numerical modelling of laser welding of al alloy

8/7/2019 Numerical Modelling of Laser welding of Al alloy

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Oulmtenul HFE_ nr. 8/?445 ◃ ehnuhrem-ghrtem ?1

YZ]JEMY CA Z@M MAAMIZY CA LHYM_ OMHG

GCJM ICNYEJM_MJ OU N]GM_EIHL YEG]LHZECN

CA VMLJENF TM_AC_GHNIM AC_ GEI_C

VMLJENF CA Z@EN HL Y@MMZ OU Nj2UHF

Şma luir. jr. enf. Echn-Ycren LMCQMHN]

]nevmrsethtmh „Zrhnselvhneh‗, Orhœcv

Mstm hosclvmnt hl ]nevmrsetĉũee „Zrhnselvhneh‗ jen Orhœcv, Ahiulthtmh jm Zm`nclcfeh Icnstruiũeelcr jm Ghœene,Ymiũeh utelhbul œe tm`nclcfeh sujĉree. H mamituht sthfeul lh ]. „Zrhitcrul‗ jen Orhœcv œe lh E.T.Z. Întcrsurh

Ouzĉulue, hpce h acst enfenmr prcemithnt lh Enstetutul jm Imrimthrm pmntru Hutcvmèiulm œe Zrhitchrm ’ Orhœcv,lh jmphrthgmntul punũe gctchrm jermitchrm. Jen 8500 mstm ihjru jejhitei lh ]nevmrsethtmh „Zrhnselvhneh‗ jenOrhœcv, lh Ihtmjrh jm enfenmreh ghtmrehlmlcr œe sujĉree. Mstm jcitcr enfenmr hl ]nevmrsetĉũee „Tcletm`neih‗ jen

Ouiurmœte, jen ?44?. H icntreouet lh prcemithrmh punũelcr gctchrm iu ghrm unfè jm verhrm pmntru trhitchrmhfreiclm œe enjustrehlm, lh prcemithrmh œe cgclcfhrmh struiturelcr jm rmzestmnũĉ sujhtm pmntru trhitchrm enjustrehl

se hfreiclm. H puoleiht ghnuhlm œe gcncfrhaee pm plhn lcihl, imntrhl œe în iclhocrhrm iu unevmrsetĉũe jenstr ĉenĉthtm, prmiug œe hrteiclm în rmvestm œe oulmtenmlm uncr icnamrenũm jm spmiehlethtm jen ũhr ĉ œe jen str ĉenĉthtm.

_MR]GHZ. Yujhrmh iu lhsmr Nj2UHF h tholmlcr suo

ũ

ere jen hlehbm jm Hl egpunm icnje

ũ

ecn

re smvmrm prevenj frhjemn

ũ

ee tmrgeie fmnmrh

ũ

e

jm sursh lhsmr în pemsmlm im acrgmhz

îgoenhrmh. En ihzul utelez

ree sursme lhsmr în gcjul icntenuu mstm mxtrmg jm frmu jm hsefurht

sthoelethtmh fmcgmtreme îgoen

ree sujhtm jen ihuzh jeaeiult

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ee în gmn

ũ

enmrmh icnsthnt h entmnset

ũ

ee sursme lhsmr e în pcze

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ecnhrmh

himstmeh în zcnh îgoen

ree. Himhsth mstm ihuzh hjcpt

ree gcjulue pulshtcreu pmntru sursh tmrgei

. _mzclvhrmh prcolmgmlcr lmfhtm jm

vhreh

ũ

eh icmaeiemntulue jm hoscro

ũ

em h i

ljuree fmnmrhtm jm sursh tmrgei

, întrm hprcxeghtev 0 pmntru ihzul hthiulue suprham

ũ

me sclejm

e hprcxeghtev :4 ..=4 pmntru ihzul în ihrm ghtmrehlul sm tcpm

tm se mstm fmnmrht irhtmrul jm hthi h icnjus lh gcjmlhrmh rmfegulue

pulsurelcr lhsmr. Y-h i

utht un rmfeg acrght jentr-un trmn jm pulsure iu entmnset

ũ

e e jurhtm jeamretm. Iïgpul tmrgei prcjus jm sursh

lhsmr h acst ihliulht utelezïnj gmtcjh vclugmlcr aenetm. Tm ohzh hnhlezme jestreou

ũ

eme tmgpmrhturee în oheh jm sujur

s-hu jmtmrgenht

vclugmlm jm icntrcl în ihrm hphr amncgmnm jm vhpcrezhrm e ecnezhrm e s-h co

ũ

enut htït acrgh fmcgmtrei

h irhtmrulue prcjus jm

sursh jm sujur

iït e jestreou

ũ

eh vetmzmlcr pm suprhah

ũ

h himstueh. Jhtmlm hstaml co

ũ

enutm hu acst utelezhtm în prcimsul jm gcjmlhrm iu

vclugm aenetm, vhrehnth imlulmlcr ghrihtm (GHI) h egpulsurelcr, jestreou

ũ

eme rmhlm h mnmrfeme în oheh jm sujur

ih e h acrgme

fmcgmtreim h suprham

ũ

me leomrm h himstmeh (suprhah

ũ

h jentrm oheh jm sujur

e pmrjmhuh jm fhzm jm prctmi

ũ

em).

Iuventm i`mem2

sujhrm iu lhsmr UHF, gmtcjh vclugmlcr aenetm, jestreouũeh tmgpmrhturee, oheh jm sujurĉ.

HOYZ_HIZ. En wmljenf ca tèn Hl s`mmt oy h Nj2UHF lhsmr omhg, t`m gcjm ca lhsmr `mhtenf ca t`m phrts omicgm mxtrmgmly egpcrthnt.

Vm ihn i`ccsm omtwmmn icntenuug cr pulsm lhsmr gcjm. En t`m ihsm ca icntenuug lhsmr gcjm, t`m sthoelety ca wmljmj s`hpm

fmcgmtry omicgms jeaaeiult tc om fmt. Z`m lettlm vhrehtecns en lhsmr spct pcwmr cr pcsetecn ihn fmnmrhtm ensthoelety ca wmljmj omhj

fmnmrhtmj. En t`m lhsmr pulsm wmljenf, t`m pcsetecn ca lhsmr spct cn t`m phrts ihn om mhsy icrrmitmj en t`m phusms omtwmmn twc lhsmr

pulsm trhens. Z`m egpcrthnim ca t`m lhsmr pulsm s`hpms omicgm t`m gcst egpcrthnt phrhgmtmr t`ht fmt t`m wmljenf pmnmtrhtecn

sthoelety hnj wmljmj omhj s`hpm. En crjmr tc mvhluhtm t`m maamit ca lhsmr pulsm s`hpm jurenf Nj2UHF lhsmr wmljenf ca tèn Hl s`mmt

hnj tc prmjeit t`m wmljenf pmracrghnim oy nugmreihl segulhtecn, h t`rmm-jegmnsecnhl QAG `mht alcw hnhlyses hnj h 9J aluej hnj

`mht alcw es prmsmntmj acr jeaamrmnt lhsmr pulsm s`hpms hnj rmlhtmj wmljenf phrhgmtmrs. Z`m segulhtecn rmsults s`cw t`ht t`m wmljenf

sthoelety es frmhtly haamitmj oy t`m gcjulhtecn ca lhsmr pulsm s`hpm acr t`m shgm lhsmr mnmrfy hnj wmljenf phrhgmtmrs

Kmywcrjs2 UHF lhsmr wmljenf, nugmreihl segulhtecn, QAG `mht alcw hnhlyses.

8. ENZ_CJ]IZECN

En crjmr tc wmlj hn Hl hllcy, icnimntrhtmj mnmrfys`culj gmlt t`m wmljenf rmfecn omacrm t`m icnjuitecnhwhy ca t`mrghl mnmrfy t`rcuf` t`m Hl hllcy. Z`mrmacrm,lhsmr wmljenf es h vmry maaeiemnt why tc wmlj Hl hllcys.Lhsmr wmljenf wet` h Nj2 UHF lhsmr, wèi` `hs h s`crtwhvm lmnft` prmsmnt hjvhnthfms en icntrhst wet` ct`mrlhsmr scurims, lekm IC? lhsmr, senim t`m s`crt whvmlmnft` fevms sghllmr spct sezm hnj rmsults en èf`mr lhsmr

omhg hoscrohnim cn hn Hl surahim. En t`m ihsm ca lcwwmljenf spmmj, t`m lhsmr s`cctenf icnjetecn es nct scireteihl; t`m wmljmj pccls fmnmrhtm cvmrlhppenf, out ht hahst wmljenf spmmj t`m setuhtecn t`m setuhtecn omicgmjeaamrmnt. Jurenf t`m pulsm jurhtecn, t`m lhsmr omhggcvms tc t`m wmljenf arcnt out cvmrhll mnmrfy jmnsetyacr gmltenf es lcw. Zùs, èf` pmhk pcwmr es nmmjmj acrahst wmljenf, hnj t`mn t`m rmlhtmj pulsm jurhtecn hnjarmqumniy s`culj om i`hnfmj. @ef` pmhk pcwmr esjeshjvhnthfmcus acr t`m icntrcllenf ca gmlt pccl



MAAMIZY CA LHYM_ OMHG GCJM ICNYEJM_MJ OU N]GM_EIHL YEG]LHZECN


cvmr`mhtenf, wèi` enjuims vhpcrezhtecn. Z`m hjvhn-thfms ca gcjmlenf t`m lhsmr pulsm hnj ès gcjulhtecns`hpm ihn om usmj tc prmvmnt wmljenf jmamits.

?. Z@MC_MZEIHL OHIKF_C]NJ

?.8. T`yseihl gcjml

Z`m ellustrhtecn ca t`m wmljenf fmcgmtry es s`cwn enaefurm 8. Z`m pulsmj Nj2UHF lhsmr omhg es aciusmj cnt`m surahim ca h outt bcent; hnj t`m wmljenf spmmj esicnsthnt. Z`m lhsmr omhg hoscrohnim enirmhsms wet` t`mspmiegmn tmgpmrhturm, senim t`m lhsmr omhg hoscrohnimcn h gmthl surahim es h aunitecn ca tmgpmrhturm. V`mnt`m gmthl es gmltmj, t`m gmthl p`hsm nc lcnfmr `hs hirysthl struiturm out hn hgcrp`cus p`hsm. Ea t`m gmthl p`hsm i`hnfms tc t`m hgcrp`cus p`hsm, t`m lhsmr omhghoscrohnim enirmhsms ahstmr. Zùs t`m lhsmr omhghoscrohnim cn Hl es hjhptmj hs hpprcxeghtm vhlums htt`m fevmn icnjetecns. Et es hssugmj t`ht t`m lhsmr omhghoscrohnim es hocut 0% ht rccg tmgpmrhturm hnjrmhi`ms =4% ht t`m gmltenf pcent. (?) Z`m t`mrghlicnjuitevety hnj spmieaei `mht ca Hl hrm aunitecns catmgpmrhturm. En t`m ihliulhtecn ca tmgpmrhturmjestreoutecn oy QAG segulhtecn en tès wcrk hnj t`mtmgpmrhturm jmpmnjmniems ca icnjuitevety hnj vesicsetywmrm icnsejmrmj en icgputmr segulhtecn. Hlsc t`m lhtmnt`mht ca gmltenf hnj armmzenf whs icnsejmrmj en t`micgputmr segulhtecn oy t`m tmgpmrhturm rmicvmrygmt`cj. (9) En tès segulhtecn, lhsmr omhg mnmrfy jmnsetywhs nct suaaeiemntly èf` mncuf` tc acrg kmy`clms,wèi` wculj ihusm jmmp pmnmtrhtecn wmljenf. Zùs t`mlhsmr omhg jcms nct pmnmtrhtm jmmp entc gcltmn pccl oyt`m kmy`clm gmi`hnesg. En t`m icgputmr segulhtecnihliulhtecn, t`m sezm ca t`m gcjml whs 84gg en lmnft`,:.6 gg en wejt` hnj ?gg en t`m tèiknmss; t`m gms`nugomr ca mlmgmnts whs hocut ?5:,444. Cnm mlmgmntsezm whs hpprcxeghtmly 844 μg Ö 844 μg Ö 844 μghnj t`m hjhptevm gms` gmt`cj well om usmj en t`m hrmhca aciusmj lhsmr omhg spct sezm whs hocut 944 μg ÖÖ 944 μg. Z`m hocvm hssugptecns wmrm sugghrezmj hsfevmn omlcw hnj wmrm icnsejmrmj en t`m icgputmr

segulhtecn ihliulhtecn2 ’

t`m lhsmr omhg hoscrohnim, t`mrghl icnjuitevetyhnj spmieaei `mht wmrm jmpmnjmnt upcn t`m tmgpmrhturmca t`m spmiegmn, hnj t`m jmnsety ca t`m spmiegmn whsicnsthnt;

’

t`m maamit ca plhsgh whs nct icnsejmrmj out t`mrhjehtecn `mht lcss whs icnsejmrhtm;

’

t`m p`hsm i`hnfm whs thkmn entc hiicunt oy t`mtmgpmrhturm rmicvmry gmt`cj;

’

t`m gmlt tmgpmrhturm whs susthenmj omlcw t`mmvhpcrhtecn pcent hnj t`m mvhpcrhtecn `mht lcss whsthkmn entc hiicunt acr t`m ghss rmgcvhl;

’ t`m vesicsety ca t`m gmltenf es tmgpmrhturm jmpmnjmnt;

’

t`m armm surahim lcsms `mht oy rhjehtecn hnj t`micnvmitecn `mht lccsmj es nmflmitmj; ’

t`m icnvmitecn `mht mxi`hnfm omtwmmn t`m gmlt hnjsclej p`hsm es mxprmssmj ohsmj cn _m hnj Tr nugomrs.

Aef. 8. Hspmit ca fmcgmtreihl wmljmj phrts.

Aef. ?. Yygocls acr Aenetm Qclugm.

?.?. Fcvmrnenf mquhtecn hnj Ocunjhry

icnjetecn

Fmnmrhl acrg ca `mht alcw mquhtecn. Z`m nugmreihl

segulhtecn whs icnjuitmj oy t`m t`rmm-jegmnsecnhltrhnsemnt prcolmg.Hlt`cuf` t`m spmiegmn `hs h icgplmx s`hpm, t`m

segpleaemj fmcgmtry es hjhptmj hnj t`m phrtehl jea-amrmntehl mquhtecn acr `mht trhnsamr es fevmn en t`macllcwenf mquhtecn (8),

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t x y z t ( 8)



I_MHZEQEZHZM, ENQMNZEIď, _COCZEIď


w`mrm Z es tmgpmrhturm, x, y, hnj z hrm t`m iccrjenhtecnjermitecns, rmspmitevmly, λ es t`mrghl icnjuitevety, ψ est`m jmnsety, I p es t`m `mht ihphiety, hnj t es tegm. Z`mfmnmrhlezmj mquhtecn arcg t`m icntrcl vclugm gmt`cj,wèi` whs hjhptmj acr mxpleiet gmt`cj ohsmj cn

cpmrhtcry t`mcry, es fevmn en t`m acllcwenf mquhtecn (?).[ W ?8?8?8

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w`mrm2 HIJxe ’ icnjuitecn surahim hrmh icntrcl Y Ie, HIQxe ’icnvmitecn surahim hrmh icntrcl Y Ie., Q ’ aenetm vclugm;Κt ’ tegm sthoelety entmrvhl hnhlysm; Κ x, Κ y, Κ z ’ gms`lmnft`s; n x ’ nugomr ca surahims; I p ’ spmieaei `mht; ψ ’jmnsety; οIQe,b,k ’ t`mrghl rmsesthnt icmaaeiemnt ca mlmgmntca He,b,k , ’ [ LWIQ icnvmitecn cpmrhtcr; [ LW _J ’ rhjehtecncpmrhtcr ; HIQ e,b,k ’ hrmh ca icntrcl surahim He,b,k ,; Xe ’ `mht

enput oy lhsmr ensejm t`m icntrcl vclugm.Aefurm ? s`cws t`m ncgmnilhturm ca t`m icntrcl

vclugm hpprchi` hnj h gms` jevejmj oy t`m ennmr ncjhl pcent gmt`cj, wèi` es icnvmnemnt acr h icgplmx s`hpm prcolmg. Z`m enetehl icnjetecn whs jmaenmj t`ht t`mtmgpmrhturm ca t`m spmiegmn whs ?59 K ht t`m enetehlsthtm hs mquhtecn (9).

Z 7 Z 4 ( x, y, z ) ht t 7 4 (9).

Z`m acrimj icnvmitevm `mht trhnsamr whs icn-sejmrmj en ocunjhry, hnj t`m hvmrhfm icnvmitevm `mhttrhnsamr icmaaeiemnt `g wetèn t`m mnterm rmfecn ca t`m tcphnj octtcg surahim whs rmquermj acr sclvenf mquhtecn(?). Z`m hvmrhfm icnvmitevm `mht trhnsamr icmaaeiemnt

whs cothenmj oy acllcwenf mquhtecn

w`mrm λ es t`m t`mrghl icnjuitevety ca her, N uss es t`m Nussmlt nugomr hnj L t`m lmnft` ca t`m mlmgmnt(Κx, Κy, Κz). Z`m mxprmssecn ca t`m Nussmlt nugomr es.

( ) 9

80,4:9,4 Tr ?56:,86_mTr 491,4 ⋍+∟⋍7uss N (:)

Z`m aexmj tmgpmrhturm ocunjhry icnjetecn whshpplemj tc t`m surahim mximpt acr t`m uppmr hnj octtcgsurahim rmfecn. Ea t`m mnterm ghss ca mlmgmnt whsmvhpcrhtmj oy h èf` pcwmr jmnsety ca lhsmr omhg, t`m ocunjhry icnjetecn whs i`hnfmj arcg icnjuitecn tc

icnvmitecn en t`m rmamrmnim mlmgmnt untel t`m nmxt stmpihliulhtecn. Z`m aexmj tmgpmrhturm ca t`m gcltmnmlmgmnt whs hssugmj tc susthen hnj t`m lhsmr omhgerrhjehtmj cn t`m nmxt mlmgmnt omlcw t`m mlmgmnt, wèi`whs mvhpcrhtmj.

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Aef. 9. Mxpmregmnthl rmsults ca wmljmj rmfecn hnj segulhtecn rmsultsca tmgpmrhturm jestreoutecn. Lhsmr pulsm s`hpm wet` 9 lmvmls.

Aerst2 1=44 V, 4.? gsmi; ? nj2 :444V, 4.? gsmi; 9 rj2 9444 V,4.: gsmi; armqumniy2 04@z; sihnnenf spmmj2 ?4 gg/smi; omhg

gcjm2 gulte-gcjm.h ’ ircss smitecnhl vemw; o ’ tcp vemw.

Mnmrfy ohlhnim cn t`m errhjehtmj aenetm vclugm.Z`m ohlhnim ca mnmrfy cn lhsmr omhg spct errhjehtmj



MAAMIZY CA LHYM_ OMHG GCJM ICNYEJM_MJ OU N]GM_EIHL YEG]LHZECN


aenetm vclugm thkm en hiicunt t`m mnmrfy lcsm en t`m p`hsm i`hnfm prcimss, (gmltenf, vhpcrezhtecn, ecnezh-tecn) t`m icnvmitecn hnj prmssurm cn t`m irhtmrs s`hpmhnj aenhlly t`m jeaausecn `mht en t`m nmefòcrs aenetmvclugms. (81)

9. MPTM_EGMNZHL T_CIMJ]_MY

En crjmr tc icgphrm t`m nugmreihlly segulhtmjrmsults wet` mxpmregmnthl rmsults, t`m mxpmregmnts wmrm pmracrgmj wet` h pulsmj Nj2UHF lhsmr, acr wèi` etwhs pcsseolm tc gcjulhtm t`m lhsmr pulsm s`hpm. Z`m omhg gcjm whs gulte-gcjm lhrfmly jum tc t`m cpteihlaeomr jmlevmry systmg. Z`m pulsm s`hpm gcjulhtecns

usmj en tès wcrk wet` 9- jevesecns hnj t`m aciusmj omhg sezm whs hpprcx. 944 μg en jehgmtmr.

:. _MY]LZY HNJ JEYI]YYECN

Z`m mxpmregmnt whs ihrremj cut wet` t`m shgm lhsmrerrhjehtecn icnjetecn acr t`m nugmreihl segulhtecn encrjmr tc vmreay t`m segulhtecn. Aefurm 9 s`cws t`mmxpmregmnthl rmsult hnj t`m segulhtmj tmgpmrhturmjestreoutecn acr gulte-gcjm lhsmr omhg. Z`m Aefurm :hnj Aefurm = s`cw t`m rmsults ca tmgpmrhturm s`hpm ca pulsm gcjm hnj lcnfetujenhl hnj trhnsvmrshl smitecn cat`m mxpmregmnthl shgplms hnj t`m nugmreihl rmsults.

h) o) i)

Aef. :. Zmgpmrhturm enjuimj oy lhsmr pulsm s`hpm.2h ’ h lhsmr pulsm s`hpm wet` 9 sthfm (8 st2 :=44 V, 4.? gsmi; ?nj2 9444 V, 4.? gsmi; 9rj2 arcg =44 V tc ?=44 V, 4.: gsmi);

o ’ tmgpmrhturm ca t`m tcp surahim hs h aunitecn ca tegm acr vhrecus pulsms s`hpms wet` jeaamrmnt pcwmr en t`m tèrj sthfm;i ’ tmgpmrhturm vhrehtecn hs h aunitecn ca tegm en t`m wmlj pccl ht jeaamrmnt jmpt`s arcg t`m surahim (?=44 V en t`m 9 rj sthfm).

h) o) i)

Aef. =. Ircss-smitecnhl vemw ca t`m wmlj rmfecn hnj segulhtmj tmgpmrhturm prcaelms wet`vhrecus sihnnenf spmmjs. (8st2 :=44V, 4.? gsmi, ?nj2 ?044 V, 4.: gsmi, 9rj2 8=44 V, 4.? gsmi, 884 @z)2

h ’ sihnnenf spmmj2 84 gg/smi; o ’ sihnnenf spmmj2 94 gg/smi; i ’ sihnnenf spmmj2 =4 gg/smi.

=. ICNIL]YECN

En wmljenf ca tèn Hl s`mmt oy h pulsmj Nj2UHFlhsmr, t`m lhsmr pcwmr lmvml es t`m gcst enalumntehl enwmljenf om`hvecr. Z`m segulhtecn rmsults s`cw t`ht t`mwmljenf sthoelety es frmhtly haamitmj oy t`m gcjulhtecnca t`m lhsmr pulsm s`hpm acr shgm lhsmr mnmrfy hnjwmljenf phrhgmtmrs. Hs t`m rmithnfulhr lhsmr pulsms`hpm es gcjulhtmj tc `hvm t`rmm sthfms wet` èf`,gmjeug hnj lcw pcwmr lmvml acr aerst, smicnj hnj tèrj

sthfm rmspmitevmly, gcrm mnmrfy es hoscromj en t`m gmlt pccl hnj t`m icclenf rhtm well om rmjuimj. Z`m segu-

lhtmj rmsults fevm fccj hfrmmgmnt wet` mxpmregmnthlrmsults, w`mrm scunj wmlj s`hpm hnj irhik-armm wmlj pccl hrm cothenmj.

_MAM_MNIMY

[8W Ue`-Acnf Zzmnf, B. ca Ghtmrehls Trcimssenf , Qcl. 844, ?444; pp 819-864.



I_MHZEQEZHZM, ENQMNZEIď, _COCZEIď

Oulmtenul HFE_ nr. 8/?445 ◃ ehnuhrem-ghrtem 94

[?W Z. @. Keg, K. I. I`cnf, O. U. Ucc, B. Y. Lmm2 B. ca Ghtmrehl

Yiemnim, Qcl. 94, Nc. 9, 855=; pp.60:-65?.[9W I.T. @cnf hnj V. @. Ohmk, B. ca t`m Kcrmhn Enst. ca Gmthls,

Qcl.?1, Nc.0, 8550; pp.084-0?8.[:W U. Ohyhzetcflu hnj G. N. Czesek, Mlmgmnts ca @mht Zrhnsamr ,

GiFrhw-@ell (Nmw Ucrk), 8500; pp.?45-?8:.

[=W E. Y. Lmcvmhnu hnj F`. Rfurh, Gcjmllenf t`m @mht hnj Aluej Alcw en t`m Vmljmj Tccl arcg @ef` Tcwmr Hri Ycurims.Ghtmrehls Yiemnim Acrug Qcls. =04-=0? en Bunm ?440.`ttp2//www.siemnteaei.nmt/GYA/4-060:5-909-?S::9.pja .

[1W C. Frcnf. Gmthllurfeihl Gcjmllenf ca Vmljenf. Ymicnj Mjetecn.Z`m Enstetutm ca Ghtmrehls. 855:.

[6W @.Y. Ihrslhw hnj B.I. Bhmfmr2 Icnjuitecn ca @mht en Yclejs;85=5, Cxacrj, Cxacrj ]nevmrsety.

[0W _. @ultfrmn, _.L. Crr, _J. Hnjmrscn hnj K.K. Kmlly2 Ymlmitmj

Qhlums ca Z`mrgcjy. Trcp.; 8519, Nmw Ucrk, B. Velmy & Ycns.

[5W H. H. Hgsjmnhnj A. @. @hrlcw2 _mpcrt L.H. :964, Lcs HlhgcsYiemnteaei Lho., (8564).

[84W O. J. Nei`cls hnj I. V. @ert2 B. Icgputhtecnhl T`yseis, 0(856 l), :9:.

[88W N.N. _ykhlen, H.E. Tufen hnj Q.H. Qhsel'mvh2 Vmlj. Trcj.,85=5, 1, :?-=?.

[8?W C._. Gy`r hnj 4. Frcnf2 Hith Gmthll. Ghtmr., 8554, 90, ::5-:14.

[89W N. I`restmnsmn2 Vmljenf Gmthllurfy Icgpmnjeug, 850=, ]ne-vmrsety ca Zrcnj`meg,

[8:W IM. Bhikscn2 Vmlj. B., 8514, 95, ??1s-?94s.[8=W C.G. Hksmlsmn hnj F. Yhfgc2 Zmi`neihl _mpcrt YZA9:

H058:6 , 8505, Zrcnj`meg (Ncrwhy),[81W E.Y. Lmcvmhnu, O-I Keg,F`. Rfurh, I.T. @cnf2 Z`m maamit ca

lhsmr omhg gcjm icnsejmrmj oy Nugmreihl Yegulhtecn caVmljenf Tmracrghnim acr t`m Geirc Vmljenf ca Z`en Hl Y`mmt oy

Nj 2 UHF. O_HGHZ ?449 Entmrnhtecnhl Icnamrmnim. Orhscv.

numerical modelling of laser welding of al alloy

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