- Email: [email protected]
Collapse loads for circumferentially through-wall cracked pipes subjected to combined torsion and bending moments
Engineering Fracture Mechanics xxx (2014) xxx–xxx
Contents lists available at ScienceDirect
Engineering Fracture Mechanics journal homepage: www.elsevier.com/locate/engfracmech
Collapse loads for circumferentially through-wall cracked pipes subjected to combined torsion and bending moments Kunio Hasegawa a,⇑, Yinsheng Li a, Kazuya Osakabe b a b
Japan Nuclear Energy Safety Organization (JNES), Toranomon Towers Office, Toranomon 4-1-28, Minato-ku, Tokyo 105-0001, Japan Mizuho Information & Research Institute (MHIR), Kanda nishi-cho 2-3, Chiyoda-ku, Tokyo 101-8443, Japan
a r t i c l e
i n f o
Article history: Available online xxxx Keywords: Flaw evaluation Collapse load Combined bending and torsion moment Circumferential crack Cracked pipe Through-wall crack
a b s t r a c t Pressurized piping items in power plants may experience combined torsion and bending moments during operation. Currently, there is a lack of guidance in flaw evaluation procedures for combined loading modes of pressure, torsion and bending loads. Recently, collapse bending moments for pipes under torsion moments were analyzed by finite element modelling. Equivalent moments defined as the root of the sum of the squares of the torsion and bending moments are shown to be equal to pure bending moments for various diameter pipes containing circumferentially part through cracks. This paper focuses on behaviour of plastic collapse moments for pipes with circumferential through-wall cracks using finite element analysis, and describes the behaviour of the equivalent bending moments for flaw evaluation procedures, referring the results of part through cracked pipes. Ó 2014 Published by Elsevier Ltd.
1. Introduction Piping items in power plants may experience internal pressure, axial load, bending and torsion loads during operation. Several methods for predicting failure loads for circumferential cracked pipes under combined loadings had been developed for assessment of piping integrity [1,2]. The proposed methods for combined loads are applicable on Mode I type loading of internal pressure, axial tension and bending. That is, Mode II type of torsion moment is not included in these methods. When cracks detected in piping items are assessed by using fitness-for-service Codes, such as ASME Boiler and Pressure Vessel Code Section XI [3] or JSME S NA1-2008 [4] Code. These ASME and JSME Codes provide evaluation procedures for predicting plastic collapse loads for cracks in pipes subjected to internal pressure and bending moment under fully plastic conditions. Currently, torsion load is also not included in these Codes. In addition, the depths of the cracks are less than or equal to 75% of pipe wall thickness for the evaluation procedures. This is because the Codes do not allow leakage from pipes. A guidance including the torsion moment is developed for pipes with circumferential part through wall cracks. It is reported that combined bending and torsion moments at collapse can be estimated by pure bending moments, when the combined bending and torsion moments are given by the equivalent moment defined as the root of the sum of the squares of the torsion and bending moments [5–12]. On the other hand, evaluation of collapse load for circumferential through-wall crack is necessary for leak-before-break evaluation [13,14] and temporary acceptance of coolant leakage from power plant piping [15]. This paper focuses on combined torsion and bending moments at collapse for a pipe containing a circumferential through-wall crack, and shows validity of the equivalent moment at plastic collapse for circumferential through-wall crack, referring the equivalent moment for a part through wall crack. ⇑ Corresponding author. Tel.: +81 3 4511 1751; fax: +81 3 4511 1897. E-mail addresses: [email protected] (K. Hasegawa), [email protected] (Y. Li), [email protected] (K. Osakabe). 0013-7944/$ - see front matter Ó 2014 Published by Elsevier Ltd. http://dx.doi.org/10.1016/j.engfracmech.2013.12.013
Please cite this article in press as: Hasegawa K et al. Collapse loads for circumferentially through-wall cracked pipes subjected to combined torsion and bending moments. Engng Fract Mech (2014), http://dx.doi.org/10.1016/j.engfracmech.2013.12.013
2
K. Hasegawa et al. / Engineering Fracture Mechanics xxx (2014) xxx–xxx
Nomenclature a D0 Mb, MB MB0 Meq Mt, MT Mx, My, Mz R t b h hb
circumferential crack depth pipe outside diameter applied and collapse bending moments under given torsion moment collapse bending moment without torsion moment (pure bending moment) equivalent collapse moment applied and collapse torsion moments orthogonal moment components at a given position in a piping system pipe mean radius nominal pipe wall thickness angle to neutral axis of cracked pipe one half of circumferential crack angle applied bending angle flow stress primary membrane stress in the pipe at the crack location torsion stress American Society of Mechanical Engineers finite element The Japan Society of Mechanical Engineers
rf rm s ASME FE JSME
2. Plastic collapse moment by bending and torsion 2.1. Plastic collapse bending moment by limit load criteria In case of a circumferential part-through crack, plastic collapse bending moment for a pipe is provided by ASME B&PV Code Section XI [3] and JSME (Japan Society of Mechanical Engineers) Code on Fitness – for – Service Rules [4]. The concept of the plastic collapse moment was developed by Battelle Columbus Laboratories [16]. Fig. 1 illustrates the stress distribution at incipient plastic collapse in a pipe. The internal stress distribution in the pipe wall in the cracked section is assumed to be at plus or minus the flow stress, as depicted in Fig. 1. From the equilibrium of bending moment and axial force, plastic collapse bending moment MB0 is given as follows; For more common case of h + b 6 p
h i a MB0 ¼ 2rf R2 t 2 sin b sin h t
ð1Þ
with
b¼
1 2
a t
p hp
rm rf
ð2Þ
where rf is the flow stress, h the half crack angle, a the crack depth, t the wall thickness, R the mean radius of the pipe, b the neutral angle, and rm the membrane stress. The flow stress is normally taken as the average value of the yield stress and ultimate tensile strength of the pipe material [3,4]. If the crack is long enough and both ends of the crack length are in the region of compression stress area, the plastic collapse moment MB0 is given as follows; For less common case of h + b > p
a MB0 ¼ 2rf R2 t 2 sin b t
ð3Þ
Fig. 1. Nomenclature and stress distribution of a pipe with a circumferential crack.
