Presented at the COMSOL Conference 2008 Hannover
2
The metals usedThe metals used
MaterialsMaterials AISI 316 L austenitic stainless steel CuCu
ElementElement SiSi CrCr MnMn FeFe NiNiCuCu
at 091091 20272027 209209 70007000 673673 9999
Solubility Cu(austenite) = 18 at
Solubility Fe(Cu) = 057‐2 at
FeCu systemFeCu system
Limited miscibility under
undercooling conditions
No intermetallics
Maximal solubility of Cu in
austenic Fe matrix is about
15 at
Two types of morphologyTwo types of morphology
I = 40 mA U = 25 kV P = 1000 W v =600 mmmin
FE
I=30 mA U = 375 kV P = 1125 W v = 600 mmmin
3
Structure Element at Cu Fe Cr Nildquodropletrdquo-like structure
A 80 656 20 64B 115 631 192 62C 214 566 166 52D 94 45 12 03C2 213 552 172 63
ldquoemulsionrdquo-like structureA 05 706 208 81B 79 657 20 64C 213 565 165 57D 94 45 12 03E 911 56 20 13F 149 625 180 46
ldquoldquodropletdropletrdquordquo ldquoldquoemulsionemulsionrdquordquo
Result Local composition as function of temperature and time Mecanism of structure formationResultResult Local composition as function of temperature and time Mecanism of structure formation
Modeling of microstructuresModeling of microstructures
MODELMODEL
2D thermal model
4
5
ldquoldquodropletdropletrdquordquo
ldquoldquoemulsionemulsionrdquordquo
Model descriptionModel description
Realistic geometryRealistic geometry Hypothesis Hypothesis
Simplifications Simplifications
the model deals only with solidification period of melted zone life
convection is neglected
steel is considered as homogeneous material with diffusion coefficient of γ‐Fe
ldquodropletrdquo structure the droplets are formed by eroding of steel by copper‐rich flux
ldquoemulsionrdquo structure undercooling phenomena with secondary phase separation
6
Model descriptionModel descriptionCooling laws used in calculations ldquoemulsionrdquo-type
weld (a) ldquodropletrdquo-type weld (b)
)( TktTc p nablaminusnabla=partpartρ
Heat transferHeat transfer
A=Asolid + (Aliquid ndash A solid)flc2hs(T-Tf ) A = k ρ Cp
Tδ Joints ldquoemulsionrdquo ldquodropletrdquoGauss approximation
T(K) = y0 + (A(wsqrt(PI2)))exp(-2(tw)^2)y0 1159264 13338w 001523 00367A 162814 426R2 099 099
The approximations of cooling laws used in calculations
Discontinuity of properties
Heat equation
The position of modeling zone at global geometry of the weld
Boundary conditions
Hot side Cold sideCooling law
Thermal isolation
Hot side
Electron beam
0)( )( =nablasdotminusnabla CuFeCu cD
0)( )( =nablasdotminusnabla FeCuFe cD
)exp(TR
EDDT sdotminussdot= Ddomain=DTflc2hs(Tstart-T )Tδ
copper‐rich zones
steel‐rich zones
7
Model descriptionModel descriptionDiffusionDiffusion
0 at 0 at CuCu
95 at 95 at CuCu
18 at 18 at CuCu
8 at 8 at CuCu
18 at 18 at CuCu
0 at 0 at CuCu
18 at 18 at CuCu
8 at 8 at CuCu
95 at 95 at CuCu
95 at 95 at CuCu
18 at 18 at CuCu
Ts (Cu95Fe5)Ts (Cu95Fe5)
Ts (Cu20Fe80)Ts (Cu20Fe80)
Ts (Cu20Fe80)Ts (Cu20Fe80)
Ts (Cu20Fe80)Ts (Cu20Fe80)C(M) at ‐ C(M) = Csteelγ(M) 100M = Fe CrNi γ(M) ‐molar part of M in original steel
C(M) at ‐ C(M) = Csteelγ(M) 100M = Fe CrNi γ(M) ‐molar part of M in original steel
Post treatmentPost treatment
Initial conditions
8
Emulsion model choice of start points of diffusionEmulsion model choice of start points of diffusion
Diffusion starts immediately after beam pass and Diffusion starts immediately after beam pass and small globulas do existsmall globulas do exist
Small globulas would be dissolvedFront of diffusion is too large
Diffusion starts after solidification of steel and Diffusion starts after solidification of steel and small globulas do exist from beginningsmall globulas do exist from beginning
There is no diffusion observed
Diffusion starts after beam pass in A and B and Diffusion starts after beam pass in A and B and after Ts (Cu20Fe80) at the regions C D E ad F after Ts (Cu20Fe80) at the regions C D E ad F (when small globulas are already formed (when small globulas are already formed during undercooling of the weld)during undercooling of the weld)Large diffusion front in AB and small in CD E and F
AA BB CC DD
EE
EE
9
Results Results ldquoldquodropletdropletrdquordquo ldquoldquoemulsionemulsionrdquordquo
FE
10
ValidationValidationComparison between calculated profiles and real copper concentraComparison between calculated profiles and real copper concentration tion founded by SEMfounded by SEM‐‐ESD analysis in ESD analysis in ldquoldquoemulsionemulsionrdquordquo‐‐like (a) and like (a) and ldquoldquodropletdropletrdquordquo‐‐like (b) like (b) microstructures microstructures
Interface Distance micromldquodropletrdquocalculated observed
AD 14 17BD 4 3CD 4 3C2D 24 18
ldquoemulsionrdquocalculated observed
AB 31 29CD 17 14CE 13 11DF 17 23
Comparison of diffusion Comparison of diffusion distances on different interfaces distances on different interfaces
11
ConclusionsConclusions
Present numerical models of Present numerical models of microstructures development are microstructures development are in good correspondence with in good correspondence with SEM images and the results of SEM images and the results of local ESD analysis local ESD analysis
The temperature evolution is The temperature evolution is realisticrealistic
The results confirm our hypothesis The results confirm our hypothesis on the way of microstructure on the way of microstructure formation under different welding formation under different welding conditionsconditions
There are two mechanisms of microstructures formation depending on operational parametens
olaquo dropletraquo structure is formed by eroding of steel surface by copper fluxolaquo emulsionraquo structure is formed under undercooling conditions
There are two mechanisms of microstructures formation depending on operational parametens
olaquo dropletraquo structure is formed by eroding of steel surface by copper fluxolaquo emulsionraquo structure is formed under undercooling conditions
2
The metals usedThe metals used
MaterialsMaterials AISI 316 L austenitic stainless steel CuCu
ElementElement SiSi CrCr MnMn FeFe NiNiCuCu
at 091091 20272027 209209 70007000 673673 9999
Solubility Cu(austenite) = 18 at
Solubility Fe(Cu) = 057‐2 at
FeCu systemFeCu system
Limited miscibility under
undercooling conditions
No intermetallics
Maximal solubility of Cu in
austenic Fe matrix is about
15 at
Two types of morphologyTwo types of morphology
I = 40 mA U = 25 kV P = 1000 W v =600 mmmin
FE
I=30 mA U = 375 kV P = 1125 W v = 600 mmmin
3
Structure Element at Cu Fe Cr Nildquodropletrdquo-like structure
A 80 656 20 64B 115 631 192 62C 214 566 166 52D 94 45 12 03C2 213 552 172 63
ldquoemulsionrdquo-like structureA 05 706 208 81B 79 657 20 64C 213 565 165 57D 94 45 12 03E 911 56 20 13F 149 625 180 46
ldquoldquodropletdropletrdquordquo ldquoldquoemulsionemulsionrdquordquo
Result Local composition as function of temperature and time Mecanism of structure formationResultResult Local composition as function of temperature and time Mecanism of structure formation
Modeling of microstructuresModeling of microstructures
MODELMODEL
2D thermal model
4
5
ldquoldquodropletdropletrdquordquo
ldquoldquoemulsionemulsionrdquordquo
Model descriptionModel description
Realistic geometryRealistic geometry Hypothesis Hypothesis
Simplifications Simplifications
the model deals only with solidification period of melted zone life
convection is neglected
steel is considered as homogeneous material with diffusion coefficient of γ‐Fe
ldquodropletrdquo structure the droplets are formed by eroding of steel by copper‐rich flux
ldquoemulsionrdquo structure undercooling phenomena with secondary phase separation
6
Model descriptionModel descriptionCooling laws used in calculations ldquoemulsionrdquo-type
weld (a) ldquodropletrdquo-type weld (b)
)( TktTc p nablaminusnabla=partpartρ
Heat transferHeat transfer
A=Asolid + (Aliquid ndash A solid)flc2hs(T-Tf ) A = k ρ Cp
Tδ Joints ldquoemulsionrdquo ldquodropletrdquoGauss approximation
T(K) = y0 + (A(wsqrt(PI2)))exp(-2(tw)^2)y0 1159264 13338w 001523 00367A 162814 426R2 099 099
The approximations of cooling laws used in calculations
Discontinuity of properties
Heat equation
The position of modeling zone at global geometry of the weld
Boundary conditions
Hot side Cold sideCooling law
Thermal isolation
Hot side
Electron beam
0)( )( =nablasdotminusnabla CuFeCu cD
0)( )( =nablasdotminusnabla FeCuFe cD
)exp(TR
EDDT sdotminussdot= Ddomain=DTflc2hs(Tstart-T )Tδ
copper‐rich zones
steel‐rich zones
7
Model descriptionModel descriptionDiffusionDiffusion
0 at 0 at CuCu
95 at 95 at CuCu
18 at 18 at CuCu
8 at 8 at CuCu
18 at 18 at CuCu
0 at 0 at CuCu
18 at 18 at CuCu
8 at 8 at CuCu
95 at 95 at CuCu
95 at 95 at CuCu
18 at 18 at CuCu
Ts (Cu95Fe5)Ts (Cu95Fe5)
Ts (Cu20Fe80)Ts (Cu20Fe80)
Ts (Cu20Fe80)Ts (Cu20Fe80)
Ts (Cu20Fe80)Ts (Cu20Fe80)C(M) at ‐ C(M) = Csteelγ(M) 100M = Fe CrNi γ(M) ‐molar part of M in original steel
C(M) at ‐ C(M) = Csteelγ(M) 100M = Fe CrNi γ(M) ‐molar part of M in original steel
Post treatmentPost treatment
Initial conditions
8
Emulsion model choice of start points of diffusionEmulsion model choice of start points of diffusion
Diffusion starts immediately after beam pass and Diffusion starts immediately after beam pass and small globulas do existsmall globulas do exist
Small globulas would be dissolvedFront of diffusion is too large
Diffusion starts after solidification of steel and Diffusion starts after solidification of steel and small globulas do exist from beginningsmall globulas do exist from beginning
There is no diffusion observed
Diffusion starts after beam pass in A and B and Diffusion starts after beam pass in A and B and after Ts (Cu20Fe80) at the regions C D E ad F after Ts (Cu20Fe80) at the regions C D E ad F (when small globulas are already formed (when small globulas are already formed during undercooling of the weld)during undercooling of the weld)Large diffusion front in AB and small in CD E and F
AA BB CC DD
EE
EE
9
Results Results ldquoldquodropletdropletrdquordquo ldquoldquoemulsionemulsionrdquordquo
FE
10
ValidationValidationComparison between calculated profiles and real copper concentraComparison between calculated profiles and real copper concentration tion founded by SEMfounded by SEM‐‐ESD analysis in ESD analysis in ldquoldquoemulsionemulsionrdquordquo‐‐like (a) and like (a) and ldquoldquodropletdropletrdquordquo‐‐like (b) like (b) microstructures microstructures
Interface Distance micromldquodropletrdquocalculated observed
AD 14 17BD 4 3CD 4 3C2D 24 18
ldquoemulsionrdquocalculated observed
AB 31 29CD 17 14CE 13 11DF 17 23
Comparison of diffusion Comparison of diffusion distances on different interfaces distances on different interfaces
11
ConclusionsConclusions
Present numerical models of Present numerical models of microstructures development are microstructures development are in good correspondence with in good correspondence with SEM images and the results of SEM images and the results of local ESD analysis local ESD analysis
The temperature evolution is The temperature evolution is realisticrealistic
The results confirm our hypothesis The results confirm our hypothesis on the way of microstructure on the way of microstructure formation under different welding formation under different welding conditionsconditions
There are two mechanisms of microstructures formation depending on operational parametens
olaquo dropletraquo structure is formed by eroding of steel surface by copper fluxolaquo emulsionraquo structure is formed under undercooling conditions
There are two mechanisms of microstructures formation depending on operational parametens
olaquo dropletraquo structure is formed by eroding of steel surface by copper fluxolaquo emulsionraquo structure is formed under undercooling conditions
Two types of morphologyTwo types of morphology
I = 40 mA U = 25 kV P = 1000 W v =600 mmmin
FE
I=30 mA U = 375 kV P = 1125 W v = 600 mmmin
3
Structure Element at Cu Fe Cr Nildquodropletrdquo-like structure
A 80 656 20 64B 115 631 192 62C 214 566 166 52D 94 45 12 03C2 213 552 172 63
ldquoemulsionrdquo-like structureA 05 706 208 81B 79 657 20 64C 213 565 165 57D 94 45 12 03E 911 56 20 13F 149 625 180 46
ldquoldquodropletdropletrdquordquo ldquoldquoemulsionemulsionrdquordquo
Result Local composition as function of temperature and time Mecanism of structure formationResultResult Local composition as function of temperature and time Mecanism of structure formation
Modeling of microstructuresModeling of microstructures
MODELMODEL
2D thermal model
4
5
ldquoldquodropletdropletrdquordquo
ldquoldquoemulsionemulsionrdquordquo
Model descriptionModel description
Realistic geometryRealistic geometry Hypothesis Hypothesis
Simplifications Simplifications
the model deals only with solidification period of melted zone life
convection is neglected
steel is considered as homogeneous material with diffusion coefficient of γ‐Fe
ldquodropletrdquo structure the droplets are formed by eroding of steel by copper‐rich flux
ldquoemulsionrdquo structure undercooling phenomena with secondary phase separation
6
Model descriptionModel descriptionCooling laws used in calculations ldquoemulsionrdquo-type
weld (a) ldquodropletrdquo-type weld (b)
)( TktTc p nablaminusnabla=partpartρ
Heat transferHeat transfer
A=Asolid + (Aliquid ndash A solid)flc2hs(T-Tf ) A = k ρ Cp
Tδ Joints ldquoemulsionrdquo ldquodropletrdquoGauss approximation
T(K) = y0 + (A(wsqrt(PI2)))exp(-2(tw)^2)y0 1159264 13338w 001523 00367A 162814 426R2 099 099
The approximations of cooling laws used in calculations
Discontinuity of properties
Heat equation
The position of modeling zone at global geometry of the weld
Boundary conditions
Hot side Cold sideCooling law
Thermal isolation
Hot side
Electron beam
0)( )( =nablasdotminusnabla CuFeCu cD
0)( )( =nablasdotminusnabla FeCuFe cD
)exp(TR
EDDT sdotminussdot= Ddomain=DTflc2hs(Tstart-T )Tδ
copper‐rich zones
steel‐rich zones
7
Model descriptionModel descriptionDiffusionDiffusion
0 at 0 at CuCu
95 at 95 at CuCu
18 at 18 at CuCu
8 at 8 at CuCu
18 at 18 at CuCu
0 at 0 at CuCu
18 at 18 at CuCu
8 at 8 at CuCu
95 at 95 at CuCu
95 at 95 at CuCu
18 at 18 at CuCu
Ts (Cu95Fe5)Ts (Cu95Fe5)
Ts (Cu20Fe80)Ts (Cu20Fe80)
Ts (Cu20Fe80)Ts (Cu20Fe80)
Ts (Cu20Fe80)Ts (Cu20Fe80)C(M) at ‐ C(M) = Csteelγ(M) 100M = Fe CrNi γ(M) ‐molar part of M in original steel
C(M) at ‐ C(M) = Csteelγ(M) 100M = Fe CrNi γ(M) ‐molar part of M in original steel
Post treatmentPost treatment
Initial conditions
8
Emulsion model choice of start points of diffusionEmulsion model choice of start points of diffusion
Diffusion starts immediately after beam pass and Diffusion starts immediately after beam pass and small globulas do existsmall globulas do exist
Small globulas would be dissolvedFront of diffusion is too large
Diffusion starts after solidification of steel and Diffusion starts after solidification of steel and small globulas do exist from beginningsmall globulas do exist from beginning
There is no diffusion observed
Diffusion starts after beam pass in A and B and Diffusion starts after beam pass in A and B and after Ts (Cu20Fe80) at the regions C D E ad F after Ts (Cu20Fe80) at the regions C D E ad F (when small globulas are already formed (when small globulas are already formed during undercooling of the weld)during undercooling of the weld)Large diffusion front in AB and small in CD E and F
AA BB CC DD
EE
EE
9
Results Results ldquoldquodropletdropletrdquordquo ldquoldquoemulsionemulsionrdquordquo
FE
10
ValidationValidationComparison between calculated profiles and real copper concentraComparison between calculated profiles and real copper concentration tion founded by SEMfounded by SEM‐‐ESD analysis in ESD analysis in ldquoldquoemulsionemulsionrdquordquo‐‐like (a) and like (a) and ldquoldquodropletdropletrdquordquo‐‐like (b) like (b) microstructures microstructures
Interface Distance micromldquodropletrdquocalculated observed
AD 14 17BD 4 3CD 4 3C2D 24 18
ldquoemulsionrdquocalculated observed
AB 31 29CD 17 14CE 13 11DF 17 23
Comparison of diffusion Comparison of diffusion distances on different interfaces distances on different interfaces
11
ConclusionsConclusions
Present numerical models of Present numerical models of microstructures development are microstructures development are in good correspondence with in good correspondence with SEM images and the results of SEM images and the results of local ESD analysis local ESD analysis
The temperature evolution is The temperature evolution is realisticrealistic
The results confirm our hypothesis The results confirm our hypothesis on the way of microstructure on the way of microstructure formation under different welding formation under different welding conditionsconditions
There are two mechanisms of microstructures formation depending on operational parametens
olaquo dropletraquo structure is formed by eroding of steel surface by copper fluxolaquo emulsionraquo structure is formed under undercooling conditions
There are two mechanisms of microstructures formation depending on operational parametens
olaquo dropletraquo structure is formed by eroding of steel surface by copper fluxolaquo emulsionraquo structure is formed under undercooling conditions
Result Local composition as function of temperature and time Mecanism of structure formationResultResult Local composition as function of temperature and time Mecanism of structure formation
Modeling of microstructuresModeling of microstructures
MODELMODEL
2D thermal model
4
5
ldquoldquodropletdropletrdquordquo
ldquoldquoemulsionemulsionrdquordquo
Model descriptionModel description
Realistic geometryRealistic geometry Hypothesis Hypothesis
Simplifications Simplifications
the model deals only with solidification period of melted zone life
convection is neglected
steel is considered as homogeneous material with diffusion coefficient of γ‐Fe
ldquodropletrdquo structure the droplets are formed by eroding of steel by copper‐rich flux
ldquoemulsionrdquo structure undercooling phenomena with secondary phase separation
6
Model descriptionModel descriptionCooling laws used in calculations ldquoemulsionrdquo-type
weld (a) ldquodropletrdquo-type weld (b)
)( TktTc p nablaminusnabla=partpartρ
Heat transferHeat transfer
A=Asolid + (Aliquid ndash A solid)flc2hs(T-Tf ) A = k ρ Cp
Tδ Joints ldquoemulsionrdquo ldquodropletrdquoGauss approximation
T(K) = y0 + (A(wsqrt(PI2)))exp(-2(tw)^2)y0 1159264 13338w 001523 00367A 162814 426R2 099 099
The approximations of cooling laws used in calculations
Discontinuity of properties
Heat equation
The position of modeling zone at global geometry of the weld
Boundary conditions
Hot side Cold sideCooling law
Thermal isolation
Hot side
Electron beam
0)( )( =nablasdotminusnabla CuFeCu cD
0)( )( =nablasdotminusnabla FeCuFe cD
)exp(TR
EDDT sdotminussdot= Ddomain=DTflc2hs(Tstart-T )Tδ
copper‐rich zones
steel‐rich zones
7
Model descriptionModel descriptionDiffusionDiffusion
0 at 0 at CuCu
95 at 95 at CuCu
18 at 18 at CuCu
8 at 8 at CuCu
18 at 18 at CuCu
0 at 0 at CuCu
18 at 18 at CuCu
8 at 8 at CuCu
95 at 95 at CuCu
95 at 95 at CuCu
18 at 18 at CuCu
Ts (Cu95Fe5)Ts (Cu95Fe5)
Ts (Cu20Fe80)Ts (Cu20Fe80)
Ts (Cu20Fe80)Ts (Cu20Fe80)
Ts (Cu20Fe80)Ts (Cu20Fe80)C(M) at ‐ C(M) = Csteelγ(M) 100M = Fe CrNi γ(M) ‐molar part of M in original steel
C(M) at ‐ C(M) = Csteelγ(M) 100M = Fe CrNi γ(M) ‐molar part of M in original steel
Post treatmentPost treatment
Initial conditions
8
Emulsion model choice of start points of diffusionEmulsion model choice of start points of diffusion
Diffusion starts immediately after beam pass and Diffusion starts immediately after beam pass and small globulas do existsmall globulas do exist
Small globulas would be dissolvedFront of diffusion is too large
Diffusion starts after solidification of steel and Diffusion starts after solidification of steel and small globulas do exist from beginningsmall globulas do exist from beginning
There is no diffusion observed
Diffusion starts after beam pass in A and B and Diffusion starts after beam pass in A and B and after Ts (Cu20Fe80) at the regions C D E ad F after Ts (Cu20Fe80) at the regions C D E ad F (when small globulas are already formed (when small globulas are already formed during undercooling of the weld)during undercooling of the weld)Large diffusion front in AB and small in CD E and F
AA BB CC DD
EE
EE
9
Results Results ldquoldquodropletdropletrdquordquo ldquoldquoemulsionemulsionrdquordquo
FE
10
ValidationValidationComparison between calculated profiles and real copper concentraComparison between calculated profiles and real copper concentration tion founded by SEMfounded by SEM‐‐ESD analysis in ESD analysis in ldquoldquoemulsionemulsionrdquordquo‐‐like (a) and like (a) and ldquoldquodropletdropletrdquordquo‐‐like (b) like (b) microstructures microstructures
Interface Distance micromldquodropletrdquocalculated observed
AD 14 17BD 4 3CD 4 3C2D 24 18
ldquoemulsionrdquocalculated observed
AB 31 29CD 17 14CE 13 11DF 17 23
Comparison of diffusion Comparison of diffusion distances on different interfaces distances on different interfaces
11
ConclusionsConclusions
Present numerical models of Present numerical models of microstructures development are microstructures development are in good correspondence with in good correspondence with SEM images and the results of SEM images and the results of local ESD analysis local ESD analysis
The temperature evolution is The temperature evolution is realisticrealistic
The results confirm our hypothesis The results confirm our hypothesis on the way of microstructure on the way of microstructure formation under different welding formation under different welding conditionsconditions
There are two mechanisms of microstructures formation depending on operational parametens
olaquo dropletraquo structure is formed by eroding of steel surface by copper fluxolaquo emulsionraquo structure is formed under undercooling conditions
There are two mechanisms of microstructures formation depending on operational parametens
olaquo dropletraquo structure is formed by eroding of steel surface by copper fluxolaquo emulsionraquo structure is formed under undercooling conditions
5
ldquoldquodropletdropletrdquordquo
ldquoldquoemulsionemulsionrdquordquo
Model descriptionModel description
Realistic geometryRealistic geometry Hypothesis Hypothesis
Simplifications Simplifications
the model deals only with solidification period of melted zone life
convection is neglected
steel is considered as homogeneous material with diffusion coefficient of γ‐Fe
ldquodropletrdquo structure the droplets are formed by eroding of steel by copper‐rich flux
ldquoemulsionrdquo structure undercooling phenomena with secondary phase separation
6
Model descriptionModel descriptionCooling laws used in calculations ldquoemulsionrdquo-type
weld (a) ldquodropletrdquo-type weld (b)
)( TktTc p nablaminusnabla=partpartρ
Heat transferHeat transfer
A=Asolid + (Aliquid ndash A solid)flc2hs(T-Tf ) A = k ρ Cp
Tδ Joints ldquoemulsionrdquo ldquodropletrdquoGauss approximation
T(K) = y0 + (A(wsqrt(PI2)))exp(-2(tw)^2)y0 1159264 13338w 001523 00367A 162814 426R2 099 099
The approximations of cooling laws used in calculations
Discontinuity of properties
Heat equation
The position of modeling zone at global geometry of the weld
Boundary conditions
Hot side Cold sideCooling law
Thermal isolation
Hot side
Electron beam
0)( )( =nablasdotminusnabla CuFeCu cD
0)( )( =nablasdotminusnabla FeCuFe cD
)exp(TR
EDDT sdotminussdot= Ddomain=DTflc2hs(Tstart-T )Tδ
copper‐rich zones
steel‐rich zones
7
Model descriptionModel descriptionDiffusionDiffusion
0 at 0 at CuCu
95 at 95 at CuCu
18 at 18 at CuCu
8 at 8 at CuCu
18 at 18 at CuCu
0 at 0 at CuCu
18 at 18 at CuCu
8 at 8 at CuCu
95 at 95 at CuCu
95 at 95 at CuCu
18 at 18 at CuCu
Ts (Cu95Fe5)Ts (Cu95Fe5)
Ts (Cu20Fe80)Ts (Cu20Fe80)
Ts (Cu20Fe80)Ts (Cu20Fe80)
Ts (Cu20Fe80)Ts (Cu20Fe80)C(M) at ‐ C(M) = Csteelγ(M) 100M = Fe CrNi γ(M) ‐molar part of M in original steel
C(M) at ‐ C(M) = Csteelγ(M) 100M = Fe CrNi γ(M) ‐molar part of M in original steel
Post treatmentPost treatment
Initial conditions
8
Emulsion model choice of start points of diffusionEmulsion model choice of start points of diffusion
Diffusion starts immediately after beam pass and Diffusion starts immediately after beam pass and small globulas do existsmall globulas do exist
Small globulas would be dissolvedFront of diffusion is too large
Diffusion starts after solidification of steel and Diffusion starts after solidification of steel and small globulas do exist from beginningsmall globulas do exist from beginning
There is no diffusion observed
Diffusion starts after beam pass in A and B and Diffusion starts after beam pass in A and B and after Ts (Cu20Fe80) at the regions C D E ad F after Ts (Cu20Fe80) at the regions C D E ad F (when small globulas are already formed (when small globulas are already formed during undercooling of the weld)during undercooling of the weld)Large diffusion front in AB and small in CD E and F
AA BB CC DD
EE
EE
9
Results Results ldquoldquodropletdropletrdquordquo ldquoldquoemulsionemulsionrdquordquo
FE
10
ValidationValidationComparison between calculated profiles and real copper concentraComparison between calculated profiles and real copper concentration tion founded by SEMfounded by SEM‐‐ESD analysis in ESD analysis in ldquoldquoemulsionemulsionrdquordquo‐‐like (a) and like (a) and ldquoldquodropletdropletrdquordquo‐‐like (b) like (b) microstructures microstructures
Interface Distance micromldquodropletrdquocalculated observed
AD 14 17BD 4 3CD 4 3C2D 24 18
ldquoemulsionrdquocalculated observed
AB 31 29CD 17 14CE 13 11DF 17 23
Comparison of diffusion Comparison of diffusion distances on different interfaces distances on different interfaces
11
ConclusionsConclusions
Present numerical models of Present numerical models of microstructures development are microstructures development are in good correspondence with in good correspondence with SEM images and the results of SEM images and the results of local ESD analysis local ESD analysis
The temperature evolution is The temperature evolution is realisticrealistic
The results confirm our hypothesis The results confirm our hypothesis on the way of microstructure on the way of microstructure formation under different welding formation under different welding conditionsconditions
There are two mechanisms of microstructures formation depending on operational parametens
olaquo dropletraquo structure is formed by eroding of steel surface by copper fluxolaquo emulsionraquo structure is formed under undercooling conditions
There are two mechanisms of microstructures formation depending on operational parametens
olaquo dropletraquo structure is formed by eroding of steel surface by copper fluxolaquo emulsionraquo structure is formed under undercooling conditions
6
Model descriptionModel descriptionCooling laws used in calculations ldquoemulsionrdquo-type
weld (a) ldquodropletrdquo-type weld (b)
)( TktTc p nablaminusnabla=partpartρ
Heat transferHeat transfer
A=Asolid + (Aliquid ndash A solid)flc2hs(T-Tf ) A = k ρ Cp
Tδ Joints ldquoemulsionrdquo ldquodropletrdquoGauss approximation
T(K) = y0 + (A(wsqrt(PI2)))exp(-2(tw)^2)y0 1159264 13338w 001523 00367A 162814 426R2 099 099
The approximations of cooling laws used in calculations
Discontinuity of properties
Heat equation
The position of modeling zone at global geometry of the weld
Boundary conditions
Hot side Cold sideCooling law
Thermal isolation
Hot side
Electron beam
0)( )( =nablasdotminusnabla CuFeCu cD
0)( )( =nablasdotminusnabla FeCuFe cD
)exp(TR
EDDT sdotminussdot= Ddomain=DTflc2hs(Tstart-T )Tδ
copper‐rich zones
steel‐rich zones
7
Model descriptionModel descriptionDiffusionDiffusion
0 at 0 at CuCu
95 at 95 at CuCu
18 at 18 at CuCu
8 at 8 at CuCu
18 at 18 at CuCu
0 at 0 at CuCu
18 at 18 at CuCu
8 at 8 at CuCu
95 at 95 at CuCu
95 at 95 at CuCu
18 at 18 at CuCu
Ts (Cu95Fe5)Ts (Cu95Fe5)
Ts (Cu20Fe80)Ts (Cu20Fe80)
Ts (Cu20Fe80)Ts (Cu20Fe80)
Ts (Cu20Fe80)Ts (Cu20Fe80)C(M) at ‐ C(M) = Csteelγ(M) 100M = Fe CrNi γ(M) ‐molar part of M in original steel
C(M) at ‐ C(M) = Csteelγ(M) 100M = Fe CrNi γ(M) ‐molar part of M in original steel
Post treatmentPost treatment
Initial conditions
8
Emulsion model choice of start points of diffusionEmulsion model choice of start points of diffusion
Diffusion starts immediately after beam pass and Diffusion starts immediately after beam pass and small globulas do existsmall globulas do exist
Small globulas would be dissolvedFront of diffusion is too large
Diffusion starts after solidification of steel and Diffusion starts after solidification of steel and small globulas do exist from beginningsmall globulas do exist from beginning
There is no diffusion observed
Diffusion starts after beam pass in A and B and Diffusion starts after beam pass in A and B and after Ts (Cu20Fe80) at the regions C D E ad F after Ts (Cu20Fe80) at the regions C D E ad F (when small globulas are already formed (when small globulas are already formed during undercooling of the weld)during undercooling of the weld)Large diffusion front in AB and small in CD E and F
AA BB CC DD
EE
EE
9
Results Results ldquoldquodropletdropletrdquordquo ldquoldquoemulsionemulsionrdquordquo
FE
10
ValidationValidationComparison between calculated profiles and real copper concentraComparison between calculated profiles and real copper concentration tion founded by SEMfounded by SEM‐‐ESD analysis in ESD analysis in ldquoldquoemulsionemulsionrdquordquo‐‐like (a) and like (a) and ldquoldquodropletdropletrdquordquo‐‐like (b) like (b) microstructures microstructures
Interface Distance micromldquodropletrdquocalculated observed
AD 14 17BD 4 3CD 4 3C2D 24 18
ldquoemulsionrdquocalculated observed
AB 31 29CD 17 14CE 13 11DF 17 23
Comparison of diffusion Comparison of diffusion distances on different interfaces distances on different interfaces
11
ConclusionsConclusions
Present numerical models of Present numerical models of microstructures development are microstructures development are in good correspondence with in good correspondence with SEM images and the results of SEM images and the results of local ESD analysis local ESD analysis
The temperature evolution is The temperature evolution is realisticrealistic
The results confirm our hypothesis The results confirm our hypothesis on the way of microstructure on the way of microstructure formation under different welding formation under different welding conditionsconditions
There are two mechanisms of microstructures formation depending on operational parametens
olaquo dropletraquo structure is formed by eroding of steel surface by copper fluxolaquo emulsionraquo structure is formed under undercooling conditions
There are two mechanisms of microstructures formation depending on operational parametens
olaquo dropletraquo structure is formed by eroding of steel surface by copper fluxolaquo emulsionraquo structure is formed under undercooling conditions
0)( )( =nablasdotminusnabla CuFeCu cD
0)( )( =nablasdotminusnabla FeCuFe cD
)exp(TR
EDDT sdotminussdot= Ddomain=DTflc2hs(Tstart-T )Tδ
copper‐rich zones
steel‐rich zones
7
Model descriptionModel descriptionDiffusionDiffusion
0 at 0 at CuCu
95 at 95 at CuCu
18 at 18 at CuCu
8 at 8 at CuCu
18 at 18 at CuCu
0 at 0 at CuCu
18 at 18 at CuCu
8 at 8 at CuCu
95 at 95 at CuCu
95 at 95 at CuCu
18 at 18 at CuCu
Ts (Cu95Fe5)Ts (Cu95Fe5)
Ts (Cu20Fe80)Ts (Cu20Fe80)
Ts (Cu20Fe80)Ts (Cu20Fe80)
Ts (Cu20Fe80)Ts (Cu20Fe80)C(M) at ‐ C(M) = Csteelγ(M) 100M = Fe CrNi γ(M) ‐molar part of M in original steel
C(M) at ‐ C(M) = Csteelγ(M) 100M = Fe CrNi γ(M) ‐molar part of M in original steel
Post treatmentPost treatment
Initial conditions
8
Emulsion model choice of start points of diffusionEmulsion model choice of start points of diffusion
Diffusion starts immediately after beam pass and Diffusion starts immediately after beam pass and small globulas do existsmall globulas do exist
Small globulas would be dissolvedFront of diffusion is too large
Diffusion starts after solidification of steel and Diffusion starts after solidification of steel and small globulas do exist from beginningsmall globulas do exist from beginning
There is no diffusion observed
Diffusion starts after beam pass in A and B and Diffusion starts after beam pass in A and B and after Ts (Cu20Fe80) at the regions C D E ad F after Ts (Cu20Fe80) at the regions C D E ad F (when small globulas are already formed (when small globulas are already formed during undercooling of the weld)during undercooling of the weld)Large diffusion front in AB and small in CD E and F
AA BB CC DD
EE
EE
9
Results Results ldquoldquodropletdropletrdquordquo ldquoldquoemulsionemulsionrdquordquo
FE
10
ValidationValidationComparison between calculated profiles and real copper concentraComparison between calculated profiles and real copper concentration tion founded by SEMfounded by SEM‐‐ESD analysis in ESD analysis in ldquoldquoemulsionemulsionrdquordquo‐‐like (a) and like (a) and ldquoldquodropletdropletrdquordquo‐‐like (b) like (b) microstructures microstructures
Interface Distance micromldquodropletrdquocalculated observed
AD 14 17BD 4 3CD 4 3C2D 24 18
ldquoemulsionrdquocalculated observed
AB 31 29CD 17 14CE 13 11DF 17 23
Comparison of diffusion Comparison of diffusion distances on different interfaces distances on different interfaces
11
ConclusionsConclusions
Present numerical models of Present numerical models of microstructures development are microstructures development are in good correspondence with in good correspondence with SEM images and the results of SEM images and the results of local ESD analysis local ESD analysis
The temperature evolution is The temperature evolution is realisticrealistic
The results confirm our hypothesis The results confirm our hypothesis on the way of microstructure on the way of microstructure formation under different welding formation under different welding conditionsconditions
There are two mechanisms of microstructures formation depending on operational parametens
olaquo dropletraquo structure is formed by eroding of steel surface by copper fluxolaquo emulsionraquo structure is formed under undercooling conditions
There are two mechanisms of microstructures formation depending on operational parametens
olaquo dropletraquo structure is formed by eroding of steel surface by copper fluxolaquo emulsionraquo structure is formed under undercooling conditions
8
Emulsion model choice of start points of diffusionEmulsion model choice of start points of diffusion
Diffusion starts immediately after beam pass and Diffusion starts immediately after beam pass and small globulas do existsmall globulas do exist
Small globulas would be dissolvedFront of diffusion is too large
Diffusion starts after solidification of steel and Diffusion starts after solidification of steel and small globulas do exist from beginningsmall globulas do exist from beginning
There is no diffusion observed
Diffusion starts after beam pass in A and B and Diffusion starts after beam pass in A and B and after Ts (Cu20Fe80) at the regions C D E ad F after Ts (Cu20Fe80) at the regions C D E ad F (when small globulas are already formed (when small globulas are already formed during undercooling of the weld)during undercooling of the weld)Large diffusion front in AB and small in CD E and F
AA BB CC DD
EE
EE
9
Results Results ldquoldquodropletdropletrdquordquo ldquoldquoemulsionemulsionrdquordquo
FE
10
ValidationValidationComparison between calculated profiles and real copper concentraComparison between calculated profiles and real copper concentration tion founded by SEMfounded by SEM‐‐ESD analysis in ESD analysis in ldquoldquoemulsionemulsionrdquordquo‐‐like (a) and like (a) and ldquoldquodropletdropletrdquordquo‐‐like (b) like (b) microstructures microstructures
Interface Distance micromldquodropletrdquocalculated observed
AD 14 17BD 4 3CD 4 3C2D 24 18
ldquoemulsionrdquocalculated observed
AB 31 29CD 17 14CE 13 11DF 17 23
Comparison of diffusion Comparison of diffusion distances on different interfaces distances on different interfaces
11
ConclusionsConclusions
Present numerical models of Present numerical models of microstructures development are microstructures development are in good correspondence with in good correspondence with SEM images and the results of SEM images and the results of local ESD analysis local ESD analysis
The temperature evolution is The temperature evolution is realisticrealistic
The results confirm our hypothesis The results confirm our hypothesis on the way of microstructure on the way of microstructure formation under different welding formation under different welding conditionsconditions
There are two mechanisms of microstructures formation depending on operational parametens
olaquo dropletraquo structure is formed by eroding of steel surface by copper fluxolaquo emulsionraquo structure is formed under undercooling conditions
There are two mechanisms of microstructures formation depending on operational parametens
olaquo dropletraquo structure is formed by eroding of steel surface by copper fluxolaquo emulsionraquo structure is formed under undercooling conditions
9
Results Results ldquoldquodropletdropletrdquordquo ldquoldquoemulsionemulsionrdquordquo
FE
10
ValidationValidationComparison between calculated profiles and real copper concentraComparison between calculated profiles and real copper concentration tion founded by SEMfounded by SEM‐‐ESD analysis in ESD analysis in ldquoldquoemulsionemulsionrdquordquo‐‐like (a) and like (a) and ldquoldquodropletdropletrdquordquo‐‐like (b) like (b) microstructures microstructures
Interface Distance micromldquodropletrdquocalculated observed
AD 14 17BD 4 3CD 4 3C2D 24 18
ldquoemulsionrdquocalculated observed
AB 31 29CD 17 14CE 13 11DF 17 23
Comparison of diffusion Comparison of diffusion distances on different interfaces distances on different interfaces
11
ConclusionsConclusions
Present numerical models of Present numerical models of microstructures development are microstructures development are in good correspondence with in good correspondence with SEM images and the results of SEM images and the results of local ESD analysis local ESD analysis
The temperature evolution is The temperature evolution is realisticrealistic
The results confirm our hypothesis The results confirm our hypothesis on the way of microstructure on the way of microstructure formation under different welding formation under different welding conditionsconditions
There are two mechanisms of microstructures formation depending on operational parametens
olaquo dropletraquo structure is formed by eroding of steel surface by copper fluxolaquo emulsionraquo structure is formed under undercooling conditions
There are two mechanisms of microstructures formation depending on operational parametens
olaquo dropletraquo structure is formed by eroding of steel surface by copper fluxolaquo emulsionraquo structure is formed under undercooling conditions
10
ValidationValidationComparison between calculated profiles and real copper concentraComparison between calculated profiles and real copper concentration tion founded by SEMfounded by SEM‐‐ESD analysis in ESD analysis in ldquoldquoemulsionemulsionrdquordquo‐‐like (a) and like (a) and ldquoldquodropletdropletrdquordquo‐‐like (b) like (b) microstructures microstructures
Interface Distance micromldquodropletrdquocalculated observed
AD 14 17BD 4 3CD 4 3C2D 24 18
ldquoemulsionrdquocalculated observed
AB 31 29CD 17 14CE 13 11DF 17 23
Comparison of diffusion Comparison of diffusion distances on different interfaces distances on different interfaces
11
ConclusionsConclusions
Present numerical models of Present numerical models of microstructures development are microstructures development are in good correspondence with in good correspondence with SEM images and the results of SEM images and the results of local ESD analysis local ESD analysis
The temperature evolution is The temperature evolution is realisticrealistic
The results confirm our hypothesis The results confirm our hypothesis on the way of microstructure on the way of microstructure formation under different welding formation under different welding conditionsconditions
There are two mechanisms of microstructures formation depending on operational parametens
olaquo dropletraquo structure is formed by eroding of steel surface by copper fluxolaquo emulsionraquo structure is formed under undercooling conditions
There are two mechanisms of microstructures formation depending on operational parametens
olaquo dropletraquo structure is formed by eroding of steel surface by copper fluxolaquo emulsionraquo structure is formed under undercooling conditions
11
ConclusionsConclusions
Present numerical models of Present numerical models of microstructures development are microstructures development are in good correspondence with in good correspondence with SEM images and the results of SEM images and the results of local ESD analysis local ESD analysis
The temperature evolution is The temperature evolution is realisticrealistic
The results confirm our hypothesis The results confirm our hypothesis on the way of microstructure on the way of microstructure formation under different welding formation under different welding conditionsconditions
There are two mechanisms of microstructures formation depending on operational parametens
olaquo dropletraquo structure is formed by eroding of steel surface by copper fluxolaquo emulsionraquo structure is formed under undercooling conditions
There are two mechanisms of microstructures formation depending on operational parametens
olaquo dropletraquo structure is formed by eroding of steel surface by copper fluxolaquo emulsionraquo structure is formed under undercooling conditions