A statistical based circumferentially cracked pipe fracture mechanics analysis for design or code implementation

Nuclear Engineering and Design 111 (1989) 173-187 North-Holland, Amsterdam

173

A STATISTICAL BASED CIRCUMFERENTIALLY CRACKED PIPE FRACTURE MECHANICS ANALYSIS FOR DESIGN OR CODE IMPLEMENTATION Gery M. W I L K O W S K I a n d Paul M. S C O T T Batelle, Columbus Division 505 King Avenue Columbus, Ohio 43201-2693, USA

Received 26 May 1988

This paper discusses a simple engineering approach to evaluate surface flaws in carbon steel or stainless steel piping and their weldments. It is based on statistical data from a large number of pipe fracture experiments. To ensure a reasonably conservative approach, a 95-percent confidence level was established. Toughness and pipe size effects are accounted for in one correction factor, while ovalization and flow stress effects are accounted for in two other factors. The limitations and possible improvements to such an approach are also discussed.

1. Introduction This paper discusses a relatively simple statistically based design approach for the evaluation of fracture loads for surface flaws in carbon or stainless steel pipe and their weldments. It is based upon ductile failure occurring rather than cleavage. The approach was first described in the 5th Semiannual Report of the Degraded Piping Program [1]. This is a simpler approach than that being developed in the ASME Section XI code for carbon steels, and considers the effects of ovalization, the actual material strength (if known), and possible use of Charpy energy data to estimate the toughness of the material.

2. Statistical screening criterion for evaluation of the load-carrying capacity of austenitic or carbon steel pipes with flaws The statistical analysis described in this section can be easily implemented in a code, such as ASME Section XI Code or used for design purposes. This general approach is compatible with the current procedure in Article IWB-3640 for austenitic piping [2]. In IWB-3640, the net-section-collapse analysis forms the technical basis for the evaluation of circumferentially cracked stainless steel pipes. For low thoughness stainless steel flux welds, the stress is multiplied by a correction factor ( Z ) in the IWB-3640 analysis to predict the failure stresses.

The Z-factor [3] comes from an analysis using the G E / E P R I J-estimation scheme for a through-wall crack in a pipe. The analysis showed that the correction factor varies with pipe diameter, toughness, and slightly with the through-wall crack length. Since the effect of crack length is negligibly small, the Z-factor in IWB-3640 was simplified to be only a function of the pipe diameter and toughness of the weld. To account for differences in toughness levels between weld procedures, separate equations were developed for shielded-metal arc welds (SMAW) and submerged arc flux welds (SAW). The Z-factor equations are Z = 1.1511 + 0.013(O - 4)]

for SMAW,

(la)

z = 1.3011 + 0.010(D - 4)]

for SAW,

(lb)

where D = outside pipe diameter in inches. Note that for pipe diameters less than 24 inch (610 mm), the Z-factors should be computed based on a value for the outside diameter of 24 inch (610 mm). This requirement is intended to account for uncertainties in the thermal stress contributions for the smaller pipe sizes. The suggested approach in this paper is in the same spirit as the Z-factor correction. For circumferentially cracked pipes, it is based on a simplification of the dimensionless plastic-zone parameter used in the surface crack screening criterion developed as part of the Degraded Piping Program (see ref. [1]). For axially cracked pipes, a stress multiplier is based on the extensive past research by Eiber, Maxey, Kiefner, and Duffy [4-6].

0 0 2 9 - 5 4 9 3 / 8 9 / $ 0 3 . 5 0 © Elsevier Science Publishers B.V. ( N o r t h - H o l l a n d Physics P u b l i s h i n g Division)

G.M. Wilkowski, P.M. Scott / Fracture mechanics analysis

174

The results of the axially cracked pipe research were later verified at MPA-Stuttgart on German materials [7].

95-percent reliability level (i.e., two standard deviations below the average) for data with a dimensionless plastic-zone greater than 1.0. Since we were looking for a 95-percent.reliability level relationship, the average of the yield and ultimate was chosen as flow stress in all of these calculations. The approach here of using the yield and ultimate strength properties of the materials has the advantage of being applicable to both stainless and carbon steels. This is simpler and more accurate than the ASME IWB-3640 approach of defining the flow stress in terms of the design stress, Sm. This is especially true if the approach is applied to Class 1 as well as Class 2 piping where the ASME Code definitions of Sm in terms of yield and ultimate strengths are different. This statistical relation is shown in fig. 1 with a large amount of experimental data. Note that in this figure, the net-section-collapse stress is based on a flow stress defined as the average of the yield and ultimate strengths of the material. In this case, actual material property values for the pipe materials tested were used to calculate the flow stress. From fig. 1 it can be seen that, in general, the circumferential through-wall cracked pipe data are lower than the surface-cracked pipe data. Hence the through-wall crack analysis used to develop the Z-factor in IWB-3640 should yield reasonable lower bound results when applied to surface-cracked pipe.

