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Elastic-plastic finite element analyses of stable crack growth and fracture instability in a girth welded pipe
Nuclear Engineering and Design 89 (1985) 283-293 North-Holland, Amsterdam
283
ELASTIC-PLASTIC FINITE ELEMENT ANALYSES OF STABLE CRACK A N D F R A C T U R E I N S T A B I L I T Y IN A GIRTH W E L D E D PIPE J.W. CARDINAL,
GROWTH
E.Z. POLCH, P.K. NAIR, and M.F. KANNINEN
Engineering and Materials Sciences Division, Southwest Research Institute, San Antonio, TX 78284, USA
Received 18 April 1985
Detailed elastic-plastic finite element fracture mechanics analyses were conducted on a 16 inch diameter Type 304 stainless steel pipe containing a circumferential through-wall crack located in a girth weld. Calculations were performed to analyze the welded pipe treated as (1) a monolithic pipe entirely composed of the base metal, and (2) a composite of base metal and weldment. In the latter, each constituent was assigned distinct mechanical and fracture properties. In both solutions applied J values were calculated for a fixed axial load combined with a monotonically increasing applied bending moment. The material J-resistance curves appropriate for the two problems were each used to initiate and grow the initial crack in a stable manner until fracture instability occurred under load control. It was found that the extent of stable crack growth and the applied loads at fracture instability are distinctly different in the two analyses. It is concluded that more precise fracture mechanics approaches than those now in current use are required for accurate assessments of weld cracking problems.
1. Introduction Because nuclear plant piping systems employ materials that are ductile and tough, linear elastic fracture mechanics techniques will not usually suffice for fracture assessments when cracks are discovered. Unfortunately, rigorous standardized elastic-plastic fracture mechanics approaches are not yet available for practical applications. Because of those constraints, the current state-of-the-art centers on the use of deformation plasticity analyses that assume net section plastic flow or other idealized conditions and, in addition, ignore the important fact that pipe cracks are generally located in or near a weld. Because of these constraints, the current approaches, widely known as estimation methods, often give rise to significantly different predictions for the margin of safety when applied to cracked nuclear plant piping systems [1]. The assumptions and idealizations that underlie each of the various estimation methods are not always recognized by those who must base ignore/ repair/remove decisions on the results of these analyses, Recognizing this situation, the CSNI, in
conjunction with the US Nuclear Regulatory Commission (NRC), arranged a workshop meeting at the Southwest Research Institute in San Antonio, Texas, 21-22 June 1984. The objective of the workshop was to help elastic-plastic fracture mechanics practitioners and those having a practical need for this technology achieve a better basic understanding of the elasticplastic analysis methods currently being applied to nuclear plant piping systems. To provide benchmarks, elastic-plastic finite element solutions were obtained. This paper presents the results of those computations. Details of the estimation method solutions that were presented can be found in ref. [2].
2. Background Cracks are continually being found in nuclear reactor power plant piping systems; see ref. [1] for examples. Because of the high ductility and toughness levels in nuclear plant piping, these discoveries have created the need for reliable elastic-plastic fracture mechanics analysis techniques. When a crack is
0029-5493/85/$3.30 O Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
284
J. W. Cardinal et al. / Elastic-plastic finite element analyses
detected in an operating nuclear power plant piping system, it is necessary to determine if the cracked pipe requires immediate repair or replacement, or if continued operation can be allowed. In addition, there is the distinct possibility that some cracks will go undetected. This makes it necessary to quantify the conditions under which leak-before-break will occur. Elastic-plastic fracture mechanics.therefore plays a critical role in both flaw evaluation and leak-beforebreak analyses for nuclear power plant integrity. In addition, such approaches are also important in eliminating double-ended guillotine breaks as a design basis event [3]. The double-ended guillotine break (DEGB) was originally postulated in the US for the purpose of sizing containment and emergency core cooling systems. But, it has also been used for defining mechanical loads and for evaluating the postbreak consequences of pipe rupture. The mechanical loads resulting from a postulated D E G B , together with seismic and other loads, are used for designing component supports and other structural members. The postbreak consequences resulting from a postulated D E G B produce a need for massive pipe whip restraints and jet impingement shields. These components are not only expensive to design and install, they tend to reduce the reliability of inservice inspections while increasing the radiation exposure associated with in-service inspection and maintenance operations. The postulated D E G B creates significant difficulties for old as well as new plants. For example, a postulated D E G B at the reactor pressure vessel nozzle led to the axisymmetric loss of coolant accident (LOCA) load issue [4]. The currently proposed basis for eliminating the postulated D E G B relies heavily on deterministic EPFM analyses. These are needed to demonstrate that a through-wall crack of sufficient length to be reliably detected by leakage has an adequate margin against failure under normal and anticipated accident loading conditions. Unfortunately, current EPFM estimation techniques all too often give disparate predictions. It is therefore difficult to make the appropriate decision on pipes with real or postulated cracks. Compounding the need for more accurate and reliable elastic-plastic piping fracture mechanics analysis techniques is the further necessity to treat the heterogeneity and material property differences that arise when the crack is found in a weld. This issue is the focal point of the computations described in this paper.
2L
-
0 = 0.645 rad R i - 7 . 5 inches Ro = 8.0 inches L 35 feet
Fig. 1. Cracked pipe geometry and loading.
