The Effect of Plastic Deformation on the

Martensite-to-Austenite Transition in an Iron-Nickel Alloy L. E. POPE

The effect of p las t ic deformat ion in t roduced by ro l l ing at room t e m p e r a t u r e on the aus - teni te s t a r t t e m p e r a t u r e of an Fe-30 .3 wt pct Ni-0.005 wt pct C alloy has been d e t e r - mined . The aus teni te s t a r t t e m p e r a t u r e i n c r e a s e s monotonica l ly with deformat ion . Mic roha rdnes s m e a s u r e m e n t s show that the aus teni te s t a r t t e m p e r a t u r e i n c r e a s e s with the yield s t reng th of the m a r t e n s i t e . The t e m p e r a t u r e at which m a r t e n s i t e r e - v e r s a l in i t i a tes is not affected by the amount of m a r t e n s i t e p r e s e n t , and, t he re fo re , is not dependent on the m a r t e n s i t e plate s ize . It is suggested that the r e v e r s e m a r - t ens i te t r a n s f o r m a t i o n in i t i a tes at the m a r t e n s i t e - a u s t e n i t e in te r face and is con- t ro l led by in ter face propagat ion.

T H E s t r a in sens i t iv i ty of m a r t e n s i t i c t r a n s f o r m a t i o n s in Fe -N i al loys is wel l e s tab l i shed . Recent s tudies have shown that the effects of s t r a in on the m a r t e n - s i t e - t o - a u s t e n i t e t r a n s f o r m a t i o n can be pred ic ted with approximate the rmodynamic mode l s , t'2 It has a lso been observed that p r i o r p las t ic deformat ion can modify the t e m p e r a t u r e at which a specif ic m a r - t ens i t i c t r a n s f o r m a t i o n begins.3-7 In p a r t i c u l a r , p las t ic deformat ion applied below the aus teni te s t a r t t e m p e r a t u r e , As, has been observed to promote m a r - t ens i l e r e v e r s a l , ~ i.e., the m a r t e n s i t e - t o - a u s t e n i t e t r a n s f o r m a t i o n . Mel 'n ikov , et al. 8 found that the effect of plastic deformation on As of an Fe-30 pct Ni alloy depends on the temperature at which the deformation was applied; plastic deformation applied at room temperature (below Ad, the lowest tempera- ture at which deformation can initiate martensite r e v e r s a l ) shifted the r e v e r s e t r a n s f o r m a t i o n cu rves to higher t e m p e r a t u r e s while p las t ic deformat ion applied 60 ~ to 100~ below As (above Ad) lowered the r e v e r s e t r a n s f o r m a t i o n cu rves .

Even though the p r e sen t study is concerned with m a r t e n s i t e r e v e r s a l , i t is in format ive to cons ider obse rva t ions on the a u s t e n i t e - t o - m a r t e n s i t e (forward) t r a n s f o r m a t i o n which has been more extens ively s tudied. The forward t r a n s f o r m a t i o n is more s imply defined s ince the s ta r t ing m a t e r i a l is a s ingle phase aus teni te as compared to the two phase m a r t e n s i t e - aus teni te m a t e r i a l in m a r t e n s i t e r e v e r s a l s tudies . Also, the suggest ion has been made that s tudies of the forward t r a n s f o r m a t i o n a re helpful in the i n t e r - p re ta t ion of m a r t e n s i t e r e v e r s a l data. Specif ical ly , Bre inan and Anse l l ' s tudied the effect of deformat ion on the forward t r a n s f o r m a t i o n in an Airkool-S s tee l and found that the dec rea se in the m a r t e n s i t e s t a r t t e m p e r a t u r e , Ms, with deformat ion applied above M d (the highest t e m p e r a t u r e at which deformat ion can ini t ia te the fo rmat ion of mar t ens i t e ) co r r e l a t ed with the change in aus ten i te yield s t reng th . They concluded that M s dec reased with i n c r e a s i n g yield s t reng th as a consequence of reduced d is loca t ion mobi l i ty , which may a l t e rna te ly affect e i ther the nuc lea t ion of new m a r t e n s i t e or the propagat ion of

L. E. POPE is Member of Technical Staff, Physics of Solids Research Department, Sandia Laboratories, Albuquerque, N. Mex.

Manuscript submitted January 18, 1972.

the m a r t e n s i t e - a u s t e n i t e in te r face . I nc r ea s ing the yie ld s t reng th by al loying dec reased Ms in the same m a n n e r . In a s i m i l a r s tudy, Ankara 1~ used t r a n s - fo rmat ion cycl ing of an Fe -30 pct Ni al loy to i n c r e a s e the aus teni te yie ld s t reng th and also found a dec rea se in Ms with i nc r ea s ing yield s t rength , which he a t t r i - buted to a change in d i s loca t ion densi ty .

