Metal-Induced An Evaluation Mechanisms

Embrittlement of Metals of Embrittler Transport

PAUL GORDON

An ana lys i s is made of the poss ib le e m b r i t t l e r t r a n spo r t mechan i sms in liquid meta l - induced e m b r i t t l e m e n t (LMIE) and solid me ta l - induced e m b r i t t l e m e n t (SMIE). The analy- s i s and compar i son with exper imen t s makes it appear l ikely that a) in LMIE bulk liquid flow is the t r a n s p o r t mechanism; liquid meta l s which " w e t " the base meta l can penet ra te to the t ips of even ve ry sharp cracks , con t r a ry to some s ta tements in the l i t e ra ture ; b) in SMIE surface se l f -d i f fus ion of the e m b r i t t l e r is the t r a n spo r t mechanism; and c) vapor t r an spo r t could play a role for a few high-vapor p r e s s u r e e m b r i t t l e r s - s u c h as Zn, Cd, and poss ib ly H g - b u t is not a viable t r anspo r t mechan i sm for most e m b r i t t l e r s .

THE e m b r i t t l e m e n t of n o r m a l l y ducti le meta l s by in- t i m a t e - i . e . , a t o m i c - c o n t a c t with lower mel t ing me ta l s while s imul t aneous ly under tens i le s t r e s s has most f r e - quently been cal led liquid meta l e m b r i t t l e m e n t - L M E . Since it is now known, however, that such e m b r i t t l e - ment takes place with the e m b r i t t l e r in the solid, ~ as well as the liquid, s tate, we p re fe r to cal l the phe- nomenon me ta l - i nduced e m b r i t t l e m e n t - M I E , with the des igna t ions LMIE and SMIE used to indicate, r e - spect ively , liquid meta l - induced and solid m e t a l - i n - duced e m b r i t t l e m e n t . The e m b r i t t l e m e n t is most f r e - quently mani fes ted by a reduct ion in f r ac tu re s t rength and duct i l i ty with no change in yield s t rength . F r a c - tu re involves two s tages , the f i r s t cons i s t ing of em- b r i t t l e r - i n d u c e d and control led c rack ing by tens i le decohesion ( i n t e rg ranu la r or t r a n s g r a n u l a r cleavage), and the second of n o r m a l f rac ture , independent of the e m b r i t t l e r , by duct i le rup ture or, in BCC m a t e r i a l s below thei r n i l -duc t i l i ty t e m p e r a t u r e s , by cleavage. The f i r s t s tage is the stage of MIE. The phenomenon is ubiquitous and of cons iderab le p rac t i ca l , as well as sc ient i f ic , i n t e r e s t (e.g., see the d i s cus s ion in Ref. 2).

As in the case of c racking phenomena in genera l , the fo rmat ion of MIE cracks can be analyzed in t e r m s of c r ack nuclea t ion and c rack propagat ion. The na tu re of the e m b r i t t l e m e n t p roce s s at the c rack tip (and in c rack ini t iat ion) has been the subject of a number of d i scuss ions (see, for example, Refs. 3 to 11). The poss ib le mechanism(s ) of e m b r i t t l e r t r an spo r t in c rack propagat ion has r ece ived less at tention; it is to this subject that the p resen t paper is addressed .

It is well es tab l i shed that the propagat ion of MIE c racks cannot proceed without the cont inual supply of e m b r i t t l e r to the crack tip ( e . g . , see Ref. 12). It is neve r the l e s s poss ib le , of course , that the e m b r i t t l e r t r an spo r t p roces s may not be the r a t e - d e t e r m i n i n g step in the propagat ion. Repeated r enuc lea t ion along the c rack path could some t imes be n e c e s s a r y , and this p rocess could be s lower than e m b r i t t l e r t r anspor t . T e t e l m a n and Kunz 8 have proposed, for example, that at high s t r e s s levels , the t r an spo r t ra te may fix the propagat ion ra te , but that at low s t r e s s e s the crack

PAUL GORDON is Professor, Department of Metallurgical and Ma- terials Engineering, Illinois Institute of Technology, Chicago, Illinois 60616.

Manuscript submitted May 2, 1977.

METALLURGICAL TRANSACTIONS A

must r enuc lea te every t ime it meets a new b a r r i e r - t r a n s v e r s e gra in boundar ies , for e x a m p l e - a n d this r enuc lea t ion may be r a t e - d e t e r m i n i n g . In only two inves t igat ions have m e a s u r e m e n t s been made which could have detected renuc lea t ion . One of these was concerned with LMIE, and no renuc lea t ion was de- tected.13 The other 14 studied SMIE and shows an elonga- t ion v s t ime curve in delayed fa i lu re for Cd on 4340 s tee l at 300~ which is d iscont inuous; this was in te r - pre ted to mean discont inuous c rack propagat ion, but not enough expe r imen ta l de ta i l was given to allow a judgment as to whether the d i scont inu i t i es might have been due to i n s t r u m e n t lag r a the r than renuc lea t ion in propagat ion. A thorough inves t igat ion of the poss i - ble occu r rence of repeated nuclea t ion and i ts poss ib le re la t ionsh ip to t r a n spo r t is ce r t a in ly needed; this sub- ject, however, will not be addressed fu r the r here .

The poss ib le e m b r i t t l e r t r a n s p o r t m e c h a n i s m s which have been suggested for MIE are vapor t r a n s - port , 1 bulk liquid flow, 1~ and var ious diffusion p roce s se s including e m b r i t t l e r diffusion through the base meta l g ra in boundar ies , 15 heterogeneous diffusion of a mono- a tomic layer or a double -a tomic layer of e m b r i t t l e r 3'16 over the c rack surface , and surface se l f -d i f fus ion of the embr i t t le r .2 Though there is not yet enough data in the l i t e r a tu re to w a r r a n t posi t ive ident i f ica t ion of the actual mechan i sm(s ) involved, some useful i n t e r im evaluat ions can be made.