3. Analysis procedure The specific problem addressed in the CSNI/NRC workshop was a 70 foot long, 16 inch diameter, Type 304 stainless steel pipe containing a 74 ° circumferential through-wall crack located in the center of a girth weld [2]. The circumferential crack geometry is shown in fig. 1. For the analysis of the case when the crack is located in the weld, the weld was assumed to be equal in width to the thickness of the pipe. The pipe is subjected to a constant axial stress of 10 ksi combined with monotonically increasing applied bending moment. The objectives of the analyses were to obtain the applied J values as a function of increasing bending moment and, through the use of given J-resistance values, to determine the applied bending moments at crack initiation and at loadcontrolled instability. The mechanical and fracture properties of base metal and the weldment, corresponding to an operating temperature of 550°F, are shown in figs. 2 and 3, respectively. An approximate fit of the experimental data was used to model the material behavior of the entire monolithic pipe for the CSNI/NRC workshop problem [2]. Subsequently, however, tensile data for the base metal and weldment were obtained from raw
J.W. Cardinal et al. I Elastic-plastic finite element analyses 80
?0
workshop base metal curve and the McCabe weldment data. The input parameters used in the analyses are summarized in table 1. The analyses were performed using a modified version of A D I N A [6] capable of calculating elasticplastic energy release rates. Implementation of the energy release rate calculations into the A D I N A code generally followed the virtual crack extension methodology originally introduced by Hellen [7, 8] and Parks [9-11]. An analytical expression for the energy release rate more suitable for numerical analysis of general three-dimensional crack configurations that was subsequently derived by de Lorenzi [12] is used in the SwRI version of the
~-Weldment (McCabedata)
60 ~
~
,o
~
~ Base Metal (McCabedata)
~ 3o 20 tO 0
I I L I L L I L L I I L I I ] ~ I I I 0,1 TRUESTRAIN(in/in)
285
0.2
Fig. 2. T y p e 304 stainless steel and w e l d m e n t stress-strain
curves at 5500F. Table 1 Material properties employed in the analysis data supplied directly by McCabe [5] in the form of load versus specimen diameter reduction. These data were transformed to true stress-true strain by converting the measured diametral strains to longitudinal strains. From fig. 2, it can be seen that the curves generated from the McCabe data for the base metal agree reasonably well with the workshop curve fit. Hence, to facilitate comparisons between the two solutions, the welded pipe analysis employed the
Material Property
Base metal
Weldment
E (ksi) cry (ksi) ~, ],c (in-lb/inch2)
31 250 25.0 0.3 4 500
29 940 53.9 0.3 2 000
20000 18000 16000 14000
/
12000 10000 •~
,ooo
8000 6000 4000 2000 0 0
,1 .1
I .2
1 .3
I .4
I .5
l .6
1 .7
I .8
1 .9
i 1.0
1 1.1
CRACK EXTENSION inches
Fig. 3. Material J-resistance curves.
I 1.2
L 1.3
I 1.4
L 1.5
L 1.6
I 1.7
L 1.8
I 1.9
286
J. W. Cardinal et al. / Elastic-plastic finite element analyses
A D I N A code. The pipe was modeled using eightnoded, isoparametric, three-dimensional solid elements with a 2 × 2 × 2 order of integration. For simplicity, one element was used through the thickness of the pipe. Since the virtual crack extension method assumes small displacements and small strains, the AD1NA calculations consider material nonlinearities only. Geometrical nonlinearities are not accounted for in the model behavior. The experimental stress-strain data for the base metal and the weldment were incorporated into the analyses using elastic-plastic material models with isotropic hardening. The von Mises yield criterion and flow rule were used. Prior to the development of a detailed model of the cracked pipe, a coarse grid pipe model using the full symmetric half length of the pipe (420 inch) was studied to determine the influence of the crack on the compliance of the pipe. This coarse grid model, shown in fig. 4, contained 378 elements, each of which subtended a circumferential arc of the pipe ranging from 18° to 30 °. It was found that linear bending deformations in the pipe were reasonably exhibited beyond a distance of 40 inch from the crack plane. For the development of the detailed cracked pipe model, a pipe with a symmetric half-length of 80 inch was chosen to assure the proper bending deformation at the crack. Fig. 5 presents the detailed finite element model of the pipe used in the solution of the workshop problem. This model contains 495 eight-noded solid elements and a total of 3085 active degrees of freedom. Modeling details near the crack tip are illustrated in the enlarged views of the model shown in figs. 6 and 7. For the welded pipe analysis, material properties corresponding to the McCabe weldment data were used for the elements extending around the pipe circum-
see fig. 6
~
~
(1
I/
It
P
Z
x
Fig. 4. Coarse grid finite element model of cracked pipe (L = 420 inch).
ference within 0.5 inch of the crack plane. Elements at the crack tip and along the circumferential crack growth path have dimensions of 0.1 inch x 0.1 inch × 0.5 inch, where the 0.5 inch dimension corresponds to the pipe wall thickness. At an axial distance of 3 inches from the crack tip, the geometry of the pipe is discretized such that each element subtends a circumferential arc of 10°. The J-integral was calculated by considering the contributions to the energy released by a virtual crack extension of all elements within a zone having a
li
/[
Z
Fig. 5. Detailed finite element model of the cracked pipe (L = 80 inch).
~
IL
II
[L
,u ....
J. W. Cardinal el al. I Elastic-plastic .finite element analyses
" /
~/
,/
~7 , ,/' ~
~ _ Y ' ,'
Crack Tip---,.
/ I1'~/'~ // /' i
Z
287
~
I
"
L 3.o-2 Fig. 6. Enlargement of detailed model.
Fig. 7. Detailed model ahead of crack.
18000 t BASE METAL MATERIAL Jr CURVE
16000 14000 12000 C c,, i
c .w
10000 8000
WELDMENT MATERIAL Jr CURVE
6000 40004 -
---APPLIED J CURVES ~ ] - - INSTABILITY POINT
2000~ 0.1
I
0.2
I
0.3
I
0.4
I
0.5
I
0.6
I
0.7
I
0.8
CRACK EXTENSION inches Fig. 8. Applied J-curves compared with material J-resistance curves for the monolithic and composite pipe models.