The purpose of the p r e s e n t study is to inves t iga te the effect of deformat ion applied below Ad on the m a r t e n s i t e - t o - a u s t e n i t e (i.e., the r e v e r s e ) t r a n s - fo rmat ion in an Fe-30 .3 wt pct Ni--0.005 wt pct C al loy, and to thereby infer the m e c h a n i s m s r e s p o n - s ib le for the effect of the p r i o r deformat ion . This is accompl ished by de t e rmin ing As for samples con- ta ining var ious m a r t e n s i t e pe rcen tages subjected to cont ro l led deformat ion . The change in yield s t reng th accompanying the deformat ion is in fe r red f rom m i c r o h a r d n e s s m e a s u r e m e n t s on both the aus - tenite and m a r t e n s i t e . Al te rna te models for the in i - t ia t ion of the new austeni te phase are d i scussed .

1) EXPERIMENTAL

Specimens were fabricated from a blend of high purity iron and nickel powders which were pressed and sintered and then rolled with intermittent anneal- ings to a final thickness of 0.004 in. (4 mils). The chemical composition is shown in Table I. After final reduction to 4 mils the sheet material was annealed 4 h at 1000~ in a hydrogen atmosphere, cooled at 200~ per hour to 200~ and air cooled to room tem- perature. Samples containing 33, 50, 67, and 95 pct martensite were prepared by controlling both the quench temperature and the time at the quench tem- perature. The maximum martensite percentage, 95 pct, was obtained by quenching in liquid nitrogen for 72 h as compared to 33 pct martensite being formed by quenching at -24~ for 7 rain. Specific values for the martensite content in each sample were determined by standard surface metallography. X-ray scans showed considerable preferred orien- tation, hence no useful information on phase compo- sitions was obtained through X-ray measurements. The martensitic microstructure for the 95 pct mar- tensite sample is shown in Fig. 1. It is observed that some relatively long ~'bands" of martensite exist with a more random fine martensite structure be-

METALLURGICAL TRANSACTIONS VOLUME 3, AUGUST 1972-2151

Table I. Material Chemical Composition

Element Fe Ni C S Mn Si Cu Mo AI Mg Ti P Ca

Weight Percent Balance 30.3 <0.005 <0.001 <0.005 <0.005 <0.005 <0.005 <0.005 <0.005 <0.005 <0.001 <0.005

Fig. 1--Typical microstructure of the 95 pct martensite sam- ple with no deformation. 2 pct nital etch, 30 pct Na metabi- sulfite stain. The light and dark regions, according to micro- hardness measurements, are both martensite; no retained austenite is observed at this magnification (X50). The long strips of martensite probably result from individual marten- site plates forming in a near parallel manner in adjacent austenite grains.

tween the " b a n d s . " Mic roha rdnes s m e a s u r e m e n t s showed both the light and dark " b a n d s " to be m a r - tens i te ; the gradat ion in color may be a r e s u l t of m ic roseg rega t i on . The m i c r o s t r u c t u r e of samples containing less than 95 pct m a r t e n s i t e was observed to have the e s sen t i a l fea tures of that shown in Fig. 1 except that the amount of fine s t ruc tu re between the " b a n d s " of m a r t e n s i t e dec reased as the m a r t e n s i t e pe rcen t dec reased . The applicat ion of deformat ion did not produce an observable change in the bas ic fea tures of the m i c r o s t r u c t u r e nor a detectable change in the m a r t e n s i t e percen tage . The s tandard Knoop indentor with a 25 g load was used to m e a s u r e the m i c r o h a r d n e s s of the re ta ined aus teni te and the m a r t e n s i t e p la tes . Care was taken to make m i c r o - ha rdness m e a s u r e m e n t s away f rom the m a r t e n s i t e - aus teni te in te r face . In addition, the average of 10 read ings is r epor ted for each datum point .

Mar tens i t e samples containing 50 and 95 pct m a r - tens i te were deformed by ro l l ing at room t e m p e r a - ture* to p rese lec ted th icknesses giving reduct ions

*Room temperature is considerably below A d which is about 210~ 3

in th ickness of 0, 5, 10, 20, 30, and 42.5 pct. For a given m a r t e n s i t e pe rcen tage , each succeedingly higher level of deformat ion rece ived the exact

2 1 5 2 - V O L U M E 3 , AUGUST 1972

ro l l ing sequence of the p rev ious level of de fo rma- tion p r io r to addit ional ro l l ing passes at l a rge r ro i l ing p r e s s u r e s . The specific number of passes at each ro i l ing p r e s s u r e was carefu l ly r eco rded , which allowed addi t ional s amples to be made with good reproduc ib i l i ty . The ra te of reduct ion in th ickness per ro l l ing pass was l e s s than 1 pct and was kept approximate ly cons tant for samples of d i f ferent m a r t e n s i t e pe rcen tages . F i na l th icknesses were m e a s u r e d to within • 0.05 mi l s . Since some non- un i fo rmi ty existed ac ros s a sample , an average be - tween edge and center th ickness was used.

