HAL Id: jpa-00225351
https://hal.archives-ouvertes.fr/jpa-00225351
Submitted on 1 Jan 1985
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of
sci-entific research documents, whether they are
pub-lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
INTERNAL FRICTION AND DILATOMETRIC
QUANTITATIVE ANALYSIS OF THE ISOTHERMAL
MARTENSITIC TRANSFORMATION IN Fe-Ni-C
ALLOYS
C.A.V. de A. Rodrigues, C. Prioul
To cite this version:
JOURNAL DE PHYSIQUE
Colloque C10, suppldment au n012, Tome
46,
ddcembre1985
page C10-G57INTERNAL FRICTION AND DILATOMETRIC QUANTITATIVE ANALYSIS OF THE ISOTHERMAL MARTENSITIC TRANSFORMATION IN Fe-Ni-C ALLOYS
C.A.V. DE A. RODRIGUES AND
C.
PRIOULEcole Centrale des Arts et Manufactures, Laboratoire des
MatBriaux,
92290Chstenay-Malabry, F n n C e
R6sum6
-
Nous montrons que le frottement intirieur est proportionnel au coefficient de dilatation lors de la transformation martensitique isotherme d'alliages Fe-Ni-C. Aucune contribution li6e2
la mobilit6 des dislocations n'6tant observge, nous sugg6rons que le frottement intirieur est da uniquement 1 la mobilit6 de l'interface 3 - 0 ( ' .Abstract
-
Internal friction is shown to be proportional to expansivity during the isothermal martensitic transformation of Fe-Ni-C alloys. Since no contribution due to dislocation mobility was observed in our internal friction results, we suggest that internal friction is due only to the mobility of the 8-
&'interface.I
-
INTRODUCTIONIn a previous study [I], internal friction was shown to be proportional to expan- sivity (Q-1 = A x
a
) during the isothermal martensitic transformation of a Fe-19Ni-0.51C (wt.%) alloy havi& a subzero Mb temperature. A detailed quali- tative analysis of this isothermal transformation was presented recently for Fe-Ni and Fe-Ni-C alloys [2].The purpose of this paper is to study the influence of experimental conditions (heating rate and test frequency) on the coefficient of proportionality A for several Fe-Ni-C alloys.
I1
-
EXPERIMENTAL PROCEDUREThe chemical composition, the grain size, and the Mb temperatures of the alloys studied in the present investigation, which were prepared as previously [2], are given in Table I.
a o&ned by t i e r d i d dilatometry
h O ?i
Table I
-
Chemical composition of the alloys.Internal friction
measurements
on cylindrical specimens (diameter3
mm; useful length 50 mm) were carried out on an automatic inverted torsion pendulum[J].
Unless otherwise stated, the strain amplitude was less than €0 = 5 r 10-6 andC Ni Mn Si P 5 Grain size (pm) Mb(Kl
.
Exprirnmt* Tuhn',,
,,
zrraN
mtim D l a m t r y IC10-658 JOURNAL DE PHYSIQUE
the t e s t frequency was 1.5 Hz. Dilatometric r e s u l t s were obtained with a tube- type v i t r e o u s s i l i c a d i f f e r e n t i a l dilatometer and an automatic data a c q u i s i t i o n and processing system [4]. Cylindrical specimens were 20 mm i n length and 4 mm i n diameter. The expansivity (o< ) was obtained by taking the derivative of a cubic- s p l i n e polynomial f i t t i n g performed t o the AL/L experimental data.
For both techniques, samples having an a u s t e n i t i c s t r u c t u r e were s e t up a t room temperature. After i n s i t u quenching t o Tq = 77 K (cooling r a t e : *c = 1.5 K/min) and a 100 minute isothermal holding a t t h i s temperature, meqsurements were per- formed during reheating t o room temperature (heating r a t e Th : see i n s e r t i n Figures). A mixed s t r u c t u r e containing about 85 pct of l e n t i c u l a r martensite and 15 p c t of retained a u s t e n i t e i s qbtained a f t e r such a thermal cycle.
