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Analytical and experimental fracture assessment of carbon steel piping with circumferential through-wall cracks under bending
ELSEVIER
Inc. J. Pres. Ves. & Piping 69 (1996) 207-212 Copyright 0 1996 Elsevier Science Limited Printed in Northern Ireland. All rights reserved 0308-0161/96/$15.00
0308-0161(95)00127-l
Analytical and experimental fracture assessment of carbon steel piping with circumferential through-wall cracks under bending H. Xu, P. N. Li, Y. J. Xie Research Institute
of Process Equipment
and Pressure Vessels, East China Shanghai 200237, P.R. China
University
of Science and Technology,
Z. R. Huang Department
of Mechanical
Engineering,
Jiangsu Institute
of Petrochemical
Technology,
Jiangsu 213016, P.R. China
(Received 25 October 1995;accepted 16 November 1995)
In this paper the true stress-straincurves of carbon steel pipes are described by a three-segmentfitting method rather than the Ramberg-Osgood relation for their yield plateau characteristics.Failure assessmentcurves for carbon steel piping containing circumferential through-wall cracks were obtained by different options in the CEGB/RG approach. The J-integral was calculated using a new expression proposed by the authors. Initiation and maximum moments of piping under bending were predicted by several methods and measured by experiments. Calculated moments were quite close to test results. Copyright 0 1996Elsevier ScienceLtd.
1 INTRODUCTION
In the third version of the CEGB/R6 approach,6 three different options for failure assessment curves (FACs) are offered. They range from the simplest universal curve (option l), which is independent of material and geometry, to the most complex curve (option 3), which is derived for a particular geometry and material. Both the finite-element calculation method and the EPRI engineering method can be used to calculate the J-integral when the option 3 FAC is to be established. When only the ranges of the yield stress, ultimate strength and JIc of the material are available, rather than the exact material stressstrain curve and its JIc and JR curve, some approximate predictive methods can be used to analyze the fracture behavior of piping, such as the U factor presented by Xu’ and the 2 factor given in the IWB-3650 procedure in the ASME Code, Section XI.’
When the mechanical and fracture properties such as the stress-strain curves, fracture toughness and JR curve of a material are obtained, finite-element methods can be used to calculate the applied J-integral, and the results can then be used to predict the initiation and maximum loads of the piping with flaws. This method is time consuming and inconvenient for practical application.’ The EPRI J estimation scheme* is known to be an effective engineering method to calculate the J-integral. The J-integral tearing modulus method3 can be used to analyze the maximum (instability) moments for piping with cracks under bending. With the failure assessment diagram (FAD) approach,4,5 the failure moments (the initiation and instability moments, or the plastic collapse moments) can be predicted. 207
208
H. X2.4et al.
2 TRUE STRESS-STRAIN CARBON STEEL PIPES
CURVES
OF
3 FACs FOR CARBON STEEL PIPING CONTAINING CIRCUMFERENTIAL THROUGH-WALL CRACKS
The true stress-strain curves of hot drawn and cold drawn carbon steel pipes are shown in Fig. 1. It can be shown that the curve for hot drawn carbon steel pipe exhibits a long yield plateau. The yield plateau in the curve of cold drawn carbon steel pipe is not obvious, but both curves possess three-segment characteristics. It is thus impossible to describe this kind of curve properly by only one expression, such as the RambergOsgood relation. Li et ~1.~ proposed the three-segment fitting method to deal with the stress-strain curves with yield plateau. They extended the expression in Appendix A of the EPRI NP-1931’ from two segments to three segments as following & -=-
u
EOl
CO1
& -=
-
&a1
( uo1
-=&
_u
E02
u
u
5
UOl
n* (To1 <
u
52
(To2
(1)
) I
n’
( go2 >
u >
co2
1
Fitted parameters of carbon steel pipes from eqn (1) for the stress-strain curves in Fig. 1 are listed in Table 1.
