2d fe simulation of material flow in the fsw process

Journal of Manufacturing ProcessesVol. 6/No. 2

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AbstractSolid mechanics based finite element models and compu-

tational procedures have been developed by the authors tostudy and simulate the friction stir welding process. In thispaper, two-dimensional simulation results of the material flowpattern and spatial velocity field around the rotating tool pinduring welding, and the positions of material particles aroundthe pin after welding, are presented. Material flow pattern pre-dictions are found to compare favorably with experimentalobservations. Simulation results suggest that material parti-cles in front of the tool pin tend to pass and get behind therotating pin from the retreating side of the pin. Similaritiesbetween predicted velocity fields based on two different tool-workpiece interface models are described in detail, and im-plications of these findings (e.g., to fluid dynamics basedmodels) are discussed.

Keywords: Friction Stir Welding, Material Flow, Finite Ele-ment Simulation, Solid Mechanics Model

IntroductionFriction stir welding (FSW) is a new solid-state

joining process (Thomas et al. 1991) in which join-ing of material is achieved without melting and whichhas been found to be effective for joining hard-to-weld metals, such as aluminum alloys (Dawes andThomas 1996). As such, FSW has many advantagesover traditional fusion welding and has been receiv-ing increasing attention from the industry.

Compared to other joining processes (e.g., gasmetal arc welding), there exist relatively few studiesof FSW in the literature. Most published papers onthis subject (e.g., Mahoney et al. 1998; Murr, Liu,and McClure 1998; Reynolds and Duvall 1999) aredevoted to experimental characterizations of mate-rial properties of friction stir welds. More recent work(Li, Murr, and McClure 1999; Colligan 1999;Reynolds 2000) has focused on observing materialflow patterns in the FSW process.

Theoretical effort aimed at understanding theFSW process, such as computational modeling andsimulation, has been limited mainly because of thecomplexity of this thermomechanical process (e.g.,material flow, temperature rise, large plastic de-formation, contact, and friction). Thermal modelsusually are focused on temperature prediction andneglect the material flow phenomenon. In particu-lar, the papers by McClure et al. (1998) and Gouldand Feng (1998) described analytical methods forcomputing the temperature field, and the study byChao and Qi (1999) used the finite element methodto obtain the temperature field solution. The paperby Russell and Shercliff (1999) presented an ana-lytical model to determine the temperature fieldas well as microstructure evolution. Frigaard,Grong, and Midling (2001) employed the finitedifference method and developed a three-dimen-sional heat flow model, which could also calcu-late the microstructure evolution and hardnessdistribution in friction stir welds.

Several researchers have carried out fluid dynam-ics based simulations that include material flow ef-fects. Smith et al. (1999) reported an effort todetermine material properties (e.g., viscosity) forfluid dynamics simulations. Bendzsak, North, andSmith (1999) presented preliminary results fromthree-dimensional heat and material flow simula-tions in which viscous dissipation was the heatsource (frictional heating between the rotating tooland the workpiece was not considered). Seidel andReynolds (2001) described a two-dimensional simu-lation study based on fluid dynamics that predictedmaterial flow patterns that compare well with ex-perimental results. A three-dimensional rigidviscoplasticity model using computational fluid dy-namics was carried out by Ulysse (2002) that pro-vided a parametric evaluation of the effect of toolspeeds on the temperature field.

Two-Dimensional Finite ElementSimulation of Material Flow in theFriction Stir Welding Process

Xiaomin Deng and Shaowen Xu, Dept. of Mechanical Engineering, University of South Carolina,Columbia, South Carolina, USA. E-mail: [email protected]

Based on a presentation by the authors at the 29th North AmericanManufacturing Research Conference (NAMRC XXIX), 2001 (see Dengand Xu 2001).


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Because of their difficulties, solid mechanics basedmodels and simulations that include material floweffects appeared in the literature later than thermalor thermomechanical (non flow based) models andfluid dynamics models (which usually do not includeconsideration of elastic responses of the workpiece).In a short communication by Xu et al. (2001), a two-dimensional modeling and simulation effort, basedon the Arbitrary Lagrangian-Eulerian (ALE) finiteelement formulation and with material flow effects,was reported in which predicted marker positionscompared well with experimental data. Details of theabove effort and additional material flow results (e.g.,velocity fields) were presented in Deng and Xu(2001), which serves as the basis of the current pa-per. The above effort was extended into the three-dimensional case, and initial results were given inXu and Deng (2002). Utilizing a “hydro” code, basedon the finite difference method and a steady-stateEulerian formulation, Askari et al. (2001) studiedthree-dimensional material flow in friction stir weld-ing. Dong et al. (2001) considered the plunging phaseof the FSW process using the finite element method, inwhich material flow characteristics in the plunging phasewere estimated using a finite difference based weld pooldynamics model.

In addition to thermal, fluid dynamics, and solidmechanics models discussed above, there exists an-other type of analytic models (e.g., Nunes 2001) thatutilizes insightful simplifications (e.g., kinematicsassumptions) to derive expressions that describe indetail material flow characteristics of the FSW pro-cess. It seems that this model can yield spatial veloc-ity field distributions comparable to those predictedby the current authors, as described below (also seeDeng and Xu 2001).

The current paper describes the details of a two-dimensional solid mechanics based finite element

modeling and simulation procedure for studyingFSW, developed using a general-purpose commer-cial code, and presents results pertaining to the ma-terial flow pattern and spatial velocity field aroundthe rotating tool pin during friction stir welding. Asin any first attempt at gaining a progressive under-standing of complex physical processes, the authorshave made several simplifications and assumptionsin this effort so that the problem becomescomputationally tractable. These will be discussedin detail in subsequent sections.

Problem DescriptionAs shown schematically in Figure 1, this study

deals with a butt weld that joins two identical platesmade of Al 6061-T6 alloy. The tool pin is held be-tween the two plates and rotates with an angular speedof � and moves relative to the plates (or the platesmove relative to the pin) with a constant velocity ofv. A leading (or advancing) side and a trailing (orretreating) side can be defined. Joining of the platesis achieved through the combined action of fric-tion heating generated at the shoulder-plate inter-face and the extrusion/forging effect created by themovement of the pin between two tightly heldplates.

As a first-order approximation, and to work withinthe bounds of current computational constraints, theFSW process is modeled as a two-dimensional prob-lem. It is assumed that the plates to be joined arethick enough such that a state of plane strain can beachieved in the mid-plane. Because the tool is madeof a material much stiffer than the plate material, thetool pin is taken to be rigid.

Even though a fully coupled thermomechanicalsimulation procedure has been devised using a gen-eral-purpose commercial finite element code, inwhich deformation and material flow fields, as wellas the temperature field, can be computed simulta-neously, the limitation of our current PC-based com-puting power makes such a procedure impractical atthis time. As such, the simulation procedure employedin this study is focused on determining the deforma-tion and material flow fields. To compensate for thelack of a predicted temperature field, measured tem-perature values from an actual FSW test (McClure etal. 1998) are used to construct an approximate tem-perature field for the FSW process. This temperaturefield is then used as input for the solid mechanics

Figure 1Schematic of Friction Stir Welding Process

Tool shoulder

Load

Tool pin

Loading side

Trading side


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model for the same FSW process. As such, a prob-lem geometry that accommodates the simulation ofthe preceding FSW test is used. Specifically, the ra-dius of the pin is R = 3.25 mm, and the dimensions ofthe two plates are 100 mm in length (along the weld),30 mm in width, and 6.4 mm in thickness. A toolrotation speed of 400 rpm and a plate translation speedof 2 mm/s are used in the FSW test.

Temperature values in the test were measured atthe mid-plane (3.18 mm below the surface) of theplates with thermocouples inserted in small holesdrilled in the plates. The holes were aligned along aline normal to the welding direction. Temperaturehistory values at various distances away from the weldline were then measured. Based on the measured val-ues and steady-state condition, temperature variationsalong lines passing the measurement points and par-allel to the weld line can be derived. These line varia-tions are then fitted to functions along the lines, whichare used to approximate the temperature field in thesolid mechanics analysis. Figure 2 shows the fittedtemperature history values.

Finite Element ModelIn this study, the finite element simulation proce-

dure for the FSW process is developed using variousoptions in the general-purpose code ABAQUS. Thetwo-dimensional geometry described above is dividedinto four-node quadrilateral elements. Reduced inte-gration with hourglass control is used to avoid mesh-locking problems associated with largeincompressible plastic deformation. For a convergedmesh, 30 rings of elements are used around the toolpin, with each ring containing 80 elements. The meshconsists of 24,000 elements and 24,460 nodes. Thesmallest elements are placed nearest to the tool pinboundary and have the dimension of 0.14 mm × 0.25mm. At the horizontal and vertical boundaries of therectangular problem domain (see Figure 1), materialparticles move with a constant speed of v relative tothe pin in the direction opposite to the translationmovement of the pin.

To accelerate the computation, the tool rotationand translation speeds are both increased 1000 timesin the analysis, so that the ratio v/�R (which is 0.0147in the test and represents the ratio of the plate mov-ing speed relative to the pin and the tangential speedof the pin at its boundary due to pin rotation) staysthe same as in the test. This acceleration is necessary

at this stage because simulation with the actual, slowspeeds cannot be completed in a realistic period oftime. To minimize the effect of change in absolutespeed, the dependence of material behavior on therate of deformation is eliminated in this analysis bytreating the plate material (Al 6061-T6) as a rate-independent elastic-plastic material. However, theeffect of temperature on yielding is considered ex-plicitly in this analysis. True stress-strain curves andother properties for the material at different tempera-tures are shown in Figure 3 and Table 1 (where T istemperature, E is the Young’s modulus, �u is theultimate strength, and � is the Poisson’s ratio).These data are obtained from the references byBrown, Mindlin, and Ho (1993) and Masubuchi(1980).

Isotropic material behavior with isotropic hard-ening is considered. The constitutive relations aregiven by the von Mises yield criterion and the as-sociated flow rule. Large deformation and mate-rial flow in the FSW process are handled with theadaptive remeshing and Arbitrary Lagrangian-

Table 1Temperature-Dependent Material Properties for Al6061-T6

(Brown et al. 1993; Masubuchi 1980)

T (°C) E (GPa) σu (MPa) ν

25.00 66.94 278.12 0330

100.00 63.21 260.68 0.334

148.89 61.32 251.24 0.335

204.44 56.80 221.01 0336

260.00 51.15 152.26 0.338

315.56 47.17 73.87 0.360

371.11 43.51 36.84 0.400

426.67 28.77 21.58 0.410

482.22 20.20 10.49 0.420

Figure 2Fitted Temperature History Values

at Various Distances from Weld Line


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Eulerian (ALE) finite element formulation optionsin ABAQUS. Details of these options are includedin ABAQUS manuals.

Two different models are proposed for the pin-plateinterface. In the slipping interface model, the pinboundary is treated as a slipping interface (it includesthe sticking interface as a special case), such that platematerial particles at the interface rotate with an an-gular velocity (say �f) that is equal (the sticking in-terface case) or smaller than the rotating speed of thepin. This model is considered because it providesconnections to possible fluid dynamics models (e.g.,Seidel and Reynolds 2001), in which a boundary layermay develop along the pin boundary, or connectionsto solid mechanics models (e.g., Askari et al. 2001),in which a sticking interface is assumed so that thematerial at the interface rotates at the same speed asthe tool. It seems that a so-defined slipping interfaceoffers a simple way of simulating the effect of theboundary layer or a sticking interface. The disadvan-tage of this model is that the angular velocity �f (orthe ratio �f /�) is not known in advance—it must bedetermined indirectly through comparisons with ex-perimental results.

In the frictional contact model, the interface be-tween the pin and the plates may experience frictionalcontact described by a modified Coulomb friction lawwith a friction coefficient of µ, an option in ABAQUS.The Coulomb law is modified in the sense that thereexists a maximum critical frictional stress, say �max,

above which the frictional stress stays constant andis no longer equal to the product of the friction coef-ficient and the contact pressure. This modification isnecessary in order to model the plastic shear flowbehavior of the plate material when the applied shearstress is near the material’s shear failure stress. Inthis study, �max, is set to equal to �u, where �u is re-lated to the material’s ultimate strength �u throughthe relation �u = �u/�3 (based on the von Mises rela-tionship between the yield stress in shear and yieldstress in tension). Because �u (thus �u) has a range ofvalues due to temperature dependence and becauseABAQUS only allows a fixed value for �max, an inter-mediate value will be chosen for �max, as discussedlater in more detail. In principle, because the fric-tional contact model treats contact and friction alongthe tool-workpiece interface explicitly, it is believedto be more realistic than the slipping interface model(including the special case of a sticking interface).