2.1. Circumferentially cracked pipe analysis basis The analysis of circumferential cracked pipe is based on the plastic-zone screening criterion discussed in section 4 of the Degraded Piping Program's 4th Semiannual Report [8]. This is an empirical curve fit where,

P/P,~c f (plastic-zone size/distance from the crack =

tip to the neutral axis) = f (dimensionless plastic-zone parameter),

(2) where P is applied stress and P,s~ is failure stress predicted by the net-section-collapse analysis (NSC). To apply this analysis one must first define the flow stress. This was done by evaluating those points for which the plastic-zone parameter was greater than 1.0. The average value of the flow stress was 1.16 (Oy + ou)/2. Thus, if the flow stress definition of 1.15 times the average of the measured yield and ultimate strengths of the material, as used in ref. [9], were used, this ratio would approach 1.0. However, using the average of the yield and ultimate strengths corresponded very closely to the

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0.8

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15 20 25 30 35 40 DimensionlessPlastic Zone Parameter Fi B. ]. Compiled data using exact dimensionless plastic-zone parameter and flow stress = (Oy + %)/2.

G.M. WilkowskL P.M. Scott / Fracturemechanics analysis One exception to the general data trend shown in fig. 1 is a 6-inch (152-mm)-diameter SA-376 TP304 stainless steel pipe with a SAW. The data point for this particular experiment in fig. 1 is shaded. This specimen failed at a stress approximately 30% below what one might predict based on the average of the surface-cracked pipe data. The crack in this particular pipe had a fracture surface which was very flat and exhibited less ductility than the other SAW pipe experiments. (Note that the test specimens for the SAW pipe experiments were all fabricated at the same time using the same weld procedure.) Since welds are typically quite variable in their fracture toughness, the fact that this one 6-inch (152mm)-diameter specimen exhibited significantly less ductility should not be completely unexpected. In fig. 1, it can be seen that the failure load for this experiment would correspond to the average surface-cracked pipe failure locus, if the value of Ji were a factor of three to four lower. This variability in weld thoughness appears possible, and is supported to some degree by C(T) specimen tests at DTNSRDC [10] where one specimen gave a very low J-R curve. Included in fig. 1 are four curves. For the lowest curve the function ( f ) of eq. (2) is expressed in terms of a ln-sec equation as follows: Dimensionless Plastic Zone Parameter (DPZP) = In sec or

P -- 2 arc cos [e - DPZP]. Pn~c ~r

(3b)

Examining fig. 1, one can see that the use of this ln-sec expression would result in a very conservative assessment of the load-carrying capacity of a pipe with a through-wall crack and an even more conservative assessment of the load-carrying capacity of a surfacecracked pipe. In order to reduce the extent of this conservatism, the dimensionless plastic-zone parameter was multiplied by a factor C, as shown in eq. (4). 2 arc cos [e- -e = -Pnsc nr

C(DPZe)].

(4)

The C factors were selected based on a statistical fit of the data. The three upper curves in fig. 1 are for three different values of C based on three different statistical fits of data. The uppermost dotted curve is an average fit of all the surface-cracked pipe data to this ln-sec expression. The value of C for this curve is 21.8. The

175

dashed curve is the average fit of all the through-wall cracked pipe data to this ln-sec expression. The value of C for this curve is 4.62. The solid curve is the 95-percent reliability level curve for all the data for which the dimensionless plastic-zone parameter was less than 1.0. The value of C for this curve is 3.0. This reliability level corresponds to two standard deviations below the average from the nonlinear regression analysis. The rationale for restricting this data set to those points for which the dimensionless plastic-zone parameter was less than 1.0 is that if the plastic-zone parameter is greater than or equal to 1.0, then fully plastic conditions should exist and the net-section, collapse analysis should be appropriate. This is evident by the fact that, with one exception, for all of the data shown in fig. 1 for which the dimensionless plastic-zone parameter was greater than 1.0, the maximum experimental stress was greater than the net-section-collapse stress. Furthermore, when the P/Pnsc expression (which asymptotically approaches 1.0) was fit to the data in the region where the dimensionless plastic-zone parameter was greater than 1.0, a rather significant standard deviation resulted. Because of this relatively large standard deviation, the 95-percent confidence level curve was relatively low. In order to reduce the extent of conservatism associated with this analysis, it was felt that it was justified to restrict the statistical data set to those points for which the dimensionless plastic-zone parameter was less than 1.0. In doing so, the standard deviation was reduced and the 95-percent reliability level curve was brought closer in line with the experimental data. In order to use this analysis procedure, this dimensionless plastic-zone parameter needs to be calculated. For through-wall cracked pipe in pure bending, this plastic-zone parameter is Plastic-Zone=( Parameter

EJi I / ( ' r r - a ) D 2,~o2 ] / \ 4

(5a)

and for surface-cracked pipe in pure bending, it is ,as iczo e Parameter =

~

~-

.

(5b)

For surface-cracked pipe under pressure and bending, it is

Plastic-Zone Parameter

(5c)

176

G.M. WilkowskL P.M. Scott / Fracture mechanics analysis

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3o 2EJ i Simplified Dimensionless Plostic-Zone l~r(lrneter, 72o.f2 D

1

3.5

40

Fig. 2. Compiled data using simplified dimensionlessplastic-zone parameter and flow stress = (oy + ou)/2.