e ca !a
550 500 450
V
ii a, L,
In the third version of the CEGB/RG approach, the option 2 FAC obtained directly from the material stress-strain curve is expressed as K, =
Esref -++ LP,
L;u 2E~v,
-Ii2
I
(2)
where .srefis a reference strain obtained from the true stress-strain curve for the material at a reference stress level of u,,~ = Lruy and where uY is the yield stress of the material. This option of FAC is independent of the geometry of the structure containing defects. For the measured true stress-strain data of hot and cold drawn carbon steel pipes shown in Fig. 1, the option 2 FACs are shown in Figs 2 and 3, respectively. The option 1 FAC is also illustrated in each figure. For hot drawn carbon steel pipe, the option 2 FAC has a sharp drop near L, = 1.0 as shown in Fig. 2, due to the large yield plateau in the material stress-strain curve. Because the yield plateau in the material stress-strain curve of cold drawn pipe is not obvious, the option 2 FAC for this kind of steel pipe does not show any sharp drop. Since for the carbon steel pipes, the material stress-strain curves are described by the three-segment fitting expressions rather than the Ramberg-Osgood relation, the EPRI Jestimation scheme can not be used directly. The present authors have developed a new J-integral estimation scheme,7,9 which is expressed by the three-segment relations as follows-
400
I (3)
W25M,, J = J&h> J = J&z,) + Jp2 MO,< M 5 MO2
350
J = J&L,) + Jpj
4 Hot Drawn C.S.Pipe n Cold Drawn C.S.Pipe
250 200
‘61234567
6
9
10
Strain(%) Fig. 1. True stress-strain
curves of carbon steel pipes.
M > A402
where II4 is the applied moment, J,(a,) the linear elastic component of the J-integral corrected for plasticity, a, an effective crack length modified by the Irwin plastic zone correction, and Jp2 and Jp3 are the plastic components of the J-integral. Their expressions were derived by Xu7 using the h, functions in the EPRI handbook.” The FACs obtained with option 3 in the CEGB/R6 approach using the J expressions of eqn (3) are also shown in Figs 2 and 3,
Fracture
assessment
209
of carbon steel piping
Table 1. Fitted parameters with the three-segment expressions Pipe type
n3
Hot drawn Cold drawn
118.1 17.4
aal
3.10 4.22
co2 (MW
(MW
321.1 283.3
respectively, for hot and cold drawn pipes containing circumferential through-wall cracks. Three options of FACs for hot and cold drawn GB20 carbon steel pipes of the same geometry and crack size are shown in Fig. 4. The following conclusions can be deduced from five FACs in this figure: 1. For hot drawn carbon steel pipe containing a circumferential through-wall crack under bending, no sharp drop exists near L, = 1-O in the option 3 FAC established by the three-segment J-estimation scheme developed by the authors, although there is a large yield plateau in the material stress-strain curve. This can be supported by the distribution law of stress on the cracked pipe section under bending. Since the stresses are linearly rather than uniformly distributed, no yield plateau is exhibited during bending. 2. The sharp drop near L, = 1.0 in the option 2 FAC does not describe the behavior of circumferentially cracked piping under bending when the material stress-strain curve shows a large yield plateau. In this case, the option 2 curve falls significantly inside the option 3 curve and would lead to over-conservative assessments for piping under bending.
%l
(%I
&a2
0.160 0.152
328.4 320.1
W)
2.430 1.232
3. The option 2 and 3 FACs in the range of L, > 1 are greatly influenced by the shape and the length of the yield plateau of the material stress-strain curves. 4 ANALYTICAL PREDICTION AND EXPERIMENTAL DETECTION FOR INITIATION MOMENTS OF PIPING CIRCUMFERENTIAL THROUGH-WALL CRACKS 4.1 Experimental method initiation moments
WITH
for detecting
Two experimental techniques were used to detect the initiation moments: the direct current potential drop method and acoustic emission method. Results showed that the initiation moments detected by these two experimental methods agree with each other.7 4.2 Initiation
moments
Four analytical methods were used to determine the initiation moments: 1. J = JIc (the option 3 FAC in the R6 FAD) with the J-integral estimation scheme developed by the authors mentioned above 1.2
1.2
I
1.0
2e= 1200 1.0
28=120~,125~.1350
& 0.8
0.8
0.6
-
- Option 1 Option 2 Option 3
0.4
0.2 0.2
0.0
Fig. 2. FAG
0.5
0.0 1.0
Lr
1.5
of hot drawn carbon steel pipe under bending.
