WELDING RESEARCH

SUPPLEMENT TO THE WELDING JOURNAL, JANUARY 1993 Sponsored by the American Welding Society and the Welding Research Council

Toward Understanding Alloying Element Vaporization during Laser Beam Welding of Stainless Steel

A comprehensive model is proposed to predict vaporization rates during welding. Predictions are compared with experimental data

BY K. MUNDRA AND T. DEBROY

ABSTRACT. During laser beam welding perimental values. Synthesis of the prin­ densities, laser beam welding of many of many important engineering alloys, ciples of gas dynamics and weld pool important engineering alloys results in appreciable changes in the composition transport phenomena can serve as a basis significant changes in composition and and properties of the weld metal can for the calculation of alloying element properties of the weld metal (Refs. 1-4). occur due to pronounced vaporization vaporization rates during laser beam Because of its importance, vaporization of alloying elements from the weld pool. welding of alloys. of alloying elements during welding has Currently there is no comprehensive the­ been investigated both experimentally oretical model to predict, from funda­ Introduction and theoretically. Apart from the exami­ mental principles, laser-induced metal nation of the weld metal composition vaporization rates and the resulting weld The use of a high power density laser and structure to evaluate the direct ef­ pool composition changes. beam for welding leads to weld pool fects of vaporization, much of the previ­ The velocity distribution functions of temperatures that are often higher than ous experimental work was based on in- the gas molecules at various locations those encountered in most other weld­ situ monitoring of the alloying element above the weld pool surface and the heat ing processes. Even at modest power vaporization by emission spectroscopy transfer and fluid flow phenomena in the (Refs. 5-7). It was found that during pool have been coupled to model the welding of stainless steels, the dominant rates of the vaporization of various al­ species in the vapor phase were iron, loying elements during laser beam weld­ manganese, nickel and chromium. Eagar ing of stainless steels. The procedure al­ KEY WORDS and Block-Bolton (Ref. 8) used calcula­ lows for computation of both the evap­ tions based on the Langmuir equation to oration and condensation fluxes based Modeling demonstrate that iron and manganese were the most prominent vapor species on the equations of conservation of mass, Vaporization Rates in the welding environment. Although momentum and energy applied to the Alloying Elements vapor and the liquid phases. Computed the rates calculated by the Langmuir Laser Beam Welding values of the rates of vaporization of var­ equation have been used for the deter­ ious alloying elements and the vapor Gas Dynamics mination of the relative vaporization composition were found to be in good Weld Pool Transport rates of various alloying elements, the agreement with the corresponding ex- Evaporation Heat Loss calculated vaporization rates are gener­ Peak Temperatures ally significantly higher than the corre­ Vapor Composition sponding experimentally determined K. MUNDRA and T. DEBROY are with the Shielding Gas values at one atmosphere pressure. Even Department of Materials Science and Engi­ at pressures as low as 200 micrometers neering, Pennsylvania State University, Uni­ of Hg, the vaporization rates of pure versity Park, Pa.

