DESIGN MATHEMATICAL MODEL FOR HEAT TRANSFER IN LASER BEAM WELDING PROCESS

Transcription

1 ARPN Joural of Egieerig ad Applied Scieces Asia Research Publishig Networ (ARPN). All rights reserved. DESIGN MATHEMATICAL MODEL FOR HEAT TRANSFER IN LASER BEAM WELDING PROCESS Rafel Hemat Hameed ad Isam Mejbel Abed Departmet of Mechaical Egieerig, College of Egieerig, Uiversity of Babylo, Iraq ABSTRACT The model of eergy trasport is desiged to iclude the fusio effects by usig a movig boudary problem. This model allows accoutig for both high order temperature gradiets ad state of o-equilibrium, this prompts further realistic determiatio the distributio of temperature withi the wor-piece. The model has bee employed to simulate the evolutio of spatial temperature distributio withi the target materials whe irradiated with both CW ad pulsed laser. This model explais the weldig process i terms of the velocity of fusio surface (V * ) which has bee calculated as a fuctio of power itesity. The zoe of fusio dimesios, ad the heat affected zoe are illustrated of target metal with phase trasformatio uder the icidet power itesity i a rage of 10 5 W/cm 2. A ew scheme of weldig mechaism has bee implemeted. This scheme is based o switchig from the trasiet model of weldig to cotiuous weldig (steady state), usig a laggig method i explicit techique. This method gives more stable solutio through a computer program, which calculates the temperature distributio from a movig wor-piece. Keywords: fusio, laser beam, heat trasfer, mathematical model, weldig, movig boudary. 1. INTRODUCTION Weldig by a high-power CO 2 laser is most used i idustry today. This process is classified as a movig case. May chemical ad physical parameters are iterested i this case. It is very difficult to obtai results whe cosiderig all the parameters. Fusio weldig is oe mai fabricatio process. I weldig applicatios the laser parameters must be tailored so that udesired vaporizatio of the surface does ot occur while achievig the desired molte depth. There are umerous worable applicatios which laser weldig attaied to productio status. It is compete with several techique. I these situatios, the laser process proffers advatages that are substatial for the worable applicatio. These iclude: The loss of physical cotact with localized heatig, the electrode ad prompt coolig because of the small laser spot ad high heat flux. The ability to weld umerous various mierals ad various geometries, ad the capability to weld compoets i a cotrolled atmosphere or sealed withi optically trasparet materials. Bertolotti ad Sibilia [1981] explaied aalytical solutios for the peetratio of the meltig frot that was foud by resolvig the equatio of fusio iterface motio. Itgotte by the coductio heat equatio for the liquid area, ad by the eergy coservatio at the fusio frot. Solutios are gaied both for costat ad Gaussia light beams ad for the case of costat thermal properties, whilst itroducig the thermal coductivity discotiuity at the fusio iterface. Liu ad Asibu [1998] aticipated movig adaptive fiite elemet aalysis for dual - beam laser weldig tailored blas. The phase chage impact, temperature reliace to the properties of material, both radiatio ad covectio heat trasfer are regarded. Oly four-ode quadrilateral fiite elemets have utilized i this model. However, they assumed it is lumped i the orietatio of z-axis, ad resolves for temperature averaged over the thicess. Error happes from the simplifyig the model of fiite elemet, which cosists the cotact boudary coditio, disregard the evaporatio pulls ad flow of i the weld pool. Mahrle ad Schmidt [1998] showed a model for the emulatio of the temperature dispesatio through deep peetratio laser beam weldig of a fie sheets. The temperature reliace of the material properties is couted. For a steady state, the impact of the covective heat trasfer is tae based o a umerical resolutio of the Navier-Stoes equatios. The calculatio is carried out employ a fiite differece scheme o staggered grids. This simulatio of the temperature distributio is limited to thi sheets while Piearsa et al., [2014] developed a mathematical model i three dimesios of the weldig process