Fig. 3. FACs
0.5
1.0
*
Lr
1.5
of cold drawn carbon steel pipe under bending.
H. Xu et al.
210
0.0 I 0.0
0.5
Fig. 4. FACs
‘.O
of hot and cold drawn under bending.
1.5
Lr
carbon
steel niues 1
1
(see eqn (3)), where Jlc = 279-27 kN/m which is determined by the full-scale circumferentially cracked pipe specimen.7 2. Factor U expression presented by the authors;7 U is defined as plastic limit moments divided by initiation moments. 3. R6 FAD with option 1 FAC. 4. R6 FAD with option 2 FAC. The predicted and measured initiation moments and their relative errors are summarized in Table 2. According to Table 2, the J-estimation scheme proposed by the authors can quite accurately predict the initiation moments and all four methods are conservative; among them the option 1 FAC of R6 FAD is most conservative. 5 ANALYTICAL PREDICTION EXPERIMENTAL DETECTION MAXIMUM MOMENTS
AND FOR
Four analytical methods were used to predict the maximum moments: Table
2. The
Pipe identifier
predicted
and
Geometry (mm)
measured
initiation moments in parentheses
in
kN .m
and
R6 FAD opt. 2 FAC
R6 FAD opt. 3 FAC
18.77 (4:;;“)
19.64 (-4.23%) 18.33
20.58 (0.37%) 19.13 (-3.93%) 17.69 (-7.63%)
1.59 X 6
120
6-2
diameter
159 X 6
125
159 X 6
Loads (P) versus load-line displacements (A) for two pipes under four-point bending are shown in Fig. 6. Crack initiation was detected by.the direct current potential drop method when crack initiation was taken to occur when the P-A curve deviated from the initial linear portion significantly (points A and B in Fig. 6). Values of initiation and maximum moments (loads) for each pipe are quite close to each other. Therefore, after the crack initiated, only a little
R6 FAD opt. 1 FAC
diameter
diameter
6 COMPARISON OF MEASURED INITIATION AND MAXIMUM MOMENTS
Crack angle (deg)
6-l
6-3
1. J-integral tearing modulus method with the J-integral estimation scheme developed by the authors. 2. Factor 2 general expression in IWB-3650 in the ASME Code Section XI. 3. R6 FAD with option 1 FAC. 4. R6 FAD with option 3 FAC established by the J-estimation scheme developed by the authors.7,9 The loci of assessment points under the maximum moment (unstable growth moment) with ductile crack growth for one pipe are analyzed in the failure assessment diagram with option 1 and option 3 FACs as shown in Fig. 5. C, and C, are predicted crack initiation points, and E, and E, the contact points of assessment loci under the maximum moment with FACs. The predicted maximum moments and relative errors to measured ones for three pipes are summarized in Table 3. With the J-estimation scheme developed by the authors, the maximum moments for circumferentiaily cracked pipes can be quite accurately predicted by both the J/T modulus method and the failure assessment diagram approach.
135
(-14.1%) 15.64 (-18.5%)
(,;:g%’ (-11.8%)
their Factor u 19.54 (-4.71%) 18.59 (-6.69%) 16.69 (-13.0%)
relative
errors, Measured moments 20.51 19.91 19-19
Fracture
I
assessment
29=135O
211
of carbon steel piping
(
120 % v
100
a 0.6
80
0.4
. Pipe 2 (Init.Point o Pipe 3 (Init.Point
0.2 00 1.0
A) B)
1.5
Lr
Fig. 5. Crack growth analysis by the CEGB R6 FAD.
0
2
4
6
8
10
12
14
A(mr-4
load increment is needed to lead the crack growth. This means that the potential of the load bearing capability after crack initiation is very limited, and it is reasonable and essential to assessthe crack initiation for this kind of piping.