288
J. W. Cardinal et al. / Elastic-plastic finite element analyses
dimension of 12 inch in all directions from the crack tip. Thus, when interpreting the J results, it must be kept in mind that plastically deformed regions may exist outside of this zone. The choice of 12 inch for use in this problem was arrived at by preliminary test calculations, considerations of the pipe geometry, and acknowledgment of the fact that, outside this region, plastic strains were three to four orders of magnitude below those contained within this "radius of influence". In the analyses, the applied bending moment was increased until J~,. was reached. Crack growth was then modeled by forcing the applied load and crack length to be such that the calculated J value matched the J resistance value for that amount of crack extension. This was accomplished by releasing the crack tip node under constant load, using a gradual reduction in force until the crack extended the length of one element. After this extension, the load was increased until the calculated J value reached the corresponding material value. This dictated a further increment of crack extension. This procedure was repeated until the applied J in the constant-load crack extension portion of the computation equalled or exceeded the material J resistance level for the longer crack. The crack length prior to the extension at which this occurred was taken as the load-controlled instability point. This procedure is illustrated in fig. 8. In fig. 8, the vertical line segments result from increasing the applied bending moment at constant crack length while the slightly inclined line segments represent crack growth under constant load. At instability, (indicated by the square symbols in the figure), it can be seen that crack extension at constant load causes the slope of the applied J curve to be equal to that of the material J-resistance curve. Thus, since any further load increase would keep the applied J curve above the J-resistance curve, instability has been reached.
4. Computational results Two elastic-plastic finite element computations were performed. In the first, the pipe was considered to have everywhere the mechanical and fracture properties of the base metal. In the second, the pipe was modelled as a composite of the base metal and the weldment with each constituent having its own mechanical and fracture properties. Table 2 summarizes
the results obtained for these analyses. Results show that crack initiation occurs at an applied bending moment of 2013 inch kips for the monolithic pipe model and at 1578 inch kips for the composite pipe model. The corresponding plastic zone distribution for each case at the respective crack initiation loads are given in figs. 9 and 10. Here the cylindrical pipe geometry is mapped into a rectangular plane surface for ease of viewing the plotted plastic zone areas. It can be seen that in each figure there is an extensive zone that has yielded in bending in the area remote from the crack tip. The presence of a compressive yield zone, indicated by the cross-hatched area, can also be seen in the monolithic pipe model. Instability was calculated to take place at an applied bending moment of 2535 inch kips for the monolithic pipe model and at 2013 inch kips for the composite pipe model. Plastic zone distributions for each case at the respective instability loads are given in figs. 11 and 12. It can be seen that net section plasticity has been achieved along the crack plane at the monolithic pipe instability condition. A small compressive zone appears at instability for the composite pipe model and the yielded zones are much less widespread. In fact, by comparing figs. 9 and 12, it can be seen that, if the weldment arrea is neglected, the initiation plasticity distribution for the monolithic pipe model corresponds almost exactly to the plastic zones present at instability for the composite pipe model. This is somewhat coincidental since the bending moments for each of these conditions, are just equal (see table 2). Similarly, figs. 10 and 12 indicate that only a very small area of weldment near the crack tip deforms plastically. Applied J values as a function of bending moment are plotted in figs. 13 and 14 for the monolithic and composite pipe models, respectively. These figures show that the monolithic pipe model can withstand an applied J value three times that of the composite pipe model prior to reaching instability. The calculated bending moment capacity of the monolithic pipe model is 8% greater than that of the composite pipe model. Moment-rotation curves for each case are shown in figs. 15 and 16, indicating that the monolithic pipe model rotates approximately 2.5 times as much as the composite pipe model prior to instability. The computational results indicate that the extent of stable crack growth at fracture instability is 0.3 inch for the monolithic pipe model but only 0.1 inch for the composite pipe model. The accuracy of the latter value is particularly suspect in that it is of the same order as
J. W. Cardinal et al. I Elastic-plastic finite element analyses
289
Table 2 Summary of elastic-plastic finite element fracture analysis results
Initiation moment (inch kip) Rotation" at initiation (degrees) Amount of stable crack growth (inch) Instability moment (inch kip) Rotation" at instability (degrees) Instability J (lb/inch2)
Monolithic pipe model
Composite pipe model
2013 • 0.46 0.3 2535 1.02 11792
1578 0.26 0.1 2013 0.41 3733
" Pipe rotation is calculated using the length of the detailed finite element model (80.0 inch).
C/4 CRACK.= TIP
C/4
(
8 0 " - -
Fig. 9. Monolithic pipe plastic zone at M = 2013 inch kips (initiation).
~'~ L~ WELD(0.5")
t
C/4 CRACK,,,_~ h Fig. 10.
0/4
80"
Composite pipe plastic zone at M = 1578 inch kips (initiation).
,,_-
290
J. W. Cardinal et al. / Elastic-plastic finite element analyses
C/4
CRACK--
~.~//y..~
C/4
_3 L
80"
Fig. 11. Monolithic pipe plastic zone at M = 2535 inch kips (instability).
~--- WELD (0.5"}
F_..Y~
-~
C/4
.
/
~
L__............
/ / , .( / . , ×~"/,'//
. ..//////////////
.'//.A.~/~.
"
.///,
. "/.Y/~ ~/S~;
/////.
//.
"/.~Y× YA×/
80"---
Fig. 12. Composite pipe plastic zone at M = 2013 inch kips (instability).
the mesh size ahead of the crack. A model containing a finer mesh ahead of the crack tip would provide a more precise calculation for the amount of stable crack extension and, hence, would refine the prediction of the instability load over that obtained in this work.