The pressure or axial membrane component of stress for nuclear piping in eq. (5c) is generally quite small, hence it simplifies to eq. (5b). For typical crack sizes which may be found in nuclear power plant piping, the terms {[~r+ ( d / t ) a ] / r r } {D~r/4) and ((~r- a ) / 4 ) D found in eqs. (5b) and (5a), respectively, approach { D~r/4}, so eqs. (5a), (5b) and (5c) simplify to eq. (6).

in terms of Sm. The correlation between Sm and actual flow stress is a statistical one. For instance, in fig. 2 flow stress was defined as o r = (oy + 0 , ) / 2 .

(7)

The data in fig. 1 used the actual dimensionless plasticzone parameter, whereas fig. 2 shows the same data using the simplified parameter. In fig. 2 the value of C was 3.4 for the 95-percent reliability level fit using the simplified dimensionless plastic-zone parameter.

This flow stress definition is representative of the 95percent reliability level of the data in figs. 1 and 2. For these data, tensile test data were available at the pipe test temperature for each pipe tested. The suggested procedure deviates from the IWB-3640 approach in that eq. (7) is used to define the flow stress rather than 3Sm. This has the advantage that if actual material property data (not representative data) are known for a particular heat, then actual values could be used rather than the ASME Section III Code values at the service temperature.

2.1.1. Flow stress considerations One of the pararnetes critical to both the netsection-collapse analysis and the simplified plastic-zone parameter approach is the flow stress of the material. In IWB-3640, the flow stress was defined as 3Sm, where Sm is the ASME design stress. This was done for convenience since stresses in the IWB-3641 Tables were defined

2.1.2. Pipe ovalization Another possible correction is for the ovalization of the pipe under bending. Fig. 3 shows that the net-section-collapse load overpredicts the pipes load-carrying capacity as the R / t ratio increases. This is a linear function. To account for the fact that there will be a

2EJ i Simplified Plastic-Zone Parameter (SPZP) - ,~2ofzD .

(6)

G.M. Wilkowski, P.M. Scott / Fracture mechanics analysis

177

1.25 ,,~ll~,,,,,,,,,,,,jl~. _s5 07

oru

squares fit through the data points have a value of the screening dirnensionless parameter greater I 0 (Solid poin|$>lO)

~Least /whlch /criteria ~ t h a n

~

too-

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D.~ ~

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_~ 0 5 0 0 0 0

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Stainless steel Carbon steel Starnless steel SAW

0.25 -

000

0

I

5

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I0 Meqn Pipe Radius/Pipe Wall Thickness

I

15

20

Fig. 3. Ratio of the maximum experimental load to the net-section-collapseload as a function of the ratio of the mean pipe radius to the pipe wall thickness. (Surface-crackedpipe data only, with d / t = 0.65 and 2 c/IrD = 0.5.)

reduction of the ovalization correction with increasing membrane stress, Pro, the ovalization correction is approximated as M v = 1 + [0.25 - O . 0 3 2 ( R / t ) ] [ P b / ( P m + Pb)].

(8)

2.1.3. Toughness data In fig. 2, the toughness at crack initiation (Ji) from a C(T) specimen is used. This is the toughness of that particular pipe or heat, not of representative material. (Representative material can give erroneous values since the toughness can change by more than a factor of four depending on the fabrication history or inclusion content.) The J-integral values at crack initiation (Ji) were used, even though they were not valid Jlc values by ASTM criteria. Additionally, to keep geometry effects minimized, C(T) specimens having at least 80 percent of the pipe thickness were used. All specimens were in the L - C orientation and had no side-grooves. Finally, the largest platform-sized C(T) specimen that could be machined from the pipe, with the 80-percent thickness requirement, was used. The larger planform-sized specimens are preferred since too small a C(T) specimen can sometimes give a much higher J - R curve than a large specimen [11,12].

In the absence of Ji data, Charpy V-notch plateau (CVP) energy data could be used. Fig. 4 shows a comparison of Ji and CVP energy. The linear correlation in the figure gives a reasonable lower bound. This is discussed later in this paper. For many carbon steel pipes, however, the Charpy data might be in the transition region. If the shear area percent is known, then the plateau energy can be estimated by a simple ratio as is shown in figs. 5a and 5b. Fig. 5a presents a large amount of data from Maxey [13] for carbon steel line-pipe materials. Fig. 5b presents Charpy data for nuclear grade carbon steels from this program. The nuclear pipe material data agree well with the scatter band of line-pipe steel data. This gives high confidence in the linear data trend. If Charpy energy is known, but the shear area percent is not, then that Charpy energy could be used as a lower bound estimate of the plateau energy. If neither Ji nor CVP is known, then guidelines need to be developed for lower bound values. The NRC Piping Fracture Mechanics Data Base at Materials Engineering Associates [14] should be useful in this effort. In developing such a lower bound guideline, it may be useful to also correlate the Ji to the flow stress. Frequently, the lower toughness materials will have a higher

G.M. Wilkowski, P.M. Scott / Fracture mechanics analysis

178

Charpy Upper Shelf Energy, CVP, joules 50 -tOO 150

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600

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Charpy Upper Shelf Energy, CVP, ft-lb Fig. 4, Jlc versus Charpy V-notch plateau energy for several ferritic piping steels.

flow stress. The higher flow stress will increase the failure load.

where Mp~ = -2 arc cos [e_ 3ASPZp],

11"

2.2. Proposed formulation for circumferentially cracked pipe

(Sy '~ S u )actual

(10)

Mf = (Sy -~- Su )code tables ' The c o m b i n e d circumferential crack correction, M c, for toughness, geometry, a n d flow stress, is given below. Actual Failure Load M~ = Net-Section-Collapse Load * = MpzMfMv'

(9)

* The net-section-collapse load is calculated using code values for Sy and S, and a flow stress definition of the average of Sy plus S o.

