Basicity Index Type Equations - I
Mrajek ' s Index =
Vee Ratio =
B=
% O from Metal Oxide
% O from SiO2
% CaO
% SiO2
− Mrazek ,1869
− Blum ,1901
% CaO + 1.4% MgO
% SiO2 + 0.84% P2 O5
B. I . =
B = ( % CaO + % MgO + % MnO ) − (% SiO2 + % P2 O5 + % TiO2 )
B LF =
% CaO
% SiO2 + % Al2 O3
B LF =
% CaO + 1.4% MgO
% SiO2 + 0.6% Al2 O3
B=
B=
CaF2 + CaO + MgO + BaO + SrO + Na 2 O + K 2 O + Li2 O +
SiO2 +
1
2
( Al O
2
3
+ TiO2 + ZrO2 )
CaO + MgO + BaO + SrO + Na 2 O + K 2 O + Li2 O +
SiO2 +
1
2
( Al O
2
3
1
+ TiO2 + ZrO2 )
1
2
2
( MnO + FeO )
( MnO + FeO )
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Sum of Basic Oxides
Sum of Acidic Oxides
Tuliani’s
Tuliani’sFormula,
Formula,1978
1978
Basicity Index Type Equations - II
Optical Basicity =
O. B. =
1971
1971--Duffy
Duffyand
andIngram
Ingram
Electron Donor Power of Oxygen in Oxide Systems
Electron Donor Power of Free Oxide Anions
Z A RA
AllCations 2GA
∑
ZA = Coordination Number of Cation A
# Molesof Cation A
RA =
# Molesof Oxygen Atoms
GA = Basicity Moderating Parameter dependingon Pauling' s Electronegativity
IonicFractionof Free AnionsO−2 intheDissociated Slag
BZ =
Sumof All Anionsand Cationsof theSystem
Zeke,
Zeke,1980
1980
BZ =
∑2m
Me2O
∑m
+ ∑m
(
)
Me2O
+ ∑ mMeO − mAl2O3 + 2mSiO2 + 2mTiO2
MeO
+ 3 mCaF2 + mBaF2 + mSiO2 + mTiO2 + 2mAl2O3 + nO−2
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(
)
( )
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High and Medium Strength Steels
Subjected to Welding Heat Cycle
Comparison between High and Low Heat Inputs
(Svensson, 95)
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Heat
Affected
Zone
Properties
(Düren, Korkhaus, and Niederhoff, 3R International, 87)
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Typical Problems observed in High
Strength Steel Welding
(Rowe
(Rowe and
and Liu,
Liu, 99)
99)
Metallurgical Origin:
HAZ Cracking
WM Microfissuring
HAC Cracking
(Rowe and Liu, 99)
Processing Origin:
Porosity at Long Arc or Improper Start
Slag Inclusions at Low Current
Variable Current at Different Positions
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Steel Weldability Map: Cracking
Concerns
(ASM, Welding Handbook V. 6, 93)
EH-36
HSLA-65
HY-80/100
HSLA-80/100
(Graville, 76)
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Steel Weldability Indices - Carbon
Equivalent Type Expressions
IIW
Mn + Si * Cr + Mo + V Ni + Cu
+
+
CE = C +
6
5
15
Winterton
Mn Cu Cr Ni Mo V
CE = C +
+
+
+
−
−
6
40 10 20 50 10
Cottrell
Mn Cr + Mo V Nb 0.0001
CE = C +
+
+ +
+
6
5
3 4C
S
* Omitted in the original Dearden & O’Neill formula
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Steel Weldability Indices - Carbon
Equivalent Type Expressions
DnV
D
Si Mn Ni + Cu Cr Mo V
CE = C +
+
+
+
+
+
24 10
40
5
4 14
Si Mn + Cu Cr Ni + Mo V
CE = C + +
+
+
+
25
16
20
20
15
PCM
PCM
CEN
Si Mn + Cu + Cr Mo V Ni
=C+
+
+
+ +
+ 5B
30
20
15 10 60
⎡ Si Mn Cu Ni Cr + Mo + Nb + V
⎤
CEN = C + A ( C ) ⋅ ⎢ +
+
+
+
+ 5B ⎥
6
15 20
5
⎣ 24
⎦
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Steel Weldability Indices – Fundamental
Approaches
Thermodynamic Approach
⎡C + KMnMn + KSi Si + … + KC' CLnC ⎤
CE = K o ⎢ '
⎥
'
⎢⎣ +KMnMnLnMn + KSi SiLnSi + … ⎥⎦
Kinetics Approach
′ Mn + KSi′ Si + …]
CE = K o′C [1 + KC′ C + KMn
Partitioning Approach
′′ Mn + KSi′′ Si + … + K LC
′′ LnC
⎡1 + KC′′C + KMn
⎤
CE = Ko′′C ⎢
⎥
′′
′′
′′
+
+
+
+
K
CLnC
K
MnLnMn
K
SiLnSi
…
LMn
LSi
⎣ LC
⎦
(Liu et al., 1986)
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Steel Weldability Indices - Carbon
Equivalent Type Expressions
Yurioka
H Max = 442C + 99CE II + 206 + ( 402C − 90CE II +80 ) ⋅ arctan ( x )
x ( rad ) =
log t8 / 5 − 2.3CE I − 1.35CE III + 0.882
1.15CE I − 0.673CE III − 0.601
Si Mn Cu Ni Cr Mo
+
+
+
+
+
+ ∆H
24
6
15 12 8
4
Si Mn + Cr + V Cu Ni Mo Nb
CE II = C +
+
+
+
+
+
24
5
10 18 2.5
