HIGH SPEED FSW MODELING Vanderbilt University: Welding and Automation Laboratory: Nashville, TN Dr....

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HIGH SPEED FSW HIGH SPEED FSW MODELING MODELING Vanderbilt University: Vanderbilt University: Welding and Automation Welding and Automation Laboratory: Nashville, TN Laboratory: Nashville, TN Dr. Reginald Crawford Dr. Reginald Crawford Thomas S. Bloodworth III Thomas S. Bloodworth III Paul A. Fleming Paul A. Fleming David H. Lammlein David H. Lammlein Tracie Prater Tracie Prater Dr. George E. Cook Dr. George E. Cook Dr. Alvin M. Strauss Dr. Alvin M. Strauss Dr. D. Mitch Wilkes Dr. D. Mitch Wilkes Los Alamos National Los Alamos National Laboratory: Los Alamos, NM. Laboratory: Los Alamos, NM. Dr. Daniel A. Hartman Dr. Daniel A. Hartman

Transcript of HIGH SPEED FSW MODELING Vanderbilt University: Welding and Automation Laboratory: Nashville, TN Dr....

Page 1: HIGH SPEED FSW MODELING Vanderbilt University: Welding and Automation Laboratory: Nashville, TN Dr. Reginald Crawford Thomas S. Bloodworth III Paul A.

HIGH SPEED FSW HIGH SPEED FSW MODELINGMODELING

Vanderbilt University: Welding and Vanderbilt University: Welding and Automation Laboratory: Nashville, TNAutomation Laboratory: Nashville, TN

Dr. Reginald CrawfordDr. Reginald CrawfordThomas S. Bloodworth IIIThomas S. Bloodworth IIIPaul A. FlemingPaul A. FlemingDavid H. LammleinDavid H. LammleinTracie PraterTracie PraterDr. George E. CookDr. George E. CookDr. Alvin M. StraussDr. Alvin M. StraussDr. D. Mitch WilkesDr. D. Mitch Wilkes

Los Alamos National Laboratory: Los Los Alamos National Laboratory: Los Alamos, NM.Alamos, NM.

Dr. Daniel A. HartmanDr. Daniel A. Hartman

Page 2: HIGH SPEED FSW MODELING Vanderbilt University: Welding and Automation Laboratory: Nashville, TN Dr. Reginald Crawford Thomas S. Bloodworth III Paul A.

OVERVIEWOVERVIEW

1.1. IntroductionIntroduction

2.2. Experimental Method/SetupExperimental Method/Setup

3.3. Mechanical ModelsMechanical Models

4.4. SimulationSimulation

5.5. ResultsResults

6.6. ConclusionsConclusions

7.7. Current and Future WorkCurrent and Future Work

Page 3: HIGH SPEED FSW MODELING Vanderbilt University: Welding and Automation Laboratory: Nashville, TN Dr. Reginald Crawford Thomas S. Bloodworth III Paul A.

INTRODUCTIONINTRODUCTION Current uses of FSW:Current uses of FSW:

Aerospace (Spirit, Boeing, Airbus)Aerospace (Spirit, Boeing, Airbus) Railway (Hitachi Rail)Railway (Hitachi Rail) Shipbuilding/marine (Naval vessels)Shipbuilding/marine (Naval vessels) Construction industries and others (Audi)Construction industries and others (Audi)

Moving to lighter materials (e.g. Aluminum)Moving to lighter materials (e.g. Aluminum)

ConflictConflict: 3-D contours difficult with heavy duty : 3-D contours difficult with heavy duty machine tool type equipmentmachine tool type equipment

Page 4: HIGH SPEED FSW MODELING Vanderbilt University: Welding and Automation Laboratory: Nashville, TN Dr. Reginald Crawford Thomas S. Bloodworth III Paul A.

INTRODUCTIONINTRODUCTION Ideally see widely applicable industrial robots equipped for Ideally see widely applicable industrial robots equipped for

FSWFSW

BenefitsBenefits:: lower costslower costs energy efficientenergy efficient 3-D contours etc.3-D contours etc.