My = ] + [0.25 -

O.032(R/t)][Pb/(Pm + P h ) ] .

If (Sy a n d Su)actual are u n k n o w n , then M r = 1.0. If the actual strengths are k n o w n they must also be used to calculate Mpz. Therefore, all that needs to be done to the current IWB-3641-1 a n d -2 Tables is to define the stress ratio as Stress ratio = 3 ( S F ) ( P r n + Pb + P E / S F ) SnowMc ,

(11)

G.M. Wilkowski, P.M. Scott / Fracture mechanics analysis

degree of confidence since a large pipe fracture data base was used in its development.

Natural Gas Line-Pipe Steels 120 11o

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Charpy Energy/Charpy

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Degraded Piping Program ig.@,

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Fig. 5. Correlation between Charpy V-notch energy and shear area percent to predict the plateau energy of carbon steels; (a, top) natural gas line-pipe steels, (b, bottom) nuclear piping materials from the Degraded Piping Program.

[ :.-:',=" / . 4

where S n o w = ( S y + S , ) / 2 using values in Section III of the ASME Code, SF -- Safety factor for the specific table (Note in table 1 the safety factor is included in calculating the table flaw sizes. If using the source equations, then the safety factor needs to be included in the stress ratio), P~ - axial membrane stress, Pb = bending stress, PE = thermal expansion stresses. This simple change will give reasonably accurate predictions without extensive calculations, and will give a high

0

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Fig. 6. Comparison of experimental data to Maxey, Kiefner, Eiber, and Duffy data [4-6]; (a, top) full-scale axially cracked pipe results compared to predictions using Charpy Plateau Energy, (b, bottom) relationship between Gc and Charpy shelf energy.

G.M. Wilkowski, P.M. Scott /Fracture mechanics analysis

180

Table 1 Example of modification to ASME Table IWB-3641-1 Allowable end-of-evaluation period flaw depth ~) to thickness ratio for circumferential flaws-normal operating (including upset and test) conditions. Stress ratio b)

Ratio of flaw length, If, tO pipe circumference c)

1.5 1.4 1.3 1.2 1.1 1.0 0.9 0.8 0.7 _< 0.6

0.0

0.1

0.2

0.3

0.4

>/0.5

d)

d)

d)

d)

d)

d)

0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75

0.40 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75

0.21 0,39 0,56 0.73 0,75 0,75 0,75 0.75 0.75

0.15 0.27 0.40 0.51 0.63 0.73 0.75 0.75 0.75

d) 0.22 0.32 0.42 0.51 0.59 0.68 0.75 0.75

d) 0.19 0.27 0.34 0.41 0.47 0.53 0.58 0.63

a) Flaw depth= a n, for a surface flaw, = 2a n for a subsurface flaw, t = nominal thickness. Linear interpolation is permissible. 3 ( P m + Pb + PE/2.77) b~ Stress ratio =

McSflow Pm= primary longitudinal membrane stress (Pro-< 0.5 Sin), Pb = primary bending stress, SnoW =(Sy + S u)/2 from code tables,

Mc

=MpzMrMv,

Mf Mpz SPZP E Ji

=(Sy q- Su) ..... l/(Sy -1- Su)Code tables" (Mr = 1 if actual Sy and S u values are unknown), =(2/qr) arc COS [e-34~sezPq, =2EJi/(Tr2S2owD ), = elastic modulus, = J at crack initiation if known, otherwise use Charpy energy correlation if Charpy data are available, or use lower bound values if no data are available,

M,.

=l+[0.25--O.032(R/t)l[Pb/(Pm+ Pb)].

c) Circumference based on nominal pipe diameter. d) IWB-3514.3 shall be used.

d a t a to the e q u a t i o n below. 12(CVP) E~

Ac8CS2ow

[ [ 'rrMsPm ] ] Insec - t [ 2Snow l /

(12)

where = C h a r p y V - n o t c h p l a t e a u energy (ft-lb), CVP = elastic m o d u l u s (psi), E = c r o s s - s e c t i o n area of t h e C h a r p y s p e c i m e n Ac (0.12375 in z for a full-size s p e c i m e n ) , = total axial crack l e n g t h (in.), 2c = p r i m a r y m e m b r a n e or h o o p stress (psi), em S flow = flow stress (psi), M~ = surface crack b u l g i n g factor-[1 - d / ( t M T)]/[1 -

d

d/t],

= surface crack d e p t h ,

t = p i p e thickness, MT = [1 + 1.255 ( c 2 / R t ) - 0.0135 (c2/Rt)2] °5, R = p i p e radius. Eq. (12) c a n b e t u r n e d into a simple stress multiplier. T h e e q u a t i o n b e l o w gives this relation w h e r e the stress m u l t i p l i e r M~ is

Ma -

Snow

2( [(3ÂÂ

~

arc sec exp

2cA~Sn2ow

.