VAPOR TRANSPORT

Transport through the vapor phase of the embrittler was originally proposed as the operative mechanism to explain the finding that embrittlement cracking in the Pb-on-steel system takes place below the melting point of Pb. I These authors also felt, however, that this transport mechanism was rate-controlling above the melting point as well, for they envisioned that the liquid embrittler could not get to the tip of sharp cracks, leaving a gap between liquid and crack tip to be traversed by vapor atoms. This view may have been partly prompted by statements in the earlier literature such as, for example, that a crack radius of 10 -2 mm (I0 -3 in.) or larger is needed to give ob- served cracking rates by bulk liquid flow, 12 or that ex- ternally applied pressures of 10 7 kPa (10 5 atm) would

ISSN 0360- 2133/78/0210-0267500,75/0 �9 1978 AMERICAN SOCIETY FOR METALS AND VOLUME 9A, FEBRUARY 1978-267

THE METALLURGICAL SOCIETY OF AIME

b e n e c e s s a r y f o r the l i q u i d to b e a t t he t ip of c r a c k s s m a l l e r t h a n a b o u t 10 -2 m m (10 "a i n . ) a T h e v a p o r t r a n s p o r t m e c h a n i s m h a s a l s o b e e n r e f e r r e d to in t h e l i t e r a t u r e a s a p o s s i b l e g e n e r a l e m b r i t t l e r t r a n s p o r t m e c h a n i s m ( s e e , f o r e x a m p l e , Re f . 17). I t w i l l b e s h o w n h e r e , h o w e v e r , t h a t t h i s t r a n s p o r t m e c h a n i s m i s a p l a u s i b l e one on ly f o r a few h i g h v a p o r p r e s s u r e e m b r i t t l e r s s u c h as Z n a n d Cd, and p o s s i b l y Hg, bu t no t f o r m o s t o t h e r e m b r i t t l e r s .

T o t h i s e n d l e t u s c o n s i d e r a n e m b r i t t l e m e n t s y s - t e m f o r w h i c h i t i s a s s u m e d e m b r i t t l e r t r a n s p o r t i s t h r o u g h t he e m b r i t t l e r v a p o r p h a s e ; in a p r o p a g a t i n g c r a c k , t h e n , t h e e m b r i t t l e r s o u r c e , e i t h e r s o l i d o r l i qu id , i s a s s u m e d to b e s e p a r a t e d f r o m the c r a c k t ip b y s o m e d i s t a n c e A - t h e t o t a l c r a c k l e n g t h (or s o m e p o r t i o n t h e r e o f ) - w h e r e A is m u c h g r e a t e r t h a n a t o m i c d i m e n s i o n s . U n d e r s u c h c o n d i t i o n s e m b r i t t l e r a t o m s would ge t to the c r a c k t ip by a t h r e e - s t e p p r o c e s s - 1 ) e v a p o r a t i o n f r o m t h e e m b r i t t l e r s u r f a c e f a c i n g t he c r a c k t ip , 2) t r a n s i t t h r o u g h the v a p o r p h a s e , and 3) d e p o s i t i o n a n d a d s o r p t i o n a t t he c r a c k t ip .* T o t e s t

*It should be reemphasized that both in this argument and in that for liquid flow later a gap having A much greater than atomic dimensions is assumed at the crack tip in order to show that one in fact will not exist; in the arguments, then, the concepts of a three-step process in vapor transport and of thermodynamic properties such as contact angle and vapor pressure are valid, though they may not be if A is of approximately atomic dimensions. It should also be noted that for cracking in metals, even brittle cracking, there is always some accompanying plastic deformation and consequent crack blunting at the crack tip, insuring that crack dimensions at the tip will be well above atomic dimensions.

w h e t h e r s u c h a p r o c e s s i s v i a b l e , we s h a l l c a l c u l a t e t r a n s p o r t t i m e s f o r the p r o c e s s a n d c o m p a r e t h e s e w i t h the k n o w n f a c t t h a t a t t e m p e r a t u r e s j u s t a b o v e t h e e m b r i t t l e r m e l t i n g p o i n t m o s t MIE f a i l u r e s t a k e p l a c e v i r t u a l l y " i n s t a n t a n e o u s l y " a t s u f f i c i e n t l y h i g h s t r e s s e s . F o r v i a b i l i t y i t w i l l be a s s u m e d t h a t c a l c u - l a t e d t r a n s p o r t t i m e s m u s t b e of t he o r d e r 1 s o r l e s s a t t he e m b r i t t l e r m e l t i n g p o i n t .

C o n s i d e r i n g f i r s t t he d e p o s i t i o n of t he v a p o r a t o m s a t t he c r a c k t ip , u n d e r d y n a m i c e q u i l i b r i u m c o n d i t i o n s o n l y a f r a c t i o n of t h o s e i m p i n g i n g w i l l b e a d s o r b e d , t h i s f r a c t i o n d e c r e a s i n g w i t h i n c r e a s i n g t e m p e r a t u r e . N e v e r t h e l e s s , f o r s i m p l i f i c a t i o n we s h a l l a s s u m e a l l t h e a t o m s w h i c h i m p i n g e a r e a d s o r b e d ; i t i s to be n o t e d t h a t t h i s a s s u m p t i o n in e f f e c t m e a n s t he c a l c u l a t e d t r a n s p o r t t i m e s w i l l b e m i n i m u m v a l u e s , t h u s g i v i n g t h e v a p o r t r a n s p o r t c o n c e p t the b e n e f i t of any doub t .