I11
-
EXPERIMElNTAL RESULTSWe have reported i n Figures l ( a ) and (b) the influence of the heating r a t e ( t h ) on the i n t e r n a l f r i c t i o n and expansivity peaks obtained during the isothermal m a r t e n s i t i c transformation. From these peaks, obtained a s previously [1,2], we found the following r e l a t i o n s h i p s , f o r a l l o y 4 :
2
~ - ~ = 1 . 7 0 x l O ~ x o ( f o r T q = 7 7 K , f c = 1 . 5 K / m i n a n d f h = 1 . 5 K / m i n ;
1
~ - ' = 0 . 1 8 x 1 0 x o < f o r T q = 7 7 K , T c = 1 . 5 ~ / m i n a n d T h = O . l 5 ~ / m i n . Comparison between curves 1 and 2 shows t h a t the temperature of t h e maxima decrease with decreasing heating r a t e .F . IPI I LSI t I-LISIV* 2 - 1.SW.r 2 D 2
-
6 t I L, 1 0 100 200 300 TEMPERATURE (K) ( a ) i n t e r n a l f r i c t i o n (b) expansivi t y Fig. 1-
Influence of the heating r a t e .The influence of the t e s t frequency (N) on t h e i n t e r n a l f r i c t i o n evolution and i n t e n s i t y of the maxima i s reported i n Figures 2(a) and (b) respectively f o r a l l o y 4. Figure 2 ( a ) shows t h a t t h e temperature of the maxima i s not frequency dependent whereas Figure 2(b) i n d i c a t e s t h a t the i n t e n s i t y of the maxima i s inversely proportional t o the t e s t frequency.
We have reported i n Table I1 the values of the propoftionality c o e f f i c i e n t A
(Q-1 = A x o ( ) obtained f o r a l l o y s 1 t o
4
(Tq = 77 K; Tc = Th = 1.5 K/min; and N = 1.5 Hz). I n order t o express i n t e r n a l f r i c t i o n a s a function of martensiteF i g . 2
-
I n f l u e n c e of t h e t e s t frequency on t h e i n t e r n a l f r i c t i o n p l o t ( a ) and Q-lmaX. (b).
b u r s t , a t h e r m a l and i s o t h e m a l k i n e t i c s ( B = 8.049 x 10-3). Values of B o b t a i n e d f o r a l l o y s 2 and 4, u s i n g t h e same procedure a s d e s c r i b e d i n [5], a r e a l s o r e - ported i n Table 11. R e s u l t s p r e s e n t e d i n t h i s Table show t h a t c o e f f i c i e n t A d e c r e a s e s , whereas c o e f f i c i e n t B i n c r e a s e s , with i n c r e a s i n g carbon c o n t e n t .
AL
Table I1
-
Values of A (Q-l= A x d) and B (-= L B x f ) f o r Fe-Ni-C a l l o y s . I V-
DISCUSSION Alloy 1 2 3 4The e x i s t e n c e of t h e r e l a t i o n s h i p Q -1 = A x & was demonstrated p r e v i o u s l y
[I].
However, F i g u r e s 1 and 2 i n d i c a t e t h a t A depends on experimental c o n d i t i o n s ( h e a t i n g r a t e and t e s t frequency) and on t h e chemical composition of t h e a l l o y
co able
11). Values o f A found f o rh
= 1.5 K/min and Th = 0.15 K/min ( ~ i ~ s . l ( a ) and l ( b ) ) show t h a t A i s p r o p o r t i o n a l t o h e a t i n g r a t e . Furthermore, s i n c e i n t e r n a l f r i c t i o n i s i n v e r s e l y p r o p o r t i o n a l t o t h e t e s t frequency ( ~ i g s . 2 ( a ) and 2 ( b ) ) , Q-1 = A x oC can be w r i t t e n a s :h
=c
.
-
.