(13)

T a b l e s IWB-3641-3 a n d IWB-3641-4 c o u l d simply b e m o d i f i e d b e d e f i n i n g a stress ratio, SR, as Stress R a t i o = 3(SF) Pm

SnowMa "

(14)

G.M. Wilkowski,P.M. Scott / Fracturemechanicsanalysis

181

Table 2 Example of modifications to ASME Table IWB-3641-3 Allowable end-of-evaluation period flaw depth a) to thickness ratio for axial flaws - normal operating (including upset and test) conditions Stress ratio b _< 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Nondimensional flaw length c) (l~/~/~) 0.0

0.5

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

11.0

>/12.0

0.75 0.75 0.75 0.75 0.75 0.75 d)

0.75 0.75 0.75 0.75 0.75 0.70 d)

0.75 0.75 0.75 0.73 0.62 0.42 d)

0.75 0.72 0.64 0.53 0.40 0.23 d)

0.74 0.65 0.55 0.44 0.32 0.17 d)

0.70 0.61 0.51 0.40 0.28 0.15 d)

0.68 0.59 0.49 0.38 0.26 0.14 d)

0.67 0.58 0.48 0.37 d) d) d)

0.66 0.57 0.47 d) d) d) d)

0.65 0.56 d) d) d) d) d)

0.64 0.55 d) d) d) d) d)

0.64 d) d) d) d) d) d)

0.64 d) d) d) d) d) d)

d) d) d) d) d) d) d)

Notes: a) Flaw depth= a n for a surface flaw, = 2 a , for a subsurface flaw. Linear interpolation is permissible. b)

3PD ] Stress ratio = [ (__~_t )/( SnowMa) ,

where P = maximum pressure for normal operation conditions, D = nominal outside diameter of the pipe, t = nominal thickness, Silo w

= ( S y -[- S u ) / 2 ,

Ma

=(~r/2)(arcsec[exp(

8~rE(CVP) ] ]

lfA~Snow ]1)'

E = elastic modulus, CVP = Charpy V-notch plateau energy (ft-lb), Ac = cross-sectional area of Charpy specimen (0.12375 in2 or 80 mm 2 for full-size specimen), c) If = end-of-evaluation period for flaw length, r = nominal radius of the pipe, t = nominal thickness. d) IWB-3514.3 shall be used. A n example is given in table 2, where the safety factor (SF) is already included in calculation of the tables. If the source equations are used, t h e n the safety factor m u s t b e included in the stress ratio. Note that if for some reason only Jic data are available a n d not C h a r p y data, the linear relation in fig. 4 m a y give too high a C h a r p y plateau energy. Instead, a n u p p e r b o u n d of these data should be used to calculate a lower b o u n d C h a r p y plateau energy. The relation below is one possibility. CVP = Ji/23,

(15)

where C V P is in ft-lb a n d Ji is in i n - l b / i n 2.

4. Limitations of statistical analysis method T h e statistical analysis m e t h o d presented here is a relatively simple m e t h o d for engineering design proce-

dures. T h e r e are, however, several limitations which should be considered. Some of these are discussed below.

4.1. Limitations on the use of Jk and Charpy energy correlations The a p p r o a c h used to define the effect of toughness involved using a single parameter, J I c " Even though an initiation toughness p a r a m e t e r h a d been used, the statistical evaluation of the pipe fracture experiments examined the m a x i m u m loads r a t h e r t h a n the initiation load. U s i n g a single toughness p a r a m e t e r has obvious simplicity advantages over a procedure that uses the entire fracture resistance curve of the material. This is a n engineering a p p r o a c h t h a t is useful since generally as the initiation toughness increases then the crack growth resistance toughness also increases. This has been shown for pressure vessel steels where correlations have been

182

G.M. Wilkowski, P.M. Scott / Fracture mechanics analysis

developed between Charpy plateau energy and J - R curves [14]. If piping materials show drastically different d J / d a values during crack growth for the same J[~, then the statistical approach shown here could be in error, either conservatively or noncorservatively depending on the unique behavior of the material.

from other investigators have shown that at 482°F (250°C), the Charpy plateau energy correlation to Jlc is lower than shown in our work, i.e., the correlation constant is 5 rather than 6 as shown in fig. 4 [19]. In this case, the J]c of the carbon steel was lowered by a factor of approximately two by dynamic strain-aging. Of even greater concern was the recent results on A106 Grade B pipe where the Jic decreased from 1714 i n - l b / i n2 (300 k J / m 2) at room temperature to 286 i n - l b / i n2 (50 k J / m 2) at 536°F (280°C) (see ref. [20]). This was a drop in tougness of a factor of six, which is larger than previously reported by any other investigators. At this time the Charpy data for that steel is not known. In addition to the decrease in initiation toughness, at temperatures of approximately 100 o F (55 o C) above the minimum initiation toughness temperature, it has been observed that the crack growth resistance toughness decreases. This toughness decrease is due to crack instabilities that are believed to be induced by dynamic strain-aging [18]. Such instabilities have occurred in laboratory specimens as well as in pipe fracture experiments. Fig. 7a shows results from a C(T) specimen, while fig. 7b shows results from a through-wall-cracked, 28-inch (711-mm) diameter, carbon steel, pipe test at 550°F (288°C). The dynamic crack jumps correspond to the sudden decrease in load. Fig. 8 shows more significant effects of dynamic strain-aging induced crack instabilities. In fig. 8a, the crack instability occurred in a carbon steel weld single-edge notched tension test simulating radial growth of an internal surface crack at