WELDING RESEARCH SUPPLEMENT I 1-s mentally determined values. Further­ more, the effects of the nature and the flow rate of the shielding gas on the va­ porization rate were examined on the basis of the model. Gas Inlet H Gas Jet Experimental Procedure Axial Nozzle The details of the experimental pro­ Adjustment cedure are given in Refs. 2 and 15 from Laser Beam where the experimental data were taken Vapor Deposit for the validation of the model. A con­ Quartz Tube tinuous wave carbon dioxide laser was ) *- to Pump used to irradiate samples of AISI 202 Plexiglass steel as shown in Fig. 1. The total rate Chamber Sample of vaporization was determined from the loss in sample weight and the laser ma­ X-Y Table terial interaction time. A portion of the vaporized material was collected as con­ Fig. I — A schematic diagram of the experimental setup. densate on the inner surface of a hol­ low, cylindrical, open-ended quartz tube which was held stationary and co­ axial with the laser beam. The rates of metal drops were found (Ref. 9) to be convection in the weld pool. DebRoy, vaporization of the individual alloying about an order of magnitude lower than Basu and Mundra (Ref. 13) combined elements were determined from the total the principles of weld pool transport the values calculated by the Langmuir vaporization rate and the composition equation. phenomena and the vapor phase gas dy­ of the condensate was analyzed by elec­ namics for the calculation of laser-in­ When a metal is irradiated with a very tron probe microanalysis (EPMA). high power density laser beam, a signif­ duced vaporization of pure metals. The icant amount of vapor condensation can computed results agreed well with the take place and the kinetics of conden­ experimental data for the vaporization Theoretical Investigation sation must be taken into account in the of iron and titanium. The agreement be­ calculation of the net vaporization rate. tween the experimental and theoretical Temperature and Velocity Profiles in the Anisimov (Ref. 10) calculated the vapor results for pure metals indicates promise Molten Pool condensation rate by solving the gas dy­ of such a comprehensive calculation namics equations in a thin layer adja­ scheme in realistic modeling of the rates The rates of vaporization of the vari­ cent to liquid metal-vapor interface, of vaporization of alloying elements dur­ ous alloying elements from the weld known as the Knudsen layer. However, ing laser beam welding of alloys. pool are strongly dependent on the tem­ the calculations of temperature at the The work reported in this paper is perature distribution at the pool surface. metal surface were done from an ap­ aimed at understanding laser-induced Direct reliable measurements of temper­ proximate energy balance which in­ vaporization of stainless steels. The fluid ature profile at pool surface is difficult cluded only the energy required for the flow and temperature fields in the since the weld pool is small in size and vaporization, and completely ignored molten pool were simulated by the so­ is often covered by an intense plasma heat transfer due to conduction and con­ lution of the Navier-Stokes equations (Refs. 5-7) which interferes with most vection. For vaporization of aluminum, and equation of conservation of energy. noncontact temperature measurement Knight (Ref. 11) derived a set of gas dy­ The heat transfer to the shielding gas and procedures. Procedures based on the se­ namic equations across the Knudsen the evaporative heat loss (Ref. 14) due lective vaporization of alloying elements layer and calculated the fraction of the to vaporization of the alloying elements (Ref. 2) do not provide spatial resolution vaporized material that condenses for a were taken into account in the calcula­ of the temperature at the pool surface. given local surface temperature. Re­ tions. The computed weld pool temper­ A recourse is to simulate temperature cently, Chan and Majumdar (Ref. 12) ature distribution was used together with fields by mathematical modeling of the used Knight's equations to calculate the principles of gas dynamics and mass essential physical features of the pro­ laser-induced material vaporization transfer for the calculation of the vapor­ cess. The task involves numerical solu­ rates from molten aluminum, titanium ization rates during laser beam welding tion of the Navier-Stokes equation and and a superalloy. In the works of Knight of AISI 202 stainless steel in the contin­ the equation of conservation of energy. (Ref. 11) or Chan and Majumder (Ref. uous wave mode. The rates of vaporiza­ This approach has been adopted in this 1 2), the temperature calculations were tion of alloying elements due to a total paper. Since the appropriate equations performed in one dimension. Further­ pressure gradient at the pool surface are well documented in standard text­ more, no comparison between the the­ were determined from the equations of books, and the boundary conditions and oretical predictions and the experimen­ conservation of mass, momentum and other details of the application of these tal results was undertaken for the irradi­ translational kinetic energy in the gas equations to welding are available in the ation of either pure metals or alloys. phase. In addition, mass transfer rates recent welding literature (Refs. 1 6-1 8), due to concentration gradients were de­ these are not presented here. Special fea­ Since Anisimov's work (Ref. 10), sig­ termined using available correlations tures of the computational scheme that nificant progress has been made in the amongst various dimensionless num­ have been taken into account in-the application of transport phenomena for bers. The theoretically predicted rates boundary conditions include the heat the calculation of weld pool tempera­ of vaporization of iron, manganese, transfer to the shielding gas from the sur­ ture and velocity fields. At present, weld nickel and chromium from a molten AISI face of the pool and the evaporative heat pool temperature calculations are com­ 202 stainless steel weld pool were com­ loss due to vaporization of alloying ele­ monly performed by taking into account pared with the corresponding experi­ ments. Zacharia, et al. (Ref. 14), has both heat conduction and Marangoni

2-s I JANUARY 1993 shown that vaporization can signifi­ cantly influence the temperature field (£-u J Shielding Gas p^p^ pressure on the pool surface. The local heat flux 2 Wavefront from the pool surface, Jh, in J/m -s is given by Shielding Gas p2, J^,T2 Contact Discontinuity Ju -h{T, \£',Atf, (1) where T-, is the local weld pool surface temperature, Tg is the ambient tempera­ ture, J, is the vaporization flux in kg/m2- s of an element i, AH, is the enthalpy of vaporization of the element i in J/kg, n is the number of alloying elements and h is the heat transfer coefficient in J/m2- s-K. The heat transfer coefficient for a gas jet impinging on a surface was de­ rived from the graphical results of Fig. 2 — A schematic diagram of the velocity distribution junctions in the Knudsen layer and Schlunder and Gniclinski (Ref. 19) and in adjacent regions. is given by the following relation:

2Pr SA2Re™kl, Re" pressure and the excess pressure pro­ where m = u/V2 Rv Tv, Rv = R/Mv, R is 1 + -200 vides a driving force for the vapor to the gas constant in J/mole-K, yv is the move away from the surface. The veloc­ ratio of specific heats of the vapor, which 0.483- 0.108- + 7.71xl0~ (2) ity distribution functions of the vapor is treated as a monoatomic gas, and M d v molecules escaping from the weld pool is the average molecular weight of the where d is the diameter of the nozzle in surface at various locations are shown vapor in kg/kg-mole meters, r is the radial distance on the schematically in Fig. 2. Near the weld pool surface in meters, k is the thermal pool surface, the molecules cannot erfc'm)- conductivity of shielding gas in J/m-s-K travel in the negative direction, and as p, K + 2"" at temperature Tav, which is the arith­ a consequence, the distribution function 1 75 metic average of T, and T„, Re is the is half-Maxwellian. Close to the weld 1 — V n m e"' erfc(m) (4) Reynolds number at the nozzle exit and pool surface there exists a space of sev­ 2T Pr is the Prandtl number. eral mean free paths length, known as where erfc is the complimentary error the Knudsen layer (Ref. 10), at the outer function. Vaporization Due to Pressure Gradient edge of which the velocity distribution The condensation factor, (3, is given reaches the equilibrium distribution. by In laser processing of the metals and Here, the vapor molecules can have all alloys, the temperatures reached on the possible velocities from - °° to + °°, at least in principle, as observed in Fig. 2. 2 surface can be very high and often ex­ p = \(2m +l) (5) ceed the boiling point (Refs. 20, 21). For A portion of the vaporized material con­ example, von Allmen (Ref. 22) deter­ denses on the liquid surface. mined molten pool temperatures in ex­ The density, p,, can be computed The temperature Tv, density pv, pres­ cess of boiling point for laser treatment from P} and T1( assuming that the vapor sure P and the mean velocity of the of copper. Batanov, etal. (Ref. 23), in­ v behaves like an ideal gas. The equilib­ vapor, u, at the edge of the Knudsen dicated that temperatures on the surface rium vapor pressure, P^ at the pool sur­ layer can be related to temperature, T,, of the laser irradiated material can be face is obtained from the equilibrium pressure, P and the density, p-,, of the higher than the normal boiling point of 1; vapor pressure-temperature relation­ vapor at the liquid surface by treating the material. Paul and DebRoy (Ref. 16) ships of the various alloying elements. the Knudsen layer as a gas-dynamic dis­ and Zacharia, etal. (Ref. 24), have re­ continuity. Anisimov (Ref. 10) and ported temperatures close to the boiling Knight (Ref. 11) derived expressions for point for laser beam welding. Khan and — = > a, — (6) the changes in the vapor density, tem­ P.. Sf P. DebRoy (Ref. 2) measured the liquid perature, velocity and the extent of con­ pool surface temperatures close to the where P is the ambient pressure, a, is densation by using the velocity distribu­ g boiling point from the ratio of the rates the activity of the alloying element i and tion functions presented in Fig. 2 and of vaporization of alloying elements. Pj° is the equilibrium vapor pressure of solving the equations of conservation of Chan and Majumdar (Ref. 1 2) have also the pure element i at T-, and n is the num­ mass, momentum and translational ki­ reported temperatures greater than boil­ ber of alloying elements. Since the tem­ netic energy across the Knudsen layer. ing point for the laser irradiation of alu­ peratures at the weld pool surface are Since the details of the procedure are minum, titanium and a superalloy. The­ very high, the activities were taken to available in their papers, only a sum­ oretical calculations of the vaporization be equal to the corresponding mole frac­ mary of the results, commonly referred rates by Knight (Ref. 11) and Anisimov tions. The average molecular weight of to as the jump conditions, are presented (Ref. 10) are based on the premise that the vapor, M , in the Knudsen layer is in Equations 3 to 5. v the liquid pool surface temperatures are given by: higher than the boiling point. At temperatures higher than the boil­ 0,1, • 1 m 7,-1 m M,, = ]£ M, (7) ing point, the pressures in the vicinity 11 + (3) /, +1 2 Y, +1 2 of the pool are greater than the ambient

WELDING RESEARCH SUPPLEMENT I 3-s Velocity Field

. 3.9 x 10 -4m-

to c X

3

Ur 0.7 m/s

Temperature Field

3182 K

2800 3000 3200 3400 3600 3800

1811 K Temperature (K)

Fig. 3 — Velocity and temperature fields for a laser power of 560 W Fig. 4 — Flow state diagram for AISI 202 stainless steel in helium at­ and helium gas flow rate of 6 L/min. mosphere. The Mach number for various lines is indicated in the figure.

where M; is the molecular weight of where P„ and P2 are the pressures in front where S is the speed of sound in vapor species i, a, is the activity i in the liquid of and behind the wavefront, respec­ at temperature Tv. Since the rate of va­ metal, and Pj° is the equilibrium vapor tively. yg is the ratio of specific heats for porization of an alloying element will pressure of the pure element i at T^ shielding gas and T = Vyv RVTV/Vy„ RgTg. be proportional to its partial pressure Since there are four unknowns in Equa­ The Mach number, M, is related to m over the pool, its flux, Jpi is given by tions 3 to 5, viz. Tv, pv, & and m, it is according to the equation necessary to have an additional equa­ ELMLJ (11) tion to have unique values of these vari­ (9) ' P, Mr ' ables. The necessary equation is ob­ A1 2 tained by relating the pressure at the In Equation 8, Pi,/P can be computed Vaporization Due to edge of the Knudsen layer to the ambi­ g from Equation 6 for a given local surface Concentration Gradient ent conditions. Across the Knudsen layer temperature and, since P = P , for an the vapor wavefront moves into the 2 v ideal gas, P2/P1 can be expressed as a At the pool surface, the concentra­ shielding gas, as shown in Fig. 2. The function of m with the help of Equations tions of the alloying elements in the moving interface between the vapor and 3 and 4. Thus, Equation 8 is effectively vapor is considerably higher than their the shielding gas is a contact disconti­ reduced to a nonlinear equation in m respective concentrations in the bulk nuity. Across this discontinuity, the pres­ and can be solved iteratively or graphi­ shielding gas. The vaporization flux of sures are the same, i.e., P = P . The 2 v cally to obtain m and the Mach number an element i due to concentration gra­ pressure rise at the liquid-vapor inter­ 2 for a given local weld pool surface tem­ dient, Jc 1 in kg/m -s, is then defined as face propagates as a pressure wave as perature. The values of T , p and B., cor­ shown in Fig. 2. The wavefront may be v v responding to a local temperature T-, can treated as a pressure discontinuity, and (12) be determined from Equations 3 to 5 by ,., , RT the pressure change across the wave- using the computed value of m. The front may be obtained by applying the Mach number and the density p can where P,° is equilibrium vapor-pressure Rankine-Hugoniot relation (Ref. 25). v then be used to calculate the vaporiza­ of the element i over pure liquid i in at­ 2 mosphere, Mj is the molecular weight tion flux, ]p, in kg/m -s, due to pressure 2L5.- gradient at the pool surface correspond­ of the element i in kg/kg-mole, R is the 3 P. P, ~ ing to a local surface temperature T,. gas constant in m atm /kg-mole K and K j is the mass transfer coefficient of the 7+1 T7. + 1 g 1 + ysMV •^ Mr + , 1+ -^ MT (8) element i in m/s. The mass transfer co­ J=p,MS (10) 4 \ { 4 efficient was derived form the graphical

4-s I JANUARY 1993 cs P

X 3 E c «3 N "C c c Cd > 2800 3000 3200 3400 3600 3800

Temperature (K) 0.00 0.01 0.02 0.03 0.04

Radius x 10"2 (m) Fig. 5 — Mach number and density for AISI 202 stainless steel for Fig. 6 — Vaporization flux for various alloying elements, and the various temperatures at the edge of Knudsen layer in helium atmo­ total flux from the model presented in this paper. sphere. results of Schlunder and Gniclinski (Ref. Schmidt number of the element at aver­ most instantaneously. For a high power 19) and is given by age temperature Tav. The total vaporiza­ density laser beam, the time required to tion flux, Jj, for an element i is then given reach steady state is very small. 2Sc"J1 Re's D Re0-'5 by Zacharia, et al. (Ref. 24), noted that in 200 laser beam welding quasi-steady state is Ji=Jp.,+l., d4) 0.483-0.108-+7.71X10 (13) achieved very quickly. Mehrabian, et al. d •fcF (Ref. 26), showed that the time required where d is the diameter of the nozzle in Results and Discussion to reach the maximum melt depth in iron meters, r is the radial distance on the for a laser power of 2 x 105 W/cm2 is of pool surface in meters, D is the diffusiv­ Velocity and Temperature Fields the order of 1 ms. Thus, for almost the ity of the element in shielding gas in m2/s entire duration of a large laser pulse of at temperature Tav/ Re is the Reynolds When the laser beam strikes the sur­ several milliseconds span, the molten number at the nozzle exit and Sc is the face of the samples, melting occurs al­ pool remains in a steady state. The

150 "SD H Experimental y£ QD Present Work 0 Langmuir 120" 6' X m § c X o 3 •B .2 60 o j Li C EX Mn Fe Cr Ni Total

Fig. 8 — Comparison of the experimental vaporization rates with the rates calculated from the Langmuir equation and from the model pre­ sented in this paper. 0.00 0.01 0.02 0.03 0.04 Radius x 10"2 (m)

Fig. 7 — Vaporization flux for various alloying elements and the total flux computed using Langmuir equation.

WELDING RESEARCH SUPPLEMENT I 5-s Table 1 — Data Used for Calculations in the Table 3 — Comparison of Predicted Values of Weld Pool Geometry and Peak Temperatures Welding of AISI 202 Stainless Steel with Experimental Data for the Welding of AISI 202 Stainless Steel

Property/Parameter Value Parameter Experimental'"11 Model Prediction

Density (kg/m3) 7200.0 Welding pool width (m) 8.2 X 10-4 7.8 X 1CT4 Melting point (K) 1811.0 Weld pool depth (m) 2.3 X 10-4 2.0 X 10"4 Laser power (W) 560.0 Peak temperatures (K) 3093 ±44 3182 Radius of the beam (m) 2.0 X 10-" Effective viscosity 0.05 (a) Refs. 2, 15. (kg/m-s) Thermal diffusivity of solid 3.3 X 10"3 (m2/s) Thermal diffusivity of 7.5 X 10"5 Table 4 — Composition of the Alloying Table 5 — Comparison of the Predicted liquid (m2/s) Elements in the AISI 202 Stainless Steel Vapor Composition with the Experimentally Specific heat of solid 710.6 Determined Values for the Welding of AISI (J/kg-K) Composition Activity 202 Stainless Steel Specific heat of liquid 836.0 Elements (wt-°o) (mole fraction) (J/kg-K) Composition Ratio Absorption coefficient 0.17 Manganese 6.58 0.066 (Moles of i/ Present Temperature coefficient -5.3 X 10-< Chromium 17.80 0.190 Moles of j) Experimental Work of surface tension Nickel 4.77 0.045 (N/m-K) Iron 70.14 0.698 JFe/lMn 108 ± 0.07 1.00 Ratio of specific heats of 1.667 vapor (7V) JN/JMH 0.05 + 0.01 0.05 steady state temperature and velocity fields, obtained from the solution of Navier-Stokes equations and the equa­ sulting in a relatively shallow pool. The tions of conservation of mass and en­ maximum radial velocity is of the order Table 2 — Enthalpies of Vaporization of the ergy are shown in Fig. 3. The calcula­ of 0.7 m/s, which is close to the value Alloying Elements'1' tion takes into consideration the con­ reported by Zacharia, et al. (Ref. 24). vective heat loss to the shielding gas and The computed strong temperature gra­ Enthalpy the evaporative heat loss at the pool sur­ dient on the surface of the pool is con­ Element (kj/kg) face in accordance with Equation 1. The sistent with the absorption of a signifi­ data used for the calculations are pre­ cant amount of energy in a small local­ Iron 6087 ized area near the laser beam axis. The Manganese 4005 sented in Tables 1 and 2. The details of Chromium 6577 the calculations of thermal diffusivity theoretically predicted pool diameter Nickel 6388 and viscosity of the shielding gas are pre­ and depth, presented in Table 3, were sented in Appendix B. For low concen­ found to be in good agreement with the (a) Ref. 27. tration of surface active elements, the experimentally observed values (Refs. temperature coefficient of surface ten­ 2, 15). Furthermore, the theoretically sion is negative (Ref. 29). Therefore, the predicted peak temperature indicated in velocities at the weld pool surface, Table 3 was found to be in good agree­ shown in Fig. 3, are radially outward re­ ment with the temperature experimen-

3400 200

& 3300 He u f 1*4 s—' 3 J 100 V E s 3200" 'N Ar CT, o 'C O 0- 3100 > 0 3000 2900 3000 3100 3200 3300 3400 Temperature (K) Flow Rate (l/min ) Fig. 10 — Pressure gradient driven vaporization flux as function of temperature in helium and argon. Fig. 9 — Peak temperatures calculated as a function of gas flow rate and the type of the shielding gas used.

6-s I JANUARY 1993 2500 a Beam Energy Absororbed • Net Energy Absorbed Considering -? 2000" Evaporation in He 0 No Evaporative Heat Loss CN ED With Evaporative Heat Loss e Net Energy Absorbed Considering 1500 Evaporation in Ar

C 1000 o

500"

•lj H i H q- Helium Argon 0.00 0.01 0.02 0.03 0.04 0.05

Fig. 11 — Comparison of vaporization rate in helium and argon for a Radius x 10"2(m) flow rate of 6 L/min with or without consideration of evaporative heat loss. Fig. 12 — Energy absorbed vs. radius. tally determined by Khan and DebRoy the vapor across the Knudsen layer is mentally determined vaporization rates (Ref. 2). uniquely defined and is given by the for the AISI 202 stainless steel are com­ The computed results demonstrate Mach number of the line that intersects pared with the rates computed from the the importance of weld pool evapora­ the equilibrium vapor pressure curve at model and the values calculated from tive heat flux in the calculation of the a given temperature. For example, the the Langmuir equation for the same peak temperature. For a gas flow rate of Mach number of the vapor across the steel. It is observed that the experimen­ 6 L/min of helium, the peak temperature Kundsen layer at weld pool surface tem­ tally determined vaporization rates are was found to be 3222 K when the evap­ perature of 3200 K is 0.3 and the equi­ closer to the values predicted by the pre­ orative heat loss was not considered librium vapor pressure at the pool sur­ sent model than the rates calculated whereas when the heat loss was consid­ face is 2.5 atm. The values of the Mach from the Langmuir equation. Further­ ered, the peak temperature dropped to number and the density of the vapor more, the predicted ratios of the vapor­ 3182 K. These results are consistent with across the Knudsen layer calculated ization rates of the alloying elements are the observations of Zacharia, etal. (Ref. from Equation 4 for various surface tem­ in good agreement with the correspond­ 14), who reported a significant drop in peratures are presented in Fig. 5. The ing experimentally determined values the temperature when evaporative heat computed values of both the Mach as observed from Table 5. loss from the pool surface was consid­ number and the vapor density indicate The effects of the nature and the flow ered. their strong dependence on the surface rate of the shielding gas on the weld pool temperature due mainly to the strong temperature are observed from the re­ Vaporization Rates correlation between the vapor pressure sults in Fig. 9 where the calculated peak and temperature. From the values of the temperatures in helium and argon are From the temperature field in Fig. 3, Mach number and the density, total va­ indicated. The observed temperature dif­ it is evident that the temperatures porization flux and the flux of the indi­ ference in the two cases is about 35 K. reached at the weld pool surface are vidual alloying elements due to pressure At a peak temperature of about 3200 K, high and the temperature at the center gradient are calculated from Equations this difference would be difficult to de­ of the pool is greater than the boiling 10 and 11. The vaporization rate due to termine experimentally. For a given point of pure iron. The temperature at concentration gradient is calculated shielding gas, the calculations indicate which the pressure on the surface is from mass transport considerations, that with the increase in the gas flow equal to 1 atm was calculated to be 2952 which take into account the gas flow rate, the peak temperature on the pool K from the equilibrium vapor pressure- conditions and the nature of the shield­ surface does not change significantly as temperature relationship for the various ing gas in accordance with Equation 12. can be observed from Fig. 9. The radial distribution of the vapor­ alloying elements given in Appendix C To understand the effect of the type and the composition of the AISI 202 ization flux of the alloying elements and the total flux due to the combined ef­ of shielding gas, let us consider isother­ stainless steel indicated in Table 4. mal evaporation in helium and argon When the local surface temperature is fects of total pressure and concentration gradients are plotted in Fig. 6. Similarly, driven by the pressure gradient alone, higher than this value, the pressure at since the pressure gradient driven mass the weld pool surface is greater than the the radial distribution of the vaporiza­ tion flux of the individual alloying ele­ transfer rate is significantly higher than ambient pressure. In such a case, the re­ the concentration gradient driven rate. lations among the temperature, pressure ments and the total flux calculated from the Langmuir equation are plotted in Fig. In such a case, at a given temperature, and the Mach number for a material can the computed results in Fig. 10 indicate be represented on a plot of temperature 7. Comparison of the results in Figs. 6 and 7 indicates that the flux of the al­ a higher vaporization rate in helium than vs. pressure for various values of Mach that in argon. This is due to the fact that number. The plot, commonly referred loying elements predicted from the Langmuir equation is much higher than condensation of vapor molecules is to as the flow state diagram, obtained more pronounced in argon than in he­ from the solution of Equations 3 to 9, is the corresponding value predicted from the present work. In Fig. 8, the experi­ lium due to the differences in the physi­ shown in Fig. 4. The Mach number of cal properties of the two gases, particu-

