Numerical Simulation of Transient 3-D Surface Deformation of a Completely Penetrated GTA Weld

Transcription

1 WELDING RESEARCH Numeical Simulation of Tansient 3-D Suface Defomation of a Completely Penetated GTA Weld An analytical model that loes the dynamic behavio of a weld pool will help in the development of a senso that detects complete joint penetation in gas tungsten ac welding BY C. S. WU, P. C. ZHAO, AND Y. M. ZHANG ABSTRACT. By establishing the coelation between tansient behavio of a weld pool suface defomation and wokpiece penetation, and quantitatively analyzing the suface defomation at the top and bottom sufaces at the moment the pool penetates and thei dynamic esponses to welding pocess paametes will povide basic data fo the development of topside vision-based penetation contol in gas tungsten ac welding (GTAW). A tansient numeical model was developed to investigate the dynamic behavio of a completely penetated GTAW joint. A complete and compehensive scheme was used in which many factos, such as moving ac, 3-D fluid and heat flow fields, tansient state, completely penetated weld, and suface defomation at both the top and bottom sufaces wee consideed. The tansient development of 3-D suface defomation and shape of a weld pool duing the peiod fom patial penetation to complete penetation is pedicted. The simulated esults showed that the atio cuves of the maximum depession to the length and width at the top suface of the weld pool at diffeent times clealy indicated basic infomation on penetation. Theefoe, the elation of the atios vs. time can be used as an indicato to judge whethe the joint is penetated. Intoduction C. S. WU and P. C. ZHAO ae with Institute of Mateials Joining, Shandong Univesity, Jinan, China, wucs@sdu.edu.cn. Y. M. ZHANG is with Cente fo Manufactuing and Depatment of Electical and Compute Engineeing, Univesity of Kentucky, Lexington, Ky. Gas tungsten ac welding (GTAW) is the most used ac welding pocess fo citical and accuate joining. Fo this pocess, 100% complete joint penetation must be ensued without melt-though o ovepenetation (Ref. 1). To this end, automated sensing and contol of the GTAW pocess must be ealized (Ref. ). In pactice, the backside weld bead width is usually employed to detemine the extent of penetation. Although the backside bead width can be sensed by a backside senso, thee ae limitations of access and coodinating the motion between the toch and senso, and it is often necessay that the senso be attached to and moved with the toch to fom a weld-face o topside senso. Howeve, the invisibility of the backside and the stong ac light adiation togethe cause temendous difficulties fo such sensos. To find a feasible senso fo automated contol, vaious methods have been studied, including pool oscillation (Ref. 3), ultasound (Ref. 4), and an infaed senso (Ref. 5). Although significant pogess has been made, pactical applications ae still esticted. Weld pool behavio contains enough infomation on penetation. The pool suface is defomed because of the plasma impingement. Pevious eseaches have found that the esultant depession of the weld pool suface coelates to the penetation depth of the weld pool (Refs. 6 8), but thee is a lack of quantitative analysis of such a coelation. Establishing the coelation between dynamic behavio of weld pool suface defomation and the penetation infomation, while quantitatively analyzing the suface defomation at the top and bottom sufaces when the joint KEY WORDS Weld Pool Suface Defomation Penetation Coelation Numeical Simulation is penetated and thei dynamic esponse to welding pocess paametes will povide much basic data fo the ealization of a topside vision-based penetation contol fo the GTAW pocess. Thus, numeical simulation of the suface defomation and