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Damage assessment method of P91 steel welded tube under internal pressure creep based on void growth simulation
International Journal of Pressure Vessels and Piping 87 (2010) 611e616
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International Journal of Pressure Vessels and Piping journal homepage: www.elsevier.com/locate/ijpvp
Damage assessment method of P91 steel welded tube under internal pressure creep based on void growth simulation Takashi Ogata*, Takayuki Sakai, Masatsugu Yaguchi Central Research Institute of Electric Power Industry, 2-6-1 Nagasaka, Yokosuka, Kanagawa, Japan
a r t i c l e i n f o
a b s t r a c t
Article history: Received 18 January 2010 Accepted 13 July 2010
Development of creep damage assessment methods for longitudinal welded piping of P91 steel is important and an urgent subject to maintain reliable operation of boilers in ultra super critical thermal power plants. Internal pressure creep tests were conducted on P91 steel longitudinal welded tubes to characterize the evolution of creep damage in a heat-affected zone (HAZ) of the longitudinal welded pipe. Failure occurred at a heat-affected zone without significant macroscopic deformation. It was found that initiation of creep voids had concentrated at mid-thickness region rather than surface. Threedimensional finite element (FE) creep analysis of the creep tested specimens was conducted to identify stress and creep strain distribution within the specimen during creep. Finite element creep analysis results indicated that triaxial tensile stress yielded at the mid-thickness region of the HAZ. It was suggested that the triaxial stress state caused acceleration of the creep damage evolution in the heataffected zone resulting in internal failure of the tube specimens. Void growth behavior in the heataffected zone was well predicted with the previously proposed void growth simulation method by introducing void initiation function to the method. A “limited strain” was defined as rupture criterion and dependency of the maximum stress and multiaxiality on the “limited strain” was derived by the void growth simulation. Creep damage distribution in the HAZ under the internal creep test was calculated by proposed damage assessment method. Ó 2010 Elsevier Ltd. All rights reserved.
Keywords: P91 Longitudinal weld joint Internal pressure creep Creep void Life prediction
1. Introduction In Japan, more than half of electricity from thermal power plants is generated by ultra super critical (USC) power plants in which steam temperature is above 593 C and steam pressure is above 24.1 MPa. High chromium ferritic steels such as 9Cr and 12Cr steels are being used for high temperature boiler components in the USC plants. Recently, it was reported that the creep strength of welded joints of high chromium steels is significantly lower than that of base metals [1]. Reduction of creep rupture strength of welded joints in high chromium steels is much larger than that in ferritic low alloy steels [2]. It was found that the reduction of creep rupture strength in high chromium steel welded joints was caused by following reasons from previous studies [3,4]. Creep damage in the welded joint preferentially accumulated at fine grain region in heat-affected zone (HAZ) where creep deformation resistance is lower than other portions [4]. Creep void initiation and growth are accelerated due to multiaxial stress state in the HAZ [3]. The authors [5] have also found that creep rupture life of welded joints failed at the HAZ was approximately 1/5 of base * Corresponding author. E-mail address: [email protected] (T. Ogata). 0308-0161/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijpvp.2010.08.009
metals, and creep strain concentrated in the HAZ of the welded joint. Therefore so called “Type IV” cracking occurs in actual components. On the other hand, studies on creep damage characterization of internal pressure creep tests of longitudinal welded joints, which are susceptible of the Type IV failure, are very limited, in spite of the fact that most of the longitudinal welded pipes are subjected to internal pressure at high temperatures. In this study, internal creep rupture and interrupted tests of P91 longitudinal welded tube specimens were performed to identify internal pressure creep rupture property and damage evolution process in the HAZ. A finite element creep analysis is conducted to clarify stress and strain distribution at the HAZ and void growth simulation procedure is applied to predict void growth behavior. In addition, creep damage assessment method for the HAZ of P91 longitudinal welded pipes is proposed based on the void growth simulation procedure. 2. Internal pressure creep tests 2.1. Test procedure Material used in this study is P91 steel. Chemical composition of the P91 is shown in Table 1. Longitudinal welded tubes with 60 mm
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Table 1 Chemical composition of a tested material. C
Si
Mn
P
S
Cr
Mo
V
Cu
Ni
Al
Nb
N
0.09
0.26
0.44
0.014
0.001
8.29
0.88
0.2
0.001
0.006
0.01
0.06
0.45
in outer diameter, 10 mm in thickness, 350 mm in length were manufactured by GTA welding. Post-welded heat treatment was made at 740 C with 2 h. Internal pressure creep tests were conducted at 650 C using internal pressure creep testing machines constantly pressurized by hot steam. Creep tests under internal pressure of 21.7 MPa were interrupted at 2165 and 3795 h. Creep life fractions, so called “creep damage” in this study, of two interrupted specimens are 32 and 56%, respectively. Creep damage condition in the HAZ of theses interrupted specimens was observed by an optical microscope and a scanning electron microscope (SEM). 2.2. Test results Rupture times of the internal pressure creep tests in addition to the uniaxil creep tests of the cross weld specimens previously conducted [5] are plotted against a nominal stress in Fig. 1. The nominal stress of the internal pressure creep tests, snom was calculated from the equation,
snom
D ¼ p y 2t
(1)
where p is internal pressure, D is specimen diameter, t is specimen thickness and y is a constant which is determined as to correlate internal pressure creep data to uniaxial creep data. In this study, the y was determined to be 0.38. The internal pressure creep rupture data were correlated with the uniaxial creep rupture data as shown in Fig. 1. The above equation can be simply used to predict creep rupture life of internal pressure creep of longitudinal welded tubes from uniaxial creep rupture data of cross weld specimens. To understand the void initiation and growth states, microstructure of the 32 and 56% creep damage specimens and the rupture specimen were more precisely examined by the SEM. Four different HAZ portions in the section of the tube specimen were designated with “A” to “D”, and each HAZ was divided into five locations with equal distance from the outer to inner surface (sections 1e5). The center area of each location was observed. For the rupture specimen, two HAZ portions opposite to the cracking HAZ were examined. Many
100 Uniaxial base metal
90
Stress (MPa)
80 70 60 50
Uniaxial cross weld Internal pressure
40
30 2 10
3
10
4
10
Rupture time (hour) Fig. 1. Internal pressure creep rupture test results.