CK(T)J (1) Nri?l
BI+=
B x f l - 8.104 x - 8 . 6 9 5 ~ A (GI-' = A x a 1 3.9 x lo2 2.7 x lo2 2.3 x lo2 1.7 x 10'C : c o n s t a n t ; N : t e s t frequency; H ( T ) ~ + ~ and Q - 1 ( ~ ) [ h a r e .e x p a n s i v i t y and i n t e r n a l f r i c t i o n v a l u e s measured a t t h e same h e a t i n g r a t e Th. Assuming t h a t thermal expansion i s p r o p o r t i o n a l t o m a r t e n s i t e c o n t e n t whatever t h e temperature,
JOURNAL
DE
PHYSIQUEo ( ( ~ )
= A ( & )
= B . d f + f . d BdT L dT dT ( 2 )
Considering t h a t t h e second term can be neglected we have f o r expression ( 1 ) :
This r e l a t i o n s h i p i s i n agreement with t h e formalism proposed by Belko e t a l . [6] and Delorme e t a l . [7] f o r athermal m a r t e n s i t i c transformations. However, s i n c e f o r i s o t h e r m a l m a r t e n s i t i c transformations m a r t e n s i t e content i s time and temperature dependent, expression ( 1 ) i s v a l i d only f o r comparison between i n t e r n a l f r i c t i o n and d i l a t o m e t r i c e v o l u t i o n s obtained a t t h e same h e a t i n g r a t e . We suggest t h a t i n t e r n a l f r i c t i o n measured during m a r t e n s i t i c transformation
can be expressed a s :
g-1 = g-1 + Q-1
1 2 ( 4 )
The first term ( Q - l ) , which we a s s o c i a t e t o t h e m o b i l i t y of t h e 5
-
d' i n t e r f a c e , i s observed f o r \ow frequency experimentselor or me's
model [TI) o r f o r high amplitude experiments (Dejonghe's model [ e l ) . Then e x p r e s s i o n( 3 )
i n d i c a t e s t h a t t h e m o b i l i t y of t h e 'd - c%' i n t e r f a c e is s m a l l e r i n t h e presence of carbon s i n c eA x B d e c r e a s e s with i n c r e a s i n g carbon c o n t e n t (Table 11). I n agreement w i t h Koshimiau and Benoit [ 9 ] , ~ o t t K a r d t ' s work
[lo]
suggests t h a t , i n Cu-Zn-A1 a l l o y s , t h e second term of e x p r e s s i o n ( 4 ) , observed f o r high frequency experiments, i s due t o d i s l o c a t i o n mobility. We b e l i e v e t h a t t h i s second term, i n e x i s t e n t i n t h e case of t h e isothermal m a r t e n s i t i c transformation s i n c e Q-1 tends t o zero f o r high frequency experiments (Figures 2 ( a ) and 2 ( b ) ) b u t observed during t h e athermal m a r t e n s i t i c transformation i n Fe-Ni-C a l l o y s [ll], can a l s o be a t t r i b u t e d t o d i s l o c a t i o n mobility. The absence of t h e d i s l o c a t i o n m o b i l i t y c o n t r i - b u t i o n (Q-9) d u r i n g t h e i s o t h e r m a l m a r t e n s i t i c transformation i s i n agreement with previous s t u d i e s [2], i n which we suggested t h a t t h e i s o t h e r m a l transforma- t i o n reduces t h e l e v e l of t h e i n t e r n a l s t r e s s e s i n t h e v i c i n i t y of t h e athermal m a r t e n s i t i c p l a t e s . Consequently, we propose t h a t t h e second term o f expression ( 4 ) should be a s s o c i a t e d t o t h e m o b i l i t y of t h e d i s l o c a t i o n s c r e a t e d by t h e athermal m a r t e n s i t i c transformation.REFERENCES
[I]
PRIOUL C., RODRIGUES C.A.V. de A., and PLUSQWLLEC J., Journal de Physique 44 (1983) C9-229.[2] ~ D R I G U E S C.A.V. de A., PRIOUL C . , and HYSPECKA L., Metall. Trans. A
15A
(1984) 2193.[3] PRIOUL C., PASQUET M., CARRARD M., PLUSQUELLEC J., and AZOU P., M6m. S c i . Rev. M6t. 79 (1982) 203.
[4] RODRIGUES ~ A . v . d e A * , PLUSQUELLEC J . , and AZOU P., M6m. S c i . Rev. M6t.
79
(1982) 149.[5] RODRIGUES C.A.V. de A., SOJKA J., and HYSPECKA L., Proceedings of t h e I n t e r n a t i o n a l Conference on S t e e l s f o r High Parameters S e r v i c e Conditions, 1985, Ostrava, C ~ e c h o s l o v a k i a .
[6] BELKO V. N.
,
DARINSKIY B.M.,
POSTNIKOV V. S.,
and SHARSHAKOV I. M.,
Physics of Metals and Metallography3
(1969) 140.[7] DELORME J.F., SCHMID R., ROBIN I., and GOBIN P., J o u r n a l de Physique
2
(1971) C2-101.DEJONGHE W., DE BATIST R., and DELAEY L., S c r i p t a Met.