5. Discumion of remits As discussed in the preceding, the incremental crack extensions in this analysis were performed under
constant load. In conjunction with the relatively crude mesh size that was used in these analyses, this results in the stair-step nature of the applied J curves shown in fig. 8. Ideally, the crack should be extended as the load is increased (or the displacement, if displacement control is used), such that the material J-resistance curve is followed more exactly. This could be accomplished by first performing a trial analysis for crack extension assuming growth under constant load or displacement, then correcting this by increasing the load appropriately to remain on the material J-resis-
15
291
14 13 12 11 10 9 8 7 6 5 4 3 2
I
400
800
1200
1600
2000
2400
I
2800
BENDING MOMENT [in - kips)
Fig. 13. Applied J versus bending moment for the monolithic cracked pipe. 15 14 13 12 11 10 9-
_~ .~_ .~
8 7 6 5 4 3 2 1' 0
I
400
800
1200
1600
BENDING MOMENT [in - kips)
Fig. 14. Applied J versus bending moment for the composite pipe model.
2000
I
I
2400
2800
292
J. W. Cardinal et al. / Elastic-plastic finite element analyses 2800 2600
, D
2400 2200 2000
1800 .E
1600 z Lu
1400
o ©
t200
Z
lOOO 7 LU
8O0 6OO 4O0 2O0 0 0.0
J
I 0.2
l
I 0.4
I
I 0.6
I
I 0.8
I
I 1.0
I
i 1,2
ROTATION (degrees)
Fig. 15. M - 0 c u ~ e f o r t h e monolit~c pipe model.
2800
tance curve. This "predictor-corrector" procedure will be used in all subsequent computations of this kind. In the analysis of the composite pipe, the crack growth behavior is entirely controlled by the weldment J-resistance curve. Although the crack is located in the weld, the "radius of influence" used to calculate J in the analysis extends well out into the base metal of the pipe. It could be argued that, since such a large volume of base metal is used in the calculation of J, a "hybrid material J-resistance" curve should be used to model the composite effect of both materials in this analysis. Such a curve would be more properly obtained from "generation phase" calculations performed on welded test specimens - see for example, re[. [13]. In this type of calculation, a finite element model of a welded test speciment would be forced to respond to the exact experimental load and crack length history, thereby obtaining a "material" J-resistance curve for a welded member. This approach is now being pursued.
2600 2400 2200 2000 1800 .E Z W
1600 1400
o 12oo o Z Z w
1ooo 800 60O 4O0 2OO
I 0.0
J 0.2
I
I I J 0.4 0.6 ROTATION (degrees)
Fig. 16. M-O curve forthecomposi~ pipe model.
6. C o a c i l i o m While current elastic-plastic finite element analysis approaches are still evolving, they nonetheless offer
J. W. Cardinal et ai. / Elastic-plastic finite element analyses important insights for the practical complications in pipe fracture problems that are not well treated by the estimation methods. This is particularly true for cracks that are located in weldments. The results provided in this paper show the importance of developing analysis approaches in which the weldment is to be considered explicitly; i.e., with a finite domain in which stress-strain and resistance curve properties that are distinct from those of the base metal are employed. Thus, in common with crack growth in welds by other mechanisms - see refs. 113, 14] for examples - elastic-plastic fracture is also affected by the weld metal properties. It can be concluded that more rigorous analysis procedures must be developed to provide accurate assessments of the margin of safety in nuclear plant piping systems.
Acknowledgment This research was performed as part of the Oak Ridge National Laboratory Heavy Section Steel Technology Program under ORNL Contract No. 37X97036C. The authors would like to express their appreciation to Dr. Claud Pugh of ORNL and to Jack Strosnider, Charles Serpan and Milton Vagins of the US Nuclear Regulatory Commission for giving them the opportunity to perform this work.
Re|erences [1] M.F. Kanninen, C.H. Popelar and D. Brock, A critical survey on the application of plastic fracture mechanics to nuclear pressure vessels and piping, Nucl. Engrg. Des., 67 (1981) 27.
293
[2] M.F. Kanninen, editor, Proc. CSNI/NRC Workshop on Ductile Piping Fracture Mechanics, San Antonio, Texas, 21-22 June 1984, to be published by the US Nuclear Regulatory Commission (1985). [3] B.D. Liaw, Future content and implementation of section XI - a regulatory view, J. Pressure Vessel Technol. 107 (1985) 1. [4] J.E. Strosnider (US Nuclear Regulatory Commission), private communication to M.F. Kanninen, SwRI (20 June 1984). [5] D.E. McCabe (Westinghouse), private communication to M,F. Kanninen, SwRI (25 June 1984). [6] ADINA - A finite element program for automatic dynamic incremental nonlinear analysis, User's manual (September 1981) ADINA Engineering Report AE 811. [7] T.K. Hellen, The finite element calculations of stress intensity factors using energy techniques, 2nd International Conference on Structural Mechanics in Reactor Technology (SMiRT), Paper G/3, Berlin, Germany, 1973. [8] T.K. Hellen, On the method of virtual crack extensions, Intern. J. Numerical Methods in Engrg. 9 (1975) 187. [9] D.M. Parks, A stiffness derivative finite technique for determination of crack-tip stress intensity factors, Intern, J. Fracture 10 (1974) 487. [10] D.M. Parks, The virtual crack extension method for nonlinear material behavior, Computer Methods in Applied Mechanics and Engrg. 12 (1977) 353. [11] D.M. Parks, Virtual crack extension: A general finite element technique for J-integral evaluation, eds. D.R.J. Owen and A.R. Luxmoore, (Swansea University Press, Swansea, UK 1978) p. 464. [12] H.G. de Lorenzi, On the energy release rate and the J-integral for 3-D crack configurations, Intern. J. Fracture 19 (1982) 183. [13] M.F. Kanninen and C.H. Popelar, Advanced fracture mechanics (Oxford Press, New York, 1985). [14] M.F. Kanninen, F.W. Brust, J. Ahmad and I.S. AbouSayed, The numerical simulation of crack growth in weld induced residual stress fields, in: Residual Stress and Relaxation, ed. E. Kula, (Plenum Press, New York, 1982) p. 227.
