Validation of room-temperature primary creep crack-growth analysis for surface-cracked pipes

Nuclear Engineering and Design 142 (1993) 69-75 North-Holland

69

Validation of room-temperature primary creep crack-growth analysis for surface-cracked pipes B.N. L e i s a n d F . W . B r u s t

Engng. Mechanics Dept., Battelle, 505 King Avenue, Columbus, OH 43201-2693, USA Received 8 March 1993

This paper briefly reviews the theoretical considerations that underlie the development of an engineering analysis of ductile, time dependent flaw growth as adapted to axial surface flaws in cylindrical containers such as pipes and tanks. Thereafter the validation of this analysis by comparison of the predicted and observed behavior of an extensive database for part-through-wall defects in pipes is presented. The results of this comparison indicate that the analysis provides an accurate means to characterize the flaw growth and related failure pressure for this class of flawed structures. The results indicate a close correspondence of predicted and observed behavior that is free of bias with respect to flaw length and depth and the grade of steel used to fabricate these full scale test specimens. Readers interested in more complete documentation of the analysis and the validation studies are directed to the report covering model formulation and validation (Leis et al, June 1991).

I. Introduction

2. Primary creep crack growth model

Proof tests in ductile materials may cause a crack to grow without failing the component. The crack may grow to a length that will lead to component failure during service at relatively moderate loads due to the history-dependent damage that occurs at the crack tip during the proof test. T i m e - d e p e n d e n t crack growth greatly enhances this effect. Hence, it is very important to be able to quantify the effects of time-dependent as well as time-independent crack growth and damage that occurs during a proof test. The effect of this damage on the subsequent service loading also must be understood. Previous papers have presented the details of the primary creep crack-growth model [1-4]. The purpose of this paper is to briefly review the theoretical considerations and then to present analysis of an extensive database for part-through-wall defects in pipes to serve as validation for this formulation. Readers interested in details of the analysis should consult the above-noted references. Readers interested in m o r e complete documentation of the analysis and the validation studies should consult the report covering model formulation and validation [4]. 0029-5493/93/$06.00

In a body loaded as in fig. 1, a plastic zone develops during the initial loading. For instantaneous power-law plasticity, the total strain is represented in the usual way. Since plastic strain dominates the stress-strain response near the crack tip, the near-tip stresses thus resemble the well-known H R R field as long as r is small.

O.ij = j(1/np + 1)r-(1/np+ 1,fij ( O,

F/p).

(1)

For t > 0, creep straining begins as the load is held constant. The simplified power-law constitutive response in rate form after t > 0 is represented as 4ij = ~ + e~ + Eb,

(2a)

l+v v ~; = E ~'j - E 6"kk6ii'

(2b)

• 3 n .. _ ( r i p EP. = ~-/~0tt Do e 2UlVe

2).~. t~

Ue,.Jij,

k~e]

(2C)

'Jij"

In eq. (2), a superimposed dot represents the material time derivative, E and v represent the elastic modulus and Poisson's ratio, B 0 and n o represent

© 1993 - E l s e v i e r S c i e n c e P u b l i s h e r s B.V. A l l rights r e s e r v e d

B.N. Leis, F. IV.. Brust / Crack-growth analysis

70 P P

crock~x

//~,,i0 ....

,2>. Fig. 1. Illustration of deformation response near a crack tip during a load-and-hold sequence

