Transcript Recent Topics of Welding Metallurgy Relating to Hot

Osaka University
Recent Topics of Welding Metallurgy
Relating to Hot Cracking
and Embrittlement in Iron and
Nickel-base Alloys
Kazutoshi Nishimoto
Department of Manufacturing Science
Graduate School of Engineering
Osaka University
Lab. Material Joining Process
Contents
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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
Lab. Material Joining Process
Contents
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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 nickelbase alloys
Nieq＝%Ni＋30×%C＋0.5×%Mn
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δferrite content
σ phase
embrittlement
The use of
new alloys or new
welding processes
Hot cracking
Cold cracking
Embrittlement by grain
coarsened
・475℃ embrittlement
Need for researches to
understand their
response to these
problems.
Creq＝%Cr＋%Mo＋0.5×%Si＋0.5×%Nb
■ 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.⇒
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Prevalent problems in welds of iron-base and nickelbase alloys
Nieq＝%Ni＋30×%C＋0.5×%Mn
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δferrite content
σ phase
embrittlement
The use of
new alloys or new
welding processes
Hot cracking
Cold cracking
Embrittlement by grain
coarsened
・475℃ embrittlement
Need for researches to
understand their
response to these
problems.
Creq＝%Cr＋%Mo＋0.5×%Si＋0.5×%Nb
■ 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. ⇒
Contents
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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
Lab. Material Joining Process
Spinodal Phase Decomposition in Chromium
Containing Iron base Alloys
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 2G
0
C 2
(a)
Cα’’
C0
Cα’
G
C
Cα’’
Nucleation and growth
Spinodal decomposition
C0
Cα’ Initial
(b)
α
Spinodal
decomposition
α’+α’’
G
0
Cα’ Cα
Cα’’
1
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) Free energy curve
(b) Phase diagram and Spinodal curve
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Theoretical Analysis of Spinodal Decomposition during
iso-thermal Process
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Cahn-Hilliard's non-linear
diffusion equation

c
 D
x
c
=
t
x
Cr
Cr
c
 K
x
–2
x
3
Cr
3
Fourier expression of
diffusion equation

Q(h)
2
= – h { D0 + 2h 2 2 K0 Q(h) + 1 D1 R(h)
t
2
+ 1 D2S(h) + 1 D3T(h) +  }
3
4
4
– 2h { 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
Osaka University
Cahn-Hilliard's non-linear
diffusion equation (extended)

c
=
t
Cr
c
x
x
 D
 K
Cr
–2
c
x
x
3
Input of parameters
, c Cr, thermal cycle
Input of initial composition-wave Q0(h)
Calculation of temp. &
material constants
Cr
3
Interdiffusion coefficient

2
2

G

D= M(Cr) 2 = M0c Fec Cr G
2
cCr
cCr
Gradient energy coefficient
K =  0 M(cCr) [(cCr,T) + {(cCr,T) /cCr}cCr]
■ Developed the method of analysis for the decomposition in
thermal cycle process by extending the Cahn-Hilliard nonlinear diffusion equation to this processes and applied it to a
computer simulation of phase decomposition for 30Cr-2Mo
steel.⇒
Replacement of Fourier
waves for convolution
Fourier transformation FFT
Rf = Q fQf, Sf = RfQf, Tf = SfQf
Uf = k3QfQf, Vf = UfQf, Wf = V fQf
Inverse Fourier transformation IFFT
Calculation of ŽQ(h)/Žt
Q(h)t+t = Q(h) t + {ŽQ(h)/Žt}tt
Display?
NO
YES
Output of Q(h) & graphing
Completion of
thermal cycle?
NO
t = t + t
YES
End
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Osaka University
Two dimensional
Evolution the Cr-rich
phase induced by
Spinodal Decomposition
in 30Cr-2Mo steel

c
 D
x
c
=
t
x
Cr
Cr
c
 K
x
–2
x
3
Cr
3
■ 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
Osaka University
Relationship between ΔHv and ΔvTE
Cut-through model
(Mott-Nabarro's equation)
3/ 2
mV 4 / 3N 1/ 6e 3/ 2  1 
HV 
ln