ProblemProblem: High axial forces required to FSW (1-12+ kN or 225-: High axial forces required to FSW (1-12+ kN or 225-2700+ lbs), difficult to maintain even using robust robots 2700+ lbs), difficult to maintain even using robust robots especially at large distances from the base unitespecially at large distances from the base unit

Possible solutionPossible solution: Utilize increased rotational : Utilize increased rotational speed/decreased axial force relationship to aid in developing speed/decreased axial force relationship to aid in developing a larger operational envelope for high speed FSWa larger operational envelope for high speed FSW

Page 5: HIGH SPEED FSW MODELING Vanderbilt University: Welding and Automation Laboratory: Nashville, TN Dr. Reginald Crawford Thomas S. Bloodworth III Paul A.

EXPERIMENTAL METHODEXPERIMENTAL METHOD PurposePurpose: Examine axial forces during high speed friction : Examine axial forces during high speed friction

stir welding with respect to mechanistic defect stir welding with respect to mechanistic defect development due to process parameter variationdevelopment due to process parameter variation

Two Mechanical ModelsTwo Mechanical Models Smooth Tool Pin (Preliminary)Smooth Tool Pin (Preliminary) Threaded Tool Pin (More Comprehensive)Threaded Tool Pin (More Comprehensive)

Parameters (Variables) Rotational Speed (RS) Travel Speed (TS)

Page 6: HIGH SPEED FSW MODELING Vanderbilt University: Welding and Automation Laboratory: Nashville, TN Dr. Reginald Crawford Thomas S. Bloodworth III Paul A.

EXPERIMENTAL METHODEXPERIMENTAL METHOD

Model solved with CFD package FLUENT for Model solved with CFD package FLUENT for steady state solutionssteady state solutions

Force simulated for the three spatial dimensions Force simulated for the three spatial dimensions as well as torqueas well as torque

Experimental force and torque data recorded Experimental force and torque data recorded using a Kistler dynamometer (RCD) Type 9124 Busing a Kistler dynamometer (RCD) Type 9124 B

Page 7: HIGH SPEED FSW MODELING Vanderbilt University: Welding and Automation Laboratory: Nashville, TN Dr. Reginald Crawford Thomas S. Bloodworth III Paul A.

EXPERIMENTAL SETUPEXPERIMENTAL SETUP VU FSW Test BedVU FSW Test Bed: Milwaukee #2K Universal : Milwaukee #2K Universal

Milling Machine utilizing a Kearney and Treker Milling Machine utilizing a Kearney and Treker Heavy Duty Vertical Head Attachment modified Heavy Duty Vertical Head Attachment modified to accommodate high spindle speeds.to accommodate high spindle speeds.

SamplesSamples- AA 6061-T6: 76.2 x 457.2 x 6.35 mm - AA 6061-T6: 76.2 x 457.2 x 6.35 mm (3 x 18 x ¼”)(3 x 18 x ¼”)

Rotational SpeedsRotational Speeds: 1000-5000 RPM: 1000-5000 RPM

Travel SpeedsTravel Speeds: 290 - 1600 mm min: 290 - 1600 mm min-1 -1

(11.4 in min(11.4 in min-1-1 – 63 in min – 63 in min-1-1))

Page 8: HIGH SPEED FSW MODELING Vanderbilt University: Welding and Automation Laboratory: Nashville, TN Dr. Reginald Crawford Thomas S. Bloodworth III Paul A.

Backing Plate

Air/Oil Lube System

Air/Oil Delivery Lines

V-Belt and Pulley System

20 HP Motor

Axial Position Monitor

Vertical Head

Dynamometer

Tool

Sample

VUWAL Test BedVUWAL Test Bed

Page 9: HIGH SPEED FSW MODELING Vanderbilt University: Welding and Automation Laboratory: Nashville, TN Dr. Reginald Crawford Thomas S. Bloodworth III Paul A.

EXPERIMENTAL SETUPEXPERIMENTAL SETUP The tool was set up for a constant 2The tool was set up for a constant 2oo lead angle lead angle

Fine adjustments in plunge depth have been Fine adjustments in plunge depth have been noted to create significant changes in force data noted to create significant changes in force data as well as excess flash buildupas well as excess flash buildup

Therefore, significant care and effort was put Therefore, significant care and effort was put forth to ensure constant plunge depth of 3.683 forth to ensure constant plunge depth of 3.683 mm (.145”)mm (.145”)

Shoulder plunge constant: .1016 mm (.0040 in)Shoulder plunge constant: .1016 mm (.0040 in)

Page 10: HIGH SPEED FSW MODELING Vanderbilt University: Welding and Automation Laboratory: Nashville, TN Dr. Reginald Crawford Thomas S. Bloodworth III Paul A.