voids including connected ones were observed at the HAZ in the damage and rupture specimens except near outer and inner surfaces where the number of voids was significantly less than that in the mid-thickness region. Numbers of voids per area of 1 mm2, which is called a “void number density”, at the observed locations in four HAZs were counted. The void number density in different HAZ portions of both the damage and rupture specimens are shown in Fig. 2. The void number density of the rupture specimen is much larger than that of the damage specimens. It can also be seen that the void number density at the mid-thickness region is larger than that near surface region in both the damage and rupture specimens, and absolute value of the void number density varies with the HAZ portion even in the same cross-section. These results indicate that the creep damage proceeds preferentially in the mid-thickness region rather than the surfaces.
3. Stress analysis and void growth simulation 3.1. FE creep analysis results Three-dimensional finite element (FE) creep analysis of the longitudinal welded tube specimen was performed in this study to discuss relation between stress state and creep damage condition and a creep damage assessment method. The longitudinal welded tube specimen model consists of a base metal, a weld metal and a HAZ, and geometry of the HAZ in the actual specimen was traced in the model. Norton law was adopted as a creep constitutive equation. The coefficients and the index in Norton law of each material were determined from the creep tests of each material as previously reported [5]. The index is 6.53 for all materials, and the coefficients are 5.39 1018, 3.75 1018 and 2.66 1016 for the base metal, the weld metal and the HAZ, respectively. To express continuous change of the material property, the coefficient of Norton law for the four elements at the boundary between the HAZ and the base metal, the weld metal were linearly changed. In the analyses, internal pressures of 25.6e17.5 MPa adopted in the tests were imposed at 650 C. Each creep analysis has been continued to the rupture time of the experiment under each internal pressure. As under internal pressure creep conditions, a circumferential stress, which is larger than an axial and a radial stresses, corresponds to the maximum principal stress, the circumferential stress in the HAZ is called as the maximum stress in this study unless particularly noted. The stress components distribution after loading and 1000 h from the inner to the outer surface in the center of the HAZ is shown in Fig. 3. The circumferential stress takes the maximum value at the inner surface after loading and it decreases toward the outer surface. On the other hand, the circumferential stress at the inner surface is the minimum, and the maximum value yields at the mid-thickness after 1000 h. Fig. 4 shows distribution of a triaxiality factor from the outer to inner surface in the HAZ. The triaxiality factor is calculated by the next equation,
TF ¼ ðs1 þ s2 þ s3 Þ=sm i1=2 .pffiffiffi h sm ¼ ðs1 s2 Þ2 þðs2 s3 Þ2 þðs3 s1 Þ2 2
(2) (3)
where s1, s2, s3 are the principal stresses. The triaxiality factor is the highest at the mid-thickness region with value of 3.5, and it
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613
Fig. 2. Void number density at heat-affected zone in sections of interrupted and rupture specimens.
a
80
b 80
Initial loading Radial
Circum ferential
A x ial
Stress (MPa)
60
Stress (MPa)
After 1000 hnours Radial
40 20 0 20
Circum ferential
Axial
60 40 20 0 20
40 0(Outer)
10 (Inner)
Distance from outer surface (mm)
40 0(Outer)
10 (Inner)
Distance from outer surface (mm)
Fig. 3. Stress distribution from outer to inner surface along centerline at HAZ.
decreases toward the outer and the inner surface to 2 and 1, respectively. It was found that the maximum value of the circumferential stress yields at the mid-thickness of the HAZ portion with the maximum triaxiality factor. These results correspond to the void observation results where the void number density at the midthickness is larger than that at near surfaces.