The large drop in f e r romagne t i c pe rmeab i l i t y which accompanies m a r t e n s i t e r e v e r s a l was used to detect the t r ans fo rma t ion . The inductance of a coil su r round ing the sample was moni tored as the sample was heated through the t r ans i t ion . This technique was f i r s t r epor ted by Samara and Gia rd in i H as a method for studying the p r e s s u r e sens i t iv i ty of the Cur ie t e m p e r a t u r e . Subsequent ly , Rohde and Graham 1 have employed the same technique to detect m a r t e n - s i te r e v e r s a l s . For the alloy being invest igated the aus teni te s t a r t t e mpe r a t u r e is about 390~ which is well below the m a r t e n s i t e Cur ie t e mpe r a t u r e (~700~ On the other hand, the Cur ie t e mpe r a t u r e of the aus - tenite is about 60~ Thus for the t e m p e r a t u r e s of i n t e r e s t , the m a r t e n s i t e is s t rongly f e r romagne t i c , and the re t a ined aus teni te is pa ramagne t i c . As the spec imen is heated through the t r ans i t ion , the change in inductance of the coil is approximate ly p r o p o r - t ional to the volume of m a r t e n s i t e t r ans fo rmed . 1 As as de t e rmined by the inductance technique has been shown to be in good a g r e e me n t with that de t e rmined by d i l a tomet r i c ~ and r e s i s t i v i t y 2 m e a s u r e m e n t s .

The data were col lected by moni to r ing the detect ion coil inductance cont inuously f rom 22~ unt i l the m a r - tens i te had complete ly t r a n s f o r m e d as indicated by an inductance reading close to the air core inductance value . A heating ra te of 4.5 to 5~ was used. Severa l duplicate m e a s u r e m e n t s were made to e s t a - b l i sh the expe r imen ta l r eproduc ib i l i ty , and expe r i - men ta l sca t t e r is shown as e r r o r ba r s in the r e su l t s sec t ion. Both the a i r core and spec imen inductance were found to i nc r ea se sl ightly with i nc reas ing t e m - pe r a t u r e , an effect which is due to the t he r ma l ex- pans ion of the coil .

2) RESULTS

The inductance vs temperature curves for 0, 5, i0, and 30 pct reductions in thickness of the 95 pct martensite samples are shown in Fig. 2. It is appa- rent from the figure that the transformation occurs over a broad temperature range. The As value is chosen as the temperature where the sample in- ductance was a maximum prior to a steady decrease as the transformation proceeded to completion. As is observed to increase with increasing deformation.

METALLURGICAL TRANSACTIONS

1.0

0.8

~ 0 . 6 z

- 0 . 4

0.2

' . . . . I . . . . I ' '

300 . . . . 3150 . . . . ~ . . . . TEMPERATURE, ~

i

l

o "0" DEFORMATION 5% DE FOI~C#,T I ON

n 10% DEFORhtATION c ~ BEFORMATION

\

450 500

Fig. 2--Normalized inductance vs temperature reverse mar- tensitic transformation curves for the 95 pct martensite sam- ples for 0, 5, 10, and 30 pct deformation (percent reduction in thickness). Additional transformation curves for 20 and 42.5 pct deformation are not shown because they are basi- cally parallel to and not resolvable from the 30 pct defor- mation curve.

In F ig . 2 each cu rve has been n o r m a l i z e d so that the s p e c i m e n inductance is 1.0 at As. F o r the de tec t ion coi l g e o m e t r y and m a t e r i a l used , the change in the inductance of the coi l (for t e m p e r a t u r e s g r e a t e r than As) c o r r e l a t e s approx imate ly with the vo lume of m a r t e n s i t e t r a n s f o r m e d . ~

It is a lso apparent f r o m Fig . 2 that the t r a n s - fo rmat ion t e m p e r a t u r e r ange , taken as the t e m - p e r a t u r e for 90 pct comple t ion (Inductance = 0.1) minus As, is r educed by 15~ for 5 pct de fo rmat ion r e l a t i v e to the 0 pct de fo rmat ion cu rve . A continued sharpening of the t r ans i t ion cu rve ex i s t s up to 10 pct de fo rmat ion with m o r e ex tens ive de fo rma t ion producing a somewhat b roadened t rans i t ion shif ted to higher t e m p e r a t u r e s . F o r the 50 pct m a r t e n s i t e s a m p l e s , a sharpening of the t r a n s f o r m a t i o n curve a lso ex is ted up to 10 pct de fo rmat ion .

The dependence of As on de fo rmat ion is shown in F ig s . 3(a) and 3(b) for s amp le s containing 50 and 95 pct m a r t e n s i t e , r e s p e c t i v e l y . The data for the 50 pc t m a r t e n s i t e s amp le , F ig . 3(a), a r e fit s a t i s f a c - to r i ly by a s t a t i s t i c a l l e a s t squa re s s t r a igh t l ine . On the other hand, the As-deformation curve for the 95 pct m a r t e n s i t e s amp le , F ig . 3(b), is obse rved to be pa rabo l i c . It should be noted, however , that for 5 pct de fo rma t ion or g r e a t e r , As for the 95 pct m a r - tens i te s amp le s is l a r g e r than As for the 50 pct m a r - t ens i t e s a m p l e s .