283
ELASTIC-PLASTIC FINITE ELEMENT ANALYSES OF STABLE CRACK A N D F R A C T U R E I N S T A B I L I T Y IN A GIRTH W E L D E D PIPE J.W. CARDINAL,
GROWTH
E.Z. POLCH, P.K. NAIR, and M.F. KANNINEN
Engineering and Materials Sciences Division, Southwest Research Institute, San Antonio, TX 78284, USA
Received 18 April 1985
Detailed elastic-plastic finite element fracture mechanics analyses were conducted on a 16 inch diameter Type 304 stainless steel pipe containing a circumferential through-wall crack located in a girth weld. Calculations were performed to analyze the welded pipe treated as (1) a monolithic pipe entirely composed of the base metal, and (2) a composite of base metal and weldment. In the latter, each constituent was assigned distinct mechanical and fracture properties. In both solutions applied J values were calculated for a fixed axial load combined with a monotonically increasing applied bending moment. The material J-resistance curves appropriate for the two problems were each used to initiate and grow the initial crack in a stable manner until fracture instability occurred under load control. It was found that the extent of stable crack growth and the applied loads at fracture instability are distinctly different in the two analyses. It is concluded that more precise fracture mechanics approaches than those now in current use are required for accurate assessments of weld cracking problems.
1. Introduction Because nuclear plant piping systems employ materials that are ductile and tough, linear elastic fracture mechanics techniques will not usually suffice for fracture assessments when cracks are discovered. Unfortunately, rigorous standardized elastic-plastic fracture mechanics approaches are not yet available for practical applications. Because of those constraints, the current state-of-the-art centers on the use of deformation plasticity analyses that assume net section plastic flow or other idealized conditions and, in addition, ignore the important fact that pipe cracks are generally located in or near a weld. Because of these constraints, the current approaches, widely known as estimation methods, often give rise to significantly different predictions for the margin of safety when applied to cracked nuclear plant piping systems [1]. The assumptions and idealizations that underlie each of the various estimation methods are not always recognized by those who must base ignore/ repair/remove decisions on the results of these analyses, Recognizing this situation, the CSNI, in
conjunction with the US Nuclear Regulatory Commission (NRC), arranged a workshop meeting at the Southwest Research Institute in San Antonio, Texas, 21-22 June 1984. The objective of the workshop was to help elastic-plastic fracture mechanics practitioners and those having a practical need for this technology achieve a better basic understanding of the elasticplastic analysis methods currently being applied to nuclear plant piping systems. To provide benchmarks, elastic-plastic finite element solutions were obtained. This paper presents the results of those computations. Details of the estimation method solutions that were presented can be found in ref. [2].
2. Background Cracks are continually being found in nuclear reactor power plant piping systems; see ref. [1] for examples. Because of the high ductility and toughness levels in nuclear plant piping, these discoveries have created the need for reliable elastic-plastic fracture mechanics analysis techniques. When a crack is
0029-5493/85/$3.30 O Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
284
J. W. Cardinal et al. / Elastic-plastic finite element analyses
detected in an operating nuclear power plant piping system, it is necessary to determine if the cracked pipe requires immediate repair or replacement, or if continued operation can be allowed. In addition, there is the distinct possibility that some cracks will go undetected. This makes it necessary to quantify the conditions under which leak-before-break will occur. Elastic-plastic fracture mechanics.therefore plays a critical role in both flaw evaluation and leak-beforebreak analyses for nuclear power plant integrity. In addition, such approaches are also important in eliminating double-ended guillotine breaks as a design basis event [3]. The double-ended guillotine break (DEGB) was originally postulated in the US for the purpose of sizing containment and emergency core cooling systems. But, it has also been used for defining mechanical loads and for evaluating the postbreak consequences of pipe rupture. The mechanical loads resulting from a postulated D E G B , together with seismic and other loads, are used for designing component supports and other structural members. The postbreak consequences resulting from a postulated D E G B produce a need for massive pipe whip restraints and jet impingement shields. These components are not only expensive to design and install, they tend to reduce the reliability of inservice inspections while increasing the radiation exposure associated with in-service inspection and maintenance operations. The postulated D E G B creates significant difficulties for old as well as new plants. For example, a postulated D E G B at the reactor pressure vessel nozzle led to the axisymmetric loss of coolant accident (LOCA) load issue [4]. The currently proposed basis for eliminating the postulated D E G B relies heavily on deterministic EPFM analyses. These are needed to demonstrate that a through-wall crack of sufficient length to be reliably detected by leakage has an adequate margin against failure under normal and anticipated accident loading conditions. Unfortunately, current EPFM estimation techniques all too often give disparate predictions. It is therefore difficult to make the appropriate decision on pipes with real or postulated cracks. Compounding the need for more accurate and reliable elastic-plastic piping fracture mechanics analysis techniques is the further necessity to treat the heterogeneity and material property differences that arise when the crack is found in a weld. This issue is the focal point of the computations described in this paper.
2L
-
0 = 0.645 rad R i - 7 . 5 inches Ro = 8.0 inches L 35 feet
Fig. 1. Cracked pipe geometry and loading.