4.2. Concerns about the effect of dynamic strain-aging A second point of concern involves the use of Charpy energy to evaluate the toughness of carbon steel piping at LWR temperatures. The Charpy energy correlation shown in this paper assumes that the Charpy plateau (upper shelf) energy, which may be determined close to room temperature, is directly related to the J~c of the material at service temperatures. A lower bound relation between Charpy plateau energy and J~c was shown in fig. 4 for our data and limited data from other investigators. The significant scatter to these data is not fully understood yet, but may be due to dynamic strain-aging effects as well as differences in strainhardening. A major concern with the Charpy energy approach has to deal with the effect of dynamic strain-aging on the fracture toughness of nuclear grade carbon steels at operating conditions [18]. From the data in the Degraded Piping Program, we have seen that dynamic strain-aging can lower the initiation toughness, Ji, of some carbon steels by a factor of two in the temperature range of 250 to 400°F (121 to 204°C). Recent data

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G.M. Wilkowski, P.M. Scott / Fracture mechanics analysis

550°F (288°C). In this case, the instability occurred at crack initiation without any prior stable ductile crack growth. Fig. 8b shows the recent results from a test at David Taylor Naval Ship Research and Development Center on a carbon steel TIG weld in A106 Grade B pipe at 550°F (288°C) [21]. In this experiment, there was sufficient stable ductile crack growth to reach the maximum load, but an instability occurred which resuited in the crack growing halfway around the pipe

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and the load decreasing to 54% of the maximum load. This occurred in a low compliance pipe test, so that the dynamic crack growth was due mainly to a metallurgically induced instability believed to be from dynamic strain-aging. The above results come from observations on quasistatic fracture tests. Dynamic strain-aging is well known to be not only sensitive to temperature but also strain rate. Fig. 9 shows such effects as observed from serrations on tensile tests at various temperatures and strain rates. Note that at 288°C and a strain rate of 10 -4, the bulk of the steel may be below the dynamic strain aging region. However, the crack tip is at a higher strain rate which could be in the dynamic strain-aging sensitive region. This perhaps explains why at 550°F (288°C) the dynamic crack jumps occur; that is, at 550°F (288°C) the crack tip is at a higher strain rate and may be in the dynamic strain-aging susceptible region. This brings up an interesting question about the fracture behavior that would occur at seismic rates. Seismic loading rates are approximately four orders of magnitude higher than quasi-static loading rates. At these higher rates, it is possible that some materials may be pushed above the dynamic strain-aging region, while others may experience dynamic strain-aging effects at seismic rates. This same strain-rate sensitivity aspect of dynamic strain-aging is what makes the Charpy test misleading even if it was conducted at LWR tempera-

184

G.M. Wilkowski, P.M. Scott / Fracture mechanics analysis

tures. The Charpy test is an impact test with a blunt notch rather than a sharp crack, hence the crack tip strain rates are much different than service loading rates. As a result of these observations, there is concern over generally applying the Charpy energy correlation to all carbon steel piping. A statistical correlation between chemical composition of carbon steels (free nitrogen and carbon in particular since they are responsible for dislocation pinning) and toughness degradation at LWR temperatures and strain rates is needed to validate which carbon steels can use Charpy energy correlations safely.

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In the approach described, an empirically derived ovalization correction was used. This correction function, M v, was developed from a large base of surfacecracked pipe fracture data. It was based upon experiments on pipe with similar dimensionless flaw geometries ( d / t = 0 . 6 5 and 2 c = h a l f of the pipe circumference). This correction was developed using data where the pipe toughness should be sufficient for fully plastic conditions to occur. Although we termed it an ovalization correction, it fundamentally includes any corrections to the net-section-collapse analysis. This was well ordered with the pipe R / t ratio. It is probably also a function of the crack geometry. For instance, there are several papers where for pipe in pure bending with short surface-crack lengths the net-section-collapse load was found to overpredict the actual failure load [23,24]. Consequently, M v may also be a function of the crack size. In the absence of such a correlation, the M v function should be used, especially for pipes with R / t ratios greater than 7. 4.4. Effects of surface crack size on toughness correction parameter, Mpz

The correction for surface-crack length due to ovalization as noted above is applicable to the limit-load solutions, i.e., the M v parameter. In addition, there may be a correction on the toughness parameter, Mr,z, due to crack size. The approach employed in developing the Mpz parameter was similar to the concept used in the ASME IWB-3640 analysis for low toughness stainless steel weld corrections. In that approach, the Z-factor is a toughness correction on the net-section-collapse predicted load. The Z-factor comes from a through-wall-

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cracked pipe analysis procedure which is not very sensitive to the crack length. Since the development of the statistical approach, two finite length surface-cracked pipe analyses were developed and evaluated as part of the U.S. NRC Degraded Piping Program [25]. These procedures calculate an equivalent stress along the surface crack so that the E P R I / G E tension-loaded 360-degree surfacecracked pipe solutions can be used. New H, and G, functions were developed in place of the E P R I / G E h-functions. These incorporate the following variables: R / t , d / t , crack length, and the strain-hardening exponent of the material. Both a thin-wall solution, SC.TNP, and a thick-wall pipe solution, SC.TKP, were developed.