3
Mn Cu Ni Cr Mo
+
CE III = C +
+
+
+
3.6 20 9
5
4
CE I = C +
∆H = f ( B , N )
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For fully martensite microstructure:
HVM = 884C (1 − 0.3C 2 ) + 294
Steel Weldability Indices ∆t8/5 Calculation
Rosenthal Solution (1946)
∆t8/5 is directly related to the heat input (H)
⎛ ηH ⎞
∆t8 5 = 8.149 x10 −4 ⎜
⎟
2
πκ
⎝
⎠
η = Efficiency
H = Heat input
∆t 8 5
⎛ ηH
⎞
= 2.767 x10 ⎜ 2
⎜ 4h πκρ C ⎟⎟
p ⎠
⎝
−6
2
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κ = Thermal conductivity
ρ = Specific gravity
Cp = Specific Heat
Steel Weldability Indices - Carbon
Equivalent Type Expressions
Lorenz & Düren
H = 2019 ⎡⎣(1 − 0.5log t8 / 5 ) ⋅ C + 0.3 ( CE − C ) ⎤⎦ + 66 (1 − 0.8log t8 / 5 )
Mn Si Cr Mo V Ni Cu
+ +
+
+ +
+
8 11 5
6
3 17 9
Mn + Cu Si Cr + V Mo Ni
CE * = C +
+ +
+
+
16
25
10
15 40
CE = C +
* For pipeline grade steels
Düren – For 100% Microstructure (M or B) in HAZ
HVM = 802C + 305
Mn Si Cr Mo V Ni Cu ⎞
⎛
+ +
+
+ +
+
HVB = 350 ⎜ C +
⎟ + 101
8 11 5
6
3 17 9 ⎠
⎝
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WELD STRENGTH MODEL
RP0.2 ( MPa ) = 3.1H Max ( 0.1) − 80
n
n = 0.065 ( t8 / 5 )
Akelsen, Rørvik, Onsøien, and Grong
0.17
Blackburn et al. (1997)
YS = 232 + 1.9t − 0.26T50 − 0.09GS
⎛ dT ⎞
UTS = 313 − 8.3ln ⎜ 1.8
⎟ + 3.8t − 0.36T50 − 0.08GS
dt ⎠
⎝
YS = 0.2 % offset yield strength, ksi
t
= thickness, cm
T50 = 50 % transformation temperature, oC
GS = austenite grain size
UTS = ultimate tensile strength, ksi
dT = calculated cooling rate, oC/s
dt
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Application: Steel Weldability Index
Weld
Metal
Base
Metal
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Heat Affected
Zone Properties
Empirical
Relationships
(Svensson, 95)
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Weld Metal
Properties
Empirical
Relationships
(Svensson, 95)
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Possibilities of Crack-Free
X-100 Steel Welds
250
6 mm Cylindrical Specimens
with spiral notch
Heat Input: 8-9 kJ/cm
Thickness of Backing Plate:
20 mm
Critical implant
Stress/Yield Strength:
100%
[H]Dif ≥ 40 cm3/100g
TM Steels up to X-100
No Cracking
o
Preheating Temperature ( C)
200
150
Risk of Cracking
100
50
(According to Implant Test Results
using Cellulosic Electrodes)
0
0.15
0.20
0.25
0.30
0.35
0.40
0.45
Carbon Equivalent (%)
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0.50
(Hillenbrand, Niederhoff, Hauck,
Pertender, Wellnitz, 1997)
Hydrogen Embrittlement Susceptibility:
Martensite Start Temperature - Ms
∆ Martensite Start Temperature - ∆Ms
Andrew – Linear (1965)
Ms = 539 – 423C – 30.4Mn – 17.7 Ni – 12.1Cr – 7.5Mo
Self et al. (1986) – Wrought Metal:
Ms = 521 – 350C – 14.3Cr – 17.5Ni –28.9Mn – 37.6Si – 29.5Mo
– 1.19Cr.Ni + 23.1(Cr+Mo)C
Self et al. (1986) – Weld Metal:
Ms = 521 – 350C – 13.6 Cr – 16.6Ni – 25.1Mn – 30.1Si – 40.4Mo
– 40 Al – 1.07Cr.Ni + 21.9(Cr+0.73Mo)C
∆Ms = MsWM - MsHAZ
Other Ms Equations include Payson & Savage (1944), Carapella (1944),
Rowland & Lyle (1946), Grange & Stewart (1946), Nehrenberg (1946),
Steven & Haynes (1956), and Others.
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Cracking-No Cracking Map
for High Strength Steel Welds
(Rowe and Liu, 99)
(Wang and Liu, 97)
(Olson, Wang, Liu et al, 96)
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Weld Undermatching and Overmatching:
Non-Uniform Hydrogen Distribution
0.4
1/2
∆H (HWM - HHAZ) (ml/100g metal.atm )
0.5
0.3
(Wang and Liu, 97)
Overmatched
Overmatched
Weld
Weld Metal
Metal
0.2
0.1
Microfissuring
Transverse Cracking
Evenmatched
Evenmatched
Weld
Weld Metal
Metal
0.0
-0.1
HAZ
Cracking
-0.2
-0.3
Undermatched
Undermatched
Weld
Weld Metal
Metal
-0.4
-0.5
-60
-40
-20
0
20
o
∆Ms (MsWM - MsHAZ) ( C)
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40
60