Some grain size effects in creep and fracture

::;,'r[pta

ME'T'ALLIIR(]IC.A

Vol. ['r~ntud

['vrL~am,m r'r.,:,,.,,

4 , p p . 3t~l SO~, l q 7 ( ) tn the United ~:;tate,:,

SOB]; GRAIN SZZE EFFECTS IN CP,£EP AND FRACTURE; B. ~i, l a h i r , e D e p a r t m e n t o f MetaJ.lLmCr.-.-.3,, Unive.Pa|tV C o l l e g e , (rIP¢'uivud

F.PbrlJ;Jr'y

Corm.~.demable dJ.ve~sJ, t y of o p | n i o n

exists

73,

In t h e s t e a d y - s t a t e

creep rate,

{

'

o r varJ.atJon,.':

r.h.)th J.ncr, eases ar, d decPeases

, have been r, eT~or~ed ( i ) s

d.

]q711)

r,ega.Pdiin~., t h e e f f e c t s

in gr,aJ.n s i z e on hiRh te=~t')e.PatLLPe cPeep behavJouP,

diame¢~,

Swansea~ U.K.

wi,tl'i decr, easJ.nR ~..,,r,ai.ri

3

OthtP irweati,gati,ona (2'')

have c o n c l u d e d

that

~

rlecr, e.~,'.es ¢o d S

mlnlmu~L v,cJ.ue a t a P..Piti,eal g ~ a i n s i z e and then ir,'Pe=,l.,~.,3 w.Tr]l ~,lrther, decr, e,~s,, i,ri gPai,n d i a m e t e r .

Alternatively,

it

on gPalrl ai,ze o r d y ur.Jder c o n d i t i o n s ]able

h,:~; L>eerl .suggested ( 4 )

that

~herl kTPajn bourda.Py s l i d i n g

~". depends a

n*dk~s dn dpl:)r'ec?-

oonr.PLbU~ion t o t h e overaJ, l cr, eep d e f o r m a t i o n . In most caaes~ gz'dJn s i z e s t u , t l e s

P.ond~t|on and l i i t t l e stages of creep.

I'h=ve l.,een c o n i ' i n e , t

ro the s t e a d y - s i d l e

a t t e n ¢ J . o n lid .¢.' J:~een ,Jevoted to t h e tPan~Jen, Recently,

it

tPue c r e e p a t r , . , | r i , ¢, tritl'i t i m e ,

has bPen ~temonstrate~t t h a t t,

oveP a l m o s t

the e n r i r ~

and ter, t l a p y

rhe var, i a t i , n n o f

the

ereel:.~ cupve carl be

desc.~i.bed a c c u . P a t e l y by t h e s q u a t { o n ( 5 ' b ) "

¢o + ~:T ( l

- e -mr)

+

~st

¢

~'b e P ( ~ - t t )

'''(J')

~he.~e ¢o is t h e i . n s r a n t a n e o u a st-Pai,n on l o a d i n ~ , stPaiin~ m a p a r a m e t e r z'el.a[ed t o the r a t e

~,], [ h e tranaJ.ent, cr'eep

o f exJ~austi.on o f

tr'ansJ.ent c r e e p ,

and p ape teL1ptlaj',v t P e e p pa~'ametez*s and t t i,s the ti,me t o the o n s e t o f ¢z'eep.