W i t h r e g a r d to the t r a n s i t s t e p , a t t he low v a p o r p r e s s u r e s c h a r a c t e r i s t i c of e m b r i t t l e r s n e a r t h e i r m e l t i n g p o i n t s , t he m e a n f r e e p a t h , X, of t he m e t a l v a p o r a t o m s i s t y p i c a l l y l o n g e r t h a n t he t o t a l e m b r i t - t l e m e n t c r a c k l eng t h . F o r a n i d e a l ga s , X i s g i v e n by t h e k i n e t i c t h e o r y of g a s e s a s

1 kT = - - - - [1]

7rq2 deP

w h e r e k is B o l t z m a n n ' s c o n s t a n t , T t h e a b s o l u t e t e m - p e r a t u r e , p t h e p r e s s u r e , and d the m o l e c u l a r d i a m e - t e r . F o r m e t a l v a p o r , t a k i n g d e ~ 10 -13 m m 2 a n d T ---- 600 K (a t y p i c a l e m b r i t t l e m e n t t e m p e r a t u r e ) , t h e n

1.9 • 10 -2 - - - m m f o r p in k P a .

P

S i n c e t h e v a p o r p r e s s u r e s of m o s t e m b r i t t l e r s a t t h e i r m e l t i n g p o i n t s a r e of t he o r d e r 10 -7 k P a (10 -9 a i m ) o r l e s s ( s e e T a b l e I) , t h e m e a n f r e e p a t h is s e e n to b e

Table I, Embrittler Vapor Pressures and Calculated Vapor Transport Times at the Embritller Melting Temperatures

Embrittler Vapor Pressure, kPa t, s

Zn 2 X 10 "2 5 X lO "3

Cd I X I0 "2 1 X tO "z Hg(a t R.T.) 3 X 10 -4 3 X 10 -1

l s Sb 4 X l 0 "7 3 X 10 z

K 1 X 10 -7 1 X 10 ~

l h

Na 2 X 10 "8 5 X 103

TI 4 X 10 -9 3 X 10 4

1 day

Pb 5X I0 "~~ 2X IO s Bi 2 X i 0 "n 5 X 106 Li 2 X l f f tl 5X !0 6

1 y r = 3 X 107s In 3 X 10 -22 3 X lO 17

10 ~~ yrs

Sn 8 X 10 "24 1 X 1019 Ga 6 X 10 "39 2 X 10 35

(1 atm ~ 10 2 kPa).

m u c h l a r g e r t h a n t y p i c a l e x p e r i m e n t a l c r a c k l e n g t h s of a few m m o r l e s s . T h u s , the v e l o c i t y , v, of the v a p o r a t o m s m a y b e t a k e n a s t h a t g i v e n by s e t t i n g t he a t o m i c k i n e t i c e n e r g y ~ leT, or

w h e r e m is t h e a t o m i c m a s s . T a k i n g T a g a i n ~ 600 K and t he a t o m i c w e i g h t to b e a b o u t 100 g, v ~ 3 • 105 m m / s . T h e t i m e t a k e n to t r a v e r s e a c r a c k of l e n g t h , s a y , 1 to 10 m m i s on ly of t he o r d e r 10* s . T h e t r a n s i t s t e p t h e n w i l l s e r v e a s no b o t t l e n e c k t n a p r o - c e s s w h i c h m u s t m e e t t he c r i t e r i o n of t <- 1 s .

In t he e v a p o r a t i o n s t e p , the n u m b e r of a t o m s e m i t t e d p e r u n i t t i m e p e r u n i t a r e a f r o m a l i qu id o r s o l i d s u r - f a c e u n d e r p r e s s u r e s low e n o u g h f o r t he v a p o r p h a s e to b e c o n s i d e r e d i d e a l i s , a g a i n f r o m t h e k i n e t i c t h e o r y

of g a s e s ,

P n : (2TrmkT)~ [3]

w h e r e P i s t he e q u i l i b r i u m v a p o r p r e s s u r e . * T h e t o t a l

*It is assumed here that no other gases are present in the crack; this is realistic for the situation being considered because the base metal is at temperatures where its vapor pressure is virtually zero, and the ambient atmosphere is excluded by the embrittler.

n u m b e r e m i t t e d p e r s a c r o s s t he e n t i r e c r a c k i s t h e n nhw, w h e r e h i s the c r a c k h e i g h t a n d w t h e w i d t h a t t h e e m b r i t t l e r s o u r c e . If we now m a k e t he c o n s e r v a t i v e s i m p l i f y i n g a s s u m p t i o n t h a t o n l y a m o n o l a y e r of e m - b r i t t l e r m u s t b e l a i d down on t h e c r a c k s u r f a c e s to s u p p o r t p r o p a g a t i o n , * t h e n t he s u p p l y t i m e , w h i c h is

*The actual amount may, of course, be more or less; it will be seen from the calculated times obtained that the exact value assumed is not important to the general conclusions.

now s e e n to b e t he t o t a l t r a n s p o r t t i m e , i s

n u m b e r of a t o m s in m o n o l a y e r _ 2L w 2L t ~ r a t e of s u p p l y - aZonhw = n-~oh

I4] w h e r e t he c r o s s s e c t i o n of a m e t a l a t o m h a s b e e n a p - p r o x i m a t e d a s t he c r y s t a l l a t t i c e p a r a m e t e r , ao,

