Engineering Fracture Mechanics xxx (xxxx) xxxx
Contents lists available at ScienceDirect
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: huihu@ecust.edu.cn (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
Engineering Fracture Mechanics xxx (xxxx) xxxx
Z. Zhou, et al.
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.
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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.
25 1/4
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.
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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
Engineering Fracture Mechanics xxx (xxxx) xxxx
Z. Zhou, et al.
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.
σmP =
2·σys
σmSR =
2·σys
σmSR =
7·σys
(5)
3
3
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
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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.
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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.
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