The dependence of m i c r o h a r d n e s s on de fo rmat ion is a l so shown in F i g s . 3(a) and 3(b) for both the m a r - tens i te and aus teni te in the 50 pct m a r t e n s i t e s am p le s and for the m a r t e n s i t e in the 95 pct m a r t e n s i t e s a m - p ie s . Cons ide r ing the m a r t e n s i t e phase , the Knoop ha rdness number vs de fo rma t ion plots have the same ge ne ra l f e a tu r e s as the As vs de fo rma t ion plots for the 50 and 95 pct m a r t e n s i t e s a m p l e s , r e s p e c t i v e l y . However , for 5 pct de fo rma t ion of the 50 pct m a r - tens i te s amp le , the m i c r o h a r d n e s s of the r e t a ined aus teni te i n c r e a s e d s igni f icant ly m o r e than the m i c r o h a r d n e s s of the m a r t e n s i t e , F ig . 3(a). It is not be l i eved that this d i f f e rence in the i n c r e a s e of the m i c r o h a r d n e s s of the two phases can be expla ined

440

430

420

410

4OO

390

380

I I I I I I I

"' /} �9 MARTENSITE HARDNESS

�9 AUSTENITE H A R D N E ~ r

T

, , / %

J J

J_

L 1 L L i L I

0 10 20 30 DEFORMATION

(a)

380

340

300

z

26O

220 ~

180

140

1 I I I I

440 370

430 330

o~ 420 290

<=

410 250 ~

400 �9 MARTENSITE HARDNESS 210

390 ~ 170 i I I I I

0 I0 20 30 40

% DEFO RMATION

(b)

Fig. 3--Austenite start temperature and Knoop hardness numbers vs deformation. The er ror bars forA s have ref- erence to the experimental reproducibility between samples prepared independently. The er ror bars on the hardness numbers refer to the scatter between the average of 10 hardness readings on different samples. A hardness number of 95 was measured for the annealed austenite prior to mar- tensite formation. (a) 50 pct martensite samples, (b) 95 pet martensite samples.

METALLURGICAL TRANSACTIONS VOLUME 3, AUGUST 1972 2153

' ' ' ' ' ' I I ' ' ' ' r ' ' ' ' i , , , , f

1.0 ~.

O o ~6~ M A R T E N S I T E

(1 8 ,~ 67% M A R T E N S I TE o 50~ M A R T E N S I T E

0 . 6

0 . 4

0.2

0.0

300 350 4 0 0 4 5 0 500

T E M P E R A T U R E , ~

Fig. 4--Inductance vs temperature reverse martensitic trans- formation curves for 33, 50, 67, and 95 pct martensite.

by the d i f ference in work hardening of the phases ; r a t h e r , it is concluded that more p las t ic s t r a in occu r red in the r e t a ined aus ten i te . To support this conclus ion the r e a d e r is r eminded that the de fo rma- tion plotted in Fig . 3 r e f e r s to the total sample r e - duction in th ickness and not to the deformat ion in e i ther the r e t a ined aus teni te or the m a r t e n s i t e phases , whereas the m i c r o h a r d n e s s m e a s u r e m e n t s a re a moni to r of the change in s t rength of a phase with deformat ion within that phase . Hence, the m i c r o - h a r d n e s s - d e f o r m a t i o n plots for the 50 pct m a r t e n s i t e samples do not r ea l ly show the work hardening c h a r - a c t e r i s t i c s of e i ther phase . In con t ra s t , s ince ve ry l i t t le aus teni te is p r e s e n t in the 95 pct m a r t e n s i t e s a m p l e s , the m i c r o h a r d n e s s - d e f o r m a t i o n curve for this m a t e r i a l is probably typical of m a r t e n s i t e work hardening . The di f ference between the As and m i c r o - ha rdnes s vs deformat ion plots of the m a r t e n s i t e phase for 50 and 95 pct m a r t e n s i t e s amples is t h e r e - fore a t t r ibuted to the d i f ferent amount of deformat ion accumula ted in the m a r t e n s i t e for a given total r e - duction in spec imen th ickness .

In Fig. 4 the inductance vs t e m p e r a t u r e t r ans i t i on cu rves for spec imens containing 33, 50, 67 and 95 pct m a r t e n s i t e a re shown. All the data for spec imens containing 33 to 67 pct m a r t e n s i t e are well fit by a s ingle curve which is s igni f icant ly sha rpe r than the t r ans i t i on curve for the 95 pct m a r t e n s i t e spec imen . Within expe r imen ta l e r r o r As is observed to be in - dependent of the pe rcen t m a r t e n s i t e .