power-law plasticity material constants, Sij is the stress deviator, tye is equivalent stress, and n c, p, and B 1 represent material constants for a strain-hardening creep law. (The use of a time-hardening formulation has also been considered, as detailed in refs. [1], [2] and [4].) For t > 0, creep straining begins. If n c > np (which is the situation examined extensively in the literature), the third term of eq. (2a) dominates very near the crack tip and a creep zone develops at the crack tip, which grows with time. The crack-tip stresses thus relax and the crack-tip stress field becomes another H R R field growing within the initial plastic H R R field (see, for instance ref. [5]). Consider the case of n c < n p , which is the case addressed by the present analysis procedure. For this case a plastic zone may develop at the crack tip upon loading at time t = 0. After the hold period begins, the stress level very near the crack tip increases rather than decreases, and the effective plastic zone increases in size. That this is so may be seen by observing that the second term of eq. (2a) dominates the first and the third terms in this situation, so that the plastic H R R field of eq. (1) dominates the near-field stress and strain states. Hence, rather than going from a 'plastic' H R R field to a 'creep' H R R field, which occurs for n c > n o and results in stress relaxation, the 'plastic' H R R field remains for t > 0 and the stresses increase since the strength of the H R R field, J, increases. Thus 'loading' or 'stressing' takes place in the vicinity of the crack tip despite the fact that the far-field load remains constant in time *. The above-described processes were illustrated in detail [1,2] by results from finite-element analyses of cracked bodies. Since loading or stressing takes place during the hold periods, the J-integral should still govern the

* Load (or stress) shedding occurs away from the crack.

strength of the H R R field and, hence, govern the crack-initiation and growth process for this situation. Crack initiation, growth, and instability can, therefore, be characterized within the J-tearing theory and related limitation [6,7]. It is noteworthy in this regard that reasonable predictions are obtained even if the conditions [7] are violated (see ref. [8] and the numerous references cited therein).

3. Simple model-crack driving force for two-dimensional problems

Consider cases where n c < n o and loading ensues at the crack tip during the hold periods; i.e., the stresses at the crack tip increase as creep occurs. Since the continued stressing during the hold time does not constitute a drastic change in loading path at each material point, we may assume that the material does not exhibit memory under these circumstances. Hence, we assume that the stress field that is achieved after loading and subsequent hold at any given instant of time t 1 is not greatly different from that achieved by assuming that, at time t 1, the specimen was loaded assuming time-independent response but with material properties representative of those for the current time. The elastic-plastic time-dependent material response is considered in the following form, which is a variation of the Ramberg-Osgood stress-strain relationship. -- = -- +t~(t 6 f)

(3)

~r0

In this equation, Eo = ~,o/E, where cr0 is an arbitrary reference stress, and a ( t ) and n ( t ) are material parameters that are functions of time. The values of these parameters and their time dependence was a strong function of the steel being characterized [9]. We estimate the time-dependent value of J by analogy to the engineering procedure [10] as jD =Je

+ Jp(t),

jp(t)=a(t)O.oeochl(~o)

n(t)+l

(4)

In eq. (4), c is the uncraeked ligament, P is load, and P0 is a reference load [10]. The time-dependent values for a and n are obtained by developing RambergOsgood constants for isochronous stress-strain curves at discrete instances of time (see ref. [11]).

B.N. Leis, F.W. Brust / Crack-growth analysis The two-dimensional analysis procedure may be summarized as follows. When the specimen is initially loaded, J is estimated with n and a defined for t = 0. Thereafter, o~(t) and n(t) are used in eq. (3) and eq. (4) then used to estimate J for time = t . By time marching, one may estimate J as a function of time until the end of the hold period. If at the end of the hold period more load is applied, the procedure starts over. Theoretical justification and further details are elaborated upon [1,2,4]. In summary, J is calculated by time marching. Crack growth ensues when J = Jic and crack instability occurs when d J / d a > dJR/da. Of course, if global unloading or large amounts of crack growth occur, this assumption is violated and the associated results may be in error. The implications of these assumptions are explained in detail in the references cited previously.