7 CONCLUSION
1. The stress-strain curve for hot drawn carbon steel pipe exhibits a long yield plateau. 2. The yield plateau in the stress-strain curve for cold drawn carbon steel pipe is not obvious. 3. The three-segment fitting method can properly describe the material stress-strain curves of carbon steel pipes. 4. The J-integral estimation scheme developed Table 3. The
predicted
and
measured
Pipe identifier
Geometry (mm)
Crack angle (deg)
6-l
diameter 159 X 6
120
6-2
diameter 159 X 6
125
6-3
diameter 159 x 6
135
Fig. 6. Loads versus load-line displacements for pipes under bending.
by the authors can be applied to analyze and assess the fracture of carbon steel piping with circumferential cracks quite accurately. In this way, h, values for J, estimation in the EPRI handbooks could still be used, although the material stressstrain curves are not described by the Ramberg-Osgood relation. 5. The direct current potential drop and acoustic emission methods can quite accurately detect the crack initiation of circumferentially cracked piping. The experimental results by the two methods agree with each other. 6. The initiation and maximum moments for circumferentially cracked piping of carbon steel under bending are quite close to each other.
maximum moments in parentheses R6 FAD opt. 1 FAC 19.02 (-10.5%) 17.76 (-14.4%) 15.59 (-21.4%)
in
kN .m
and
their
relative
errors,
R6 FAD opt. 3 FAC
JIT modules
Factor Z
Measured moments
20.76
20.76
19.60
21.26 20.75 19.83
H. Xu et al.
212
REFERENCES 1. Kumar, V. & German, M. D., Nonlinear analysis of surface cracks in cylinders. The Joint ASMEISES Applied
2. 3.
4. 5.
Mechanics
and Engineering
Science Conference,
Berkeley, California, June 1988. Kumar, V., German, M. D. & Shih, C. F., An engineeringapproach for elastic-plastic fracture analysis.EPRI NP-1931,1981. Paris, P. C., Tada, H., Zahoor, A. & Ernst, H., The theory of instability of the tearing mode of elasticplastic crack growth, elastic-plastic fracture. ASTM STP668, 1979,pp. 5-36. Bloom, J. M. & Malik, S. N., Procedure for the assessment of the integrity of nuclear pressurevessels and piping containing defects.EPRI NP-2431,1982. Harrison, P. P., Loosemore,K. & Milne, I., Assessment of the integrity of structures containing defects. CEGB
Report R/H/R6,1976. 6. Mime, I., Ainsworth, R. A., Dowling, A. R. & Stewat, A. T., Assessmentof integrity of structure containing defects. CEGB Report R/H/RG-rev.3, 1986. 7. Xu, H., The engineeringassessment method for flaws in piping. Ph.D. Dissertation, East China University of Scienceand Technology, Shanghai,P.R. China, 1995(in Chinese). 8. ASME XI IWB-3650 and Appendix H, Flaw Evaluation Procedures
and Acceptance
Criteria for Ferritic
Piping.
ASME, New York, 1989. 9. Li, P. N., Hu, Z. M., Wang, W. Q. & Ju, D. Y., The FACs of GB 16MnR Steel and Application in Engineering, Trans. 3rd National Conference on Pressure Vessels and Piping, Hefei, P. R. China, 1992 (in Chinese). 10. Zahoor, A., Ductile Fracture Handbook, Vol. 1, EPRI NP-6301,1989.
Inc. J. Pres. Ves. & Piping 69 (1996) 207-212 Copyright 0 1996 Elsevier Science Limited Printed in Northern Ireland. All rights reserved 0308-0161/96/$15.00
0308-0161(95)00127-l
Analytical and experimental fracture assessment of carbon steel piping with circumferential through-wall cracks under bending H. Xu, P. N. Li, Y. J. Xie Research Institute
of Process Equipment
and Pressure Vessels, East China Shanghai 200237, P.R. China
University
of Science and Technology,
Z. R. Huang Department
of Mechanical
Engineering,
Jiangsu Institute
of Petrochemical
Technology,
Jiangsu 213016, P.R. China
(Received 25 October 1995;accepted 16 November 1995)
In this paper the true stress-straincurves of carbon steel pipes are described by a three-segmentfitting method rather than the Ramberg-Osgood relation for their yield plateau characteristics.Failure assessmentcurves for carbon steel piping containing circumferential through-wall cracks were obtained by different options in the CEGB/RG approach. The J-integral was calculated using a new expression proposed by the authors. Initiation and maximum moments of piping under bending were predicted by several methods and measured by experiments. Calculated moments were quite close to test results. Copyright 0 1996Elsevier ScienceLtd.