3) DISCUSSION

Plastic deformation of a martensite-austenite aggregate at room temperature will cause dislo- cation multiplication in both the martensite and austenite. In this section the dependence of As and microhardness on deformation will be compared to various dislocation models. Initially, pertinent characteristics of the thermodynamic approach used to explain reverse martensite transformations will be summarized. Then, it will be shown that the effect of prior deformation on As can be explained on the basis of a correlation between As and the martensite yield strength. The origin of the dependence of As on martensite yield strength can be interpreted on

2154-VOLUME 3, AUGUST 1972

the bas i s of e i ther the ease of nuclea t ion or on the ease of in te r face propagat ion . Both poss ib i l i t i e s wil l be cons idered . Other f ea tu res of the e x p e r i - menta l data wil l then be d i scussed .

3.1) The rmodynamic Model For Reve r se Mar tens i t e T r a n s f o r m a t i o n s

T h e r m o d y n a m i c a l l y , the m a r t e n s i t e - t o - a u s t e n i t e t r a n s f o r m a t i o n wil l in i t ia te when the f ree energy of the aus teni te is l ess than that of the pa ren t m a r t e n - s i te . F o r the Fe-30 pct Ni alloy a la rge t e m p e r a t u r e h y s t e r e s i s ex is t s for the m a r t e n s i t e - a u s t e n i t e t r a n s - fo rmat ion cycle . The exis tence of the t e mpe r a tu r e h y s t e r e s i s is a t t r ibuted to the p r e sence of an energy b a r r i e r which m u s t be overcome. Thus , m a r t e n s i t e r e v e r s a l occurs when the pa ren t m a t e r i a l is heated to a t e m p e r a t u r e , As, somewhat above the t e m p e r a - ture at which the f ree ene rg ie s of the pa ren t and aus teni te phases are equal, To. It is genera l ly accepted that the wel l defined As c o r r e l a t e s with a c r i t i c a l value of the total dr iv ing force which is de t e rmined by the energy b a r r i e r . The wide t e m - p e r a t u r e range r equ i r ed to complete the m a r t e n s i t e r e v e r s a l , F igs . 2 and 4, is i n t e rp re t ed to mean that a cont inual ly i nc r ea s ing dr iv ing force is r equ i r ed . Consequent ly , e i ther the t r a n s f o r m a t i o n of m a r t e n - s i te to aus teni te i n c r e a s e s the opposing forces or affects the nuclea t ion of new austeni te by e l imina t ing the l a rges t nucle i or by r emov ing p r e f e r r e d nuc l ea - tion s i t e s .

The energy b a r r i e r which opposes m a r t e n s i t e r e v e r s a l ex is t s as a consequence of the shape de - fo rmat ion (both a volume dec rea se and a shape change) which accompanies the t r ans fo rma t ion . The shape change is accommodated by sur face re l i e f , 12'13 p las t ic flow in the re ta ined aus teni te ~4'15 and the new aus t e - n i te , ~6 and p las t ic flow in the m a r t e n s i t e 13 adjacent to the new aus ten i te , while the volume dec rea se is accommodated by e las t ic s t r a i n s . The work hardening p r oc e s s at room t e m p e r a t u r e p r io r to m a r t e n s i t e r e v e r s a l can i n c r e a s e the b a r r i e r due to a dec rea se in d is loca t ion mobi l i ty .

3.2) Yield Strength

The data presented herein show that As increases with deformation applied below Ad, It is possible that the initiation of martensite reversal is affected by the introduction of additional dislocations in the strain hardening process which decreases dislocation mobility. Recently, Breinan and Ansell 9 observed that the transition temperature for the forward mar- tensite transformation decreased proportionally with increasing yield strength of the austenite. If analogous dependencies exist between the forward and reverse martensite transformations, the observed dependence of As on deformation may be attributable either to changes in the yield strength of the martensite or the retained austenite. It is reasonable that As may depend upon the martensite yield strength since interfaces propagate through the martensite. Further- more, plastic deformation in the martensite surround- ing the new austenite accompanies martensite re- versal. 13 On the other hand, plastic deformation also occurs in the retained austenite during martensite

METALLURGICAL TRANSACTIONS

1 ' I ' 1 ' I

[] 5 ~ MARTENSITE o 95% MARTENSITE ,,~lc:=~.~"

430 ~ f ~

410

390

I | I ~ I I 1 230 250 270 290

KNOOP HARDNESS NUMBER Fig. 5--As vs Knoop hardness number. By a statistical least squares fitting technique A s increases with Knoop hardness with a slope of 0.93~ per Knoop hardness number for both the 50 and 95 pct martensite samples. The data for this crossplot is taken from Fig. 3, and the error bars are as defined in Fig. 3.

r e v e r s a l , ~4'1S and As could poss ib ly co r r e l a t e with the yield s t reng th of the r e t a ined aus teni te . We can d i s t ingu ish between these two poss ib i l i t i e s in the following way.