4. Model for axial surface-cracked pipes Because estimation schemes are not available for evaluating J for surface cracks and the class of problems and materials addressed involves time-dependent updating of rather limited plasticity, the primary creep model is based upon a modification of elastic solutions for J. For elliptic surface cracks subjected to tensile loading, detailed compilations of finite-element solutions are readily available in the literature for most flaw geometries of interest here if elastic condition prevail and the surface-cracked pipe can be represented by flat-plate results. Primary creep is included through a time-dependent Irwin estimate of the plastic zone inserted into the elastic solution. Hence the method relies on the small-scale yielding assumption. However, reasonable and conservative predictions result when the method is applied outside this region of strict applicability. The elastic component is written as

2 [Tra'~

Je=O'H(~-){F(a/c,a/t,~b)}2{E/(1-u2)}

1

,(5)

where a is crack depth, 2c is crack length, t is the pipe wall thickness, o-n is the applied hoop stress caused by internal pressure loading, and ~b defines the location along the crack to evaluate Je (see fig. 2 for geometry definition). In eq. (5), Q is the square of the complete elliptic integral of the second kind as approximated [12] in Equations (5a) and (5b).

Q = 1 + 1.464(a/c) 165 for a / c < 1.0

(5a)

Q = 1 + 1.464(c/a) l6s for a / c > 1.0

(5b)

71

Fig. 2. Geometric parameters for part-through-wall flaws

F in Equation (5) was developed using the finite-element alternating method for a pipe R / t ratio of 40 (Stonesifer et al, 1991), which is typical for the gas line pipe of concern here supplemented where valid by fiat-plate results [12]. The time-dependent nonlinear component of J for external axial-surface cracked pipes, J(t), is estimated by including a plastic-zone correction in the elastic solution by analogy to the approach suggested by Kujawski and Ellyin [13], as detailed [1,2,4]. Within that framework, the nonlinear component of J, Jp(t) is given by

Jp(t) = (O'u)2{ Q ~"n'(rp(t)) -~_~2) }{F(a/c, a/t,

4))}2, (6)

where r p ( t ) = rp(n(t), a(t)), the other parameters are defined earlier and the function F is as noted above (see ref. [14]). The value of j-driving force for cracking, denoted as jD, is then found as the sum of eqs. (5) and (6). Finite-elements analyses were performed to examine the appropriateness of the analysis assumptions, which are inherent in the primary creep damage model for surface cracks. As detailed elsewhere [1,2,4], these results indicate the assumptions and simplifications embedded in the time-marching estimation scheme provide reliable engineering estimates of crack driving force. Further assessment of the utility of this simplified scheme follows in comparisons of predictions for a full-scale test, details for which can be found elsewhere (see refs. [15] and [4]). Use of the primary creep crack-growth model within the J-tearing framework requires measures of the material resistance to cracking in the same way as timedependent solutions. The following section outlines how the J-resistance curve, denoted as j R , was determined for this validation study.

B.N. Leis, F.W. Brust / Crack-growth analysis

72

5. Estimation of resistance to flaw growth, j R The behavior of axial through-wall flaws is tracked in terms of j o at the deepest point along the flaw (i.e., where j o is greatest); self-similar growth is assumed elsewhere. It follows that the J-resistance curve must represent the through-wall growth behavior of the steel. Because the database to be used later in the validation study represents pipeline steels, the JR curve must be expressed in terms of parameters commonly used to characterize the behavior of line-pipe steels. Parameters commonly used and available to represent line-pipe steel are flow stress, st, and Charpy-Vee Plateau energy, CVP. As detailed by Leis and Brust [11] and implemented in the current formulation [4], the j R behavior can be correlated with sf and CVP initiation resistance, Jlc, and growth resistance, d j R / d a , for axial growth (i.e., the transverse long (TL) orientation). Behavior of the growth in the through-wall direction (i.e., transverse-short (TS) orientation) can be empirically deduced from the TL response. The average trends derived from available j R behavior of pipe steels lead to the equations of the form FS

Jl~lTs = C1sfCVP [TL, d JR = C2E -1sf. CVP[TL 2 FS da YS

(7)

The values of the correlation constants C l and C 2 can be found from curve fits such as that developed by Leis and Brust [11]. The notation CVP] Fs denotes the full-size Charpy plateau energy in the TL orientation * By virtue of the correlation that underlies these equations and fixes values for C1 and Cz, the CVP value must develop at or below the temperature for which these correlations are applied.

6. Model predictions and validation for creep crack growth Figure 3 presents a typical comparison of predicted and observed flaw initiation, growth, and failure behavior on coordinates of pressure and flaw extension. Note that the predictions are conservative with crack initiation predicted somewhat earlier than the corresponding experimental results. The predicted final crack length is slightly conservative as is the failure pressure.

* Transverse Charpies from unflattened pipe with the notch cut in the through-thickness direction.

Figure 3 shows that much of the crack growth occurs during the hold periods, which means that neglecting time-dependent effects could lead to nonconservative predictions of crack growth and failure. Also shown here as the dashed line labelled time-independent failure pressure is the failure prediction using the empirical equation developed by Kiefner et al [16], where CVP = 32, and the flow stress is 73,700 psi (508 MPa). The method [16], which does not include crackgrowth effects explicitly and ignores time-dependent effects, also underpredicts the failure pressure. Other comparison of observed and predicted flaw growth behavior covering a range of flaw geometries and pressure histories have been made [1,15,4]. These results show that the model generally predicts crack initiation at pressures slightly lower than the experimental initiation pressure.

7. Model validation for surface-cracked line pipe Thus far, the adaptation of the J-tearing to analysis of flaw growth in line-pipe steels has been found to reasonably predict initiation, growth, and failure pressure for a rather limited database. The quality of these predictions can be seen, for example, for a specific geometry and loading in fig. 3. Note that the predictions in fig. 3 represent two different sets of J - R curves. The trend labelled as "low" resistance curve represents the lower bound resistance typical of this class of steel; whereas, that labelled as "high" represents the upper bound typical for this steel. Both sets of resistance curves provide a good indication of the failure pressure. However, only the curve labelled as high resistance closely matches the observed time dependent cracking. The present section broadens the database to further explore the validity of the model. This broadened has involves the application of the model to predict the failure pressure for a wide range of full-scale burstpressure tests using surface-flawed pipe sections. Still further validation data for additional geometries and loadings can be found elsewhere [4]. The database for the present study of validation covers nearly 50 axial part-through-wall (PTW) (i.e., surface cracked) full-scale tests [16]. This database represents steels in Grades X52, X60, and X65, covering the usual C-Mn, as well as high-strength, low-alloy steels in diameters ranging from 14 to 42 inches. Predictions of failure pressure have been made using the present model for cases in this database provided that the failures occurred in the base metal as characterized

B.N. Leis, F.W.. Brust / Crack-growth analysis

73

Crock Growth, mm 0

,,oo1 /,

0.5

IO

i.5

, /

Experiment

High res stonce curve

---

800

Z.O

~8

FoiluIm pred

Trne independent failure pressure . . . . .

~6

Low resistance curve

r,

600 --

O.

g


•

36" x 0.394" (914 x I0 mm) X52 pzpe

•

Flow # 3

g2t tX

(o0=0.298" (Z57 ram))

400--

-- 2 200 --

I

I

I

I

I

I

I

0.01

0.02

003

0.04

00,5

006

0(37

oi o

Crock G m w l h ,

I

o

008

009

inch

Fig. 3. Observed and predicted flaw growth for axial part-through-wall flaws

by the mechanical properties and toughness tabulated with the failure pressures. Specifically, this excludes flaws cut into or growing in the weld line of the pipe. Note that the following validation specifically addresses only straight-away pressure-to-failure (SAPF) full-scale tests.

