A Study on the Surface Depression of the Molten Pool with ...

WELDING RESEARCH

WELDING JOURNAL / AUGUST 2014, VOL. 93312-s

Introduction Arc force is the main factor for arcbehavior during the arc weldingprocess, which is composed ofelectromagnetic and plasma jet forces(Ref. 1). The welding current has ahuge effect on arc behavior, includingthe method of pulsed arc welding(Ref. 2). With pulsed welding, theelectromagnetic force in arc plasmachanged with pulse frequency. Radialand axial elements were also both af-

fected (Ref. 3). And radial force wasthe key for the significant arcconstriction and stiffness. Simultane-ously, the energy density of arcplasma increased, and a largepenetration was obtained with thepulsed arc welding process (Refs. 4,5). The axial element was the one oftwo main compositions of arc forcewith axial electromagnetic force,which was known as the reason forsurface depression of the molten pool(Ref. 6). With the larger arc force, the

deeper penetration can be found withthe previous experimental results(Ref. 7). Fluid and geometry of the moltenpool is important for weld appearance,microstructure, and properties (Refs.8, 9). And the surface deformation isthe key factor for the fluid and solidifi-cation (Refs. 10–12). Large depressionon the surface is a benefit for themolten process of base metal as moredirect heat input (Ref. 13). Meanwhile,the arc force has a more significant ef-fect for the liquid metal status (Ref.14), which may also alter drivingforces in the molten pool. As knownpreviously, surface tension,electromagnetic and plasma dragforces, plus buoyancy are the drivinginfluences for the fluidity of themolten pool (Refs. 15–17), which aredifferent with various materials andsurface deformation. As a result,different welding methods and materi-als will cause different surface depres-sions. The reason for surfacedepression is realized as composedforces, such as surface tension, gravity,arc force, and pressure in liquid metal.And the depression happened in theinterface between arc plasma andmolten metal, which made it to becomplex. With a conventional weldingprocess, the previous results (Ref. 13)indicated that the surface depressioncaused by arc force was no more than5% h (h is the thickness of the basemetal) that could be ignored (averagewelding current Iavg < 110 A). Theerror of penetration was less than 5%

A Study on the Surface Depression of theMolten Pool with Pulsed Welding

The effect of the arc force with pulsed arc welding was examined

BY M. YANG, Z. YANG, B. CONG, AND B. QI

ABSTRACT Arc force was the main factor for arc behavior during the arc welding process,which had an effect on the molten pool. Ultrahigh-frequency pulsed gas tungsten arcwelding (UHFP-GTAW) created the larger arc force and weld penetration with experi-mental research. The arc force caused surface depression that pushed the heat sourcedownward to the bottom of the molten pool. As a result, the fluid status and geome-try of the molten pool were changed. The surface depression was calculated with theresultant liquid-gas interface. Zero solutions of the balance functions were obtainedwith approaching curves. The results indicated an available condition with arc curveassumption and an acute angle of the spherical cap were known to be accurate. Ellip-soid assumption was discussed with a larger arc force (80 kHz) that guaranteed theangle of the spherical cap θ > 90 deg. The transient simulation was carried out, andthe results indicated the surface depression improved the penetration although lowheat conductivity of titanium was seen. Furthermore, double circulation can befound in the molten pool that was caused by both electromagnetic force and surfacetension. The velocity demonstrated the dominance of surface tension with amaximum up to 1.74 m/s. And it also proved the effect of counterclockwise circula-tion on penetration by electromagnetic force.

KEYWORDS • Arc Force • Surface Depression • Pulsed Arc Welding • Gas Tungsten Arc Welding (GTAW)

M. YANG ([email protected]), Z. YANG, B. CONG, and B. QI are with the Department of Materials Processing,Beijing University of Aeronautics and Astronautics, China.