by usig Yb:YAG laser beam. This model was simulated by usig a fiite volume method to predict the temperature distributios through the weldig pool ad heat affected zoe (HAZ). The resource of laser heat is calculated by the method of rigig iterpolatio. Experimetal wor was doe o S355steel metal. Azizpour et al., [2015] predicted a model i a threedimesioal by usig the fiite elemet code (SYSWeld) to simulate of laser beam weldig of Ti6A14V sheet. They demostrated the temperature distributio ad weld geometry. They used a cotiuous wave mode CO 2 laser with the maximum power of 2.2 W. I additio, they ivestigated the effect of focal positio, power, speed, ad the shapes of molte pool. Mwema [2017] used the solid wors software to predict the trasiet temperature profiles through the weldig process of metallic ad ometallic materials usig moveable laser power resource. Also, the weldig bead shape ad the thermal profile for Nd:YAG laser weldig operatio of AISI304 steel lap joit has bee elaborated. The result explais that the temperature close to the resource of the laser very high cotrasted with that close to the edge. I additio, this study idicated that the depth of the beam peetratio rise with icreasig the power itesity of a laser. The equatio of movig without give ay solutio. It produced 8372

2 ARPN Joural of Egieerig ad Applied Scieces Asia Research Publishig Networ (ARPN). All rights reserved. a iterpolatio equatio to give the relatioship betwee the velocity movemets with the power itesity supplied by the laser source. From above researchers, obody too the effect of phase trasformatio i simulatio software, ad the movig of a wor piece through weldig process. I the preset, a model i a three-dimesioal fiite differece method with implicit techique is predicted to simulate the trasiet temperature distributio i fusio ad heat affected zoes due to the effective of phase trasformatio (solid-liquid iterface) ad fusio latet heat of metal by usig cotiuous mode of CO 2 laser through the weldig process. I additio, the ew scheme i a steady state is preseted i order to explai the movig of wor-piece through the weldig process. 2. THERMAL PHENOMENA Cotiuous wave (CW) laser worig at output power i a practical system i the W rage is curretly available with the wave legth of 10.6 Mm. It used for weldig where scale effects have allowed the accomplishmet of weldig cofiguratios. The metal used S355 steelad heated with a CO 2 laser beam of 10 5 W/cm 2 irradiace ad 0.2 mm spot diameter. The umerical solutio of distributig source has bee utilized to simulate the temperature distributio. I the curret wor, cosidered that total laser power is the icidet over a roudabout regio. The dispersios of itesity iside the focus is a complex fuctio of positio ad time, however, laser-iduced thermal effect do ot appear to be excessively sesitive to this distributio as log as that the temperature is ispected far from the immediate zoe this imply that the associatio happes. Cosequetly, usually advatageous to expect as over that all the five structure i the itesity distributio is lost ad that all the five structure i the itesity distributio is lost ad that the thermal effect is the equivalet as that which would be delivered by absorptio of the equivalet total power over a roud zoe whose radius may be piced empirically. The laser radiatio is absorbed withi a defiite depth of the material thicess. The temperature distributio is to be calculated withi the layer at which the laser radiatio is absorbed. The absorptio of laser eergy evetuates i a layer beig cm thic. Sice, for the applicable laser itesities the width of the warmed area is ormally umerous micros, oe ca portray the igestio layer by surface heat iput. Therefore, material is assumed to chage from solid to liquid without ay extra eergy beig required. It has accepted that the thermal costats autoomous of both the laser force ad the temperature. The reflectivity of a metal surface is a importat parameter, which cotrols the fractio of the laser radiatio absorbed. The reflectivity is a fuctio of temperature ad wavelegth of the metal. At 10.6 µm wavelegth, the reflectivity of the surface for the cold metal is much higher. The laser-metal iteractio mechaism is depedet maily o the laser pulse power itesity, duratio, wavelegth, ad o the target material thermophysical properties that were detailed by Ready [1978]. 