268-VOLUME 9A, FEBRUARY 1978 METALLURGICAL TRANSACTIONS A

s q u a r e d and L i s the t o t a l c r a c k d e p t h . T h u s , s u b s t i - t u t i n g [31 in to [4]

/ (8 k)"2 / { L [5] ! - -

W e h a v e found t h a t t y p i c a l L / h r a t i o s r u n b e t w e e n 20 a n d 150 in the e m b r i t t l e m e n t of s t e e l , a s i l l u s t r a t e d in F i g . 1; t a k i n g L / h ~- 80, n o t i n g t h a t f o r m o s t m e t a l s (rnT) 1/2 a t the m e l t i n g p o i n t ~ 2 • 10 -1~ (g .K) 1/2 (w i t h i n

~ 10 -13 a f a c t o r of a b o u t 2.5) a n d s e t t i n g a o m m 2, t h e n a t the e m b r i t t l e r m e l t i n g t e m p e r a t u r e

10 -4 t ~ - 7 s e c o n d s f o r P in k P a . [6]

B a s e d on Eq . [6], v a p o r t r a n s p o r t t i m e s f o r m o s t of t he l o w - m e l t i n g e m b r i t t l e r s a r e l i s t e d in T a b l e I . C o m p a r i n g w i t h t he c r i t e r i o n t -< 1 s, we s e e t h a t on ly f o r Zn , Cd and p o s s i b l y Hg c a n v a p o r t r a n s p o r t be ex - p e c t e d to b e a v i a b l e m e c h a n i s m in MIE f a i l u r e . M e a s u r e d d e l a y e d f a i l u r e t i m e s in t h e Hg L M I E c r a c k - ing of 2024 T3 a l u m i n u m a t r o o m t e m p e r a t u r e TM a r e s h o w n in F i g . 2.* I t is s e e n t h a t o v e r a wide r a n g e of

*These data were obtained on flat tensile samples, cross-section 2 X 10 mm, which were first wet with Hg and then loaded, within 10-30 s later, by a servo- controlled, hydraulically actuated machine capable of reaching full load in a few milliseconds. The failure path lengths were of the order 1 to 5 mm.

s t r e s s e s a b o v e a " t h r e s h o l d " s t r e s s l e v e l the f a i l u r e t i m e s a r e a b o u t 2 • 10 -2 s; t h i s m a y b e t a k e n to b e

w i t h i n e x p e r i m e n t a l a n d c a l c u l a t i o n e r r o r l i m i t s of t h e 3 • 10 -1 s g i v e n in T a b l e I f o r Hg a t r o o m t e m p e r a - t u r e . In the c a s e of P b , In, and Sn, h o w e v e r , w h i c h

4

z

C- o

cr -I -

0 . 3 - 1 1 L I 1 - 4 -

40 60 80 IO0 120 140

APPLIED STRESS - % OF /2% OFFSET YIELD STRESS

Fig. 2-Delayed fai lure t ime vs applied s t r e s s for 2024 T3 aluminum embr i t t l ed by Hg at room tempera tu re .

(r

(b)

Fig. I--LMIE cracks--Zn on 4140 steel at 431~ magnified 65 times. Crack length-to-height ratios, L/h, indicated adjacent to photographs.

(c) Fig. 3-LMIE e r a c k - Z n on 4140 s tee l at 431~ (a) Optical micrograph , magnified 250 t imes ; (b) optical micrograph , magnified 500 times; (c) SEM X-ray fluorescence of Zn from the crack, magnified 1400 times. The field represented in (c) is shown by inset on (b).

METALLURGICAL TRANSACTIONS A VOLUME 9A, FEBRUARY 1978-269

have been repor ted to act as seve re e m b r i t t l e r s of s t ee l both above and below their mel t ing t e m p e r a - tu re s , 1'2 it is seen f rom Table I that the vapor t r a n s - por t t imes would be of the o rder 1 week, 101~ ye a r s and 10 z8 y e a r s , r espec t ive ly , c lear ly e l imina t ing this as a poss ib le mechan i sm.

LIQUID FLOW TRANSPORT

Above the embrittler melting point, bulk liquid flow is the most obvious transport mechanism. Accordingly, most discussions of LMIE in the literature implicitly or explicitly assume that such liquid flow is an in- trinsic part of the embrittlement. However, as pointed out above, some confusion has developed as to whether or not the liquid can reach the tip of sharp cracks. Some meta l lographic evidence that l iquid can and does get at leas t ve ry close to the c rack tip in sharp c racks is p re sen ted in Fig. 3 for the e m b r i t t l e m e n t of 4140 s tee l by liquid Zn, (M.P. 419.5~ at 431~ The c rack i l l u s t r a t ed is a sma l l c rack b ranch ing off the main c rack which is in the upper r ight of Fig. 3(a). The tip of the c rack is viewed at 500 t imes in Fig. 3(b), the mott led m a t e r i a l in the c rack being the Zn. To demon- s t r a t e that this m a t e r i a l is Zn, the tip of the c rack was examined with the X - r a y f luorescence capabi l i ty of a scanning e lec t ron mic roscope set to detect Zn f l u o r e s - cence. The r e su l t s a re p ic tured in Fig. 3(c) at 1400 t imes with the a r ea examined outl ined on the photomi- c rograph of Fig. 3(b); in 3(c) the concent ra ted white dots r e p r e s e n t Zn (the randomly sca t t e red white dots a re background " n o i s e " ) . It is c l ea r that the Zn has pene t ra ted v i r tua l ly to the v i s ib le tip of most of the c rack branches ; these tips have radi i of less than 10 -3 mm.