G.M. WilkowskL P.M. Scott / Fracture mechanics analysis Comparisons of the thin-wall, SC.TNP, and the thick-wall solutions, SC.TKP, to experimental data are shown in fig. 10. The thin-wall pipe solutions tends to overpredict the failure loads as the R / t ratio increases. The thick-wall pipe solution consistently underpredicts the failure loads independent of the R / t ratio. These results were for cracked pipes under bending with the crack length equal to half of the pipe circumference and the depth of the crack approximately 65% of the thickness. To evaluate the effect of crack length, the thick-wall solution was used for pipe under pure bending and with a constant depth of 66% of the pipe thickness. The results in fig. 11 show that as the crack length decreased the predicted bending loads at failure became closer to the net-section-collapse predicted loads. Hence using the longer crack solution to determine the effect of toughness on the failure loads would be conservative in this case. The finite length surface-cracked pipe analysis procedure, however, is currently developed only for pipes in pure bending. Modifications to the SC.TKP and SC.TNP analyses can be made for tension and combined bending, but are not in place at this time. To evaluate the effect of axial membrane stresses, experimental dat from ref. [4] were compared to the net-section-collapse analysis predictions. The data in fig. 12 show that as the surface-crack length decreased from 100% to 25% of the circumference, the failure stress

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relative to the net-section-collapse predicted failure stress decreased significantly. This decrease was approximately a factor of three. For crack lengths shorter than 25% of the pipe circumference, the failure loads should eventually approach the net-section-collapse predicted loads. Hence, for axial tension stresses the effect of surface-crack length on the predicted failure stresses is more complicated than for the pure bending case. The above discussion shows that the lengths of the surface crack can affect the actual failure stresses. This effect is a complicated function of the crack length and the magnitude of tension and bending loads. Until further studies are conducted, such effects can be accounted for by taking a conservative evaluation using existing data as was done by using the 95-percent reliability bounding solution.

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and conclusions

The statistical plastic-zone screening criteria approach described in this paper is a simple method that can be used for evaluation of the maximum load-carrying capacity of both carbon steel and stainless steel pipes with surface cracks. Since it is a simple method, it needs to conservatively account for more complicated effects. Of the limitations discussed in Section 4 of this paper, perhaps the factor of greatest concern that may give nonconservative results is the effect of dynamic strain-aging on the toughness of carbon steel base metals and welds. This effect is especially important if Charpy

186

G.M. Wilkowski, P.M. Scott / Fracture mechanics analysis

energy data is to be used to estimate the toughness of the steel. A screening criteria to assess which carbon steels are sensitive to dynamic strain-aging toughness degradation may be needed before the Charpy energy approach is appropriate to use for all carbon steels.

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thickness, Z-factor stress multiplier used in IWB-3640, half of circumferential crack angle, flow stress using actual properties, actual ultimate strength, actual yield strength.

Acknowledgement References

This work was based upon results from the U.S. N R C Degraded Piping Program. That program is funded by the Materials Engineering Branch of the Office of Nuclear Regulatory Research. Mr. Michael Mayfield is the N R C Program Manager.

Nomenclature h c c

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cross-sectional area of a Charpy specimen, half crack length, constant in statistical analysis, Charpy V-notch plateau energy, surface crack depth, outside pipe diameter, dimensional plastic-zone parameter, elastic modulus, initiation toughness define by ASTM E813, initiation toughness not necessarily meeting ASTM E813 requirements, stress multiplier for axial cracks, stress multiplier for circumferential cracks, stress multiplier accounting for actual flow stress, stress multiplier for plastic-zone parameter, stress multiplier for bulging in axial surfacecracked pipe, stress multiplier for bulging in axial throughwall cracked pipe, stress multiplier for ovalization, pressure, primary stress, primary membrane stress, thermal expansion stress, primary membrane stress, failures stress predicted by net-section-collapse analysis, mean radius, inside radius, flow stress using Code properties, ASME design stress, simplified plastic-zone parameter, safety factor,