1 INTRODUCTION
In the third version of the CEGB/R6 approach,6 three different options for failure assessment curves (FACs) are offered. They range from the simplest universal curve (option l), which is independent of material and geometry, to the most complex curve (option 3), which is derived for a particular geometry and material. Both the finite-element calculation method and the EPRI engineering method can be used to calculate the J-integral when the option 3 FAC is to be established. When only the ranges of the yield stress, ultimate strength and JIc of the material are available, rather than the exact material stressstrain curve and its JIc and JR curve, some approximate predictive methods can be used to analyze the fracture behavior of piping, such as the U factor presented by Xu’ and the 2 factor given in the IWB-3650 procedure in the ASME Code, Section XI.’
When the mechanical and fracture properties such as the stress-strain curves, fracture toughness and JR curve of a material are obtained, finite-element methods can be used to calculate the applied J-integral, and the results can then be used to predict the initiation and maximum loads of the piping with flaws. This method is time consuming and inconvenient for practical application.’ The EPRI J estimation scheme* is known to be an effective engineering method to calculate the J-integral. The J-integral tearing modulus method3 can be used to analyze the maximum (instability) moments for piping with cracks under bending. With the failure assessment diagram (FAD) approach,4,5 the failure moments (the initiation and instability moments, or the plastic collapse moments) can be predicted. 207
208
H. X2.4et al.
2 TRUE STRESS-STRAIN CARBON STEEL PIPES
CURVES
OF
3 FACs FOR CARBON STEEL PIPING CONTAINING CIRCUMFERENTIAL THROUGH-WALL CRACKS
The true stress-strain curves of hot drawn and cold drawn carbon steel pipes are shown in Fig. 1. It can be shown that the curve for hot drawn carbon steel pipe exhibits a long yield plateau. The yield plateau in the curve of cold drawn carbon steel pipe is not obvious, but both curves possess three-segment characteristics. It is thus impossible to describe this kind of curve properly by only one expression, such as the RambergOsgood relation. Li et ~1.~ proposed the three-segment fitting method to deal with the stress-strain curves with yield plateau. They extended the expression in Appendix A of the EPRI NP-1931’ from two segments to three segments as following & -=-
u
EOl
CO1
& -=
-
&a1
( uo1
-=&
_u
E02
u
u
5
UOl
n* (To1 <
u
52
(To2
(1)
) I
n’
( go2 >
u >
co2
1
Fitted parameters of carbon steel pipes from eqn (1) for the stress-strain curves in Fig. 1 are listed in Table 1.
e ca !a
550 500 450
V
ii a, L,
In the third version of the CEGB/RG approach, the option 2 FAC obtained directly from the material stress-strain curve is expressed as K, =
Esref -++ LP,
L;u 2E~v,
-Ii2
I
(2)
where .srefis a reference strain obtained from the true stress-strain curve for the material at a reference stress level of u,,~ = Lruy and where uY is the yield stress of the material. This option of FAC is independent of the geometry of the structure containing defects. For the measured true stress-strain data of hot and cold drawn carbon steel pipes shown in Fig. 1, the option 2 FACs are shown in Figs 2 and 3, respectively. The option 1 FAC is also illustrated in each figure. For hot drawn carbon steel pipe, the option 2 FAC has a sharp drop near L, = 1.0 as shown in Fig. 2, due to the large yield plateau in the material stress-strain curve. Because the yield plateau in the material stress-strain curve of cold drawn pipe is not obvious, the option 2 FAC for this kind of steel pipe does not show any sharp drop. Since for the carbon steel pipes, the material stress-strain curves are described by the three-segment fitting expressions rather than the Ramberg-Osgood relation, the EPRI Jestimation scheme can not be used directly. The present authors have developed a new J-integral estimation scheme,7,9 which is expressed by the three-segment relations as follows-
400
I (3)
W25M,, J = J&h> J = J&z,) + Jp2 MO,< M 5 MO2
350
J = J&L,) + Jpj
4 Hot Drawn C.S.Pipe n Cold Drawn C.S.Pipe
250 200
‘61234567
6
9
10
Strain(%) Fig. 1. True stress-strain
curves of carbon steel pipes.