3. Analysis procedure The specific problem addressed in the CSNI/NRC workshop was a 70 foot long, 16 inch diameter, Type 304 stainless steel pipe containing a 74 ° circumferential through-wall crack located in the center of a girth weld [2]. The circumferential crack geometry is shown in fig. 1. For the analysis of the case when the crack is located in the weld, the weld was assumed to be equal in width to the thickness of the pipe. The pipe is subjected to a constant axial stress of 10 ksi combined with monotonically increasing applied bending moment. The objectives of the analyses were to obtain the applied J values as a function of increasing bending moment and, through the use of given J-resistance values, to determine the applied bending moments at crack initiation and at loadcontrolled instability. The mechanical and fracture properties of base metal and the weldment, corresponding to an operating temperature of 550°F, are shown in figs. 2 and 3, respectively. An approximate fit of the experimental data was used to model the material behavior of the entire monolithic pipe for the CSNI/NRC workshop problem [2]. Subsequently, however, tensile data for the base metal and weldment were obtained from raw
J.W. Cardinal et al. I Elastic-plastic finite element analyses 80
?0
workshop base metal curve and the McCabe weldment data. The input parameters used in the analyses are summarized in table 1. The analyses were performed using a modified version of A D I N A [6] capable of calculating elasticplastic energy release rates. Implementation of the energy release rate calculations into the A D I N A code generally followed the virtual crack extension methodology originally introduced by Hellen [7, 8] and Parks [9-11]. An analytical expression for the energy release rate more suitable for numerical analysis of general three-dimensional crack configurations that was subsequently derived by de Lorenzi [12] is used in the SwRI version of the
~-Weldment (McCabedata)
60 ~
~
,o
~
~ Base Metal (McCabedata)
~ 3o 20 tO 0
I I L I L L I L L I I L I I ] ~ I I I 0,1 TRUESTRAIN(in/in)
285
0.2
Fig. 2. T y p e 304 stainless steel and w e l d m e n t stress-strain
curves at 5500F. Table 1 Material properties employed in the analysis data supplied directly by McCabe [5] in the form of load versus specimen diameter reduction. These data were transformed to true stress-true strain by converting the measured diametral strains to longitudinal strains. From fig. 2, it can be seen that the curves generated from the McCabe data for the base metal agree reasonably well with the workshop curve fit. Hence, to facilitate comparisons between the two solutions, the welded pipe analysis employed the
Material Property
Base metal
Weldment
E (ksi) cry (ksi) ~, ],c (in-lb/inch2)
31 250 25.0 0.3 4 500
29 940 53.9 0.3 2 000
20000 18000 16000 14000
/
12000 10000 •~
,ooo
8000 6000 4000 2000 0 0
,1 .1
I .2
1 .3
I .4
I .5
l .6
1 .7
I .8
1 .9
i 1.0
1 1.1
CRACK EXTENSION inches
Fig. 3. Material J-resistance curves.
I 1.2
L 1.3
I 1.4
L 1.5
L 1.6
I 1.7
L 1.8
I 1.9
286
J. W. Cardinal et al. / Elastic-plastic finite element analyses
A D I N A code. The pipe was modeled using eightnoded, isoparametric, three-dimensional solid elements with a 2 × 2 × 2 order of integration. For simplicity, one element was used through the thickness of the pipe. Since the virtual crack extension method assumes small displacements and small strains, the AD1NA calculations consider material nonlinearities only. Geometrical nonlinearities are not accounted for in the model behavior. The experimental stress-strain data for the base metal and the weldment were incorporated into the analyses using elastic-plastic material models with isotropic hardening. The von Mises yield criterion and flow rule were used. Prior to the development of a detailed model of the cracked pipe, a coarse grid pipe model using the full symmetric half length of the pipe (420 inch) was studied to determine the influence of the crack on the compliance of the pipe. This coarse grid model, shown in fig. 4, contained 378 elements, each of which subtended a circumferential arc of the pipe ranging from 18° to 30 °. It was found that linear bending deformations in the pipe were reasonably exhibited beyond a distance of 40 inch from the crack plane. For the development of the detailed cracked pipe model, a pipe with a symmetric half-length of 80 inch was chosen to assure the proper bending deformation at the crack. Fig. 5 presents the detailed finite element model of the pipe used in the solution of the workshop problem. This model contains 495 eight-noded solid elements and a total of 3085 active degrees of freedom. Modeling details near the crack tip are illustrated in the enlarged views of the model shown in figs. 6 and 7. For the welded pipe analysis, material properties corresponding to the McCabe weldment data were used for the elements extending around the pipe circum-
see fig. 6
~
~
(1
I/
It
P
Z
x
Fig. 4. Coarse grid finite element model of cracked pipe (L = 420 inch).
ference within 0.5 inch of the crack plane. Elements at the crack tip and along the circumferential crack growth path have dimensions of 0.1 inch x 0.1 inch × 0.5 inch, where the 0.5 inch dimension corresponds to the pipe wall thickness. At an axial distance of 3 inches from the crack tip, the geometry of the pipe is discretized such that each element subtends a circumferential arc of 10°. The J-integral was calculated by considering the contributions to the energy released by a virtual crack extension of all elements within a zone having a
li
/[
Z
Fig. 5. Detailed finite element model of the cracked pipe (L = 80 inch).
~
IL
II
[L
,u ....
J. W. Cardinal el al. I Elastic-plastic .finite element analyses
" /
~/
,/
~7 , ,/' ~
~ _ Y ' ,'
Crack Tip---,.
/ I1'~/'~ // /' i
Z
287
~
I
"
L 3.o-2 Fig. 6. Enlargement of detailed model.
Fig. 7. Detailed model ahead of crack.
18000 t BASE METAL MATERIAL Jr CURVE
16000 14000 12000 C c,, i
c .w
10000 8000
WELDMENT MATERIAL Jr CURVE
6000 40004 -
---APPLIED J CURVES ~ ] - - INSTABILITY POINT
2000~ 0.1
I
0.2
I
0.3
I
0.4
I
0.5
I
0.6
I
0.7
I
0.8
CRACK EXTENSION inches Fig. 8. Applied J-curves compared with material J-resistance curves for the monolithic and composite pipe models.
