Nishimoto.ppt

Recent Topics of Welding Metallurgy
Relating to Hot Cracking
and Embrittlement in Iron and
Nickel-base Alloys
Lab. Material Joining Process
Kazutoshi Nishimoto
Department of Manufacturing Science
Graduate School of Engineering
Osaka University
Osaka University

Contents
1. Background
2. Prediction of Degree of Embrittlement
■475 ℃ Embrittlement
■Sigma Phase Embrittlement
3. Mechanism of Weld Cracking
■Solidification Cracking in Laser Welding
■Ductility-dip Cracking
4. Summary
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Prevalent problems in welds of iron-base and nickel-
base alloys
Hot cracking
Cold cracking
σ phase
embrittlement
Embrittlement by grain
coarsened
・475℃ embrittlement
Nieq＝%Ni＋30×%C＋0.5×%Mn
Creq＝%Cr＋%Mo＋0.5×%Si＋0.5×%Nb
δferrite content
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The use of
new alloys or new
welding processes
Need for researches to
understand their
response to these
problems.
■ New welding processes such as laser welding may cause changes in a susceptibility to weld
cracking that requires further investigation.
■ Invar alloy which has recently become widely used in cryogenic plants, is found sensitive to hot
cracking, but its mechanism is not clarified yet.⇒

Prevalent problems in welds of iron-base and nickel-
base alloys
Hot cracking
Cold cracking
σ phase
embrittlement
Embrittlement by grain
coarsened
・475℃ embrittlement
Nieq＝%Ni＋30×%C＋0.5×%Mn
Creq＝%Cr＋%Mo＋0.5×%Si＋0.5×%Nb
δferrite content
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The use of
new alloys or new
welding processes
Need for researches to
understand their
response to these
problems.
■ Embrittlement is also a serious problem in weldments of especially ferritic or duplex stainless
steels.
■ Although many investigations have been conducted into the material behavior producing
embrittlement, rather few of these are useful for predicting the degree of embrittlement of the alloys
during welding and/or in post-heat treatment. ⇒

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Spinodal Phase Decomposition in Chromium
Containing Iron base Alloys
Cα’’
Cα’
C 0
C
Cα’’
Cα’
C 0
Nucleation and growth
Spinodal decomposition
Initial Middle Final
■ When ferritic or duplex
stainless steels containing
more than about 20 % Cr are
exposed to temperatures of
673-823K, they may suffer
from "475 ℃
embrittlement", which
somewhat limits the
operating temperatures of
their applications.
(a)
(b)
G
G
0 1
Cα
Cα’ Cα’’
α
α’+α’’
Spinodal
decomposition
2
G
C2  0
(a) Free energy curve
(b) Phase diagram and Spinodal curve

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Theoretical Analysis of Spinodal Decomposition during
iso-thermal Process

cCr
t
=
 D cCr
x
x
– 2
 K 
3
cCr
x3
x
Cahn-Hilliard's non-linear
diffusion equation
Fourier expression of
diffusion equation

Q(h)
t
= – h
2
{ D0 + 2h2
2
K0 Q(h) + 1
2
D1 R(h)
+ 1
3
D2S(h) + 1
4
D3T(h) +  }
– 2h4
{K1U(h) + K2V(h) + K3W(h) +  }
■ The Cahn-Hilliard non-linear
diffusion equation is one of the most
useful approaches to spinodal phase
decomposition.
■ Recently, Miyazaki proposed a
general formula with a Fourier
expression of this non-linear diffusion
equation. However, these approaches
are meant to be used, for isothermal
heat-treatment, and cannot be directly
applied these to a phenomenon during
the welding process.

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The Method of Analysis for Spinodal Decomposition
in thermal cycle process

cCr
t
=
 D cCr
x
x
– 2
 K 
3
cCr
x3
x
Cahn-Hilliard's non-linear
diffusion equation (extended)
Interdiffusion coefficient
Gradient energy coefficient

D= M(Cr) 2
G
cCr
2 =M0cFecCr
2
G
cCr
2

K= 0 M(cCr) [(cCr,T) + {(cCr,T) /cCr}cCr]
Input of parameters
, cCr, thermal cycle
Input of initial composition-waveQ0(h)
Replacement of Fourier
waves for convolution
Fourier transformation FFT
Rf = QfQf, Sf = RfQf, Tf = SfQf
Uf = k3QfQf, Vf = UfQf, Wf = VfQf
Inverse Fourier transformation IFFT
Calculation of ŽQ(h)/Žt
Q(h)t+t = Q(h)t + {ŽQ(h)/Žt}tt
Output of Q(h) & graphing
Display?
YES
NO
Calculation of temp. &
material constants
Completion of
thermal cycle?
NO
End
YES
t = t + t
■ Developed the method of analysis for the decomposition in
thermal cycle process by extending the Cahn-Hilliard non-
linear diffusion equation to this processes and applied it to a
computer simulation of phase decomposition for 30Cr-2Mo
steel.⇒