Please cite this article in press as: Hasegawa K et al. Collapse loads for circumferentially through-wall cracked pipes subjected to combined torsion and bending moments. Engng Fract Mech (2014), http://dx.doi.org/10.1016/j.engfracmech.2013.12.013
K. Hasegawa et al. / Engineering Fracture Mechanics xxx (2014) xxx–xxx
3
with
b¼
a rm 1 t rf 2
p
a t
ð4Þ
In case of a through-wall crack, both end of the crack are always tensile stress region. That is h + b 6 p, even when the crack length is long enough. There is not a situation of h + b > p. The collapse moment for a pipe with through-wall crack is obtained by Eqs. (1) and (2) replacing a = t, it is written as [14];
MB0 ¼ 2rf R2 t½2 sin b sin h
ð5Þ
with
b¼
1 2
php
rm rf
ð6Þ
Eqs. (1) and (3) are the basis formulas of plastic collapse moments for pipes with part through cracks, and Eq. (5) can estimate plastic collapse for pipes with through-wall cracks. These equations are called limit load criteria or net-section stress criteria and they are applicable for thin-walled pipes. When determining allowable flaw depth and length, Eqs. (1) and (3) are used with combination of safety factors [17]. When assessing leak-before-break [14] and temporary acceptance of coolant leakage from pipes [15], Eq. (5) is used for estimating break load. These equations are only applied for bending moment with internal pressure as membrane stress rm and lack of torsion moment. 2.2. Combined bending and torsion moments In accordance with design and construction Codes for pipes without cracks [18,19], combination of bending and torsion loads are resolved into orthogonal moment components and summed into an equivalent load by vector summation. For example, the equivalent moment is given by;
Meq ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi M2x þ M2y þ M 2z
ð7Þ
where the equivalent moment Meq is a resultant moment applied in the calculation to combine the orthogonal moment components, Mx, My and Mz at a given position in a piping system. In the design and construction Codes, needless to say, the assumption is that these piping systems do not have any cracks. In addition, the Eq. (7) is generally applied for elastic stress condition. Ref. [11] shows that part through cracked pipes subjected to bending and torsion moments had been analyzed and the collapse moments can be described as moments defined as the root of the square of the torsion and bending moments. The pipes analyzed were 4-in (114.3 mm), 10.75-in. (268 mm) and 24-in. (609.6 mm) diameter pipes. The equivalent collapse moment Meq is defined as,
Meq ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi M2B þ M2T
ð8Þ
where MB is the bending moment and MT the torsion moment at collapse, respectively. The stress at the cracked section of the pipe is a plastic condition at the collapse, accompanying large deformation of the pipe. The equivalent moment Meq is almost constant for a part through cracked pipe subjected to torsion stress less than 20% of the flow stress. The Meq is equal to pure bending moment MB0 at collapse for a pipe with a part-through crack, where the depth is less than or equal to 75% of pipe wall thickness. In order to obtain the equivalent moment Meq for through-wall cracked pipes, plastic collapse bending moments with torsion moments are analyzed by FE analysis, as below. 3. Finite element analysis for wall thinning pipes 3.1. Analytical conditions Plastic collapse bending moments for 24-in. schedule 80 straight pipes with circumferential through-wall cracks were calculated under the condition of torsion moment and internal pressure by FE analysis. The model is illustrated in Fig. 2. The pipe outer diameter D0 is 609.6 mm and the wall thickness t is 30.9 mm. The length of the pipe is eight times larger than the outer diameter. The crack is located at the center of the pipe length. All of the positions at one end of the pipe are fixed, and the torsion and bending moments are applied at the other end of the pipe. Internal pressure of 8 MPa is also applied for the pipe, where 8 MPa corresponds to hoop stress of 74.9 MPa. The pressure of 8 MPa employed is coolant pressure for boiling water reactors. The angles of through-wall cracks for calculations are two cases, 2h = 90° and 135°. The crack is located in tensile stress side during the bending load. The crack depth and angle are a, and 2h, respectively, where through-wall crack depth is a = t. The crack is located such that its center coincides with the plane of the maximum tensile stress due bending. Please cite this article in press as: Hasegawa K et al. Collapse loads for circumferentially through-wall cracked pipes subjected to combined torsion and bending moments. Engng Fract Mech (2014), http://dx.doi.org/10.1016/j.engfracmech.2013.12.013
4
K. Hasegawa et al. / Engineering Fracture Mechanics xxx (2014) xxx–xxx
Fig. 2. Model of a cracked pipe receiving bending moment and torsion moment under internal pressure.
Pure torsion moment under internal pressure of 8 MPa was also calculated for circumferentially cracked pipe. Torsion angle was applied at the end of the pipe end, and the applied moment-torsion angle and the maximum torsion moment were obtained by FE analysis. Calculation conditions for the FE analysis are tabulated in Table 1. The FE analysis was conducted by ABAQUS standard 6.7-4. Mesh break down is shown in Fig. 3. Von Mises criterion was used for yield hypothesis. Large deformation formulation is invoked in order to obtain plastic collapse moment accurately under large deformation. The material employed in this paper is elastic-fully plastic stress–strain curve with the yield strength of 372 MPa, which is identified with the flow stress of the material. 3.2. Sequence of loading The sequence of the loading is; first pressurizing the pipe to the pressure of 8 MPa, then applying the given torsion moment MT on the pipe end, and finally the bending moment was imposed by incremental bending angle at the remote end, as illustrated in Fig. 2. The applied torsion moment is calculated from the corresponding shear stress s. The relation between the nominal torsion moment MT and shear stress s not taking account of the crack is expected by MT = 2pR2ts, where R is the pipe mean radius. 4. Calculation results 4.1. Moment–deflection curves and deformations Calculation results of bending moments Mb and bending angle hb for pipes with circumferential through wall cracks under constant torsion stress of s/rf and internal pressure of 8 MPa are calculated by FE analysis. Table 2 shows the results of bending moments at collapse and equivalent moments as a parameter of torsion stress. Before understanding the deformation Table 1 Calculation conditions for FE analysis. Program Stress strain curve Geometrical non-linearity Yield stress, ry = rf Young’s modulus, E Strain hardening, H Internal pressure (Hoop stress) Pipe diameter, D0 Pipe wall thickness, t Crack depth, a/t Crack angle, 2h
ABAQUS 6.7-4 Elastic-fully plastic Considered 372 MPa 200 GPa 0 8 MPa (74.9 MPa) 609.6 mm 30.9 mm 1.0 90°, 135°
Fig. 3. FE mesh break down of a circumferential cracked pipe.