'the r e l a t i o n s h i p s

parametePs

i,n e q u a t i o n

~hiieh e x i s t

betweer= ~ s '

I arid the d u r a t i o n s

~'b

~eP't~.,:LPy

t h e trarJ'~J.ent an,t ~er,¢i,=Lr, v

el- ~ile variou:3 c r e e p staEes , slJg~.~.st

tha~ tPansi,erlt ~ s t e a d y - s t a t e and ~e.~tJar,y cPeep s h o l ~ d riot be r'egar~Jed dr,; urmeldtP.¢J ( =.,,P,) stages . 'T'he pPellent J n v e s t i , g a t ion was tlier-efor,e desi,g, ned t o exdJtilne the effects

o f vapi.a~i,on-~= in F'PaJn a | ~ e not onJ.y on z r a n a l e n ~ and s t e a d y Std¢~ c'r,eep

but a l s o on ter'tl,~LPy c r e e p and fPacttLPe. ~,,x]~~ePi.merit d l ._. The work was c a r r i e d r)etai/s

of

the m a t e r ' i d l

t e s t [ r i g , procedLLPea ( 8 )

out

PT~ c'u d uJr,e

uszn~, d d i l u t e

nickel

silo v (containing.

¢).1 ,~t.'~,Ag,).

and specbnerl r,repar, at lon ( 7 ) =rod the r'orlscanr s [ P e s s cr,eep

have been re~,oPrud p r e v L o u s i v .

3 ('~ 1

The sl'~ec'imens were ,~nneal~.d

{no

~t.,2

~.,;IT, E! E!FFEI.I'T'L~ IN CREEP AND

GRAIN

For, di~-l,e.rerlt t ~niem

FRAC'T'IIRE

Vnl.

f()(.)O°(" in vac, uo t o rmn.duee st~J:~le Rr,~in s i z e s

at

4,

~rl thu Pan~,e

21 - HSpm. F'r,e v j u u s s t u d iec, ind h:ate t h a t ~:,r'ain dJ.ametur, [8 l,ounrl

at

d sim[ Jar y a P [ d r ton oi, cpee[.~ p r ' o r , ~ t [us w i t h

all str, e88e~ ( 2 ~ k )

carPi~4 o u t u n d e r d srr'ese', of

'T'ile pr, e s e n t

L1+2()() L b f / i n y

h()()°L~,

,at

testinE

w.~.,', tiler, e l o p e

3'his c ' o m p , ~ r a t i v e / y low

teUl:.,*=..~,+tur,e wr+s chosen Jn o1~:ler, tu avnJd h,~'r'aJn +,rowzlºl and r e c r y s t a / / [ s a t creep (7),

sJrlee ~,r'airl sLze i n s t a b i l i t y

[on dLLr'in£

can g i v e r'Lse t o exaj..,,+,e~ated +,r'ain s i z e

el, t e e l s ( 4 ) . R e s u l t s ,and D i s c u s s L o n I.

Cr, eep ( ILLr,V~, ["or eaq:l] c r e e p t e s t , ,

dete.r'nlined by a l e a s t t~e

(l'le

best

squares analysis

v a l u e oF r. he p , s r ~ e t e ~ s usJnR a d i g i t a l

r'eadinRs we.~e t a k e n clu~inR t h e c r e e p

cl~ve+

the average dll~erenee

life,

in e q u a t i o n

computeP.

(.)ve~ a l n ~ s t

b e t w e e n t i l e m~s~zr,~J s t P a [ n

J. was

Alº~)ut ~,0 s t r a i n /

the a n t i . r e c r e e p

and t h e c a l c u l a t e d

value

u~Ln~, the a e ~ i v e r l e o r m t a n r s was '~,().U(.)OUS,

However,, lºov aJ.l ~,n~ai.n sJ.zes,devi.atJ.ons

i:rom e q u a t i o n

IU-15'~ o t I"l,|e trarmJ.ent

I occu_wr, ed du~J.r~., t h e

[nLtial

cPeep J.J~e.

'['huse ¢~evj,jtir)ns+ w h i c h have Lleen obser'ved fop a rl=lber, of m , = t e ~ i a l s , ~lscusse,~ e l s e w h e r e (b~8) dc,.'uz'a~elV by e q u a t i o n O,

Tz,ansient

l,

'thus,

have been

cPeep cUrVes man be d e s c e i b e d

lO.lb+~ o f t h e L P a n s i e n t s t a r e .

e x c e p t d u r J n g the i n i . t L a l

and S t e a d y - S t a t e

L;eve.r, a l

the present

Creep

i n v e s t i+;,a~Jons (2+;~) have J.ndica~ed that. dE c o m p a r a t i v e l y

tempe.r,,~t~es ~3 v a P j e 8 as d + dt

Low

~rltersTledJate ~emp~atux, es t h e ~ / a r'eLatLonsl,lJp S

exllibi¢=

a mirLLmL~= and at. hJ~,h t e m p e r a t u r e s

~

v a . r i e s as l / d .

"['lie /=~r,ain s i z e ,


is sl, r , p o r t e d by tl'l~, resuJ, tl~ ob~aJ.rled ar

ex,:unjned in t h e pr, e~ent

inves~il;,ation.

t h e [nter, medLare temperatu.r,e

At J.a.~ge . ~ a i n s i z e s ,

~

varies

apl',rox-

i ~ v a t e l y a~ <.iV., but r e a c h e ~ a minJ.m~= v a l u e w i t h cJec,reasin~, j~aJ.n d.J.ameter ( F i g . The occLLPrunce o f a minJ.mLm=

I).

t h e ~ / d t, eJat i~'~r~sn~[~ has been a t t r L b u t e d (:,) t o a cl'lan~,e irl m o b i l e d [ s J . u c a t [ o n d e n s L t V wi. t h k,~atn slz, e However+ d ~ i . n g steady-state within

In

cPeel-~ ~ L~rh the suJ:~P.~[n s~.'z,e( 2 + q + q ) arid t h e d e n s i t y

of dJ.~/ocations

(10) has been four~.i t o be unailºl,ecten b.y v a P | a t i o n s rhP SUbl~,aJ. ris

diameteP

•

'T'hu dependence o t ~=,e on d ? ( F I R, / )

bound,~'~ie,~ r a t h e r , movmi~rit.

trlan suJ:~_TraJ.n boundaPJes a r e

The iriur'ease ~rl d

w|th

t h e r e l , o P e su.~:,Rusts t h a t

in ~.~ain ~..~aJn

r.hu md~or obstdcJ.es t o d[sJ.ocatJ.on

J.nc.rea,~inp t e m p e r , a ~ ' e (;~) wou_td then be

m e x n e c t e d -~[nce R r a | n bourda.r, ie~ become pro~?,r,ess|vely l e s s e f f e e t ~ . v e as bax,r i e r s to dislocation

mov~-J~ent as t h e temr~e.r,a t u r e

increases.

At hi~,her teml-~ePatu~es ~

d lslo<.'ation'-~ a.r,~jving at a h.,Tra~,n boundar, y car= move aJ.on~, the bound~.ry p l a n e by a c o m b i n a t i o r l of ~,J.ide and c l i m b ( l l ) ,

If

the +=lip v e c t o r

of

the dislocations

No.

;~

V~I.

4,

N~.

Ls rmt a t

L~

(;PlaIN

Pi~.ht

angles

to

L;IZE

E',FFE!C'T'::; IN

F"RJ~C'T'I.IRE:.

'.~tl_~

t h e bourldarw ~Lane, such move~lenc Pe~'..=ult~~. in p:,,ra[n [polJndarW

The clistances cPaveLLed by the clisLocati~ns ac.r,os~ t].le g,Pairi and aLorq~,

sLidir~,.

t he L<~ur~cr,y wi I L deter~iine the r,ar is off (he szPain to the overall

cPeep s r . P a i n +

I~,r'aJn d[amete.P ( q ~ 9 ) and t h e

(.',REEf' AN[)

Incpease

be d t t - r ' i h u r a b l e

Ll?,l./~

~ r H 3 p e a s e -. wJ.¢h ducPea:.~tnp,

'the occ'u.r,Perlc'e u], a minimum

,n ," to

;'he P , ~ t l o

t

r,estLIc zri~;, t-er:m L:IIJu[nl',~ t3~,t# ,

with

'3

the

decr, e a s i n p

In rile ;" /,J r, e l a t t ~ , r l ~ h i [ ' , (FJ.L'. / ) (2,:1) ~.~,ain d i a m e t e r , beJ.ow ~/ t h e n dppear, s (o rrl

JricPe~sirlt; , JJTIi'IOPt,=InCu 0]' g,raJ. n bourciar'y sl[~.lJng d.", a d~-~.~t'C.IpITId-

tJorl pPocess as t h e ~.,'q"ainsize decPeases. Alti~uu,e~h ~he ~ /d L~e].lavJouz, CaPotato

et a i ( P)

Pr, oel r . h o s e

o],

(["i~,,

t h e i "~ r " oL~se, v a r l o n c ; on tP,~rlsre, nt <:='eep ,.~if],er, irl sever, a t

rile

pr, e s e r r t

m,dy.

In thi:~

(l"',t~,, 2)

iLlustr,.'~tLr~,

Pates.

As f(-)und by (",aJPo],ato e~ a I ( ? ) )

(Fig,. 2). ~

L) agPees weLL ~J.th t i l e ],trlclir~,L~ oi-

t'].le scPer~,thenin~.:

invesz~,atLor,,

e..l:],e(.~¢ o f

L

0

p.ra[rl L)oundar, iuc; at

~"T' Lncr'eases w l t h

hip, h =:;¢Pain

decPeasirlg. ~'TPairl s i z e

Since c b (-- O.O(.)()I) is much s~ruLt~ than tT' the ~ e e p

is obtained

Pes['~lpr.lJ

deL'P~.,dl:3es ,:IS iJ ,'lt~Cp~,:lSt:,E;

PdCU ,~r Zer'(a time)

l:-r, om e.lUdtion i as

O ~

=

(~

LIBIrlL~, t h i s

...('~,)

mr.,r t ~"rq

eXl':Pessior= ro e v a L l J a t e ~. , t h e Pat. i s r.' /~ O

(.)

S

is '~, 4 Pop ,aLL L.~'ain si+,es,

F.Jquat i o n 'e' c'an be Pe-ar'Par~,ed as L,r The

i n ~ /(' ( 2 ) C)

S

=

I:#Pesenr.

[(~. o /~ s ) - L ]

incr, ease

in

" S/m

L T wJt:rl d e c r , e.~;,~Jng ¢I i.s riot

b u t occu.r,s t h P o u g h an [ n c P e a s e

The ~ P a n s i e n t

(1

- e-mr)

becomes

?1.

i: = corLSt a n t (, s stag, e , e ' m t s • ('~.02.

this

S

t

8

Ol" d ci=ang, e

i).

, Sl.l¢'h cllac

J.rldistIrlg,ui~],tabLe i:r,om i.,r.

J.r| equa~[¢~n L, This oc,cu.Ps

q)

...([4)

T e P t i a r , y CPeep and Pr,acc.u.Pe F'rom F ' [ g , . . 3 ,

i n ,~ s i m i l a r is

t].lurl a r'esLLLt

E /m ( r l ~ , .

'r n'l

At

in the Patio

st.a~,e appear, s t o end .~],ceP a t i m e ,

the r.PansJent tuPl~i ¢ when (5,6)

.,.(;I)

related

it

can be s e e n t h a t

manner, wit],= g P a [ n s i z e , to the tertiary p(t], ic

In t h e p P e s e n t ~,TPaln s i z e

(Fig,.

=

=

constanr.

- t s)

F,tf

=

(r'i~,.

stage,

tl: ~ vdPv (t

t

- t

(= b)

t

)~

...('=)

that

constant

t F d e p e n d s ~rl m and r.~ as

(=

L:~)

equatJ.on F, car= be wr, l t t e n --

constant

S i n c e m ', p~ t-r,om e q u a t i o n s on g'Pa~n s i z e

ro t-r,a c t ~ e ,

t h e ter, t i a r ' y

...(h)

c a s e , m ar~:l p h a v e a p [ J P o x i m a t e l v

L) so tha¢

mtl:

'1~le d u ~ a t L o r l o f

has beer= shown ( 8 )

rnt s t p ( t l :

and r h e t i m e

r

paLPameter'+ p , a~ ( h + 8 )

t t)

Pr, e v i o u s l y ,

Is,

(~- 1':')

q~ b and ?,

3) wouJ.d be e x p e c t e d .

the. same v a l u e ,at ,~ g i v e n

as ...(?)

t h e same d e p e n d e n c e o[" c~..., t t wnd t].

'.~O4

GRAIN SIZE

EFFECTS

IN (CREEP AN[) FRAC'T'I.IRE

In a l l cases, h,actu:,e occu_,~ed by cavitation. boundaries has been found not to vary with d(12).

Vol.

4,

No.

The cavity spacing along g~'aln

On this basis, i f cavity grow'~h

occm,s by diffus|on of vacancies Pron. the sur,roundi~, boundary(13), the cavity growth rates, and hence i f , should be independent oP d, contrary to the obse4~ed behaviour ( F i g . 3). siidi~(il

A J . t ~ , n a t i v e l y , I t has been proposed that c a v l ~ t e s g~o. by ~ a l n boundary lq) <hough the r a t i o ~gb/¢TOT |ncreasee as d d e c r e a s e s , the a c t u a l

sl|d|r~7, dIs~.ance on any one boundary decreases w ; [ h decz, easin~ ~.TraIn di~Lmeter ( q ' 9 ) Thus,

In a~,Treement w i t h the present r e s u l t s ,

lowe~p g r o w t h r a t e s , and t h ~ e t ' o P e lori~.e.l~

times co ~ , a c t t m e , ~ould r e s u i r as d d e c r e a s e s , as shown i n F|g. 3.

The v|ew t h a t

c a v i t y glPo~rch is ~ove=,ned L>y detca-mation processes i s ai~n :;ur,i,oPzed by the obse.r,ved der,endervce of t f

on [he d e f o n , s t l o n parameters m and p ( e q u a t i o n s 6 and 7 ) .

f'i~.. ~ shows the pervcenta~,e o~ bound=miss on which c ~ v i t i e s

and cracks developed

as a f u n c t i o n o f the t r u e ar%.,,le, ~, between the bounda.Py and the t e n s i l e a x i s top specimens hav~n~, ~,rain d i a m e t e r s of ~/iJm and hlpm. t r u e arl~ula.P d | s t r i b u t i o n

The method o f d e t e r ' m i n i n g the

o~ c a v i t a t e d boundaries has been d e s c r i b e d previou,=Ly ( i ~ )

C l e a r l y ¢he p r o p o r t L o n or c a r | t a r e d boundaries increases as the boundaries become more n~r, i y p e r p e n d i c u l a r to the s t r e s s d i r e c t i o n .

FuJ-thex,more, t h e sngu/az- d i s t r i b u -

t i o n i s the same over, the preser, t range of gr, a | n s~zes. The t o t a l (Fig.

~).

occu.Pred,

elorl~,atlorl at t-PactLLPe, CTOT, increased ~ l t h decreasing., 8;Pain d i a m e t e r

['TOT ~ s

taken as the s'~ra{rl r e a d i n g r e c o r d e d ;ramediately b e f o r e r u p t t m e

r x~am|natiorl o~ the creep ctu, ves showed tha~ the e x z s a s i o n , t s '

era ot steady s t a t e creep does rc~r vary ~Lrked.ty wi¢h d ( F i g .

?).

up to the

Thus, the v ~ m i a t i o n

of ~TO'I' w i t h d i s la.pge£y a ='esutt of d|ffe.pences In the ex-tens~on occuJprir~g du.pi~g the cert~ar, y ~za.~,e. F r a c t u r e takes p l a c e when a crack of s u f f i c i e n t Is tor~=ed.

deve.~oped on sevex,aJ, g r a i n boundary f a c e t s ( 1 5 ) . right

l e n g t h to p='op~gate spontaneously

T h i s occu~,s du.rin~ ~he / a t e ~ e r ~ i a r y stage by i n t ~ , l i n k a g e

ar~p,les to the s t r e s s diJ, ec¢Jon (Fi~.,,. q ) .

oP cx,acks

(:Tracks fo~'m m a i n l y or= boundax.tes at The l~rd~ up of cracks on these

bound,~ries n e c e s s i t a t e s the spread of the crack a/or, g ad~oird.ng {nclJned hour,de.pies which h~ve a lower i n c i d e n c e oP c a v i t i e s ot a crack o f c r i t i c a l

(rig.

q).

Ien~,th becomes more d i P f i c u l t

As o becomes ~m=dtlep, the fol"B=atJ.on s i n c e jr

~nvolves spread of the

cracks ¢~oul~h a lar,geJ, number o~ i n c l i n e d b o u n d a r i e s , r e s u l t i n g ductility,

(rig.

~)).

i n an i n c r e a s e in

5

V,~l.

,I, N~.

!,

(.;RAIN S[7..E EFFECTS IN CREEP AND FRAC'T'IIRE

'~(,S

()lO •

mt,ITll

I,O

a~O

al"",~ i I 0~:,4 I

~\

,,m i

m~.~

F' '

(XJCI# •

ii o

l,,,' /

• __o

i

I

I -'

l-

lw

mi

°"6-

° ~

ll--

- - W

rH'k

I.L

i,

e& t

( ~4Jb

a/dl

,,t

• -a

ii#, ,m OoO__ o-

(~Lr)Of

~

,~

i

2(')

~ m and

']'lie dependence of Lo, ¢T~ ~s

p

wiCh gr,:~irl d i~me'~uP

and ¢,T,UI, on g r a i n

rJ/ [l(X':

~"

~ 8(

r-

21,urn

_J..

it, r

o

,~,~ ii-&

r

J

-

" %, •

•

4

"

II,

~l, IW

I

I'

UI

• 'Im

4n

~' 14- I.)

I-

m,,

j_J

I

I

'"I

i

gr, a i n

i

i

i

i

i

i

F'li]. q

FIC,. 3 'T'he v a r [ a ¢ i o n ot

i

T!~)E. ANGLE(°) 1'3£TWEEN GP..AJNL=kOUNDAkJYAND E~5 E ~ C,1-1C')N

L,PAIN rllAklE" TF F' (/Jm)

with

•

• I.1

''"

•..

1

d [amm.e.e

-- ~.-~l/.Jm cJ

o-

- ~ o

--~-----~

F'[(~m 2

FIO. l '?he var, lac Jori oF (

• ~

--~

t -m~ i t .

dJ.amerP~'

and t f

The

[pue a n g u / a ~

dZstP~Jution

oP

cavi t a r e d ,t:_,'~lPdJ.r| l')ouJ'lClanies #:or' specuaeru=l hav[r~, gX'aln d l a B e i e r , s oi" ? l arid bilJm

300

GRAIN SIZE

EFFECTS

IN CREEP AN[) FRACTIIRE

VI~I.

a,

N~.

',

Refemences 1,

A.K. MukheJ, i e e , d,r.'. B i r d and d . £ . Born.

2.

f . Oaz'ofsio, W.F. Domts and f , von Gem~lns.,ez1~ Trans. Met. Soc. A.I.H.F'..

3,

P. Sbab.In.i.an and J.R.l.,ane.

q.

C.R. B a r , t e t t , J . 6 .

Trana.A.S.M. b~, 155 ( l q b g )

'Frans. A.L;.B. 4._.bb,£77 (1953)

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