Though evidence such as that in Fig. 3 supports liquid flow t r anspor t , it is not conclusive for it does not e l imina te the poss ib i l i ty of a c rack tip void s m a l l e r than the l imi t of de tec tabi l i ty nor the poss ib le a rgu- ment that the liquid s imply flowed into the crack af ter some other p r e sumab ly f a s t e r mechan i sm was r e spon- s ible for the t r an spo r t which actual ly produced the crack . However, the s t a t emen t s quoted above that the liquid cannot be expected to reach the c rack tip appear to be based on a neglect , or mi s in t e rp re t a t i on , of the effects of sur face tens ion. Rober t son ~ co r rec t ly pointed out br ie f ly that the la rge p r e s s u r e s of 107 kPa (10 s atm) invoked by [3] could he supplied by sur face ten- s ion. In fact, as demons t r a t ed below, in the genera l case a l iquid will be drawn into a c lean s ta t ionary c rack t ip by sur face t ens ion whenever the contact angle of liquid on solid is less than 90 deg + a , where 2a is the angle be tween the two crack su r faces at the ins tan taneous posi t ion of the l i qu id -vapor - so l id s u r - faces i n t e r sec t ion (and there is no back p r e s s u r e due to foreign gases between the liquid and the c rack tip). To show this, let us a s sume the s imple , but typical c rack c r o s s - s e c t i o n p ic tured in Fig. 4. In the kinds of expe r imen t s for which data a re ava i lab le in LMIE, cracks usual ly have sma l l heights and pa ra l l e l , or a lmos t para l l e l , su r faces , as i l lus t ra ted in F igs . 2 and 3. F u r t h e r , the c rack tip radius is undoubtedly v i r tua l ly constant as the c rack propagates s ince the rad ius is fixed by the p las t ic i ty of the base me[a t as modified by the p r e sence at the c rack tip of the em- b r i t t l i ng liquid metal . Thus, it is r easonab le to a s sume

A

_

Fig. 4--Hypothetical crack cross-section in which it is as- sumed the liquid metal is not at the crack tip.

the s imple c rack shape in Fig. 4, the crack having flat, pa r a l l e l su r faces pe rpend icu la r to the page, constant tip rad ius p, and a height h = 2p. To begin with, we shal l a s sume no ex te rna l ly applied p r e s s u r e di f fer- ence on the liquid in the crack. Let us also a s s u m e for the sake of a rgumen t that l iquid e m b r i t t l e r has not pene t ra ted to the crack tip, leaving a gap of a length much g rea te r than a tomic d imens ions .* The

*See footnote on page 2.

equ i l ib r ium contact angle between liquid and solid is ~, de t e rmined by the respec t ive in ter face tens ions YSV, Y LV, and VSL. The force per unit l iqu id-vapor sur face a r ea due to sur face t e n s i o n - t h e effective p r e s s u r e di f ference ac ros s the l iquid-vapor s u r f a c e - is

1 1 [7]

where RI and R2 are the p r inc ipa l rad i i of curva ture of the liquid sur face . If the liquid in the c rack were s ta t ionary , or moving slowly, the LV sur face would be cy l indr ica l with the angle ~ main ta ined at the walls , as shown in Fig. 4. In this case R1 = H, R2 = ~ , and [7] becomes

~LV [8] a_P~- R

which can be shown for the geomet ry of Fig. 4 to be equivalent to

2u - - cOS 4. [9] A P 1 - h

The force on the liquid is in the d i rec t ion of the center of cu rva tu re and, therefore , for $ < 90 deg, the liquid wil l be drawn toward the c rack tip. The motion of the liquid will now d is tor t the LV sur face shape because the force produced is actual ly a r e su l t of movement of the a toms in and nea r the sur face tending to s h o r t e n - i .e. , to s t r a i g h t e n - t h e sur face . However, the sur face mus t always r e m a i n concave toward the tip so long as

< 90 deg; this may be seen by noting that if a convex por t ion developed, the force locally would be r eve r sed , tending again to make the sur face concave. It should also be noted that the sur face tens ion force will draw the liquid to the ve ry tip of the crack, for as the LV surface approaches the tip, the force on the LV s u r - face always r e m a i n s d i rec ted toward the tip, and con- s tant in value. (Between the plane AA, Fig. 4, and the c rack tip the sur face tens ion p r e s s u r e i n c r e a s e s as the effective h d e c r e a s e s but the a r ea of the LV su r - face d e c r e a s e s p ropor t iona te ly so that the total force on the LV su r face r e m a i n s constant) .

If, now, there is in addit ion to the sur face tens ion p r e s s u r e on ex te rna l ly applied p r e s s u r e dif ference,

270-VOLUME 9A, FEBRUARY 1978 METALLURGICAL TRANSACTIONS A

AP, on the liquid, this p r e s s u r e di f ference will p ro- vide an addi t ional impetus for the liquid to move to- ward the c r ack tip. Such an ex te rna l p r e s s u r e differ- ence, however, does tend to make the l iquid f ront convex toward the c rack tip, and might seem, the re - fore, to mi l i t a te agains t the liquid reach ing the tip of a ve ry sharp crack. This , in fact, is not so; as h de- c r ea se s the sur face tens ion p r e s s u r e i n c r e a s e s and always is l a rge r than AP at the tip of sharp c racks , i n su r ing that the liquid can reach the ve ry tip. F o r ex- ample , in LMIE test condit ions zXP is usual ly of the o rde r of 102 kPa (1 aim), and taking cos (~-~ �89 and "YLV -~ 104 J / ram2 ( 103 e rgs /cm2) , the sur face tens ion p r e s s u r e is 1/h kPa for h in ram. In the sha rpes t LMIE cracks in meta l s , h might be as s m a l l as ~lOao, where a o ~ 3 • 10 -~ mm is the a tomic d i ame te r , and as a resu l t , the sur face t ens ion t e r m could be as much as 3 • 104 l a rge r than AP.