2400

g

A "~

Since the mix of conditions represented in the fullscale database is shown to be free of bias [4], the data can be pooled and analyzed using average fracture trends for the class of line-pipe steels represented in the pool. The constants in eq. (7) have been calibrated accordingly. The analysis represented by eqs. (5)

1.4

+o"

c/o _<15 • 15 3 0 •

_

2000

• n

1600

•

L2

•

(3_

•

~m

Mean, p. =1.041

1200 > ~

800

o"

400

.Q 0

0

/~-~ 0.9

Q

0.8 (3-

I i

0 0

400

800

1200

1 6 0 0 2000

Observed Foilure Pressure, psi

2400

0.7

I

OI

I

0.2

I

0.3

I

0.4

I

0.5

L

0.6

I

0.7

I

0.8

I

0.9

Q/t

Fig. 4. Predicted flaw growth behavior from load (zero-time) and hold time-dependent phases on a hydrotest

I.O

74

B.N. Leis, F.W. Brust / Crack-growthanalysis

through (7) has been performed with a PC-based computer program. Figure 4 presents the results of predicted and observed failure pressure for the pooled database. Figure 4(a) directly compares failure pressures with the predicted result on the ordinate, Pp, and the observed experimental result on the abscissa, Pc. This figure does not show any particular bias as a function of observed burst pressure nor is there a particular bias in regard to steel grade or processing history evident in a detailed analysis of the scatter in the figure. The mean slope is 1.0415 with a standard deviation of 0.0977. This means that, on average, the model predictions are slightly nonconservative, which, in turn, means that the average J-R behavior is slightly overpredicted by the average trends embedded into the constants in eq. (7). Figure 4(b) shows that there is no bias in the predictions as a function of a/t. That is, the ratio of predicted to observed failure pressure scatters evenly for all values of the abscissa, a/t. Likewise, this figure shows no particular bias as a function of c/a. Finally, while not shown here, these results reasonably fit a normal distribution consistent with the assumption that this pooled experimental database represents an average collection of observed failure pressures for SAPF tests. The absence of bias with respect to a/t, c/a, failure pressure, and steel grade, or processing means that the pooling of data to construct fig. 4a was valid. This means that this pooled dataset could be used as the basis to modify the constants in eq. (7). That is, the "average" based on the limited literature data used in the initial fit of the constants in eq. (7) could be adjusted such that the mean value the ratio of predicted to observed failure pressure is one, Trial-and-error analysis for a case with Pp/Pc = 1.045 shows this adjustment requires a factor of 0.865 applied to both Jk and dJ/da. Such an adjustment gives rise to a mean within 1% of unity for this average database. It follows that the PTW flaw model outlined earlier provides a viable prediction tool for flaw growth in real pipes. Practical use of this validated model requires only CVP and flow stress, along with details of the pipe, the flaw of concern, and the pressure history.

able predictions of experimental data despite possible limitations that could be imposed by the assumptions upon which it is based. Support for the basic formulation for surface flaws in pipes as presented here is evident in the successful predictions of axial-surface crack growth and failure in pipe as compared with the corresponding experimental data developed for the more than 50 short-term fullscale tests used in the validation. Note that the model as presently formulated and validated does not formally include the effects of constraint on surface crack growth. However, this effect is indirectly embedded in the formulation through the use of J-R curves and Charpy data that represent the thickness of the pipe involved. The database used in validating the model represents thin walled pipes and crack aspect ratios typical of gas transmission piping. This database involves surface flaws that show significant bulging as the defect approaches failure. Such bulging causes local bending along the crack front, which in turn minimizes the effects of constraint, that is enhanced by thc higher ratios of pipe diameter to wall thickness and the small values of crack aspect ratio that are emphasized by this database. While apparently not a major factor for the present formulation and validation database, the effect of constraint could be significant in vessels with low diametcr to wall thickness ratios that contain cracks whose length is on the order of their depth. Such combinations of vessel and flaw geometry act to limit local bending along the crack tip and so enhance constraint. Readers faced with such applications are directed to studies that address the issues related to this topic (e.g., ref. [171).