growth rate equations was also developed [7]. The void growth equations for the spherical and the crack-like voids are expressed by the following equations. (Spherical void)
da ae_ c L 3 ½L þ M1 ¼ 2hðjÞ a dt
(4)
(Crack-like void)
3.2. Void growth simulation method The authors [6] previously proposed the void growth model considering combined mechanism of diffusion and power law creep deformation under constrained condition for the void growth, and derived the void growth rate equations for spherical and crack-like voids. The void growth simulation program incorporating the void
aae_ c L 5=2 da ½L þ M3=2 ¼ 4phðjÞ a dt
Measure-
Creep
800 damage Simulation ment
4.0
Triaxiality factor
(5)
600
3.0
400
2.0
200 1.0
0 0
0.0 0 (Outer)
10 (Inner)
Distance from outer surface (mm) Fig. 4. Distribution of triaxiality factor in the HAZ from the outer to inner surface.
1
2
3
4
5
Distance from outer surface (mm) Fig. 5. Comparison of void number density distribution between prediction by simulation and observation.
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800
0.02
Limited strain
700 600 500
0.01
400 300 200 30
0.005 40
50
60
70
40
80
Maximum stress (MPa)
50 60 70 Maximum stress (MPa)
80
Fig. 7. Relationship between void number density and maximum stress.
Fig. 6. Dependency of limited strain on maximum stress.
4. Creep damage assessment method
L ¼ db Db Usn =kT e_ c
1=3
hðjÞ ¼ ½1=ð1 þ cos j cosðj=2ÞÞ=sin j L ¼
3 2b L bd a þ L
a ¼
4phðjÞ ð4sinðj=2ÞÞ3=2
4.1. Creep damage based on limited creep strain
(7)
Here, the accumulated maximum creep strain in the circumferential direction at the mid-thickness of the HAZ portion until rupture time is defined as the “limited strain” which is calculated by product of the steady state creep strain rate and the rupture time. Once determine the “limited strain” under certain maximum stress and multiaxiality condition, creep rupture time is predicted from the maximum creep strain rate obtained from the FE creep analysis. The “limited strain” of each internal pressure creep test condition obtained from the above FE creep analysis of the tube specimens was plotted against the maximum stress at the midthickness portion in the HAZ in Fig. 6. The “limited strain” decreases with decreasing the maximum stress, and the maximum stress dependency of the “limited strain” is obtained from Fig. 6. The “limited strain” depends not only on the maximum stress but also on the multiaxiality. The dependency of the multiaxiality is discussed by using the void growth simulation method as follows. From the observation of damage feature of internal creep tested specimens, the void initiation and growth occur at the mid-thickness portion initially, and the void damage gradually extends through the thickness resulting in rapid coalescence of micro cracks to form a macro crack. Therefore a crack propagation period through the wall of the tube seems to be short after the void number density reaches a critical value. On the other words, a through-wall crack formation period in the HAZ, which is defined as rupture time, is conservatively predicted from the critical void number density at mid-thickness portion of the HAZ. Fig. 7 shows the void number density at mid-
(8)
h a i2 . h a i2 aþL M ¼ ln 1 4 3 a aþL aþL "
(6)
#
db Db sn L ð Þ ds Ds gs
(9)
1=2 (10)
where a is a void radius, j is a void tip angle, e_ c is creep strain rate, db is grain boundary width, Db is grain boundary diffusion coefficient, U is atomic volume, k is a Bolzmann constant, T is absolute temperature, b is void space, d is grain diameter, Ds is surface diffusion coefficient, gs is surface tension force and b is a material constant. Number of voids and initial void length on a grain boundary can be arbitrary given. A void grows with faster growth rate of either Eq. (4) or Eq. (5). Void initiation period, ti is expressed by the next equation. q
ti ¼ Asn
(11)
where A and q are material constants. A and q in Eq. (11) were determined as 2.0 108 and 3[8]. 3.3. Void growth simulation results
1 Maximum stress:50MPa
0.1 Limited strain
To verify prediction accuracy of the void growth simulation, the void growth simulation was made at the sections 1e 3, which are the same locations as observed location of void initiation condition previously, using stress values at the middle of the each section obtained from the FE creep analysis. The void number densities at the sections 1e3 in the different creep damages obtained from the void growth simulation are shown in Fig. 5. The measurement data from the specimens are also plotted in Fig. 5. The void number densities at the different sections are different depending on the local stress level and the stress multiaxiality, and the void number densities predicted by the simulation for the different sections and different creep damages are almost coincident with those measured from the specimens. It is demonstrated that the void growth simulation can apply to predict void growth behavior at the internal HAZ of welded tubes.
0.01 0.001 0.0001
Maximum stress:40MPa
0.00001
1
10
Triaxiality factor Fig. 8. Dependency of limited strain on triaxiality factor.