It is seen, therefore , that provided q5 < 90 deg (or <90 deg + c~ in c racks with opposite su r faces sl ightly in- c l ined to one another) , liquid flow t r a n s p o r t needs no high ex te rna l p r e s s u r e s nor voids at the c rack tip to be viable . The key ques t ion as to whether liquid flow is a poss ib le opera t ive mechan i sm in LMIE is, conse- quently, whether it can be expected to provide suffi- c ient v e l o c i t i e s - s h o r t enough fa i lu re t i m e s - a g a i n s t the r e s i s t a n c e to flow in a na r row crack to account for m e a s u r e d LMIE values . To answer this quest ion, we may approximate the veloci ty of flow using fluid me- chanics methods for l a m i n a r flow between para l l e l p la tes , noting, however, that the roughness of the c rack su r faces may conceivably modify the a s sumed l amina r flow and thus cause actual r a tes to be some- what lower than calculated. The re is no ready way of ca lcula t ing the poss ib le effect of this roughness , but it s e ems not l ikely to be as much as an o rder of magni- tude.

We now a s s u m e that the liquid f i l ls the c rack and the two advance together at a r a t e which can be no g rea t e r than that of bulk liquid flow, which, accord ing to fluid mechanics , is given by*

*See, for example, Fluid Mechanics, p. 284, Potter and Foss, Ronald Press Co., N.Y., 1975.

h 2 2y LV v = U ~ (~' + ~ cos~)

where ~ is the liquid v i scos i ty and L again is the total c rack length. The liquid flow t r a n s p o r t t ime is r e - lated to the veloci ty by the usua l equation

dL 73 _ - -

dr

which combined with [10] gives

LdL d t -

A

where

h ~ 27 LV A = - g ~ ( ~ + fi cos~).

As pointed out e a r l i e r , in LMIE test condit ions it is a good approximat ion to a s sume that h is constant dur - ing c rack propagat ion (see, for example, the c racks in F igs . 2 and 3), so that in tegra t ing [12] gives

METALLURGICAL TRANSACTIONS A

n~ [14] t - - ~ .

We shal l now, as before , apply the c r i t e r i on that to be opera t ive the t r a n spo r t mechan i sm must be able to provide t r a n spo r t t imes of less than 1 s at the e m b r i t - t l e r mel t ing point (to account for ins tan taneous fa i l : u res ) . Thus , taking again AP ~ 102 kPa (1 aim), 7LV

10 -~ J / m m 2 (103 ergs /cm~) , cos ~ ~ 1/2, and # for meta l s at the i r mel t ing t e m p e r a t u r e z 2 x 10 -~ Pa �9 s (2 • 10 -2 poises) we have, for L and h in mm,

[15]

giving the approximate values listed in Table If for var ious L ' s and h ' s .

Table II shows that for c racks of even ve ry sma l l tip radi i , l iquid flow t r anspo r t is expected to be v i r t u - al ly ins tan taneous for al l l iquid meta l e m b r i t t l e r s ; it is therefore a viable t r anspo r t me c ha n i sm for al l LMIE fa i lu res without the help of other t r a n spo r t me- chan i sms . For Zn, Cd, and Hg, vapor t r a n s p o r t may also be a factor . Expe r imen t s in which propagat ion could be isola ted and r a t e s measu red as a function of t e m p e r a t u r e would be ve ry useful in this quest ion, for the ac t iva t ion energ ies should be quite d i f ferent for vapor and liquid t r anspor t . It may be seen f rom Eq. [5] that the ma jo r t e m p e r a t u r e dependent quant i ty for vapor t r a n spo r t is the vapor p r e s su r e ; the act ivat ion energy in this case should be virtually equal to the heat of vaporization of the embrittler which is of the order 50 to 60 T m cals/gm-atom for the melting point T m in degrees K. In the case of liquid flow transport, the viscosity is the major temperature-de- pendent quantity (Eq. [I0]) for which the activation energy is of the order 3 to 4 T m . Thus, experiments of this type should readily distinguish between these two possible mechanisms.

TRANSPORT BY SOLID-STATE DIFFUSION

Below the embrittler melting temperature liquid [i0] flow-transport is obviously not possible, and trans-

port through the vapor phase, as shown above, is highly unlikely. We are left, therefore, only with vari- ous solid-state diffusion possibilities, namely, a) diffusion of embrittler atoms through the grain bound- aries of the base metal substrate near the crack sur-

[11] faces, b) first monolayer heterogeneous surface dif- fusion of embrittler atoms over the base metal sub- strate, c) second monolayer heterogeneous surface diffusion of the e m b r i t t l e r atoms, and d) diffusion of e m b r i t t l e r a toms over a mul t i l aye r of e m b r i t t l e r

[12] thick enough so that the top layer of e m b r i t t l e r a toms a re inf luenced only by e m b r i t t l e r a toms below them and a re therefore se l f -di f fus ing. The diffusion ra tes co r respond ing to expe r imen ta l f indings a re quite h i g h - for example, Lynn, Warke and Gordon 2 show that for

[13] the i r work and that of other inves t iga to rs on e m b r i t t l e - ment of s teel , apparen t e m b r i t t l e r D values of 10 4 to 10 -6 cm2/s a re indicated. For gra in boundary se l f -d i f - fus ion in i ron, an es t ima te based on Ojos t e in ' s 19 proposa ls gives at t e m p e r a t u r e s between 450 and 600 K D values of 10 -17 to 10 -12 cm2/s . On the bas i s of

VOLUME 9A, F E B R U A R Y 1 9 7 8 - 2 7 1

Table II. Calculated Liquid Flow Transport Times in Seconds at Embrittler Melting Temperature (h = constant)

Final Crack Length L,mm ~ 10 ~ 10' 10 ~ 10" 10 "2

Crack Height h, mm

10-1 N 10-1 N ~ 1 0 " 3 ~ 10 "5 10 "7 10 "9

10 "2 0.5 X 10' ~ ,~0,5 • 10" 0.5 • 10 "s 0.5 • I0 -v 10 -3 102 ~ 100 _. ~ ~ ~ 1 0 - 4 ~ ~ 10 "6

10 "4 10 3 10 ' 10 .3 " ~ ~ ~ ~ 1 0 " s ~ 10 "s 104 102 10 -2 10 -4 L ~ 8 0 h I 0 "6 l 0 s 10 3 10 "l 10-3

10 -7 106 10 4 ~ .......~ 10o ~ 10 "2

~'7~stan~o~s "" transport above this line

0 .5 • 1 0 - 3 ~ 10-2

~ ........_. 10 -1

lOO ....._

10 , ~ 10 2

t h e g e n e r a l d i f f u s i o n l i t e r a t u r e i t s e e m s l i k e l y t h a t s o l u t e d i f f u s i o n r a t e s t h r o u g h the b o u n d a r i e s would no t be m o r e t h a n two o r t h r e e o r d e r s of m a g n i t u d e d i f f e r e n t f r o m t h i s . E v e n a s s u m i n g , t h e n , t he k ind of s t r e s s o r s t r a i n e n h a n c e m e n t of d i f f u s i o n d i s c u s s e d by C o h e n , 2~ g r a i n b o u n d a r y d i f f u s i o n wou ld a p p e a r to b e f a r too s l o w to a c c o u n t f o r e x p e r i m e n t a l r a t e s .

S u r f a c e d i f f u s i o n , t h e r e f o r e , i s t h e p r o b a b l e m e c h a - n i s m of e m b r i t t l e r t r a n s p o r t in SMIE . W e s t w o o d a n d K a m d a r '6 p o i n t e d out , h o w e v e r , t h a t f i r s t m o n o l a y e r s u r f a c e d i f f u s i o n would a l s o b e f a r too s l o w , and s u g - g e s t e d t h a t s e c o n d m o n o l a y e r d i f f u s i o n would g ive s u f - f i c i e n t r a t e s . T h e r e a s o n f o r t h i s p r e s u m a b l y i s t h a t t he m o v e m e n t of e m b r i t t l e r a t o m s in the f i r s t a t o m i c l a y e r of e m b r i t t l e r would be d r a s t i c a l l y s l o w e d down by i n t e r a c t i o n s w i th t he f a r m o r e s l o w l y m o v i n g b a s e m e t a l a t o m s . It s e e m s p o s s i b l e , h o w e v e r , t h a t e m - b r i t t l e r a t o m s e v e n in t h e s e c o n d m o n o l a y e r wou ld " f e e l " t he b a s e m e t a l a t o m s , and t h a t , a s p r o p o s e d b y L y n n , W a r k e and G o r d o n , 2 a t l e a s t 3 to 4 a t o m i c l a y e r s of e m b r i t t l e r wou ld b e n e c e s s a r y to f r e e t he e m b r i t t l e r a t o m s in the top l a y e r to m o v e a s if t h e y w e r e s e l f - d i f f u s i n g . F o l l o w i n g G j o s t e i n ' s 19 m o d e l of s u r f a c e s e l f - d i f f u s i o n , s u c h d i f f u s i o n cou ld b e e x - p e c t e d to p r o v i d e t he n e c e s s a r y r a t e s a t t e m p e r a t u r e s a b o v e a b o u t t h r e e - q u a r t e r s of t he e m b r i t t l e r a b s o l u t e m e l t i n g t e m p e r a t u r e , e x p l a i n i n g n i c e l y the f i n d i n g of L y n n , W a r k e a n d G o r d o n 2 t h a t SMIE in t he In, Cd, P b o r Z n - o n - 4 1 4 0 s t e e l s y s t e m s b e c o m e s e v i d e n t on ly a b o v e t h r e e - q u a r t e r s of t he e m b r i t t l e r m e l t i n g t e m - p e r a t u r e . J u s t b e l o w t he m e l t i n g t e m p e r a t u r e G j o s t e i n g i v e s s u r f a c e s e l f - d i f f u s i o n r a t e s in t he r a n g e 10 -3 to 10 -6 cruZ/s, j u s t a b o u t the e x p e r i m e n t a l r a n g e f o r SMIE. F o r c r a c k s of, s a y , 1 m m l e n g t h t h e s e r a t e s g i v e t r a n s p o r t t i m e s of the o r d e r 5 to 5000 s . T h e s e a r e t i m e s c o m m e n s u r a t e w i t h m e a s u r e d SMIE d e l a y e d f a i l u r e t i m e s n e a r t he m e l t i n g p o i n t , bu t , f r o m c o m - p a r i s o n w i t h T a b l e II , s e v e r a l o r d e r s of m a g n i t u d e g r e a t e r t h a n t h o s e f o r l i qu id f low t r a n s p o r t . T h i s s u g - g e s t s t h a t d e l a y e d f a i l u r e e x p e r i m e n t s c o v e r i n g a t e m p e r a t u r e r a n g e on b o t h s i d e s of the m e l t i n g p o i n t in the s a m e s y s t e m would be h i g h l y i n s t r u c t i v e , Such e x p e r i m e n t s h a v e no t ye t b e e n r e p o r t e d in t he l i t e r a - t u r e . A t a n y r a t e , i t m a y b e s a i d t h a t t r a n s p o r t b y