 V 
3/ 2


1

1/ 2 4 / 3

 KR V ln



 V 
10
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
3 /2
1/ 2
vTE  KR V
4 /3
 1 
ln 
 V 
■ 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.
Lab. Material Joining Process
Theoretical approach for prediction of 475°C
embrittlement in 30Cr-2Mo steel
Osaka University
Relationship between ΔHv and ΔvTE
Cut-through model
(Mott-Nabarro's equation)
3/ 2
mV 4 / 3N 1/ 6e 3/ 2  1 
HV 
ln

 V 
3/ 2
3/2 and
Relationship between R1/2V1/4/3
{ln(1/V)}


1

2 4 /3
 ΔvTE
 KR V ln



 V 
10
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
3 /2
1/ 2
vTE  KR V
4 /3
 1 
ln 
 V 
■ 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
3rd pass welding
2nd pass welding
1st pass welding
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■ 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.⇒
Lab. Material Joining Process
Contents
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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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Embrittlement due to sigma phase Precipitation
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WT.%Cr
0
20
40
60
80
100
1500
α’
Temperature (℃)
α
σ
700
1400
1300
1200
X X XXα+σ
600
σ+α’
1100
1000
500
X X XX
α+α’
900
800
400
X X XX
0
0.2
0.4
0.6
0.8
NCr
700
1.0
Temperature (℉)
800
■ 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. ⇒
Phase diagram of Iron-Chromium Alloy
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Microstructures of super duplex stainless steels
(heated at 1073 K for 1.8 ks)
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NAS64
SAF2507
α
DP3W
α
γ
γ
γ
α
■ 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.
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Sigma phase precipitation Curves in super
duplex stainless steels
Area fraction of σ phase (%)
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50
45
40
35
30
25
20
15
10
5
0
101
NAS64
SAF2507
DP3W
Aging temperature
1073K
1123K
1173K
1223K
102
103
Aging time (s)
104
102
103
104
Aging time (s)
103
104 105
Aging time (s)
■ Sigma phase precipitation phenomenon follows the Johnson-Mehl type of kinetic equation in
the case of weld metals of austenitic stainless steels.⇒
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Kinetics of Sigma Phase Precipitation
---Johnson-Mehl equation---
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1.0
Logln1/(1-y)
0.5
0
-0.5
1.0
NAS64
0.5
Aging temperature
1073K
1123K
1173K
1223K
SAF2507
DP3W
0.5
0
n=1.32
-1.0
-0.5
0
-1.0
-0.5
-1.5
-1.5
-2.0
101
1.0
-2.0
NAS64 base metal
102
103
-2.5
104 101
n=1.62
SAF2507 base metal
102
103
Aging time (s)
Aging time (s)
n
y = 1 – exp (– k t )
-1.0
n=0.879
DP3W base metal
-1.5
104 102
103
104
105
Aging time (s)
1
log ln
= n log t + log k
1–y
■ 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 JohnsonMehl type kinetic equation. ⇒
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Prediction of the Amount of Sigma Phase during
thermal cycle process by additivity rule
Osaka University
Based on the isothermal
kinetics of the sigma phase
precipitation
■ Applying the
T1
T3
T2
T2
T3
Δt1 Δt2 Δt3
time
T1
Δt1
Δt2
time
f(t) = fmax(t){1-exp(k(t)Δt n)}
Additivity
rule
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 = 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
Δt3

fdt 

fsat 1 expkt
n
dt
k  k0 expQ RT
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The amount of sigma phase precipitated in SAF2507
during two types of synthetic thermal cycles
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Area fraction of σphase (%)
Pattern A
Pattern B
■ The calculated curves agree fairly
well with the measured results in both
of the thermal cycles.
6
SAF2507 base metal
5
●,▲: Measured
4
■ This correspondence suggests that
sigma phase precipitation in duplex
stainless steels during the thermal
cycle process can be predicted by
this computation.
3
Pattern B
2
1
Pattern A
0
0
1
2
3
4
5
6
7
8
Number of thermal cycles
9
10
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Impact absorbed energy (J)
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Relationship between the amount of sigma phase and
the Charpy impact energy of duplex stainless steels
aged at 1173K
80
Aging temperature : 1173K
NAS64
SAF2507
70
60
DP3W
50
40
30
20
■ In each steel, the Charpy
impact energy decreases
drastically with increases in the
amount of sigma phase.⇒
10
0
0
2 4
6 8 10 12 14 16
Area fraction of σ phase(%)
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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
(Under the assumption)
(b) Decrement in impact absorbed energy in multipass weldment
(Under the assumption)
■ 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.⇒
Lab. Material Joining Process
Contents
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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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Reasons for this enhancement of hot cracking
susceptibility in laser welds
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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.
However, hot cracking susceptibility may be enhanced in some cases of the laser
welding of stainless steels and nickel base alloys.
There are two reasons for this enhancement:
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.
■
Types and positions of hot cracking in laser welds
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Ｈot cracking susceptibility may be enhanced
in laser welding
due to a characteristic shape of
penetration in laser welds.
Center-line crack
Solidification
crack at neck
Inter-granular
crack at well
■ 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 ⇒
Hole by
shrinking during
solidification at
bead center
Liquation crack
at neck in HAZ
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Mechanism of
solidification cracking
Ｈot cracking susceptibility may be enhanced
in laser welding
due to the rapid solidification and
cooling during welding .
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(the second reason)
Local strain
Strain
Solidification
brittleness
temperature
range (BTR)
(Cracking)
(No cracking)
TL
TS
Temperature ■ In laser welding with a low
Crack
Weld
metal
溶接金属
■ 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
heat input, the strain rate during
cooling will increase, and
consequently may enhance the
hot cracking susceptibility.
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
Osaka University
BTR
Theoretical analyses
of the liquidus and
solidus temperatures
during laser welding
Strain
Local strain
Thermal
elasticplastic
analysis
(Cracking )
(No cracking)
TL
Temperature
TS
■ 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
Effect of rapid
solidification
BTR
BTR
TL
Ts
Temperature
TL TL’ Ts’ Ts
Temperature
TL decreases due to supercooling
Laser welding
Strain(%)
Arc welding
Strain(%)
Strain(%)
Osaka University
BTR
TL’ Ts’
Temperature
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.
Estimation of BTR in laser surface melted region
Effect of rapid
solidification
BTR
BTR
TL
Ts
Temperature
TL TL’ Ts’ Ts
Temperature
TL decreases due to supercooling
Laser welding
Strain(%)
Arc welding
Strain(%)
Strain(%)
Osaka University
BTR
TL’ Ts’
Temperature
Ts varied by micro-segregation of
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.
Estimation of BTR in laser surface melted region
Effect of rapid
solidification
BTR
BTR
TL
Ts
Temperature
Laser welding
Strain(%)
Arc welding
Strain(%)
Strain(%)
Osaka University
TL TL’ Ts’ Ts
Temperature
TL decreases due to supercooling
■ 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.
BTR
TL’ Ts’
Temperature
Ts varied by micro-segregation of
impurity elements
C Sj  k ne sC Lj 1

Ji = D
Ci + 1 – Ci
x
Thermo-Calc@
Theoretical model for calculation for impurity elements
segregation in solidification process
Osaka University
N-1
Distribution of S
at liquid/solid boundary
i-1
L
CjS  kne sCj1
kes  
kne s 
1 
S
i+1
S
L
L
x
  Rv
2DS
Cs
kes：Equilibrium coefficient， Rv：Solidification speed，
Ds：Diffusion coefficient
Diffusion in solid
Ci + 1 – Ci

Ji = D
x


2Dst
B
B
B
B
Ci 
i
C

C

i

1
C

C


i1
i
i
i 1
x 2 2i 1


S concentration
Non-equilibrium
coefficient Knes
12
i
N
L
S
S olidification
■ 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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1.0
1.0
LTV (mm/s)
20
40
60
0.6
0.4
0.2
0
0.8
Strain (%)
Strain (%)
0.8
P : 0.02%
1680
1640
1600
1560
Temperature (K)
1520
LTV (mm/s)
20
40
60
0.6
0.4
0.2
0
P : 0.03%
1680
1640
1600
1560
Temperature (K)
1520
■ 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
Laser traveling velocity : Increase
Analysis point and direction
θ=35°
Calculated by Quick Therm
20mm/s
θ =50°
40mm/s
θ=60
°
60mm/s
■ 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.
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Local strain at the center perpendicular to laser
scanning direction
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1.2
1.2
LTV=60
Dendrite boundary
1.0
1.0
0.8
0.8
0.6
LTV=40
0.4
LTV=20
0.2
0
1650
1600
Temperature (K)
1550
Strain (%)
Strain (%)
Center-line
LTV : Laser traveling velocity (mm/s)
θ
LTV=60
(θ=60°)
0.6
0.4
LTV=40
(θ=50°)
0.2
LTV=20
(θ=35°)
0
1650
1600
Temperature (K)
1550
■ 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.⇒
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Comparison between BTR and strain at the bead center
perpendicular to laser traveling direction
Osaka University
Strain (%)
1.2
LTV = 40 mm/s
LTV = 20 mm/s
LTV = 60 mm/s
1
0.8
0.6
0.4
0
Cracking
Cracking
0.2
1650
1600
0.02％ P+S
0.04％ P+S
1550
1650
1600
1550
Temperature (K)
1650
1600
1550
SUS316L
LTV : Laser traveling velocity
■ 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.
Lab. Material Joining Process
Comparison between BTR and strain perpendicular to
dendrite growth direction at dendrite boundaries
Osaka University
1.2
LTV = 40 mm/s
Strain (%)
LTV = 20 mm/s
LTV = 60 mm/s
1
0.8
0.6
0.4
Cracking
0.2
0
1650
0.02％ P+S
0.04％ P+S
1600
1550
1650
1600
1550
Temperature (K)
1650
1600
1550
SUS316
L
LTV : Laser traveling
velocity
■ 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.⇒
Comparison between measured and theoretically
calculated conditions to occur cracking
Osaka University
P+S content (mass％)
Cracking at dendrite boundary (Calculated)
Center-line cracking (Calculated)
0.04
Crack
（Center-line）
0.03
Crack
(Dendrite
boundary)
0.02
No crack
10
20
30
40
50
Laser traveling velocity (mm/s)
60
SUS316L
■ 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.
Enhanced susceptibility due to solidification mode shift
Osaka University
J.C.Lippold, Weld. J., 73-6 (1994) 129s-139s
100
Austenite
(A)
0.1
F/MA
Ferrite
(F)
10
S+P+B (mass%)
Solidification rate (mm/s)
1000
Arc welding
YAG welding
No crack
Crack
0.05
1
AF
0.1
FA
0
1.5
Creq/Nieq
2.0
1.4
1.6
1.8
Cr/Ni-equivalent
■ 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.
Lab. Material Joining Process
Enhanced susceptibility due to solidification mode shift
Osaka University
J.C.Lippold, Weld. J., 73-6 (1994) 129s-139s
100
Austenite
(A)
0.1
F/MA
Ferrite
(F)
10
S+P+B (mass%)
Solidification rate (mm/s)
1000
Arc welding
YAG welding
No crack
Crack
0.05
1
AF
0.1
FA
0
1.5
Creq/Nieq
2.0
1.4
1.6
1.8
Cr/Ni-equivalent
■ 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. ⇒
Lab. Material Joining Process
Condition for transition of solidification mode
Osaka University
In the case of T*δ>T*γ
FA mode
In the case of T*γ>T*δ
T  = T L + (mv ,iC – m 0.iC0 ,i)
– 2
 / R – V/ m – GD / V
*
*
i
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
(modified KGT model)
S.Fukumoto, W.Kurz, ISIJ Inter., 37-7 (1997) 677-684
S.Fukumoto, W.Kurz, ISIJ Inter., 38-1 (1998) 71-77
K ：Partition coefficient
R = 2 

mC 0 1 – K  cV
–
–G
D 1 – 1 – K Iv P
Dendrite Tip Temperature：T*
T * = T L + (mv ,iC *i – m 0.iC0 ,i)
– 2
 / R – V/ m – GD / V
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
■ 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. ⇒
Lab. Material Joining Process
Effect of dendrite growth velocity on dendrite tip
temperature of ferrite and austenite
Osaka University
Dendrite tip temperature (K)
1750
1730
1710
1690
■ The dendrite tip temperature
in austenite rises above that in
ferrite at dendrite growth
velocities exceeding 0.9mm/s.
⇒
1670
1650
1×10-2
1×10-1
1×100
1×101
1×102
Dendrite growth velocity (mm/s)
23Cr-9Ni-0.34N steel
Lab. Material Joining Process
Comparison of calculated solidification mode change with
experimental results in laser welds of stainless steel
Osaka University
AF mode
FA mode
Laser traveling velocity (mm/s)
15
Bead center
AF
FA
10
5
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.⇒
0
1.3
1.4
Creq/Nieq
1.5
23Cr-9Ni-0.34N steel
Lab. Material Joining Process
Comparison of calculated solidification mode change
with hot cracking susceptibility in laser welds of
stainless steel
Osaka University
Crack
No crack
Laser traveling velocity (mm/s)
15
Bead center
AF
FA
■ The condition to yield AF mode
coincide with the condition to occur hot
cracking.
10
5
Predicted condition
to yield crack
■ It means you can predict the risk of
hot cracking through calculation of the
mode shift from FA to AF even in laser
weld. ⇒
0
1.3
1.4
Creq/Nieq
1.5
23Cr-9Ni-0.34N steel
Lab. Material Joining Process
Contents
Osaka University
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
Lab. Material Joining Process
Mechanism of ductility-dip crack
Osaka University
Strain
Ductility curve
BTR
DTR
ε3
ε2
ε1
■ 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-dip cracking
Temperature
Lab. Material Joining Process
Mechanism of ductility-dip crack
Osaka University
Strain
Ductility curve
BTR
DTR
ε3
ε2
ε1
Ductility-dip cracking
■ 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. ⇒
Temperature
Lab. Material Joining Process
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
Total crack length (mm)
3
Double-bead
Triple-bead
2
1
0
1100〜
1200
1000〜
1100
900〜
1000
900〜
800
Peak temperature range in HAZ (K)
Fe-36Ni alloy (0.011%S)
■ 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.
Lab. Material Joining Process
Effect of S on susceptibility to ductility-dip cracking
Osaka University
Double-bead Varestraint test
Ductility-dip crack in first bead
80
Total crack length (mm)
Augmented strain
1.6%
2.4%
60
40
■ The total length of the cracks grew as
the sulfur content in the samples
increased.
20
■ This experimental result demonstrate
that sulfur is evidently detrimental to
cracking susceptibility in the weld metal.
Fe-36Ni alloy
0
0
0.010
0.005
S content (%)
0.015
Lab. Material Joining Process
The result of Auger analysis conducted on the fractured
surface in the multi-pass weld metal
Osaka University
Fe-36Ni alloy
800
600
AES spectrum
400
200
c/s
0
C
-200
O
-400
-600
-800
-1000
-1200
Ni
S
Fe
100 200 300 400 500 600 700 800 900 1000
Kinetic energy (eV)
Effect of thermal cycles at peak temperature of 1000K on S concentration
Twice：Average 7% ⇨ Three times：Average 9%
■Sulfur is segregated on its surface. Moreover, the amount of sulfur on the grain boundary increase
with increase of welding pass. ⇒
Lab. Material Joining Process
Method of calculation for S segregation at grain
boundary during multi-pass weld thermal cycles
Osaka University
Stage I : Solidification process
Melting point
Stage II : Cooling process (after solidification)
■ The concentration of sulfur at the grain boundary was
analyzed for two stages:
Melting point
■ That is,
Stage I:
Stage II:
the solidification segregation during welding,
the grain boundary segregation during the cooling
and reheating by the subsequent weld passes.
Lab. Material Joining Process
Method of calculation for S segregation at grain
boundary during multi-pass weld thermal cycles
Osaka University
Stage I : Solidification process
Distribution of S at liquid/solid boundary
S
j
L
ne s j1
C k C
kes  
kne s 
1 
x
  Rv
2DS
Melting point
kes：Equilibrium coefficient， Rv：Solidification speed，
Ds：Diffusion coefficient
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.
Lab. Material Joining Process
Method of calculation for S segregation at grain
boundary during multi-pass weld thermal cycles
Osaka University
■ 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.
Melting point
Stage II : Cooling process (after solidification)
Solute concentration change
CX 




2DX t
B
B
B
B
i
C

C

i

1
C

C
  X i X i 1
X i1
Xi
x 2 2i  1
Melting point
Boundary condition
gb
gb
4Dst  2 Dst 
Cs (t) Cs (0)

e rfc


1
exp
gb
gb
2 2
Cs () Cs (0)
1 d   1 d 
C：Concentration of solute, vacancy, complex，
k：constant，Ev：Vacancy forming energy，
Ec：Binding energy between vacancy and solute
Lab. Material Joining Process
The concentration of S at grain boundaries calculated
for multi-pass weld thermal cycles
Osaka University
■ 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.
Mechanism of ductility-dip cracking in multi-pass weld
thermal cycles
Osaka University
■ 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.
1st pass
2nd pass
3rd pass
Grain boundary
Grain boundary
segregation of sulfur
Lab. Material Joining Process
Mechanism of ductility-dip cracking in multi-pass weld
thermal cycles
Osaka University
1st
Strain
2nd
BTR
DTR
Ductility
curve
3rd
Strain
curve
Ductility-dip cracking
1st
■ 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.
Temperature
2nd
3rd
Grain boundary
Grain boundary
segregation of sulfur
Lab. Material Joining Process
Contents
Osaka University
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
Lab. Material Joining Process
Summary
Osaka University
Calculation codes
Development
Better
performance
of joint
■Quantitative prediction of microstructure and properties
■Precise understanding of mechanism
■ 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!
Lab. Material Joining Process
The method for examination of reheat cracking
susceptibility
Osaka University
2-bead Varestraint test
1st bead
3-bead Varestraint test
2nd bead
3rd bead
2nd bead
1st bead
＜Test conditions＞
Welding current ：150A
Welding voltage ：13V
Welding speed
：1.67mm/s
Augmented strain：1.6, 2.4, 3.6%
Lab. Material Joining Process
Surface appearance of laser surface melted regions
Osaka University
1mm
60μm
1mm
60μm
Lab. Material Joining Process
LTV : Laser traveling velocity (mm/s)
Center element
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Lser scanning direction
Strain (％)
Osaka University
Local strain at the center perpendicular to
laser scanning direction
Temperature (K)
The increment of local strain at the center part in
laser surface melted region during solidification
increases with increasing laser traveling velocities.
Melted region
Lab. of Material Joining Process
Perpendicular
to dendrite
growth direction
θ
θ
θ
Laser scanning direction
Osaka University
Local strain at dendrite boundaries perpendicular
to dendrite growth direction
Laser traveling velocity : Increase
Element located at
0.3mm from center
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Melted region
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Lab. of Material Joining Process
Osaka University
Local strain at dendrite boundaries perpendicular
to dendrite growth direction (Calculated)
Laser traveling velocity : Increase
Strain (％)
LTV : Laser traveling velocity (mm/s)
θ
θ
θ
Temperature (K)
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.
Lab. of Material Joining Process