M > A402
where II4 is the applied moment, J,(a,) the linear elastic component of the J-integral corrected for plasticity, a, an effective crack length modified by the Irwin plastic zone correction, and Jp2 and Jp3 are the plastic components of the J-integral. Their expressions were derived by Xu7 using the h, functions in the EPRI handbook.” The FACs obtained with option 3 in the CEGB/R6 approach using the J expressions of eqn (3) are also shown in Figs 2 and 3,
Fracture
assessment
209
of carbon steel piping
Table 1. Fitted parameters with the three-segment expressions Pipe type
n3
Hot drawn Cold drawn
118.1 17.4
aal
3.10 4.22
co2 (MW
(MW
321.1 283.3
respectively, for hot and cold drawn pipes containing circumferential through-wall cracks. Three options of FACs for hot and cold drawn GB20 carbon steel pipes of the same geometry and crack size are shown in Fig. 4. The following conclusions can be deduced from five FACs in this figure: 1. For hot drawn carbon steel pipe containing a circumferential through-wall crack under bending, no sharp drop exists near L, = 1-O in the option 3 FAC established by the three-segment J-estimation scheme developed by the authors, although there is a large yield plateau in the material stress-strain curve. This can be supported by the distribution law of stress on the cracked pipe section under bending. Since the stresses are linearly rather than uniformly distributed, no yield plateau is exhibited during bending. 2. The sharp drop near L, = 1.0 in the option 2 FAC does not describe the behavior of circumferentially cracked piping under bending when the material stress-strain curve shows a large yield plateau. In this case, the option 2 curve falls significantly inside the option 3 curve and would lead to over-conservative assessments for piping under bending.
%l
(%I
&a2
0.160 0.152
328.4 320.1
W)
2.430 1.232
3. The option 2 and 3 FACs in the range of L, > 1 are greatly influenced by the shape and the length of the yield plateau of the material stress-strain curves. 4 ANALYTICAL PREDICTION AND EXPERIMENTAL DETECTION FOR INITIATION MOMENTS OF PIPING CIRCUMFERENTIAL THROUGH-WALL CRACKS 4.1 Experimental method initiation moments
WITH
for detecting
Two experimental techniques were used to detect the initiation moments: the direct current potential drop method and acoustic emission method. Results showed that the initiation moments detected by these two experimental methods agree with each other.7 4.2 Initiation
moments
Four analytical methods were used to determine the initiation moments: 1. J = JIc (the option 3 FAC in the R6 FAD) with the J-integral estimation scheme developed by the authors mentioned above 1.2
1.2
I
1.0
2e= 1200 1.0
28=120~,125~.1350
& 0.8
0.8
0.6
-
- Option 1 Option 2 Option 3
0.4
0.2 0.2
0.0
Fig. 2. FAG
0.5
0.0 1.0
Lr
1.5
of hot drawn carbon steel pipe under bending.
Fig. 3. FACs
0.5
1.0
*
Lr
1.5
of cold drawn carbon steel pipe under bending.
H. Xu et al.
210
0.0 I 0.0
0.5
Fig. 4. FACs
‘.O
of hot and cold drawn under bending.