Acknowledgements This work was supported by the American Gas Association under the auspices of the Structural Integrity Subcommittee of the Line Pipe Research Supervisory Committee. The guidance and support of the membership of the Structural Integrity Subcommittee throughout the development of this technology is gratefully acknowledged.

8. Conclusion References This paper has demonstrated the importance of primary creep crack growth via experimental data and the analysis of such growth by a simple engineering model. The simple engineering model provides reason-

[1] F.W. Brust and B.N. Leis, A study of primary creep crack growth at room temperature, Proc. of the 5th International Conference on Numerical Methods in Fracture

B.N. Leis, F. IV.. Brust / Crack-growth analysis

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

Mechanics, ed. A.R. Luxmoore, and D.R.J. Owen, Freiburg, FRG (April 23-27, 1990) pp. 321-332. F.W. Brust and B.N. Leis, A new model for characterizing primary creep damage, Internat. J. of Fracture, 54 (1992) 45-63. F.W. Brust and B.N. Leis, The effects of primary creep on elastic-plastic crack growth, Fatigue, Degradation, and Fracture (1990), Ed. W.H. Bamford et al., ASME publication, PVP-Vol. 1959 and MPC-Vol. 30 (June 1990). B.N. Leis, F.W. Brust and P.M. Scott, Development and validation of a ductile flaw growth analysis for gas transmission line pipe, A.G.A. NG-18 Report No. 193 (June 1991), available from The American Gas Association, Catalog Number L51643. H. Reidel, Creep deformation at crack tips in elasticviscoplastic solids, J. of Mechs. and Physics of Solids 29 (1981) 35-49. J.W. Hutchinson, Fundamentals of the phenomenological theory of nonlinear fracture mechanics, J. of Appl. 50 (1983) 1042-1051. P.C. Paris and J.W. Hutchinson, Stability of analysis of J controlled crack growth, ASTM STP 668 (1979) pp. 3764. F.W. Brust, Approximate fracture methods for pipes: Parts I and II, NUREG/CR-4853 (February 1987); also, two related papers in Nucl. Engng. Des. 127 (1991) 1-31. B.N. Leis, W.J. Walsh and F.W. Brust, Mechanical behavior of selected line pipe steels, A.G.A. NG-18 Report No. 192 (September 1990), available from The American Gas Association, Catalog Number L51624.

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[10] V. Kumar, M.D. German and C.F. Shih, An engineering approach for elastic-plastic fracture analysis, EPRI Report No. NP-1931 (July 1981). [11] B.N. Leis and F.W. Brust, Ductile fracture properties of selected line pipe steels, A.G.A. NG-18 Report No. 183 (January 1990), available from the American Gas Association, Catalog Number L51604. [12] J.C. Newman and I.S. Raju, An empirical stress-intensity factor equation for the surface crack, Engng. Fracture Mechs. 15, Nos. 1-2 (1981) 185-192. [13] D. Kujawski and F. Ellyin, On the size of plastic zone ahead of crack tip, Engng. Fracture Mechs. 25, No. 2 (1986) 229-236. [14] R.B. Stonesifer, F.W. Brust and B.N. Leis, Stress intensity factors for long axial O.D. surface cracks in large R / t pipes, ASTM STPll31 (1992) pp. 29-45. [15] F.W. Brust and B.N. Leis, A model and experimental results of primary creep crack growth at room temperature in surface cracked pipes, accepted for publication in Int. J. of Pressure Vessels and Piping 52 (1992) 273-298. [16] J.F. Kiefner, W.A. Maxey, R.J. Eiber and A.R. Duffy, Failure stress levels of flaws in pressurized cylinders, ASTM STP 536 (1973) pp. 461-481. [17] D.M. Parks, Advances in characterization of elastic-plastic crack tip fields, in: Topics in Fracture and Fatigue (Springer, 1992). [18] J.C. Newman, A review and assessment of the stress-intensity factors for surface cracks, ASTM STP 687, ed. J.B. Chang (1979) pp. 16-42.