solidification mechanisms in fusion welds, savage, nippes, erickson, wj_1976

7/27/2019 Solidification Mechanisms in Fusion Welds, Savage, Nippes, Erickson, WJ_1976

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WEL-EJirMC RESEARCHSUPPLEMENT TO THE WELDING JOURNAL, AUGUST 1976Sponsored by the American Welding Society and the Welding Research Counci l

Solidification Mechanisms inFusion WeldsDuring weld solidification, the size of cellular substructure growth increases linearly relative to the reciprocalof the thermal gradient at the solid-liquid interface

BY W. F. S A V A G E , E. F. N I P P E S A N D J. S. E R I C K S O N

A B S T R A C T . F u s i o n w e l d s in a 4 9 %n i cke l - i r o n a l l o y w e r e s t u d i e d tode te rmine the i n f l uence o f the the rma lg rad ien t in the so l id , G s , and thegrowth ve loc i t y of t he so l i d - l i qu id int e r face , R, on t he na tu re of th e c e l l u la r and c e l l u l a r d e n d r i t i c g r o w t hmo d e s f o r me d d u r i n g w e l d so l i d i f i c a t i o n .T o w a r d t h i s e n d , an e x p e r i m e n t a lt e ch n i q u e wasd e v e l o p e d for m e a su r i n g t h e t e mp e r a t u r e d i s t r i b u t i o n int he so l i d a round the we ld poo l wh ichw a s s o l i d i f y i n g u n d e r t w o - d i m e n s iona l hea t - f l ow cond i t i ons .T h e d i r e c t i o n in w h i ch ce l l u l a rg r o w t h o ccu r r e d wasco n t r o l l e d byw e l d i n g on a 49% n i cke l - i ron a l l oyw h i ch e xh i b i t e d a cu b e - o n - f a ce t e x ture wi th a d i rec t i on pa ra l l e l t o

the ro l l ing d i rect ion in the p lane o f theshee t . Bypre -o r i en t i ng the tes t specimens p r i o r to w e l d i n g , it w a s p o s s ib le to con t ro l t he d i rec t i on inw h i chthe ce l l u la r subst ruc tu re g rew re l at ive to t he so l i d - l i q u id i n te r face .W. F. SAVAGE is Professor of Metallurgical Engineering andDirector of WeldingResearch and E. F. NIPPES is Professor ofMetallurgical Engineering, RensselaerPolytechnic Institute, Troy, Ne w York; J. S.ERICKSON. former Graduate Fellow atRensselaer Polytechnic Institute, is Super-visor, Casting Process DevelopmentGroup, Pratt & Whitney Aircraft Division,United Aircraft. E ast Hartford, Connecticut.

Paper presented at the AWS 57th An-nual Meeting held in St. Louis, Missouri,during May 10-14, 1976.

I t was found tha t the tempera tu re ina d i r e c t i o n p e r p e n d i cu l a r to th e t r a i l i ng edge of t he we ld poo l decre asedin an exponen t i a l manner w i th d i s tance f rom the so l i d - l i qu id i n te r face .The the rm a l g rad ien t i n the so l i d c o n t i nuous l y decreased f rom the f us ionl i ne toward the we ld cen te r l i ne at th et ra i l i ng edge of t he we ld p o o l .The size of thece l l u la r subst ructu re i ncrea sed l i nea r ly as a func t i on of1/GS, w h e r e G s e q u a l s the t h e r m a lg r a d i e n t in theso l i d unde r constan tg rowth ve loc i t y cond i t i ons . Fu r the r m o r e , the size of the ce l l u la r sub s t ruc tu re decreased w i th an i nc reasein g row th ve loc it y unde r constan tt h e r ma l g r a d i e n t co n d i t i o n s .The ce l l u la r - to -ce l l u la r de nd r i t i ct rans i t i on was found to o c c u r at essent ia l ly the same ra t i o of Gs /R"2d u r i n g the so l i d i f i ca t i on of f u s i o nw e l d s in t h i s ma te r i a l .I n t r o d u c t i o n

I t has long been recognized that ani n e v i t a b l e co n se q u e n ce ofal loy s o l i d i f i ca t ion is t he red i s t r i bu t i on of so lu tea n d , t he re fo re , the p resence of c o m p o s i t i o n a l v a r i a t i o n s w i t h i n thec a s t i n g . S e g r e g a t i o n , w h e t h e r itbe ona ma c r o ormicro sca le , can be de t r i me n t a l in t ha t it p r o d u ce s l o ca l i ze dva r ia t i ons in bo th the so l i d i f i ca t i ont e mp e r a t u r e a n d me ch a n i ca l p r o p e r t ies of ca s t ma t e r i a l . F u r t h e r m o r e , t h ep r e se n ce of c h e m i c a l i n h o m o g e n e i t ies in the ma t e r i a l ca n n o t be rem o v e d , inmany ins tances, even a f te r

p r o l o n g e d e xp o su r e at e leva ted t e m p e r a t u r e s .A g rea t dea l of resea rch has beend i r e c t e d t o w a r d d e t e r m i n i n g howch a n g e s in the g r o w t h co n d i t i o n sp resen t du r i ng so l i d i f i ca t i on a f fec t theo b se r ve d se g r e g a t i o n p a t t e r n s . Unf o r tuna te l y , t h i s wea l th of i n f o r ma t i o nhas not been app l i ed ex tens i ve l y tot h e u n d e r s t a n d i n g of we ld so l i d i f i ca t i on i n gene ra l . The p rob lem o f s tudyi ng the we ld so l i d i f i ca t i on p rocess hasb e e n co mp l i ca t e d by the fact thatwe ldmen ts so l i d i f y unde r the rma l andg rowth cond i t i ons w ide l y d i f f e ren tthan those found in la rger s ized cast i ngs . F o r e xa mp l e :1. The g rowth ve loc i t y of th e s o l i d -l iqu id in ter face can be 10 to 100 t imesg r e a t e r d u r i n g w e l d i n g t h a n t h a t

f o u n d in ca s t i n g s .2. T h e t h e r ma l g r a d i e n t p r e se n t inboth the l iqu id and so l id at th e s o l i d i fy ing in ter face can be 1 ,000 to 10,000t imes g rea te r in the ca se of we ldso l i d i f i ca t i on than tha t expe r ienced inl a rge r cas t i ngs .3. The w e l d i n g p a r a me t e r s emp loyed exe r t as ign i f i can t i n f l uence ont h e g e o me t r y of t he so l i d - l i qu id i n te r face present a t the t ra i l ing edge o f thew e l d p o o l . This resu l ts in su b s t a n t i a lva r i a t i ons in bo th the t h e r ma l g r a d ien ts and g rowth ve loc i t i es p resen t

a t the so l i d i f y i ng i n te r face du r ingw e l d i n g .Th is pape r descr i bes an i nvest i ga t i on wh ich wasd e s i g n e d to ga in amo r e t h o r o u g h u n d e r s t a n d i n g of thew e l d - so l i d i f i ca t i o n p r o ce ss . In par t i c -W ELD IN G R ES E AR CH S U P P L E M E N T ! 213-S


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"SOLID- ^ C -

P L A N A R I N T E R F A C E7 S O L I D \

C U R V E D I N T E R F A C E( a ) S O L U T E F L O W

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" j j j y L I Q U I DS O L I DP L A N A R I N T E R F A C E C U R V E D IN T E R F A C E

( b ) H E A T F L O WFig. 1 Schem atic diagram illustrating the direction of: (a) solute flow from aplanar interface as compared to a curved interface, an d (b) heat flow to aplanar interface as compared to a curved interface.