Since p rev ious ly r epor t ed ha rdness vs yield s t reng th data ~7 show an approximate ly l i nea r r e l a - t ionship for the Fe -30 pct Ni al loy, m i c r o h a r d n e s s m e a s u r e m e n t s can be used to infer the approximate yield s t r eng ths of the m a r t e n s i t e and aus teni te . A c ros sp lo t of As vs Knoop h a r d n e s s n u m b e r s of the m a r t e n s i t e is shown in F ig . 5 for both the 50 and 95 pct m a r t e n s i t e s amp le s . The l ine drawn is a s t a t i s t i ca l l eas t squa re s fit of As to ha rdness n u m b e r s . As is seen , the data for both 50 and 95 pct m a r t e n s i t e s amples are adequately r e p r e s e n t e d by the s t ra igh t l ine . As i n c r e a s e s with the m a r t e n - s i te yield s t reng th with a s t a t i s t i ca l slope of 0.93~ per Knoop ha rdnes s n u m b e r .

By s i m i l a r a rgumen t , it is shown that the i n c r e a s e of As with p las t ic s t r a i n does not co r r e l a t e l i nea r ly with the r e t a ined aus teni te ha rdnes s (yield s t rength) . The independence of A s on pe rcen t m a r t e n s i t e , F ig . 4, also suppor ts the conc lus ion that As does not depend on the re t a ined aus teni te yield s t rength . Dur ing the forward t r a n s f o r m a t i o n the aus teni te su r round ing the newly fo rmed m a r t e n s i t e is de formed, with g r ea t e s t de format ion occu r r ing in the immedia te v ic in i ty of the m a r t e n s i t e p la tes . 6'~4-16 In this work the re ta ined aus teni te of the 50 pct m a r t e n s i t e s p e c i - men was found to have a m i c r o h a r d n e s s n u m b e r 60 pct l a rge r than the annealed aus ten i te . As the pe rcen t m a r t e n s i t e is i nc r ea sed , the yield s t reng th of the r e t a ined aus teni te wil l cont inue to i n c r e a s e . Thus , the r e t a ined aus teni te yie ld s t r eng th i n c r e a s e s with the pe r cen t m a r t e n s i t e but As r e m a i n s cons tant . It is thereby concluded that As does not co r r e l a t e with the r e t a ined aus teni te yield s t rength .

The p rev ious suggest ion that the in i t ia t ion of m a r - tens i te r e v e r s a l is affected by the s t r a i n hardening

p r o c e s s now s e e m s ver i f i ed . S t ra in hardening the m a r t e n s i t e i n c r e a s e s the m a r t e n s i t e yield s t rength which d e c r e a s e s d is locat ion mobi l i ty . The i n c r e a s e in As with deformat ion c o r r e l a t e s (and i n c r e a s e s monotonical ly) with the m a r t e n s i t e yield s t rength and indica tes that d is locat ion motion is r equ i r ed for m a r t e n s i t e r e v e r s a l .

3.3) Nucleat ion Vs In te r face Propaga t ion

The inf luence of m a r t e n s i t e yield s t reng th on the ease of nuc lea t ion is not c l ea r . If the nuclea t ion of new aus teni te depends on d is loca t ion motion, an i n c r e a s e in m a r t e n s i t e yield s t rength would h inder d i s loca t ion mot ion, thus reducing the ease of aus - teni te nuclea t ion . Hence, p las t ic s t r a i n which r a i s e s the m a r t e n s i t e yield s t reng th should i nc r ea se As as was observed . On the other hand, other models i n t e r - p r e t nuc lea t ion as r equ i r i ng a specif ic d is loca t ion a r r a y . P las t i c s t r a i n should then a s s i s t in the f o r m a - t ion of d is loca t ions and s t r a i n cen te r s where these d i s loca t ions can " c o a l e s c e " and lower their f ree energy by fo rming aus teni te embryos . This p roce s s p red ic t s a dec rea se in As; a conclus ion con t r a ry to the obse rva t ions r epor ted he re in . These r e su l t s show that if nuc lea t ion plays an impor t an t role in m a r t e n - s i te r e v e r s a l , a d is loca t ion m e c h a n i s m is r equ i r ed .

The expe r imen ta l r e su l t s can also be explained on the ba s i s that m a r t e n s i t e r e v e r s a l i s cont ro l led by in te r face propagat ion. P r ev ious meta l lographie ob- s e rva t ions of sur face re l i e f lz'17'18 and hydros ta t ic p r e s s u r e m e a s u r e m e n t s ~9 indicate that m a r t e n s i t e r e v e r s a l in i t i a tes along the m a r t e n s i t e plate p e r i - phery . Subsequent ly , the m a r t e n s i t e t r a n s f o r m s to aus teni te in a p iecewise m a n n e r 17 where in the newly formed aus teni te is in contact with e i ther the re ta ined aus ten i te or p rev ious ly formed new aus ten i te . These obse rva t ions suggest that nuc lea t ion of new aus ten i te , in the usua l s ense , may not occur . The r e v e r s a l of m a r t e n s i t e may thus depend on the propagat ion of the o r ig ina l m a r t e n s i t e - a u s t e n i t e in te r face . The hypo- thes i s that in te r face propagat ion cont ro ls m a r t e n s i t e r e v e r s a l is supported by prev ious obse rva t ions . Shapiro and K r a u s s observed with the e l ec t ron mic roscope that the new austeni te has no mid r ib . 13 They i n t e r p r e t e d this to mean that the r e v e r s e m a r - t ens i te t r a n s f o r m a t i o n p roceeds in only one d i rec t ion f rom the plane of in i t ia t ion . In addit ion, Garbach and Butakova ~2 observed meta l lograph ica l ly that for i n i - t ia t ion of m a r t e n s i t e r e v e r s a l that the new aus teni te was a cont inuat ion of the r e t a ined aus teni te ; the o r ig ina l m a r t e n s i t e - a u s t e n i t e boundary had d i sap - pea red . F u r t h e r m o r e , the re la t ionsh ip between As and p las t ic s t r a i n as found in the p r e s e n t study c o r r e - la tes with in te r face propagat ion cont ro l l ing m a r t e n - s i te r e v e r s a l . As deformat ion is in t roduced into the m a r t e n s i t e the d is loca t ion densi ty and the m a r t e n s i t e yie ld s t reng th i n c r e a s e . Hence, a l a r g e r dr iv ing force is needed for in te r face propagat ion through the m a r - t ens i te which r e s u l t s in a l a rge r t r ans i t i on t e m p e r a - tu re .

The gene ra l i n t e rp re t a t i on based on the p rev ious cons ide ra t ions is that m a r t e n s i t e r e v e r s a l is con- t ro l led by the m a r t e n s i t e yield s t rength . This i n t e r - p re ta t ion gives phys ica l mean ing to the gene ra l

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t h e r m o d y n a m i c m o d e l . T h e w e l l de f i ned A s i s d e t e r - m i n e d by the i n t r i n s i c m a r t e n s i t e y i e l d s t r e n g t h . As m a r t e n s i t e r e v e r s a l p r o c e e d s , d e f o r m a t i o n in the m a r t e n s i t e s u r r o u n d i n g the new a u s t e n i t e r a i s e s the m a r t e n s i t e y i e ld s t r e n g t h in tha t v i c i n i t y ; and h e n c e , a l a r g e r d r i v i n g f o r c e (h igher t e m p e r a t u r e ) i s r e q u i r e d fo r f u r t h e r t r a n s f o r m a t i o n . T h u s , the wide t e m p e r a t u r e r a n g e o b s e r v e d fo r m a r t e n s i t e r e v e r s a l i s e x p l a i n e d by an e v e r i n c r e a s i n g oppos ing f o r c e wh ich a c c o m p a n i e s the m a r t e n s i t e - t o - a u s t e n i t e t r a n s i t i o n . P l a s t i c s t r a i n s i n t r o d u c e d a t r o o m t e m - p e r a t u r e (below Ad) p r i o r to t r a n s f o r m a t i o n r a i s e the m a r t e n s i t e y i e ld s t r e n g t h t h e r e b y i n c r e a s i n g the b a r r i e r f o r i n t e r f a c e p r o p a g a t i o n ; thus , A s i n c r e a s e s wi th p l a s t i c s t r a i n in the m a r t e n s i t e .

Though the d e p e n d e n c e of A s on m a r t e n s i t e y i e l d s t r e n g t h can be e x p l a i n e d on the b a s i s of n u c l e a t i o n wh ich r e q u i r e s a d i s l o c a t i o n m e c h a n i s m , the m o r e p r o b a b l e e x p l a n a t i o n s e e m s to be tha t i n t e r f a c e p r o p - aga t ion c o n t r o l s m a r t e n s i t e r e v e r s a l .

3.4) O t h e r F e a t u r e s Of T h e E x p e r i m e n t a l Da ta

I t was po in t ed out e a r l i e r tha t fo r 5 p c t d e f o r m a t i o n o r g r e a t e r , As w a s l a r g e r fo r the 95 p c t m a r t e n s i t e s a m p l e s as c o m p a r e d to A s of the 50 p c t m a r t e n s i t e s a m p l e s . T h i s i s e x p l a i n e d by the r e l a t i v e a m o u n t of s t r a i n wh ich o c c u r s in the m a r t e n s i t e fo r a g i v e n t o t a l r e d u c t i o n in t h i c k n e s s . H a r d n e s s m e a s u r e m e n t s showed m o r e s t r a i n o c c u r r e d in the m a r t e n s i t e of the 95 pc t m a r t e n s i t e s a m p l e s fo r a g iven d e f o r m a t i o n . T h e r e f o r e , the y i e ld s t r e n g t h i n c r e a s e d m o r e , and the t r a n s i t i o n t e m p e r a t u r e i s h i g h e r .

In F i g . 4 i t was o b s e r v e d tha t the 33 to 67 pc t m a r t e n s i t e s a m p l e s a l l had the s a m e t r a n s i t i o n c u r v e wh ich d i f f e r e d f r o m the 95 p c t m a r t e n s i t e s a m p l e . As the p e r c e n t m a r t e n s i t e i n c r e a s e s the s i z e of the new m a r t e n s i t e p l a t e s b e c o m e s p r o - g r e s s i v e l y s m a l l e r . S ince A s i s not d e p e n d e n t upon the a m o u n t of m a r t e n s i t e p r e s e n t in a s a m p l e , the s m a l l p l a t e s i z e d o e s no t a f f e c t the i n i t i a t i on of the t r a n s i t i o n . I t i s p o s s i b l e , h o w e v e r , tha t the s m a l l p l a t e s wh ich t y p i c a l l y f o r m in p a r a l l e l r o w s b e t w e e n two l a r g e p l a t e s c a u s e d e f o r m a t i o n in the l a r g e p l a t e s wh ich in l o c a l r e g i o n s r a i s e s the m a r t e n s i t e y i e ld s t r e n g t h and t h e r e b y b r o a d e n s the t r a n s f o r m a t i o n c u r v e . T h i s s u g g e s t i o n i s b a s e d on the a s s u m p t i o n tha t g r e a t e r than 67 p c t m a r t e n s i t e i s r e q u i r e d b e f o r e a s i g n i f i c a n t change o c c u r s in the a m o u n t of s u c h d e f o r m a t i o n in the m a r t e n s i t e . I t i s a l s o p o s s i - b le tha t the f r a g m e n t a t i o n p r o c e s s of the s m a l l m a r - t e n s i t e p l a t e s c o n t r i b u t e s to the b r o a d e n i n g .

CONCLUSIONS

T h e e x p e r i m e n t a l r e s u l t s l e a d to the fo l l owing c o n c l u s i o n s :

1) F o r an F e - 3 0 . 3 wt p c t Ni a l loy p l a s t i c d e f o r m a - t ion app l i ed be low A d r a i s e s A s .

2) F o r s p e c i m e n s c o n t a i n i n g z e r o d e f o r m a t i o n A s w a s found to be i n d e p e n d e n t of the p e r c e n t m a r t e n - s i t e fo r the r a n g e 33 to 95 p c t m a r t e n s i t e . H e n c e , A s i s i n d e p e n d e n t of m a r t e n s i t e p l a t e s i z e .

3) T h e i n i t i a t i on of m a r t e n s i t e r e v e r s a l c o r r e l a t e s l i n e a r l y wi th the m i c r o h a r d n e s s (y ie ld s t r e n g t h ) of the m a r t e n s i t e . T h e i n c r e a s e in A s with m a r t e n s i t e y i e ld s t r e n g t h w a s m e a s u r e d in th i s e x p e r i m e n t to be 0.93~ p e r Knoop h a r d n e s s n u m b e r .

4) T h e c o r r e l a t i o n of A s with the m a r t e n s i t e y i e l d s t r e n g t h is c o n s i s t e n t wi th p r e v i o u s o b s e r v a t i o n s and the t h e r m o d y n a m i c a p p r o a c h fo r e x p l a i n i n g m a r - t e n s i t e r e v e r s a l . T h e d e p e n d e n c e of A s on m a r t e n - s i t e y i e l d s t r e n g t h can be e x p l a i n e d e i t h e r by n u c l e a - t ion which r e q u i r e s a d i s l o c a t i o n m e c h a n i s m or by i n t e r f a c e p r o p a g a t i o n c o n t r o l l i n g m a r t e n s i t e r e v e r s a l . T h e m o r e c o m p l e t e e x p l a n a t i o n a p p e a r s to be the one b a s e d on i n t e r f a c e p r o p a g a t i o n .

5) T h e m i c r o h a r d n e s s m e a s u r e m e n t s and the i n d e - p e n d e n c e of A s on p e r c e n t m a r t e n s i t e show tha t A s i s not s t r o n g l y i n f l u e n c e d by the y i e ld s t r e n g t h of the r e t a i n e d a u s t e n i t e .

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

T h e au tho r i s g r a t e f u l to R . A. G r a h a m , L . R . E d w a r d s , and T . V. N o r d s t r o m fo r t h e i r c r i t i c a l r e - v i e w of the m a n u s c r i p t . D u r i n g the c o u r s e of the w o r k he lp fu l d i s c u s s i o n s w e r e he ld wi th R . A. G r a h a m , R . W. Rohde , and L . R . E d w a r d s . T h e au tho r i s g r a t e - ful f o r the c a p a b l e t e c h n i c a l a s s i s t a n c e of G. T . H o l - m a n .

T h i s w o r k w a s s u p p o r t e d by the U. S. A t o m i c E n e r g y C o m m i s s i o n .

R E F E R E N C E S

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Box 5800, Albuquerque, New Mexico, 1971.

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