T. Ogata et al. / International Journal of Pressure Vessels and Piping 87 (2010) 611e616
615
Fig. 9. Contour of creep damage distribution at HAZ region of a longitudinal welded tube.
thickness portion of the HAZ in the rupture specimens against the maximum stress obtained from the FE creep analysis previously mentioned. The vertical axis in Fig. 7 indicates the critical void number density at different maximum stress level. The critical void number density increases with decreasing the maximum stress value indicating that creep deformation proceeds to rupture before initiating sufficient voids at higher stress level. The critical void number density at the maximum stress value less than 52 MPa seems to be constant as approximately 720(1/mm2). Although it is not clear for further lower stress level, conservative life prediction may be made by adopting a critical void number density as 720(1/mm2). The void initiation and growth simulation was carried out under the maximum stress value of 50 and 40 MPa with different values of triaxial factor, and the “limited strain” at each condition was calculated from a product of the maximum creep strain rate and rupture time which is defined as a time of the void number density reaching the critical value of 720(1/mm2). Relationship between the “limited strain” and the triaxial factor obtained from the void simulation is shown in Fig. 8. Assuming that the maximum stress dependency on the “limited strain” maintains for different values of triaxial factor, the “limited strain” is expressed by the following equation. 5:4 elim ¼ 9:38 103 s1:62 max TF
(12)
The “limited strain” under a certain maximum stress and stress multiaxiality condition is calculated by the above
equation. Creep damage in the HAZ is defined by the following equation.
Dc ¼ e1loc =elim
(13)
where e1loc is the maximum creep strain at local portion in HAZ. 4.2. Damage assessment results Creep damage evolution in the HAZ of the longitudinal welded tube under 21.7 MPa internal pressure at 650 C was calculated by Eqs. (12) and (13) based on the FE analysis mentioned in Section 3.1. The creep damage contours at different creep damage levels are shown in Fig. 9. It is seen that creep damage starts from mid-thickness region and grow toward surface regions indicating macro crack starts from mid-thickness and extends through the section. Finite element creep analyses of longitudinal welded elbow pipes with two different shape of weld metal under the internal pressure condition have been carried out using a three materials finite element model [8]. Creep damages in the HAZ of the pipes are calculated by the above method and creep damage contours in the HAZ are shown in Fig. 10. It can be seen that creep damage distribution patterns in the HAZs is different depending on shape of weld metal. Creep damage progresses through the HAZ region in the straight fusion line as shown in Fig. 10(a), while
Fig. 10. Contour of creep damage distribution at HAZ region of welded elbow pipes.
616
T. Ogata et al. / International Journal of Pressure Vessels and Piping 87 (2010) 611e616
it concentrates at root portion of mid-thickness region in the HAZ for the case of discontinuous fusion line. Thus creep damage evolution in a HAZ of a longitudinal welded pipe can be predicted by using damage assessment method based on the “limited strain”.
5. Conclusions Internal pressure creep rupture tests and interrupted tests were conducted on P91 longitudinal welded tube specimens at 650 C, and damage condition at heat-affected zone (HAZ) of the specimens were carefully observed by a scanning electron microscope. The void number density per area at mid-thickness region is much larger than that at near surface regions corresponding to higher maximum stress and triaxiality factor regions obtained from finite element creep analysis of the specimen. The void numbers density per area at different portion of the HAZ were quantitatively predicted by the void growth simulation procedure indicating the procedure can be applied to predict void growth behavior internal of the material. A creep damage prediction method at the HAZ based on the “limited strain” was proposed and dependency of the maximum stress and triaxiality factor on “limited strain” was derived from the void growth simulation results. Creep damage distribution at the HAZ in
longitudinal welded tubes and pipes are simply predicted from FE analysis using three materials model.
References [1] Brett SJ, Oates DL, Johnston C. In-service Type IV cracking in a Modified 9Cr header. In: Proceeding of ECCC Creep Conference, September, London; 2005, p. 563e572. [2] Ogata T, Yaguchi M. Creep and creep-fatigue life assessment of boiler weldment parts. In: Proceedings of ECCC Creep Conference, 12e14 September, London; 2005, p. 909e917. [3] Kimura K, Kume R, Saito K, Fujiyama K. "Estimation of creep damage for components of Mod.9Cr-1Mo steel. J JSME A 2001;67(No. 661):1429e35 (in Japanese). [4] Tabuchi M, Watanabe T, Kubo K, Matsui M, Kinugawa J, Abe F. Microstructures and creep strength of welded joints for W strengthened high Cr ferritic steel. J Soc Mater Sci 2001;50(No. 2):116e21 (in Japanese). [5] Ogata T, Sakai T, Yaguchi M. Creep damage evolution and life assessment of P91 weld join. In: Proceeding of the Third International Conference on Integrity of High Temperature Welds, London, UK, April 24e26. London, UK: IOM Communication Ltd; 2007. p. 285e94. [6] Ogata T. Cavity growth simulation of 2.25Cre1Mo steel under creepefatigue loading. In: Proceeding of ASME pvp conference, PVP2005-71041; 2005. [7] Ogata T. Creep void growth simulation for reliable maintenance of high temperature components. ASME Paper No. IMECE200-79215; 2005. [8] Ogata T, Sakai T, Yaguchi M, 2007. Clarification of creep damage condition and development of damage assessment method of P91 longitudinal welded tube under internal pressure creep. Dencyuken Houkoku Q07002 (in Japanese).