s u r f a c e s e l f - d i f f u s i o n of t he e m b r i t t l e r c a n p r o v i d e f a s t e n o u g h d i f f u s i o n r a t e s ; w h e t h e r s u c h d i f f u s i o n c a n t a k e p l a c e in t he s e c o n d l a y e r of e m b r i t t l e r a t o m s , a s p r o p o s e d by W e s t w o o d and K a m d a r , 16 o r r e q u i r e s t h r e e o r m o r e a t o m i c l a y e r s of e m b r i t t l e r a la L y n n , W a r k e , a n d G o r d o n , 2 r e m a i n s to b e e s t a b l i s h e d .

S U M M A R Y

A n a l y s i s m a k e s i t a p p e a r l i k e l y t h a t : 1) T h e e m b r i t t l e r t r a n s p o r t m e c h a n i s m in SMIE

c o n s i s t s of s u r f a c e d i f f u s i o n of e m b r i t t l e r a t o m s o v e r a l a y e r of e m b r i t t l e r t h i c k e n o u g h (a few a t o m i c d i a m e - t e r s ) so t h a t t he m o v i n g e m b r i t t l e r a t o m s in the top atomic layer are essentially self-diffusing.

2) The transport mechanism tn LMIE is bulk liquid flow; liquid metals which "wet" the base metal can

penetrate to the tips of even very sharp cracks under the impetus of surface tension, contrary to some statements in the literature.

3) For a few high-vapor pressure embrittlers- such as Zn, Cd, and possibly Hg-vapor transport could play a role. For all other embrittlers the rate of evaporation from the solid or liquid embrittler makes vapor transport far too slow.

A C K N O W L E D G M E N T

T h e a u t h o r t a k e s t h i s o p p o r t u n i t y to e x p r e s s a p p r e - c i a t i o n to the D i v i s i o n of M a t e r i a l s R e s e a r c h of t he N a t i o n a l S c i e n c e F o u n d a t i o n f o r t h e i r s p o n s o r s h i p of t h i s w o r k u n d e r C o n t r a c t N o s . G H - 4 1 6 1 6 a n d DMR 77- 04272 .

R E F E R E N C E S

1. This has been shown by several investigators; the earliest to relate it to LMIE were S. Mostovoy and N. N. Breyer: Trans. ASM, 1968, vol. 6 I, pp. 219-32.

2. J. C. Lynn, W. R. Warke, and Paul Gordon: Mater. Sci. Eng., 1975, vol. 18, pp. 51-62. This paper lists many references establishing solid metal-induced em- brittlement.

272-VOLUME 9A, FEBRUARY 1978 METALLURGICAL TRANSACTIONS A

3. W, Rostoker, J. M. McCaughey, and H. Markus: Embrittlement by Liquid Metals, Reinhold Publ. Corp., N.Y., 1960.

4. N. S. Stoloff and T. L. Johnston: Acta Met., 1963, vol. 11, pp. 251-56, 5. A, R. C. Westwood, C. M. Preece, and M. H. Kamdar: Fracture, vol. III, H.

Liebowitz, e d., Academic Press, 1971. 6. W. M. Robertson: 7q'ans. TMS-A1ME, 1966, vol. 236, pp. 1478-82. 7. M. J. Kelley and N. S. Stoloff: Met. Trans. A, 1975, vol. 6A, pp. 159-66. 8. A. S. Tetelman and Stephanie Kunz: Report of Materials Dept., UCLA, AROD

Contract DAHC-04-69.C-0008, March, 1973. 9. J. Y. Rinnovatore, J. D. Corrie, and H. Markus: Trans. ASM, 1966, vol. 59,

pp. 665-71. 10. C. M. Preece and A. R. C. Westwood: Trans. ASM, 1969, vol. 62, pp. 418-25. 11. M. A. Krishtal: Soy. Phys.-Dokl., 1970, no. 6, vol. 15, pp, 614-17.

12. F. N. Rhines, J. A. Alexander, and W. F. Barclay: Trans. ASM, 1962, vol. 55, pp. 22--44.

13. H. Nichols and W. Rostoker: Trans. ASM, 1965, vol. 58, pp. 155-63. 14. Y. lwata, Y. Asayama, and A. Sakamoto: Nippon Kinzaku Gakkaishi, 1967,

vol, 31, no. 1, pp. 77-83. 15. Liquid flow and grain boundary diffusion have been so generally invoked that

it is not known to this writer to whom to ascribe the genesis. 16. A. R. C. Westwood and M. H. Kamdar: Phil. Mug., 1963, vol. 8, pp. 787-804. 17. C. M. Preece: lnml. Conf. Stress Corrosion Cracking and Hydrogen Embrittle-

merit of lron Base Alloys, Unieux-Fiminy, France, 1973. 18. Paul Gordon and J. Zych: Project THEMIS, lIT, unpublished research. 19. N. A. Gjostein: Diffusion, pp. 241-74, ASM, Metals Park, Ohio, 1973. 20. Morris Cohen: Trans. Jap. Inst. Metals, 1970, vol. 11, no. 3, pp. 145-51.

M E T A L L U R G I C A L TRANSACTIONS A VOLUME 9A, F E B R U A R Y 1 9 7 8 - 2 7 3