3. MATHEMATICAL ANALYSIS Heat equatios have bee used to describe coductio withi the metal irradiated with fast ad rise time, high itesity pulses. It is importat to determie the temperature profile i metals accurately, sice the temperature distributio withi the wor-piece greatly affects phase trasitios ad hece, machiig characteristics. Therefore, ew models must be sought to reduce this discrepacy. I order to facilitate reasoable aalysis of the weldig process, a umber of assumptios ad simplificatios have to be made to solve the two models which are describig this process. There are: a) The itesity of a laser beam i W/cm 2 is adequate to the reaso fusig of the frot surface of the metal, which is i the rage W/cm 2. b) The liquid, which is created due to the fusig of metals, is limpid to the eergy of the icidet laser. c) Losses of heat due to re-radiat are egligible. d) Beam focusig effects due to lesig are assumed igore. e) Ivariable physical ad thermal properties of irradiated metal while it is solid ad liquid. f) Tae the effect of latet heat fusio or the quatity of heat required to raise the temperature to meltig poit. g) I a ew model predicted a mechaism of weldig. New scheme does switchig from usteady trasiet state to steady state through movig of wor- piece. This is the assumptio i the scheme ad uses the laser heat source, which varies expoetially with spatial distributio. h) The metal is opaque, i.e., the laser beam does ot peetrate oticeably ito the medium, with uchagig absorptivity. i) Losses of heat to the outside ca be approximated utilizig a sigle, ad steady the coefficiet of heat trasfer for both the radiative ad the covective losses are dispesable. The equatio of heat coductio for a solid slab uder a peetratig laser source at a three-dimesioal is give by Dowde [2001] T ρ c p = T ( ) + T ( ) + T ( ) + Q(x, y, z, t) (1) t x x y y z z The three-dimesioal developed model i Cartesia coordiate has bee assumed to give a solutio to the equatio (1) as the laser power is icidet over a 8373

3 ARPN Joural of Egieerig ad Applied Scieces Asia Research Publishig Networ (ARPN). All rights reserved. rouded zoe ( w 2 ). Figure-1 shows the coordiate system for the semi-ifiite medium. I the curret wor a ew assumptio has bee made, that the absorptio occurs i three directios. The, the equatio (2) becomes: Q = (1 R)Iδ exp (( δ( x 2 + y 2 + z 2 )) ( x2 +y 2 w2 )) (3) Subject to the boudary coditios to illumiate equatio (1) umerically: Figure-1.The system of cartesia coordiate. Q is the resource term (heat productio per uit volume per uit time) ad it describes the absorptio process as expressed by Bass [1983] as: Q = (1 R)Iδ exp (( δz) ( x2 +y 2 w2 )) (2) x, y, z ; T T ; z = 0: T z = 0 Ad the premier coditio is T(x, y, z, 0)=T A fiite-differece method with implicit techique has bee used to resolve the partial differetial equatio (1), so that the problem could be solved by a computer. It has bee cosidered the approximatio i the regio over which we have laid a orthogoal grid with a equal spacig. Assumig x, y, ad z equal 3 micrometer ad t equal of 200 aosecods. The grid is represeted by Figure-2. The computer program gives more reliability to compute the temperature profile agaist x, y, ad z coordiates depedig upo the boudary coditios that gives a differet form of the equatio (1) i implicit fiite differece techique. Priciples of stability aalysis with umerical schemes are illustrated by Petrovic ad Stupar[1996]. The equatio (1) ca be writte i fiite differece form with implicit techique as: T i,j, = λt i+1,j, 6λT i,j, + λt i 1,j, + λt i,j+1, + λt i,j 1, + λt i,j,+1 + λt i,j, 1 + Q αδt + T i,j, (4) Figure-2.Geometry ad mesh distributio. a) At frot surface i poit (c) where x=y=z, ad z=0, T = 0 as show i Figure-3(a). z Figure-3. Types of fixed boudary coditio. The surface heatig for short time util the surface temperature reaches meltig poit 1800 K, the equatio (4) becomes 8374