its dynamic behavio to the GTAW pocess is of geat significance fo designing the pocess contol algoithm. Although thee have been significant advances in the numeical simulation of the GTAW pocess (Refs. 9 4), little attention has been paid to the tansient dynamics of the 3-D weld pool suface defomation at both the topside and backside of a fully penetated weld pool and its coelation to the extent of penetation. Pevious studies have shown that the pool depession has a diect effect on the penetation (Refs. 6 8). In fact, the weld pool sufaces at both the font and back ae depessed when thee is complete penetation, and the amplitude of such depession could be a eflection of the extent of penetation (Refs. 5, 6). Fo dynamic contol, quantitative analysis is equied to eveal how the pocess vaiables (weld pool geomety and suface depession) change with the welding paametes (welding cuent and velocity). In this pape, a numeical model is developed to descibe the tansient behavio of a 3-D GTA weld pool with complete penetation and suface defomation, and the quantitative elationship between the pool suface depession at the font side and the extent of penetation. Fomulation In ode to descibe the development of weld pool shape, suface defomation, themal field, and fluid flow field, a GTAW ac is consideed to be impinging on the wokpiece along the z diection and it moves in the x diection at a constant speed u 0. A moving (x, y, z) coodinate sys S DECEMBER 004

2 tem is so chosen that its oigin is located at the intesection between the ac centeline and the wokpiece suface. Fo such a thee-dimensional tansient poblem, the govening equations include the enegy, momentum, and continuity equations. Because of the suface defomations at both topside and backside of the weld pool, some new boundaies appeaed at both top and bottom sufaces, and thei positions changed with time. Theefoe, the calculation domain is no longe a egula ectangula one, which causes some bounday conditions to be difficult to deal with. To epesent the iegula boundaies, a coodinate tansfomation is adopted. The independent vaiable in tansfomed space (z) is elated to the vetical coodinate in physical space (z) accoding to z F x, y, t z = Bxyt,, Fxyt,, - ( ) ( ) - ( ) (1) whee F(x,y,t) and B(x,y,t) ae functions that define the uppe and lowe sufaces of the weld pool, espectively. The tansfomation maps the iegulaly shaped egions into ectangula computational domains in which the two cuvilinea sufaces ae stationay duing any given time inteval, and ae defined by z = 0 and z = 1. Then, the govening equations descibing the fluid flow and heat tansfe phenomena in a weld pool ae essed as: + V V z = 0 () V + ( Vl ) V = Fb - t + p p z + m sv + Cv (3) T c p Vt T s k st kct t + = ( ) + (4) whee V is the fluid velocity vecto with the components (u, v, w) in x, y, and z diections, V l is the fluid velocity vecto with the components (u, v, w l ) in x, y, and z diections, V t is the fluid velocity vecto with the components (u, v, w t ) in x, y, and z diections, is the density, c p is the specific heat, p is the pessue, m is the viscosity, k is the themal conductivity, and othe symbols ae defined as follows: = + + x i y j k (5) = + + x i y j k (6) WELDING RESEARCH Table 1 Othe Themophysical Popeties and Paametes Used in the Calculation Popety o Paamete Symbol Value Melting point T m 1763 K Ambient tempeatue T 93 K Density 700 kg m 3 Latent heat of vapoization L b J kg 1 Gavitational acceleation g 9.8 m s Suface adiation emissivity e 0.4 Magnetic pemeability m m H m 1 Suface tension g 1.0 N m 1 Tempeatue coefficient of suface tension g/ T N m 1 K 1 Themal ansion coefficient b 10 4 Cuent density distibution paamete s j 1.5 mm Heat flux distibution paamete s q.5 mm Ac powe efficiency h 0.65 Plate thickness H 3 mm = + s + x i y j S k z (7) m wl = V z - z (8) k wt = V z - z c p (9) V Cv = xy xyz m Î (10) T CT = xy xy z Î m (11) = + xy x i y j (1) Fo the body foce tem, Fb = J Bm - bg( T -T ) (13) whee b is the volume ansion coefficient, g is the acceleation of gavity, T is the ambient tempeatue, and the electomagnetic foce J B m is calculated based on Wu s analytical solutions (Refs. 1 and 15) essed as follows: ( J Bm ) = x mmi - p s j 4 s j z x H Î s j ( J Bm ) = y mmi - p s j 4 s j z y H Î s j (14) (15) ( ) = mmi J Bm z 4p H z H Î s j (16) whee m m is the magnetic pemeability, I is the welding cuent, s j is the effective adius of the cuent distibution in Gaussian fom, H is the thickness of the wokpiece, and = x + y. When the wokpiece is not completely penetated, the weld pool has only one fee suface F(x,y,t), which is defomed unde the combined action of ac pessue, hydostatic foce, and suface tension. If the wokpiece is completely penetated, the weld pool has two fee sufaces, i.e., the uppe suface F(x,y,t) and the lowe suface B(x,y,t). Unde the condition of patial penetation, the shape of weld pool suface F(x,y,t) can be descibed by the following equation: F pa - gf + C = 5 1 g F s (17) whee p a is the plasma ac pessue, C 1 the Langangian constant, g the suface tension, and F s = z F(x,y,t) = 0. The ac pessue p a can be descibed by (Ref. 7) Pac mij = m 4p (18) whee J is the cuent density at the wokpiece suface, which can be assumed to be in Gaussian distibution (Ref. 8) I J ( ) = ps j s j (19) WELDING JOURNAL 331 -S

3 WELDING RESEARCH Table Compaison of the Maximum Depession at Top Suface Pedicted Measued Weld Depession Weld Depession width (mm) width (mm) (mm) (mm) Top side Bottom side (SS304 wokpiece, thickness 3 mm, 110 A, 1 V, 15 mm/min) Fig. 1 The suface defomation vs. time (wokpiece, SS304; thickness, 3 mm; 100 A; 14 V; 15 mm/min). Equation 17 should satisfy with the constaint condition (0) whee S t is the aea of fusion zone at the wokpiece s uppe suface (z = 0), i.e., the domain of F(x,y,t) at the plane z = 0. The Langangian constant C 1 can be detemined by using Equation 0. If the wokpiece is completely penetated, the uppe suface F(x,y,t) and the lowe suface B(x,y,t) of the weld pool can be essed as Fs pa - gf+ C = g Fs Bs gb ( - F) + C = g B s (1) () whee B s = z B(x,y,t) = 0, and C is the Langanian constant, to make Equations 1 and satisfactoy with the constaint condition ÚÚ Fdxdy - ÚÚ Bdxdy = 0 S S T ÚÚ F dxdy = 0 S T B (3) whee S B is the aea of the fusion zone at the wokpiece s lowe suface (z = H), i.e., the domain of B(x,y,t) at the plane z = H. In tansient state, the weld pool geomety changes with time t, so the domains S T and S B also vay with time. In this way, the vaiations of F(x,y,t) and B(x,y,t) with time t ae descibed. The bounday conditions fo solving the govening Equations 4 ae as follows: Fo the fee suface of weld pool, u g m =- T T x (4) v g m =- T T y (5) w = 0 (6) - k T z = qac -qc -qevp (7) when, EI ( x- u t) qac( x y) = 6h 0 0,, pab1 + b 3( x- u0 t) y b a 1 Î when, EI ( x- u t) < qac( x y) = 6h 0 0,, pab1 + b 3( x- u0 t) y b a Î qc = hc( T - T ) qevp = me Lb ( ) ( ) (8) (9) (30) (31) whee a(b 1 + b ) = 1s q, a = 1.87s q, b 1 =.51s q, b = 3.91s q, h the ac powe efficiency, E the ac voltage, and s q the distibution paamete of ac heat flux. In this eseach, h c is the combined heat tansfe coefficient fo the convection and adiation bounday, T is the ambient tempeatue, L b is the latent heat of evapoation, and m e is the evapoation mass ate. Fo a metal such as steel, h c and m ev can be witten as (Refs. 9, 30) h c = et 1.61 (3) log(m ev ) = A B/T 0.5logT (33) whee e is the emissivity of the wokpiece suface, and A and B ae constants (A = 8.641, B = 18836). Fo the symmetic plane (y = 0), V = T 0, = 0 y y (34) In the solid, V = 0 (35) The bounday conditions fo Equations 19, 1, and ae witten as: Fo the domain outside the melting zone, F = 0, B = 0 (36) Fo the points at the melting zone bounday on the oxz-plane, F = B 0, = 0 x x (37) Fo the initial conditions: t = 0, T(x,y,z,0) = T, F(x,y,0) = 0, B(x,y,0) = 0 (38) Methods of Solution The govening equations and bounday conditions ae solved by means of the finite diffeence technique. The scheme of diffeences has a high degee of nonlineaity, as the chaacteistic values fo the mateial ae taken as tempeatuedependent. Coupling occus between and within the elevant aspects of the poblem. Thus, a special iteative pocedue is necessitated. The pogam fist calculates the tempeatue field in the solid wokpiece. Once the melt zone emeges, the whole domain is divided into two egions, i.e., the fluid flow zone in the weld pool and the solid zone outside the pool. The calculations of fluid flow and heat tansfe inside the pool and the conductive heat tansfe outside the pool ae conducted simultaneously. Then, the shape of the weld pool suface is calculated accoding to the pessue and enegy equilibium conditions. The liquid-solid bounday is detemined by the enthalpy at the melting point. Based 33 -S DECEMBER 004

4 WELDING RESEARCH A B C D Fig. The tansient development of weld pool suface defomation (wokpiece, SS304; thickness, 3 mm; 100 A; 14 V; 15 mm/min). A Defomation at top suface (side view, enlaged in z diection); B defomation at bottom suface (side view, enlaged in z diection); C defomation at top suface (font view, enlaged in z diection); D defomation at bottom suface (font view, enlaged in z diection). on the defomed pool suface, the fluid flow and tempeatue fields ae ecalculated. Then, the configuation of the weld pool suface and geomety is adjusted, and a epeated calculation pocedue commences. Once the wokpiece is completely penetated, the appopiate equilibium conditions of pessue ae applied to detemine the shape of the weld pool and its suface defomation at both topside and bottom side. The fluid flow and heat tansfe within the pool ae ecalculated, and the pool geomety is modified. Iteations ae pefomed until the selected convegence citeion is satisfied. The oveall algoithm consists of individual pocedues which ae pefomed iteatively. The iteative calculations fo the tansient poblems ae caied out. At each time step, all physical subpocesses ae solved numeically until the convegence citeion is met, and then time is incemented and the calculation pocedue is epeated. The additional souce tem method is utilized to tansfom both enegy and momentum bounday conditions into discete foms, and the discete govening equations in body-fitted coodinates ae established. Nonunifom gids ae used with fine spacing inside the weld pool and coase away fom it to impove the simulation accuacy and speed up the convegence. Vaious subpocess poblems ae calculated sepaately and impoved by tuns duing the whole iteative pocedue. In this way, the stongly coupling poblems ae solved effectively and successfully. Results Numeical simulations ae pefomed fo GTAW on stainless steel 304. A half wokpiece with a welding domain of mm ae divided into the mesh of gid points. Fo the 304 mateial, the specific heat c p, dynamic viscosity µ, and themal conductivity k ae tempeatue dependent, which can be essed as follows (Ref. 31): Ï T T 780K T K K k = ( W m K ) 780 T 167 Ì T 167K T 177K Ó T 177 T C p = Ï T T 773K T ( J kg ) 773K T 873K Ì T 873K T 973K Ó T 973K T (39) Ï T 1713K T 1743K T m = ( 10 kg m s ) 1743K T 1763K Ì T 1763K T 1853K Ó T 1853K T 1873K (40) (41) Othe themophysical popeties and paametes used in the calculation ae summaized in Table 1. The development of the weld pool includes the following stages: weld pool foming afte the ac ignition, the pool anding, and the pool eaching quasisteady state. The welding conditions wee as follows: 1) Test piece was 304 stainless steel with 50 mm length, 60 mm width, and 3 mm thickness. ) The welding cuent was 100 A. 3) The ac voltage was 14 V. 4) The welding speed was 15 mm/min. The figues and tables denote conditions as wokpiece, SS304; thickness, 3 mm; 100 A; 14 V; and 15 mm/s. Fo the welding conditions used, the weld pool emeges at t = 0.8 s, then ands continuously, gets fully penetated at t = 3.54 s, and eaches the quasi-steady state at t = 4.4 s. Figue 1 shows the tansient development of the pool suface defomation, i.e., the maximum values of the depession at both sides and the hump at the topside vs. time. Afte the weld pool is fomed at t = 0.8 s, the pool suface defomation is poduced. As the pool volume ands with inceasing time, the extent of the pool suface defomation gets bigge, and both maximum depession and hump at topside incease with time. The test plate is completely penetated t = 3.54 s. In the mean time, the bottom suface of the weld pool stats to defom, so the whole weld pool is depessed. Then, the hump at topside deceases, while the depessions at both sides ise at a highe ate. When the themal pocess eaches the quasi-steady state at t = 4.4 s, the weld pool geomety keeps constant, the hump at the topside becomes zeo, and the depessions of the weld pool at both sides attain thei maxi- WELDING JOURNAL 333 -S

5 A WELDING RESEARCH B Fig. 3 The atios of Dd max /W and Dd max /L vs. time (wokpiece, SS304; thickness, 3 mm; 100 A; 14 V; 15 mm/min). A The atio of the maximum depession to the pool width; B the atio of the maximum depession to the pool length. mum and do not vay anymoe with time. It can be seen that the inceasing ate of the pool suface depessions is quite diffeent befoe and afte the pool is completely penetated. Figue illustates the tansient development of weld pool suface defomation at both the top and bottom sides of the weld pool. In this figue, A and B ae the longitudinal sections (side view), while C and D ae the tansvese coss sections (font view). Compaed to the top suface of the weld pool, the bottom suface gets depessed moe seiously and quickly. The maximum depession at the bottom suface inceases fom 0 mm at t = 3.54 s (the moment when the pool is just completely penetated) to 0.6 mm at t = 4.4 s (the instant when the quasi-steady state is eached). The inceasing ate is mm/s. As shown in Fig. D, thee is a mino oscillation of the pool suface defomation at the bottom side afte the weld pool geomety eaches quasisteady state. But the amplitude of such oscillation is so low that the bottom suface contous at t = 4. s and t = 4.4 s ae nealy identical with each othe. Fo the top suface depession, the inceasing ates of maximum depession ae mm/s befoe complete penetation (fom 0 mm at t = 0.8 s to mm at t = 4.0 s) and mm/s afte complete penetation (fom mm at t = 4.0 s to 0.16 mm at t = 4.4 s), espectively. Since the vaiation ate of the top suface depession of the weld pool has a maked incease afte the pool is completely penetated, it can be taken as an indicato to judge whethe the plate is penetated o not. On the othe hand, the pool length and width at the topside ae also changed afte complete penetation is achieved. To quantitatively descibe the coelation of the topside suface depession with the extent of penetation, two chaacteistic vaiables ae used to eflect the vaiation of the whole weld pool geomety, i.e., the atio of the maximum depession Dd max to the pool width W (Dd max /W), and the atio of Dd max to the pool length L (Dd max /L). Figue 3 shows the atios of Dd max /W and Dd max /L vs. time. The thee-segment cuves of such atios eflect the infomation on the penetation. Duing the anding of the nonpenetated weld pool, the values of Dd max /W and Dd max /L ise slowly with time. At the moment the weld pool is fully penetated (t = 3.54 s), the ising ates of Dd max /W and Dd max /L ae suddenly inceased, i.e., the slopes of two cuves incease in a maked way. The fist kink point on the cuves coesponds to the moment when the weld pool gets fully penetated. When the quasi-steady state is obtained at t = 4.4 s, the weld pool geomety is in a elatively stable condition, Dd max /W and Dd max /L ae nealy constant, so the cuves ae just staight lines afte 4.4 s. The second kink point on the cuves coesponds to the moment when the weld pool eaches the quasi-steady state. Because the depession of the weld pool suface at the topside has the chaacteistics mentioned above, it can be employed as an indicato of weld penetation extent. In pactice, the topside senso can be developed to measue the weld pool suface depession fo weld penetation contol. Expeimental measuements ae made to veify the model. Afte welding, a macogaph of a weld coss section is made to measue the weld dimension. Table is the compaison between the pedicted and eimental weld depessions on a weld coss section. They ae in ageement with each othe. Conclusions 1) A 3-D tansient numeical model is developed fo investigating the dynamic behavio of the weld pool geomety, suface defomation, heat tansfe, and fluid flow in a full-joint penetated GTA weld pool. Based on the model, the weld pool emeges at t = 0.8 s, then it ands continuously, gets fully penetated at t = 3.54 s, and eaches the quasi-steady state at t = 4.4 s, fo the welding conditions used (wokpiece, SS304; thickness, 3 mm; 100 A; 14 V; 15 mm/s). ) Fo the top suface depession, the inceasing ates of maximum depession ae mm/s befoe complete penetation (fom 0 mm at t = 0.8 s to mm at t = 4.0 s) and mm/s afte complete penetation (fom mm at t = 4.0 s to 0.16 mm at t = 4.4 s), espectively. Compaed to the top suface of the weld pool, the bottom suface gets depessed moe seiously and quickly, with the maximum depession of 0.6 mm and the inceasing ate of mm/s. 3) The vaiation ate of the atios of the maximum pool suface depession at the topside to the pool width, and to the pool length, can be descibed if the plate is completely penetated. The simulation esults lay a foundation fo topside senso-based pocess contol of the GTAW pocess. Acknowledgments The authos ae gateful fo the financial suppot fo this poject fom United States National Science Foundation unde Gant No. DMI , and The National Natual Science Foundation of China unde Gant No They would like to thank T. T. Feng, M. X. Zhang, and J. K. Hu fo thei help in eiments, and H. G. Wang fo his help in gaph dawing. Refeences 1. Swaim, W Gas tungsten ac welding made easy. Welding Jounal 77(9): Zhang, Y. M., Kovacevic, R., and Lin., L Adaptive contol of full penetation GTA welding. IEEE Tans. on Contol Systems Technology 4(4): S DECEMBER 004

6 3. Xiao, Y. X., and Ouden, G. den Weld pool oscillation duing GTA welding of mild steel. Welding Jounal 7(8): 48-s to 434-s. 4. Calson, N. M., and Johnson, J. A Ultasonic sensing of weld pool penetation. Welding Jounal 67(11): 39-s to 46-s. 5. Wikle, H. C., Kottilingam, S., Zee, R. H., and Chen, B. A Infaed sensing techniques fo penetation depth contol of the submeged ac welding pocess. Jounal of Mateials Pocessing Technology, 113: Fiedman, E Analysis of weld puddle distotion and its effect on penetation. Welding Jounal 57(6): 161-s to 166-s. 7. Lin, M. L., and Eaga, T. W Influence of ac pessue on weld pool geomety. Welding Jounal 64(6): 163-s to 169-s. 8. Rokhlin, S. I., and Guu, A. C A study of ac foce, pool depession, and weld penetation duing gas tungsten ac welding. Welding Jounal 7(8): 381-s to 390-s. 9. Oepe, G. M., and Szekely, J Heatand fluid-flow phenomena in weld pools. Jounal of Fluid Mechanics, 147(10): Oepe, G. M., Szekely, J., and Eaga, T. W The ole of tansient convection in the melting and solidification in ac weldpools. Metall. Tans. B, 17: Kou, S., and Wang, Y. H Compute simulation of convection in moving ac weld pools. Metall. Tans. A, 17 (1): Tsao, K. C., and Wu, C. S Fluid flow and heat tansfe in GMA weld pools. Welding Jounal 67(3): 70-s to 75-s. 13. Zachaia, T., David, S. A., Vitek, J. M., and Deboy, T Weld pool development duing GTA and lase beam welding of type 304 stainless steel, pat I theoetical analysis. Welding Jounal 68: 499-s to 509-s. WELDING RESEARCH 14. Zachaia, T., Easlan, A. H., Aidun, D. K., and David, S. A Thee-dimensional tansient model fo ac welding pocess. Metall. Tans. B, 0(10): Wu, C. S., and Tsao, K. C Modelling the thee-dimensional fluid flow and heat tansfe in a moving weld pool. Engineeing Computations 7(3): Zachaia, T., David, S. A., Vitek, J. M., and Deboy, T Modeling of intefacial phenomena in welding. Metall. Tans. B, 1(6): Choo, R. T. C., Szekely, J., and Westhoff, R. C Modeling of high-cuent acs with emphasis on fee suface phenomena in the weld pool. Welding Jounal 69(9): 346-s to 361-s. 18. Choo, R. T. C., Szekely, J., and David, S. A On the calculation of the fee suface tempeatue of gas-tungsten-ac weld pools fom fist pinciples: pat II modeling the weld pool and compaison with eiments. Metall. Tans. B, 3(6): Wu, C. S., and Don, L Compute simulation of fluid dynamics and heat tansfe in full-penetated TIG weld pools with suface depession. Computational Mateials Science, : Domey, J., Aidun, D. K., Ahmadi, G., Regel, L., and Wilcox, W. R Numeical simulation of the effect of gavity on weld pool shape. Welding Jounal 74(8): 63-s to 68-s. 1. Wu, C. S., and Zheng, W Analysis of fluid flow and heat tansfe in a moving pulsed TIG weld pool. Intenational Jounal fo the Joining of Mateials, 9: Wu, C. S., Sun, J. S Detemining the distibution of the heat content of fille metal doplet tansfeed into GMA weld pools. Poc Instn Mech Engs, Pat B: Jounal of Engineeing Manufactue, Vol. 1B, Ko, S. H., Choi, S. K., and Yoo, C. D Effects of suface depession on pool convection and geomety in stationay GTAW. Welding Jounal 80: 39-s to 45-s. 4. Wu, C. S., and Yan, F Numeical simulation of tansient development and diminution of weld pool in gas tungsten ac welding. Modeling and Simulation in Mateials Science and Engineeing, 1: Kovacevic, R., and Zhang, Y. M Real-time image pocessing fo monitoing of fee weld pool suface. ASME Jounal of Manufactuing Science and Engineeing, 119: Saeed, G., and Zhang, Y. M Mathematical fomulation and simulation of specula eflection based measuement system fo gas tungsten ac weld pool suface. Measuement Science and Technology, 14: Lin, M. L., and Eaga, T. W Pessue poduced by gas tungsten acs. Metall. Tans. B, 17(9): Tsai, N. S., and Eaga, T. W Distibution of the heat and cuent fluxes in gas tungsten acs. Metall. Tans. B, 16(4): Goldak, J., Bibby, M., Mooe, J., and Patel, B Compute modeling of heat flow in welds. Metall. Tans., 17B: Choi, M., and Geif, R A study of heat tansfe duing welding with applications to pue metals o alloys and low o high boiling tempeatue mateials. Numeical Heat Tansfe, 11: Wu, C. S. Compute simulation of theedimensional convection in taveling MIG weld pools Engineeing Computations, 9(5): CAN WE TALK? The Welding Jounal staff encouages an exchange of ideas with you, ou eades. If you d like to ask a question, shae an idea o voice an opinion, you can call, wite, o fax. Staff addesses ae listed below, along with a guide to help you inteact with the ight peson. 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