288
J. W. Cardinal et al. / Elastic-plastic finite element analyses
dimension of 12 inch in all directions from the crack tip. Thus, when interpreting the J results, it must be kept in mind that plastically deformed regions may exist outside of this zone. The choice of 12 inch for use in this problem was arrived at by preliminary test calculations, considerations of the pipe geometry, and acknowledgment of the fact that, outside this region, plastic strains were three to four orders of magnitude below those contained within this "radius of influence". In the analyses, the applied bending moment was increased until J~,. was reached. Crack growth was then modeled by forcing the applied load and crack length to be such that the calculated J value matched the J resistance value for that amount of crack extension. This was accomplished by releasing the crack tip node under constant load, using a gradual reduction in force until the crack extended the length of one element. After this extension, the load was increased until the calculated J value reached the corresponding material value. This dictated a further increment of crack extension. This procedure was repeated until the applied J in the constant-load crack extension portion of the computation equalled or exceeded the material J resistance level for the longer crack. The crack length prior to the extension at which this occurred was taken as the load-controlled instability point. This procedure is illustrated in fig. 8. In fig. 8, the vertical line segments result from increasing the applied bending moment at constant crack length while the slightly inclined line segments represent crack growth under constant load. At instability, (indicated by the square symbols in the figure), it can be seen that crack extension at constant load causes the slope of the applied J curve to be equal to that of the material J-resistance curve. Thus, since any further load increase would keep the applied J curve above the J-resistance curve, instability has been reached.
4. Computational results Two elastic-plastic finite element computations were performed. In the first, the pipe was considered to have everywhere the mechanical and fracture properties of the base metal. In the second, the pipe was modelled as a composite of the base metal and the weldment with each constituent having its own mechanical and fracture properties. Table 2 summarizes
the results obtained for these analyses. Results show that crack initiation occurs at an applied bending moment of 2013 inch kips for the monolithic pipe model and at 1578 inch kips for the composite pipe model. The corresponding plastic zone distribution for each case at the respective crack initiation loads are given in figs. 9 and 10. Here the cylindrical pipe geometry is mapped into a rectangular plane surface for ease of viewing the plotted plastic zone areas. It can be seen that in each figure there is an extensive zone that has yielded in bending in the area remote from the crack tip. The presence of a compressive yield zone, indicated by the cross-hatched area, can also be seen in the monolithic pipe model. Instability was calculated to take place at an applied bending moment of 2535 inch kips for the monolithic pipe model and at 2013 inch kips for the composite pipe model. Plastic zone distributions for each case at the respective instability loads are given in figs. 11 and 12. It can be seen that net section plasticity has been achieved along the crack plane at the monolithic pipe instability condition. A small compressive zone appears at instability for the composite pipe model and the yielded zones are much less widespread. In fact, by comparing figs. 9 and 12, it can be seen that, if the weldment arrea is neglected, the initiation plasticity distribution for the monolithic pipe model corresponds almost exactly to the plastic zones present at instability for the composite pipe model. This is somewhat coincidental since the bending moments for each of these conditions, are just equal (see table 2). Similarly, figs. 10 and 12 indicate that only a very small area of weldment near the crack tip deforms plastically. Applied J values as a function of bending moment are plotted in figs. 13 and 14 for the monolithic and composite pipe models, respectively. These figures show that the monolithic pipe model can withstand an applied J value three times that of the composite pipe model prior to reaching instability. The calculated bending moment capacity of the monolithic pipe model is 8% greater than that of the composite pipe model. Moment-rotation curves for each case are shown in figs. 15 and 16, indicating that the monolithic pipe model rotates approximately 2.5 times as much as the composite pipe model prior to instability. The computational results indicate that the extent of stable crack growth at fracture instability is 0.3 inch for the monolithic pipe model but only 0.1 inch for the composite pipe model. The accuracy of the latter value is particularly suspect in that it is of the same order as
J. W. Cardinal et al. I Elastic-plastic finite element analyses
289
Table 2 Summary of elastic-plastic finite element fracture analysis results
Initiation moment (inch kip) Rotation" at initiation (degrees) Amount of stable crack growth (inch) Instability moment (inch kip) Rotation" at instability (degrees) Instability J (lb/inch2)
Monolithic pipe model
Composite pipe model
2013 • 0.46 0.3 2535 1.02 11792
1578 0.26 0.1 2013 0.41 3733
" Pipe rotation is calculated using the length of the detailed finite element model (80.0 inch).
C/4 CRACK.= TIP
C/4
(
8 0 " - -
Fig. 9. Monolithic pipe plastic zone at M = 2013 inch kips (initiation).
~'~ L~ WELD(0.5")
t
C/4 CRACK,,,_~ h Fig. 10.
0/4
80"
Composite pipe plastic zone at M = 1578 inch kips (initiation).
,,_-
290
J. W. Cardinal et al. / Elastic-plastic finite element analyses
C/4
CRACK--
~.~//y..~
C/4
_3 L
80"
Fig. 11. Monolithic pipe plastic zone at M = 2535 inch kips (instability).
~--- WELD (0.5"}
F_..Y~
-~
C/4
.
/
~
L__............
/ / , .( / . , ×~"/,'//
. ..//////////////
.'//.A.~/~.
"
.///,
. "/.Y/~ ~/S~;
/////.
//.
"/.~Y× YA×/
80"---
Fig. 12. Composite pipe plastic zone at M = 2013 inch kips (instability).
the mesh size ahead of the crack. A model containing a finer mesh ahead of the crack tip would provide a more precise calculation for the amount of stable crack extension and, hence, would refine the prediction of the instability load over that obtained in this work.
