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A method to determine minimum design metal temperature of pressure vessels made from ferritic steel by Master Curve approach
Engineering Fracture Mechanics xxx (xxxx) xxxx
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Engineering Fracture Mechanics journal homepage: www.elsevier.com/locate/engfracmech
A method to determine minimum design metal temperature of pressure vessels made from ferritic steel by Master Curve approach ⁎
Zhongqiang Zhou, H. Hui , Yalin Zhang, Xiangchun Cong, Hui Bai School of Mechanical and Power Engineering, East China University of Science and Technology, Shanghai 200237, China
A R T IC LE I N F O
ABS TRA CT
Keywords: Minimum design metal temperature Impact exemption curve Low temperature fracture toughness Reference temperature T0MC
The four impact exemption curves in ASME are convenient to estimate the minimum design metal temperature (MDMT) of ferritic steel. However they can’t distinguish low temperature fracture toughness of ferritic steel well. Materials with similar fracture toughness, divided into different impact exemption curves will have different MDMT and conservative degree. And the MDMT of ferritic steel are estimated by the steel grade. There are differences in toughness for steel with same steel grade from different factories and different heats and batches of the same factory. In this paper, the seven MDMT curves, identified with labels I, II, III, IV, V, VI and VII are proposed based on assumed yield strength and seven reference temperatures, (T0MC = 20 °C, 0 °C, −20 °C, −40 °C, −60 °C, −80 °C and −100 °C) which can cover the temperature range for commonly used pressure vessels made from ferritic steel. The MDMT for a ferritic steel can be determined once the reference temperature and yield strength are measured. SA508-3 and Q345R, as a representative of ferritic steel are used to illustrate the applicability of the MDMT curves.
1. Introduction Pressure vessels play an important roles in the development of the industry, especially in the petroleum industry, chemical industry and nuclear power plant and so on. The pressure vessels made from ferritic steel and operated at low temperature usually have the obvious phenomenon of ductile to brittle transition [1]. A small temperature drop can lead to a sharp drop in the fracture toughness. So the requirement for pressure vessels made from ferritic steel are strict. During the past decades, much efforts have been devote to the development of national codes for design against brittle fracture. ASME Boiler and Pressure Vessel Code (BPVC) VIII-2 provide the impact exemption curves which can be used to estimate the minimum design metal temperature (MDMT) of pressure vessels made from ferritic steel [2,3]. The impact exemption curves are divided into two categories according to the condition of as weld (AW) and post-weld heat treatment (PWHT). As shown in Figs. 1 and 2, steels usually used in the fabrication of pressure vessels are divided into four kinds of impact exemption curves, identified with labels, A, B, C and D, based on the difference of notch toughness [4]. There is a reference temperature, T0akv, for each of the impact exemption curves. For the four kinds of impact exemption curves, the values of T0akv are 45.56 °C, 24.44 °C, 3.33 °C and −11.11 °C and the yield strength is conservatively assumed as σys = 550 MPa. It is convenient and conservative to estimate the MDMT by using four exemption curves. In order to compare the difference between the four exemption curves in ASME and the curves determined by the actual yield strength, σys and reference temperature, T0akv, six steels are used which are the representative of four exemption curves. The chemical components and mechanical properties ⁎
Corresponding author. E-mail address: [email protected] (H. Hui).
https://doi.org/10.1016/j.engfracmech.2019.106631 Received 18 January 2019; Received in revised form 31 July 2019; Accepted 19 August 2019 0013-7944/ © 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: Zhongqiang Zhou, et al., Engineering Fracture Mechanics, https://doi.org/10.1016/j.engfracmech.2019.106631
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Nomenclature MDMT T0MC BPVC AW PWHT T0akv σys Pf σb KJC K0 Kmin B
B0 KJC(med) Mlimit σm p σSR m Kr Lr FAD KI KP I KSR I Kmat Φ σref α TD
minimum design metal temperature reference temperature used in the Master Curve boiler and pressure vessel code as weld condition post-weld heat treatment reference temperature used in Charpy impact energy yield strength cumulative failure probability at KJC ultimate tensile strength the fracture toughness temperature dependent normalization parameter lower bound fracture toughness Specimen thickness
reference specimen thickness media fracture toughness a dimensionless constant primary stress residual stress Toughness ratio load ratio failure assessment diagram the stress intensity factor primary stress intensity factor residual stress intensity factor material toughness plasticity correction factor the reference stress a reference stress parameter the minimum design metal temperature
Fig. 1. Four kinds of Impact exemption curves for AW condition in ASME. 50
PWHT
Minimum Design Metal Temperature/
40
A
30 20
B
10 0 -10
C
-20
D
-30 -40 -50 -60
0
10
20
30
40
50
60
70
80
90
100
Nominal Thickness/mm Fig. 2. Four kinds of Impact exemption curves for PWHT condition in ASME.
of six steels are shown in Tables 1 and 2. As shown in Figs. 3 and 4, it is obvious that the exemption curves of the six materials all below the curve D. Therefore, the four impact exemption curves can’t distinguish low temperature fracture toughness of ferritic steel well. As shown in Fig. 3, the MDMT of SA508-3, Q345R and SA516 Gr. 70 are almost identical. However, the three materials are associated with three different impact exemption curves in ASME (curve of D, A and B). Materials with similar low temperature fracture toughness can’t be divided into the same impact exemption curve. So the MDMT and conservative degree will be different. 2
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Table 1 Components of six ferritic steels. Material
C
Mn
Mo
Ni
Si
P
S
Cu
V
Q345R SA516Gr.70 [5] SA533B [6] SA516Gr.60 [7] SA508-3 SA738B
0.18 0.22 0.20 0.13 0.19 0.09
1.33 1.14 1.43 0.916 1.48 1.5
– 0.002 0.46 0.014 0.5 0.23
– 0.01 0.57 0.099 0.74 0.52
0.42 0.24 0.16 0.215 0.19 0.32
0.021 0.019 0.008 0.007 0.005 0.01
0.015 0.008 0.002 0.005 0.002 0.002
– 0.02 0.010 0.262 0.04 0.02
– – 0.005 0.001 – –
Table 2 Mechanical properties of six ferritic steels. Material
Status
σb /MPa
σys /MPa
T0akv/ °C
T0MC/ °C
Q345R SA516Gr.70 [5] SA533B [6] SA516Gr.60 [7] SA508-3 SA738B
normalized normalized normalized normalized normalized normalized
521.0 500 655 498 568.3 635.39
319.5 260 525 400 429.2 527.8
−29 −20 −75.4 −60 −30 −94.6
−63 – – – −61 –
Fig. 3. The minimum design metal temperature curves of six ferritic steel for AW condition.
