Integrity Flaw Behavior During and Following High Pressure Testing," proceedings of the 7th Symposium on Line Pipe Research, AGA, 1986, pp. 15.1-15.12.
- Kiefner, J. F., and Forte, T. P., "HYDROSTATIC RETESTING-1: Model predicts hydrostatic retest intervals," OGJ, Jan. 7, 1985, pp. 93-96, and "HYDROSTATIC RETESTING-Conclusion: Model shows value of wide pressure margins," OGJ, Jan. 14, 1985, p. 83-86.
- Kiefner J. F., Maxey, W. A., and Eiber, R. J., "A Study of the Causes of Failures of Defects That Have Survived a Prior Hydrostatic Test," NG18 Report No. 111 to American Gas Association, Nov. 3, 1980.
- Leis, B. N., Goetz, D. P., and Scott, P.M., "Prediction of Inelastic Crack Growth in Ductile Line Pipe Materials," 7th Symposium on Line Pipe Research, American Gas Association, 1986, pp. 16.1-16.31.
- Hutchinson, J. W., "Plastic Stress and Strain Fields at a Crack Tip," J. Mechanical Physical Solids. Vol. 16 (1968), pp. 337-347. See also, Rice, J. R., and Rosengrem, G. F., "Plane Strain Deformation Near a Crack Tip in a Power Law Hardening Material," J. Mechanical Physical Solids, Vol. 16 (1968), pp. 112.
- Hutchinson, J. W., and Paris, P. C., "Stability Analysis of Controlled Crack Growth," in Elastic Plastic Fracture, ASTH STP 668, American Society for Testing and Materials, 1979, pp. 37-64.
- Leis, B. N., and Zahoor, A., "Cyclic Inelastic Deformation Aspects of Fatigue Cracked Growth," proceedings of the 12th National Symposium on Fracture Mechanics, ASTM STP 700, 1980, pp. 65-96.
- Wilkowski, G. M., et al., Degraded Piping Program-Phase 11, NUREG/CR4082, 1984.
- Anon, ASTM Standard E813; Jic A Measure of Fracture Toughness.
- Shih, C. F., German, M. D., and Kumar, V., "An Engineering Approach for Examining Crack Growth and Stability in Flawed Structures," G. E. Report No. 80CRD205, August 1980.
- Tada, H., Paris, P. C., and Irwin, G. R., The Stress Analysis of Cracks Handbook, Del Research Corp., 1977 (Rev).
- Kumar, V., et al., "An Engineering Approach for Elastic Plastic Fracture Analysis," EPRI NP1931, July 1981.
- Newman, J. C., and Raju, I. S., "An Empirical Stress Intensity Factor Equation for the Surface Crack," Engr. Frac. Mech., Vol. 15, No. 12, pp. 185-192, 1981.
- Kiefner, J. F., Maxey, W. A., Eiber, R. J., and Duffy, A. R., "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, pp. 461-481, 1973.
- Leis, B. N., Rungta, R., and Jentgen, R. L., "Stress Corrosion Cracking and Fatigue A Mechanics Based Step to an Interactive Model," in Localized Crack Chemistry and Mechanics in Environment Assisted Cracking, AIME, pp. 211-228, 1984.
- Ernst, H. A., and Paris, P. C., "Technique of Analysis of Load Displacement Records by J Integral Method," U.S. Nuclear Regulatory Commission, NUR- EG/CR122, 1980.
- Tiffany, C. F., Lorenz, P. M., and Shah, R., "Extended Loadings of Cryogenic Tanks," NASA CR2252, 1966.
- Tsuru, and Garwood, S., "Some Aspects of Time Dependent Ductile Fracture of L ine Pipe Steels," Vol. 3, ICM III, Cambridge, England, pp. 519-528, 1979.

*Copyright 1990 Oil & Gas Journal. All Rights Reserved.*