YANG SUPP AUGUST 2014_Layout 1 7/14/14 5:01 PM Page 312

WELDING RESEARCH

AUGUST 2014 / WELDING JOURNAL 313-s

without surface depression duringsimulation by stainless steel. Ultrahigh-frequency pulsed gastungsten arc welding (UHFP-GTAW)created a much larger arc force thatcaused significant surface depression.With more than 20 kHz, the arc forceincreased by 200% at least, comparedwith conventional gas tungsten arcwelding (C-GTAW). The more obvioussurface deformation was made by thelarge arc force that had a huge impacton fluid status in the molten pool.With simulation by stainless steel,the arc force was added in the axis ofarc plasma under plane assumption.The results indicated that double cir-culation existed in the molten poolwith UHFP-GTAW. And such doublecirculation was recognized as the rea-son for increased penetration (Refs.18–20). Also, fluidity andtemperature distribution,respectively, were improved. The ex-perimental results demonstrated thelarger arc force and penetration canbe found under titanium alloys (Ti-6Al-4V) with UHFP-GTAW. With thelarge arc force, the surface depressionwill exist, which may be stillimportant for weld penetration andgeometry. In addition, titanium alloywas paramagnetic so that itsmagnetic permeability μm was substi-tuted by μ0.

The paperproduced thestudy on surfacedepression bythe arc force dur-ing UHFP-GTAW. The weld-ing process wascarried out forsupportingexperimental re-sults. The depression height would becalculated that was the transient statusfor simulation. Surface tension, gravity,and liquid pressure were known as thethree key factors for mathematic calcu-lation. The reason for penetration wasdiscussed with Ti-6Al-4V. The studywill also analyze the fluid and tempera-ture distribution with depressioncaused by arc force.

Experimental Procedure

Welding Experiments

Ti-6Al-4V titanium alloy was thebase metal with dimensions of 100 ×60 × 2.5 mm. Under UHFP-GTAW, theswitch frequency is 20~80 kHz withcurrent upslope/downslope rate(di/dt) more than 50 A/μs. Theschematic welding currents areillustrated in Fig. 1. In the figure, Ib is

the background current and Ip is thepulsed current. The times of the back-ground and pulsed currents are tb andtp, respectively; as a result, the pulsecircle time is represented as T = tb + tpand the frequency f = 1/T. The dutycycle of the pulse duration is deducedto be δ = tp/T. The parameters of the pulsedcurrent are shown in Table 1. The elec-trode radius was 1.2 mm and made of2% cerium and 98% tungsten. The dis-tance between the electrode and theworkpiece was 3 mm. Metallographicspecimens were prepared using theetchant HF:HNO3:H2O = 3:10:100.The microstructure of the welds wascaptured by Olympus BX51M. Figure 2 shows the measurementapparatus for the arc force during thewelding process. The data of arc forcetransported from the sensor to acqui-sition card and then displayed by soft-ware with a changing curve of the arc

Fig. 1 — Schematic welding currents.

Fig. 2 — Measurement apparatus for the arc force during the welding process.

Table 1 — Parameters of Welding Process for Ti6Al4V Titanium Alloys

Experiment No. Ib/A Ip/A f/kHz δ (%) Argon (99.99%) qc /(L∙min–1) Welding Speed v/(mm∙min–1)

Torch Trailer Back

1 80 — — — 15 20 5 1502 40 100 20 50 15 20 5 1503 40 100 40 50 15 20 5 1504 40 100 60 50 15 20 5 1505 40 100 80 50 15 20 5 150


WELDING RESEARCH


force during the welding process. Thetrestles under the workpiece made thedistance between the arc plasma andsensor, which was helpful for eliminat-ing electromagnetic interference. Themeasured results for every group ofparameters were captured at leastthree times.