WELDING RESEARCH SUPPLEMENT I 7-s 10. Anisimov, S. I., and Rakhmatulina, A. Kh. 1973. Soviet Physics-jETP 37:441 -444. 10 Langmuir 11. Knight, C. J. 1979. AIAA journal Present Work 17:519-523. Data from Collur et al. 1 2. Chan, C. L., and Mazumder, J. 1 987. o j. Appl. Phys. 62:4579-4586. 13. DebRoy, T., Basu, S., and Mundra, K. X He 1991J. Appl. Phys. 70:1313-1319. o 14. Zacharia, T., David, S. A., and Vitek, J. M. 1990. Metall. Trans. B22B:233-241. 15. Khan, P. A. A. 1987. Ph.D. thesis, De­ Fig. 13 — Vaporization partment of Materials Science and Engineer­ rate predicted from the ing, Pennsylvania State University, Univer­ model and from the He sity Park, Pa. Langmuir equation for o 16. Paul, A., and DebRoy, T. 1988. Met­ different types of cx Ar all. Trans. B 19B:851-858. shielding gas at various 17. Oreper, G. M., and Szekely, J. 1984. flow rates. Experimen­ I. Fluid Mech. 147:53-79. tal vaporization rates 2 3 4 5 18. Zacharia, T., Eraslan, A. H., and are taken from Ref. 4. Aidun, D. K. 1988. Welding journal b7(\):\ 8- Flow Rate (l/min) s to 27-s. 19. Schlunder, E. U., and Gniclinski, V. 1967. Chem.-lng.-Tech. 39:578-584. larly the densities. The connective heat from the principles of gas dynamics and 20. Anisimov, S. I., Bonch-Bruevich, A. M., El'yashevich, M. A., Imas, Ya A., loss to the shielding gas is considerably weld pool transport phenomena are Pavlenko, N. A., and Romanvov, G. S. 1967. smaller than the laser beam energy ab­ shown to be in good agreement with the Soviet Physics-Technical Physics. sorbed by the weld pool. Therefore, if experimental values. Vaporization rates 11:945-952. the evaporative cooling were ignored predicted by the Langmuir equation 21. Dabby, F. W., and Paek, U. 1972. and the computed weld pool surface were found to be much higher than the IEEE lournal of Quantum Electronics QE- temperature distributions were identical experimental rates. The computed com­ 8:106-111. in helium and in argon, the computed position of the vapor was in reasonable 22. von Allmen, M. 1987. Laser-Beam In­ vaporization rates in helium would have agreement with the experimentally de­ teractions with Materials. Springer-Verlag, p. been much higher in helium than that termined value. The theoretically pre­ 161. in argon, as can be observed from Fig. dicted weld pool geometry and the peak 23. Batanov, V. A., Bunkin, F. V., 1 1. In the absence of evaporative heat temperature were in good agreement Prokhorov, A. M., and Fedorov, V. B. 1973. Soviet Physics ]ETP 3b(2):311-322. loss, the radial distribution of the net en­ with the corresponding experimentally 24. Zacharia, T., David, S. A., Vitek, J. M., ergy absorption is shown by the upper­ determined values. Evaporative heat loss and DebRoy, T. 1989. Welding journal most curve in Fig. 1 2. However, when was found to significantly decrease the 68(12):499-sto509-s. the evaporative heat loss is considered, temperature at the pool surface. Inde­ 25. Vincenti, W. and Itrtiger, J. 1965. In­ the net absorbed energy in argon atmo­ pendent experimental results on the ef­ troduction to Physical Gas Dynamics. Wiley, sphere is slightly higher than that in he­ fect of shielding gas flow rate and the New York, N.Y. lium, as can be observed in Fig. 12. The type of shielding gas on the vaporiza­ 26. Mehrabian, R., Kou, S., Hsu, S. C, difference in the net energy absorption tion rate could be explained on the basis and Munitz, A. 1978. AIP Conference Pro­ in argon and helium results in about 35 of the model for the laser-induced va­ ceedings, MRS, Boston, Mass. K lower peak temperature in helium at­ porization based on gas dynamics and 27. lida, T., and Guthrie, R. L. 1986. The mosphere as has been discussed earlier. weld pool transport phenomena. Physical Properties of Liquid Metals, Oxford The lower temperature in helium com­ Science Publications, p. 8. 28. Khan, P. A. A., and DebRoy, T. 1985. pensates the difference in vaporization Acknowledgment Metall. Trans. B 16B:853-856. rates when evaporative heat loss is con­ 29. Sahoo, P., DebRoy, T., and McNal- This work was supported by the U.S. sidered. The resulting vaporization rate lan, M. J. 1987. Metall. Trans. B. Department of Energy, Office of Basic is about 1 5% higher in helium than in 196:483^91. Energy Sciences, Division of Materials argon. The calculated results are consis­ 30. Hirschfelder, J. O., Curtiss, C. F., and tent with the observations of Collur, ef Science, under grant number DE-FC02- Bird, R. B. Molecular Theory of Gases and al. (Ref. 4), who measured vaporization 84ER45158. Liquids, John Wiley & Sons, Inc., New York, rates during laser beam welding of AISI N.Y. References 201 stainless steel in different shielding 31. Hultergen, R., Desai, P. D., Hawkins, gases at various shielding gas flow rates. 1. Khan, P. A. A., DebRoy, T., and David, D. T., Gleiser, M., Kelley, K. K., and Wag- He found that the vaporization rate did S.A. 1983. Welding Journal 67(1 ):1-s to 7-s. man, D. D. 1973. Selected Values of the Ther­ modynamic Properties of the Elements. ASM not change significantly with either the 2. Khan, P. A. A., and DebRoy, T. 1984. International, Materials Park, Ohio, pp. 6, 7. shielding gas flow rate or with the type Metall. Trans. B, 15B:641-644. 3. Cieslak, M. )., and Fuerschbach, P. W. 32. Honig, R. E„ and Kramer, D. A. 1970. of gas as shown in Fig. 13. The rates pre­ 1988. Metall. Trans. B 19B:319-329. Physicochemical Measurements in Metal Re­ dicted by the model are in fair agree­ 4. Collur, M. M., Paul, A., and DebRoy, search. Interscience Publishers, New York, ment with the experimental data. Fur­ T. 1987. Metall. Trans. B 18B:733-740. N.Y., vol.4, pp. 505-517. thermore, the vaporization rates pre­ 5. Miller, R„ and DebRoy, T. 1990. J. App. 33. Turkdogan, E. T. 1980. Physical dicted by the Langmuir equation are sig­ Phys. 68(5):2045-2050. Chemistry of High Temperature Technology, nificantly higher than the correspond­ 6. Collur, M. M., and DebRoy, T. 1989. Academic Press, 1980. ing experimental values. Metall. Trans. B 20B:277-286. Appendix A 7. Dunn, C. J., Allemand, C. D., and Eagar, T. W. 1986. Metall. Trans. A List of Symbols 17A:1851-1863. Conclusions 8. Block-Bolten, A., and Eagar, T. W. a, activity of the alloying element i 1984. Metall. Trans. B 1 5B:461-469. cl diameter of the nozzle Laser-induced vaporization rates of 9. Sahoo, P., Collur, M. M„ and DebRoy, D diffusivity of element i in the the various alloying elements predicted T. 1988. Metall. Trans. B 1 9B:967-972. shielding gas 8-s I JANUARY 1993 vapor velocity distribution yv ratio of specific heats at constant function at the pool surface pressure and volume for the Table 6 — Data Used for the Calculation of velocity distribution function of vapor the Thermophysical Properties the vapor transported toward the p2 density across the moving weld pool surface interface between the shielding Parameter o-(A) e/k vapor velocity distribution gas and the vapor Iron 2.43 3545.2 function at the edge of Knudsen PT density of the vapor at the pool Manganese 2.58 2817.9 layer surface Chromium 2.46 3738.2 h heat transfer coefficient pv density of the vapor at the edge Nickel 2.38 3641.5 AHi enthalpy of vaporization of of Knudsen layer Argon 3.418 124.0 2.576 10.2 element i Helium Jci vaporization flux of an element i Appendix B clue to concentration gradient atmospheres were calculated using the Jh local heat flux from the pool Calculation of Thermophysical Proper­ following equations: surface ties of Cases and Vapor. 4 vaporization flux of the element log p0Mn = -5.58 x 1 0" T - 1.503 x i due to a combination of The thermal conductivity of 104/T+12.609/1.013x105 (Ref. 31) pressure and concentration shielding gas is given by 3 gradients log poNi = -3.519x10 /T + 74.94 log 3 7 2 total vaporization flux of all _ 3.9523x10" \ T T -1 8.042 x 1 0~ T +15.14x1 0- T - (IA) 5 elements due to pressure gradient ala'Ar) 4M, 214.297/1.013 x 10 (Ref. 32) vaporization flux of element i 3 clue to pressure gradient where K„ is in J/m-s-k, o is the collision log P°Cr = -1 3.505 x 10 /T + 33.658 3 7 2 thermal conductivity of the diameter in angstroms, T* = kBT/e where log T - 9.29 x 1 0- T + 8.381 x 10- T - s shielding gas kB is the Boltzmann constant, e is the in- 87.077/1.013 x 10 (Ref. 32) mass transfer coefficient of termolecular force parameter, Mg is the g.i molecular weight of the shielding gas 4 element i InPO Fe -4.3734 x 10 /T + 13.98 function of the Mach number and jQ^ is the slowly varying function of (Ref. 33) given by Equation 9 the dimensionless parameter kT/e. M Mach number Mi molecular weight of alloying The viscosity of the shielding gas in element i kg/m-s at temperature T is given by Mv average molecular weight of vapor 2.6693xl(r n number of alloying elements *V MT (2A) Pr Prandtl number crn:(r) P, pressure across the moving where Du is again a slowly varying func­ interface between the shielding tion of the dimensionless parameter gas and the vapor kT/e. ambient pressure Pi° equilibrium vapor pressure of the The mass diffusivity of an element i pure element i in the shielding gas, D: „, at absolute equilibrium vapor pressure at the temperature T is given by pool surface radial distance on the pool 1.8583X10'7 I ' surface M, M„ R (3A) gas constant of.Q„,r Re Reynolds number 2 S speed of sound in vapor where Dig is in m /s, M; is the molecu­ Sc Schmidt number lar weight of the element i, o, „ = (tjj + T, temperature across the moving o"„)/2, QD j is a slowly varying function interface between the shielding of T/e, „ where gas and the vapor average temperature 5, = V(£M£)< (4A) ambient temperature local weld pool surface temperature The data used for the various param­ temperature at the edge of eters are given in Table 6. The values of Knudsen layer Q were obtained from Ref. 30. mean velocity of the vapor at the edge of Knudsen layer Appendix C Greek Symbols Equilibrium Vapor Pressure Data Used 6 condensation factor given by for the Calculations Equation 5 % velocity of a vapor molecule The equilibrium vapor pressures of ratio of specific heats at constant the various vaporizing species, viz., Mn, pressure and volume for the Cr, Ni and Fe over the respective pure shielding gas liquids, at temperature T, expressed in

WELDING RESEARCH SUPPLEMENT I 9-s