Please cite this article in press as: Hasegawa K et al. Collapse loads for circumferentially through-wall cracked pipes subjected to combined torsion and bending moments. Engng Fract Mech (2014), http://dx.doi.org/10.1016/j.engfracmech.2013.12.013
5
K. Hasegawa et al. / Engineering Fracture Mechanics xxx (2014) xxx–xxx Table 2 Results of bending and equivalent moments for pipes with through-wall cracks calculated by FE analysis. Crack angle 2h°
Torsion stress and moment
MB, kN m
Meq, kN m
0 605 1210 1816 1916
2166 2074 1746 704 0
2166 2161 2124 1947 1916
0 605 908 1210 1235
1312 1170 928 233 0
1312 1317 1298 1233 1235
s/rf
MT, kN m
90
0 0.1 0.2 0.3 0.317
135
0 0.1 0.15 0.2 0.204
behaviour for through-wall crack, the plastic collapse moments for part through crack are introduced by using the moment–deflection curves. In case of part through crack of a/t = 0.75 and 2h = 90°, the relationship between the Mb and the hb is shown in Fig. 4 [5]. As shown in Fig. 4, the applied bending moment Mb increases with increasing bending angle hb, and attained the maximum bending moment. After the maximum bending moment, the bending moment decreases with increasing the bending angle hb. The maximum bending moment corresponds to the plastic moment MB. The plastic moments MB decrease with increasing the torsion stresses s. In case of through-wall crack, the relationship between the applied bending moment and bending angle obtained by FE analysis is shown in Fig. 5. This is the load–displacement curves for pipes with circumferential through-wall cracks of 2h = 90°. The plastic bending moment MB decreases with increasing torsion stress s, as the same behaviour of MB and s shown in Fig. 4. The MB at s/rf = 0 means pure bending moment at collapse. The pure bending moments at 2h = 90° and 135° are 2166 kN m and 1312 kN m, respectively, as tabulated in Table 2. On the other hand, pure bending moments can be estimated by Eq. (5). Estimated collapse moments using Eq. (5) for 2h = 90° and 135° are 1920 kN m and 1046 kN m, respectively, where membrane stress rm is due to only internal pressure of 8 MPa. The membrane stress is rm = 37.5 MPa, which is one half of hoop stress. The pure bending moments at collapse obtained by FE analysis are fair agreement with the estimated moments calculated by Eq. (5). Pure bending moment MB0 at collapse for a cracked pipe can be estimated by limit load criteria, as mentioned before. The estimated collapse moments using Eq. (5) were not compared with experimental data. This is because there are lots of experimental data of MB0 performed by bending tests [20,21] and each flow stress depends on the pipe material. The moments MB0 obtained in these calculations were not compared with those obtained by experimental data. This is because the calculations herein employed the elastic fully plastic stress strain curve.
3500
p = 8 MPa 3000 2500
0.1 0.2
2000
0.3
1500
0.35 D o = 609.6 mm t = 30.9mm a/t = 0.75
1000
0.4
500 0 0
0.01
0.02
0.03
0.04
0.05
Fig. 4. Load–displacement curves for pipes with part through cracks of 2h = 90° [5].
Please cite this article in press as: Hasegawa K et al. Collapse loads for circumferentially through-wall cracked pipes subjected to combined torsion and bending moments. Engng Fract Mech (2014), http://dx.doi.org/10.1016/j.engfracmech.2013.12.013
6
K. Hasegawa et al. / Engineering Fracture Mechanics xxx (2014) xxx–xxx
2500
p = 8 MPa 2000
0.1
1500
0.2
1000
Do = 609.6mm t = 30.9mm
0.3
500
a/t = 1.0
0 0
0.05
0.1
0.15
Fig. 5. Load–displacement curves for pipes with through-wall crack of 2h = 90°.
Collapse bending moment, MB, Meq (kN-m)
4000
3000
Meq
2000
MB 1000
0 0
1000
2000
3000
4000
Collapse torsion moment, MT (kN-m) Fig. 6. Plastic collapse bending moment MB and equivalent moment Meq for pipes with cracks of a/t = 0.5 and 2h = 90° [5].
4.2. Effect of torsion on bending moment The plastic collapse bending moment MB for a circumferentially cracked pipe decreases with increasing torsion stress s, as shown in Figs. 4 and 5. Figs. 6 and 7 depict the relationship between the plastic collapse bending moments MB and the torsion moments MT for pipes with part through cracks of a/t = 0.5 and 0.75. Fig. 8 shows the relationship between MB and MT for pipes with through-wall cracks. When MT = 0, the bending moment is a pure bending moment, that is MB = MB0. When MB = 0, the moment is a pure torsion moment MT0, which was obtained by FE analysis under the conditions of the same material properties and crack sizes. Plastic collapse bending moment MB for pipes with part through cracks of a/t = 0.5 and 0.75 decreases with increasing torsion moment MT, as shown in Figs. 6 and 7. It is also observed that the MB for pipes with through-wall cracks of 2h = 90° and 135° decreases with increasing MT, as shown in Figs. 8 and 9. The decreases of the MB between the part through and through-wall cracks are similar, although the values of the MB are different.
5. Equivalent moments for pipes with cracks Equivalent moments Meq given by Eq. (2) are shown in Figs. 6 and 7 for part through cracked pipes with a/t = 0.5 and 0.75 and 2h = 90°. The moments Meq are almost horizontal, but slightly decrease, when the MT are small. When MT is large, the Meq becomes small. Please cite this article in press as: Hasegawa K et al. Collapse loads for circumferentially through-wall cracked pipes subjected to combined torsion and bending moments. Engng Fract Mech (2014), http://dx.doi.org/10.1016/j.engfracmech.2013.12.013
K. Hasegawa et al. / Engineering Fracture Mechanics xxx (2014) xxx–xxx
7
Collapse bending moment, MB, Meq (kN-m)
4000
3000
Meq 2000
MB 1000
0 0
1000
2000
3000
4000
Collapse torsion moment, MT, (kN-m) Fig. 7. Plastic collapse bending moment MB and equivalent moment Meq for pipes with cracks of a/t = 0.75 and 2h = 90° [5].
Collapse bending moment, M B or M eq (kN-m)
4000
3000
Meq 2000
1000
MB
0 0
500
1000
1500
2000
2500
Collapse torsion moment, MT (kN-m) Fig. 8. Plastic collapse bending moment MB and equivalent moment Meq for pipes with cracks of a/t = 1.0 and 2h = 90°.
In case of through-wall crack, the Meq were obtained as shown in Figs. 8 and 9, for pipes with a/t = 1.0 and 2h = 90° and 135°. The value of the Meq for through-wall cracked pipe is small, compared with those for part through cracked pipes with the same crack angle of 2h = 90° as, shown in Figs. 6–8. The Meq for the pipes with through-wall crack of 2h = 90° and 135° are almost constant in the entire range of MT. The torsion moments in power plants are generally small at many positions in piping systems. Based on plant design stress survey, it is sufficient to limit the torsion stress s up to 20% of the flow stress rf. The plant torsion actual range is illustrated in Figs. 6–9, as s/rf = 0.2. The torsion moments at s/rf = 0.2 in Figs. 6–9 are the same values of 1210 kN m, which were derived from MT = 2pR2ts , as mentioned before. The Meq for pipes with part through and through-wall cracks retains almost constant with increasing the torsion moment MT in the range of torsion stress of s/rf = 0.2, where the difference of the equivalent moment Meq against pure bending moment MB is within 10% of the pure bending moment. That is, the Meq is almost equal to MB0. It should be emphasized that the plastic collapse bending moments under torsion moments can be estimated by Eq. (5) with the condition of torsion stress, as follows;
Meq ¼ MB0
for s=rf 6 0:2
ð9Þ
This means that combined bending and torsion moments at collapse can be estimated by pure bending moment MB0 not only part through but also through-wall cracked pipes. Please cite this article in press as: Hasegawa K et al. Collapse loads for circumferentially through-wall cracked pipes subjected to combined torsion and bending moments. Engng Fract Mech (2014), http://dx.doi.org/10.1016/j.engfracmech.2013.12.013
8
K. Hasegawa et al. / Engineering Fracture Mechanics xxx (2014) xxx–xxx
Collapse bending moment, M B or M eq (kN-m)
3000
2500
2000
Meq
1500
1000
MB
500
0
0
500
1000
1500
2000
Collapse torsion moment, MT (kN-m) Fig. 9. Plastic collapse bending moment MB and equivalent moment Meq for pipes with cracks of a/t = 1.0 and 2h = 135°.
6. Conclusion Plastic collapse moments for pipes with through-wall cracks subjected to combined bending and torsion moments in the presence of internal pressure were investigated by FE analyses. As the results of the FE analysis, plastic collapse bending moments decrease with increasing torsion moments for through-wall cracked pipes. However, the equivalent moments defined as the root of the sum of the squares of the bending and torsion moments are almost constant against the torsion moments in the torsion stresses of actual plant range. This means that the plastic collapse bending plus torsion moments can be estimated by the pure bending moment for circumferentially through-wall cracked pipes, as the same with part through cracked pipes.
References [1] Jones MR, Eshelby JM. Limit solution’s for circumferential cracked cylinders under internal pressure and combined tension and bending. Nuclear Electric, Report TD/SID/REP/0032; 1990. [2] Lei Y, Budden PJ. Limit load solutions for thin-walled cylinders with circumferential cracks under combined internal pressure, axial tension and bending. J Strain Anal 2004;39:673–83. [3] ASME Boiler & Pressure Vessel Code, Section XI. Rules for inservice inspection of nuclear power plant components, American Society of Mechanical Engineers, New York; 2010. [4] JSME Code S NA-1-2008. Rules on Fitness-for-service for nuclear power plants. The Japan Society of Mechanical Engineers, Tokyo; 2008. [5] Li Y, Hasegawa K, Hoang P, Bezensek B. Prediction method for plastic collapse of pipes subjected to combined bending and torsion moments. ASME PVP2010-25101; 2010. [6] Li Y, Ida W, Hasegawa K, Hoang P, Bezensek B. Effect of pressure on plastic collapse under the combined bending and torsion moments for circumferentially surface flawed pipes. ASME PVP2010-25102; 2010. [7] Hoang P, Hasegawa K, Bezensek B, Li Y. Effect of torsion on equivalent bending moment for limit load and EPFM circumferential pipe flaw evaluations. ASME PVP2010-25283; 2010. [8] Bezensek B, Li Y, Hasegawa K, Hoang P. Proposal for inclusion of torsion in Section XI flaw evaluation procedures for pipes containing surface crack-like flaw. ASME PVP2010-25133; 2010. [9] Hoang P, Hasegawa K, Bezensek B, Li Y. Effect of torsion on equivalent bending moment for limit load and EPFM circumferential pipe flaw evaluations. J Press Vess Technol 2010;134:061206. December 2012. [10] Li Y, Hasegawa K, Hoang P, Bezensek B. Prediction method for plastic collapse of pipes subjected to combined bending and torsion moments. J Press Vess Technol 2012;134:061207. December 2012. [11] Bezensek B, Li Y, Hasegawa K, Hoang P. Inclusion of torsion loads in Section XI flaw evaluation procedures for pipes containing circumferential planar surface crack-like flaw on the basis of Limit Load Analysis. J Press Vess Technol 2012;134:031003. December 2012. [12] Li Y, Hasegawa K, Miura N, Hoshino K. Experimental investigation of failure estimation method for stainless steel pipes with a circumferential crack subjected to combined tensile and torsion loads. J Press Vess Technol 2013;135:041405. August 2013. [13] Hasegawa K, Okamoto A, Yokota H, Yamamoto Y, Shibata K, Matsumura K. Crack opening area of pressurized pipe for leak-before-break evaluation. JSME Int J Ser I 1991;34(3):332–8. [14] British Standard, Guide to methods for assessing the acceptability of flaws in metallic structures, Annex F: a procedure for leak-before-break assessment. BS 7910; 2005. [15] ASME Boiler & Pressure Vessel Code, Section XI Code Case N-513-3. Evaluation criteria for temporary acceptance of flaws in moderate energy class 2 or 3 piping; January 2009. [16] Canine MF, Broek D, Marschall CW, Rybicki EF, Sampath SG, Simonen FA, Wilkowski GM. Mechanical fracture predictions for sensitized stainless steel piping with circumferential cracks. EPRI NP-192; September 1976. [17] Norris DM, Marston TU, Tagart SW. Acceptance criteria for circumferential flaw in stainless steel piping. ASME PVP 1982;58:185–99.
Please cite this article in press as: Hasegawa K et al. Collapse loads for circumferentially through-wall cracked pipes subjected to combined torsion and bending moments. Engng Fract Mech (2014), http://dx.doi.org/10.1016/j.engfracmech.2013.12.013
K. Hasegawa et al. / Engineering Fracture Mechanics xxx (2014) xxx–xxx
9
[18] ASME Boiler & Pressure Vessel Code, Section III. Rules for construction of nuclear facility components, Division 1, Subsection NC, Class 2 components, NC-3653.3. American Society of Mechanical Engineers, New York; 2010. [19] AFCEN RCC-M, Design and construction rules for mechanical components for PWR nuclear islands. Subsection C-3658 determination of moments and section modulus; 2007 Edition. [20] NUREG/CP-0051. CSNI report no. 82. CSNI specialist meeting on Leak-Before-Break in nuclear piping. Monterey, California, USA; August 1984. [21] Scott PM, Ahmad J. NUREG/CR-4872. BMI-2149, Experimental and analytical assessment of circumferentially surface-cracked pipes under bending; April 1987.
Please cite this article in press as: Hasegawa K et al. Collapse loads for circumferentially through-wall cracked pipes subjected to combined torsion and bending moments. Engng Fract Mech (2014), http://dx.doi.org/10.1016/j.engfracmech.2013.12.013
Contents lists available at ScienceDirect
Engineering Fracture Mechanics journal homepage: www.elsevier.com/locate/engfracmech
Collapse loads for circumferentially through-wall cracked pipes subjected to combined torsion and bending moments Kunio Hasegawa a,⇑, Yinsheng Li a, Kazuya Osakabe b a b
Japan Nuclear Energy Safety Organization (JNES), Toranomon Towers Office, Toranomon 4-1-28, Minato-ku, Tokyo 105-0001, Japan Mizuho Information & Research Institute (MHIR), Kanda nishi-cho 2-3, Chiyoda-ku, Tokyo 101-8443, Japan
a r t i c l e
i n f o
Article history: Available online xxxx Keywords: Flaw evaluation Collapse load Combined bending and torsion moment Circumferential crack Cracked pipe Through-wall crack
a b s t r a c t Pressurized piping items in power plants may experience combined torsion and bending moments during operation. Currently, there is a lack of guidance in flaw evaluation procedures for combined loading modes of pressure, torsion and bending loads. Recently, collapse bending moments for pipes under torsion moments were analyzed by finite element modelling. Equivalent moments defined as the root of the sum of the squares of the torsion and bending moments are shown to be equal to pure bending moments for various diameter pipes containing circumferentially part through cracks. This paper focuses on behaviour of plastic collapse moments for pipes with circumferential through-wall cracks using finite element analysis, and describes the behaviour of the equivalent bending moments for flaw evaluation procedures, referring the results of part through cracked pipes. Ó 2014 Published by Elsevier Ltd.
1. Introduction Piping items in power plants may experience internal pressure, axial load, bending and torsion loads during operation. Several methods for predicting failure loads for circumferential cracked pipes under combined loadings had been developed for assessment of piping integrity [1,2]. The proposed methods for combined loads are applicable on Mode I type loading of internal pressure, axial tension and bending. That is, Mode II type of torsion moment is not included in these methods. When cracks detected in piping items are assessed by using fitness-for-service Codes, such as ASME Boiler and Pressure Vessel Code Section XI [3] or JSME S NA1-2008 [4] Code. These ASME and JSME Codes provide evaluation procedures for predicting plastic collapse loads for cracks in pipes subjected to internal pressure and bending moment under fully plastic conditions. Currently, torsion load is also not included in these Codes. In addition, the depths of the cracks are less than or equal to 75% of pipe wall thickness for the evaluation procedures. This is because the Codes do not allow leakage from pipes. A guidance including the torsion moment is developed for pipes with circumferential part through wall cracks. It is reported that combined bending and torsion moments at collapse can be estimated by pure bending moments, when the combined bending and torsion moments are given by the equivalent moment defined as the root of the sum of the squares of the torsion and bending moments [5–12]. On the other hand, evaluation of collapse load for circumferential through-wall crack is necessary for leak-before-break evaluation [13,14] and temporary acceptance of coolant leakage from power plant piping [15]. This paper focuses on combined torsion and bending moments at collapse for a pipe containing a circumferential through-wall crack, and shows validity of the equivalent moment at plastic collapse for circumferential through-wall crack, referring the equivalent moment for a part through wall crack. ⇑ Corresponding author. Tel.: +81 3 4511 1751; fax: +81 3 4511 1897. E-mail addresses: [email protected] (K. Hasegawa), [email protected] (Y. Li), [email protected] (K. Osakabe). 0013-7944/$ - see front matter Ó 2014 Published by Elsevier Ltd. http://dx.doi.org/10.1016/j.engfracmech.2013.12.013
Please cite this article in press as: Hasegawa K et al. Collapse loads for circumferentially through-wall cracked pipes subjected to combined torsion and bending moments. Engng Fract Mech (2014), http://dx.doi.org/10.1016/j.engfracmech.2013.12.013
2
K. Hasegawa et al. / Engineering Fracture Mechanics xxx (2014) xxx–xxx
Nomenclature a D0 Mb, MB MB0 Meq Mt, MT Mx, My, Mz R t b h hb
circumferential crack depth pipe outside diameter applied and collapse bending moments under given torsion moment collapse bending moment without torsion moment (pure bending moment) equivalent collapse moment applied and collapse torsion moments orthogonal moment components at a given position in a piping system pipe mean radius nominal pipe wall thickness angle to neutral axis of cracked pipe one half of circumferential crack angle applied bending angle flow stress primary membrane stress in the pipe at the crack location torsion stress American Society of Mechanical Engineers finite element The Japan Society of Mechanical Engineers
rf rm s ASME FE JSME
2. Plastic collapse moment by bending and torsion 2.1. Plastic collapse bending moment by limit load criteria In case of a circumferential part-through crack, plastic collapse bending moment for a pipe is provided by ASME B&PV Code Section XI [3] and JSME (Japan Society of Mechanical Engineers) Code on Fitness – for – Service Rules [4]. The concept of the plastic collapse moment was developed by Battelle Columbus Laboratories [16]. Fig. 1 illustrates the stress distribution at incipient plastic collapse in a pipe. The internal stress distribution in the pipe wall in the cracked section is assumed to be at plus or minus the flow stress, as depicted in Fig. 1. From the equilibrium of bending moment and axial force, plastic collapse bending moment MB0 is given as follows; For more common case of h + b 6 p
h i a MB0 ¼ 2rf R2 t 2 sin b sin h t
ð1Þ
with
b¼
1 2
a t
p hp
rm rf
ð2Þ
where rf is the flow stress, h the half crack angle, a the crack depth, t the wall thickness, R the mean radius of the pipe, b the neutral angle, and rm the membrane stress. The flow stress is normally taken as the average value of the yield stress and ultimate tensile strength of the pipe material [3,4]. If the crack is long enough and both ends of the crack length are in the region of compression stress area, the plastic collapse moment MB0 is given as follows; For less common case of h + b > p
a MB0 ¼ 2rf R2 t 2 sin b t
ð3Þ
Fig. 1. Nomenclature and stress distribution of a pipe with a circumferential crack.
Please cite this article in press as: Hasegawa K et al. Collapse loads for circumferentially through-wall cracked pipes subjected to combined torsion and bending moments. Engng Fract Mech (2014), http://dx.doi.org/10.1016/j.engfracmech.2013.12.013
K. Hasegawa et al. / Engineering Fracture Mechanics xxx (2014) xxx–xxx
3
with
b¼
a rm 1 t rf 2
p
a t
ð4Þ
In case of a through-wall crack, both end of the crack are always tensile stress region. That is h + b 6 p, even when the crack length is long enough. There is not a situation of h + b > p. The collapse moment for a pipe with through-wall crack is obtained by Eqs. (1) and (2) replacing a = t, it is written as [14];
MB0 ¼ 2rf R2 t½2 sin b sin h
ð5Þ
with
b¼
1 2
php
rm rf
ð6Þ
Eqs. (1) and (3) are the basis formulas of plastic collapse moments for pipes with part through cracks, and Eq. (5) can estimate plastic collapse for pipes with through-wall cracks. These equations are called limit load criteria or net-section stress criteria and they are applicable for thin-walled pipes. When determining allowable flaw depth and length, Eqs. (1) and (3) are used with combination of safety factors [17]. When assessing leak-before-break [14] and temporary acceptance of coolant leakage from pipes [15], Eq. (5) is used for estimating break load. These equations are only applied for bending moment with internal pressure as membrane stress rm and lack of torsion moment. 2.2. Combined bending and torsion moments In accordance with design and construction Codes for pipes without cracks [18,19], combination of bending and torsion loads are resolved into orthogonal moment components and summed into an equivalent load by vector summation. For example, the equivalent moment is given by;
Meq ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi M2x þ M2y þ M 2z
ð7Þ
where the equivalent moment Meq is a resultant moment applied in the calculation to combine the orthogonal moment components, Mx, My and Mz at a given position in a piping system. In the design and construction Codes, needless to say, the assumption is that these piping systems do not have any cracks. In addition, the Eq. (7) is generally applied for elastic stress condition. Ref. [11] shows that part through cracked pipes subjected to bending and torsion moments had been analyzed and the collapse moments can be described as moments defined as the root of the square of the torsion and bending moments. The pipes analyzed were 4-in (114.3 mm), 10.75-in. (268 mm) and 24-in. (609.6 mm) diameter pipes. The equivalent collapse moment Meq is defined as,
Meq ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi M2B þ M2T
ð8Þ
where MB is the bending moment and MT the torsion moment at collapse, respectively. The stress at the cracked section of the pipe is a plastic condition at the collapse, accompanying large deformation of the pipe. The equivalent moment Meq is almost constant for a part through cracked pipe subjected to torsion stress less than 20% of the flow stress. The Meq is equal to pure bending moment MB0 at collapse for a pipe with a part-through crack, where the depth is less than or equal to 75% of pipe wall thickness. In order to obtain the equivalent moment Meq for through-wall cracked pipes, plastic collapse bending moments with torsion moments are analyzed by FE analysis, as below. 3. Finite element analysis for wall thinning pipes 3.1. Analytical conditions Plastic collapse bending moments for 24-in. schedule 80 straight pipes with circumferential through-wall cracks were calculated under the condition of torsion moment and internal pressure by FE analysis. The model is illustrated in Fig. 2. The pipe outer diameter D0 is 609.6 mm and the wall thickness t is 30.9 mm. The length of the pipe is eight times larger than the outer diameter. The crack is located at the center of the pipe length. All of the positions at one end of the pipe are fixed, and the torsion and bending moments are applied at the other end of the pipe. Internal pressure of 8 MPa is also applied for the pipe, where 8 MPa corresponds to hoop stress of 74.9 MPa. The pressure of 8 MPa employed is coolant pressure for boiling water reactors. The angles of through-wall cracks for calculations are two cases, 2h = 90° and 135°. The crack is located in tensile stress side during the bending load. The crack depth and angle are a, and 2h, respectively, where through-wall crack depth is a = t. The crack is located such that its center coincides with the plane of the maximum tensile stress due bending. Please cite this article in press as: Hasegawa K et al. Collapse loads for circumferentially through-wall cracked pipes subjected to combined torsion and bending moments. Engng Fract Mech (2014), http://dx.doi.org/10.1016/j.engfracmech.2013.12.013
4
K. Hasegawa et al. / Engineering Fracture Mechanics xxx (2014) xxx–xxx
Fig. 2. Model of a cracked pipe receiving bending moment and torsion moment under internal pressure.
Pure torsion moment under internal pressure of 8 MPa was also calculated for circumferentially cracked pipe. Torsion angle was applied at the end of the pipe end, and the applied moment-torsion angle and the maximum torsion moment were obtained by FE analysis. Calculation conditions for the FE analysis are tabulated in Table 1. The FE analysis was conducted by ABAQUS standard 6.7-4. Mesh break down is shown in Fig. 3. Von Mises criterion was used for yield hypothesis. Large deformation formulation is invoked in order to obtain plastic collapse moment accurately under large deformation. The material employed in this paper is elastic-fully plastic stress–strain curve with the yield strength of 372 MPa, which is identified with the flow stress of the material. 3.2. Sequence of loading The sequence of the loading is; first pressurizing the pipe to the pressure of 8 MPa, then applying the given torsion moment MT on the pipe end, and finally the bending moment was imposed by incremental bending angle at the remote end, as illustrated in Fig. 2. The applied torsion moment is calculated from the corresponding shear stress s. The relation between the nominal torsion moment MT and shear stress s not taking account of the crack is expected by MT = 2pR2ts, where R is the pipe mean radius. 4. Calculation results 4.1. Moment–deflection curves and deformations Calculation results of bending moments Mb and bending angle hb for pipes with circumferential through wall cracks under constant torsion stress of s/rf and internal pressure of 8 MPa are calculated by FE analysis. Table 2 shows the results of bending moments at collapse and equivalent moments as a parameter of torsion stress. Before understanding the deformation Table 1 Calculation conditions for FE analysis. Program Stress strain curve Geometrical non-linearity Yield stress, ry = rf Young’s modulus, E Strain hardening, H Internal pressure (Hoop stress) Pipe diameter, D0 Pipe wall thickness, t Crack depth, a/t Crack angle, 2h
ABAQUS 6.7-4 Elastic-fully plastic Considered 372 MPa 200 GPa 0 8 MPa (74.9 MPa) 609.6 mm 30.9 mm 1.0 90°, 135°
Fig. 3. FE mesh break down of a circumferential cracked pipe.
Please cite this article in press as: Hasegawa K et al. Collapse loads for circumferentially through-wall cracked pipes subjected to combined torsion and bending moments. Engng Fract Mech (2014), http://dx.doi.org/10.1016/j.engfracmech.2013.12.013
5
K. Hasegawa et al. / Engineering Fracture Mechanics xxx (2014) xxx–xxx Table 2 Results of bending and equivalent moments for pipes with through-wall cracks calculated by FE analysis. Crack angle 2h°
Torsion stress and moment
MB, kN m
Meq, kN m
0 605 1210 1816 1916
2166 2074 1746 704 0
2166 2161 2124 1947 1916
0 605 908 1210 1235
1312 1170 928 233 0
1312 1317 1298 1233 1235
s/rf
MT, kN m
90
0 0.1 0.2 0.3 0.317
135
0 0.1 0.15 0.2 0.204
behaviour for through-wall crack, the plastic collapse moments for part through crack are introduced by using the moment–deflection curves. In case of part through crack of a/t = 0.75 and 2h = 90°, the relationship between the Mb and the hb is shown in Fig. 4 [5]. As shown in Fig. 4, the applied bending moment Mb increases with increasing bending angle hb, and attained the maximum bending moment. After the maximum bending moment, the bending moment decreases with increasing the bending angle hb. The maximum bending moment corresponds to the plastic moment MB. The plastic moments MB decrease with increasing the torsion stresses s. In case of through-wall crack, the relationship between the applied bending moment and bending angle obtained by FE analysis is shown in Fig. 5. This is the load–displacement curves for pipes with circumferential through-wall cracks of 2h = 90°. The plastic bending moment MB decreases with increasing torsion stress s, as the same behaviour of MB and s shown in Fig. 4. The MB at s/rf = 0 means pure bending moment at collapse. The pure bending moments at 2h = 90° and 135° are 2166 kN m and 1312 kN m, respectively, as tabulated in Table 2. On the other hand, pure bending moments can be estimated by Eq. (5). Estimated collapse moments using Eq. (5) for 2h = 90° and 135° are 1920 kN m and 1046 kN m, respectively, where membrane stress rm is due to only internal pressure of 8 MPa. The membrane stress is rm = 37.5 MPa, which is one half of hoop stress. The pure bending moments at collapse obtained by FE analysis are fair agreement with the estimated moments calculated by Eq. (5). Pure bending moment MB0 at collapse for a cracked pipe can be estimated by limit load criteria, as mentioned before. The estimated collapse moments using Eq. (5) were not compared with experimental data. This is because there are lots of experimental data of MB0 performed by bending tests [20,21] and each flow stress depends on the pipe material. The moments MB0 obtained in these calculations were not compared with those obtained by experimental data. This is because the calculations herein employed the elastic fully plastic stress strain curve.
3500
p = 8 MPa 3000 2500
0.1 0.2
2000
0.3
1500
0.35 D o = 609.6 mm t = 30.9mm a/t = 0.75
1000
0.4
500 0 0
0.01
0.02
0.03
0.04
0.05
Fig. 4. Load–displacement curves for pipes with part through cracks of 2h = 90° [5].
Please cite this article in press as: Hasegawa K et al. Collapse loads for circumferentially through-wall cracked pipes subjected to combined torsion and bending moments. Engng Fract Mech (2014), http://dx.doi.org/10.1016/j.engfracmech.2013.12.013
6
K. Hasegawa et al. / Engineering Fracture Mechanics xxx (2014) xxx–xxx
2500
p = 8 MPa 2000
0.1
1500
0.2
1000
Do = 609.6mm t = 30.9mm
0.3
500
a/t = 1.0
0 0
0.05
0.1
0.15
Fig. 5. Load–displacement curves for pipes with through-wall crack of 2h = 90°.
Collapse bending moment, MB, Meq (kN-m)
4000
3000
Meq
2000
MB 1000
0 0
1000
2000
3000
4000
Collapse torsion moment, MT (kN-m) Fig. 6. Plastic collapse bending moment MB and equivalent moment Meq for pipes with cracks of a/t = 0.5 and 2h = 90° [5].
4.2. Effect of torsion on bending moment The plastic collapse bending moment MB for a circumferentially cracked pipe decreases with increasing torsion stress s, as shown in Figs. 4 and 5. Figs. 6 and 7 depict the relationship between the plastic collapse bending moments MB and the torsion moments MT for pipes with part through cracks of a/t = 0.5 and 0.75. Fig. 8 shows the relationship between MB and MT for pipes with through-wall cracks. When MT = 0, the bending moment is a pure bending moment, that is MB = MB0. When MB = 0, the moment is a pure torsion moment MT0, which was obtained by FE analysis under the conditions of the same material properties and crack sizes. Plastic collapse bending moment MB for pipes with part through cracks of a/t = 0.5 and 0.75 decreases with increasing torsion moment MT, as shown in Figs. 6 and 7. It is also observed that the MB for pipes with through-wall cracks of 2h = 90° and 135° decreases with increasing MT, as shown in Figs. 8 and 9. The decreases of the MB between the part through and through-wall cracks are similar, although the values of the MB are different.
5. Equivalent moments for pipes with cracks Equivalent moments Meq given by Eq. (2) are shown in Figs. 6 and 7 for part through cracked pipes with a/t = 0.5 and 0.75 and 2h = 90°. The moments Meq are almost horizontal, but slightly decrease, when the MT are small. When MT is large, the Meq becomes small. Please cite this article in press as: Hasegawa K et al. Collapse loads for circumferentially through-wall cracked pipes subjected to combined torsion and bending moments. Engng Fract Mech (2014), http://dx.doi.org/10.1016/j.engfracmech.2013.12.013
K. Hasegawa et al. / Engineering Fracture Mechanics xxx (2014) xxx–xxx
7
Collapse bending moment, MB, Meq (kN-m)
4000
3000
Meq 2000
MB 1000
0 0
1000
2000
3000
4000
Collapse torsion moment, MT, (kN-m) Fig. 7. Plastic collapse bending moment MB and equivalent moment Meq for pipes with cracks of a/t = 0.75 and 2h = 90° [5].
Collapse bending moment, M B or M eq (kN-m)
4000
3000
Meq 2000
1000
MB
0 0
500
1000
1500
2000
2500
Collapse torsion moment, MT (kN-m) Fig. 8. Plastic collapse bending moment MB and equivalent moment Meq for pipes with cracks of a/t = 1.0 and 2h = 90°.