Results and DiscussionThe two-dimensional simulation procedure has

been used to model the FSW process with a range ofprocess parameters while keeping the problem ge-ometry, the converged finite element mesh, and thetemperature-dependent material properties the same.The objectives of these simulations are: (a) to gainsome understanding of the material flow and veloc-ity distribution characteristics around the rotating toolpin during welding, (b) to see whether the plane strainmodel with a number of simplifying assumptions cancapture the main features (at least qualitatively) ofexperimentally observed material particle positionsaround the pin, and (c) to gage the performance ofthe two proposed interface models.

First, we look at the tangential velocity distribu-tion at points along radial lines in several directionsaround the pin. Figure 4 shows the spatial variationof the tangential velocity based on the frictional con-tact interface model, and Figure 5 based on the slip-ping interface model, both for the case of v/�R =0.0147. The scales in the figures are for the velocityonly and not for the geometry. In Figure 4, µ = 0.3 isthe friction coefficient and �max = 1.167(107) Pa is anintermediate value between �u = 1.012(107) Pa at447°C and �u = 1.180(107) Pa at 432°C, where 432°Cto 447°C is the temperature range along the pin-plateinterface, based on experimental temperature mea-surements, as discussed in a previous section. In Fig-

Figure 3Temperature-Dependent True Stress-Strain Curves for Al 6061 T6

(Brown, Mindlin, and Ho 1993; Masubuchi 1980)

°°°

°

°

°°

°


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ure 5, the reduced angular speed, �f, at points sur-rounding the tool-pin interface is set to be 50% ofthe rotation speed of the tool pin, �.

The simulation results based on the two interfacemodels show both similarities and differences. Anobvious similarity is that both suggest the existenceof a boundary layer near the interface where the spa-tial velocity is very high. The main difference alsolies in the boundary layer. For example, while thespeed at the interface is forced to be the same in theslipping interface model, it varies in the frictionalcontact interface model from the maximum at thebottom interface point (which is on the retreatingor trailing side of the weld) to the minimum at thetop interface point (which is on the advancing orleading side).

To gain a better understanding of the similaritiesand differences between the two model results, addi-

tional figures are needed. Figure 6 shows the varia-tion of the normalized tangential velocity, vt/v, alongthe pin-plate interface (denoted by the angular posi-tion �), which is at a distance of r = 3.25 mm fromthe pin center. The average speed along the interfacefrom the frictional contact interface model is alsoshown. It is seen that this average speed is the sameas the prescribed speed in the slipping interfacemodel. Figure 7 shows the tangential velocity varia-tions along circular paths of two different distances(r = 3.36 mm and r = 3.84 mm) away from the pincenter, where � stands for the angular position, asdefined in Figure 6. It is clear that as r increases, thevariations from the two interface models approacheach other. In particular, at r = 3.84 mm (which is adistance of 0.59 mm from the pin-plate interface),the difference between the two simulation results isvery small. This seems to suggest that the difference

Figure 5Tangential Velocity Distribution Along Radial Lines

(Slipping Interface Model)


(Frictional Contact Interface Model)

Figure 7Tangential Velocity Variation Along Circular

Paths Around Pin-Plate Interface

Figure 6Tangential Velocity Variation Along Pin-Plate Interface


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between the two models is not as large as they ap-pear.

Because of the lack of complete experimental data,quantitative verification of simulation results for ve-locity and material flow characteristics in FSW dur-ing and after welding is currently not possible. Itappears that the only available test data in this regardare those obtained by our colleague at the Universityof South Carolina (Reynolds 2000). By using insertedmaterial strips as marker materials (which have dif-ferent compositions than the plate material) along theweld line, Reynolds was able to determine wherematerial particles along a line perpendicular to theweld line are located after the tool pin has passedthrough. For example, Figure 8 shows the post-weldmarker positions in the mid-plane of a weld. In thisFSW test, the tool pin has a radius of 5 mm and ro-tates at the speed of 215 rpm, and the plates moverelative to the pin at a speed of 2.35 mm/s. The platematerial is aluminum alloy 2195-T8.

It is noted that there are differences (e.g., in platematerial and speeds) between the test that suppliedthis study with temperature measurements (McClureet al. 1998) and the test shown in Figure 8. Becauseso far no one published FSW test with the same ma-terial and geometry properties has both the tempera-ture and the marker position measurements, thecurrent authors are not able to conduct a direct andquantitative validation of the present numerical simu-lation procedure. However, if we accept that themarker positions shown in Figure 8 represent a com-mon material flow pattern in FSW, a qualitative com-parison of the simulation results with the test data

can then be made. As such, the main purpose of thecomparison is to see if the solid mechanics simula-tion procedure can capture the main features of ma-terial flow pattern in FSW. To this end, simulationmarker positions shown in Figures 9 and 10 are ex-amined.

In these figures, the predicted marker positions areindicated by the crossed squares, each representingthe position of a material particle after the rotatingpin has past. These particles were originally alignedalong a straight narrow band perpendicular to the weldline. The contour lines around the pin represent thespatial flow velocity distribution around the pin. Agood qualitative agreement between the measured andsimulated marker positions is observed. The abilityof the plane strain simulation procedure to capturean experimentally observed material flow pattern inFSW was first reported in a brief technical note bythe current authors and their collaborators (Xu et al.2001) and represents an important step toward thedevelopment of a three-dimensional simulation pro-cedure for the FSW process.

One advantage of the developed computer simu-lation tool is that it allows us to understand and visu-alize the effect of process parameters (such as tooltranslation and rotation speeds) on the FSW process.The same ability is not always readily achievable oreconomical with experimental techniques. For ex-ample, Figures 11 and 12 show the positions of themarkers in Figures 9 and 10 when the tool rotationspeed � is reduced 10 times (note that the ratio �f /�in Figure 11 is 1 instead of 0.5 as in Figure 9, whichis used to further demonstrate a similarity in the flowpatterns produced by the two interface models). It isseen that the marker band above the pin is now benttoward the plate moving direction. This behavior isintuitively correct because now, with a reduced rota-tion speed, the marker materials moving with the plateexperience less counter motion exerted on them bythe rotation of the pin (note that the tangential veloc-ity due to rotation is opposite to the plate velocityrelative to the pin).

In both Figure 11 and Figure 12, the contoursaround the pin provide a view of a steady-state spa-tial velocity distribution during the FSW process. Thesimilarity between the velocity fields produced bythe two interface models explains the similarity inthe post-weld marker positions. In particular, a senseof how the tangential velocity varies in space along

Figure 8Post-Weld Marker Positions in a Friction Stir Welding Test

(Reynolds 2000)

Leading side

Trailing side

Plate moving direction

Rotatingdirection

+Pin


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the radial direction can be gained from Figures 13and 14. It is seen that, with reference to Figures 4and 5, the boundary layer around the pin is nowthicker, probably because of a more diminished domi-nance of the rotation effect due to a reduced rotationspeed, but the similarity between the two flow fieldsis stronger in this case.

A more quantitative comparison between the flowfields predicted by the two interface models is givenin Figures 15 and 16, in which the tangential veloc-ity variation along circular paths around the tool pinis plotted as a function of the angular position � (seedefinition in Figure 6). The distance of the paths fromthe center of the pin is indicated in the figures. Sev-eral observations can be made from the velocity fieldsshown in Figures 15 and 16 as well as in figures shownearlier (Figures 4, 5, 7, 13, and 14).

First, although in the slipping interface model mate-rial particles along the interface are made to rotate withthe pin with the same speed, away from the interface

the spatial velocity distribution tends to approach thatproduced by the frictional contact interface model. Thissuggests a convergence of the two different modelingapproaches. On one hand, a frictional contact interfacemodel is a natural choice for solid mechanics problemsinvolving contact and friction, even though a prescribedinterface velocity boundary is much simpler. On the otherhand, fluid dynamics models cannot treat contact andfriction but they can readily handle prescribed velocityboundary conditions along the pin-plate interface,whether the prescribed velocity is the same as or smallerthan the velocity due to the actual pin rotation. Thisobservation thus provides an important basis for the fluiddynamics based modeling effort for the FSW process.

Second, a phenomenon that is not intuitive andnot immediately apparent from the figures is themanner in which material particles flow past the ro-tating pin as the plate moves relative to the pin. Theauthors have used the visualization capability of thesimulation tool and produced movies showing

Figure 10Predicted Post-Weld Marker Positions(Frictional Contact Interface Model)

Figure 9Predicted Post-Weld Marker Positions

(Slipping Interface Model)

Figure 11Predicted Post-Weld Marker Positions When Rotation Speed

is Reduced 10 Times (Slipping Interface Model)

Figure 12Predicted Post-Weld Marker Positions When Rotation Speed

is Reduced 10 Times (Frictional Contact Interface Model)


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clearly how marker materials in front of the pin movetoward the pin and flow around the pin. What wehave observed from the movies is that, when markermaterials directly in front of the rotating pin passthe pin, they do not get around the pin from bothsides of the pin. Rather, they tend to rotate with thepin when they approach the pin-plate interface andwill always get behind the pin from the trailing (re-treating) side of the pin (which is the side in thelower portion of Figures 4, 5, 13, and 14). Onlymaterial particles near the very edge of the leading(advancing) side of the pin (corresponding to � = 90°)will move past the pin without first rotating with thepin. This material flow pattern is now also clear fromFigures 4, 5, 7, 13, 14, 15, and 16. These figures allindicate that the tangential velocity field around the pin

is geared toward the rotating direction of the pin, ex-cept very near � = 90°, where the tangential velocity isreduced to zero or becomes slightly negative.

An additional observation from the movies is thatmaterial particles in the leading side of the weld linebefore welding will tend to stay together in the lead-ing side after welding, and those in the trailing sidewill tend to stay together in the trailing side, perhapswith some overlapping across the weld line. Mea-sured marker positions (see Reynolds 2000) have con-firmed this simulation result.

Concluding Remarks

A plane-strain finite element procedure has been de-veloped to simulate the friction stir welding (FSW) pro-

Figure 16Tangential Velocity Variation Along Circular Paths Around

Pin-Plate Interface (Frictional Contact Interface Model)


When Rotation Speed is Reduced 10 Times(Slipping Interface Model)

Figure 13Tangential Velocity Distribution Along Radial Lines When Rotation

Speed is Reduced 10 Times(Frictional Contact Interface Model)

Figure 15Tangential Velocity Variation Along Circular Paths Around

Pin-Plate Interface (Slipping Interface Model)


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cess focusing on velocity field and material flow char-acteristics. Two models have been proposed for the pin-plate interface. Simulation predictions of post-weldmarker positions based on both models compare wellwith experimental measurements.

In conclusion, the authors would like to stress that,due to computational constraints and the lack of experi-mental data, several simplifications have been made incarrying out this study to make the problem tractable.As such, the comparison in this paper with test results ismeant to demonstrate the capability of the simulationprocedure to capture the essential features of the FSWprocess, and not to provide a quantitative prediction atthis stage. However, work is under way by the authorsto eliminate the simplifications. As experimental dataand computational resources become available in duetime, more accurate and realistic simulations of the FSWprocess will become available.

AcknowledgmentsThis work was sponsored by the National Science Foun-

dation (grant no. DMI-9978611). Discussions with Profes-sor A.P. Reynolds, Professor Y.J. Chao, Dr. W. Tang, andMr. T.U. Seidel are gratefully acknowledged.

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Authors’ Biographies

X. Deng is a professor of mechanical engineering at the University ofSouth Carolina. He received his BS degree in 1982 from the Beijing Uni-versity of Aeronautics and Astronautics (China) and his MS (1985) andPhD (1990) from the California Institute of Technology. His current re-search interests include modeling and simulation of manufacturing (ma-chining and welding) processes, 3-D mixed-mode fracture criterion andsimulation code development, and nanomechanical analysis using mo-lecular dynamics simulations.

S. Xu is a post-doctoral research associate in the Dept. of MechanicalEngineering at the University of South Carolina. He received his BS (1985)and MS (1992) degrees from the Huazhong University of Science andTechnology (China) and his PhD (2003) from the University of SouthCarolina. His research interests include finite element modeling and sim-ulation of engineering systems and manufacturing processes,nanomechanical simulations, and experimental material characterizationof welded joints (e.g., friction stir welds).

2d fe simulation of material flow in the fsw process

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