< IOO> DIRECTION IN TH Ef PLANE OFTHE SHEETI PERPENDICULAR TO THEV WELDING DIRECTION

-WELD

- INSTANTANEOUS POSITIONOF SOL ID-LIQU ID INTERFACEWELDING DIRECTION -

Fig. 2 Ideal schematic representation ofthe preferred orientation of thebase metal and the resultant cellular substructure

ular t h e i n v e s t i g a t i o n c o n c e n t r a t e d o nd e t e r m in i n g t h e t h e r m a l d i s t r i b u t i o na b o u t a we ld p o o l s o l i d i f y i n g u n d e rt w o - d i m e n s i o n a l h e a t - f l o w c o n d i t i o n s .T h e a c q u i s i t i o n o f t h e s e t h e r m a ld a t a p e r m i t t e d a n a c c u r a t e a s s e s s m e n t o f t h e t h e r m a l g r a d ie n t a n dso l id i f i ca t ion ra tes p resen t a t t he t r a i l i ng edge o f t he we ld p o o l . By j u d i c io u s c o n t r o l o f t h e c r y s t a l l o g r a p h i co r i e n t a t i o n o f t h e we ld s p e c im e n , i twa s p o s s ib l e t o s t u d y t h e f u n d a m e n t a l n a t u r e o f t h e we ld - s o l i d i f i c a t i o ns u b s t r u c t u r e a s d e s c r i b e d i n d e t a ilb e l o w .Solidification Mechanics Considerations

T he c o n c e p t o f c o n s t i t u t i o n a ls u p e r c o o l i n g ( Re f. 1) wa s p r o b a b l yone o f t he mos t s ign i f i can t f ac to rsl e a d in g t o a t h e o r e t i c a l e x p la n a t i o n o fa l l o y s o l i d i f i c a t i o n . T h i s t h e o r y wa sm a t h e m a t i c a l l y d e s c r i b e d b y T il l e r e fal (Re f. 2 ) and m ore recen t ly app l iedt o t h e u n d e r s t a n d in g o f we ld s o l i d

i f i c a t i o n b y S a v a g e a n d c o wo r k e r s(Ref . 3 ,4) . In these invest igat ions i twa s s h o wn t h a t t h e l i q u i d m e t a lahead o f a so l id i f y ing in te r f ace cou ldb e s u p e r c o o le d a n d , t h e r e f o r e , b e u n s tab le even in t he p resence o f a pos i t iv e t h e r m a l g r a d ie n t i n t h e l i q u i d .T h i s s u p e r c o o l i n g wa s a t t r i b u t e d t othe inab i l i t y o f t he a l loy sys tem tor e d i s t r i b u t e s o lu t e f r o m t h e l i q u i d t os o l i d p h a s e s e f f e c t i v e l y d u r i n g t h es o l i d i f i c a t i o n p r o c e s s . Co r r e l a t i o n swere f ound to ex is t be tween the s ta b i l i t y o f t he so l id i f y ing in te r f ace andt h e d e g r e e o f c o n s t i t u t i o n a l s u p e r c o o l i n g p r e s e n t .S o l i d i f i c a t i o n p a r a m e t e r s s u c h a sa l loy so lu te con ten t , t he t he rma l g ra d ien t in t he l iqu id , and t he g rowth ra teo f t he so l id i f y ing in te r f ace were f oundto in f luence the resu l t an t so l id i f i ca t i o n s u b s t r u c t u r e . I n t h e a b s e n c e o fc o n s t i t u t i o n a l s u p e r c o o l i n g ( wh i c h f o ra g iven a l loy sys tem is ind ica t ive o fs t e e p t h e r m a l g r a d ie n t s a n d / o r l o wg r o w t h r a t e s ) , a p l a n a r i n t e r f a c ewou ld p reva i l . On the o ther hand i f t het h e r m a l g r a d ie n t s o r g r o w t h r a t e swe r e s u c h t h a t c o n s t i t u t i o n a l s u p e r c o o l i n g e x i s t e d , t h e n t h e i n t e r fa c ewo u ld b e c o m e u n s t a b le a n d b r e a kdown in to one o f t he severa l dendr i t i c - g r o w t h m o d e s .

I n a d d i t i o n t o t h e c o n s t i t u t i o n a l -s u p e r c o o l i n g c r i te r i o n , o t h e r d y n a m i c c h a n g e s m u s t b e c o n s id e r e d i no r d e r to d e s c r i b e p l a n a r - i n t e r f a c es tab i l i t y f u l l y . A mathemat ica l pe r tu r b a t i o n a n a l y s i s wa s fo r m u la t e d b yM u l l i n s a n d S e k e r k a ( Re f . 5 ) wh o c o n s id e r e d t h e d y n a m ic c h a n g e s t h a t o c cu r in t he so lu te and the rma l f ie ldss u r r o u n d in g a p e r t u r b a t i o n o r ce l lf o r m e d o n t h e s o l i d i f y i n g i n t e r f a c e .

I n a d d i t i o n t h e f r e e - e n e r g y c h a n g eassoc ia ted w i t h t he f o rmat ion o f ac u r v e d i n t e r f a c e w a s c o n s i d e r e d .The i r ana lys is showed tha t t he s tab i l i t y of the in ter face was af fected by thes o l u t e , h e a t t r a n s p o r t , a n d f r e e -e n e r g y c o n d i t i o n s wh i c h e x i s t a t t h eso l id i f y ing in te r f ace ; a lso , t hese c o n d i t i o n s we r e i n f l u e n c e d b y t h e c u r v a ture present at the t ip of the cel l orp e r t u r b a t i o n . F o r e x a m p le , F i g . 1o f f e rs a c o m p a r i s o n b e t we e n s o lu t ef low f rom a cu rv ed and p lanar in te r f ace . No te t ha t t he p resence o f ac u r v e d i n t e r fa c e r e d u c e s t h e o v e r l a ppresen t be tween the so lu te f ie lds ona d j a c e n t p o i n t s o n t h e i n t e r f a c e .Co n s e q u e n t l y , t h e r e d i s t r i b u t i o n o fs o lu t e is a c c o m p l i s h e d m o r e r e a d i l ya t a cu rved in te r f ace t han a t a p lanarin te r f ace . There fo re , t he e f f ec t o f acurved in te r f ace (o f t en re fe r red t o asthe "po in t e f f ec t o f d i f f us ion" ) i s t op r o m o t e i n s t a b i l i t y o r c e l l f o r m a t i o n .

Hea t t r anspor t f r om the l iqu id t o t heso l id has an oppos i t e e f f ec t onp lanar - in te r f ace s tab i l i t y . F igu re 1c o m p a r e s a p l a n a r a n d c u r v e d i n t e rf ace in t he p resence o f a pos i t i ve t empera tu re in t he l iqu id s im i la r t o t ha twh i c h e x i s t s d u r i n g we ld i n g . F r o m t h egeomet ry i t can be seen tha t hea tt ranspor t i s more e f f i c ien t f o r a p lanarin te r f ace t han f o r an in te r f ace w i t h apos i t i ve cu rva tu re in t he so l id . Th ere fo re , hea t t r anspor t w i l l t end t o p ro m o t e p l a n a r - i n t e r f a c e s t a b i l i t y .I n te r f ac ia l f r ee -energy was a lsocon s ide red in t he ana lys is in t ha t as

t h e i n t e r f a c e b e c o m e s c u r v e d t h e nthe in te r f ac ia l f r ee -energy o f t he sys t e m w i l l i n c re a s e . T h e r e f o r e , t h e p r e s ence o f a p lanar in te r f ace t ends t o re d u c e t h e f r e e - e n e r g y o f t h e s y s t e mand p romotes in te r f ace s tab i l i t y . Per t u r b a t i o n a n a l y s i s p r e d i c t s t h a twh e t h e r a p l a n a r in t e r f a c e r e m a in ss t a b le o r b r e a k s d o wn i n t o a c e l l u l a rg r o w t h m o d e w i l l u l t im a t e l y d e p e n don the magn i t ude o f each o f t he f ac t o r s m e n t i o n e d a b o v e .A n u m b e r o f e x p e r im e n t a l i n v e s t i g a t i o n s h a v e a l s o b e e n c o n d u c t e d