In case of through-wall crack, the Meq were obtained as shown in Figs. 8 and 9, for pipes with a/t = 1.0 and 2h = 90° and 135°. The value of the Meq for through-wall cracked pipe is small, compared with those for part through cracked pipes with the same crack angle of 2h = 90° as, shown in Figs. 6–8. The Meq for the pipes with through-wall crack of 2h = 90° and 135° are almost constant in the entire range of MT. The torsion moments in power plants are generally small at many positions in piping systems. Based on plant design stress survey, it is sufficient to limit the torsion stress s up to 20% of the flow stress rf. The plant torsion actual range is illustrated in Figs. 6–9, as s/rf = 0.2. The torsion moments at s/rf = 0.2 in Figs. 6–9 are the same values of 1210 kN m, which were derived from MT = 2pR2ts , as mentioned before. The Meq for pipes with part through and through-wall cracks retains almost constant with increasing the torsion moment MT in the range of torsion stress of s/rf = 0.2, where the difference of the equivalent moment Meq against pure bending moment MB is within 10% of the pure bending moment. That is, the Meq is almost equal to MB0. It should be emphasized that the plastic collapse bending moments under torsion moments can be estimated by Eq. (5) with the condition of torsion stress, as follows;
Meq ¼ MB0
for s=rf 6 0:2
ð9Þ
This means that combined bending and torsion moments at collapse can be estimated by pure bending moment MB0 not only part through but also through-wall cracked pipes. Please cite this article in press as: Hasegawa K et al. Collapse loads for circumferentially through-wall cracked pipes subjected to combined torsion and bending moments. Engng Fract Mech (2014), http://dx.doi.org/10.1016/j.engfracmech.2013.12.013
8
K. Hasegawa et al. / Engineering Fracture Mechanics xxx (2014) xxx–xxx
Collapse bending moment, M B or M eq (kN-m)
3000
2500
2000
Meq
1500
1000
MB
500
0
0
500
1000
1500
2000
Collapse torsion moment, MT (kN-m) Fig. 9. Plastic collapse bending moment MB and equivalent moment Meq for pipes with cracks of a/t = 1.0 and 2h = 135°.
6. Conclusion Plastic collapse moments for pipes with through-wall cracks subjected to combined bending and torsion moments in the presence of internal pressure were investigated by FE analyses. As the results of the FE analysis, plastic collapse bending moments decrease with increasing torsion moments for through-wall cracked pipes. However, the equivalent moments defined as the root of the sum of the squares of the bending and torsion moments are almost constant against the torsion moments in the torsion stresses of actual plant range. This means that the plastic collapse bending plus torsion moments can be estimated by the pure bending moment for circumferentially through-wall cracked pipes, as the same with part through cracked pipes.
References [1] Jones MR, Eshelby JM. Limit solution’s for circumferential cracked cylinders under internal pressure and combined tension and bending. Nuclear Electric, Report TD/SID/REP/0032; 1990. [2] Lei Y, Budden PJ. Limit load solutions for thin-walled cylinders with circumferential cracks under combined internal pressure, axial tension and bending. J Strain Anal 2004;39:673–83. [3] ASME Boiler & Pressure Vessel Code, Section XI. Rules for inservice inspection of nuclear power plant components, American Society of Mechanical Engineers, New York; 2010. [4] JSME Code S NA-1-2008. Rules on Fitness-for-service for nuclear power plants. The Japan Society of Mechanical Engineers, Tokyo; 2008. [5] Li Y, Hasegawa K, Hoang P, Bezensek B. Prediction method for plastic collapse of pipes subjected to combined bending and torsion moments. ASME PVP2010-25101; 2010. [6] Li Y, Ida W, Hasegawa K, Hoang P, Bezensek B. Effect of pressure on plastic collapse under the combined bending and torsion moments for circumferentially surface flawed pipes. ASME PVP2010-25102; 2010. [7] Hoang P, Hasegawa K, Bezensek B, Li Y. Effect of torsion on equivalent bending moment for limit load and EPFM circumferential pipe flaw evaluations. ASME PVP2010-25283; 2010. [8] Bezensek B, Li Y, Hasegawa K, Hoang P. Proposal for inclusion of torsion in Section XI flaw evaluation procedures for pipes containing surface crack-like flaw. ASME PVP2010-25133; 2010. [9] Hoang P, Hasegawa K, Bezensek B, Li Y. Effect of torsion on equivalent bending moment for limit load and EPFM circumferential pipe flaw evaluations. J Press Vess Technol 2010;134:061206. December 2012. [10] Li Y, Hasegawa K, Hoang P, Bezensek B. Prediction method for plastic collapse of pipes subjected to combined bending and torsion moments. J Press Vess Technol 2012;134:061207. December 2012. [11] Bezensek B, Li Y, Hasegawa K, Hoang P. Inclusion of torsion loads in Section XI flaw evaluation procedures for pipes containing circumferential planar surface crack-like flaw on the basis of Limit Load Analysis. J Press Vess Technol 2012;134:031003. December 2012. [12] Li Y, Hasegawa K, Miura N, Hoshino K. Experimental investigation of failure estimation method for stainless steel pipes with a circumferential crack subjected to combined tensile and torsion loads. J Press Vess Technol 2013;135:041405. August 2013. [13] Hasegawa K, Okamoto A, Yokota H, Yamamoto Y, Shibata K, Matsumura K. Crack opening area of pressurized pipe for leak-before-break evaluation. JSME Int J Ser I 1991;34(3):332–8. [14] British Standard, Guide to methods for assessing the acceptability of flaws in metallic structures, Annex F: a procedure for leak-before-break assessment. BS 7910; 2005. [15] ASME Boiler & Pressure Vessel Code, Section XI Code Case N-513-3. Evaluation criteria for temporary acceptance of flaws in moderate energy class 2 or 3 piping; January 2009. [16] Canine MF, Broek D, Marschall CW, Rybicki EF, Sampath SG, Simonen FA, Wilkowski GM. Mechanical fracture predictions for sensitized stainless steel piping with circumferential cracks. EPRI NP-192; September 1976. [17] Norris DM, Marston TU, Tagart SW. Acceptance criteria for circumferential flaw in stainless steel piping. ASME PVP 1982;58:185–99.
Please cite this article in press as: Hasegawa K et al. Collapse loads for circumferentially through-wall cracked pipes subjected to combined torsion and bending moments. Engng Fract Mech (2014), http://dx.doi.org/10.1016/j.engfracmech.2013.12.013
K. Hasegawa et al. / Engineering Fracture Mechanics xxx (2014) xxx–xxx
9
[18] ASME Boiler & Pressure Vessel Code, Section III. Rules for construction of nuclear facility components, Division 1, Subsection NC, Class 2 components, NC-3653.3. American Society of Mechanical Engineers, New York; 2010. [19] AFCEN RCC-M, Design and construction rules for mechanical components for PWR nuclear islands. Subsection C-3658 determination of moments and section modulus; 2007 Edition. [20] NUREG/CP-0051. CSNI report no. 82. CSNI specialist meeting on Leak-Before-Break in nuclear piping. Monterey, California, USA; August 1984. [21] Scott PM, Ahmad J. NUREG/CR-4872. BMI-2149, Experimental and analytical assessment of circumferentially surface-cracked pipes under bending; April 1987.
Please cite this article in press as: Hasegawa K et al. Collapse loads for circumferentially through-wall cracked pipes subjected to combined torsion and bending moments. Engng Fract Mech (2014), http://dx.doi.org/10.1016/j.engfracmech.2013.12.013