Contents lists available at ScienceDirect
International Journal of Pressure Vessels and Piping journal homepage: www.elsevier.com/locate/ijpvp
Damage assessment method of P91 steel welded tube under internal pressure creep based on void growth simulation Takashi Ogata*, Takayuki Sakai, Masatsugu Yaguchi Central Research Institute of Electric Power Industry, 2-6-1 Nagasaka, Yokosuka, Kanagawa, Japan
a r t i c l e i n f o
a b s t r a c t
Article history: Received 18 January 2010 Accepted 13 July 2010
Development of creep damage assessment methods for longitudinal welded piping of P91 steel is important and an urgent subject to maintain reliable operation of boilers in ultra super critical thermal power plants. Internal pressure creep tests were conducted on P91 steel longitudinal welded tubes to characterize the evolution of creep damage in a heat-affected zone (HAZ) of the longitudinal welded pipe. Failure occurred at a heat-affected zone without significant macroscopic deformation. It was found that initiation of creep voids had concentrated at mid-thickness region rather than surface. Threedimensional finite element (FE) creep analysis of the creep tested specimens was conducted to identify stress and creep strain distribution within the specimen during creep. Finite element creep analysis results indicated that triaxial tensile stress yielded at the mid-thickness region of the HAZ. It was suggested that the triaxial stress state caused acceleration of the creep damage evolution in the heataffected zone resulting in internal failure of the tube specimens. Void growth behavior in the heataffected zone was well predicted with the previously proposed void growth simulation method by introducing void initiation function to the method. A “limited strain” was defined as rupture criterion and dependency of the maximum stress and multiaxiality on the “limited strain” was derived by the void growth simulation. Creep damage distribution in the HAZ under the internal creep test was calculated by proposed damage assessment method. Ó 2010 Elsevier Ltd. All rights reserved.
Keywords: P91 Longitudinal weld joint Internal pressure creep Creep void Life prediction
1. Introduction In Japan, more than half of electricity from thermal power plants is generated by ultra super critical (USC) power plants in which steam temperature is above 593 C and steam pressure is above 24.1 MPa. High chromium ferritic steels such as 9Cr and 12Cr steels are being used for high temperature boiler components in the USC plants. Recently, it was reported that the creep strength of welded joints of high chromium steels is significantly lower than that of base metals [1]. Reduction of creep rupture strength of welded joints in high chromium steels is much larger than that in ferritic low alloy steels [2]. It was found that the reduction of creep rupture strength in high chromium steel welded joints was caused by following reasons from previous studies [3,4]. Creep damage in the welded joint preferentially accumulated at fine grain region in heat-affected zone (HAZ) where creep deformation resistance is lower than other portions [4]. Creep void initiation and growth are accelerated due to multiaxial stress state in the HAZ [3]. The authors [5] have also found that creep rupture life of welded joints failed at the HAZ was approximately 1/5 of base * Corresponding author. E-mail address: [email protected] (T. Ogata). 0308-0161/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijpvp.2010.08.009
metals, and creep strain concentrated in the HAZ of the welded joint. Therefore so called “Type IV” cracking occurs in actual components. On the other hand, studies on creep damage characterization of internal pressure creep tests of longitudinal welded joints, which are susceptible of the Type IV failure, are very limited, in spite of the fact that most of the longitudinal welded pipes are subjected to internal pressure at high temperatures. In this study, internal creep rupture and interrupted tests of P91 longitudinal welded tube specimens were performed to identify internal pressure creep rupture property and damage evolution process in the HAZ. A finite element creep analysis is conducted to clarify stress and strain distribution at the HAZ and void growth simulation procedure is applied to predict void growth behavior. In addition, creep damage assessment method for the HAZ of P91 longitudinal welded pipes is proposed based on the void growth simulation procedure. 2. Internal pressure creep tests 2.1. Test procedure Material used in this study is P91 steel. Chemical composition of the P91 is shown in Table 1. Longitudinal welded tubes with 60 mm
612
T. Ogata et al. / International Journal of Pressure Vessels and Piping 87 (2010) 611e616
Table 1 Chemical composition of a tested material. C
Si
Mn
P
S
Cr
Mo
V
Cu
Ni
Al
Nb
N
0.09
0.26
0.44
0.014
0.001
8.29
0.88
0.2
0.001
0.006
0.01
0.06
0.45
in outer diameter, 10 mm in thickness, 350 mm in length were manufactured by GTA welding. Post-welded heat treatment was made at 740 C with 2 h. Internal pressure creep tests were conducted at 650 C using internal pressure creep testing machines constantly pressurized by hot steam. Creep tests under internal pressure of 21.7 MPa were interrupted at 2165 and 3795 h. Creep life fractions, so called “creep damage” in this study, of two interrupted specimens are 32 and 56%, respectively. Creep damage condition in the HAZ of theses interrupted specimens was observed by an optical microscope and a scanning electron microscope (SEM). 2.2. Test results Rupture times of the internal pressure creep tests in addition to the uniaxil creep tests of the cross weld specimens previously conducted [5] are plotted against a nominal stress in Fig. 1. The nominal stress of the internal pressure creep tests, snom was calculated from the equation,
snom
D ¼ p y 2t
(1)
where p is internal pressure, D is specimen diameter, t is specimen thickness and y is a constant which is determined as to correlate internal pressure creep data to uniaxial creep data. In this study, the y was determined to be 0.38. The internal pressure creep rupture data were correlated with the uniaxial creep rupture data as shown in Fig. 1. The above equation can be simply used to predict creep rupture life of internal pressure creep of longitudinal welded tubes from uniaxial creep rupture data of cross weld specimens. To understand the void initiation and growth states, microstructure of the 32 and 56% creep damage specimens and the rupture specimen were more precisely examined by the SEM. Four different HAZ portions in the section of the tube specimen were designated with “A” to “D”, and each HAZ was divided into five locations with equal distance from the outer to inner surface (sections 1e5). The center area of each location was observed. For the rupture specimen, two HAZ portions opposite to the cracking HAZ were examined. Many
100 Uniaxial base metal
90
Stress (MPa)
80 70 60 50
Uniaxial cross weld Internal pressure
40
30 2 10
3
10
4
10
Rupture time (hour) Fig. 1. Internal pressure creep rupture test results.