wh i c h e x a m in e d t h e r e l a t i o n s h ip b e tween the s ize o f t he va r ious so l id i f i c a t i o n s u b s t r u c t u r e s a n d s o l i d i f i c a t ion va r iab les such as so lu te con ten t ,t h e r m a l g r a d ie n t a n d g r o w t h r a t e .Ru t te r and C ha lme rs (Re f . 1 ) , f o r ex a m p le , s h o we d i n d e c a n t i n g e x p e r i m e n t s t h a t c o r r u g a t i o n o r c e l l s p a c in gd e c r e a s e d w i t h i n c r e a s in g g r o w t hra te . I n add i t ion t he i r inves t iga t ionshowed tha t t he ce l l s ize inc reased asthe so lu te con ten t o f t he a l loy in c reased o r t he t he rma l g rad ien t in t hel i q u i d d e c r e a s e d .Other inves t iga to rs (Re fs . 6 ,7 ) haves h o wn t h a t f o r a g i v e n s o lu t e c o n t e n t ,c e l l s i z e v a r i e d l i n e a r l y w i t h t h ep a r a m e t e r 1/GLR. T h e s e i n v e s t i g a t ions a lso showed tha t ce l l s ize cou ldvary by a f ac to r o f t h ree o r f ou r de -

2 1 4 -8 I A U G U S T 1 9 7 6


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0 . 0 4 0 . 0 8 0 .120 .160 . 2 0 0 . 2 4 0 . 2 8 0 . 3 2 0 . 3 6 0DISTANCE ALONG THE WELD C EN TE RLIN E, INCH .Fig. 3 Tempe rature distribution in the solid about the weld pool for weld test #29

pend ing on o r i en ta t i on o f the ce l l s r e l a t i ve to the so l i d - l i qu id i n te r face .More recent ly, Savage e f a / (Ref . 8)have examined the s i ze o f the ce l l u l a r m i c r o s t r u c t u r e f o r me d i n t h esyn thes i s o f we ld so l i d i f i ca t i on us ingcrys ta l l i ne o rgan ic ma te r i a l s . The re su l t s o f t h i s i n ve s t i g a t i o n w a s i na g r e e me n t w i t h t h e o b se r va t i o n s r e po r ted above , i n tha t ce l l s i ze wasfound to be l inear ly re la ted to thep a r a m e t e r 1/GLR. Also , o r i en ta t i on o fthe ce l l -g rowth d i rec t i on re la t i ve tothe so l i d - l i qu id i n te r face cou ld s ign i f i can t l y i n f l uence ce l l u la r spac ing .Statement of the Problem

Prev ious work i n the a rea o f s o l i d i f i ca t i on mechan ics has i n gene ra lsh o w n co r r e l a t i o n s b e t w e e n t h e o b se r ve d so l i d i f i ca t i o n su b s t r u c t u r e sa n d p a r a m e t e r s su ch a s t h e r ma l g r a d ien t , a l l oy so lu te con ten t , and g rowthra te . T h e e xp e r i me n t a l s t u d i e s c o n ducted to da te , howeve r , have no tbeen ab le to s tudy each o f these v a r i ab les i ndependen t l y ove r a l a rgerange o f va lues . The we ld ing p rocesso f fe rs a un ique oppo r tun i t y to s tudyt h e i n d e p e n d e n t r e l a t i o n sh i p s b e tween so l i d i f i ca t i on va r i ab les and theo b se r ve d m i c r o s t r u c t u r e s .Objectives

I t became apparen t tha t an expe r i me n t sh o u l d b e d e s i g n e d w h i ch co u l dmeasu re each o f the p rev ious l y m e n t i oned va r i ab les in an i nde pen den tfash ion wh i l e ma in ta in ing con t ro l o fo r i e n t a t i o n o f t h e c e l l u l a r - g r o w t hd i rec t i on re la t i ve to the so l i d i f y i ng i n t e r f a c e . K e e p i n g t h e s e f a c t o r s i n

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m i n d , a r e se a r ch p r o g r a m w a s i n i t i a ted w i th the ob jec t i ves ou t l i nedb e l o w :1. T o d e t e r m i n e t h e t h e r ma l d i s t r i bu t i o n abou t a we ld poo l so l i d i f y i ng unde r two -d imens iona l hea t - f l owco n d i t i o n s .2. To de te rmine how va r ia t i ons i nthe fo l l ow ing pa ram ete rs i nd i v idua l l yi n f l uence the s i ze o f the ce l l u la r sub s t r u c t u r e o b se r ve d d u r i n g so l i d i f i ca t i on o f fus ion we lds :(a) G s t h e t h e r ma l g r a d i e n t p r e s ent in the so l id a t the so l id - l iqu idin te r face ,(b) R the growth ve loci ty o f theso l i d - l i qu id i n te r face .3 . To de te rmine how va r ia t i ons i nt h e f o l l o w i n g p a r a me t e r s i n f lu e n cethe ce l l u la r - to -ce l l u la r dend r i t i c t r a n s i t i on du r ing the so l i d i f i ca t i on o f fu s i o n w e l d s :(a ) G< t h e t h e r m a l g r a d i e n t

present in the so l id a t the po in to f t r a n s i t i o n ,(b) R the grow th ve loci ty o f theso l i d - l i q u i d i n t e r f a ce a t t h epo in t o f t rans i t i on .

Materials and ExperimentalProcedureMaterial Selection

The ma te r i a l used th roughou t th i si nvest i ga t i on was a 49% n i cke l - i rona l l oy w i th the fo l l ow ing chemica l a n a l ys is : Ni 4 8 . 5 1 % ; C 0 .023%; Mn 0.42%; P 0 .004%; S 0 .003%; Cr 0 .03%; Mo 0 .02%; Cu 0 .02%;Fe ba lance .The ma te r i a l was i n the fo rm o f0 .014 in . (0 .36 mm ) th ick sheet . A f terannea l i ng i n d ry hyd rogen fo r fou rhou rs (4 h) a t 2150 F (1177 C) f o l lowed by a s low coo l a t the ra te o f100 F/h (55 C/h) , th is mater ia l ex-

W EL D IN G R ES EA RC H S U P P L E M E N T ! 2 1 5 - 8


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h ib i t s a cube -on - face tex tu re w i th a j 10o | plane in the p lane o f the sheetand a d i rec t i on pa ra l l e l t o thero l l i ng d i rec t i on .Welding Equipment and Procedure

Al l we lds eva lua ted i n th i s i nvest i ga t i on were fu l l -pene t ra t i on fus ionw e l d s ma d e b y t h e G T A W p r o ce ssus ing s t ra igh t -po la r i t y , d i rec t cu r ren t .Du r ing we ld ing the tes t spec imenswere c lam ped in a s ta in less s tee lh o l d - d o w n f i x t u r e e q u i p p e d w i t h ca r t r i dge hea t i ng e lemen ts wh ich cou ldbe heated as h igh as 1200 F (649 C)p r i o r to we ld ing . Th i s p rov ided anadd i t i ona l means o f va ry ing the the r ma l g rad ien t i n the s o l i d .Argon sh ie ld ing was supp l i ed bo thf rom the to rch and a sepa ra te i n le t tothe we ld ing chamber a t 35 c fh (99l iters/h) and 15 cfh (43 l i te rs/h) , re spect i ve l y . The we ld ing cond i t i ons fo reach tes t spec imen a re l i s ted i nTab le 1 .

Crystallographic Orientation of WeldSpecimensIt has been shown (Re fs . 3,9) t ha twe ld so l i d i f i ca t i on occu rs by ep i tax ia l

8 .00

0 3 0 60 90D I ST AN C E F R O M SO L I D - L I Q U I D

INTERFACE, INCHES X IO 3Fig. 4 Plots ot In (T-T0) vs. distance fromthe solid-liquid interface tor weld test #75where the interface is moving at 3 , 5.7, an d7 ipm

nuc lea t i on f rom the ex i s t i ng g ra ins i nth e unmelted base me ta l . Growth thenoccu rs i n the easy g rowth d i rec t i onmost favo rab l y a l i gned w i th the maximum the rma l g rad ien t p resen t a t theso l i d - l i qu id i n te r face .As no ted ea r l i e r , t he 49% n i cke l -i ron a l l oy s tud ied du r ing th i s i nvest i ga t i on exh ib i t s a cub e -o n - fac e textu re w i th a d i rec t i on i n the r o l l i ng d i rec t i on . Th i s co r responds to the< 1 0 0 > e a sy - g r o w t h d i r e c t i o n f o u n di n f a c e - c e n t e r e d c u b i c m a t e r i a l s .The re fo re by p re -o r i en t i ng the tes tspec imens i n the we ld f i x tu re , i t wasposs ib le to con t ro l t he d i rec t i on o fce l lu lar growth re la t ive to the s o l i d i f y i ng i n te r face .

Fo r a l l we lds s tud ied , the ro l l i ng d i r e c t i o n ( a < 1 0 0 > ) w a s o r i e n t e dpe rp end icu la r to the we ld in g d i rec t i o n . I n add i t i on the we ld ing pa rame te rs were ad jus ted so tha t a tea r d r o p - sh a p e d w e l d p u d d l e w a s o b t a i n e d . T h i s p r o ce d u r e e n su r e d t h a t ,fo r those g ra ins exh ib i t i ng the p rope ro r i en ta t i on , g rowth wou ld occu r i n thep lane o f the shee t pe rpend icu la r tothe fus ion l i ne a long a d i rect i on and cou ld con t i nue to g row in th i sd i rec t i on to the we ld cen te r l i ne as de p icted in F ig . 2.Measurement of Thermal Gradientand Solidification Rate

I n o rde r to ob ta in the the rma l d i s t r i bu t i on i n the so l i d abou t the we ldp o o l , 0 .005 i n . (0 .13 mm ) ch r om e l -a l u me l t h e r mo co u p l e s w e r e p e r cu s s ion -we lded to the unde rs ide o f thet e s t sp e c i me n a t p r e d e t e r m i n e d d i s tances f rom the we ld cen te r l i ne . Th i sp e r m i t t e d t h e t e mp e r a t u r e t o b e o b ta ine d a t kn ow n po in ts re la t ive to thewe ld cen te r l i ne as the we ld poo l t rave l e d p a s t t h e t h e r mo co u p l e s .

T h e o u t p u t f r o m t h e t h e r mo co u p les was fed i n to a d i rec t -deve lop ing ,reco rd ing osc i l l og raph a long w i th theou tpu t f rom a l i nea r t ransduce r ac t i -

O F A R C

va ted as the e lec t rode t rave rsed pastthe f i r s t t he rmocoup le . Th i s a l l owedt h e co n ve r s i o n of t e m p e r a t u r e - t i med a t a t o t e mp e r a t u r e - d i s t a n ce p l o t s .Pho tog raphs o f the we ld c ra te r andwe ld r i pp le marks were used to c o n s t ruc t a com pos i te d iag ram o f the i n s tan taneous pos i t i on o f the s o l i d -l i qu id i n te r face abou t the pe r iphe ry o fthe we ld p o o l . F igu re 3 sum ma r i zes i ng rap h ica l fo rm a t yp i ca l se t o f the r ma l -d i s t r i b u t i on da ta ob ta in ed us ingt h i s t e ch n i q u e .

S i n ce t h e sp e c i me n s w e r e f u l l -pene t ra t i on fus ion we lds on 0 .014 i n .(0 .36 mm) th i ck ma te r i a l , t he re i s essen t i a l l y no the rm a l g rad ie n t th ro ughthe shee t th i ckness. The re fo re , a two -d i me n s i o n a l h e a t - f l o w co n d i t i o n w a sp resen t du r i ng w e ld ing . It was de te r mined expe r imen ta l l y tha t the t e m pera tu re d i s t r i bu t i on i n the so l i d i n ad i rec t i on pe rpen d icu la r to the s o l i d i f y i ng i n te r face fo l l owed an exponen t i a l decay o f the fo rm:T - Tn = Ae (Dwhe re Z i s the pe rpen d icu la r d i s tance f rom the so l i d i f y i ng i n te r face , Ti s the tempera tu re a t d i s tance Z , To isthe i n i t i a l p la te tempera tu re , and Aand B a re constan ts . A l i nea r re la t ionsh ip resu l ts i f equat ion (1) is c o n ve r t e d t o l o g a r i t h m i c f o r m :In (T - TQ) = -BZ + In A (2 )

F igu re 4 show s t yp i ca l te mp er a tu re -d i s tance da ta p lo t ted i n th i sma n n e r . T h e t e mp e r a t u r e g r a d i e n t inth e s o l i d , G s , a t the so l id - l iqu id in ter face i s de f i ned as :dTdZ = -A B (3 )

w h e r e A e q u a l s t h e so l i d u s t e mp e r a ture o f the a l loy, 2550 F, (1399 C)minus the i n i t i a l p la te tempera tu re ,T o , f o r the pa r t i cu la r tes t cons ide red ,and B is in the slope o f the l ine def i ned by equa t i on 2 .

The g rowth ve loc i t y o f the s o l i d -l iqu id in ter face a t the t ra i l ing edge o fthe we ld poo l i s de te rmined , on theo the r hand , by the dynamic equ i l i b r i u m w h i ch p r e va i l s d u r i n g w e l d i n g .

WELDING DIRECTION -INSTANTANEOUS POSITION.OF SOLID-L IQUID INTERFACE

WELDINGVELOCITY, V

MEASUREMENT

WELD c_

FUSION-LINE^CELLS GROWINGPERPENDICULAR TO THEFUSION LINE IN THE PLANEOF THE SHEET

Fig. 5 Graphical technique employed to determine growth rateat a particular locationFig. 6 Schematic representation ot the technique employed tomeas ure cell spacing a t a particular thermal gradient and grow thvelocity

2 1 6 -s I A U G U S T 1 9 7 6


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Table 2 Summary of Test Data Showing Relationship Between G x and.G maxat the Trailing Edge of the Weld Pool fora Tear-Drop Shape Weld Configuration

W e l dTe s t111315161825272911151825272 911152 5

A v e r a g e g r o w t hv e l o c i t y n o rma lto t ra i l ing

edge o f we ldp o o l , k m

33333333555555777

9 . anglebe tween G xa r | d G max.d e g r e e s

101010101113129

191819202119262925

Fig. 7 Three-dim ensional model of the tempe rature distribution in the solid about theweld pool for weld test #75

Af te r the we ld p roceeds fo r a sho r td i s tance , th i s dynamic equ i l i b r i um i ses tab l i shed an d the we ld poo l assu m e s a co n s t a n t sh a p e .In order to main ta in an invar iantpuddle shape, a t any po in t on the in t e r f a ce , t h e co mp o n e n t o f g r o w t hve loc i t y pa ra l l e l t o the we ld ing d i rect i on must equa l the we ld ing ve loc i t y .The g row th ve loc i t y in any o the r d i rect ion on the so l id i fy ing in ter face is avecto r quan t i t y equa l i n magn i tude tothe we ld ing ve loc i t y mu l t i p l i ed by theco s i n e o f t h e a n g l e b e t w e e n t h eg rowth vec to r and the we ld ing d i rect i o n . There fo re , the g rowth ra te o f thein te r face f rom the fus ion l i ne to thewe ld cen te r l i ne i s a func t i on o f thegeomet ry o f the we ld pudd le .

T o c i r cu mve n t t h e p r o b l e m o f me a su r ing the angu la r re la t i onsh ips p re c i se l y and to p rov ide an accu ra teeva lua t i on o f i n te r face g rowth ra te , ag r a p h i ca l t e ch n i q u e w a s e mp l o ye d t ode te rmine the g rowth ra te a t a pa r t i c u lar locat ion. F igure 5 i l lust ra tes th istechn ique . F rom a 10X macrog raph o fthe r i pp le mark ings on the su r face o fthe w e l d , an accu ra te ou t l i ne was ob ta ined o f the t ra i l ing edge o f the weldp u d d l e . T h i s o u t l i n e w a s r e p r o d u ce dby sh i f t i ng a d i s tan ce AY f rom Pos i t ion 1 to Pos i t ion 2, as ind ic ated inFig . 5.

If AY i s equa l to a cons tan t , C , t ime sthe we ld ing ve loc i t y , V , the d i s tancebe tween the two pos i t i ons me asu redin any g iven d i rect ion wi l l be equal tothe p roduct o f the constan t , C , andthe g rowth ve loc i t y , R , requ i red toma in ta in dynamic s tab i l i t y o f the i n te r

f a c e . Thus, s ince on l y g ra ins w i th< 1 0 0 > d i r e c t i o n s n o r m a l t o t h ew e l d i n g d i r e c t i o n w e r e co n s i d e r e d ,the d istance, r , in F ig . 5 would beequal to R/C, and the growth ra te , R,i s s imp ly the p roduc t , Cr .Determination of Cell Size

Cons ide r the d iag ram shown in F ig .6 . As the we ld poo l p rog resses, thepo in t A on the so l i d - l i qu id i n te r facewi l l t race out a l ine AA'A" para l le l tothe we ld cen te r l i ne . The re fo re , anypo in t a long AA 'A" has been exposedto the same the rma l g rad ien t andg rowth ve loc i t y du r i ng so l i d i f i ca t i on .S ince the ce l l s a re g row ing pe rpen d icu lar to l ine AA'A", any ce l ls a longth is l ine have been exposed to thesa me t h e r ma l g r a d i e n t a n d g r o w t hve loci ty a t the so l id i fy ing in ter face. Al i n e - i n t e r ce p t me a su r i n g t e ch n i q u ew a s e mp l o ye d t o d e t e r m i n e t h e ce l ls i ze a long l i ne AA 'A" fo r each comb i n a t i o n o f t h e r ma l g r a d i e n t a n dg rowth ve loc i t y s tud ied .Discussion and ResultsThermal Distribution in the SolidAbout the Weld Pool

An eva lua t i on o f the expe r imen ta lthe rma l da ta showed tha t the t e m pera tu re as a func t i on o f the pe rpe n d i cu la r d i s tance f rom the we ld i n te r f a c e d e c a y s in a n e x p o n e n t i a lma n n e r . A t h r e e - d i m e n s i o n a l mo d e li l lust ra t ing the nature o f th is decay issh ow n in F ig . 7 . I t was fu r the r n otedt h a t t h e ma x i mu m t h e r m a l g r a d i e n t in

the s o l i d , norma l to the so l i d - l i qu id i n te r face , p rog ress i ve l y decreased i nmagn i tude f rom the fus ion l i ne to thewe ld cen te r l i ne a long the t ra i l i ng edgeof the weld p o o l .The locus o f peak tempera tu re as afunct i on o f d i s tance f rom the we ldcen te r l i ne was found to be a s t ra igh tl ine tangent to the lead ing edge o f theweld puddle , as can be seen in F ig . 3 .Th i s wou ld i nd i ca te tha t the the rma lwave gene ra ted i n the so l i d du r i ngwe ld ing behaves i n a fash ion s imi l a rto that o f the bow wave created by aboat as i t passes through the water .I t has been shown by Savage andAronson (Re f . 4 ) tha t the geomet ry o fthe so l i d - l i qu id i n te r face a t the t r a i l ing edge o f the weld poo l can substant ia l ly in f luence the nature o f theco mp e t i t i ve g r o w t h p r o ce ss d u r i n gso l i d i f i ca t i on . Th i s , i n t u r n , i n f l uencesthe amoun t o f p re fe r red o r i en ta t i onfound w i th in the we ld fus ion zone .

The two ex t reme types o f we ldg e o me t r y n o r ma l l y e n co u n t e r e d d u r i ng we ld ing a re the e l l i p t i ca l -sh apedw e l d p u d d l e a n d t h e t e a r - d r o p -shap ed we ld p udd le i l l us t ra ted in F ig .8 . In the case o f two -d im ens iona l hea tf l o w , t h e ma x i mu m t h e r ma l g r a d i e n t ,Gmax, w i l l be pe rpen d icu la r to thet ra i l ing edge o f the weld poo l and wi l ll ie in the p lane o f the sheet . Th is grad ien t can be reso l ved i n to two componen t g rad ien ts i n d i rec t i ons pe rpen d i cu la r and pa ra l l e l t o the we ld ingd i r e c t i o n , as i l lust ra ted in F ig . 8 . Def i n ing the d i rec t i ons pe rpend icu la rand pa ra l l e l t o the we ld ing d i rec t i onas x and y, respect ive ly, the fo l lowing

W EL DIN G R ES EA RC H S U P P L E M E N T I 2 1 7 -8


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TEAR-DROP-SHAPED WELD PUDDLE

WELD POOLPUDDLEASSUMED A SHAPEPARALLEL TO THE WELD f

LOCUS OF SOLIDUSISOTHERM

-WELDING DIRECTIONELLIPTICAL-SHAPED WELD PUDDLE

Fig. 8 Idealized schematic showing the relationship between Gmax, Gx, an d G y for a tear-drop-shaped weldpuddle and an elliptical-shaped weld puddle

exp ress ions can be wr i t t en fo r theset w o co mp o n e n t g r a d i e n t s , G x a nd G yG x = G m a x c os f l (4 )G y = Gmax cos (90 d e g - 6 1 ) (5 )w h e r e : 0 = the ang le be tween G m a xand G x

T h e m a g n i t u d e o f t h e t h e r m a lg rad ien t i n the so l i d i s a d i rec tmeasure o f the ab i l i ty o f the system toext rac t hea t f rom the we ld poo l to theco o l e r su r r o u n d i n g s . T h e r e f o r e , t h el a r g e r t h e v a l u e o f t h e t h e r m a lg rad ien t , t he g rea te r the hea t -s ink ingcapac i t y o f the sys tem.In the case o f an e l l i p t i ca l -shapedwe ld pudd le , the d i rec t i on o f the maxi mu m t h e r ma l g r a d i e n t co n t i n u o u s l ychanges f rom the fus ion l i ne to thewe ld cen te r l i ne a long the t ra i l i ng edgeof the weld p o o l . Th is re f l ec ts theab i l i t y o f the sys tem to ex t rac t morehea t i n the l ong i tud in a l , o r y -d i rec-t i o n , a s co mp a r e d t o t h e t r a n sve r se ,o r x - d i r e c t i o n , a s s o l i d i f i c a t i o np roceeds f rom the fus ion l i ne towardsthe we ld cen te r l i ne .

In t h e ca se o f a t e a r - d r o p - sh a p e dw e l d p u d d l e , t h e sa me r e l a t i o n sh i p sh o l d . However , the pudd le tends toe longa te a long the cen te r l i ne due tothe inab i l i ty o f the system to ext ractheat fast en ou gh in th is d i re ct io n toma in ta in an e l l i p t i ca l shape .Fo r a g i ven se t o f we ld ing cond i t i o n s a d yn a m i c e q u i l i b r i u m i s e s t a b

l i s h e d b e t w e e n t h e h e a t - s i n k i n gcapac i t y i n the y -d i rec t i on as co m p a r e d t o t h e x - d i r e c t i o n . Me a su r e men ts were made o f the ang le 6be tween G max and G fo r the weldsrepo r ted i n Tab le 2 .

WELDING DIRECTION Fig. 9 Diagram illustrating the shape of the solidus isotherm at thetrailing edge of the weld pool where the heat-sinking capability of thesystem is minimal in a direction parallel to the weld centerline

shown in F ig . 10. I t was noted that a tthe fusion l ine a reg ion o f p lanarg row th ex i s te d . S ince con st i t u t i ona lsupe rcoo l i ng canno t occu r un t i l aso lu te sp i ke fo rms ahead o f the ad v a n c i n g s o l i d - l i q u i d i n t e r f a c e , i tf o l l ows tha t ce l l s shou ld no t fo rm a tthe onset o f so l id i f ica t ion . In fact , thecr i t i ca l cond i t i on fo r const i t u t i ona lsupercoo l ing wi l l no t be met unt i l thei n i t i a l t r a n s i e n t b u i l d u p o f so l u t ecauses the e f fec t i ve l i qu idus o f the l i qu id near the so l id in ter face to fa l lbe low the ac tua l tempera tu re p resen ta t tha t po in t . The re fo re , du r i ng the in i t ia l t ransient bu i ldup o f so lu te , thep lana r g rowth mode w i l l p reva i l . Howeve r , when su f f i c i en t const i t u t i ona lsup e rco o l i ng ex i s ts at the adva nc ingin ter face, the p lanar in ter face wi l lb reak down in to the ce l l u la r g rowthm o d e .

Since the base me ta l exh ib i ted a< 1 0 0 > c r ys t a l l o g r a p h i c d i r e c t i o n i nthe p lane o f the shee t pe rpend icu la rto the fusion l ine , the ce l ls shown inFig . 10 g rew ep i tax ia l l y f rom the un -melted base me ta l i n th i s d i rec t i o n .The ce l l u la r subst ruc tu re , the re fo re ,appears as a pa ra l l e l a r ray o f co r ru ga t i ons on the shee t su r face .I t was fu r the r obs e rve d tha t unde rco n s t a n t g r o w t h ve l o c i t y co n d i t i o n s ,the ce l l s ize increased l inear ly wi th theinve rse o f the tempera tu re g rad ien t i nth e s o l i d , G s In t h i s case , G s i s takena s t h e t e m p e r a t u r e g r a d i e n t r e so l ve da long the ce l l -g rowth ax i s . Theseresu l ts are re po r te d in Ta b le 3 an d inFig . 11 fo r th ree d i f f e ren t g row thve l o c i t i e s r e so l ve d a l o n g t h e ce l lg r o w t h a x i s .

T h e r e l a t i o n sh i p s f o u n d b e t w e e nG s , R and ce l l s i ze a re i n ag reemen tw i th theo re t i ca l cons ide ra t i ons . C o n s ide r the f l ow o f so lu te f rom a p lana rand cu rved i n te r face as dep ic ted i nF ig . 1. Note that fo r both in ter fac eshapes, so lu te tends to f l ow be tweenthe so l i d and l i qu id phases i n a d i rect i on no rma l to the i n te r face . Thep rese nce o f a cu rv ed i n te r face , suchas that wh ich would exist a t the ce l lt ips , t ends to reduce the ove r lap p resen t be tween the so lu te f i e l ds a t ad ja cen t po in ts on the i n te r face , the rebyp romot ing the red i s t r i bu t i on o f so lu te .

It was found tha t fo r a g i ven g rowthve loc i t y (measu red no rma l to theso l i d - l i qu id i n te r face ) the ang le 0b e t w e e n t h e m a x i m u m t h e r m a lg rad ien t , G max , and the t ran sve rs ethe rma l g rad ien t , Gx, va r i ed l ess than4 deg fo r those we lds exh ib i t i ng at e a r d r o p co n f i g u r a t i o n . T h e se d a t aa re repo r ted i n Tab le 2 .The r e fo re , fo r a g i ven g rowth ve loci t y no rma l to the so l i d - l i qu id i n te r f a c e , the rat io of G y to G x w a s e sse n t i a l l y constan t . The pudd le e longa teda long the we ld cen te r l i ne un t i l t h i sd y n a m i c e q u i l i b r i u m w a s e s t a b l i s h e d . U n d e r mo r e se ve r e co n d i t i ons a po in t was reached i n thesys t e m w h e r e t h e h e a t - s i n k i n g ca p a c i t y i n the y d i rec t i on was min ima l . A tth is po in t a long the weld in ter face, thep u d d l e w a s f o r ce d t o a ssu me a sh a p epara l le l to the weld center l ine Fig .9 . Th is ind icates that there is a l imi t tothe amoun t o f hea t wh ich can be d i s

s ipated in a d i rect ion para l le l to thewe ld cen te r l i ne . The po in t a t wh icht h i s o ccu r s d e p e n d s u p o n t h e t h e r ma lp rope r t i es o f the ma te r i a l and the t ypeo f f i x t u r i n g e mp l o ye d .The Influence of Temperature Gradientand Solidification Rate on Cell Size

The ob ject ive o f th is phase o f theinvest i ga t i on was to de te rmine the i n f l uence o f the tempera tu re g rad ien t i nth e so l id , G ? , and the g rowth ve loc i t yo f the so l id i fy ing in ter face, R, on ce l ls ize. Since a l l expe r imen ts were pe r fo rmed on the same hea t o f ma te r i a l ,t he nomina l so lu te con ten t o f thesys tem was he ld constan t .

A t yp i ca l p h o t o m i c r o g r a p h o f t h eso l i d if i ca t io n su b s t r u c t u r e o b se r ve d is2 1 8 - 8 I A U G U S T 1 9 7 6


7/9

As the thermal gradient ( G s orG L )* increases, the cell size shoulddecrease if growth velocity and solutecontent remain constant. This resultsfrom the fact that an increase in thermal gradient wil l reduce the amountof constitut ional supercooling or theavailable driving force for formation ofthe cellular substructure.For the cells to remain stable, they

must continue to grow into the l iquideven though the dr iv ing force isbeing reduced. This can only be accomplished if the radius of curvatureat the cell tips decreases in order toprovide more effective redistributionof solute to the l iquid. Since cell sizedepends on cell-t ip radius, an increase in therma l grad ient results in adecrease in cell size.In a similar manner, an increase ingrowth velocity results in a decreasein cell size under constant thermalgradient and solute content conditions. This can be visualized if twocellular interfaces are consid ered thatare growing at two different growthvelocit ies. For the faster growing interface to remain stable, it must increase the amount of solute beingredistributed to the l iquid. This can beaccomplished if the faster growingcells exhibit a smaller rad ius of curvature of the cell tips due to the pointeffect of dif fusion mentioned earlier.Figure 12 shows the inf luence ofgrowth velocity on cell size under constant temperature gradient conditions. Consistent with theory, cell sizedecreases as the growth velocity increases.The Influence of Growth Velocity andTemperature Gradient on the Cellular-to-Cellular Den dritic T ransition

applied to the welding situation.Previous investigators (Refs. 6, 10,11) have reported that for a givensolute content and cell orientationrelative to the solid-l iquid interface,transition occurs at a particular ratio

of G L /R 1'2 where G L and R are measured in a direction perpendicular tothe sol idi fy ing interface. Furthermore, the G L /R " 2 ratio could vary depending on the orientation of the cellsrelative to the solid-l iquid interface.

SOLIDIFIED W E L D M E T A L^_ L I Q U I D

W E L D M E T A LC E L L U L A RS U B S T R U C T U R E( H E X A G O N A L I NCROSS SECTION)S O L I D - L I Q U I DI N T E R F A C E4-R E G I O N O F -P L A N A R G R O W T H REGION OFC E L L U L A RG R O W T H

^ = r r -

T S =

_ i _ -

BFig. 10 Example of the Planar-to-Cellular Growth Transition: (a) schematic illustration; (b) photomicrograph of planar-to-cellular growth transition in a GTAweld made on a 49% nickel-iron alloy. Etchant: 10% ammonium persulfate solution, X 370 (reduced 68% on reproduction)

The objective of this phase of thei n v e s t i g a t i o n w a s t o d e t e r m i n ewhether the inf luence of thermalgradient and growth velocity on thecellular-to-cellular dendrit ic transit ion as reported by other investigators (Refs. 6, 10, 11) is valid when

'The thermal gradient in the liquid, GL, isdirectly related to the thermal gradient inthe solid, Gs , at the solid-liquid interface,by the equation for continuity of heat f lowacross the interface. For one-dimensionalheat f low the equation is:G s = KL GL/KS * LPR/KSwhere: Ks = thermal cond uctivity ot thesolid; K i = thermal conductivity of the liquid; R = grow th velocity of the interface; L= latent heat of fusion; P = density ot thesolid.A similar, though more complex relationship exists, at any point, between G Lan d G s for the case of two-dimensionalheat flow. Therefore, under constantgrowth velocity conditions, a given increase in G s will result in a propo rtionateincrease in G L .

Table 3 - - Sum mary of Data Corre la t ing Ce l l Spac ing wi th the Compo nent o lR and G s Oriented Para l le l to the Ce l l Growth Ax is

W e l dtes t15111816132 12 52 72 91511182 1252 72 911152 125

R, para l le l toth e c e l l g ro w t hax is , i p m33333333366666668888

G s para l le l toth e c e l l g ro w t ha x i s , deg F/ in .31 ,90026 ,32522 , 26 018,97013,55018,00022 , 5 0 015,68013,80024 ,19020 ,60017,79013,16018 ,24012,5659 ,65014,795

17,56510,58012,000

l /Gs ind e g F x 1 0 > *3.133.804.495.267.375.554.446.387.244.13

4.855.617.605.467.9510.356.765.699.458.33

A v e ra g e c e l ld i a me t e r ,m i c ro n s 2


8/9

3IN/MIN 6IN/MIN

C 3

4 5 6l/G. IN/F xlO

Fig. 11 Average cell diameter vs. 1/GS under constantgrowth velocity conditions

-i 1 1 1 1 1 r

(Gs = 18,000F/IN.)J i i i_2 3 4 5 6

R, IN./MIN.7 8 9

Fig. 12 Average cell diameter vs. R under co nstant therma l gradient inthe solid

Table 4 Summary of Data Showing the Influence of Thermal Gradient and GrowthVelocity on the Cellular-to-Cellular Dendritic Transition

W e l dt e s t211125272 9

Ang le o f i nc l i nat ion of ce l lg rowth ax is tos o l i d - l i q u i din te r face , deg4427 .5252320

R , p e rp e n d i c u lar to so l i d -l i qu id in te r face , km7.58.07.06.05.5

G s , p e r p e n d i c u lar to so l i d -l i qu id in te r face , deg F/ in .

12.10013,65013,31011,30010.520

G s / R > ,deg F x min . " 2in . w4,4324 ,8235.0224,6124 ,496

The G L / R " 2 ra t i o was, the re fo re , c o n s i d e r e d t o b e a m e a su r e o f t h ea mo u n t o f co n s t i t u t io n a l su p e r - co o l ing or dr iv ing force for ce l lu larb r e a k d o w n .Dur ing we ld so l i d i f i ca t i on , the the r ma l g r a d i e n t ( G s or G L ) p e r p e n d i cu la r to the so l i d - l i qu id i n te r faceco n t i n u o u s l y d e c r e a se s f r o m t h e f u sion l ine to the weld center l ine a longthe t ra i l ing edge o f the weld p o o l .Concur ren t w i th th i s decrease i n the r ma l g r a d i e n t i s a co r r e s p o n d i n g i n crease in the growth ve loci ty o f theso l id i fy ing in ter face. As a resu l t , theG L / R 1 ' 2 ra t i o con t i nuous l y decreasesas so l i d i f i ca t i on p roceeds f rom the fu sion l ine to the weld center l ine a longthe t ra i l ing edge o f the weld p o o l .I t was obse rved tha t , as so l i d i f i ca t i on p roceeded f rom the fus ion l i netoward the we ld cen te r l i ne , a s tagew a s r e a c h e d i n t h e so l i d i f i ca t i o np rocess where the ce l l u la r subst ructu re s ta r ted to b reak down in to ace l l u l a r - d e n d r i t i c g r o w t h mo d e . S i n cea l l we ld ing was pe r fo rmed on thesam e hea t o f ma te r i a l , t he n omina l

so lu te content o f the system was he ldco n s t a n t . T h e p r o b l e m, t h e r e f o r e , b e came one o f de te rmin ing the va lue o fthe rma l g rad ien t and g rowth ve loc i t yco r respond ing to the po in t o f t rans i t ion .

Some d i f f i cu l t i es a r i se , howeve r , i nde te rmin ing exact l y wha t po in t i n theso l i d i f i ca t i o n p r o ce ss co r r e sp o n d s t ob r e a kd o w n o f t h e ce l l u l a r su b s t r u c t u r e . Figure 13 shows a reg ion in thewe ld fus ion zone where the ce l l u la r -to -ce l l u la r dend r i t i c t rans i t i on wasf i r s t obse rved . L ine A-A rep resen tsthe locus o f po in ts in the fusion zonewh ich have been exposed to essen t i a l l y the same the rma l g rad ien t andg rowth ve loc i t y du r i ng so l i d i f i ca t i on .The G L / R 1 2 ra t i o i s the re fo re essen t ia l ly constant a long l ine A-A.Exa mina t i on o f the so l i d i f i ca t i onsubst ruc tu re shows tha t a mix tu re o fce l l s and ce l l u la r dend r i tes coex i s t a tth i s s tage in the so l i d i f i ca t i on p rocess .The re fo re , an es t ima te o f the t rans i t i on c r i t e r i on must i nc lude a de f i n i t ion as to what const i tu tes the onset o fce l l u l a r - d e n d r i t i c g r o w t h .Prev ious i nvest i ga to rs (Re fs . 6 , 10 ,11) have de f i ned the t rans i t i on as tha tp o i n t w h e r e co n t i n u o u s s i d e b r a n ch ing is f i rst observed a long the ce l lwal ls . Th is de f i n i t i on was adop ted fo rth i s i nvest i ga t i on .An es t ima te o f the t rans i t i on po in twas made by ca l cu la t i ng the G s / R ' ' 2ra t i o wh ich co r responded to the onse to f ce l l u la r dend r i t i c g rowth , as de f ined above. The u t i l i za t ion o f G sra ther than G L was necessa ry s ince

the va lue o f G r w a s n o t e x p e r i m e n t a l l y d e t e r m i n e d .S ince the two the rma l g rad ien ts a rere la ted to one ano the r , as p rev ious l yd e s c r i b e d , they both re f lect the extento f const i t u t i ona l supe rcoo l i ng aheado f the so l i d - l i qu id i n te r face . The re f o r e , the G s /R 1 '2 ra t i o se rves thesame funct i on as G L / R " 2 i n de te r min ing the t rans i t i on po in t .

Fo r those we lds where da ta wereava i lab le , the va lue o f G s /R 1 '2 at thepo in t whe re t rans i t i on was f i r s t ob se rved was ca l cu la ted . Bo th G s a n dR were mea su re d i n a d i rec t i on pe r pend icu la r to the so l i d - l i qu id i n te r f a c e . I n add i t i on , the ang le be tweenthe ce l l g rowth ax i s and the no rma l tothe so l i d - l i qu id i n te r face was de te r m i n e d . These da ta a re repo r ted i nTab le 4 .

A 13% var ia t ion in the va lue o fG s / R " 2 was found to ex i s t . Theseresu l t s i nd i ca te tha t the ce l l u la r - to -ce l l u la r dend r i t i c t rans i t i on tends tooccur a t essent ia l ly the same ra t io o fG s / R " 2 dur ing the so l i d i f i ca t i on o fwe lds . The re fo re , the G s /R 1 '2 rat io isa reasonab le measu re o f the onse t o fce l l u l a r - d e n d r i t i c g r o w t h d u r i n g t h eso l i d i f i ca t i on o f fus ion we lds .No sys tema t i c va r i a t i on was ob se rved be tween the va lue o f Gs /R 1 '2ca l cu l a t e d a n d o r i e n t a t i o n o f t h ece l lu lar growth axis re la t ive to theso l i d - l i qu id i n te r face .The i n f l uence o f so lu te con ten t onthe ce l l u la r - to -ce l l u la r dend r i t i c t r a n si t ion on the o ther hand can be seenin F ig . 14. I t was observed that inthose reg ions ad jacen t to g ra in boun da r ies where the so lu te con ten t washigher, t he ce l l u la r - to -ce l l u la r d e n dr i t i c t rans i t i on tended to occu r a t amuch larger ra t io o f G s /R 1 '2 . Th isobse rva t i on is in ag re em en t w i th da tap rev ious l y repo r ted by o the r i nvest igators. As the so lu te content o f thesys t e m i s i n c r e a se d , t h e r a t i o o fG L / R " 2 where ce l l u la r dend r i tes a ref i r s t obse rved i ncreases. Th i s re f l ec ts the i n f l uence o f so lu te con ten t

220 -s i A U G U S T 1 9 7 6


9/9

EJSSiFig. 13 Example ot the cellular-to-cellular dendritic transition ina 49% nickel-iron alloy. The GTA weld was made by using 17A.9V , 17 ipm (7.2 mm/s) travel speed and an Initial plate temper-ature of 445 F (230 C) . Etchant: 10% ammonium persulfate solution. X125 (reduced 51% on reproduction)

Fig. 14 Example of the influence of solute content of the cel-lular-to-cellular dendritic transition in a 49% nickel-iron-alloy. TheGTA weld was made by using 16 A, 10 V, 17ipm (7.2 mm/s) travelspeed and an initial plate tem perature of 1065 F (627 C). Etchant:10% amm onium persulfate solution. X160 (reduced 51% on reproduction)

on the ex ten t o f cons t i t u t iona l super coo l ing p resen t a t t he so l id i f y ing in t e r f a c e .

C o n c l u s i o n s1. T h e f o l l o w in g c o n c lu s i o n s p e r t a in to th e th e r m a l d i s t r i b u t i o n a r o u n dt h e we ld p o o l s o l i d i f y i n g u n d e r t wo -d im e n s io n a l h e a t - f l o w c o n d i t i o n s :(a ) The tempera tu re in a d i rec t ionp e r p e n d i c u la r t o t h e t r a i l i n g i n

t e r f ace o f t he we ld poo l de c reases w i t h d is tance in an ex p o n e n t i a l m a n n e r .( b ) T h e t h e r m a l g r a d ie n t i n t h esol id , G s , a t t he so l id - l iq u id i n t e r f a c e c o n t i n u o u s l y d e c reases f rom the f us ion l ine t ot h e we ld c e n t e r l i n e a l o n g t h et ra i l ing edge o f t he we ld poo l .( c ) T h e l o c u s o f p e a k t e m p e r a tu res in t he so l id t end t o l ie ona s t ra igh t l ine t angen t t o t helead ing edge o f t he we ld p o o l .( d ) T h e g e o m e t r y o f t h e s o l i d -l iqu id in te r f ace a t t he t ra i l ingedg e o f t he we ld p oo l i s a f unc t i o n of t h e d y n a m i c e q u i l i b r i u m e s t a b l i s h e d b e t we e n t h ehea t - s ink ing capab i l i t y o f t hes y s t e m i n d i r e c t i o n s p e r p e n d i c u l a r a n d p a r a l l e l t o t h ew e l d i n g d i r e c t i o n .

2. T h e f o l l o w in g c o n c lu s i o n s p e r ta in to the in f luence of G s a n d R o nthe na tu re o f t he ce l lu la r and c e l l u l a r - d e n d r i t i c g r o w t h m o d e s f o r m e ddur ing t he so l id i f i ca t ion o f f us ionwe lds in a 49 % n icke l - i r on a l loy :(a ) The ce l l s ize inc reases l inear lyw i t h t he inverse o f t he t he rma lg rad ien t in t he so l id , G s , u n d e rc o n s t a n t g r o w t h v e lo c i t y c o n d i t i o n s .(b ) Th e ce l l s ize dec reas es w i t h in c reas ing g rowth ve loc i t y o f t hes o l i d - l i q u i d i n t e r f a c e , R , u n d e rc o n s t a n t t h e r m a l g r a d ie n t i nt h e s o l i d .( c ) T h e c e l l u l a r - t o - c e l l u l a r d e n dr i t i c t r ans i t ion t ends t o occura t essen t ia l l y t he same ra t io o fG s / R " 2 f o r t he we ld ing c o n d i t i o n s s t u d ie d .

References1. Rutter, J. W. and Chalmers, B "APrismat ic Substructure Formed DuringSolidif ication of Metals," Canadian Jour-

nal of Physics, 31, 1953.2. Tiller, W. A. and Jackson, K. A.,Rutter, J. W.. and Chalmers, B., "The Redistr ibut ion of Solute Atoms During Solidif ication of Metals," Acta Metallurgica, 1.July 1953.3. Savage, W. F., Lundin, C. D., andAronson, A. H., "Weld Metal Solidif ication

Mechanics," Welding Journal, Vol. 44 (4),April 1965, Res. Sup., 175-s to 181-s.4. Savage, W. F. and Aronson, A. H.,"Preferred Orientation in the Weld FusionZone," Welding Journal, Vol. 45 (2), Feb.1966, Res. Sup., 85-s to 89-s.5. Mullins, W. W. and Sekerka, R. F.,"Stability of a Planar Interface DuringSolidif ication of a Dilute Binary Alloy,"Journal of Applied Physics, 35, February,1964.6. Tiller, W. A. and Rutter, J. W., "TheEffect of Growth Conditions Upon theSolidif ication of a Binary Alloy," CanadianJournal of Physics, 34 1956.7. Coulthard, J. O. and Elliot, R., "TheDependence of the Size of the CellularInterface Structure in Dilute Binary Alloyson Solidif icat ion Condit ions," Journal ofthe Institute of Metals, 95 January, 1967.8. Savage. W. F. and Hrubec, R. S"Synthesis of Weld Solidif ication UsingCrystalline Organic Materials," WeldingJournal, Vol. 51 (5). May 1972, Res. Sup.,260-s to 271-s.9. Savage, W. F., Lundin, C. D., andChase, T. F., "Solidif ication of FusionWelds in Face-Centered Cubic Metals,"Welding Journal Vol. 47 (11), Nov. 1968,Res. Supl. 522-s to 526-s.

10. Holme s. E. L., Ru tter, J, W. and W ine-gard, W. C, "Growth C ondit ions for Stability of a Cellular Solid-Liquid Interface,"Canadian Journal of Physics, 35, 1957.11. Plaskett, T. S. and Winegard, W. C ,"Cell to Dendrite Transition in Tin BaseAlloys," Canadian Journal of Physics, 38,1960.

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