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Two dimensional
Evolution the Cr-rich
phase induced by
Spinodal Decomposition
in 30Cr-2Mo steel

cCr
t
=
 D cCr
x
x
– 2
 K 
3
cCr
x3
x
■ In the early stage of
decomposition ,until the 2nd cycle,
composition variations develop
monotonically with time; however, they
periodically fluctuate until the spinodal
decomposition has further progressed.
■ On the basis of thus calculated results,
we tried to predict the degree of
embrittlement due to the spinodal
decomposition.

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Theoretical approach for prediction of 475°C
embrittlement in 30Cr-2Mo steel
Cut-through model
(Mott-Nabarro's equation)
Hv : Hardness increment, R : Radius of precipitates,
K : Constant, V : Volume fraction of precipitates,
m : Stiffness, N : Numbers of dislocation,
e : Misfit between matrix and precipitates
HV 
mV 4 /3
N1/6
e3/2
10
ln
1
V










3/2
 KR1/2
V 4 /3
ln
1
V










3/2
vTE  KR1/ 2
V 4 /3
ln
1
V










3 /2
Relationship between ΔHv and ΔvTE
■ The change in hardness ΔHv due to the phase decomposition well agree with the value of
R1/2V4/3{ln(1/V)}3/2 which is a hardenability parameter derived from Mott-Nabarro
precipitation hardening theory.
■ This fact suggests that hardening in this case follows the theory proposed by Mott-Nabarro.

Osaka University
Theoretical approach for prediction of 475°C
embrittlement in 30Cr-2Mo steel
Cut-through model
(Mott-Nabarro's equation)
Hv : Hardness increment, R : Radius of precipitates,
K : Constant, V : Volume fraction of precipitates,
m : Stiffness, N : Numbers of dislocation,
e : Misfit between matrix and precipitates
HV 
mV 4 /3
N1/6
e3/2
10
ln
1
V










3/2
 KR1/2
V 4 /3
ln
1
V










3/2
vTE  KR1/ 2
V 4 /3
ln
1
V










3 /2
Relationship between ΔHv and ΔvTE
Relationship between R1/2V 4/3{ln(1/V)}3/2 and ΔvTE
■ On the other hand, experimentally
determined the functional relationship
between the change in the transition
temperature of the Charpy impact
energy ΔvTE, and that in the Vickers
hardness ΔHv.⇒

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Example of the Calculated value of ΔvTE in the triple
pass GTA weldment of 30Cr-2Mo steel
■ The high value ofΔvTE due to the 475℃
embrittlement can be clearly recognized in
the HAZ near the bottom of the plate on
the 2nd/3rd pass welding, and it becomes
dominant as the weld pass progresses.
■ It can be also seen that the severely
embrittled zone corresponds to the a
position that has undergone triple heatings
to about 800K.⇒
1st
pass
welding
2nd
pass
welding
3rd
pass
welding

Embrittlement due to sigma phase Precipitation
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■ Sigma phase precipitation, which
degrades not only mechanical
properties but also corrosion
resistance in alloys, is well known, but
still a serious problem in stainless
steel weldments. ⇒
Temperature
(℃)
Temperature
(℉)
WT.%Cr
NCr
800
700
600
500
400
0 0.2 0.4 0.6 0.8 1.0
700
800
900
1000
1100
1200
1300
1400
1500
100
80
60
40
20
0
α α’
σ
α+σ σ+α’
α+α’
X X XX
X X XX
X X XX
Phase diagram of Iron-Chromium Alloy

Microstructures of super duplex stainless steels
(heated at 1073 K for 1.8 ks)
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NAS64 SAF2507 DP3W
α
γ
α
γ
α
γ
■ The microstructures of the super duplex stainless steels heated at 1073 K for 1.8ksec,
which demonstrate sigma phase precipitation.
■ Sigma phase precipitated mainly at delta/gamma boundaries in these steels.

Sigma phase precipitation Curves in super
duplex stainless steels
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■ Sigma phase precipitation phenomenon follows the Johnson-Mehl type of kinetic equation in
the case of weld metals of austenitic stainless steels.⇒
NAS64 SAF2507 DP3W
Aging time (s)
50
45
40
35
30
25
20
15
10
5
0
101 102 103 104 102 103 104 103 104 105
Aging time (s) Aging time (s)
Area
fraction
of
σ
phase
(%)
Aging temperature
1073K
1123K
1173K
1223K

Kinetics of Sigma Phase Precipitation
---Johnson-Mehl equation---
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y = 1 – exp (– k tn
) log ln
1
1 – y
= n log t + log k
■ A good linear relationship is found between the aging time and the fraction precipitated, which
indicates that the sigma phase precipitation in duplex stainless steels also follows the Johnson-
Mehl type kinetic equation. ⇒
NAS64 SAF2507 DP3W
Aging time (s)
1.0
101 102 103 104
Logln1/(1-y)
0.5
0
-0.5
-1.0
-1.5
1.0
0.5
0
-0.5
-1.0
-1.5
-2.0
-2.5
1.0
0.5
0
-0.5
-1.0
-1.5
-2.0
101 102 103 104 102 103 104 105
Aging time (s) Aging time (s)
NAS64 base metal
n=1.32
SAF2507 base metal DP3W base metal
n=1.62 n=0.879
Aging temperature
1073K
1123K
1173K
1223K

Prediction of the Amount of Sigma Phase during
thermal cycle process by additivity rule
Osaka University
T1
T2
T3
Δt1 Δt2 Δt3
time
Δt1 Δt2 Δt3
T1
T2
T3
time
F = fmax(1){1-exp(k(1)Δt n)}
+ fmax (2){1-exp(k(2)Δt n)}
+ fmax (3){1-exp(k(3)Δt n)}
+・・・
F：Saturated volume of precipitation
f(t) = fmax(t){1-exp(k(t)Δt n)}
Additivity
rule
■ Applying the
additivity rule and
assuming that the
saturated volume
fraction of the sigma
phase and the rate
constant k vary with
temperature, we can
calculate the amount of
sigma phase
precipitated during an
arbitrary thermal cycle
with this equation.
F  fdt fsat 1 exp ktn
 
 

 dt
k  k0 exp Q RT
 
Based on the isothermal
kinetics of the sigma phase
precipitation

The amount of sigma phase precipitated in SAF2507
during two types of synthetic thermal cycles
Osaka University
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
Area
fraction
of
σphase
(%)
Number of thermal cycles
SAF2507 base metal
●,▲: Measured
Pattern A
Pattern B
Pattern A Pattern B
■ The calculated curves agree fairly
well with the measured results in both
of the thermal cycles.
■ This correspondence suggests that
sigma phase precipitation in duplex
stainless steels during the thermal
cycle process can be predicted by
this computation.

Relationship between the amount of sigma phase and
the Charpy impact energy of duplex stainless steels
aged at 1173K
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■ In each steel, the Charpy
impact energy decreases
drastically with increases in the
amount of sigma phase.⇒
0 2 4 6 8 10 12 14 16
10
0
20
30
40
50
60
70
80
Area fraction of σ phase(%)
Impact
absorbed
energy
(J)
Aging temperature : 1173K
NAS64
SAF2507
DP3W

Calculated amounts of the sigma phase and degree of
embrittlement due to sigma phase precipitation
Osaka University
(a) Area fraction of sigma phase in multipass weldment
(b) Decrement in impact absorbed energy in multipass weldment
■ The most embrittled zone locates in HAZ parallel to the weld interface and the level of the
Charpy impact energy in this region is reduced by at most 17J from that of the unaged base
metal.⇒
(Under the assumption)
(Under the assumption)

Reasons for this enhancement of hot cracking
susceptibility in laser welds
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However, hot cracking susceptibility may be enhanced in some cases of the laser
welding of stainless steels and nickel base alloys.
Generally speaking, decreasing the welding heat input is one of the most
effective countermeasures for preventing hot cracking.
From this reason, laser welding is a preferable safeguard against this
problem, because it can provide a lower welding heat input.
■ Due to a characteristic shape of penetration in laser welds ; 'the key
hole type of penetration.
■ Due to the rapid solidification and cooling that takes place during
welding with an extremely low heat input.
There are two reasons for this enhancement:

Types and positions of hot cracking in laser welds
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Center-line crack
Solidification
crack at neck
Inter-granular
crack at well
Hole by
shrinking during
solidification at
bead center
Liquation crack
at neck in HAZ
■ In the case of the key hole type of penetration of
laser welds, various types of cracking may be
experienced.
■ These types of cracking is caused by the strain
concentration at the specific part in the welds or in
HAZ ⇒
due to a characteristic shape of
penetration in laser welds.
Ｈot cracking susceptibility may be enhanced
in laser welding

Mechanism of
solidification cracking
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Temperature
Strain
TL TS
(No cracking)
(Cracking)
Solidification
brittleness
temperature
range (BTR) Local strain
溶接金属
Crack
Weld metal
■ In general, solidification
cracking will develop under the
condition that the thermal strain
subjected to the welds exceeds
more than the critical value that
it can bear. That is,
solidification cracking will occur
when the strain curve during
cooling intersect with the
solidification brittleness
temperature range ; BTR
■ In laser welding with a low
heat input, the strain rate during
cooling will increase, and
consequently may enhance the
hot cracking susceptibility.
due to the rapid solidification and
cooling during welding .
Ｈot cracking susceptibility may be enhanced
in laser welding
(the second reason)

Relationship between laser traveling velocity and total
crack length in laser welds (SUS316L (P+S:0.04%))
Osaka University
60μm
60μm
■ Evidently, an increase in the laser traveling velocity produces a greater susceptibility to hot
cracking in laser welds.
■ In addition, note that as the laser traveling velocity rises, the location where hot cracks occur
changes from the dendrite boundaries to the center line of the welds.

Two major factors to influence hot cracking
susceptibility in laser welds
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Temperature
Strain
TL
TS
(No cracking)
(Cracking )
Theoretical analyses
of the liquidus and
solidus temperatures
during laser welding
Thermal
elastic-
plastic
analysis
BTR
Local strain
■ The BTR in laser welds will vary because of changes in the liquidus and solidus temperatures due
to the rapid solidification.
■ The strain rate in laser welds will also enhance due to rapid cooling.

Estimation of BTR in laser surface melted region
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Ts’
BTR
Temperature
Strain(%)
TL Ts
BTR
TL
Strain(%)
Ts
Temperature
TL’
BTR
Strain(%)
TL’ Ts’
Temperature
Arc welding Laser welding
Effect of rapid
solidification
TL decreases due to supercooling Ts varied by micro-segregation of
impurity elements
■ Determined the BTR in laser welds by theoretical analyses of the liquidus and solidus temperatures
based on the BTR for GTA welding obtained by the Varestraint test.

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Ts’
BTR
Temperature
Strain(%)
TL Ts
BTR
TL
Strain(%)
Ts
Temperature
TL’
BTR
Strain(%)
TL’ Ts’
Temperature
Effect of rapid
solidification
impurity elements
modified KGT model
■ In order to estimate the liqudus temperature, we calculated the dendrite tip temperature (T*), which
corresponds to the liquidus temperature through calculation by the modified KGT model.

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Ts’
BTR
Temperature
Strain(%)
TL Ts
BTR
TL
Strain(%)
Ts
Temperature
TL’
BTR
Strain(%)
TL’ Ts’
Temperature
Effect of rapid
solidification
impurity elements

Ji = D
Ci +1 – Ci
x
C j
S
 knesCj1
L
Thermo-Calc@
■ To determine the solidus temperature, we have
conducted a theoretical analysis on the effect of the
micro-segregation of impurity elements during welding
on the solidus temperature by using the data-base of
Thermo-calc.

Theoretical model for calculation for impurity elements
segregation in solidification process
Osaka University
L
S
Cj
S
 knes
Cj1
L
knes 
kes  
1 
  Rv
x
2DS
Ci 
2Dst
x2
2i1
 
i Ci1
B
 Ci
B
  i1
 Ci
B
 Ci1
B
 
 
Distribution of S
at liquid/solid boundary
Non-equilibrium
coefficient Knes
Diffusion in solid
kes：Equilibrium coefficient， Rv：Solidification speed，
Ds：Diffusion coefficient
12
i-1
N-1
N
i
i+1
S L
L
S
S ol
i
di
f
i
cat
i
on
S
concent
rat
i
on

Ji = D
Ci +1 – Ci
x
Cs
■ In this analysis,assumed the morphology of a dendrite to be a hexagonal column and evaluated
distribution of the solute concentration with a one-dimensional diffusion model in which the solute
diffused in the direction perpendicular to the grain boundary⇒

BTR calculated in laser welds of SUS316L
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P : 0.02% P : 0.03%
1680 1640 1600 1560 1520
Temperature (K)
1.0
0.8
0.6
0.4
0.2
0
Strain
(%)
LTV (mm/s)
20
40
60
1680 1640 1600 1560 1520
Temperature (K)
1.0
0.8
0.6
0.4
0.2
0
Strain
(%)
LTV (mm/s)
20
40
60
■ The solidus temperature in the laser welds is found enhanced with a rise in the laser traveling
velocity due to the increase in the solidification rate.
■ On the other hand, the liqudus temperature in the laser welds decrease due to supercooling in
laser welds⇒

Direction of the the strain analyzed at the surface
of the welds
Osaka University
Analysis point and direction
Calculated by Quick Therm
θ=60
°
θ=35°
θ =50°
Laser traveling velocity : Increase
■ The thermal strain is another important factor to consider the occurrence of cracking in welds
■ Used the 3-dimensional thermal elastic-plastic software package "Quick Therm" to calculate the
strain formed during welding in laser welds and analysed the strain which is perpendicular not only to
the center line of the weld but also dendrite boundaries.
20mm/s 40mm/s 60mm/s

Local strain at the center perpendicular to laser
scanning direction
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LTV : Laser traveling velocity (mm/s)
Center-line
1.2
1.0
0.8
0.6
0.4
0.2
0
1650 1600 1550
Temperature (K)
Strain
(%)
LTV=60
LTV=40
LTV=20
1.2
Dendrite boundary
1.0
0.8
0.6
0.4
0.2
0
1650 1600 1550
Temperature (K)
Strain
(%)
LTV=60
LTV=40
LTV=20
■ Examples of calculation which show that the change in the thermal strain
occurring during solidification increases with increasing laser traveling velocities.
■ In contrast, in the case of dendrite boundaries, the strain taking place with a
laser traveling velocity of 40mm/s is larger than that under other conditions.⇒
(θ=35°)
(θ=50°)
(θ=60°)
θ

Comparison between BTR and strain at the bead center
perpendicular to laser traveling direction
Osaka University
0.02％ P+S
0.04％ P+S
0
Strain
(%)
1.2
1
0.8
0.6
0.4
0.2
Temperature (K)
LTV = 20 mm/s LTV = 40 mm/s LTV = 60 mm/s
LTV : Laser traveling velocity
1650 1550
1600 1650 1550
1600 1650 1550
1600
■ Examine the possibility of solidification cracking in laser welds by superimposing plots of the
BTR and the strain produced during cooling in laser welds.
■When the laser traveling velocity is 40 or 60mm/s, the strain perpendicular to the center line of
the welds crosses to the BTR, which means that solidification cracks will occur at the center of
the welds in this laser traveling velocity range.
Cracking
Cracking
SUS316L

Comparison between BTR and strain perpendicular to
dendrite growth direction at dendrite boundaries
Osaka University
0.02％ P+S
0.04％ P+S
0
Strain
(%)
1.2
1
0.8
0.6
0.4
0.2
Temperature (K)
LTV = 20 mm/s LTV = 40 mm/s LTV = 60 mm/s
LTV : Laser traveling velocity
1650 1550
1600 1650 1550
1600
Cracking
1650 1550
1600
■ The strain curve estimated for dendrite boundaries crosses the BTR when the laser traveling
velocity equals 40mm/s.
■ This result suggests that solidification cracks will occur at the dendrite boundaries in the welds
in this laser traveling velocity range.⇒
SUS316
L

Comparison between measured and theoretically
calculated conditions to occur cracking
Osaka University
Laser traveling velocity (mm/s)
P+S
content
(mass％)
10 40 50 60
30
20
0.02
0.03
0.04
Center-line cracking (Calculated)
Cracking at dendrite boundary (Calculated)
Crack
（Center-line）
Crack
(Dendrite
boundary)
No crack
■ Good agreement between these two conditions determined by calculation and experimentals.
■ These results suggest that the cause of solidification cracking in laser welds is actually the increase
in the strain rate during solidification, in spite of the fact that the BTR becomes narrower due to rapid
solidification.
SUS316L

Enhanced susceptibility due to solidification mode shift
Osaka University
J.C.Lippold, Weld. J., 73-6 (1994) 129s-139s
■ There is another factor to be considered which may influence hot cracking susceptibility in
austenitic stainless steels in laser welding.
■ It is known that the solidification mode in austenitic stainless steel weld metals shifts from
primarily ferrite to primarily austenite when the solidification rate becomes sufficiently high.
1.8
1000
100
10
1
0.1
1.5 2.0
Creq/Nieq
Solidification
rate
(mm/s)
Austenite
(A)
Ferrite
(F)
F/MA
FA
AF
Arc welding YAG welding
0.1
0.05
0
1.4 1.6
Cr/Ni-equivalent
S+P+B
(mass%)
Crack No crack

Enhanced susceptibility due to solidification mode shift
Osaka University
J.C.Lippold, Weld. J., 73-6 (1994) 129s-139s
■ Laser welding with a low heat input can provide in some cases such solidification condition
to cause solidification mode shift.
■ Alloys solidified in primarily austenite mode is more sensitive than ones in primarily ferrite
mode.
■ This is another reason for the increased hot cracking susceptibility of stainless steels in
laser welding. ⇒
1.8
1000
100
10
1
0.1
1.5 2.0
Creq/Nieq
Solidification
rate
(mm/s)
Austenite
(A)
Ferrite
(F)
F/MA
FA
AF
Arc welding YAG welding
0.1
0.05
0
1.4 1.6
Cr/Ni-equivalent
S+P+B
(mass%)
Crack No crack

Condition for transition of solidification mode
Osaka University
In the case of T*
γ>T*
δ
In the case of T*
δ>T*
γ

T *
= TL + (mv ,iCi
*
– m0.iC0,i)

– 2 / R – V/ m – GD / V
FA mode AF mode
■ In general, the phase which has the higher dendrite tip temperature is more likely to be the
primary phase on solidification. Therefore the solidification mode shift can be predicted if the
dendrite tip temperature of each phase is known.

Theoretical model for dendrite growth
Osaka University

R = 2 
–
mC0 1 – K cV
D 1 – 1 – K Iv P
– G

T *
= TL + (mv ,iCi
*
– m0.iC0,i)

– 2 / R – V/ m – GD / V
K ：Partition coefficient
R ：Dendrite tip radius
V ：Dendrite growth velocity
ΔT：Undercooling related to the tip radius
G ：Temperature gradient
D ：Liquid interdiffusion coefficient
P ：Peclet number
Iv(P)：Ivantsov's solution
ξc ：Absolute stability coefficient
mv,i：Velocity dependent liquidus slope
Γ：Gibbs-Thomson parameter
S.Fukumoto, W.Kurz, ISIJ Inter., 37-7 (1997) 677-684
S.Fukumoto, W.Kurz, ISIJ Inter., 38-1 (1998) 71-77
(modified KGT model)
Dendrite Tip Temperature：T*
■ Used the modified Kurz-Giovanola-Trivedi (KGT) model, which was extended to multicomponent
alloys by Kurz in order to calculate the dendrite tip temperature.
■ According to the model, the dendrite tip radius, R, is expressed as a function of dendrite growth
velocity, V, as shown in this equation .
■ For multicomponent alloys, the dendrite tip temperature, T*, is given by this equation. ⇒

Effect of dendrite growth velocity on dendrite tip
temperature of ferrite and austenite
Osaka University
1750
1730
1710
1690
1670
1650
1×10-2 1×10-1 1×100 1×101 1×102
Dendrite growth velocity (mm/s)
Dendrite
tip
temperature
(K)
■ The dendrite tip temperature
in austenite rises above that in
ferrite at dendrite growth
velocities exceeding 0.9mm/s.
⇒
23Cr-9Ni-0.34N steel

Comparison of calculated solidification mode change with
experimental results in laser welds of stainless steel
Osaka University
Bead center
AF mode
FA mode
FA
AF
15
10
5
0
1.3 1.4 1.5
Creq/Nieq
Laser
traveling
velocity
(mm/s)
Predicted condition
to yield crack
■ By using the above mentioned
results, you can also predict the risk
of hot cracking by calculation
assuming that the solidification mode
change from FA to AF will enhance
cracking susceptibility.
■ For instance, this figures show
the theoretically predicted transition
line from FA to AF at the center part
of the weld metals for nitrogen
containing austenitic stainless
steels.⇒

Comparison of calculated solidification mode change
with hot cracking susceptibility in laser welds of
stainless steel
Osaka University
Bead center
Crack
No crack
FA
AF
15
10
5
0
1.3 1.4 1.5
Creq/Nieq
Laser
traveling
velocity
(mm/s)
Predicted condition
to yield crack
■ The condition to yield AF mode
coincide with the condition to occur hot
cracking.
■ It means you can predict the risk of
hot cracking through calculation of the
mode shift from FA to AF even in laser
weld. ⇒

Mechanism of ductility-dip crack
Osaka University
Strain
Temperature
BTR DTR
ε1
ε2
ε3
Ductility-dip cracking
■ Ductility-dip cracking can
occur in various alloys which
exhibit a loss of ductility below
the solidus temperature, when
they are subjected to a strain
sufficient to produce cracking
during cooling in welding.
■ A ductility-dip crack formed in
weld metals is normally very small,
and is sometimes called a 'micro
fissuring'. ⇒
Ductility curve

Mechanism of ductility-dip crack
Osaka University
Strain
Temperature
BTR DTR
ε1
ε2
ε3
■ Recently Invar alloy has
attracted special interest as a
suitable material for cryogenic
applications, such as fuel
transport pipes due to its low
thermal expansion coefficient and
good toughness at low
temperatures.
■ Invar alloy is however, found
to be very susceptible to micro
fissuring in multi-pass welds of
heavy sectioned pipes.
But, the mechanism of micro
fissuring in the weld metals of
Invar alloys is still uncertain. ⇒
Ductility curve

Surface of weld metal of Invar alloy after triple bead
longitudinal Varestraint
Osaka University
■ Many cracks in original weld pass
which was reheated by a subsequent
pass. Cracks preferentially occurred
along the columnar grains and/or
around the center line of the original
weld bead.
Fe-36Ni alloy

Effect of weld thermal cycles on cracking susceptibility
Osaka University
Double-bead
Triple-bead
Total
crack
length
(mm)
0
1
2
3
1100〜
1200
1000〜
1100
900〜
1000
900〜
800
Peak temperature range in HAZ (K)
■ The total lengths of the cracks in the triple-bead test were much greater than those in the
double-bead test. We can see that this tendency predominated in the peak temperature range
between 1000K and 1100K.
Fe-36Ni alloy (0.011%S)

Effect of S on susceptibility to ductility-dip cracking
Osaka University
Double-bead Varestraint test
Ductility-dip crack in first bead
Augmented strain 1.6%
2.4%
80
60
40
20
0
0 0.005 0.010 0.015
S content (%)
Total
crack
length
(mm)
■ The total length of the cracks grew as
the sulfur content in the samples
increased.
■ This experimental result demonstrate
that sulfur is evidently detrimental to
cracking susceptibility in the weld metal.
Fe-36Ni alloy

The result of Auger analysis conducted on the fractured
surface in the multi-pass weld metal
Osaka University
Effect of thermal cycles at peak temperature of 1000K on S concentration
Twice：Average 7% ⇨ Three times：Average 9%
AES spectrum
S
C O
Fe
Ni
100 200 300 400 500 600 700 800 900 1000
Kinetic energy (eV)
c/s
-1200
-1000
-800
-600
-400
-200
0
200
400
600
800
■Sulfur is segregated on its surface. Moreover, the amount of sulfur on the grain boundary increase
with increase of welding pass. ⇒
Fe-36Ni alloy

Method of calculation for S segregation at grain
boundary during multi-pass weld thermal cycles
Osaka University
Stage I : Solidification process
Stage II : Cooling process (after solidification)
Melting point
Melting point
■ The concentration of sulfur at the grain boundary was
analyzed for two stages:
■ That is,
Stage I: the solidification segregation during welding,
Stage II: the grain boundary segregation during the cooling
and reheating by the subsequent weld passes.

Osaka University
Cj
S
 knes
Cj1
L
knes 
kes  
1 
  Rv
x
2DS
Distribution of S at liquid/solid boundary
kes：Equilibrium coefficient， Rv：Solidification speed，
Ds：Diffusion coefficient
Stage I : Solidification process
Melting point
Melting point
■ The same model as the one described in the
previous section was adopted for the solidification
segregation during welding. thus, the concentration of
sulfur after completion of solidification was calculated
by this equation.

Osaka University
Cs
gb
(t) Cs
gb
(0)
Cs
gb
() Cs
gb
(0)
 1 exp
4Dst
1
2
d2


 


erfc
2 Dst
1 d






CX 
2DX t
x2
2i1
 
i CX i1
B
 CX i
B
  i1
 CX i
B
 CX i1
B
 
 
Solute concentration change
Boundary condition
Stage II : Cooling process (after solidification)
Melting point
Melting point
C：Concentration of solute, vacancy, complex，
k：constant，Ev：Vacancy forming energy，
Ec：Binding energy between vacancy and solute
■ As for the grain boundary segregation during the cooling and
reheating by subsequent weld passes, we calculated the change
in the sulfur concentration at the grain boundary after
solidification by the these equations based on the equilibrium
segregation theory.

Osaka University
The concentration of S at grain boundaries calculated
for multi-pass weld thermal cycles
■ In the solidification process, the sulfur concentration in the liquid phase rose as the solidification
proceeded.
■ During cooling, the sulfur concentration at the grain boundaries first rapidly fell, and then
increased again with correspondent to the increase of its equilibrium concentration at the grain
boundaries.

Osaka University
The concentration of S at grain boundaries calculated
for multi-pass weld thermal cycles
■ In the reheating process, the grain boundary sulfur concentrations decreased at temperatures above
about 1100 K, due to the reduced equilibrium concentration.
■ However, in the reheating process in which the peak temperature was less than 1000 K, the grain
boundary concentration of sulfur increased again with elevations in its equilibrium concentrations.

Osaka University
Mechanism of ductility-dip cracking in multi-pass weld
thermal cycles
Grain boundary
1st pass 2nd pass 3rd pass
■ The theoretical analysis makes it clear;
1) the sulfur segregation at the grain
boundary in multi-pass welds was
enhanced by multi-pass weld thermal
cycles
2) became dominant when a weld metal was
reheated twice at a temperature range
between 900 and 1100 K.
Varestraint test results have shown that this region was the
most susceptible to cracking.
Grain boundary
segregation of sulfur

Mechanism of ductility-dip cracking in multi-pass weld
thermal cycles
Osaka University
■ These results suggest that
the cause of cracking in the
multi-pass welds of Inver alloy
can be attributed to decrease
in the critical strain of DTR
caused by grain boundary
weakening due to sulfur
segregation
■ which has been accelerated
by the multi-pass weld thermal
cycles.
Grain boundary
1st 2nd 3rd
Grain boundary
segregation of sulfur
Strain
Temperature
BTR DTR
Ductility
curve
Strain
curve
1st
2nd
3rd

Summary
Osaka University
Development
■Quantitative prediction of microstructure and properties
■Precise understanding of mechanism
Better
performance
of joint
Calculation codes
■ In the last few decade,mathematical approaches using computer technologies in the welding
metallurgy have significantly contributed to its recent developments. Such approaches have enabled a
more precise understanding of welding metallurgical phenomena and a more accurate comprehension
of the mechanism for weld defects, including weld cracking through a visualization of the results.
■ Moreover, mathematical approaches have provided important information to control weld defects,
which ensures better weldment performance and the reliability of welded joints. Further
development of mathematical modeling should be more encouraged.

Osaka University
Thank you for kind your attention!

The method for examination of reheat cracking
susceptibility
Osaka University
＜Test conditions＞
Welding current ：150A
Welding voltage ：13V
Welding speed ：1.67mm/s
Augmented strain：1.6, 2.4, 3.6%
1st bead
2nd bead
2nd bead
1st bead
3rd bead
3-bead Varestraint test
2-bead Varestraint test

Surface appearance of laser surface melted regions
Osaka University
1mm 1mm
60μm 60μm

Local strain at the center perpendicular to
laser scanning direction
Osaka University
Lab. of Material Joining Process
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Ç™Ç±ÇÃÉsÉNÉ`ÉÉÇ¾å©ÇÈÇ…ÇÕïKóvÇÇ•
ÅB
Lser
scanning
direction
Melted region
Center element
The increment of local strain at the center part in
laser surface melted region during solidification
increases with increasing laser traveling velocities.
Strain
(％)
Temperature (K)

Local strain at dendrite boundaries perpendicular
to dendrite growth direction
Osaka University
QuickTimeý Ç²
ÅB
QuickTimeý Ç²
ÅB
QuickTimeý Ç²
ÅB
θ θ θ
Laser
scanning
direction
Element located at
0.3mm from center
Melted region
Perpendicular
to dendrite
growth direction

Local strain at dendrite boundaries perpendicular
to dendrite growth direction (Calculated)
Osaka University
θ
θ
θ
The increment of local strain in the condition of laser traveling velocity of 40mm/s is larger than the
strain in other conditions. That is, in this case, not only the laser traveling velocity but also the dendrite
growth direction affects the local strain at dendrite boundaries.
Strain
(％)
Temperature (K)

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