4 ARPN Joural of Egieerig ad Applied Scieces Asia Research Publishig Networ (ARPN). All rights reserved. = 4λT i+1,j, T i,j, + 2λT i,j,+1 6λT i,j, + T i,j, + Q αδt (5) V = (1 R)I (ρl m +ρc(t L T m )) (13) Where is the coverget = αδt x2. Also, heatig through x- axis, ad y-axis where x ad z=0 whe T = 0. The, z equatio (4) at x-axis becomes: T i,j, = λt i+1,j, 2λT i,j, 1 At y-axis T i,j, = 2λT i+1,j, 2λT i,j,+1 6λT i,j, + λt i 1,j, + 2λT i,j+1, + + T i,j, + Q αδt (6) 6λT i,j, + λt i,j+1, + λt i,j 1, + + T i,j, + Q αδt (7) b)at z=z (t), whe the fusig happe i this layer at x ad y=0. The, the boudary coditio of phase trasformatio to liquidis referrig to Figure-3-b. As eergy balace at the surface ecessitates that the eergy give to the fusio material equivalets the eergy coducted from the solid, hece ρl m Z (t) t = s T z z = Z (t) (8) ρl m V = s T z z = Z (t) T i,j,+1 T i,j, 1 s = ρl 2 z m V T i,j, 1 = T i,j,+1 ρl mv 2 z (9) s Where L m is the specific latet heat of fusio, ad V * is velocity of fusio surface adz (t), z are the distace. The, isertig the boudary coditio of equatio (9) i equatio (1) becomes: T i,j, = 4λT i+1,j, 6λT i,j, + 2λT i,j,+1 λ ρlv 2 z T i,j, + Q s + αδt (10) Phase trasformatio also happes at z =Z (t), ad x. The equatio (4) becomes: T i,j, = λt i+1,j, 6λT i,j, + λt i 1,j, 2λT i,j,+1 λ ρlv 2 z s + 2λT i,j+1, + + T i,j, + Q αδt (11) Aother Phase trasformatio through lie y-axis at z =Z (t), ad y. Equatio (4) Forms as: T i,j, = 2λT i+1,j, 2λT i,j,+1 + T i,j, 6λT i,j, + λt i,j+1, + λt i,j 1, + λ ρlv 2 z + Q αδt (12) s Stee ad Kamalu [1983] show from a simple oe-dimesioal heat balace that the velocity of the fusio frot ito wor-piece is give by the expressio: c)liquid phase: Whe z>z (t), ad z, the fusio of metal startig ad movig i fusio zoe with velocity of fusio V *, the equatio (4) is formed as coductio eergy equatio as: 1 T + V α t α T = 2 T + 2 T + 2 T + Q z x 2 y 2 z 2 (14) This equatio is applied through z-axis, x-z, ad y-z plaes. After z >z (t), equatio (14) becomes as: T i,j, = 4λT i+1,j, V t )λt 2 z i,j, 1 + T i,j, + Q Ad through x-z plae is: 6λT i,j, + (λ V t T i,j, = λt i+1,j, 6λT i,j, + λt i 1,j, (λ V t Q 2 z )T i,j,+1 + (λ + αδt (15) + 2λT i,j+1, + ) T 2 z i,j,+1 + (λ + V t ) λt 2 z i,j, 1 + T i,j, + αδt (16) At y-z plae equatio (14) becomes T i,j, = 2λT i+1,j, 6λT i,j, + λt i,j+1, (λ V t ) T 2 z i,j,+1 + (λ + V t 2 z )λt i,j, 1 + λt i,j 1, + + T i,j, + Q αδt (17) d)upo the assumptio umber 7, the process plaig scheme for curret model of laser weldig is composed of two steps: a) The weldig happes istataeously after the fusio process which the temperature distributio at weld process is calculated by trasiet model which is reported i previous steps. b) I weldig process the differetial equatio goverig heat flow withi the wor-piece will be: u T α y = 2 T x T y T z 2 + Q (18) Where u is the velocity of movemet of worpiece relative to heat spot, where y is the flow of heat directio. A ew assumptio i ew scheme, it is the switchig from trasiet model to simulate the weldig process i oe poit to steady state scheme to move the fusio zoe to the aother poits i the destiatio of y- coordiate. The boudary coditios deped i o the value of temperature reached i adjacet fusio zoe, which reached at least the meltig temperature or more. The flow heat coductio equatio (18) is oliear. This equatio usually cotais the coefficiet that represets a fuctio of the uow fuctio to be solved. Aderso 8375

5 ARPN Joural of Egieerig ad Applied Scieces Asia Research Publishig Networ (ARPN). All rights reserved. et al. [1984] showed that the laggig method is the techique to liearizatio procedure of equatio (18), this method is approximated by the partial derivative T, which y will be approximated by the forward-differece method alog the y-directio u T i,j, Ti,j, represeted with this method ad becomes: T i,j, = 1 λt i,j,+1 (λt u i+1,j, + λt i,j, 1 y + λt i 1,j, ) + (1 6λ. The, equatio (8) is + λt i,j+1, u )T i,j, + Q i,j, + λt i,j 1, + αδx u (19) Where λ = α at x= y= z, ad u is cosider to be Δx ow. The oly uow value i previous expressio is the fuctio T i,j,, which is calculated upo the value of fuctio from the previous iteratiot i,j,. 4. RESULTS AND DISCUSSIONS The algorithm s emulatio program of the CO 2 laser process of weldig is used for a metal sheet made of S 355 steel. It was heated with laser beam of 10 5 W/cm 2 irradiace ad 0.2 mm spot diameter. The dimesios of sheet metal are ( ) mm of legth, width, ad thicess respectively. This metal has bee selected because it has less reflectivity at 10.6 µm also; it has lower thermal coductivity ad thermal diffusivity tha other metals. The space is discretised by computatioal grid with x = y = z = 3µm, ad time iterval is 200 aosecods. The thermal ad optical properties are depicted i Table-1. Table-1.Thermal ad optical properties which are utilized i the simulatio. Properties Symbol Value Solid Phasedesity S 7800 g.m -3 Liquid Phase desity L 6800 g.m -3 Specific heat of solid phase c S 650 J.(g.K) -1 Specific heat of liquid phase c L 840 J.(g.K) -1 Solid phasethermal coductivity S 45 W.(m.K) -1 Liquid phase thermal coductivity L 35 W.(m.K) -1 Meltig poit T m 1800 K Boilig poit T b 3010 K Latet heat of fusio L f J.g -1 Thermal diffusivity Α m 2.s -1 Absorptio coefficiet Δ m -1 Reflectivity R [at 10.6 µm] 0.90 Absorptivity A=(1-R) [at 10.6 µm] 0.1 Algorithm results give the descriptio of spatial ad temporal temperature distributio usig 3-dimesio Cartesia model at time itervals of 200 aosecods. These results seem to be more realistic to explai the spatial temperatures distributio agaist x, y, ad z-axis. It should be metioed that the temperature distributio i y-axis is the same as that distributio i x-axis. Figure-4 shows the spatial temperature distributios at differet time itervals at power itesity value of 10 5 W/cm 2 through x-axis. Geerally, the spatial temperature gradiet ear the surface is very steep returig to a shallow egative gradiet as the target metal ambiet temperature is approached. This effect is amplified as time evolves. These results desigate a higher thermal profile ear the surface. Oce the weldig process becomes sigificat. A large egative gradiet is geerated i the surface; this is cosistet with the laws of thermodyamics as eergy ca oly flow from a high to low temperature. That was poited at high level itervals time at 2600 ad 3400 aosecods. The maximum fusio zoe happes at the surface is 3 µm. that meas the phase trasformatio from solid to liquid was sigificat startig at time 2600 s i x=0 ad cotiuous util time 3400 s at x=3 µm. 8376

6 ARPN Joural of Egieerig ad Applied Scieces Asia Research Publishig Networ (ARPN). All rights reserved. value of the power itesity was used. That meas to avoid reachig the boilig temperature (i.e. vaporizatio process). I the preset aalysis the model simulated the maximum time of weldig process was 3400 s ad the temperature of fusio metal was reached to K. Figure-4. Temperature profile versus x-distace for various heatig times i S 355 steel at 10 5 W/cm 2. Figure-5 illustrates the spatial temperature distributio at a differet time itervals at I=10 5 W/cm 2 (i z-axis). A simulatio of evolutio of temperature profile was evaluated at the assumptio of heat source was distributed. As the depth extets the laser radiatio beig absorbed at the layers ext to the surface. This implies a less thermal gradiet betwee these layers ad the surface layer. Therefore, higher temperature levels ca more liely, be maitaied at the surface. It has bee show that the ew model i the weldig process gives a large positive gradiet of temperature at the depth of metal because of the high eergy meltig material beig removed. However, this pheomeo which is clearer i steel tha other metals due to the properties ad the lac of resolutio of the z-axis. Figure-6. Temporal variatio of temperature i S 355 steel at 10 5 W/cm 2. Figures-7 ad 8 preset the results i isothermal cotours maps, which show the distributio of maximum temperature of meltig pool o x-z surface at y=0 (from the face of the weld at the frot surface) as illustrated i Figure-7. z-axis (micro) x-axis (micro) Temperature (K) Figure-7. Isothermal cotour of meltig pool at frot surface x-z, y=0 ad time 3400 s Temperature (K) Figure-5. Temperature profile versus metal deep for various heatig times i S 355 steel at 10 5 W/cm 2 Figure-6 domiates the temporal distributio of temperature through the weldig process. It was poited that the temperature icreases with icreasig time. It has bee idicated the time whe the phase trasformatio from solid to liquid is started at time 2400 s. That, it should be cotrolled the time of weldig process ad the z-axis (micro) y-axis (micro) Figure-8. Isothermal cotour of meltig pool at side surface y-z, x=0 ad time 3400 s. Figure-8 represets the isothermal cotour i y-z plae at x=0 (from the face of the weld at the side 8377

7 ARPN Joural of Egieerig ad Applied Scieces Asia Research Publishig Networ (ARPN). All rights reserved. surface). These figures illustrate the fusio geometry diameter. Thus it ca be see that the fusio zoe of diameter will deped upo laser power itesity, ad metal thermal diffusivity varies with weldig phase trasformatio velocity (i.e. V * is the velocity of phase chage from solid to liquid). This velocity was calculated as a fuctio of power itesity. It is foud from the predictio model the dimesios of meltig pool. These are 3 micros i x ad y axis as melt width at the frot surface, ad 15 micros as melt depth i z-axis. These results of temperature distributios of meltig pool ad its geometry are similar with experimetal results, which were reported by piearsaet al., [2014] eve they used aother type of laser. Figures 9 ad 10 show umerically calculated temperature distributios i the laser weldig process. These figures explai the results of isothermal cotours map for heat affected zoe (HAZ) after fusio boudary o x-z plae, ad y-z plae. It has bee show the temperatures values decrease after fusio boudary. These values are less tha the meltig poit of metal (i.e. less tha 1800 K). These figures are idicated the heat affected zoe through the weldig process. It is oted these values of (HAS) are 18 micros from the ceter of meltig pool i x-axis, ad 15 micros i z-axis. The temperature values reduce after meltig lie from K at 3 micros i the bac surface of metal to K at 18 micros through x-axis. Figure-9. Isothermal cotour of HAS at frot surface (x-z),y=0, ad time = 3400 s. by estimatig from umerical simulatio i the face of the weld at the frot surface x-z plae, ad i the face at side surface of y-z plae. It was foud the heat peetratio depth readig util 38 micros i x ad y axis, ad 18 micros i depth z-axis. z-axis (micro) z-axis (micro) x-axis (micro) Figure-11. Isothermal cotour of heat peetratio depth at frot surface x-z, y=0, ad time 3400 s y-axis (micro) Temperature (K) Temperature (K) Figure-12. Isothermal cotour of heat peetratio depth at frot surface y-z, x=0, ad time 3400 s. Figure-13 demostrates the three dimesioal surface cotour of temperature distributio through the etire domai of the weldig process icludes the meltig pool, ad heat affected zoe. This surface cotour represets the weldig process dimesios i x-z plae with temperature distributios with time of 3400 aosecods. The meltig pool zoe is poited at the cetre of x-z plae i depth, ad with 3 micros i width from the cetre. The, after the boudary of meltig zoe the heat affected zoe is observed. Figure-10. Isothermal cotour of HAS at side surface (y-z),y=0,ad time = 3400 s. Figures-11 ad 12 domiate the heat peetratio depth i metal more clearly through the weldig process Figure-13. Surface cotour of temperature distributio i three dimesios at time 3400 s. 8378

8 ARPN Joural of Egieerig ad Applied Scieces Asia Research Publishig Networ (ARPN). All rights reserved. From the ew scheme of equatio (18) which was predicted the movig of the weldig zoe from poit i sectio side of metal to aother poits i y-axis directio due to the movig of wor-piece by differet traverse speed. I that case, fusio pool must be movig i order to produce series poits of weldig through movig the wor-piece i y-axis. Figures-14 ad 15 domiate this pheomeo to show a series of the weldig process produced with CO 2 laser at power itesity 10 5 W/cm 2 for S 355 steel metal. These figures are produced at two values of traverse speed of wor-piece uder costat focusig coditios. It is see that weldig happeed at the first time through the distace alog three axes startig from zero distace of these axes util few micros. The solid