Transport Phenomena in Surface Alloying of Metals Irradiated By High Energy Laser Beam

Transcription

1 Adances in Mdern Mechanical Engineering ransrt Phenmena in Srface Alling f Metals Irradiated B High Energ Laser Beam KIRAN BHA AND PRADIP MAJUMDAR Deartment f Mechanical Engineering Nrthern Illinis Uniersit DeKalb, Illinis 651 USA majmdar@ni.ed Abstract: - Laser srface alling has receied cnsiderable attentin in recent times as it can lcall change material rerties and retain blk rerties in the interir f the base material. All der is desited in a mlten l f sbstrate material t imre srface rerties like hardness resistance t ear and crrsin f a material. he effect f temeratre deendent srface tensin cefficient is identified as the rimar driing frce in deeling the fl field in a mlten l f metals. his std resents simlatin f flid mtin and distribtin f all element in a mlten l f sbstrate material sbjected t high-energ laser beam. A mathematical mdel fr mmentm, energ and cncentratin is resented and nmerical reslts are btained sing cmtatinal cde. A arametric std is cndcted t anale the effect f laser beam arameters, and shae and sie f mlten l n the srface tensin drien fl fields and qalit f the alled ne in terms f nifrm distribtin, deth f alled ne as ell as rate f desitin. Ke-Wrds: - Srface Alling, Laser Beam, ransrt Phenmena, mtatinal Mdel 1 Intrdctin Laser srface treatment has receied cnsiderable attentin recentl de t the imred srface rerties that can be achieed, eseciall frm the int f ie f hardness, ear and crrsin resistances. It is f great imrtance frm the manfactring int f ie here ne ants t change srface rerties f a rdct, bt t retain blk rerties in the interir. Laser srface treatments hel in imring the rerties like hardness resistance t ear and crrsin f a material thereb rdcing ne materials. Lasers can alter material srface rerties f a cmnent t sit a secific indstrial alicatin and cmmnl sed fr srface engineering. he erfrm ersatile srface treatments ith great recisin, l heat int and therefre l distrtin and fast ccle times. hese treatments inclde nn-melting srface treatments like transfrmatin and shck hardening, melting srface treatments like glaing and cladding. he main adantages f laser srface melting can be smmaried as: i. increased rdctiit; ii. redced manfactring csts and ii, imred rdct qalit, i. increased design and rdctin fleibilit,. ne manfactring rtnities, i. enhancement f mechanical rerties at the srface, and ii. imred resistance t ear and crrsin at secified lcatins. Lasers are er efficient in heating lcalied regins, and hence, the find a ide alicatin in srface treatment rcesses. he srface f a material can be selectiel mdified t gie serir ear and crrsin resistance. A ariet f srface treatment rcesses sch as laser cladding, laser srface alling and laser heat treatment can be achieed b rer cmbinatins f laser er densit and interactin time. Laser srface alling inles melting f the sbstrate sing high energ laser beam t a redetermined ISBN:

2 Adances in Mdern Mechanical Engineering mlten l shae and intrdcing alling elements in the mlten l. Figre 1 shs the schematic diagram f a tical laser installatin. he laser beam is transmitted thrgh a fcsing lens, hich cnerges near the fcal int f the lens. Dring the heating erid, a caial assisted gas stream, ften gen, argn, r nitrgen, is sed t achiee higher thermal cling beteen the laser beam and the material. he incident laser beam is absrbed b the sbstrate material and raidl heats the thin laer f the material srface and frms a thin laer f mlten l in the sbstrate. A mathematical mdel and arametric std are essential t anale the rle f flid fl, transrt henmena and rcessing cnditin n the all element distribtin dring laser srface alling. High recisin and cntrl f the alled ne in terms f nifrm distribtin f all element, thickness and deth are the majr challenges in the deelment f laser srface alling rcess. Assisted Gas Nle Laser Beam Lens Lens Mlten Pl Wrk Piece Figre 1 Schematic reresentatin f laser heated mlten l A cnsiderable amnt f research has been cndcted in the ast in dealing ith the rle f flid fl in the frmatin f the mlten l and distribtin f all elements. Mst f there rk shed the dminance f Marangni cnectin drien frce in the mlten l. Anthn and line [1] deeled the first ne-dimensinal mdel fr mlten flid fl dring laser melting and fnd that the fl in the mlten l is created b the srface tensin gradient ith temeratre. han et al. [7] rsed the first tdimensinal transient mdel fr cnectie heat transfer and srface tensin drien flid fl. he eamined the effects f different rcess arameters, sch as beam er densit, beam radis, srface tensin, and additinal material rerties, n free srface elcit, srface temeratre, l shae, and cling rate. In their sbseqent rk, han et al. [8] analed the stead state laser-melting rblem ithin the er range f Wm -. he fnd that the scanning elcit las an insignificant rle becase f the higher magnitde f the srface tensin elcit. Bas and Sriniasan [] cnfirmed the rk carried n b han et al and als eamined the fl attern in a laser-melted l nder stead state cnditins. he assmed a t-hat heat fl distribtin and sed the rticit-stream fnctin methd fr sling the mmentm eqatin in the mlten regin. he hae shn the eistence f t cntra-rtating cells in the fl attern. Bas and Date [3] inestigated the stead state and transient laser-melting rblems fr an aismetric mdel. Using a Gassian distribtin f int heat fl, the resented a detailed analsis f the fl field and heat transfer fr re metals b aring the beam er densit and the beam radis Raindran and Sriniasan. [15] mdeled the laser-melting rblem b the Galerkin finite element methd. Using the aarent caacit methd, in hich the latent heat is inclded in the secific heat f the material, the eamined the fl field and heat transfer in laser srface melting f an all. he neglected the flid fl in the msh ne f the slidifing liqid. Heer, the analed the fl field and heat transfer fr a tical range f srface tensin ales f steel. Kim and Sim [11] resented a detailed transient and stead state analsis f the fl field and heat transfer, inclding flid fl in the msh ne fr an all. he cmared the gemetr f the l, the free srface elcit, and the srface temeratre ith and itht cnectin in the msh ne. Mran et al. [1] resented a nmerical mdel f the ISBN:

3 Adances in Mdern Mechanical Engineering thermcaillar fl in a melted l created b a scanning W laser. he als analed the effects f scanning elcit and beam dimensin n thermcaillar fl intensit, dimensins and the shae f the melted ne. Bas and Date [5] stdied the effect f aris slidificatin arameters and l characteristics n raid slidificatin flling laser melting f alminm and steel. Pericles and Baile [13] resented nmericall the rle f srface tensin in the dnamics f the melt l inclding st slidificatin stress histr sing a cntrl lme arach. Kar and Majmder [9] determined the metastable all cmsitin and aris rcess arameter effects n the cmsitin f binar all sstem. he als mdeled heat cndctin thrgh the l and the sbstrate. Bas and Date [4] resented a arametric std f laser melting rblems fr aring beam radis and beam er sing steel and alminm. he als analed the effect f cnectin n the erall heat transfer. Raindran et al. [14] simlated the srfacetensin-drien cnectin in the laser melting b Galerkin finite element methd and shed the deendence f fl attern n srface tensin temeratre gradient. Raindran et al. [15] mdeled the srface melting b a statinar, lsed laser sing finite element mdel and resented the rle f srface tensin drien cnectin in detail. Bas et al. [6] stdied the fl field and its effect n the deth and idth f the stead state l based n nmerical and analtical methds. he alidated their reslts b carring t an eerimental std sing srface melting f Al- 4.5% all ith an electrn beam. Dharani and Majmdar [16] deeled an enthal-based cmtatinal mdel fr analing laser heating and melting f metals. She deeled a sltin algrithm and a cde t estimate the temeratre distribtin, slidliqid interface lcatin, and shae and sie f the mlten l. Kasla and Majmdar [1] based their std n the reslting temeratre and stress distribtin, the idth and deth f the mlten l frmed ith the alicatin f a high energ Gassian laser beam. he mathematical mdel deeled as based n mltidimensinal transient heat and mass transfer eqatins, and the nmerical sltin btained as based n a three-dimensinal finite element mdel. he bjectie f this rk is t std the flid mtin and distribtin f all element in a redetermined mlten l f sbstrate material sbjected t high-energ laser beam. A cmtatinal mdel is deeled t nderstand the rle f different gerning hsical henmena inclding flid fl, heat transfer and mass transfer ith erating rcess arameters. A arametric std ill be cndcted t anale the effect f erating material and laser beam arameter n the qalit f the alled ne in terms f nifrm distribtin, thickness and deth f alled ne.. Mathematical Frmlatin he hsical rcesses inled in laser srface treatment are basicall thermal in natre, hich inles creating a mlten l f sbstrate and distribting all element r slte in the l sbjected t an arimatel selected laser beam arameters. A mathematical mdel is deeled based n three-dimensinal and transient transrt f heat and mass in the resence f a flid fl in a redetermined mlten l f sbstrate sbjected t a high energ laser beam. A redetermined mlten l f sbstrate is cated ith a thin laer f all element, desited b a nle sra, and cntined t be sbjected t a high-energ laser beam. As laser beam f cnstant er ith Gassian heat fl distribtin strikes the srface f the cait, the incident radiatin is transmitted in the semi-transarent liqid l as ell as lmetricall absrbed based n the tical rerties f the material. Figre shs the schematic reresentatin f the hsical mdel. ISBN:

4 Adances in Mdern Mechanical Engineering Figre Schematic reresentatin f a mlten metal l created b laser melting. A laser beam haing a cnstant er distribtin strikes the srface f the material. Heat generated de t the absrbed incident laser beam radiatin deels a mlten l. he heat energ generated is artl cnected t the srrndings and mstl dissiated t the cler regins f the material b cndctin. he fl in this mlten l is mainl de t the srface tensin gradient rdced b the temeratre gradient at the free srface. his srface tensin gradient acts as a shear stress at the free srface thereb indcing cnectie fl ithin the mlten l as deicted in.the Figre. Laser beam characteristics he intensit f the laser beam that is incident n the rk iece is eressed as I I e he intensit f the laser beam that is absrbed in the mlten l is eressed as R he beam intensit distribtin and the ale f I is assmed sch that R A P = I ( ) da (3) P = laser er (W) R = effectie radis f the laser beam (mm) A = area (mm ) Mathematical Mdel A transient heat fl is alied at the centre f the t srface thereb creating a mlten metal l ith assciated temeratre distribtin. Heat is lst frm all sides f the late b cnectin. he flling assmtins are made ith the frmlatin f the cmbined heat and mass transfer mdel: 1. All rerties f the material are indeendent f temeratre ecet srface tensin,. he free srface f the melt is assmed t be flat, 3. he laser beam is statinar, 4. he banc frce is f negligible rder f magnitde cmared t marangni frce, 5. he fl is assmed t be laminar and Netnian, 6. he secndar effects like therm-diffsin r srret effect are neglected, 7. Alling element is assmed t be melted instantanesl and secndar effect sch as absrtin f injected article r shad effect is neglected as a first arimatin. he nn-dimensinalied three-dimensinal gerning eqatins f cntinit, mmentm and energ mass transrt in the -- lane is as flls: Gerning eqatins (1) ntinit Eqatin (1) t (4) a II a e a = absrtin cefficient I = laser beam densit at the centre (W/m ) () ISBN:

5 X-Mmentm Eqatin t R 1 (5) Y-Mmentm Eqatin t (6) R 1 Z- Mmentm Eqatin t R 1 (7) Energ Eqatin (8) Mass ncentratin Eqatin t D Ma 1 Bndar cnditins he mlten metal l is diided int t regins. he regin n the t is the free srface and the regin srrnding the metal l is the slidliqid interface. Figre 3 shs a three-dimensinal heat transfer mdel ith secified bndar cnditins. (9) h, b R e I I Slid/liqid Figre 3 hree-dimensinal schematic f the mlten metal l. Velcit bndar cnditin Shear frce balance at the free srface gies (1) (11) t hese eressins can be ritten in nndimensinal frm as q Ma 1 (1) (13) Adances in Mdern Mechanical Engineering ISBN:

6 Adances in Mdern Mechanical Engineering At slid/liqid interface (n sli cnditin) V(,, ) emeratre bndar cnditin Energ Balance at the free srface gies K (,,) h ( (,,) ) (14) (15) Energ Balance at the slid/liqid interface gies K q '' s hc ((,,) ) (,,) h r ((,,) ) ncentratin bndar cnditin At the free srface,, 1 At slid/liqid interface n (16) (17) (18) he gerning eqatins are nndimensinalied ith the flling nndimensinal ariables: R Ucr d qr d k r Marangni nmber based n energ is defined as Ma R d qr Pr d k r Marangni nmber based n diffsin is defined as Ma D R Pr D d qr d k r D 3. mtatinal Mdel A cmtatinal mdel related t the mathematical mdel resented is deeled sing FLUEN 6. cmmercial sftare and sing GAMBI grahical ser interface (GUI) fr bilding, meshing and assigning ne tes t the mdel. he gemetr f the mlten l is imrted frm the reis finite-element sltin laser heat and frmatin f mlten l fr a re metal [16]. he gemetr f the melt l is shn in Figre 4a. he meshing is dne sing et/hbrid mdel and the mesh is cmsed rimaril f tetrahedral mesh elements bt als incldes heahedral, ramidal, and edge elements here arriate. ; r ; r ; r a ; qr / k ; U c ; U c ; U c U c t t ; r a and qr / D U c d d (a) Gemetr f the mdel Gerning Parameters Renlds nmber is defined based n srface tensin frce as ISBN:

7 Adances in Mdern Mechanical Engineering (b) mtatinal mesh Figre 4 Gemetr f the mdel and cmtatinal mesh he mesh elements sed fr generating the mesh is 8-nde heahedrn lme element, 6-nde edge lme element, 4-nde tetrahedrn lme element, and 5-nde ramid lme element. he meshing is nifrm thrght the mdel. he mdel cnsists f t lmes: slid clinder and a hll cne. he ttal nmber f cells in the mdel is 4581, faces are 949, ndes are 939, cell nes are, and face nes are 7. Figre 4b shs a tical mesh f the mdel. he int fr heat srce and marangni stress are alied as a srce term sing a ser defined macr ritten in -cde cmsed f nmber ariable sch as the inde fr cell nmber ith heat srce, an arra f deriatie f the srce term ith resect t deendent ariable f the transrt, and time ale. hese deriaties ma be sed t linearie the srce term if the enhance the stabilit f the sler. Sler sed fr the cmtatinal std is segregated sler that reqires less memr cmared t the ther slers. he gerning eqatins in the sler are sled seqentiall (i.e., segregated frm ne anther). Seeral iteratins f the sltin l are erfrmed befre a cnerged sltin is btained becase f the nn-linearit f gerning eqatins. A int imlicit linear eqatin sler is sed in cnjnctin ith an algebraic mltigrid (AMG) methd t sle the resltant scalar sstem f eqatins fr the deendent ariable in each cell. he discretiatin is based n secnd-rder ind scheme fr the cnectie terms and the ressre-elcit cling is based n PISO algrithm fr transient calclatins. 4. Reslts and Discssin he finest mesh fr accrate ealatin f the nmerical mdel is selected based n the mesh refinement std. In the arametric std, the temeratre and elcit distribtin hen sbjected t aring time stes, aring lengths f time, aring er densities f the beam, aring laser beam diameter, and aring asect rati s (rati f the idth t the deth f the l) are stdied. Alminm all Al-4.5% is sed as the base material and Nickel (Ni) as the all element material. he arameters and erating cnditins fr the std are: Asect rati, AR =., Laser beam er intensit, I = 4e8W/m, Mlten l dimensins (1 5mm, 5.5mm, and 3 1.5mm), and Laser beam diameter, d= 3mm. Mesh refinement std he basic mdel has a mesh ith an interal sie f.6 and a ttal nmber f elements f he mesh intensit is aried frm an interal sie f.4 t.6 t imre the cnergence f the sltin s as t redce the ercentage relatie errr. Reslts fr the ariatin f temeratre at different lcatins and the crresnding ercentage relatie errr at the midsectin f the mdel are resented in Figres 5. It can be seen frm the reslts that as the mesh sie decreases, the ercentage relatie errr in the temeratre decreases. Strng deendence n the mesh sie can be nticed thrgh the ercentage relatie errr in Figre 5a. Reslts sh cntins cnergence f temeratre rfile t =.6. he maimm ercentage relatie errr is bel.15%. he mesh ith an interal sie f.6 gies the least ercentage errr and hence it is taken as the final mesh t btain the desired reslts. Reslts fr the ariatin f temeratre at different -lcatins and the crresnding ercentage relatie errr at the mid-sectin f the mdel are gien in Figres 6. Fr mesh refinement in -directin, reslts als sh cnergence f temeratre rfile alng - directin tards =.6 ith maimm ercentage relatie errr less than.1%. ISBN:

8 Adances in Mdern Mechanical Engineering emeratre (k) Percentage relatie errr(%) &.35.5 &.4.3 &.8.35 &.3.7 & Z ( m) (a) emeratre distribtin alng -ais at the t srface Percentage relatie errr(% ) &.35.5 &.4.3 & &.3.8 &.7.7 &.6 (b) Percentage relatie errr at the t srface f the mid-sectin Figre 5. Percentage relatie errr fr different mesh interal sie Z (m) (a) emeratre distribtin alng the midsectin (b) Percentage relatie errr alng the deth f the mid-sectin Figre 6 Mesh refinements in -directin fr different mesh sies In rder t check the sensitiit f the time ste n the cnergence, simlatin is erfrmed ith decrease in time stes: Δt =.5, Δt =., Δt =.1, Δt =.5, and Δt =. sec. It as bsered that the least ercentage errr ccrs fr time ste sie beteen Δt =.5 sec and Δt =. sec. It is bsered that the temeratre distribtin is inariable fr time ste sie Δt =.5 sec and Δt =. sec. Effect f laser beam and srface tensin gradient his sectin mainl resents the effect f inclding a laser beam and srface tensin gradient in the all article distribtin in mlten l. Reslts resented in this sectin inclde the cntr lts f temeratre and cncentratin, ectr lts deicting the fl field and the crresnding nmerical data. Figre 7 resent the cntr lts fr temeratre and the elcit ectrs fr the mdel ith and itht the inclsin f laser beam and srface tensin gradient. It can be bsered frm the lts that the temeratre in mlten l decreases aa frm the centre f the laser beam ith the alicatin f laser beam and Marangni stress hereas the temeratre increases aa frm the centre f the l hen the effect f laser beam and Marangni stress is neglected. he elcit ectr lts shn in Figre 7b sh that hen the laser beam and marangni stress is alied, the fl field takes a redefined directin ISBN:

9 Adances in Mdern Mechanical Engineering f fl that fls aa frm the centre f the laser beam becase f srface tensin gradient. recirclating eddies are isible near the t n bth left and tight sides f the l. When the laser beam and marangni stress is neglected, the fl is frm ithin the l tards its free srface mainl becase f the banc frce acting in the ard directin and de t the decrease in the temeratre frm inside the l tards its free srface. he line lts f temeratre distribtin alng a line near the t srface and alng the ertical line at the center f the l are shn fr bth cases in Figre 8. As eected temeratre distribtin flls a Gassian distribtin ith eak temeratre bel the beam center. emeratre distribtin alng the ertical line shs a eak temeratre nderneath the free srface and redced temeratre tard the bttm. In case ith n laser beam and shear stress, heat l as rimaril called b dissiating heat frm the cred bttm srface b natral cnectin. In Figre 9, the elcit distribtin near the t srface shs the strng cnectie elcities ith eak elcities near the center f t circlating eddies, indced b the srface tensin frces. emeratre (k) ith HF & S itht HF & S (a) Distribtin f temeratre at the t srface f the l em e ratre (k ) Z (m) ith HF & S ith t HF & S (b) Distribtin f temeratre alng the deth f the l Figre 8 Distribtin f temeratre in the mlten l Figre 7 Effect laser beam and srface tensin n temeratre cntr lts and elcit ectrs in the l Velcit (m/s) ith HF & S itht HF & S (a) Distribtin f elcit near the t srface f the l ISBN:

10 Adances in Mdern Mechanical Engineering Velcit (m/s) Z (m) ith HF & S itht HF & S (b) Distribtin f elcit alng the deth f the l Figre 9. Distribtin f elcit in the mlten l Figres 1 sh the ariatin f Ni all distribtin ithin l fr the abe-discssed cases fr time stes.5 sec t 6.5 sec. In the case ith laser beam er and srface tensin drien fl, the Ni-all element transrts tards the t side alls f the l drien b the strng srface tensin drien b the t recirclating eddies. Reslts sh, in 6.5 secnd, the Ni-all has enetrated als mst entire deth f the l. Heer, there is cnsiderable nn nifrm distribtin f the Niall ith in the l. In case - II ith the absence f the laser beam er and marangni stress, the transrt f Ni-all ith the sbstrate is rimaril b diffsin and the enetratin is at a sler rate, bt maintains a nifrm cncentratin distribtin f all element ithin a thin laer at the free srface. (a) time stes.5 sec and 1 sec (a) time stes 4 sec and 6.5 sec Figre 1 Ni-all cncentratin distribtin ithin the mlten l ith time. All distribtin is mre nifrm hen laser beam and marangni stress are neglected and diffsin is the nl mde fr transrt f hels and enetratin f all articles, Heer, faster all enetratin takes lace hen laser beam and marangni stress are resent, hich leads t a strng fl field that enhances all transrt b diffsin and cnectin in the sbstrate mlten l. Figres sh the distribtin f Ni all at aris deth f the mlten l and at different time stes. Reslts in Figre 1 sh that right beneath the srface (Z = -.5) f the l, all distribtin is mre nifrm hen laser beam and marangni stress is neglected. In fact at this lcatin there is cnsiderable cncentratin ISBN:

11 Adances in Mdern Mechanical Engineering ariatin ith l ith l cncentratin in the mid-sectin and high cncentratin near the edge fr the case ith laser beam and marangni stress. Aarentl, jst near the srface ith re diffsin mde hels t maintain nifrm all element cncentratin. Bt if e take int cnsideratin f the all enetratin higher deth f the l (Figre 1-13), the effect f laser beam las a majr rle. It nt nl hels in attaining the desired thickness f all desitin nifrml bt als hels in attaining it at a faster rate. Fr eamle, Ni all cncentratin at a deth f -1 mm frm the free srface attains a cncentratin ale f.18 in 4 sec and.9 in 6.5 sec hen laser beam and marangni stress is sed as cmared t a n all cncentratin hen these arameters are nt sed. Ni ncentratin ith HF & S itht HF & S (a) Ni cncentratin at -.5 mm frm the t srface at time ste.5 sec Ni ncentratin ith HF & S itht HF & S (c) Distribtin f Ni cncentratin at -.5 mm frm the t srface at time ste 6.5s Figre 11 Variatin f distribtin f Ni cncentratin at -.5 mm frm the t srface ith time Ni ncentratin ith HF & S itht HF & S Ni ncentratin ith HF & S itht HF & S (b) Distribtin f Ni cncentratin at -.5 mm frm the t srface at time ste 4s (a) Ni cncentratin at -.1 mm frm the t srface at time ste.5s Ni ncentratin i th HF & S i th t HF & S (b) Ni cncentratin at -.1 mm frm the t srface at time ste 4s ISBN:

12 Adances in Mdern Mechanical Engineering Ni nc entratin Ni ncentratin ith HF & S ith t HF & S ith HF & S ith t HF & S (c) Ni cncentratin at -.1 mm frm the t srface at time ste 6.5s Figre 1 Variatin f Ni cncentratin ithin the l ith time at a deth f -.1 mm frm the t srface ith time. Ni ncentratin ith HF & S ith t HF & S (a) Ni cncentratin at -. mm frm the t srface at time ste.5s Ni ncentratin (c) Ni cncentratin at -. mm frm the t srface at time ste 6.5 sec Figre 13 Variatin f Ni cncentratin ithin the l ith time at a deth f -. mm frm the t srface ith time. 5. nclsins A three-dimensinal mathematical mdel has been resented t std the flid fl, heat transfer, and all element cncentratin distribtin in a mlten l created in a metallic sbstrate irradiated b high energ laser beam. he material as characteried ith resect t temeratre deendent srface tensin frce as rimar frce in deeling fl field and transrt f all element. mtatinal analsis is erfrmed t std the fl atterns, temeratre and cncentratin distribtins in the mlten l. Reslts sh strng deendence f laser beam er and Marangni stress n the effectie transrt and distribtin f all element in the sbstrate metal. he mdel is sitable fr deeling laser srface alling rcess fr an cmbinatin f all and sbstrate material cmbinatins in terms f creating a nifrm distribtin f all element er a desired thickness f the srface laer. ith HF & S itht HF & S (b) Ni cncentratin at -. mm frm the t srface at time 4 sec Nmenclatre I Laser beam intensit I Laser beam intensit P Laser beam er R Laser beam radis d Laser beam diameter Glbal -crdinate Glbal -crdinate ISBN:

13 Adances in Mdern Mechanical Engineering m h h c h r Glbal -crdinate emeratre Melting temeratre Ambient temeratre Enthal nectin film cefficient Radiatin film cefficient hermal cndctiit k q s Srface heat fl q V r V R t Ma Ma D D a HF S lme heat generatin de t laser beam Radial elcit Aial elcit Srface tensin Renlds nmber Pressre Secific heat ime ste Marangni nmber based n energ Marangni nmber based n diffsin Diffsin cefficient ncentratin f the all element absrtin cefficient Heat fl Srface tensin Greek Smbl Latent heat f fsin dnamic iscsit kinematic iscsit Densit 6. References [1] Anthn,. R., and line, H. F. (1977). Srface riling indced b srface-tensin gradients dring laser srface melting and alling. Jrnal f Alied Phsics, 48, [] Bas, B., and Sriniasan, J. (1988). Nmerical std f stead state laser melting rblem. Internatinal jrnal f Heat Mass transfer, 31, [3] Bas, B., and Date, A. W. (199). Nmerical std f stead state and transient laser melting rblems-i. haracteristics f fl field and heat transfer. Internatinal Jrnal f Heat Mass transfer, 33, [4] Bas, B., and Date, A.W. (199). Nmerical std f stead state and transient laser melting rblems-ii. Effect f the rcess arameters. Internatinal jrnal f Heat Mass transfer, 33, [5] Bas, B., and Date, A.W. (199). Raid slidificatin flling laser melting f re metals-ii. Std f l and slidificatin characteristics. Internatinal jrnal f Heat Mass transfer, 35, [6] Bas, B., Sekhar, J.A., Schaefer., & Mehrabian, R. (1991). Analsis f the stead state mlten l btained b heating a sbstrate ith an electrn beam. Acta metal. mater, 39, [7] han,., Mamdar, J., and hen, M. M. (1984). -dimensinal transient mdel fr cnectin in laser melted l. Metal. rans., 15A, [8] han,., Mamdar, J., and hen, M. M. (1985). hree-dimensinal mdel fr cnectin in laser melted l. Paer resented at IALEO-85. [9] Kar, A., and Majmder, J. (1988). Onedimensinal Finite-Medim diffsin mdel fr etended slid sltin in laser cladding f Hf n nickel. Acta metal, 36, [1] Kasla Bhaani and Pradi Majmdar, hree-dimensinal Finite Element Analsis f Melting in an All Irradiated ith a High Energ Laser Beam, Prceedings f the 3 Internatinal Mechanical Engineering ngress and R& D E, Paer NO: IMEE ,. 1-8, 3 [11] Kim, W. S., and Sim, B.. (1997). Std f thermal behair and flid fl dring laser srface heating f alls. Nmerical Heat ransfer. Part A, alicatins, 31, [1] Mran, D., iriani, F.D., Dfrescne, D., & Garin, A. (199). hermcaillar effects in a melted l dring laser srface treatment. ISBN:

14 Adances in Mdern Mechanical Engineering Eighth Internatinal Smsim n Gas Fl and hemical Lasers, SPIE [13] Pericles, K.A., & Baile,. (1995). Std f Marangni henmena in laser-melted ls. Mdelling the casting rcess and redicting residal stresses. Paer resented at Nmifrm 95. [14] Raindran, K., Sriniasan, J., & Marathe, A. G. (1994). Finite element std n the rle f cnectin in laser srface melting. Internatinal jrnal f nmerical hear transfer, 6A, [15] Raindran, K., Sriniasan, J., & Marathe, A.G. (1994). Rle f srface tensin drien cnectin in lsed laser melting and slidificatin. Prc Instn Mech Engrs, [16] Sdari, Dharani and P. Majmdar, Finite element analsis f laser irradiated metal heating and melting rcesses, Jrnal f Otics & echnlg, 4, , 1. ISBN: