PRINCIPLE OF CONSTITUTION OF SURFACE ALLOYS UNDER LASER BEAM

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PRINCIPLE OF CONSTITUTION OF SURFACE ALLOYS UNDER LASER BEAM

A. Hugon, A. Galerie, M. Pons, L. Bonnetain

To cite this version:

A. Hugon, A. Galerie, M. Pons, L. Bonnetain. PRINCIPLE OF CONSTITUTION OF SURFACE ALLOYS UNDER LASER BEAM. Journal de Physique Colloques, 1987, 48 (C7), pp.C7-151-C7-158.

�10.1051/jphyscol:1987727�. �jpa-00227029�

JOURNAL DE PHYSIQUE

Colloque C7, supplement au n012, Tome 48, dbcembre 1987

PRINCIPLE OF CONSTITUTION OF SURFACE ALLOYS UNDER LASER BEAM

A. HUGON, A. GALERIE, M. PONS and L. BONNETAIN

Laboratoire Science des Surfaces et Materiaux Carbones, Ecole Nationale SupQrieure dlElectrochimie et d'Electrometallurgie, INPG, CNRS UA-413, BP 75, F-38402 Saint-Martin-d'Heres Cedex, France

ABSTRACT

A f t e r a q u a l i t a t i v e d e s c r i p t i o n of t h e r u l e s of f o r m a t i o n of l a s e r s u r f a c e a l l o y s p e r f o r m e d by s u p e r f i c i a l m e l t i n g of b o t h t h e p r e d e p o s i t e d c o a t i n g a n d t h e s u b s t r a t e , n u m e r i c a l a n d s e m i - q u a n t i t a t i v e m o d e l s r a p i d l y a l l o w i n g a r a t i o n n a l c h o i c e of t h e o p e r a t i n g c o n d i t i o n s a r e p r e s e n t e d . T h e s e m o d e l s h a v e b e e n c o m p a r e d with e x p e r i - m e n t a l results. T h e y give t h e g e n e r a l t r e n d s of t h e h e a t a n d m a s s t r a n s f e r s p r o c e s s e s d u r i n g l a s e r alloying.

I-INTRODUCTION

L a s e r b e a m s a r e a b l e t o m o d i f y m e t a l l i c s u r f a c e s in a v a r i e t y of ways. C o n s e q u e n t l y , t h e y c a n b e used f o r h e a t t r e a t m e n t o r s u r f a c e a l l o y i n g when s u r f a c e p r o p e r t i e s d i f f e r e n t f r o m t h e bulk m u s t b e o b t a i n e d (corrosion r e s i s t a n c e , w e a r resistance...).

Two m a j o r c l a s s e s o f l a s e r s u r f a c e t r e a t m e n t s c a n b e p e r f o r m e d , (i) t r e a t m e n t s w i t h o u t m e l t i n g g e n e r a l l y u s e d t o a c h i e v e s u p e r f i c i a l h a r d e n i n g [I], (ii) t r e a t m e n t s with m e l t i n g used t o m o d i f y t h e s u p e r f i c i a l c o m p o s i t i o n ( h o m o g e n e i s a t i o n ) , t h e c r i s t a l l i n i t y ( a m o r p h i s a t i o n ) o f a l l o y s [2-81 o r t o i n c o r p o r a t e f o r e i g n e l e m e n t s i n t o t h e s u b s t r a t e [9-201.

T h i s l a s t c l a s s of l a s e r s u r f a c e t r e a t m e n t s i s s t i l l in t h e l a b o r a t o r y s t a g e ; i t s e e m s however t h a t powder i n j e c t i o n i n t o t h e m e l t pool [1,21-251 would t a k e a p l a c e in i n d u s t r i a l p r o c e s s e s b e c a u s e t h e l a s e r t o o l o f f e r s m a n y a d v a n t a g e s c o m p a r e d w i t h o t h e r s u r f a c e t r e a t m e n t s , in p a r t i c u l a r , t h e possibility of processing o n l y c h o s e n r e g i o n s of t h e piece.

O u r a i m , i n t h i s p a p e r , i s t o c o r r e l a t e t h e v a r i a b l e s of t h e physical p r o c e s s e s l e a d i n g t o ' s u r f a c e a l l o y s a n d t h e working a n d m a t e r i a l p a r a m e t e r s . I n d e e d , t o c o n t r o l t h e process, a n e x p e r i m e n t e r i s f a c e d with a m u l t i d i m e n s i o n a l p r o b l e m [26]. F r o m t h e b a s i c laws of t h e physical p r o c e s s e s involved, i t is possible t o e s t a b l i s h m o d e l s a n d t o c o m p a r e t h e m t o well c h o s e n e x p e r i m e n t a l r e s u l t s i n o r d e r t o r e a c h a s y s t e m a t i z a t i o n of t h e l a s e r process.

11-QUALITATIVE DESCRIPTION O F THE FORMATION O F LASER S U R F A C E ALLOYS T h e r e s u l t of a l a s e r i r r a d i a t i o n d e p e n d s o n n u m e r o u s p a r a m e t e r s which m a y b e p l a c e d i n t w o f i l e s , (i) t h o s e c h a r a c t e r i z i n g t h e l a s e r , (ii) t h o s e d e p e n d i n g o n t h e m a t e r i a l t o b e t r e a t e d . We s h a l l o n l y t a l k a b o u t c o n t i n u o u s w a v e l a s e r s which a r e g e n e r a l l y u s e d in m e t a l l u r g y . T h e f i r s t f i l e r e p r e s e n t s t h e working p a r a m e t e r s which a r e , t h e l a s e r power, t h e b e a m d i a m e t e r a n d t h e s c a n r a t e of t h e s a m p l e . T h e s e c o n d f i l e enc!oses t h e physical p r o p e r t i e s of t h e c o a t i n g a n d of t h e s u b s t r a t e in t h e solid a n d liquid s t a t e s . All t h e physical q u a n t i t i e s used a r e l i s t e d a t t h e e n d of t h i s p a p e r w i t h t h e i r d e f i n i t i o n a n d t h e i r dimension.

When t h e r a d i a t i o n s t r i k e s t h e c o a t i n g - s u b s t r a t e s y s t e m , t h e h e a t produced in a v e r y t h i n superficial l a y e r m a y l e a d t o t h e melting. A t t h i s i n s t a n t , t h e m e l t i n g of t h e c o a t i n g b e g i n s a t t h e c o a t i n g - a i r i n t e r f a c e ; t h e m e l t i n g i n t e r f a c e m o v e s t h r o u g h t h e

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987727

C7-152 J O U R N A L D E PHYSIQUE

m a t e r i a l b e c a u s e of t h e t h e r m a l c o n d u c t i o n a n d of t h e c o n v e c t i o n in t h e liquid phase.

When t h e m e l t i n g i n t e r f a c e r e a c h e s t h e c o a t i n g - s u b s t r a t e i n t e r f a c e s e v e r a l possibilities a r i s e ; (i) if t h e m e l t i n g p o i n t of t h e s u b s t r a t e is m u c h h i g h e r t h a n t h a t of t h e c o a t i n g , a n o v e r h e a t i n g of t h e liquid c o a t i n g will b e n e c e s s a r y t o r e a c h t h e m e l t i n g p o i n t of t h e s u b s t r a t e ; (ii) if t h e m e l t i n g p o i n t of t h e s u b s t r a t e i s s m a l l e r t h a n t h a t of t h e c o a t i n g , t h e m e l t i n g i n t e r f a c e will g o a w a y f r o m t h e c o a t i n g - s u b s t r a t e i n t e r f a c e ; when t h e c o a t i n g a n d t h e s u b s t r a t e a r e b o t h liquid, t h e high c o n v e c t i o n r a t e s l e a d t o a vigourous mixing, allowing t h e f o r m a t i o n of a s u r f a c e alloy. I t is g e n e r a l l y shown t h a t t h e d r i v e n f o r c e o f t h e c o n v e c t i o n is t h e s u r f a c e t e n s i o n g r a d i e n t which i s d u e t o t h e t e m p e r a t u r e (or c o n c e n t r a t i o n ) d i f f e r e n c e b e t w e e n t h e c e n t e r a n d t h e e d g e s of t h e m e l t pool l e a d i n g t o a m o t i o n of t h e liquid f r o m t h e high ( c e n t e r ) t o t h e low t e m p e r a t u r e s (edges). T h e c o m p l e t e s t u d y of t h i s m a t t e r m o t i o n l e a d s t o t a k e i n a c c o u n t t h e s u r f a c e t e n s i o n forces; t h i s p h e n o m e n o n involve c o n v e c t i o n r a t e s o n e o r t w o o r d e r m a g n i t u d e g r e a t e r t h a n t h e s c a n r a t e of t h e l a s e r [27-331.

A m o d e l giving a c o m p l e t e d e s c r i p t i o n of t h e process would t a k e i n t o a c c o u n t , t h e i r r a d i a t i o n p a r a m e t e r (q,d,V), t h e physical p r o p e r t i e s of t h e m a t e r i a l s (o,k,p,Tf,H,CX) a n d t h e h e a t a n d m a s s t r a n s f e r s i n t h e m u l t i p h a s e flow. A t t h e p r e s e n t t i m e , a c o m p l e t e m o d e l d o e s n o t e x i s t , b u t s o m e g o o d a t t e m p t s h a v e b e e n m a d e [27-331. F r o m lack t o g i v e a f u l l d e s c r i p t i o n , w e h a v e c h o s e n t o p r e s e n t d i f f e r e n t m o d e l s with progressive c o m p l i c a t i o n s , e a c h m o d e l bringing, w i t h o u t t o o m u c h c o m p l e x i t y , p a r t i a l i n f o r m a t i o n s ( s o m e t i m e s e n o u g h f o r t h e a i m e d applications).

In t h e s e c t i o n 111, w e p r e s e n t a s i m p l e m o d e l t a k i n g o n l y i n t o a c c o u n t t h e c o n d u c t i o n h e a t t r a n s f e r a n d t h e p h a s e c h a n g e s . This m o d e l , n e g l e c t i n g t h e c o n v e c t i o n , m a y b e justified f o r metals. I n d e e d , t h e work of Srinivasan a n d al. [30] h a s shown t h a t , f o r t h e m a t e r i a l s which h a v e a P r a n d t l n u m b e r lower t h a n 0.1 ( c a s e of m e t a l s ) , t h e c o n v e c t i o n v e r y s l i g h t l y m o d i f i e s t h e h e a t t r a n s f e r in t h e m e l t pool.

In t h e s e c t i o n IV, w e p r o p o s e a s e m i - q u a n t i t a t i v e m o d e l t a k i n g i n t o a c c o u n t m o r e p a r a m e t e r s (convection p a r a m e t e r s ) . T h i s s t u d y will a l l o w t o p o i n t o u t t h e d r i v e n f o r c e s of t h e c o n v e c t i o n a n d t o g i v e s o m e t r e n d s of t h e m e c h a n i s m of alloying.

111-CONDUCTION MODEL 111-1 NUMERICAL RESULTS

T h e n u m e r i c a l r e s u l t s o b t a i n e d f r o m a c o n d u c t i o n m o d e l w i t h moving b o u n d a r i e s (solid-liquid i n t e r f a c e ) h a v e a l l o w e d u s t o study, f o r a g i v e n c o a t i n g - s u b s t r a t e s y s t e m t h e i n f l u e n c e of t h e working p a r a m e t e r s (q,d,V) a n d t h e i n f l u e n c e of t h e n a t u r e a n d of t h e t h i c k n e s s of t h e c o a t i n g .

F r o m f i g u r e s I a n d 2 w e c a n n o t e t h a t , (i) f o r l o n g i n t e r a c t i o n t i m e s (i.e. s m a l l s c a n r a t e s ) t h e t e m p e r a t u r e r e a c h e s a s t a t i o n n a r y v a l u e , (ii) s e v e r a l c o u p l e s (q, T o r V) a r e possible t o o b t a i n t h e s a m e result. I t i s in f a c t t h e l a w q E = c o n s t a n t which a l l o w s t o d e t e r m i n e t h e c o u p l a g e w h e n t h e s t a t i o n n a r y state is n o t r e a c h e d .

F r o m a p r a c t i c a l p o i n t of view, a g o o d c o m p r o m i s e b e t w e e n power a n d s c a n r a t e will a l l o w t o r e a c h t h e wished r e s u l t w i t h o u t using p r o h i b i t i v e power o r s c a n r a t e . This m o d e l r a p i d l y a l l o w s t h i s c h o i c e t o b e made.

T h e n a t u r e a n d t h e t h i c k n e s s of t h e c o a t i n g a l s o g r e a t l y i n f l u e n c e t h e h e a t t r a n s f e r . T h e m o d e l c a n e a s i l y g i v e t h e g e n e r a l t r e n d s ; a m o r e d e t a i l l e d d e s c r i p t i o n of t h e s e r e s u l t s i s given in a n o t h e r p a p e r [34].

111-2 CONCLUSIONS

T h i s s i m p l e m o d e l allows t o e s t a b l i s h t h e w o r k i n g c o n d i t i o n s t o r e a c h t h e melting.

M e l t i n g m u s t b e n e c e s s a r y r e a c h e d t o o b t a i n a l l o y i n g b u t i t is n o t s u f f i c i e n t t o p r e d i c t t h e f o r m a t i o n of a s u r f a c e alloy. I n d e e d , t h i s m o d e l g i v e s n o i n f o r m a t i o n a b o u t t h e m i x i n g of t h e liquid m a t e r i a l s g o v e r n e d by t h e physical q u a n t i t i e s of t h e flow. A g o o d c o r r e l a t i o n was h o w e v e r f o u n d b e t w e e n n u m e r i c a l a n d e x p e r i m e n t a l r e s u l t s f o r p u r e m e t a l s a n d s o m e b i n a r y s y s t e m s (Fe-Ni, Fe-AI..) [26,351.

Tlvap ^{Fe +} 200 prn Al

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F i g u r e 1: Thermal evolution of t h e s u r f a c e of mild s t e e l c o a t e d with 200pm of aluminium f o r d i f f e r e n t values of absorbed power density a n d f o r a fixed value of t h e scan r a t e (V=l cmls); T1fus=660°C; T2fus=1535"C.

F i g u r e 2: Thermal evolution of t h e s u r f a c e of mild s t e e l c o a t e d with 200pm of aluminium f o r d i f f e r e n t values of scan r a t e a n d f o r a fixed value of t h e absorbed power density; T1fus=66OoC; T2fus=1535"C.

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JOURNAL DE PHYSIQUE IV-THE CONVECTION

In t h e s e c t i o n d e a l i n g with t h e p r o c e s s e s of f o r m a t i o n of l a s e r s u r f a c e alloys, w e h a v e p o i n t e d o u t t h a t t h e c o n v e c t i o n m o t i o n m a y b e d u e t o t h e d i f f e r e n c e of t e m p e r a t u r e b e t w e e n t h e c e n t e r a n d t h e e d g e s of t h e m e l t pool l e a d i n g t o a f o r c e ( d e p e n d i n g o n t h e s u r f a c e t e n s i o n g r a d i e n t ) which d r i v e s t h e liquid f r o m t h e c e n t e r t o t h e e d g e s of t h e pool. T h e p r o b l e m t h a t w e h a v e t o s o l v e is t o know if t h i s f o r c e i s t h e o n l y driving f o r c e f o r c o n v e c t i o n a n d w h a t a r e t h e m o d i f i c a t i o n s t o b e d o n e t o t h e c o n d u c t i o n m o d e l t o t a k e i t i n t o account.

IV-1 NATURAL GRAVITATIONAL O R INTERFACIAL CONVECTION

T h e n a t u r a l c o n v e c t i o n w i t h i n a fluid is, by d e f i n i t i o n , d u e t o physical q u a n t i t i e s g r a d i e n t s which involve forces, e v e n t u a l l y b i n d e d t o p r e s s u r e forces; ( t h e f o r c e d c o n v e c t i o n b e i n g d u e t o p r e s s u r e f o r c e s d i r e c t l y applied).

T h e m o s t known n a t u r a l c o n v e c t i o n w i t h i n a f l u i d a r i s e s f r o m v o l u m i c w e i g h t g r a d i e n t s ; t h e s e g r a d i e n t s a r e d u e t o t e m p e r a t u r e o r l a n d c o n c e n t r a t i o n inhomo- g e n e i t i e s ; t h i s k i n d of n a t u r a l c o n v e c t i o n would b e c a l l e d g r a v i t a t i o n a l n a t u r a l c o n v e c t i o n ( t h e r m a l o r of c o n c e n t r a t i o n ) .

R e c e n t l y , i n m a t e r i a l s processing u n d e r m i c r o g r a v i t y conditions, t h e i n f l u e n c e of i n t e r f a c i a l q u a n t i t i e s ( s u r f a c e t e n s i o n g r a d i e n t s ) w a s shown t o b e of i m p o r t a n c e i n c o n v e c t i o n m e c h a n i s m [36].

We a r e g o i n g t o discuss, f r o m a s i m p l i f i e d m o d e l , t h e r e s p e c t i v e i n f l u e n c e s of t h e d i f f e r e n t a c t i n g forces. O u r a i m i s t o d e d u c e t h e p r e p o n d e r a n c e r e g i o n s of t h e s e t w o k i n d s of convection. In t h e f i r s t p a r t of t h e discussion, o n l y t e m p e r a t u r e g r a d i e n t s will b e t a k e d i n t o account.

T h e c o n v e c t i v e f l o w i s s t u d i e d i n a r e c t a n g u l a r c a v i t y ( f i g u r e 3). T h i s g e o m e t r y m a y b e a n a p p r o x i m a t i o n of a m e l t pool. T h r e e f o r c e s t a k e p l a c e in t h e c a v i t y , (i) t h e vlscous s t r e s s f o r c e s (Fp) which slow t h e m o t i o n , (ii) t h e b u o y a n c y f o r c e s (Fg) which d e p e n d o n t h e t h e r m a l g r a d i e n t s i n t h e w h o l e volume, (iii) t h e s u r f a c e t e n s i o n f o r c e s (F, ) which d e p e n d o n t h e s u r f a c e t h e r m a l g r a d i e n t .

f a c e

F i g u r e 3 : A p p r o x i m a t i o n o f t h e m e l t p o o l by a c a v i t y T h e s e f o r c e s c a n b e e x p r e s s e d [ 3 4 ] :

F p = p u h l l d

T h e d i m e n s i o n l e s s n u m b e r c h a r a c t e r i z i n g ' t h e n a t u r a l c o n v e c t i o n d e p e n d i n g o n d e n s i t y g r a d i e n t s (p) d u e t o t e m p e r a t u r e o r l a n d c o m p o s i t i o n g r a d i e n t s i s t h e Grashof n u m b e r (Gr). I t e x F e s s e s t h e c o m p a r a t i v e i m p o r t a n c e of g r a v i t a t i o n a l f o r c e s (Fg) a n d viscous f o r c e s (Fp): F g / F p = G r I R e ( R e i s t h e R e y n o l d s number).

T h e d i m e n s i o n l e s s n u m b e r c h a r a c t e r i z i n g t h e i n t e r f a c i a l c o n v e c t i o n i s t h e M a r a n g o n i n u m b e r (Mr) o r t h e Reynolds-Marangoni n u m b e r (Ra). T h e y e x p r e s s t h e c o m p e t i t i o n b e t w e e n t h e s u r f a c e t e n s i o n f o r c e s (Fa) a n d t h e viscous f o r c e s (Fp): Fa/Fp : Rg/(A.Re)

T h e d i f f e r e n t d i m e n s i o n l e s s numbers, A, R e , Gr, Pr, R a , Mr a r e d e f i n e d in t a b l e I.

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1

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R e y n o l s n u m b e r R e = u d l v

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P r a n d t l n u m b e r P r = V/CY

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6

A T ~ ~ ~ I V ~ ⁷

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Reynolds-Marangoni n u m b e r R,= U ' A T ~ I ~ V ~ ~

1

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M a r a n g o n i n u m b e r -- - - - M r = R a .Pr - -

I

T a b l e 1: d e f i n i t i o n s of t h e d i m e n s i o n l e s s n u m b e r s ( f o r a t e m p e r a t u r e g r a d i e n t AT) T h e r a t i o b e t w e e n t h e g r a v i t a t i o n a l f o r c e s a n d t h e s u r f a c e t e n s i o n f o r c e s a l l o w s t o d e t e r m i n e t h e c o m p a r a t i v e i m p o r t a n c e of t h e t w o k i n d s of c o n v e c t i o n d e s c r i b e d above:

Fg/Fa = (Gr.A)/Ra

F r o m t h i s d e s c r i p t i o n of t h e d r i v e n f o r c e s of t h e f l u i d flow in a c a v i t y , w e c a n c o n c l u d e t h a t t h e c o m p a r a t i v e i n f l u e n c e of t h e t w o k i n d s of c o n v e c t i o n will d e p e n d o n t h e q u a n t i t y (Gr.A)/Ra. T h e a s p e c t r a t i o (A) involves a t w o - d i m e n t i o n n a l c r i t e r i o n .

T h i s s t u d y i s i n f a c t v e r y simplified. A m o r e d e t a i l e d s t u d y would a l l o w us t o g i v e a b e t t e r c r i t e r i o n ; i n s t e a d of t h e q u a n t i t y A, i t would b e n e c e s s a r y t o m a k e a p p e a r a f u n c t i o n of A, which c a n b e z e r o when A t e n d s t o z e r o , t h e g r a v i t a t i o n a l f o r c e s b e i n g v e r y w e a k c o m p a r a t i v e l y t o t h e i n t e r f a c i a l forces.

IV-2 APPLICATION T O LASER MELTING

G e n e r a l l y , f o r l a s e r m e l t i n g , i t c a n b e c o n s i d e r e d t h a t t h e m e l t d e p t h (h) m a y v a r y f r o m O.ld to d (d i s t h e w i d t h of t h e m e l t pool). T h e a s p e c t r a t i o A m a y t h e n v a r y f r o m 0.1 t o 1. T h e c a l c u l a t e d v a l u e s of Gr/RO a n d (Gr.A)/Ro a r e s m a l l [34]. T h e t e m p e r a t u r e gradie-lt b e t w e e n t h e c e n t e r a n d t h e e d g e s of t h e m e l t pool i s g e n e r a l l y a b o u t 5 0 0 K.mm

.

T h e w i d t h of t h e m e l t pool i s c o n s i d e r e d t o b e e q u a l t o t h e b e a m d i a m e t e r ( d = l mm).

I t i s t h e r e f o r e d i f f i c u l t t o f i x a l i m i t f o r t h e r a t i o G r / R a o r (Gr.A)/Ra a s i n t h e m o n o d i m e n t i o n n a l a p p r o x i m a t i o n of F a v i e r a n d al. [ 3 7 ] . In l a s e r m e l t i n g processing (O.I_(ASl), i t c a n b e n o t e d t h a t t h e s e t w o r a t i o s a r e s m a l l a n d thus, w e c a n c o n c l u d e t h a t t h e c o n v e c t i o n would b e e s s e n t i a l l y d u e t o t h e s u r f a c e t e n s i o n g r a d i e n t s .

I t i s t h e r e f o r e i m p o r t a n t t o n o t e t h a t w e h a v e o n l y s t u d i e d p u r e m e t a l s s u b j e c t t o t h e r m a l g r a d i e n t s . Actually, t h e volumic w e i g h t a n d s u r f a c e t e n s i o n d e p e n d a s well o n t e m p e r a t u r e a s o n c o m p o s i t i o n , so:

a

u ao

a~

⁺ ao

a,

-

ax

a~

ax ac

ax

a n d a t t h e s u r f a c e :

For a l l o y s c o n t a i n i n g t e n s i o a c t i v e e l e m e n t s , t h e m a g n i t u d e of t h e R e y n o l d s M a r a n g o n i n u m b e r ( R u ) c a n b e d r a s t i c a l l y modified. , T h e i n t e r f a c i a l c o n v e c t i o n d u e t o a t h e r m a l g r a d i e n t would b e n e g l i g i b l e a n d t h e m o t i o n of t h e m e l t would t h e n b e d u e t o g r a v i t a t i o n a l c o n v e c t i o n o r t o i n t e r f a c i a l c o n v e c t i o n d u e t o a c o n c e n t r a t i o n g r a d i e n t .

JOURNAL DE PHYSIQUE IV-3 CONCLUSION

We h a v e shown t h a t , in t h e l a s e r m e l t p o o l s which h a v e g e n e r a l l y a n a s p e c t r a t i o l o w e r t h a n 1, t h e d r i v e n f o r c e s of t h e c o n v e c t i o n a r e t h e s u r f a c e t e n s i o n f o r c e s a r i s i n g f r o m t e m p e r a t u r e g r a d i e n t s . T h i s is t r u e when, (i) t h e m e l t c o m p o s i t i o n i s uniform, (ii) t h e s u r f a c e d o e s n o t c o n t a i n t e n s i o a c t i v e e l e m e n t s .

D u r i n g t h e f o r m a t i o n of l a s e r s u r f a c e a l l o y s b y s i m u l t a n e o u s m i x i n g of a p r e d e p o s i t e d c o a t i n g a n d of t h e s u b s t r a t e , t h e m i x i n g is m a i n l y d u e t o c o n v e c t i o n motion. T h e s u r f a c e t e n s i o n g r a d i e n t s a r i s i n g f r o m t e m p e r a t u r e a n d c o m p o s i t i o n d i f f e r e n c e s t a k e p l a c e d u r i n g t h e h o m o g e n e i s a t i o n of t h e pool. So, i t is n e c e s s a r y t o t a k e i n a c c o u n t t h e s u r f a c e t e n s ~ o n g r a d i e n t ( d u / a x ) . T h e v a l u e s of (Gr.A)/Ra o r Gr/Ro a l l o w t o d e t e r m i n e i n i t i a l l y t h e vigor of t h e f l u i d flow a n d s o t o p r e d i c t t h e f e a s i b i l i t y of a s u r f a c e alloy.

V- CONCLUSIONS

T h e d i f f e r e n t m o d e l s p r e s e n t e d a l l o w t o give p a r t i a l i n f o r m a t i o n s s o m e t i m e s s u f f i c i e n t f o r t h e a i m e d a p p l i c a t i o n s .

In t h e f i r s t m o d e l (rigid m o d e l ) w e h a v e shown t h e i n f l u e n c e of t h e working p a r a m e t e r ; g e n e r a l t r e n d s h a v e b e e n d e r i v e d f r o m t h e r m a l p a r a m e t e r s e a s i l y a v a i l a b l e . In t h e s e c o n d model, t a k i n g i n a c c o u n t t h e c o n v e c t i v e m o t i o n , w e h a v e shown t h a t t h e d r i v e n f o r c e s o f t h e c o n v e c t i o n a r e t h e s u r f a c e t e n s i o n f o r c e s ; t h e v a l u e s o f t h e r a t i o (Gr.A)/Rcr which e x p r e s s t h e r e l a t i v e i m p o r t a n c e of t h e b u o y a n c y a n d i n t e r f a c i a l f o r c e s g i v e i n f o r m a t i o n s a b o u t t h e vigor of t h e f l u i d f l o w a n d s o o n t h e h o m o g e n e i t y of t h e r e s u l t i n g s u r f a c e alloy.

LIST OF SYMBOLS

d l a s e r b e a m d i a m e t e r [L]

h t h i c k n e s s of t h e

m e l t pool [Ll

k t h e r m a l c o n d u c t i v i t y [MLT-3 - I ]

P l a s e r power [ML'T-~]

q p o w e r d e n s i t y [ M T - ~ ] q O a b s o r b e d power d e n s i t y [MT- 3 ]

R r e f l e c t i v i t y d i m e n t i o n l e s s T t e m p e r a t u r e [

81

u x-component of t h e

[LT-'1

f l u i d v e l o c i t y

g r e e k s y m b o l s

p d e n s i t y [ M L - ~ I

(Y t h e r m a l d i f f u s i v i t y [L2T-']

v

k i n e m a t i c viscosity [ L 2 ~ - l ]

p viscosity [MT-IL-']

a'

s u r f a c e t e n s i o n

g r a d i e n t [MT-'~-']

7 i n t e r a c t i o n t i m e [TI

v y - c o m p o n e n t of t h e

f l u i d v e l o c i t y

[LT-'1

V s c a n r a t e [LT-'I

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