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