Numerical Simulation of the Friction Stir Welding …fsrl.byu.edu/presentations/Numerical Simulation...

Numerical Simulation of the Numerical Simulation of the Friction Stir Welding Process Friction Stir Welding Process using Lagrangian, Eulerian & using Lagrangian, Eulerian &

ALE ApproachesALE Approaches

Simon GUERDOUX Simon GUERDOUX andand Lionel FOURMENTLionel FOURMENTCEMEF, Ecole des Mines de Paris, FranceCEMEF, Ecole des Mines de Paris, France

TracyTracy NELSON, Michael MILES NELSON, Michael MILES andand Carl SORENSENCarl SORENSENBrighamBrigham Young Young UniversityUniversity, USA, USA

OverviewOverview

BackgroundBackgroundThe Friction Stir Welding ProcessThe Friction Stir Welding ProcessModeling of FSWModeling of FSW

Numerical models : Numerical models : FFORGEORGE33®® & T& THERCASTHERCAST®®

Modeling and experimental resultsModeling and experimental resultsPlunging phase : comparison between Plunging phase : comparison between experimental and numerical resultexperimental and numerical resultWelding phase :Welding phase :Lagrangian / Eulerian simulations capabilitiesLagrangian / Eulerian simulations capabilitiesALE formulation and first resultsALE formulation and first results

Future workFuture work

BackgroundBackground

The ProcessThe Process

Friction Stir Welding ProcessFriction Stir Welding ProcessPatented in 1991 by TWIPatented in 1991 by TWIA solidA solid--state joining processstate joining processPotential commercial and military usersPotential commercial and military users

•• aerospaceaerospace•• automotiveautomotive•• marinemarine

Capable of joiningCapable of joiningaluminum,steel, aluminum,steel, stainless steelstainless steel

1. The process1. The process

I. BackgroundI. Background

2. Modeling of FSW 2. Modeling of FSW

II. Numerical models II. Numerical models FFORGEORGE33®® & T& THERCASTHERCAST®®

3. ALE formulation3. ALE formulation

III. Modeling andIII. Modeling andexperimental resultsexperimental results

1. Plunging phase1. Plunging phase

2. Welding phase2. Welding phase

Future WorkFuture Work

Plunge experimentPlunge experimentFFORGE3ORGE3®® simulationsimulationComparisonComparison

Eulerian SimulationEulerian SimulationLagrangian SimulationLagrangian Simulation

Different descriptionsDifferent descriptions

Dwelling phaseDwelling phaseThe two main stepsThe two main steps

Different main phases of FSWPDifferent main phases of FSWP

Plunging phase Dwelling phase :Plasticization

Welding phase

Advancing side

Retreating side

Weld joint

ωαF

ωω

vplunge

z

x

z

y

z

x

yPlane (y,z)Plane (x,z)

vadvance














Modeling of FSWModeling of FSW

Motivation:Motivation:

Predict material flow: try to minimize heat Predict material flow: try to minimize heat input, and eliminate defectsinput, and eliminate defects

Use to develop better tooling designsUse to develop better tooling designs

Predict mechanical properties of weld:Predict mechanical properties of weld:flow & thermal historyflow & thermal history

=> mechanical properties and eventually => mechanical properties and eventually microstructuremicrostructure














Approaches in literatureApproaches in literature

CFD approach: obtain information on CFD approach: obtain information on material flow, but neglect free surface material flow, but neglect free surface deformation and effect of deformation historydeformation and effect of deformation history

Lagrangian FE: Lagrangian FE: •• use analytical heat source and apply a use analytical heat source and apply a

compressive stress along the weld line; calculate compressive stress along the weld line; calculate residual stressesresidual stresses

•• simulate material flow, including heat from friction simulate material flow, including heat from friction and material deformation; requires complex and material deformation; requires complex remeshingremeshing

Arbitrary Lagrangian Eulerian (ALE) FE: can Arbitrary Lagrangian Eulerian (ALE) FE: can simulate flow and include heat from friction simulate flow and include heat from friction and deformation; avoids degeneration of and deformation; avoids degeneration of mesh; allows for deformation of free surfacemesh; allows for deformation of free surface














Numerical ModelsNumerical Models

• Hot, warm, and cold forging (FORGE3® )Filling and cooling of foundry parts (THERCAST®)

•3D thermo-mécanical computation

• Lagrangian (FORGE3® ) and /or ALE(THERCAST®) Finite Element Formulation

• Automatic Remeshing

⎪⎩

⎪⎨⎧

=−+∇−∇=−+∇

=−=

0..

03div)(tr vp

γgsγgσ

vε

ρρρρ

α

p

T&&Incompressibility and equilibrium

+ B.C.

FFORGEORGE33®® & T& THERCASTHERCAST®®

( )⎪⎪⎩

⎪⎪⎨

⎧

=

=+=

+=−

Iε

εIσs

εεε

T

Kp TmT

&&

&&

&&&

α

ε εε

th

vp1

),(

thvp

),(32

Pure viscoplastic behaviour (firstly) with thermal couplingStrong form of the mechanical problem :














( )extrc TThT +=⋅∇− nk

» Heat transfert by convection/radiation :

( ) gtool

tooldc v.τTThTbbbk

+++−=⋅∇− n

» Conduction with tools and heat due to friction :

Heat Sources

Norton friction equation :( )⎪⎩

⎪⎨⎧

−−−=Δ

ΔΔ−=<−

ababbaba

1),(f

).()(avec

alors0si f

nnvvvvv

vvτ

g

gp

gTn Kσ εα

aΩ

bΩabΩ∂ abδ

Contact equation :

⎪⎩

⎪⎨⎧

−−≈

≤+

+

Δt).(δδ

δ0tab

tb

ta

tab

Δttab

Δttab

nvv

0Δtδ

).(tabt

abtb

ta ≤−− nvv

ε:σ &&& ==∇− W avec ;Ω dans W)(dtdTc Tkdivρ

Heat Equation

+ B.C.

Strong form of the thermical problem :














•• Time Time discretisationdiscretisation

•• NewtonNewton--RaphsonRaphson algorithmalgorithm

•• Preconditioned Conjugate Gradient solverPreconditioned Conjugate Gradient solver

•• Parallel resolution by mesh partitioningParallel resolution by mesh partitioning

•• Updated Lagrangian formulationUpdated Lagrangian formulationwith automatic with automatic remeshingremeshing (topological, MTC)(topological, MTC)

v,b p

P1+/P1

Velocity Pressure

tVXX tttt Δ+=Δ+

Finite Element discretisation & FORGE3® solveur

( ) 0PVR ttt =,














Modeling and experimental Modeling and experimental resultsresults

Plunging phasePlunging phase

Plunge experimentPlunge experimentThermocouples Thermocouples

•• Weld MaterialWeld Material——12.7 mm to 20.6 mm radius,12.7 mm to 20.6 mm radius,at a depth of 1.6 mmat a depth of 1.6 mm

•• FSW ToolFSW Tool——1.2 mm of depth1.2 mm of depth














•• 6 Second Plunge6 Second Plunge1.19 mm/s plunge speed, 600 RPM1.19 mm/s plunge speed, 600 RPM

•• Lagrangian sensors were placed in Lagrangian sensors were placed in the FSW weld material (1.6 mm)the FSW weld material (1.6 mm)

•• RemeshRemesh every 4 time stepsevery 4 time steps•• Adiabatic contact heat transfer Adiabatic contact heat transfer

condition, Convective cooling on condition, Convective cooling on free surfacesfree surfaces

FFORGEORGE33®® simulationsimulation1. The process1. The process













Comparison :Comparison :experimental / numerical resultsexperimental / numerical results














Numerically Determined Temperatures at Six Thermocouple Locations of the FSW Plunge model in Forge3.

0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00

Tim e (seconds)

Tem

pera

ture

(deg

C) 12.7 mm

14.3 mm

15.9 mm

17.5 mm

19.1 mm

20.6 mm

Experimental Temperatures at Six Thermocouple Locations1.19 mm/s plunge speed--600 RPM

0

50

100

150

200

250

300

350

400

450

500

0.00 2.59 5.18 7.78 10.37 12.96

Time(seconds)

Tem

pera

ture

(deg

C)

-8.00

-7.00

-6.00

-5.00

-4.00

-3.00

-2.00

-1.00

0.00

1.00

2.00

Z po

sitio

n (m

m)

12.7 mm

14.3 mm

15.9 mm

17.5 mm

19.1 mm

20.6 mm

Tool Z Pos ition

Workpiece Temperature RiseWorkpiece Temperature Rise














A Comparison of the Experimental and Forge3 Temperatures at 12.7 mm (6.35 mm Pin Length)

0

50

100

150

200

250

300

350

400

450

500

0 1 2 3 4 5 6 7

Tool Position into the Weld Material (mm)

Tem

pera

ture

(deg

C)

Experimental Temp 12.7 mmForge3 Temp 12.7 mm

•• Weld Material Temperature ProfilesWeld Material Temperature Profiles

Workpiece Temperature RiseWorkpiece Temperature Rise














Tem peratures at Three Tool Locations1.19 m m /s plunge speed--600 RPM

0

100

200

300

400

500

600

0.00 2.59 5.18 7.78 10.37 12.96

Time (seconds)

Tem

pera

ture

(deg

C)

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

Z po

sitio

n (in

ches

)

Shoulder Tem p

Root Tem p

Tip of Pin Tem p

Z Pos ition

•• Tool Temperature and Workpiece IsothermsTool Temperature and Workpiece Isotherms














Geometric data :Geometric data :partpart : 127mm x 127mm x 19mm: 127mm x 127mm x 19mmexperimental welding toolexperimental welding tool (concave shoulder, 3(concave shoulder, 3°° tilted) : tilted) :

pin : pin : ∅∅==8mm , h= 7mm8mm , h= 7mmshoulder : shoulder : ∅∅==25.4mm, h=90mm25.4mm, h=90mm(cooling (cooling 1010°°C forced on 60mm from the top surface)C forced on 60mm from the top surface)

rotational speed : 15 rotation/secondrotational speed : 15 rotation/secondadvance speed : 5 mm/secondadvance speed : 5 mm/second

Thermal and mechanical data :Thermal and mechanical data :Convective exchange with air on all surfaces (Convective exchange with air on all surfaces (hhcrcr=30 W/m=30 W/m²²))Same standard behavior law for Same standard behavior law for aluminumaluminumNorton Norton viscoplasticviscoplastic law : law : coefficient αf from 0.6 at 0°C to 1.1 at 650°C (linear evolution)

q from 1 at 0°C to 0.5 at 650°C (linear evolution)

Density, conductivity, and heat capacity in paperDensity, conductivity, and heat capacity in paper

Welding phaseWelding phase














6s simulation with an arbitrary initial temperature6s simulation with an arbitrary initial temperature

Pure Eulerian Simulation : neglect of free Pure Eulerian Simulation : neglect of free surfaces movement / no surfaces movement / no remeshingremeshing














6s simulation with an arbitrary initial 6s simulation with an arbitrary initial temperature fieldtemperature field














Thermal and mechanical data :Thermal and mechanical data :Adiabatic rigid tool Adiabatic rigid tool heat due to friction and plastic deformation onlyheat due to friction and plastic deformation onlyStandard behavior law for Standard behavior law for aluminum in hot forming process (Hansel aluminum in hot forming process (Hansel SpitelSpitellaw) :law) :

““StrongStrong”” friction (Coulomb law) : friction (Coulomb law) :

εεεσ0011.0

09964.001383.00.0479T−

−−= eAef&

⎪⎪⎩

⎪⎪⎨

⎧

>=

<=

),(),(

),(

6.03.0ΔvΔv6.0

3.0ΔvΔv3.0

εε

ε

στ

σστ

TnT

Tnn

KifK

Kif

Geometric data :Geometric data :partpart : 60mm x 60mm x 20mm: 60mm x 60mm x 20mmsimplified welding toolsimplified welding tool (no concave shoulder, 3(no concave shoulder, 3°° tilted) : tilted) :

pin : pin : ∅∅==6mm , h= 6mm6mm , h= 6mmshoulder : shoulder : ∅∅==20mm, h=60mm20mm, h=60mmrotational speed : 15 rotation/secondrotational speed : 15 rotation/secondadvance speed : 1 mm/second advance speed : 1 mm/second

Lagrangian capabilities : simulation of a Lagrangian capabilities : simulation of a defect during defect during ““cold weldingcold welding””














6s simulation with a low low initial temperature6s simulation with a low low initial temperature














e1

e2

e1

e2

t1t2

Eulerian mesh

e1

e2

e1

e2

t1 t2

Lagrangian mesh

e1

e2

e1

e2

t1 t2

ALE mesh

ALE formulationALE formulation

Different Descriptions :Different Descriptions :1. The process1. The process













⎪⎩

⎪⎨

⎧

−=

∇+=

wvc

c. ϕϕϕ

dtd

dtd g v : material velocity

w : mesh velocity

Splitting Method ( used firstly )= lagrangian iteration + transport on the new mesh

Convective Approach (upwind aspect )

∫+=+

Δt

gtref

ΔttALE dt

d ϕϕϕ

The two main steps of the ALE The two main steps of the ALE description implemented in description implemented in ThercastThercast ::

Convective terms treatment Convective terms treatment 1. The process1. The process












Dwelling phaseDwelling phaseThe two main stepsThe two main steps → Mesh velocity computation : w

Velocity Centering Method

ALE

No Updated Lagrangian Mesh construction

Geometric data :Geometric data :partpart : 127mm x 127mm x 19mm: 127mm x 127mm x 19mmsimplified toolsimplified tool (no concave shoulder, not tilted) : (no concave shoulder, not tilted) :

pin : pin : ∅∅==8mm , h= 7mm8mm , h= 7mmshoulder : shoulder : ∅∅==25.4mm, h=90mm25.4mm, h=90mm(cooling (cooling 1010°°C forced on 60mm from the top surface)C forced on 60mm from the top surface)

rotational speed : 15 rotation/secondrotational speed : 15 rotation/secondno advance speedno advance speed

Thermal and mechanical data :Thermal and mechanical data :ExangeExange with bottom plate model by a coefficient with bottom plate model by a coefficient hhcrcr=300 W/m=300 W/m²² and and exchange with air on other surfaces (exchange with air on other surfaces (hhcrcr=30 W/m=30 W/m²²))Same standard behavior law for Same standard behavior law for aluminumaluminumNorton Norton viscoplasticviscoplastic law law Density, conductivity, and heat capacity depend on temperatureDensity, conductivity, and heat capacity depend on temperature

Temperature map and velocity vectors after 15s

ALE simulation of the dwelling phaseALE simulation of the dwelling phase














•• 15s simulation without any 15s simulation without any remeshingremeshingstability of ALE formulationstability of ALE formulation

(Initial temperature obtained after plunging phase)(Initial temperature obtained after plunging phase)














150

170

190

210

230

250

270

290

310

330

350

0 2 4 6 8 10 12 14 16

time (s)

tem

pera

ture

(°C

)

2 experimental

6 experimental

6 numerical

2 numericalNorton Friction

T (°C) 0 650α 1 2q 1 0.5

Norton FrictionT (°C) 0 650α 0.6 1.1q 0 0.5

Tresca Friction=0.5Tresca Friction

=0.6

ComparisonComparison withwith experimentalexperimental resultsresults














SummarySummary

• Lagrangian, Eulerian, and ALE approaches have been used to simulate FSW, using Forge3® and Thercast®

• The ALE approach is best adapted for modeling this process, because it takes into account changes in the free surface while avoiding element degeneration in high deformation zones

• Implementation of a complete ALE formulation in Forge3® code

• Test of different transport techniques : - nodal upwind- SUPG- MLS / RBF

with use of adaptive remeshing to minimize transport diffusion

• Further comparison between experiment and simulation

• Experimental work to study friction, material behavior, and heat transfer coefficients















Date post:	13-May-2018
Category:	Documents
Upload:	dodat
View:	219 times
Download:	1 times

Numerical Simulation of the Friction Stir Welding …fsrl.byu.edu/presentations/Numerical Simulation...

Documents