SMOOTH PIN MODELSMOOTH PIN MODEL Heat transfer to the support anvil ignoredHeat transfer to the support anvil ignored Tool pin and sample finite element mesh Tool pin and sample finite element mesh

consists ofconsists of 22497 tetrahedron brick elements22497 tetrahedron brick elements 5152 nodes5152 nodes

Tool properties were for H-13 tool steel (e.g. Tool properties were for H-13 tool steel (e.g. density, specific heat, and thermal conductivity)density, specific heat, and thermal conductivity)

Assumed to rotate counter-clockwise at RS (LH)Assumed to rotate counter-clockwise at RS (LH) 12.7 mm shank included to account for heat 12.7 mm shank included to account for heat

conduction from the tool/sample interfaceconduction from the tool/sample interface

Page 11: HIGH SPEED FSW MODELING Vanderbilt University: Welding and Automation Laboratory: Nashville, TN Dr. Reginald Crawford Thomas S. Bloodworth III Paul A.

SMOOTH PIN MODELSMOOTH PIN MODEL Tool assumed to rotate with Tool assumed to rotate with

uniform and constant uniform and constant angular velocity, RS. angular velocity, RS.

Weld material is assumed Weld material is assumed incoming from the left upon incoming from the left upon the rotating toolthe rotating tool

Origin of the system is Origin of the system is interface at the center of the interface at the center of the pin bottom and the samplepin bottom and the sample

Sample given metallurgic Sample given metallurgic properties (i.e. AA6061-T6)properties (i.e. AA6061-T6)

Flow Domain Outlet

Tool Rotational Direction

Sample Top

Sample Side

Flow DirectionWeld Plate

Tool ShoulderSample Bottom

Flow Domain Inlet Tool Shank

Smooth tool pin

Page 12: HIGH SPEED FSW MODELING Vanderbilt University: Welding and Automation Laboratory: Nashville, TN Dr. Reginald Crawford Thomas S. Bloodworth III Paul A.

THREADED PIN MODELTHREADED PIN MODEL 22ndnd Model incorporates Model incorporates

the #10-24 TPI Left-the #10-24 TPI Left-Handed threadHanded thread

Incorporates the threaded Incorporates the threaded tool pin, and heat sinks tool pin, and heat sinks on the shankon the shank

Heat conductivity to the Heat conductivity to the anvil is includedanvil is included

Identical metallurgic Identical metallurgic properties given to pin properties given to pin and sample as the and sample as the smooth pin modelsmooth pin model

Anvil properties - Cold Anvil properties - Cold rolled steelrolled steel

Page 13: HIGH SPEED FSW MODELING Vanderbilt University: Welding and Automation Laboratory: Nashville, TN Dr. Reginald Crawford Thomas S. Bloodworth III Paul A.

THREADED PIN MODELTHREADED PIN MODEL Tool mesh:Tool mesh:

37051 tetrahedron brick elements37051 tetrahedron brick elements 8324 nodes8324 nodes

Sample mesh:Sample mesh: 92018 tetrahedron brick elements92018 tetrahedron brick elements 20672 nodes20672 nodes

Anvil mesh:Anvil mesh: 42200 quadrilateral brick elements42200 quadrilateral brick elements 24024 nodes24024 nodes

Density of mesh increases with respect to the pin/weld Density of mesh increases with respect to the pin/weld material interfacematerial interface

Page 14: HIGH SPEED FSW MODELING Vanderbilt University: Welding and Automation Laboratory: Nashville, TN Dr. Reginald Crawford Thomas S. Bloodworth III Paul A.

FLUENT: ASSIGNMENTS AND FLUENT: ASSIGNMENTS AND ASSUMPTIONSASSUMPTIONS

GoalGoal: Compare the two models’ steady state welding : Compare the two models’ steady state welding conditions with experimentally determined dataconditions with experimentally determined data

Flow inlet given constant flow rate (TS)Flow inlet given constant flow rate (TS)

Zero heat flux conditionZero heat flux condition bounding regions transfer no heat to/from the weldbounding regions transfer no heat to/from the weld

No-slip (sticking) conditionNo-slip (sticking) condition all rotational velocity of the tool is transmitted to the weld all rotational velocity of the tool is transmitted to the weld

material at the interfacematerial at the interface

Temperature was simulated for both mechanical modelsTemperature was simulated for both mechanical models

Page 15: HIGH SPEED FSW MODELING Vanderbilt University: Welding and Automation Laboratory: Nashville, TN Dr. Reginald Crawford Thomas S. Bloodworth III Paul A.

TEMPERATURE SIMULATIONTEMPERATURE SIMULATION Temperature was simulated using the heat generation model developed Temperature was simulated using the heat generation model developed

by Schmidt H. et al. The contact stress is approximated as,by Schmidt H. et al. The contact stress is approximated as,

= 241 MPa, AA 6061-T6

•The total heat generation approximated as:

w0 = rotational speed of tool

Rs = shoulder radius

Rp = pin radius

h = height of the pin•Solutions were generally of the order 104 W/mm3

Page 16: HIGH SPEED FSW MODELING Vanderbilt University: Welding and Automation Laboratory: Nashville, TN Dr. Reginald Crawford Thomas S. Bloodworth III Paul A.

TEMPERATURE CONTINUEDTEMPERATURE CONTINUED Subsequent simulations to determine welding Subsequent simulations to determine welding

temperature were run and input into FLUENT via user temperature were run and input into FLUENT via user defined C codedefined C code

Method inherently ignores transient state including initial Method inherently ignores transient state including initial plunge and TS ramp up; creates an isothermal modelplunge and TS ramp up; creates an isothermal model

The Visco Plastic model used to determine flow stress The Visco Plastic model used to determine flow stress and viscosity ( and and viscosity ( and mm respectively) respectively)

Weld plate region: visco-plastic materialWeld plate region: visco-plastic material

Page 17: HIGH SPEED FSW MODELING Vanderbilt University: Welding and Automation Laboratory: Nashville, TN Dr. Reginald Crawford Thomas S. Bloodworth III Paul A.

VISCO-PLASTIC MODELVISCO-PLASTIC MODEL

Seidel, Ulysse, Colegrove et al. implemented VP model Seidel, Ulysse, Colegrove et al. implemented VP model very successfully at relatively low wvery successfully at relatively low wp p

RSRS: 500 rpm : 500 rpm TSTS: 120 mm min: 120 mm min-1-1 (5.11 in min (5.11 in min-1-1))

High wHigh wpp implies: implies: Increase RS orIncrease RS or Decrease TSDecrease TS

Geometries use VP model with 10-13 fold parametric Geometries use VP model with 10-13 fold parametric increase accuratelyincrease accurately

Page 18: HIGH SPEED FSW MODELING Vanderbilt University: Welding and Automation Laboratory: Nashville, TN Dr. Reginald Crawford Thomas S. Bloodworth III Paul A.

VISCO-PLASTIC MODELVISCO-PLASTIC MODEL

The VP model The VP model determines stress as,determines stress as,

Constants and Variables

Z = Zener-Hollomon parameter

R = Universal gas constant

T = absolute temperature (K)

= effective strain-rate

a, A, n, and Q = material constants

•The model is therefore a function of Temperature, T, and the effective strain-rate,

•Viscosity is approximated as,

Page 19: HIGH SPEED FSW MODELING Vanderbilt University: Welding and Automation Laboratory: Nashville, TN Dr. Reginald Crawford Thomas S. Bloodworth III Paul A.

AXIAL FORCE SIMULATIONAXIAL FORCE SIMULATION

Smooth pin model: a reference pressure was Smooth pin model: a reference pressure was included to compensate for the lack of an anvil included to compensate for the lack of an anvil (open domain)(open domain) PPrefref = F = FZZ/A/App

Threaded pin model includes anvil:Threaded pin model includes anvil: no reference pressure is necessary (closed domain)no reference pressure is necessary (closed domain)

Page 20: HIGH SPEED FSW MODELING Vanderbilt University: Welding and Automation Laboratory: Nashville, TN Dr. Reginald Crawford Thomas S. Bloodworth III Paul A.

PROCEDUREPROCEDURE Experimental sequence performed by holding the TS constant Experimental sequence performed by holding the TS constant

and increasing the RS incrementally until the weld matrix set and increasing the RS incrementally until the weld matrix set was either complete or excessive surface defect occurredwas either complete or excessive surface defect occurred

Samples etched for inspection for worm-holes (low wSamples etched for inspection for worm-holes (low wpp))

2250 RPM, 289.56 mm min-1

3000 RPM, 289.56 mm min-1

1500 RPM 2250 RPM 3000 RPM 3750 RPM

Surface deformation

944.88 mm min-1 1137 mm min-1 1353 mm min-1 1607 mm min-1

Page 21: HIGH SPEED FSW MODELING Vanderbilt University: Welding and Automation Laboratory: Nashville, TN Dr. Reginald Crawford Thomas S. Bloodworth III Paul A.

RESULTSRESULTS

Both models correlate well with experimental resultsBoth models correlate well with experimental results Greater convergence at high wGreater convergence at high wpp

Increased RS/decreased FIncreased RS/decreased Fzz relationship continues for relationship continues for

high speed FSWhigh speed FSW

TS=685.9mm min-1 (27 in min-1) TS=1137.92mm min-1 (44.8 in min-1)

Page 22: HIGH SPEED FSW MODELING Vanderbilt University: Welding and Automation Laboratory: Nashville, TN Dr. Reginald Crawford Thomas S. Bloodworth III Paul A.

RESULTSRESULTS FFzz increases as expected for increases as expected for

increasing TS when RS constantincreasing TS when RS constant

Limit to the RS increase/FLimit to the RS increase/Fzz decrease not met decrease not met

This relationship is key to This relationship is key to widespread implementation of widespread implementation of FSWFSW

It is also well known that welding It is also well known that welding torque decreases for increased torque decreases for increased RSRS MMzz<50 N @ RS>1500 rpm <50 N @ RS>1500 rpm

(M(Mzz<13 lbs)<13 lbs)

Fz vs. TS for RS = 1500 rpm

Mz vs. RS for TS = 685.9 mm min-1

Page 23: HIGH SPEED FSW MODELING Vanderbilt University: Welding and Automation Laboratory: Nashville, TN Dr. Reginald Crawford Thomas S. Bloodworth III Paul A.

CONCLUSIONSCONCLUSIONS The smooth pin model correlated better than the The smooth pin model correlated better than the

threaded pin model for all simulationsthreaded pin model for all simulations

However, threaded model more accurately represents However, threaded model more accurately represents the experimental setupthe experimental setup anvil, heat sinks, pin profileanvil, heat sinks, pin profile

Increase in RS led to greater correlation in both models Increase in RS led to greater correlation in both models with respect to the experimental datawith respect to the experimental data

Barrier to high speed FSW is overheating and Barrier to high speed FSW is overheating and subsequent surface flashsubsequent surface flash

Page 24: HIGH SPEED FSW MODELING Vanderbilt University: Welding and Automation Laboratory: Nashville, TN Dr. Reginald Crawford Thomas S. Bloodworth III Paul A.

FUTURE WORKFUTURE WORK Possible solutions to high speed FSW Possible solutions to high speed FSW

problemsproblems Non-rotating, floating, or differentially Non-rotating, floating, or differentially

rotating shoulderrotating shoulder Implementing force control schemeImplementing force control scheme

Other control possibilities include Other control possibilities include acoustic signal analysis, temperature acoustic signal analysis, temperature analysis, etc.analysis, etc.

Currently implementing three axes of Currently implementing three axes of linear position control as well as linear position control as well as thermal imagery as a possible segway thermal imagery as a possible segway to future control schemesto future control schemes

Latest rotational speeds exceeding Latest rotational speeds exceeding 6500 RPM6500 RPM

Latest travel speeds exceed 3810 mm Latest travel speeds exceed 3810 mm minmin-1-1 (150 in min (150 in min-1-1))

Repeat using butt weld configuration Repeat using butt weld configuration and investigate unconventional weld and investigate unconventional weld defects through various stress testingdefects through various stress testing

Linear Position Encoders

Thermal Camera Dynamometer

Motor Feedback

Schematic of most recent VUWAL data collection instrumentation

Page 25: HIGH SPEED FSW MODELING Vanderbilt University: Welding and Automation Laboratory: Nashville, TN Dr. Reginald Crawford Thomas S. Bloodworth III Paul A.

ACKNOWLEDGEMENTSACKNOWLEDGEMENTS Completion of this was made possible through Completion of this was made possible through

support provided by an American Welding support provided by an American Welding Society and a NASA GSRP Fellowship grantSociety and a NASA GSRP Fellowship grant

Additional funding was provided by the NASA Additional funding was provided by the NASA Space Grant Consortium of Tennessee and Los Space Grant Consortium of Tennessee and Los Alamos Natl. Laboratory. Los Alamos, NMAlamos Natl. Laboratory. Los Alamos, NM

Dr. Author C. Nunes of the NASA Marshall Dr. Author C. Nunes of the NASA Marshall Space Flight Center provided valuable expertise Space Flight Center provided valuable expertise and guidance through private communication and guidance through private communication which contributed to the completion of this workwhich contributed to the completion of this work

Page 26: HIGH SPEED FSW MODELING Vanderbilt University: Welding and Automation Laboratory: Nashville, TN Dr. Reginald Crawford Thomas S. Bloodworth III Paul A.

REFERENCESREFERENCES Cook G.E., Crawford R., Clark D.E. and Strauss A.M.: ‘Robotic Cook G.E., Crawford R., Clark D.E. and Strauss A.M.: ‘Robotic

Friction Stir Welding’. Industrial Robot 2004 31 (1) 55-63.Friction Stir Welding’. Industrial Robot 2004 31 (1) 55-63.

Mills K.C.: Recommended Values of Thermo-physical Properties for Mills K.C.: Recommended Values of Thermo-physical Properties for Commercial Alloys. Cambridge, UK 2002. Commercial Alloys. Cambridge, UK 2002.

Schmidt H., Hattel J. and Wert J.: ‘An Analytical Model for the Heat Schmidt H., Hattel J. and Wert J.: ‘An Analytical Model for the Heat Generation in Friction Stir Welding’. Modeling and Simulation in Generation in Friction Stir Welding’. Modeling and Simulation in Materials Science and Engineering 2004 12 143–57. Materials Science and Engineering 2004 12 143–57.

Crawford R: Parametric Quantification of Friction Stir Welding. M.S. Crawford R: Parametric Quantification of Friction Stir Welding. M.S. Thesis, Vanderbilt University, Nashville, Tennessee 2005.Thesis, Vanderbilt University, Nashville, Tennessee 2005.

Seidel T. U. and Reynolds A.P.: ‘Seidel T. U. and Reynolds A.P.: ‘Two-dimensional friction stir Two-dimensional friction stir welding process model based on fluid mechanics’.welding process model based on fluid mechanics’. Science and Science and Technology of Welding & Joining Technology of Welding & Joining 2003 8 (3), 175-83. 2003 8 (3), 175-83.

Page 27: HIGH SPEED FSW MODELING Vanderbilt University: Welding and Automation Laboratory: Nashville, TN Dr. Reginald Crawford Thomas S. Bloodworth III Paul A.

REFERENCESREFERENCES Colgrove P.A. and Shercliff H.R.: ‘Colgrove P.A. and Shercliff H.R.: ‘Development of Trivex friction stir Development of Trivex friction stir

welding tool Part 2 – three-dimensional flow modelling’. Science and welding tool Part 2 – three-dimensional flow modelling’. Science and Technology of Welding & Joining Technology of Welding & Joining 2004, 9(3) 352-61.2004, 9(3) 352-61.

Ulysse P.: ’Three-dimensional modeling of the friction stir-welding Ulysse P.: ’Three-dimensional modeling of the friction stir-welding process’ International Journal of Machine Tools & Manufacture 2002 process’ International Journal of Machine Tools & Manufacture 2002 42 1549–57. 42 1549–57.

Sheppard T. and Jackson A.: ‘Constitutive equations for high flow Sheppard T. and Jackson A.: ‘Constitutive equations for high flow stress of aluminum alloys’ Material Science and Technology 1997 stress of aluminum alloys’ Material Science and Technology 1997 13 203-9. 13 203-9.

FLUENT, Fluid Dynamic Analysis Package, version 6.122 Fluid FLUENT, Fluid Dynamic Analysis Package, version 6.122 Fluid Dynamics International, Evanston, IL.Dynamics International, Evanston, IL.

Talia G.E. and Chaudhuri J.: A Combined Experimental and Talia G.E. and Chaudhuri J.: A Combined Experimental and Analytical modeling Approach to Understanding Friction Stir Analytical modeling Approach to Understanding Friction Stir Welding. Department of Mechanical Engineering Presentation, Welding. Department of Mechanical Engineering Presentation, Wichita State University, Wichita State University, Wichita, KS 2004.Wichita, KS 2004.