voids including connected ones were observed at the HAZ in the damage and rupture specimens except near outer and inner surfaces where the number of voids was significantly less than that in the mid-thickness region. Numbers of voids per area of 1 mm2, which is called a “void number density”, at the observed locations in four HAZs were counted. The void number density in different HAZ portions of both the damage and rupture specimens are shown in Fig. 2. The void number density of the rupture specimen is much larger than that of the damage specimens. It can also be seen that the void number density at the mid-thickness region is larger than that near surface region in both the damage and rupture specimens, and absolute value of the void number density varies with the HAZ portion even in the same cross-section. These results indicate that the creep damage proceeds preferentially in the mid-thickness region rather than the surfaces.
3. Stress analysis and void growth simulation 3.1. FE creep analysis results Three-dimensional finite element (FE) creep analysis of the longitudinal welded tube specimen was performed in this study to discuss relation between stress state and creep damage condition and a creep damage assessment method. The longitudinal welded tube specimen model consists of a base metal, a weld metal and a HAZ, and geometry of the HAZ in the actual specimen was traced in the model. Norton law was adopted as a creep constitutive equation. The coefficients and the index in Norton law of each material were determined from the creep tests of each material as previously reported [5]. The index is 6.53 for all materials, and the coefficients are 5.39 1018, 3.75 1018 and 2.66 1016 for the base metal, the weld metal and the HAZ, respectively. To express continuous change of the material property, the coefficient of Norton law for the four elements at the boundary between the HAZ and the base metal, the weld metal were linearly changed. In the analyses, internal pressures of 25.6e17.5 MPa adopted in the tests were imposed at 650 C. Each creep analysis has been continued to the rupture time of the experiment under each internal pressure. As under internal pressure creep conditions, a circumferential stress, which is larger than an axial and a radial stresses, corresponds to the maximum principal stress, the circumferential stress in the HAZ is called as the maximum stress in this study unless particularly noted. The stress components distribution after loading and 1000 h from the inner to the outer surface in the center of the HAZ is shown in Fig. 3. The circumferential stress takes the maximum value at the inner surface after loading and it decreases toward the outer surface. On the other hand, the circumferential stress at the inner surface is the minimum, and the maximum value yields at the mid-thickness after 1000 h. Fig. 4 shows distribution of a triaxiality factor from the outer to inner surface in the HAZ. The triaxiality factor is calculated by the next equation,
TF ¼ ðs1 þ s2 þ s3 Þ=sm i1=2 .pffiffiffi h sm ¼ ðs1 s2 Þ2 þðs2 s3 Þ2 þðs3 s1 Þ2 2
(2) (3)
where s1, s2, s3 are the principal stresses. The triaxiality factor is the highest at the mid-thickness region with value of 3.5, and it
T. Ogata et al. / International Journal of Pressure Vessels and Piping 87 (2010) 611e616
613
Fig. 2. Void number density at heat-affected zone in sections of interrupted and rupture specimens.
a
80
b 80
Initial loading Radial
Circum ferential
A x ial
Stress (MPa)
60
Stress (MPa)
After 1000 hnours Radial
40 20 0 20
Circum ferential
Axial
60 40 20 0 20
40 0(Outer)
10 (Inner)
Distance from outer surface (mm)
40 0(Outer)
10 (Inner)
Distance from outer surface (mm)
Fig. 3. Stress distribution from outer to inner surface along centerline at HAZ.
decreases toward the outer and the inner surface to 2 and 1, respectively. It was found that the maximum value of the circumferential stress yields at the mid-thickness of the HAZ portion with the maximum triaxiality factor. These results correspond to the void observation results where the void number density at the midthickness is larger than that at near surfaces.