lie represets this process, which was simulated by a trasiet model at ot movig the wor-piece (i.e. u=0). The, the fusio geometry of the weldig process moves to aother poits i y-axis with two values of traverse speed as show i these figures. The red dash lie shows the switchig from the trasiet model at statioary face to the ew scheme i a steady state which was solved by laggig method. It is also see that the temperature distributio of this metal decreases as the traverse speed is icreased. Also, the temperature distributio was effected by the time of weldig. It is idicated that temperature distributio icreases with icreasig the time of metal weldig. Figure-15. Temperature profile agaist y-distace for differet travers velocities at I=10 5 W/cm 2, ad time 2600 s. 5. CONCLUSIONS a) Theoretical ivestigatio of the eergy trasport i metal caused by absorptio of laser pulse radiatio has bee exteded to iclude the effects of the fusio of the target metal with phase trasformatio (solid to liquid) uder icidet power itesity. This trasiet model demostrates the weldig process i terms of fusio velocity ad the effect of fusio latet heat for the metal target. The algorithm simulatio was solved by the implicit techique i fiite differece method. b) The spatial ad temporal temperature distributios of fusio pool ad heat affected zoe are predicted by trasiet model. Their dimesios are illustrated by a isothermal cotour map of the weldig process at the frot surface of metal i statioary poit. Figure-14. Temperature profile agaist y-distace for differet travers velocities at I=10 5 W/cm 2,ad time3400 s. c) A ew scheme is predicted to explai the cotiuous weldig through the legth of surface metal. It is the switchig from trasiet model which simulatig the weldig process i oe poit at the frot surface of target to steady state scheme for movig the fusio zoe to aother poits i the directio of y-coordiate with two values of traverse speeds of wor-piece. d) Aew assumptio of laser eergy absorptio i three dimesios (i x,y,ad z directios) has preseted i this wor lead to more realistic results. e) Laser wavelegth effects have bee cosidered implicitly withi the reflectivity calculatio ad withi the distributed heat source aalysis. This meas that the implemeted simulatio has tae all types of lasers ito cosideratio. 8379

9 ARPN Joural of Egieerig ad Applied Scieces Asia Research Publishig Networ (ARPN). All rights reserved. REFERENCES [1] Bertolotti M. ad Sibilia C Depth ad Velocity of the Laser-Melted Frot from a Aalytical Solutio of the Heat Coductio Equatio. IEEE, Joural of Quatum Electroics. 17(10): [12] Aderso D. A., Taehill J., C. ad Pletcher R.H Computatioal Fluid Mechaics ad Heat Trasfer. Boo: McGraw-Hill Publisher Compay. [2] Liu Y. N. ad Asibu E. K Fiite Elemet Aalysis of Heat Flow i Dual-Beam Laser Welded Tailored Blas. J. Maufacturig Sciece ad Egieerig. 120: [3] Mahrle A. ad Schmidt J Numerical Simulatio of Heat Trasfer durig Deep Peetratio Laser Beam Weldig. Advaced Computatioal Methods i Heat Trasfer, Editors: Nowa, A.J., Brebbia, C. A., Bialeci, R. ad Zerrouat, M. Computatioal Mechaics Publicatios. UK. [4] Piearsa W., Kubia M., Saterus Z., Domasi T., Stao S., Radceo M. V. ad Ivaov S. G Numerical Modelig of Thermal Pheomea i Yb:YAG Laser Weldig Process. Joural of Applied Mathematics ad Computatioal Mechaics. 13(3): [5] Azizpour M., Ghoreishi M. ad Khorram A Numerical Simulatio of Laser Beam Weldig of Ti6A14V Sheet. Joural of Computatioal ad Applied Research i Mechaical Egieerig. 4(2): [6] Mwema F.M Trasiet Thermal Modelig i Laser Weldig of Metallic / Nometallic Joits Usig Solid Wors Software. Iteratioal Joural of Noferrous Metallurgy. 6: [7] Ready J. F Idustrial Applicatios of Lasers. Boo: Academic press. Lodo. [8] Dowde J.M The Mathematics of Thermal Modelig-A Itroductio to the Theory of Laser Material Processig. Boo:Chapma$ Hall/ CRC. Lodo. [9] Bass M Laser Material Processig. Boo:North-Hollad publishig compay. [10] Petrovic Z. ad Stupar S Computatioal Fluid Dyamics. Boo: Belgrade Uiversity press. Mechaical Eg. Faculty. [11] Stee W.M. ad Kamalu J.N Laser Cuttig. Laser Materials Processig Bass, M. Boo: North Hollad Publishig Compay. 8380