Calculation and Simulation

Surface depression caused by thearc force during UHFP-GTAW was cal-culated with surface tension, gravity,and liquid pressure. The conditions ofthe computing process are discussed inthe results section. The depressionswith different parameters were the ev-idence for simulation of the moltenpool. Physical properties of Ti-6Al-4Vare displayed in Table 2. The heat fluxon every boundary was zero except forsurface depression. A 2-D model with surfacedepression was produced for transient

status under the effect of arc forcethat is illustrated in Fig. 3. It would becarried out in the discussion section toexplore the accuracy with 80 kHz. Thequad elements with submap type wereused for grid mesh. The calculationscale was 10 × 2.5 mm with 2860nodes, 2725 quadrilateral cells, and5316 mixed interior faces. Theassumptions were as follows: • The liquid in the molten poolcould be recognized as viscous, incom-pressible, laminar fluid; • Density variations follow theBoussinesq approximation; • The parameters of material are in-dependent of temperature except forspecific heat capacity, thermal conduc-tivity, viscosity, and surface tensioncoefficient. The heat input followed Gauss dis-tribution that was represented inEquation 1. As described in Ref. 3,there is a mathematical correlation be-tween the radius of arc plasma andpulsed frequency. Thus, the character-

istics of UHFP-GTAW would be repre-sented with various radiuses.

Where Q = heat input; η =efficiency; U = average arc voltage; I =average welding current; Rarc = radiusof arc plasma; and r0 = radius ofrandom position under arc plasma. Driving forces, such as surface ten-sion and buoyancy, were known asthe source term by the momentumequation of x/y direction. And inter-dendritic flow force was regarded asthe source term that was indicated byfunction y = f(fl), in which fl was rep-resented as Equation 2. The modelfollows the mass conservation equa-tion, momentum conservation equa-tion of the x/y direction, and the en-ergy conservation equation. The elec-tromagnetic force was the sourceterm of momentum conservation inboth x and y directions with Equation3 that could be product from thepower J × B. The derivation ofelectromagnetic force with 2-/3-Dmodel has been studied by severalscholars over the years (Refs. 24, 25);thus, it is not provided in this paper.

QUI

R

r

R= ⋅η⋅

π⋅−

⎛

⎝⎜⎜

⎞

⎠⎟⎟

3 exp3

(1)arc2

2

arc2

0

f

T T

T TT T

l T T

T T T

l

s

s

l s

s l

l

=

<

−−

>

⎧

⎨

⎪⎪⎪

⎩

⎪⎪⎪

≤ ≤

0

(2)

Fig. 3 — A 2D model with surface depression for simulation.

Table 2 — Physical Properties of Ti6Al4V

Physical Properties Value

Liquidus temperature T1(K) 1928Solidus temperature Ts(K) 1878Liquid density ρ (kg/m3) 4300Liquid viscosity μ (kg/ms) 0.0049Solid phase effective thermal conductivity ks (J/ms∙K) 5.4Liquid phase effective thermal conductivity k1 (J/ms∙K) 15.9Solid phase specific heat capacity CPS (J/kg∙K) 879Liquid phase specific heat capacity CPS (J/kg∙K) 678Temperature coefficient of surface tension dγ /dT (N/mK) –0.00028Thermal expansion coefficient β (K1) 1.1 × 10–5

Magnetic permeability μm (N/A2) 1.00005Magnetic permeability of vacuum μ0 (N/A2) 1.26 × 10–6

Melting heat L (J/kg) 3.57 × 105

Surface tension σ (mN/m) 1650


WELDING RESEARCH


Where Ts = solid phasetemperature, Tl = liquid phase temper-ature; fl = 1 in the liquid phase region;0 < fl < 1 in the solid-liquid region; fl =0 in the solid phase region.

Where Rarc = groove radius of arcplasma; h = arc length; x = xcoordinate; and y = y coordinate. The boundary of surfacedepression was the interfere betweengas and liquid. The velocity of depres-sion was driven by surface tension orMarangoni convection that could bederived with temperature coefficientdγ/dT. The heat flux distribution fol-lowed the heat input of welding. Andthe initial temperature of surface de-pression T0 = 1700 K as thedepression happened during themelting process. Heat insulation wasused at the other boundaries; thus,heat flux at the axis and edge wereboth ∂φ /∂y = 0, and similarly, thesurface and bottom were ∂φ/∂x = 0.