growth rate equations was also developed [7]. The void growth equations for the spherical and the crack-like voids are expressed by the following equations. (Spherical void)
da ae_ c L 3 ½L þ M1 ¼ 2hðjÞ a dt
(4)
(Crack-like void)
3.2. Void growth simulation method The authors [6] previously proposed the void growth model considering combined mechanism of diffusion and power law creep deformation under constrained condition for the void growth, and derived the void growth rate equations for spherical and crack-like voids. The void growth simulation program incorporating the void
aae_ c L 5=2 da ½L þ M3=2 ¼ 4phðjÞ a dt
Measure-
Creep
800 damage Simulation ment
4.0
Triaxiality factor
(5)
600
3.0
400
2.0
200 1.0
0 0
0.0 0 (Outer)
10 (Inner)
Distance from outer surface (mm) Fig. 4. Distribution of triaxiality factor in the HAZ from the outer to inner surface.
1
2
3
4
5
Distance from outer surface (mm) Fig. 5. Comparison of void number density distribution between prediction by simulation and observation.
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800
0.02
Limited strain
700 600 500
0.01
400 300 200 30
0.005 40
50
60
70
40
80
Maximum stress (MPa)
50 60 70 Maximum stress (MPa)
80
Fig. 7. Relationship between void number density and maximum stress.
Fig. 6. Dependency of limited strain on maximum stress.
4. Creep damage assessment method
L ¼ db Db Usn =kT e_ c
1=3
hðjÞ ¼ ½1=ð1 þ cos j cosðj=2ÞÞ=sin j L ¼
3 2b L bd a þ L
a ¼
4phðjÞ ð4sinðj=2ÞÞ3=2
4.1. Creep damage based on limited creep strain
(7)
Here, the accumulated maximum creep strain in the circumferential direction at the mid-thickness of the HAZ portion until rupture time is defined as the “limited strain” which is calculated by product of the steady state creep strain rate and the rupture time. Once determine the “limited strain” under certain maximum stress and multiaxiality condition, creep rupture time is predicted from the maximum creep strain rate obtained from the FE creep analysis. The “limited strain” of each internal pressure creep test condition obtained from the above FE creep analysis of the tube specimens was plotted against the maximum stress at the midthickness portion in the HAZ in Fig. 6. The “limited strain” decreases with decreasing the maximum stress, and the maximum stress dependency of the “limited strain” is obtained from Fig. 6. The “limited strain” depends not only on the maximum stress but also on the multiaxiality. The dependency of the multiaxiality is discussed by using the void growth simulation method as follows. From the observation of damage feature of internal creep tested specimens, the void initiation and growth occur at the mid-thickness portion initially, and the void damage gradually extends through the thickness resulting in rapid coalescence of micro cracks to form a macro crack. Therefore a crack propagation period through the wall of the tube seems to be short after the void number density reaches a critical value. On the other words, a through-wall crack formation period in the HAZ, which is defined as rupture time, is conservatively predicted from the critical void number density at mid-thickness portion of the HAZ. Fig. 7 shows the void number density at mid-
(8)
h a i2 . h a i2 aþL M ¼ ln 1 4 3 a aþL aþL "
(6)
#
db Db sn L ð Þ ds Ds gs
(9)
1=2 (10)
where a is a void radius, j is a void tip angle, e_ c is creep strain rate, db is grain boundary width, Db is grain boundary diffusion coefficient, U is atomic volume, k is a Bolzmann constant, T is absolute temperature, b is void space, d is grain diameter, Ds is surface diffusion coefficient, gs is surface tension force and b is a material constant. Number of voids and initial void length on a grain boundary can be arbitrary given. A void grows with faster growth rate of either Eq. (4) or Eq. (5). Void initiation period, ti is expressed by the next equation. q
ti ¼ Asn
(11)
where A and q are material constants. A and q in Eq. (11) were determined as 2.0 108 and 3[8]. 3.3. Void growth simulation results
1 Maximum stress:50MPa
0.1 Limited strain
To verify prediction accuracy of the void growth simulation, the void growth simulation was made at the sections 1e 3, which are the same locations as observed location of void initiation condition previously, using stress values at the middle of the each section obtained from the FE creep analysis. The void number densities at the sections 1e3 in the different creep damages obtained from the void growth simulation are shown in Fig. 5. The measurement data from the specimens are also plotted in Fig. 5. The void number densities at the different sections are different depending on the local stress level and the stress multiaxiality, and the void number densities predicted by the simulation for the different sections and different creep damages are almost coincident with those measured from the specimens. It is demonstrated that the void growth simulation can apply to predict void growth behavior at the internal HAZ of welded tubes.
0.01 0.001 0.0001
Maximum stress:40MPa
0.00001
1
10
Triaxiality factor Fig. 8. Dependency of limited strain on triaxiality factor.
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615
Fig. 9. Contour of creep damage distribution at HAZ region of a longitudinal welded tube.
thickness portion of the HAZ in the rupture specimens against the maximum stress obtained from the FE creep analysis previously mentioned. The vertical axis in Fig. 7 indicates the critical void number density at different maximum stress level. The critical void number density increases with decreasing the maximum stress value indicating that creep deformation proceeds to rupture before initiating sufficient voids at higher stress level. The critical void number density at the maximum stress value less than 52 MPa seems to be constant as approximately 720(1/mm2). Although it is not clear for further lower stress level, conservative life prediction may be made by adopting a critical void number density as 720(1/mm2). The void initiation and growth simulation was carried out under the maximum stress value of 50 and 40 MPa with different values of triaxial factor, and the “limited strain” at each condition was calculated from a product of the maximum creep strain rate and rupture time which is defined as a time of the void number density reaching the critical value of 720(1/mm2). Relationship between the “limited strain” and the triaxial factor obtained from the void simulation is shown in Fig. 8. Assuming that the maximum stress dependency on the “limited strain” maintains for different values of triaxial factor, the “limited strain” is expressed by the following equation. 5:4 elim ¼ 9:38 103 s1:62 max TF
(12)
The “limited strain” under a certain maximum stress and stress multiaxiality condition is calculated by the above
equation. Creep damage in the HAZ is defined by the following equation.
Dc ¼ e1loc =elim
(13)
where e1loc is the maximum creep strain at local portion in HAZ. 4.2. Damage assessment results Creep damage evolution in the HAZ of the longitudinal welded tube under 21.7 MPa internal pressure at 650 C was calculated by Eqs. (12) and (13) based on the FE analysis mentioned in Section 3.1. The creep damage contours at different creep damage levels are shown in Fig. 9. It is seen that creep damage starts from mid-thickness region and grow toward surface regions indicating macro crack starts from mid-thickness and extends through the section. Finite element creep analyses of longitudinal welded elbow pipes with two different shape of weld metal under the internal pressure condition have been carried out using a three materials finite element model [8]. Creep damages in the HAZ of the pipes are calculated by the above method and creep damage contours in the HAZ are shown in Fig. 10. It can be seen that creep damage distribution patterns in the HAZs is different depending on shape of weld metal. Creep damage progresses through the HAZ region in the straight fusion line as shown in Fig. 10(a), while
Fig. 10. Contour of creep damage distribution at HAZ region of welded elbow pipes.
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it concentrates at root portion of mid-thickness region in the HAZ for the case of discontinuous fusion line. Thus creep damage evolution in a HAZ of a longitudinal welded pipe can be predicted by using damage assessment method based on the “limited strain”.
5. Conclusions Internal pressure creep rupture tests and interrupted tests were conducted on P91 longitudinal welded tube specimens at 650 C, and damage condition at heat-affected zone (HAZ) of the specimens were carefully observed by a scanning electron microscope. The void number density per area at mid-thickness region is much larger than that at near surface regions corresponding to higher maximum stress and triaxiality factor regions obtained from finite element creep analysis of the specimen. The void numbers density per area at different portion of the HAZ were quantitatively predicted by the void growth simulation procedure indicating the procedure can be applied to predict void growth behavior internal of the material. A creep damage prediction method at the HAZ based on the “limited strain” was proposed and dependency of the maximum stress and triaxiality factor on “limited strain” was derived from the void growth simulation results. Creep damage distribution at the HAZ in
longitudinal welded tubes and pipes are simply predicted from FE analysis using three materials model.
References [1] Brett SJ, Oates DL, Johnston C. In-service Type IV cracking in a Modified 9Cr header. In: Proceeding of ECCC Creep Conference, September, London; 2005, p. 563e572. [2] Ogata T, Yaguchi M. Creep and creep-fatigue life assessment of boiler weldment parts. In: Proceedings of ECCC Creep Conference, 12e14 September, London; 2005, p. 909e917. [3] Kimura K, Kume R, Saito K, Fujiyama K. "Estimation of creep damage for components of Mod.9Cr-1Mo steel. J JSME A 2001;67(No. 661):1429e35 (in Japanese). [4] Tabuchi M, Watanabe T, Kubo K, Matsui M, Kinugawa J, Abe F. Microstructures and creep strength of welded joints for W strengthened high Cr ferritic steel. J Soc Mater Sci 2001;50(No. 2):116e21 (in Japanese). [5] Ogata T, Sakai T, Yaguchi M. Creep damage evolution and life assessment of P91 weld join. In: Proceeding of the Third International Conference on Integrity of High Temperature Welds, London, UK, April 24e26. London, UK: IOM Communication Ltd; 2007. p. 285e94. [6] Ogata T. Cavity growth simulation of 2.25Cre1Mo steel under creepefatigue loading. In: Proceeding of ASME pvp conference, PVP2005-71041; 2005. [7] Ogata T. Creep void growth simulation for reliable maintenance of high temperature components. ASME Paper No. IMECE200-79215; 2005. [8] Ogata T, Sakai T, Yaguchi M, 2007. Clarification of creep damage condition and development of damage assessment method of P91 longitudinal welded tube under internal pressure creep. Dencyuken Houkoku Q07002 (in Japanese).