The low temperature fracture toughness of SA516Gr. 70 and Q345R (belong to B and A curve respectively) may be underestimated. The MDMT of steels included in four impact exemption curves are estimated by the steel grade. There are differences in mechanical properties for steels of the same steel grade from different factories and different heats and batches of the same factory. The phenomenon is particularly evident in countries with lower steel smelting level. In addition, if a new steel is received by the four impact exemption curves it may be need a large amount of experiment data to support. So it is difficult to update the material categories that included in the four impact exemption curves. In this paper, seven MDMT curves based on seven reference temperatures, T0MC, and yield strength value of 550 MPa are proposed, similar to the four impact exemption curves in ASME. The values of T0MC are assumed as 20 °C, 0 °C, −20 °C, −40 °C, −60 °C, −80 °C and −100 °C which can cover the values of T0MC of commonly used pressure vessules made from ferritic steel. The MDMT curves are divided into seven toughness classes based on the seven temperatures, identified with labels I, II, III, IV, V, VI and VII. In order to study the influence of yield strength on MDMT, different values of yield strength (550, 500, 450, 400 and 350 MPa) are considered for the same toughness class. So the MDMT of steel can be determined when actual value of T0MC and yield strength are measured. Q345R and SA508-3 as the representative are used to illustrate the applicability of proposed MDMT curves for pressure vessels made from ferritic steel.
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Fig. 4. The minimum design metal temperature curves of six ferritic steel for PWHT condition.
2. The Master Curve 2.1. Master Curve method In the transition area, the fracture toughness of ferritic steel can be described by the Master Curve (MC) approach which was initially proposed by Wallin [8,9]. The reference temperature, T0MC can be calculated based on the data of fracture toughness experiment according to ASTM E1921 [10]. In the transition region, the brittle fracture probability Pf at a specified temperature can be determined by the function of Weibull:
B K − Kmin ⎞ ⎤ Pf = 1 − exp ⎡− ·⎛ JC ⎢ B0 ⎝ K 0 - Kmin ⎠ ⎥ ⎣ ⎦ ⎜
⎟
(1)
where KJC is equivalent fracture toughness which is converted from JC, Pf is the cumulative failure probability, K0 is a temperature dependent normalization parameter, Kmin is the lower bound fracture toughness which 20 MPa√m is typically used for ferritic steel, B is specimen thickness, B0 is reference specimen thickness and defined as 1 T (1 in). Eq. (2) was obtained by analyzing the test data of various ferritic steels, which was usually used to determine K0 [11,12]:
K 0 = 31 + 77 exp[0.019·(T − T0MC )]
(2)
When K0 is determined, the fracture toughness for ferritic steel can be expressed as Eq. (3), which is a function of cumulative failure and test temperature. 1/4
25 KJC (Pf ) = 20 + ⎡−LN (1 − Pf )1/4 ·{11 + 77 exp[0.019(T − T0MC )]}·⎛ ⎞ ⎢ ⎝B⎠ ⎣
⎤ ⎥ ⎦
(3)
Then the fracture toughness KJC(0.05) corresponding to 5% cumulative failure probability can be written as Eq. (4), which is used to calculate the MDMT in this paper.
Fig. 5. Shape and dimensions of the 1 T-SE (B) specimen. 4
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KJC (0.05) = 25.2 + 36.6 exp[0.019(T − T0MC )]
(4)
2.2. Experiment to determine T0MC of Q345R The chemical composition and mechanical property of Q345R used in experiment are shown in Tables 1 and 2. The fracture toughness is test using 1 T-SE(B) specimens at temperature −86 °C, −50 °C, −30 °C and −20 °C. The structure dimension of 1 T-SE (B) specimen is shown in Fig. 5. The fracture toughness experiment is performed on an Instron 8032 tester. The experiment temperature is controlled by a mixture of liquid nitrogen and absolute ethanol. The fracture toughness data for Q345R at different temperature are shown in Table 3. The T0MC can be obtained when the data of fracture toughness is determined. The reference temperature T0MC for Q345R using single temperature method and multi-temperature method are shown in Tables 4 and 5. The difference in reference temperature values of Q345R determined by single temperature method and multi-temperature method is small. The average value of T0MC for single temperature is −63 °C that is identical with the value determined by multitemperature method. And it has been proved that compared with single temperature method, the reference temperature determined multi-temperature method is more precise [13]. So the T0MC for Q345R is defined as −63 °C. 2.3. Experiment to determine T0MC of SA508-3 The chemical composition and mechanical properties of SA508-3 are also shown in Tables 1 and 2. Because the material of SA508-3 is precious, the fracture toughness experiment is performed using 0.5 T-SE (B) specimens at temperature −81 °C, −60 °C and −40 °C. The experiment process of SA508-3 is consistent with Q345R that has been stated above. The structure dimension of specimen is shown in Fig. 6 and the fracture toughness data of SA508-3 at different temperature are shown in Table 6. Then the reference temperature T0MC for SA508-3 using single temperature method and multi-temperature method are shown in Tables 7 and 8. The temperature difference of T0MC for SA508-3 calculated by two different methods is small. So the values of T0MC for SA508-3 is defined as −61 °C based on multi-temperature. 3. Brittle fracture prevention model Our research team [14] has revealed that some old item of the brittle fracture models are now deem to be inappropriate and developed a brittle fracture prevention model based on the Master Curve approach. 3.1. Hypothetical crack type By comparing the cylinder structure in ASME and the plate structure in EN 13445, the crack driving force KI in plate is higher than that in cylinder [15–17]. So an elliptical surface flaw with the depth, a, and length, 2c, in the plate structure is assumed as the crack type in this paper as shown in Fig. 7. The ratio of 2c/a is set to 6, and the value of a is defined as 0.25 t. Table 3 Fracture toughness test data of Q345R at different temperatures (1 T-SE (B) specimen). Temperature/°C
Sample number
KJC/MPa√m
−86
Q345R-5 Q345R-6 Q345R-3 Q345R-1 Q345R-23 Q345R-21 Q345R-7 Q345R-18 Q345R-20 Q345R-4 Q345R-22
36.4 45.2 46.9 51.2 54.8 55.3 59.8 66.7 69.2 90.8 119.4
Q345R-8 Q345R-13 Q345R-16 Q345R-14 Q345R-15 Q345R-12
72.2 75.5 101.2 130.2 137.4 169.0
−30
Q345R-9 Q345R-10
112.8 215.5
257.4
valid valid
−20
Q345R-2
150.4
154.5
valid
−50
5
KJC(limit)/MPa√m
278.2
264.5
valid valid valid valid valid valid valid valid valid valid valid valid valid valid valid valid valid
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Table 4 Values of reference temperature T0MC for Q345R steel using single temperature method. Temperature/°C
K0/MPa√m
KJC(med)/MPa√m
T0MC/°C
Number of valid KJC values
−86 −50
79.8 130.4
74.6 120.7
−62 −64
11 6
valid valid
Table 5 Values of reference temperature T0MC for Q345R steel using multi-temperature method. Temperature/°C
T0MC/°C
Value of ∑i = 1 ri ni
−86 °C, −50 °C, −30 °C, −20 °C
−63
3.1
3
valid
Fig. 6. Shape and dimensions of the 0.5 T-SE (B) specimen. Table 6 Fracture toughness data of SA508-3 at different temperatures (0.5 T-SE (B) specimen). Temperature/°C
Sample number
KJC(0.5T)/MPa√m
KJC(1T)/MPa√m
−81
3A17 3A13 3A11 3A15 3A14 3A16 3A12
66.4 70.1 78.0 81.2 89.6 104.2 109.8
59 62.2 68.7 71.5 78.5 90.8 95.5
2A13 3A1A 2A11 2A12 2A14 2A15
110.8 112.6 113.3 126.3 142.7 147.6
96.4 97.8 98.4 109.5 123.2 127.3
3A19 3A18
161.1 208.6
138.6 178.6
−60
−40
KJC(1T,limit)/MPa√m valid valid valid valid valid valid valid
189.7
valid valid valid valid valid valid
184.4
180.2
valid valid
Table 7 Values of reference temperature T0MC for SA508-3 steel using single temperature method. Temperature/°C
K0(1T)/MPa√m
KJC(1T,med)/MPa√m
T0MC/°C
Number of valid KJC values
−81 −60
79.5 111.4
74.2 103.4
−57 −62
7 6
valid valid
Table 8 Values of reference temperature T0MC for SA508-3 steel using multi-temperature method. Temperature/°C
T0MC/°C
Value of∑i = 1 ri ni
−81 °C, −60 °C, −40 °C
−61
2.3
3
6
valid
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Fig. 7. Geometric model of hypothetical crack.
3.2. Assumed stress level In order to calculate driving force, the primary stress σP m and residual stress σSR m are assumed as a function of the specified minimum yield strength. Allowing for the difference in stress level between AW and PWHT condition, the residual stresses σSR m are different.
2·σys
σmP =
(5)
3 2·σys
σmSR =
3 7·σys
σmSR =
20
(AW)
(6)
(PWHT)
(7)
3.3. Failure assessment diagram (FAD) In the assessment progress of crack-like flaws, the main purpose is to obtain toughness ratio, Kr and a load ratio, Lr based on stress level and material properties. The values of Kr and Lr represent the coordinate of a point in FAD, which is used to determine the acceptability of component. The component can run safely, if the coordinate point is not beyond the FAD curve [18]. The expression of FAD curve is described as Eq. (8)
Kr = (1 − (Lr )2.5)0.2
(8)
The toughness ratio is given by Eq. (9)
Kr =
2·KIP + ΦKISR Kmat
(9)
Where KP I and KSR I are the stress intensity factor, KI = Yσ√πa, [19] Kmat is the material toughness, Φ is the plasticity correction factor according to API 579 [20], Φ = 1 + ψ/φ The load ratio is given by Eq. (10)
Lr =
σref σys
(10)
Where σref is the reference stress, σref = σp m/(1 − α), α is the reference stress parameter, α=(a/t)/(1 + t/c) Combine Eq. (8) with Eq. (9) the toughness of material can be expressed as:
Kmat =
2KIP + ΦKISR [1 − (Lr )2.5]0.2
(11)
The fracture toughness values of Kmat should be convert into Kmat(1T), then using Kmat(1T) to replace KJC(0.05) in Eq. (4), the minimum design metal temperature can be derived as Eq. (12)
TD =
Kmat (1T ) − 25.2 1 ⎞ − T0MC LN ⎛ 0.019 36.6 ⎠ ⎝
(12)
4. The minimum design metal temperature curve In order to reduce the risk of brittle fracture, the minimum design temperature curves of pressure vessels made from ferritic steel, based on the brittle fracture prevention model and Master Curve approach are determined. 4.1. The MDMT curves based on assumed T0MC In Eq. (12) the MDMT can be determined by T0MC when Kmat(1T) is known. In this section, seven MDMT curves are proposed based on the values of seven assumed reference temperatures and the yield strength value of 550 MPa. The values of T0MC are assumed as 7
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20 °C, 0 °C, −20 °C, −40 °C, −60 °C, −80 °C and −100 °C which can cover the values of T0MC of commonly used pressure vessels made from ferritic steel. And the MDMT curves of ferritic steel are divided into seven toughness classes based on the assumed seven temperatures, identified with labels I, II, III, IV, V, VI and VII as shown in Figs. 8 and 9 for AW and PWHT conditions, respectively. In actual engineer, the MDMT of steel can be easily determined when the reference temperature and nominal thickness are known. As we can see in Figs. 8 and 9, the MDMT decreases with the decrease of reference temperature and nominal thickness. And compared with AW, the PWHT condition can be used in lower temperature. The upper limit value of thickness is defined as 38 mm, which is the maximum thickness that can be permitted for AW condition [21,22]. For PWHT condition, 100 mm is chosen as the maximum thickness value, which is based on the level of nondestructive testing [23].
4.2. The applicability of MDMT curve considering different yield strength In the calculation process of MDMT, the yield strength is assumed conservatively as 550 MPa. It can simplify the calculation process of MDMT and consist with ASME B&PV Code Section VIII, Division 2. In order to illustrate the effect of yield strength on MDMT, different yield strength are discussed for the same T0MC (T0MC = −60 °C) as shown in Figs. 10 and 11. As we can see, the MDMT decreases with the decrease of the yield strength of ferritic steel. As shown in Table 9, at the same yield strength interval, 50 MPa, the lower yield strength corresponds to a slightly larger temperature drop. So it is reasonable and conservative to determine the MDMT by linear interpolation if the actual yield strength of steel beyond the range of yield strength in this paper. In China, SA508-3 and Q345R are widely used in the construction of pressure vessels. So they are used to illustrate the applicability of this MDMT curves for pressure vessels made from ferritic steel. And the MDMT curves of SA508-3 and Q345R are also plotted in Figs. 10 and 11. As we can see, the temperature difference between the MDMT curve of T0MC = −60 °C, σys = 450 MPa and curve of SA508-3 (T0MC = −861 °C, σys = 429.2 MPa) is about 5 °C both for AW and PWHT conditions. And the temperature difference between the MDMT curve of T0MC = −60 °C, σys = 350 MPa and curve of Q345R (T0MC = −63 °C, σys = 345 MPa) is about 4 °C both for AW and PWHT conditions. The differences in MDMT value for Q345R and SA508-3 between the assumed curves and the curves based on actual reference temperature and yield strength is small. So the minimum design metal temperature of pressure vessels made from ferritic steel can be estimated well by the MDMT curves proposed in this paper.
4.3. The MDMT curves based on different yield strength and T0MC The MDMT curves of pressure vessels that are made from ferritic steel, considering different yield strength and T0MC, are shown in Figs. 12 and 13 for AW and PWHT conditions, respectively. The fracture toughness of ferritic steel are divided into seven classes, identified with the labels I, II, III, IV, V, VI and VII. For each class, different yield strength (σys = 550, 500 and 450 MPa) is considered. And linear interpolation can be used to determine the MDMT for steel that the yield strength beyond the range in this paper. In practical engineering application, the MDMT of steels can be easily and conservatively to confirm when the T0MC and yield strength are determined and adjusted upwards to the nearest toughness and strength class.
Fig. 8. The minimum design metal temperature curves of seven toughness classes for AW condition. 8
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Fig. 9. The minimum design metal temperature curves of seven toughness classes for PWHT condition.
Fig. 10. The minimum design metal temperature curves of different yield strength for AW condition (T0MC = −60 °C).
Fig. 11. The minimum design metal temperature curves of different yield strength for PWHT condition (T0MC = −60 °C).
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Table 9 Temperature drop for different yield strength ranges and different conditions. Conditions
550–500 MPa
500–450 MPa
450–400 MPa
400–350 MPa
AW PWHT
7.5 °C 8.9 °C
8.3 °C 10.0 °C
10.0 °C 12.8 °C
12.3 °C 17.0 °C
Fig. 12. The minimum design metal temperature curves of different yield strength and T0MC for AW condition.
Fig. 13. The minimum design metal temperature curves of different yield strength and T0MC for PWHT condition.
5. Conclusions In this paper, the minimum design metal temperature curves of six steels that are the representative of A, B, C and D curves are plotted based on actual yield strength, σys and reference temperature, T0akv to compare with the A, B, C and D curves. The MDMT curves of ferritic steel are presented based on the assumed yield strength and reference temperature, T0MC. The effect of yield strength (σys = 550, 500, 450, 400 and 350 MPa) on MDMT curves and the applicability of MDMT curves for SA508-3 and Q345R is discussed. From the present study, the conclusions are obtained as following: (1) The MDMT curves of six steels all below D curve as shown in Figs. 3 and 4. Therefore, the four impact exemption curves in ASME B&PV Code Section VIII, Division 2 can’t distinguish low temperature fracture toughness of steel well. Materials of SA508-3, Q345R and SA516 Gr. 70 with similar low temperature toughness can’t be divided into the same impact exemption curve. So the MDMT and conservative degree are different for the three steels. The low temperature fracture toughness of some materials may be underestimated. (2) The MDMT curves are divided into seven classes based on assumed reference temperature T0MC (T0MC = −100 °C, −80 °C, 10
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−60 °C, −40 °C, −20 °C, 0 °C and 20 °C) as shown in Figs. 8 and 9. As we can see, the MDMT decreases with the decrease of reference temperature and nominal thickness. Compared with AW condition, the MDMT is lower for PWHT condition. (3) The effect of yield strength (σys = 550, 500, 450, 400 and 350 MPa) on MDMT curve is discussed, as shown in Figs. 10 and 11. The minimum design temperature decreases with the decrease of yield strength for the same reference temperature (T0MC = −60 °C). At the same yield strength interval, 50 MPa, the lower yield strength corresponds to a slightly larger temperature drop. It has been proved that it is reasonable and conservative to determine the MDMT by linear interpolation for steel beyond the range of yield strength in this paper. (4) SA508-3 and Q345R are used to illustrate the applicability of this MDMT curves for ferritic steel. The temperature difference between MDMT curves and curves of SA508-3 and Q345R are about 5 °C and 4 °C respectively. So the minimum design metal temperature of steel can be precisely and conservatively determined by the MDMT curves presented in this paper. References [1] Cao YP. Predication of Fracture Toughness in the Ductile-To-Brittle Transition Region of Pressure Vessel Steels PhD thesis East China University of Science and Technology; 2011 [2] ASME Code. Section VIII-2. Rules for construction of pressure vessels (alternative rules), New York; 2015. [3] Farr JR, Jawad MH. Guide Book for the Design of ASME Section VIII Pressure Vessels. New York: ASME; 2001. p. 15–20. [4] Selz A. New Toughness Rules in Section VIII, Division 1 of the ASME Boiler and Pressure Code. New York: ASME; 1988. [5] Hall A. The Effect of Welding Speed on the Properties of ASME SA516 Grade 70 Steel. University of Saskatchewan; 2010. [6] Yun-Liang LI, Zhang HQ, Ying HU. Microstructure and mechanical properties of nuclear pressure vessel steel SA533B heavy plate. T Mater Heat Treat 2012;33(8):84–8. [7] Cai PX. Effect of Welding Procedure on the Microstructure and Properties of Welded Joint of Cryogenic Steel SA516Gr.60. Hohai University 2006. [8] Wallin K. The scatter in KIc results. Eng Fract Mech 1984;19:1085–93. [9] Wallin K. The master curve method: a new concept for brittle fracture. Int J Min Met Mater 1999;14:342–54. [10] ASTM E1921-11. Standard test method for determination of reference temperature, T0, for ferritic steels in the transition range, West Conshohocken, PA; 2011. [11] Merkle JG, Wallin K, McCabe DE. Technical basis for an ASTM standard on determining the reference temperature, T0, for ferritic steels in the transition range. NUREG/CR-5504; 1998. [12] Wallin K. Validity of small specimen fracture toughness estimates neglecting constraint corrections. ASTM STP 1995;1244:519–37. [13] Chen Z, Pan JH, Jin T. Estimation of fracture toughness of 16MnDR steel using Master Curve method and Charpy V-notch impact energy. Theor Appl Fract Mec 2018;96:443–51. [14] Cui QF, Hui H, Li PN. Brittle fracture prevention model for pressure vessels based on Master Curve approach. J Press Vess Technol 2017;139(1):11–405. [15] Osage DA, Prager M. Technical basis of material toughness requirements in the ASME boiler and pressure vessel code, section VIII, division 2. ASME J Press Vess Technol 2012;134(3):1–31. [16] Sandstrom R, Langenberg P, Sieurin H. Analysis of the brittle fracture avoidance model for pressure vessels in european standard. Int J Press Vess Pip 2005;82(11):872–81. [17] Cui QF, Hui H, Li PN. Applicability of the ASME exemption curve for Chinese pressure vessel steel Q345R. ASME J Press Vess Technol 2015;137:61–602. [18] Anderson TL. Fracture mechanics: fundamentals and applications Surjya Kumar Maiti. Mrs Bull 2016;41(8):635–6. [19] Newman JC, Raju IS. An empirical stress-intensity factor equation for the surface crack. Engng Fract Mech 1981;15(1–2):185–92. [20] Osage DA. API 579: a comprehensive fitness-for-service standard. Int J Press Vess Piping 2000;77(14):953–63. [21] Abson DJ, Tkach Y, Hadely I, Burdekin FM. Accessing toughness levels for steels to determine the need for PWHT. Weld J 2006;85:29–35. [22] Abson DJ, Tkach Y, Hadely I, Burdekin FM. A review of post weld heat treatment code exemptions. Weld J 2006;85:63–9. [23] Oldfield W, Server WL, Wullaert RA, Stahlkopf KE. Development of a statistical lower bound fracture toughness curve. Int J Press Vess Pip 1978;6(3):203–22.
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Engineering Fracture Mechanics journal homepage: www.elsevier.com/locate/engfracmech
A method to determine minimum design metal temperature of pressure vessels made from ferritic steel by Master Curve approach ⁎
Zhongqiang Zhou, H. Hui , Yalin Zhang, Xiangchun Cong, Hui Bai School of Mechanical and Power Engineering, East China University of Science and Technology, Shanghai 200237, China
A R T IC LE I N F O
ABS TRA CT
Keywords: Minimum design metal temperature Impact exemption curve Low temperature fracture toughness Reference temperature T0MC
The four impact exemption curves in ASME are convenient to estimate the minimum design metal temperature (MDMT) of ferritic steel. However they can’t distinguish low temperature fracture toughness of ferritic steel well. Materials with similar fracture toughness, divided into different impact exemption curves will have different MDMT and conservative degree. And the MDMT of ferritic steel are estimated by the steel grade. There are differences in toughness for steel with same steel grade from different factories and different heats and batches of the same factory. In this paper, the seven MDMT curves, identified with labels I, II, III, IV, V, VI and VII are proposed based on assumed yield strength and seven reference temperatures, (T0MC = 20 °C, 0 °C, −20 °C, −40 °C, −60 °C, −80 °C and −100 °C) which can cover the temperature range for commonly used pressure vessels made from ferritic steel. The MDMT for a ferritic steel can be determined once the reference temperature and yield strength are measured. SA508-3 and Q345R, as a representative of ferritic steel are used to illustrate the applicability of the MDMT curves.
1. Introduction Pressure vessels play an important roles in the development of the industry, especially in the petroleum industry, chemical industry and nuclear power plant and so on. The pressure vessels made from ferritic steel and operated at low temperature usually have the obvious phenomenon of ductile to brittle transition [1]. A small temperature drop can lead to a sharp drop in the fracture toughness. So the requirement for pressure vessels made from ferritic steel are strict. During the past decades, much efforts have been devote to the development of national codes for design against brittle fracture. ASME Boiler and Pressure Vessel Code (BPVC) VIII-2 provide the impact exemption curves which can be used to estimate the minimum design metal temperature (MDMT) of pressure vessels made from ferritic steel [2,3]. The impact exemption curves are divided into two categories according to the condition of as weld (AW) and post-weld heat treatment (PWHT). As shown in Figs. 1 and 2, steels usually used in the fabrication of pressure vessels are divided into four kinds of impact exemption curves, identified with labels, A, B, C and D, based on the difference of notch toughness [4]. There is a reference temperature, T0akv, for each of the impact exemption curves. For the four kinds of impact exemption curves, the values of T0akv are 45.56 °C, 24.44 °C, 3.33 °C and −11.11 °C and the yield strength is conservatively assumed as σys = 550 MPa. It is convenient and conservative to estimate the MDMT by using four exemption curves. In order to compare the difference between the four exemption curves in ASME and the curves determined by the actual yield strength, σys and reference temperature, T0akv, six steels are used which are the representative of four exemption curves. The chemical components and mechanical properties ⁎
Corresponding author. E-mail address: [email protected] (H. Hui).
https://doi.org/10.1016/j.engfracmech.2019.106631 Received 18 January 2019; Received in revised form 31 July 2019; Accepted 19 August 2019 0013-7944/ © 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: Zhongqiang Zhou, et al., Engineering Fracture Mechanics, https://doi.org/10.1016/j.engfracmech.2019.106631
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Nomenclature MDMT T0MC BPVC AW PWHT T0akv σys Pf σb KJC K0 Kmin B
B0 KJC(med) Mlimit σm p σSR m Kr Lr FAD KI KP I KSR I Kmat Φ σref α TD
minimum design metal temperature reference temperature used in the Master Curve boiler and pressure vessel code as weld condition post-weld heat treatment reference temperature used in Charpy impact energy yield strength cumulative failure probability at KJC ultimate tensile strength the fracture toughness temperature dependent normalization parameter lower bound fracture toughness Specimen thickness
reference specimen thickness media fracture toughness a dimensionless constant primary stress residual stress Toughness ratio load ratio failure assessment diagram the stress intensity factor primary stress intensity factor residual stress intensity factor material toughness plasticity correction factor the reference stress a reference stress parameter the minimum design metal temperature
Fig. 1. Four kinds of Impact exemption curves for AW condition in ASME. 50
PWHT
Minimum Design Metal Temperature/
40
A
30 20
B
10 0 -10
C
-20
D
-30 -40 -50 -60
0
10
20
30
40
50
60
70
80
90
100
Nominal Thickness/mm Fig. 2. Four kinds of Impact exemption curves for PWHT condition in ASME.
of six steels are shown in Tables 1 and 2. As shown in Figs. 3 and 4, it is obvious that the exemption curves of the six materials all below the curve D. Therefore, the four impact exemption curves can’t distinguish low temperature fracture toughness of ferritic steel well. As shown in Fig. 3, the MDMT of SA508-3, Q345R and SA516 Gr. 70 are almost identical. However, the three materials are associated with three different impact exemption curves in ASME (curve of D, A and B). Materials with similar low temperature fracture toughness can’t be divided into the same impact exemption curve. So the MDMT and conservative degree will be different. 2
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Table 1 Components of six ferritic steels. Material
C
Mn
Mo
Ni
Si
P
S
Cu
V
Q345R SA516Gr.70 [5] SA533B [6] SA516Gr.60 [7] SA508-3 SA738B
0.18 0.22 0.20 0.13 0.19 0.09
1.33 1.14 1.43 0.916 1.48 1.5
– 0.002 0.46 0.014 0.5 0.23
– 0.01 0.57 0.099 0.74 0.52
0.42 0.24 0.16 0.215 0.19 0.32
0.021 0.019 0.008 0.007 0.005 0.01
0.015 0.008 0.002 0.005 0.002 0.002
– 0.02 0.010 0.262 0.04 0.02
– – 0.005 0.001 – –
Table 2 Mechanical properties of six ferritic steels. Material
Status
σb /MPa
σys /MPa
T0akv/ °C
T0MC/ °C
Q345R SA516Gr.70 [5] SA533B [6] SA516Gr.60 [7] SA508-3 SA738B
normalized normalized normalized normalized normalized normalized
521.0 500 655 498 568.3 635.39
319.5 260 525 400 429.2 527.8
−29 −20 −75.4 −60 −30 −94.6
−63 – – – −61 –
Fig. 3. The minimum design metal temperature curves of six ferritic steel for AW condition.
The low temperature fracture toughness of SA516Gr. 70 and Q345R (belong to B and A curve respectively) may be underestimated. The MDMT of steels included in four impact exemption curves are estimated by the steel grade. There are differences in mechanical properties for steels of the same steel grade from different factories and different heats and batches of the same factory. The phenomenon is particularly evident in countries with lower steel smelting level. In addition, if a new steel is received by the four impact exemption curves it may be need a large amount of experiment data to support. So it is difficult to update the material categories that included in the four impact exemption curves. In this paper, seven MDMT curves based on seven reference temperatures, T0MC, and yield strength value of 550 MPa are proposed, similar to the four impact exemption curves in ASME. The values of T0MC are assumed as 20 °C, 0 °C, −20 °C, −40 °C, −60 °C, −80 °C and −100 °C which can cover the values of T0MC of commonly used pressure vessules made from ferritic steel. The MDMT curves are divided into seven toughness classes based on the seven temperatures, identified with labels I, II, III, IV, V, VI and VII. In order to study the influence of yield strength on MDMT, different values of yield strength (550, 500, 450, 400 and 350 MPa) are considered for the same toughness class. So the MDMT of steel can be determined when actual value of T0MC and yield strength are measured. Q345R and SA508-3 as the representative are used to illustrate the applicability of proposed MDMT curves for pressure vessels made from ferritic steel.
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Fig. 4. The minimum design metal temperature curves of six ferritic steel for PWHT condition.
2. The Master Curve 2.1. Master Curve method In the transition area, the fracture toughness of ferritic steel can be described by the Master Curve (MC) approach which was initially proposed by Wallin [8,9]. The reference temperature, T0MC can be calculated based on the data of fracture toughness experiment according to ASTM E1921 [10]. In the transition region, the brittle fracture probability Pf at a specified temperature can be determined by the function of Weibull:
B K − Kmin ⎞ ⎤ Pf = 1 − exp ⎡− ·⎛ JC ⎢ B0 ⎝ K 0 - Kmin ⎠ ⎥ ⎣ ⎦ ⎜
⎟
(1)
where KJC is equivalent fracture toughness which is converted from JC, Pf is the cumulative failure probability, K0 is a temperature dependent normalization parameter, Kmin is the lower bound fracture toughness which 20 MPa√m is typically used for ferritic steel, B is specimen thickness, B0 is reference specimen thickness and defined as 1 T (1 in). Eq. (2) was obtained by analyzing the test data of various ferritic steels, which was usually used to determine K0 [11,12]:
K 0 = 31 + 77 exp[0.019·(T − T0MC )]
(2)
When K0 is determined, the fracture toughness for ferritic steel can be expressed as Eq. (3), which is a function of cumulative failure and test temperature. 1/4
25 KJC (Pf ) = 20 + ⎡−LN (1 − Pf )1/4 ·{11 + 77 exp[0.019(T − T0MC )]}·⎛ ⎞ ⎢ ⎝B⎠ ⎣
⎤ ⎥ ⎦
(3)
Then the fracture toughness KJC(0.05) corresponding to 5% cumulative failure probability can be written as Eq. (4), which is used to calculate the MDMT in this paper.
Fig. 5. Shape and dimensions of the 1 T-SE (B) specimen. 4
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KJC (0.05) = 25.2 + 36.6 exp[0.019(T − T0MC )]
(4)
2.2. Experiment to determine T0MC of Q345R The chemical composition and mechanical property of Q345R used in experiment are shown in Tables 1 and 2. The fracture toughness is test using 1 T-SE(B) specimens at temperature −86 °C, −50 °C, −30 °C and −20 °C. The structure dimension of 1 T-SE (B) specimen is shown in Fig. 5. The fracture toughness experiment is performed on an Instron 8032 tester. The experiment temperature is controlled by a mixture of liquid nitrogen and absolute ethanol. The fracture toughness data for Q345R at different temperature are shown in Table 3. The T0MC can be obtained when the data of fracture toughness is determined. The reference temperature T0MC for Q345R using single temperature method and multi-temperature method are shown in Tables 4 and 5. The difference in reference temperature values of Q345R determined by single temperature method and multi-temperature method is small. The average value of T0MC for single temperature is −63 °C that is identical with the value determined by multitemperature method. And it has been proved that compared with single temperature method, the reference temperature determined multi-temperature method is more precise [13]. So the T0MC for Q345R is defined as −63 °C. 2.3. Experiment to determine T0MC of SA508-3 The chemical composition and mechanical properties of SA508-3 are also shown in Tables 1 and 2. Because the material of SA508-3 is precious, the fracture toughness experiment is performed using 0.5 T-SE (B) specimens at temperature −81 °C, −60 °C and −40 °C. The experiment process of SA508-3 is consistent with Q345R that has been stated above. The structure dimension of specimen is shown in Fig. 6 and the fracture toughness data of SA508-3 at different temperature are shown in Table 6. Then the reference temperature T0MC for SA508-3 using single temperature method and multi-temperature method are shown in Tables 7 and 8. The temperature difference of T0MC for SA508-3 calculated by two different methods is small. So the values of T0MC for SA508-3 is defined as −61 °C based on multi-temperature. 3. Brittle fracture prevention model Our research team [14] has revealed that some old item of the brittle fracture models are now deem to be inappropriate and developed a brittle fracture prevention model based on the Master Curve approach. 3.1. Hypothetical crack type By comparing the cylinder structure in ASME and the plate structure in EN 13445, the crack driving force KI in plate is higher than that in cylinder [15–17]. So an elliptical surface flaw with the depth, a, and length, 2c, in the plate structure is assumed as the crack type in this paper as shown in Fig. 7. The ratio of 2c/a is set to 6, and the value of a is defined as 0.25 t. Table 3 Fracture toughness test data of Q345R at different temperatures (1 T-SE (B) specimen). Temperature/°C
Sample number
KJC/MPa√m
−86
Q345R-5 Q345R-6 Q345R-3 Q345R-1 Q345R-23 Q345R-21 Q345R-7 Q345R-18 Q345R-20 Q345R-4 Q345R-22
36.4 45.2 46.9 51.2 54.8 55.3 59.8 66.7 69.2 90.8 119.4
Q345R-8 Q345R-13 Q345R-16 Q345R-14 Q345R-15 Q345R-12
72.2 75.5 101.2 130.2 137.4 169.0
−30
Q345R-9 Q345R-10
112.8 215.5
257.4
valid valid
−20
Q345R-2
150.4
154.5
valid
−50
5
KJC(limit)/MPa√m
278.2
264.5
valid valid valid valid valid valid valid valid valid valid valid valid valid valid valid valid valid
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Table 4 Values of reference temperature T0MC for Q345R steel using single temperature method. Temperature/°C
K0/MPa√m
KJC(med)/MPa√m
T0MC/°C
Number of valid KJC values
−86 −50
79.8 130.4
74.6 120.7
−62 −64
11 6
valid valid
Table 5 Values of reference temperature T0MC for Q345R steel using multi-temperature method. Temperature/°C
T0MC/°C
Value of ∑i = 1 ri ni
−86 °C, −50 °C, −30 °C, −20 °C
−63
3.1
3
valid
Fig. 6. Shape and dimensions of the 0.5 T-SE (B) specimen. Table 6 Fracture toughness data of SA508-3 at different temperatures (0.5 T-SE (B) specimen). Temperature/°C
Sample number
KJC(0.5T)/MPa√m
KJC(1T)/MPa√m
−81
3A17 3A13 3A11 3A15 3A14 3A16 3A12
66.4 70.1 78.0 81.2 89.6 104.2 109.8
59 62.2 68.7 71.5 78.5 90.8 95.5
2A13 3A1A 2A11 2A12 2A14 2A15
110.8 112.6 113.3 126.3 142.7 147.6
96.4 97.8 98.4 109.5 123.2 127.3
3A19 3A18
161.1 208.6
138.6 178.6
−60
−40
KJC(1T,limit)/MPa√m valid valid valid valid valid valid valid
189.7
valid valid valid valid valid valid
184.4
180.2
valid valid
Table 7 Values of reference temperature T0MC for SA508-3 steel using single temperature method. Temperature/°C
K0(1T)/MPa√m
KJC(1T,med)/MPa√m
T0MC/°C
Number of valid KJC values
−81 −60
79.5 111.4
74.2 103.4
−57 −62
7 6
valid valid
Table 8 Values of reference temperature T0MC for SA508-3 steel using multi-temperature method. Temperature/°C
T0MC/°C
Value of∑i = 1 ri ni
−81 °C, −60 °C, −40 °C
−61
2.3
3
6
valid
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Fig. 7. Geometric model of hypothetical crack.
3.2. Assumed stress level In order to calculate driving force, the primary stress σP m and residual stress σSR m are assumed as a function of the specified minimum yield strength. Allowing for the difference in stress level between AW and PWHT condition, the residual stresses σSR m are different.
2·σys
σmP =
(5)
3 2·σys
σmSR =
3 7·σys
σmSR =
20
(AW)
(6)
(PWHT)
(7)
3.3. Failure assessment diagram (FAD) In the assessment progress of crack-like flaws, the main purpose is to obtain toughness ratio, Kr and a load ratio, Lr based on stress level and material properties. The values of Kr and Lr represent the coordinate of a point in FAD, which is used to determine the acceptability of component. The component can run safely, if the coordinate point is not beyond the FAD curve [18]. The expression of FAD curve is described as Eq. (8)
Kr = (1 − (Lr )2.5)0.2
(8)
The toughness ratio is given by Eq. (9)
Kr =
2·KIP + ΦKISR Kmat
(9)
Where KP I and KSR I are the stress intensity factor, KI = Yσ√πa, [19] Kmat is the material toughness, Φ is the plasticity correction factor according to API 579 [20], Φ = 1 + ψ/φ The load ratio is given by Eq. (10)
Lr =
σref σys
(10)
Where σref is the reference stress, σref = σp m/(1 − α), α is the reference stress parameter, α=(a/t)/(1 + t/c) Combine Eq. (8) with Eq. (9) the toughness of material can be expressed as:
Kmat =
2KIP + ΦKISR [1 − (Lr )2.5]0.2
(11)
The fracture toughness values of Kmat should be convert into Kmat(1T), then using Kmat(1T) to replace KJC(0.05) in Eq. (4), the minimum design metal temperature can be derived as Eq. (12)
TD =
Kmat (1T ) − 25.2 1 ⎞ − T0MC LN ⎛ 0.019 36.6 ⎠ ⎝
(12)
4. The minimum design metal temperature curve In order to reduce the risk of brittle fracture, the minimum design temperature curves of pressure vessels made from ferritic steel, based on the brittle fracture prevention model and Master Curve approach are determined. 4.1. The MDMT curves based on assumed T0MC In Eq. (12) the MDMT can be determined by T0MC when Kmat(1T) is known. In this section, seven MDMT curves are proposed based on the values of seven assumed reference temperatures and the yield strength value of 550 MPa. The values of T0MC are assumed as 7
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20 °C, 0 °C, −20 °C, −40 °C, −60 °C, −80 °C and −100 °C which can cover the values of T0MC of commonly used pressure vessels made from ferritic steel. And the MDMT curves of ferritic steel are divided into seven toughness classes based on the assumed seven temperatures, identified with labels I, II, III, IV, V, VI and VII as shown in Figs. 8 and 9 for AW and PWHT conditions, respectively. In actual engineer, the MDMT of steel can be easily determined when the reference temperature and nominal thickness are known. As we can see in Figs. 8 and 9, the MDMT decreases with the decrease of reference temperature and nominal thickness. And compared with AW, the PWHT condition can be used in lower temperature. The upper limit value of thickness is defined as 38 mm, which is the maximum thickness that can be permitted for AW condition [21,22]. For PWHT condition, 100 mm is chosen as the maximum thickness value, which is based on the level of nondestructive testing [23].
4.2. The applicability of MDMT curve considering different yield strength In the calculation process of MDMT, the yield strength is assumed conservatively as 550 MPa. It can simplify the calculation process of MDMT and consist with ASME B&PV Code Section VIII, Division 2. In order to illustrate the effect of yield strength on MDMT, different yield strength are discussed for the same T0MC (T0MC = −60 °C) as shown in Figs. 10 and 11. As we can see, the MDMT decreases with the decrease of the yield strength of ferritic steel. As shown in Table 9, at the same yield strength interval, 50 MPa, the lower yield strength corresponds to a slightly larger temperature drop. So it is reasonable and conservative to determine the MDMT by linear interpolation if the actual yield strength of steel beyond the range of yield strength in this paper. In China, SA508-3 and Q345R are widely used in the construction of pressure vessels. So they are used to illustrate the applicability of this MDMT curves for pressure vessels made from ferritic steel. And the MDMT curves of SA508-3 and Q345R are also plotted in Figs. 10 and 11. As we can see, the temperature difference between the MDMT curve of T0MC = −60 °C, σys = 450 MPa and curve of SA508-3 (T0MC = −861 °C, σys = 429.2 MPa) is about 5 °C both for AW and PWHT conditions. And the temperature difference between the MDMT curve of T0MC = −60 °C, σys = 350 MPa and curve of Q345R (T0MC = −63 °C, σys = 345 MPa) is about 4 °C both for AW and PWHT conditions. The differences in MDMT value for Q345R and SA508-3 between the assumed curves and the curves based on actual reference temperature and yield strength is small. So the minimum design metal temperature of pressure vessels made from ferritic steel can be estimated well by the MDMT curves proposed in this paper.
4.3. The MDMT curves based on different yield strength and T0MC The MDMT curves of pressure vessels that are made from ferritic steel, considering different yield strength and T0MC, are shown in Figs. 12 and 13 for AW and PWHT conditions, respectively. The fracture toughness of ferritic steel are divided into seven classes, identified with the labels I, II, III, IV, V, VI and VII. For each class, different yield strength (σys = 550, 500 and 450 MPa) is considered. And linear interpolation can be used to determine the MDMT for steel that the yield strength beyond the range in this paper. In practical engineering application, the MDMT of steels can be easily and conservatively to confirm when the T0MC and yield strength are determined and adjusted upwards to the nearest toughness and strength class.
Fig. 8. The minimum design metal temperature curves of seven toughness classes for AW condition. 8
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Fig. 9. The minimum design metal temperature curves of seven toughness classes for PWHT condition.
Fig. 10. The minimum design metal temperature curves of different yield strength for AW condition (T0MC = −60 °C).
Fig. 11. The minimum design metal temperature curves of different yield strength for PWHT condition (T0MC = −60 °C).
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Table 9 Temperature drop for different yield strength ranges and different conditions. Conditions
550–500 MPa
500–450 MPa
450–400 MPa
400–350 MPa
AW PWHT
7.5 °C 8.9 °C
8.3 °C 10.0 °C
10.0 °C 12.8 °C
12.3 °C 17.0 °C
Fig. 12. The minimum design metal temperature curves of different yield strength and T0MC for AW condition.
Fig. 13. The minimum design metal temperature curves of different yield strength and T0MC for PWHT condition.
5. Conclusions In this paper, the minimum design metal temperature curves of six steels that are the representative of A, B, C and D curves are plotted based on actual yield strength, σys and reference temperature, T0akv to compare with the A, B, C and D curves. The MDMT curves of ferritic steel are presented based on the assumed yield strength and reference temperature, T0MC. The effect of yield strength (σys = 550, 500, 450, 400 and 350 MPa) on MDMT curves and the applicability of MDMT curves for SA508-3 and Q345R is discussed. From the present study, the conclusions are obtained as following: (1) The MDMT curves of six steels all below D curve as shown in Figs. 3 and 4. Therefore, the four impact exemption curves in ASME B&PV Code Section VIII, Division 2 can’t distinguish low temperature fracture toughness of steel well. Materials of SA508-3, Q345R and SA516 Gr. 70 with similar low temperature toughness can’t be divided into the same impact exemption curve. So the MDMT and conservative degree are different for the three steels. The low temperature fracture toughness of some materials may be underestimated. (2) The MDMT curves are divided into seven classes based on assumed reference temperature T0MC (T0MC = −100 °C, −80 °C, 10
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−60 °C, −40 °C, −20 °C, 0 °C and 20 °C) as shown in Figs. 8 and 9. As we can see, the MDMT decreases with the decrease of reference temperature and nominal thickness. Compared with AW condition, the MDMT is lower for PWHT condition. (3) The effect of yield strength (σys = 550, 500, 450, 400 and 350 MPa) on MDMT curve is discussed, as shown in Figs. 10 and 11. The minimum design temperature decreases with the decrease of yield strength for the same reference temperature (T0MC = −60 °C). At the same yield strength interval, 50 MPa, the lower yield strength corresponds to a slightly larger temperature drop. It has been proved that it is reasonable and conservative to determine the MDMT by linear interpolation for steel beyond the range of yield strength in this paper. (4) SA508-3 and Q345R are used to illustrate the applicability of this MDMT curves for ferritic steel. The temperature difference between MDMT curves and curves of SA508-3 and Q345R are about 5 °C and 4 °C respectively. So the minimum design metal temperature of steel can be precisely and conservatively determined by the MDMT curves presented in this paper. References [1] Cao YP. Predication of Fracture Toughness in the Ductile-To-Brittle Transition Region of Pressure Vessel Steels PhD thesis East China University of Science and Technology; 2011 [2] ASME Code. Section VIII-2. Rules for construction of pressure vessels (alternative rules), New York; 2015. [3] Farr JR, Jawad MH. Guide Book for the Design of ASME Section VIII Pressure Vessels. New York: ASME; 2001. p. 15–20. [4] Selz A. New Toughness Rules in Section VIII, Division 1 of the ASME Boiler and Pressure Code. New York: ASME; 1988. [5] Hall A. The Effect of Welding Speed on the Properties of ASME SA516 Grade 70 Steel. University of Saskatchewan; 2010. [6] Yun-Liang LI, Zhang HQ, Ying HU. Microstructure and mechanical properties of nuclear pressure vessel steel SA533B heavy plate. T Mater Heat Treat 2012;33(8):84–8. [7] Cai PX. Effect of Welding Procedure on the Microstructure and Properties of Welded Joint of Cryogenic Steel SA516Gr.60. Hohai University 2006. [8] Wallin K. The scatter in KIc results. Eng Fract Mech 1984;19:1085–93. [9] Wallin K. The master curve method: a new concept for brittle fracture. Int J Min Met Mater 1999;14:342–54. [10] ASTM E1921-11. Standard test method for determination of reference temperature, T0, for ferritic steels in the transition range, West Conshohocken, PA; 2011. [11] Merkle JG, Wallin K, McCabe DE. Technical basis for an ASTM standard on determining the reference temperature, T0, for ferritic steels in the transition range. NUREG/CR-5504; 1998. [12] Wallin K. Validity of small specimen fracture toughness estimates neglecting constraint corrections. ASTM STP 1995;1244:519–37. [13] Chen Z, Pan JH, Jin T. Estimation of fracture toughness of 16MnDR steel using Master Curve method and Charpy V-notch impact energy. Theor Appl Fract Mec 2018;96:443–51. [14] Cui QF, Hui H, Li PN. Brittle fracture prevention model for pressure vessels based on Master Curve approach. J Press Vess Technol 2017;139(1):11–405. [15] Osage DA, Prager M. Technical basis of material toughness requirements in the ASME boiler and pressure vessel code, section VIII, division 2. ASME J Press Vess Technol 2012;134(3):1–31. [16] Sandstrom R, Langenberg P, Sieurin H. Analysis of the brittle fracture avoidance model for pressure vessels in european standard. Int J Press Vess Pip 2005;82(11):872–81. [17] Cui QF, Hui H, Li PN. Applicability of the ASME exemption curve for Chinese pressure vessel steel Q345R. ASME J Press Vess Technol 2015;137:61–602. [18] Anderson TL. Fracture mechanics: fundamentals and applications Surjya Kumar Maiti. Mrs Bull 2016;41(8):635–6. [19] Newman JC, Raju IS. An empirical stress-intensity factor equation for the surface crack. Engng Fract Mech 1981;15(1–2):185–92. [20] Osage DA. API 579: a comprehensive fitness-for-service standard. Int J Press Vess Piping 2000;77(14):953–63. [21] Abson DJ, Tkach Y, Hadely I, Burdekin FM. Accessing toughness levels for steels to determine the need for PWHT. Weld J 2006;85:29–35. [22] Abson DJ, Tkach Y, Hadely I, Burdekin FM. A review of post weld heat treatment code exemptions. Weld J 2006;85:63–9. [23] Oldfield W, Server WL, Wullaert RA, Stahlkopf KE. Development of a statistical lower bound fracture toughness curve. Int J Press Vess Pip 1978;6(3):203–22.
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