[1] G.M. Wilkowski and others, Degraded Piping Program Phase II, Semiannual Report, April 1986-September 1986, by Battelle's Columbus Division, NUREG/CR-4082, BMI-2120, Vol. 5, See Section 4.1. [2] 1983 ASME Boiler and Pressure Vessel Code, Section XI - Rules for Inservice Inspection of Nuclear Power Plant Components, Article IWB-3640, Evaluation procedures and acceptance criteria for austenitic piping. [3] ASME Section XI Task Group on Pipe Flaw Evaluation: Evaluation of flaws in austenitic piping, EPRI Report NP-4690-SR (July 1986). [4] R.J. Eiber, W.A. Maxey, A.R. Duffy and R.J. Atterbury, Investigation of the initiation and extent of ductile pipe rupture, BMI Report 1908 from Battelle to the AEC (June 1971). [5] J.F. Kiefner, W.A. Maxey, R.J. Eiber and A. Duffy, Failure stress levels of flaws in pressurized cyfinders, Progress in Flaw Growth and Fracture Toughness Testing, ASTM STP 536 (1973) 461-481. [6] W.A. Maxey, J.F. Kiefner, R.J. Eiber and A. Duffy, Ductile fracture initiation, propagation, and arrest in cylindrical vessels, ASTM STP 514 (1972) pp. 70-81. [7] D. Sturm, W. Stoppler, P. Julisch, K. Hippelein and J. Muz, Fracture initiation and fracture opening under light water reactor conditions, Nucl. Engrg. Des. 72 (1982) 81-95. [8] G.M. Wilkowski and others, Degraded Piping Program Phase II, Semi-annual Report, October 1985-March 1986, by Battelle-Columbus Laboratories, NUREG/CR-4082, Volume 4 (July 1986) see pages 4.1-4.12. [9] M.F. Kanninen and others, Instability predictions for circumferentially cracked Type 304 stainless steel pipes under dynamic loading, by Battelle Columbus Laboratories, EPRI Report NP-2347 (April 1982). [10] J. Gudas, J - R curve characterization of piping materials and welds, Ninth Water Reactor Safety Research Information Meeting, Gaithersburg, Maryland, October 1981. [11] M. Nakagaki, C. Marschall and F. Brust, Analysis of cracks in stainless steel TIG welds, NUREG/CR-4806 (December 1986). [12] G.M. Wilkowski, et al., Degraded Piping Program - Phase II, Semiannual Report, October 1985-March 1986 by Battelle-Columbus Laboratories, NUREG/CR-4082, Volume 4,(July 1986) see pg. 3-62. [13] W.A. Maxey, J.F. Kiefner and R.J. Eiber, Brittle fracture arrest in gas pipelines, Battelle Report for the American

G.M. Wilkowski, P.M. Scott /Fracture mechanics analysis

[14]

[15]

[16]

[17]

[18]

[19]

[20]

Gas Association Report L51436 (April 1983) [American Gas Association, 1515 Wilson Boulevard, Arlington, Virginia 22209.] F.J. Loss, Ed., Structural integrity of water reactor pressure boundary components, NUREG/CR-3228, MEA2051, Vol. 2, U.S. Nuclear Regulatory Commission (September 1984). E. Fortner, Toughness of SA-106 Grade C carbon steel pipe, LR:82:2295-02:01, Babcock and Wilcox, Alliance, Ohio (April 27, 1982). M.G. Vassilaros, R.A. Hays, J.P. Gudas and J.A. Joyce, J-integral tearing instability analyses for 8-inch diameter ASTM A106 steel pipe, NUREG/CR-3740, U.S. Nuclear Regulatory Commission (April 1984). A.D. Wilson, The influence of inclusions on the toughness and fatigue properties of A516-70 steel, ASME Trans., J. Engrg. Mater. and Technol. 101 (July 1979) 265. G.M. Wilkowski and others, Progress and Results from the Degraded Piping Program - Phase II, Proceedings of the Fourteenth Water Reactor Safety Information Meeting, NUREG/CP-0082, Vol. 2 (February 1987). B. Mukherjee, Fracture resistance of SA106B seamless piping and welds, presented at LBB Workshop, Tokyo, Japan, Nucl. Engrg. Des. 111 (1989), in this issue. P.P. Milella, C. Maricchiolo and A. Squilloni, Pipe frac-

[21]

[22]

[23]

[24]

[25]

187

ture behavior of carbon steel at room temperature and 300 o C, presented at LBB Workshop, Tokyo, Japan, Nucl. Engrg. Des. 111 (1989), in this issue. Private Communication of Research Results from R. Hays on David Taylor Naval Ship Research and Development Center, May 1987, to be published in a future NUREG report. A.S. Keh, Y. Nakada and W.C. Leslie, Dynamic strain aging in iron and steel, in: Dislocation Dynamics, A.R. Rosenfield et al., eds. (McGraw-Hill, New York, 1968) pp. 381-408. K. Shibata and S. Miyazono, Progress of ductile pipe fracture test program at JAERI, presented at the LBB Seminar: Progress in Regulatory Policies and Supporting Research, Tokyo, Japan, May 15, 1987, NUREG/CP-0092 (March 1988). G.M. Wilkowski and R.J. Eibdr, Evaluation of tensile failure of girth weld repair grooves in pipes subjected to offshore laying stresses, ASME Journal of Energy Technology (March, 1981) pp. 48-57. P.M. Scott and J. Ahmad, Experimental and analytical assessment of circumferentially surface-cracked pipe under bending, Report by Battelle's Columbus Division, NUREG/CR-4872 (May 1987).