Results

Calculation Process

During the welding process, moltenmetal owned the free surface — Fig.4. It was the interface of liquid metaland arc plasma where the forcebalance happened. Arc curve assump-tion was carried out for volumeapproximate calculation; thus, virtualradius R equaled the distance fromthe center O to the interface. Themathematic correlation between an-gles and scales was represented inEquation 4, from which virtual radiusR can be described with Equation 5. Where R = virtual radius of virtualsphere; h = depth of surfacedepression; r = radius of weld (half ofwidth); θ = half angle of sphericalcap; and α = half corner of sphericalcap.

Further, the surface depression ofthe molten pool can be recognized asthe spherical cap of the virtual spherethat is illustrated in Fig. 5. Thevolume of the spherical cap is repre-sented with Equation 6. The gravityof squeezed liquid can be deduced fol-lowed by Equation 6.

The force balance happened on theinterface of the liquid metal and arcplasma that is illustrated in Fig. 6.The arc force was the maincomponent downward in axis. On theother side, the surface depression hadcaused some volume of liquid to besqueezed out. The feedback of suchliquid metal would own reversedgravity opposite to the arc force. Thepressure of liquid had the same effectwith gravity. And the surface tensionmade drag force through the liquidusline, which was also upward againstthe arc force. Integrating Equations 5and 6, the function of resultant isrepresented in Equation 7. Where φ = half random angle ofthe spherical cap.

( )

1 exp(2

) 1

( ) (3)

4exp

2

2

arc2

41 exp(

2) 1

02

2arc2

2

arc2

02

2 2

2

arc2

2

×

− −⎛

⎝⎜⎞

⎠⎟⎡

⎣⎢⎢

⎤

⎦⎥⎥

−⎛⎝⎜

⎞⎠⎟

×

⎧

⎨

⎪⎪⎪⎪

⎩

⎪⎪⎪⎪

=−μπ

−⎛

⎝⎜

⎞

⎠⎟

=−μπ

− −⎛

⎝⎜

⎞

⎠⎟

⎡

⎣⎢⎢

⎤

⎦⎥⎥

−⎛⎝⎜

⎞⎠⎟

J B

r

R

xh

J B

xI

R rr

R

yI

hrr

R

yh

hr

rR h

θ =

θ =−

⎧

⎨⎪⎪

⎩⎪⎪

tan2

tan(4)

Rh r

h= +

⋅2(5)

2 2

3(6)2= π ⋅ −⎛

⎝⎜⎞⎠⎟V h R

h

Fig. 4 — Geometry of surface depression in the molten pool. Fig. 5 — Spherical cap of the virtual sphere.


WELDING RESEARCH


Where F = arc force; G = gravity ofsqueezed liquid metal; P = liquid pres-sure; S = surface area; and σ sum =sum of surface tension on theliquidus line. The zero solution of Equation 7meant force balance in the interface.

The approaching curve was producedfor the solution process, and theresults were illustrated in Fig. 7 andTable 3. With conventional GTAW, thesurface depression was 0.11 mm,which was just about 4% of thickness(2.5 mm). As a result, the surface de-pression could be ignored during theconventional welding process that hadbeen mentioned in the introduction. Table 3 also displayed thecorrelation between the arc force andsurface depression. The resultsdemonstrated that surface depressionincreased with the arc force, which hadthe same trend following by pulsedfrequency. A larger arc force withUHFP-GTAW caused the biggerdepression h, which was a benefit forlarger weld penetration. Fromprevious work, compared with conven-tional GTAW, the weld widthdecreased by more than 12% and by35% with more than 70 kHz.Meanwhile, the depth and penetrationrate increased, respectively. Above all, arc force with UHFP-GTAW had been enhanced that causedsurface depression in the molten pool.

The depth of depression wascalculated with the resultant, and theresults indicated that a larger arc forcecaused deeper depression, which hadbeen proved by the experiments.

Discussion First of all, the calculation processin the results section ignored theeffect of gas shear on the surfacedepression. Historical researchdemonstrated the effect of a highercurrent level (> 200 A) was significanton the plasma jet force with a huge im-pact on the molten pool (Ref. 26).However, the average current for thestudy is less than 100 A. As a result,compared with surface tension, thedrag force of gas shear was notreferred in this study. Secondly, in the results section, thediscussion above was under the condi-tion of h ≤ R, which was available formost of the normal conditions. Thatindicated an angle of spherical cap was the acute angle. And h = R was thecritical condition with Equation 8 thatindicated critical depression was deter-mined by the arc force.

The condition of h > R (angle ofspherical cap θ > 90 deg) could be dis-cussed with Fig. 8. According to theprinciple of triangle, there should besuch conservation as shown in Equa-tion 9. That indicated the virtual ra-dius R still followed Equation 5; thus,the condition of h > R can be writtenas h > r. Similarly, the function offorces and its first derivative are rep-resented in Equations 10 and 11, re-spectively. With calculation, f′(h) < 0can be gained, which proved Equation10 was also a monotonic function.The radius r in this study belonged to[1.3, 2.08], which demonstrated theonly one zero solution h[0] for it. Thiscondition had been checked with alimited value that was the depressionequaled thickness of base metal. Theresults demonstrated that f(2.5) =5.513 > 0, which meant the zero solu-

2

sin

3

2 2 sin

6( 3 )

– 8 arctan

632

8 arctan (7)

sum

2

2

2 2

2

3 2

∫

= − − ⋅ − σ

= −ρ −ρ ⋅ −

⋅ σ ⋅ ⋅ϕ⋅ ϕ

= −ρ ⋅π ⋅ −⎛⎝⎜

⎞⎠⎟

−ρ ⋅π − ⋅σ ⋅ ⋅ θ⋅ θ

= − π ρ ⋅ +

ρ ⋅π − σ ⋅

= − π ρ − π ρ

− σ ⋅ +

ϕ

f ( h) F G P S

F gV gh S

R

F g h Rh

gh r R

F gh h r

gh r rhr

gh gr h

rhr

F

12

43

2

53

2 (8)

sum

3 2

3

= − − ⋅ − σ

= −ρ ⋅ π −ρ ⋅π ⋅ − ⋅σ ⋅ ⋅π

= − π ⋅ρ ⋅ − π⋅σ ⋅

f ( h) F G P S

F g R g r h R

F g h h

Table 3 — Approaching Results of Surface Depression

Pulsed Frequency Arc Force Weld Width Weld Depth Penetration Rate Surface Depression f/kHz F/mN B/mm H/mm φ/% h/mm

0 1.79 4.16 2.29 55.1 0.1220 4.19 3.1 1.75 56.5 0.3140 7.00 2.77 1.85 70.1 0.5360 8.84 3.21 2.15 67.0 0.6780 16.06 2.59 2.06 79.5 1.63

Fig. 6 — Force balance on the interface.


WELDING RESEARCH


tion was out of effective region. Theassumption of h > R was notavailable.

Furthermore, with pulsedfrequency f = 80 kHz, surface depres-sion equaled 1.63 mm > 1.33 mm(R[h80 kHz]) that was in the region of h> R. It was described above that the as-sumption of h > R was not available.That demonstrated the arc curveassumption was ineffective with 80

kHz. An ellipsoid cap would be moreaccurate under the condition of thelarger arc force that was illustrated inFig. 9. With ellipsoid assumption, de-pression can be more than the radiuswhen the angle of the spherical cap was acute angle. As a result, the ellip-soid molten pool geometry can be thereason for large depression with 80kHz. A surface depression with 80 kHzwas used for the 2D model. The tran-sient status of the molten pool wasdiscussed with the molten condition,fluid convection, and temperature dis-tribution; those are illustrated withFig. 10A–C. An ellipsoid cap assump-tion was used. Figure 10B displays the fluid statusduring the welding process. Comparedwith simulated results by stainlesssteel, double circulation also existswith surface depression in the moltenpool. The clockwise circulation wasdriven by surface tension that was stillthe most important factor for fluidityof the molten pool. The maximum ve-locity of it reached up to 1.74 m/s. Onthe other side, counterclockwise circu-lation was found near the bottom ofthe surface depression. That wasdriven by electromagnetic force as de-scribed in the experimental proceduresection. Further, except for the surfacedepression, the larger arc force alsocaused a huge impact with 80 kHz,which made the impulse to the liquidmetal. And the impulse could push thefluid downward to the bottom. Such im-pulse would follow the distribution with

the original line distributionrepresented as Fr = Fpeak·exp(-a|r|) forthe 2D model. As a result, themaximum impact by arc force happenednear the axis of the arc plasma that wasmeaningful for the surface depressionof the molten pool. As described before,various depressions were recognized asthe important reason for thedistribution of counterclockwise circula-tion that was driven by electromagneticforce. However, the average velocity of itwas up to 0.522 m/s, which was muchless than clockwise circulation (1.74m/s). This result demonstrated the

(9)2 2 2− = −( h R ) R r

43

(2 )

23

2 2 sin( )

6( 3 )– g

2 +arctan2

632

2 +arctan2

(10)

sum

3 2

2

2 2 2

2 2

3 2

2 2

= − − ⋅ − σ

= −ρ ⋅π − π −

⋅ − −⎛⎝⎜

⎞⎠⎟

⎡

⎣

⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥

−ρ ⋅π ⋅ − ⋅σ ⋅ ⋅ θ⋅ π θ

= − π ρ ⋅ + ρ π

⋅ − σ π−

⎛⎝⎜

⎞⎠⎟

= − π ρ ⋅ − π ρ

⋅ − σ π−

⎛⎝⎜

⎞⎠⎟

f ( h) F G P S

F gR R h

RR h

g r h R –

F gh h r r

h rrh

r h

F g h gr

h rrh

r h

232

2( )

( )(11)

2 2

2 2 2

2 2 2

= − π ρ − π ρ

− σ ⋅ −+

f '(h) gh gr

rr h

r h

Fig. 7 — Solution curve of the force balance function. Fig. 8 — Geometry with the condition of h > R.

Fig. 9 — Ellipsoid cap assumption of thesurface depression.


dominance of surface tension aboutfluid velocity status. The temperature distribution of themolten pool is illustrated in Fig. 10C,which indicates the spread speed oftemperature was little as low thermalconductivity. This result also provedthe significant grain growth oftitanium alloys that had been knownin the research field (Refs. 23, 27, 28).Further, the downward heat inputmade a high temperature at thebottom that was believed for largepenetration. And it was the maineffect of the arc force on the surfacedepression of the molten pool. Figure 11 indicates the pressure con-tour of liquid metal. The maximumvalue (6.56 kPa) happened near theedge of the weld that was also the edgeof the surface tension driving area. Incontrast, the pressure at the bottom of

the surface depression (1.91~4.57 kPa)was about half less than the edge. Thatdemonstrated the importance ofsurface tension for the fluidity of themolten pool, which had been provedwith velocity previously. And the pres-sures at the bottom and the edge of de-pression were caused by the arc forceand surface tension, respectively. Simul-taneously, significant pressure distrib-uted at the bottom of depressionindicated the effect of the arc force andalso the impulse of arc plasma. In addition, the area of liquid pres-sure was actually arc surface, and itwas recognized as plane instead in theresults section. The discussion belowwill check the availability of plane as-sumption. The area of plane was writ-ten as π r2, compared with it, the areaof spherical cap was 2 πRh. Similarlyto Equation 7, the function of result-ant is represented as Equation 12.With the same approaching analysis,the depressions of differentparameters can be obtained as 0.12,0.3, 0.53, 0.67, and 1.54 mm, respec-tively.

Compared with Table 3, the errorwas less than 3.2% during 0–60 kHz,and the maximum error was less than5.5% at 80 kHz. That meant the differ-ence between arc surface and plane as-sumption would be little when study-ing liquid pressure. That is also thereason for using plane assumption inthis research.

Conclusion 1. The high-frequency pulsed arcwelding process created the larger arcforce and penetration. The arc forcecaused surface depression of themolten pool that pushed the heatsource downward to the deep. As a re-sult, the fluid status and geometry ofthe molten pool would be changed. 2. The depression can be calculatedwith the resultant. Arc curve assump-tion was used for normal conditions(0~60 kHz), and the surfacedepression increased with pulsed fre-quency. The conditions with acuteangle of the spherical cap were knownto be accurate. With a larger arc force(80 kHz), the assumption wasimproved to ellipsoid that conditionguaranteed θ > 90 deg. 3. Ellipsoid assumption was usedfor simulation with 80 kHz. Surfacedepression improved the penetration,although the low heat conductivity oftitanium alloys, which wasinconsistent with the experimental re-sults. Double circulation displayed inthe molten pool was caused by electro-magnetic force and surface tension.The velocity demonstrated the impor-tance of surface tension with a max of1.74 m/s. Compared with it, the veloc-ity of circulation by electromagneticforce was up to 0.522 m/s that provedthe effect on penetration.

This work was supported by theNational Natural Science Foundationof China under grant No. 50975015.Fundamental research funds for theCentral Universities under grant No.YWF-14-JXXY-008. The authors alsoacknowledge the Beijing University ofAeronautics and Astronautics for sup-porting their research work.

2

sin

3

2 2 2 sin

76

32

8

arctan (12)

sum

2

3 2

∫

= − − ⋅ − σ

= −ρ −ρ ⋅ −

⋅ σ ⋅ ⋅ϕ⋅ ϕ

= −ρ ⋅π ⋅ −⎛⎝⎜

⎞⎠⎟ −ρ

⋅ π − ⋅σ ⋅ ⋅ θ⋅ θ

= − π ρ − π ρ − σ

⋅ +

ϕ

f (h) F G P S

F gV gh S

R

F g h Rh

gh

Rh R

gh gr h r

hr

F

WELDING RESEARCH


Acknowledgments

Fig. 11 — Total pressure distribution inthe molten pool.

Fig. 10 — Transient status of the moltenpool (80 kHz). A — Molten pool; B — fluidvelocity vectors; C — temperature distribution of the molten pool.

A

B

C


1. Ando, K., and Hasegawa, M. 1985.Welding arc phenomena. Beijing. ChinaMachine Press: 249, 250 (in Chinese). 2. Cook, G. E., El-deam, Hussam, andEassa, E. H. 1985. The effect of high-frequency pulsing of a welding arc. IEEETransaction on Industry Applications 1A-21(5): 1294–1299. 3. Yang, M., Qi, B., Cong, B., Liu, F.,Yang, Z., and Chu, P. K. 2013. Study onelectromagnetic force in arc plasma withUHFP-GTAW of Ti-6Al-4V. IEEETransactions on Plasma Science 41(9):2561–2568. 4. Amin, M. 1983. Pulse current param-eters for arc stability and controlled metaltransfer in arc welding. Metal Construction(15): 272–8. 5. Zacharia, T., and David, S. A. 1989.Weld pool development during GTA andlaser beam welding of type 304 stainlesssteel, Part I — Theoretical analysis. Weld-ing Journal 68(12): 499-s to 509-s. 6. Lin, M. L., and Eagar, T. W. 1985. In-fluence of arc pressure on weld pool geom-etry. Welding Journal 64(6): 162-s to 169-s. 7. Yang, Z., Qi, B., Cong, B., Yang, M.,and Li, Y. 2013. Effect of pulse frequencyon weld appearance behavior by TC4 tita-nium alloys. Transactions of the China Weld-ing Institute 34(12): 37–40. 8. Pardo, E., and Weckman, D. C. 1998.Prediction of weld pool and reinforcementdimensions of GMA welds using a finite-el-ement model. Metallurgical and MaterialsTransactions B 6(20): 937–947. 9. Sundaresan, S., Janaki, D., et al.1999. Microstructural refinement of weldfusion zones in α - β titanium alloys usingpulsed current welding. Material Scienceand Engineering, A-Structure 262: 88–100. 10. Wu, C. S. 1998. Numerical simula-tion of TIG weld pool behavior under theaction of pulsed current. Acta MetallurgicaSinica 34(4): 416–422. 11. Cao, Z. N., and Wu, C. S. 1996.Mathematical modeling of TIG moltenpool with full penetration. Transactions ofthe China Welding Institution 17(1): 62–70. 12. Wu, C. S. 2008. Welding heatprocess and pool geometry. Beijing. ChinaMachine Press: 102–104 (in Chinese). 13. Qi, B. J., Yang, M. X., Cong, B. Q.,and Liu, F. J. 2013. The effect of arc behav-ior on weld geometry by high frequencypulse GTAW process with 0Cr18Ni9Tistainless steel. International Journal of Ad-vanced Manufacturing Technology 66(9-12):1545–1553. 14. Rokhlin, S. I., and Guu, A. C. 1993. Astudy of arc force, pool depression and weldpenetration during gas tungsten arc welding.Welding Journal 72(8): 381-s to 390-s. 15. Kou, S., and Wang, Y. H. 1986. Weld

pool convention and its effect. WeldingJournal 65(3): 63-s to 70-s. 16. Oreper, G. M., and Szekely, J. 1984.Heat and fluid flow phenomena in weldpools. Journal of Fluid Mechanics 147:53–79. 17. Kim, W. H., Fan, H. G., and Na, S. J.1997. Effect of various driving forces onheat and mass transfer in arc welding. Nu-merical Heat Transfer, Part A: Applications32: 6, 633–652. 18. Kou, S., and Wang, Y. H. 1986.Computer simulation of convection inmoving arc weld pools. Metallurgical Trans-action A (17A): 2271–2277. 19. Tsai, M. C., and Kou, S. 1990. Elec-tromagnetic force induced convection inweld pool with a free surface. Welding Jour-nal 69(6): 241-s to 246-s. 20. Zacharia, D. 1989. Weld pool devel-opment during GTA and laser beam weld-ing of Type 304 stainless steel, Part I —Theoretical analysis. Welding Journal68(12): 499-s to 509-s. 21. Boyer, R., Welsch, G., and Collings,E. W., eds. 1994. Materials Properties Hand-book: Titanium Alloys. Materials Park, Ohio:ASM International. 22. Mishra, S., and DebRoy, T. 2004.Measurements and Monte Carlo

simulation of grain growth in the heat-af-fected zone of Ti-6Al-4V welds. Acta Mate-rialia 52(5): 1183–1192. 23. Oreper, G. M., and Szekely, J. 1987.A comprehensive representation oftransient weld pool development in spotwelding operations. Metallurgical Transac-tions A (18A): 1325–1332. 24. Kumar, A., and DebRoy, T. 2003.Calculation of three-dimensional electro-magnetic force field during arc welding.Journal of Applied Physics 94(2):1267–1277. 25. Tsao, K. C., and Wu, C. S. 1988.Fluid flow and heat transfer in GMA weldpools. Welding Journal 67(3): 70-s to 75-s. 26. Choo, R. T. C., and Szekely, J. 1991.The effect of gas shear stress onMarangoni flows in arc welding. WeldingJournal 70(9): 223-s to 233-s. 27. Yunlian, Q., Ju, D., Quan, H., andLiying, Z. 2000. Electron beam welding,laser beam welding and gas tungsten arcwelding of titanium sheet. Material Scienceand Engineering, A-Structure 280: 177–81. 28. Yang, Z., Sista, S., Elmer, J. W., andDebRoy, T. 2000. Three dimensionalMonte Carlo simulation of grain growthduring GTA welding of titanium. Acta Ma-terialia 48(20): 4813–4825.

WELDING RESEARCH


References

Win Potential Clientsby Showing Them Videos on

How to Save Money and TimeBy Using Your Products!

For more information visit our website at http://videos.aws.org or please contact:

Rob [email protected](800) 443-9353, ext. 243

Sandra [email protected](800) 443-9353, ext. 254

Lea [email protected](800) 443-9353, ext. 220


A Study on the Surface Depression of the Molten Pool with ...

Documents