1.5
Lr
carbon
steel niues 1
1
(see eqn (3)), where Jlc = 279-27 kN/m which is determined by the full-scale circumferentially cracked pipe specimen.7 2. Factor U expression presented by the authors;7 U is defined as plastic limit moments divided by initiation moments. 3. R6 FAD with option 1 FAC. 4. R6 FAD with option 2 FAC. The predicted and measured initiation moments and their relative errors are summarized in Table 2. According to Table 2, the J-estimation scheme proposed by the authors can quite accurately predict the initiation moments and all four methods are conservative; among them the option 1 FAC of R6 FAD is most conservative. 5 ANALYTICAL PREDICTION EXPERIMENTAL DETECTION MAXIMUM MOMENTS
AND FOR
Four analytical methods were used to predict the maximum moments: Table
2. The
Pipe identifier
predicted
and
Geometry (mm)
measured
initiation moments in parentheses
in
kN .m
and
R6 FAD opt. 2 FAC
R6 FAD opt. 3 FAC
18.77 (4:;;“)
19.64 (-4.23%) 18.33
20.58 (0.37%) 19.13 (-3.93%) 17.69 (-7.63%)
1.59 X 6
120
6-2
diameter
159 X 6
125
159 X 6
Loads (P) versus load-line displacements (A) for two pipes under four-point bending are shown in Fig. 6. Crack initiation was detected by.the direct current potential drop method when crack initiation was taken to occur when the P-A curve deviated from the initial linear portion significantly (points A and B in Fig. 6). Values of initiation and maximum moments (loads) for each pipe are quite close to each other. Therefore, after the crack initiated, only a little
R6 FAD opt. 1 FAC
diameter
diameter
6 COMPARISON OF MEASURED INITIATION AND MAXIMUM MOMENTS
Crack angle (deg)
6-l
6-3
1. J-integral tearing modulus method with the J-integral estimation scheme developed by the authors. 2. Factor 2 general expression in IWB-3650 in the ASME Code Section XI. 3. R6 FAD with option 1 FAC. 4. R6 FAD with option 3 FAC established by the J-estimation scheme developed by the authors.7,9 The loci of assessment points under the maximum moment (unstable growth moment) with ductile crack growth for one pipe are analyzed in the failure assessment diagram with option 1 and option 3 FACs as shown in Fig. 5. C, and C, are predicted crack initiation points, and E, and E, the contact points of assessment loci under the maximum moment with FACs. The predicted maximum moments and relative errors to measured ones for three pipes are summarized in Table 3. With the J-estimation scheme developed by the authors, the maximum moments for circumferentiaily cracked pipes can be quite accurately predicted by both the J/T modulus method and the failure assessment diagram approach.
135
(-14.1%) 15.64 (-18.5%)
(,;:g%’ (-11.8%)
their Factor u 19.54 (-4.71%) 18.59 (-6.69%) 16.69 (-13.0%)
relative
errors, Measured moments 20.51 19.91 19-19
Fracture
I
assessment
29=135O
211
of carbon steel piping
(
120 % v
100
a 0.6
80
0.4
. Pipe 2 (Init.Point o Pipe 3 (Init.Point
0.2 00 1.0
A) B)
1.5
Lr
Fig. 5. Crack growth analysis by the CEGB R6 FAD.
0
2
4
6
8
10
12
14
A(mr-4
load increment is needed to lead the crack growth. This means that the potential of the load bearing capability after crack initiation is very limited, and it is reasonable and essential to assessthe crack initiation for this kind of piping.
7 CONCLUSION
1. The stress-strain curve for hot drawn carbon steel pipe exhibits a long yield plateau. 2. The yield plateau in the stress-strain curve for cold drawn carbon steel pipe is not obvious. 3. The three-segment fitting method can properly describe the material stress-strain curves of carbon steel pipes. 4. The J-integral estimation scheme developed Table 3. The
predicted
and
measured
Pipe identifier
Geometry (mm)
Crack angle (deg)
6-l
diameter 159 X 6
120
6-2
diameter 159 X 6
125
6-3
diameter 159 x 6
135
Fig. 6. Loads versus load-line displacements for pipes under bending.
by the authors can be applied to analyze and assess the fracture of carbon steel piping with circumferential cracks quite accurately. In this way, h, values for J, estimation in the EPRI handbooks could still be used, although the material stressstrain curves are not described by the Ramberg-Osgood relation. 5. The direct current potential drop and acoustic emission methods can quite accurately detect the crack initiation of circumferentially cracked piping. The experimental results by the two methods agree with each other. 6. The initiation and maximum moments for circumferentially cracked piping of carbon steel under bending are quite close to each other.
maximum moments in parentheses R6 FAD opt. 1 FAC 19.02 (-10.5%) 17.76 (-14.4%) 15.59 (-21.4%)
in
kN .m
and
their
relative
errors,
R6 FAD opt. 3 FAC
JIT modules
Factor Z
Measured moments
20.76
20.76
19.60
21.26 20.75 19.83
H. Xu et al.
212
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