5. Discumion of remits As discussed in the preceding, the incremental crack extensions in this analysis were performed under
constant load. In conjunction with the relatively crude mesh size that was used in these analyses, this results in the stair-step nature of the applied J curves shown in fig. 8. Ideally, the crack should be extended as the load is increased (or the displacement, if displacement control is used), such that the material J-resistance curve is followed more exactly. This could be accomplished by first performing a trial analysis for crack extension assuming growth under constant load or displacement, then correcting this by increasing the load appropriately to remain on the material J-resis-
15
291
14 13 12 11 10 9 8 7 6 5 4 3 2
I
400
800
1200
1600
2000
2400
I
2800
BENDING MOMENT [in - kips)
Fig. 13. Applied J versus bending moment for the monolithic cracked pipe. 15 14 13 12 11 10 9-
_~ .~_ .~
8 7 6 5 4 3 2 1' 0
I
400
800
1200
1600
BENDING MOMENT [in - kips)
Fig. 14. Applied J versus bending moment for the composite pipe model.
2000
I
I
2400
2800
292
J. W. Cardinal et al. / Elastic-plastic finite element analyses 2800 2600
, D
2400 2200 2000
1800 .E
1600 z Lu
1400
o ©
t200
Z
lOOO 7 LU
8O0 6OO 4O0 2O0 0 0.0
J
I 0.2
l
I 0.4
I
I 0.6
I
I 0.8
I
I 1.0
I
i 1,2
ROTATION (degrees)
Fig. 15. M - 0 c u ~ e f o r t h e monolit~c pipe model.
2800
tance curve. This "predictor-corrector" procedure will be used in all subsequent computations of this kind. In the analysis of the composite pipe, the crack growth behavior is entirely controlled by the weldment J-resistance curve. Although the crack is located in the weld, the "radius of influence" used to calculate J in the analysis extends well out into the base metal of the pipe. It could be argued that, since such a large volume of base metal is used in the calculation of J, a "hybrid material J-resistance" curve should be used to model the composite effect of both materials in this analysis. Such a curve would be more properly obtained from "generation phase" calculations performed on welded test specimens - see for example, re[. [13]. In this type of calculation, a finite element model of a welded test speciment would be forced to respond to the exact experimental load and crack length history, thereby obtaining a "material" J-resistance curve for a welded member. This approach is now being pursued.
2600 2400 2200 2000 1800 .E Z W
1600 1400
o 12oo o Z Z w
1ooo 800 60O 4O0 2OO
I 0.0
J 0.2
I
I I J 0.4 0.6 ROTATION (degrees)
Fig. 16. M-O curve forthecomposi~ pipe model.
6. C o a c i l i o m While current elastic-plastic finite element analysis approaches are still evolving, they nonetheless offer
J. W. Cardinal et ai. / Elastic-plastic finite element analyses important insights for the practical complications in pipe fracture problems that are not well treated by the estimation methods. This is particularly true for cracks that are located in weldments. The results provided in this paper show the importance of developing analysis approaches in which the weldment is to be considered explicitly; i.e., with a finite domain in which stress-strain and resistance curve properties that are distinct from those of the base metal are employed. Thus, in common with crack growth in welds by other mechanisms - see refs. 113, 14] for examples - elastic-plastic fracture is also affected by the weld metal properties. It can be concluded that more rigorous analysis procedures must be developed to provide accurate assessments of the margin of safety in nuclear plant piping systems.
Acknowledgment This research was performed as part of the Oak Ridge National Laboratory Heavy Section Steel Technology Program under ORNL Contract No. 37X97036C. The authors would like to express their appreciation to Dr. Claud Pugh of ORNL and to Jack Strosnider, Charles Serpan and Milton Vagins of the US Nuclear Regulatory Commission for giving them the opportunity to perform this work.
Re|erences [1] M.F. Kanninen, C.H. Popelar and D. Brock, A critical survey on the application of plastic fracture mechanics to nuclear pressure vessels and piping, Nucl. Engrg. Des., 67 (1981) 27.
293
[2] M.F. Kanninen, editor, Proc. CSNI/NRC Workshop on Ductile Piping Fracture Mechanics, San Antonio, Texas, 21-22 June 1984, to be published by the US Nuclear Regulatory Commission (1985). [3] B.D. Liaw, Future content and implementation of section XI - a regulatory view, J. Pressure Vessel Technol. 107 (1985) 1. [4] J.E. Strosnider (US Nuclear Regulatory Commission), private communication to M.F. Kanninen, SwRI (20 June 1984). [5] D.E. McCabe (Westinghouse), private communication to M,F. Kanninen, SwRI (25 June 1984). [6] ADINA - A finite element program for automatic dynamic incremental nonlinear analysis, User's manual (September 1981) ADINA Engineering Report AE 811. [7] T.K. Hellen, The finite element calculations of stress intensity factors using energy techniques, 2nd International Conference on Structural Mechanics in Reactor Technology (SMiRT), Paper G/3, Berlin, Germany, 1973. [8] T.K. Hellen, On the method of virtual crack extensions, Intern. J. Numerical Methods in Engrg. 9 (1975) 187. [9] D.M. Parks, A stiffness derivative finite technique for determination of crack-tip stress intensity factors, Intern, J. Fracture 10 (1974) 487. [10] D.M. Parks, The virtual crack extension method for nonlinear material behavior, Computer Methods in Applied Mechanics and Engrg. 12 (1977) 353. [11] D.M. Parks, Virtual crack extension: A general finite element technique for J-integral evaluation, eds. D.R.J. Owen and A.R. Luxmoore, (Swansea University Press, Swansea, UK 1978) p. 464. [12] H.G. de Lorenzi, On the energy release rate and the J-integral for 3-D crack configurations, Intern. J. Fracture 19 (1982) 183. [13] M.F. Kanninen and C.H. Popelar, Advanced fracture mechanics (Oxford Press, New York, 1985). [14] M.F. Kanninen, F.W. Brust, J. Ahmad and I.S. AbouSayed, The numerical simulation of crack growth in weld induced residual stress fields, in: Residual Stress and Relaxation, ed. E. Kula, (Plenum Press, New York, 1982) p. 227.