In this paper the results of a detailed study of the isothermal martensitic transformation kinetics in an Fe-23.2wt.%Ni-2.8wt.%Mn al- loy are reported.
Materials Science and Engineering, 80 (1986) 65-74
65
The Kinetics of Isothermal Martensitic Transformation in an F e - 2 3 . 2 w t . % N i 2 . 8 w t . %Mn Alloy G. GHOSH and V. RAGHAVAN
Department of Applied Mechanics, Indian Institute of Technology, New Delhi 110016 (India) (Received July 29, 1985)
ABSTRACT
In this paper the results o f a detailed study o f the isothermal martensitic transformation kinetics in an F e - 2 3 . 2 w t . % N i - 2 . 8 w t . % M n alloy are reported. The transformation kinetics were determined as a function o f test temperature, superimposed elastic stress field and prior plastic deformation o f the austenite. Extensive quantitative metallographic measurements show that the overall transformation kinetics agree very well with the model that incorporates the vital contribution o f autocatalysis. On the assumption that the ratecontrolling step in martensitic nucleation is the thermally activated motion o f dislocations, the activation energies for nucleation were calculated under an applied elastic stress or in work-hardened austenite. These show good agreement with the experimentally determined activation energies. The present results support the Olson-Cohen suggestion that the critical step in martensite nucleation is the thermally activated motion o f the partial dislocations bounding the fault embryo.
(the burst t e m p e r a t u r e ) or by increasing the rate of the isothermal transformation [4]. For testing the validity of the kinetic models and of the critical step in t he nucleation of martensite, as well as in the understanding of t he effect of superimposed stress fields or magnetic fiels [5] and of the prior deformation of t he austenite, the isothermal m o d e is the most suitable. The t ransform at i on here can be followed as a funct i on of b o t h time and temperature, and an activation energy can be experimentally determined. In this work t he results of a detailed study of the effects of t h e t em perat ure, the superimposed elastic stress field and the prior plastic d e f o r m a t i o n of t he austenite are reported. Extensive quantitative metallographic measurements were made on t he isothermally f o r m e d martensite. The results are used to test the models proposed for the isothermal kinetics [ 6 , 7 ] , for the effect of the superimposed elastic stress field [3] and for the critical step in nucleation [8].
2. EXPERIMENTAL PROCEDURES 1. INTRODUCTION It is well k n o w n t hat martensite in iron alloys can f o r m athermally as a f u n c t i o n o f decreasing t e m p e r a t u r e , isothermally as a f u n c t i o n o f time at a cons t a nt holding temperature, or in th e f or m of a burst. There are several c o m m o n characteristics bet w e e n these three modes o f f o r m a t i o n and a t t e m pt s have been made to find correlations be t w een t h e m [1, 2]. F o r example, a superimposed elastic stress field stimulates t he t r a n s f o r m a t i o n in all t h e modes, b y increasing Ms (the t e m p e r a t u r e at which th e t r a n s f o r m a t i o n o f austenite to martensite starts during cooling) [3] or Mb 0025-5416/86/$3.50
5 m m × 5 m m forged bars of an F e - N i - M n alloy were hom ogeni zed in evacuated sealed V y c o r tubes for 60 h at 1423 K. N ext a layer o f 0.2 m m was ground f r o m the surface to ensure the removal o f any manganese-depleted layer. Chemical analysis after homogenization showed t hat the alloy contained 23.2 wt.% Ni, 2.8 wt.% Mn and 0.009 wt.% C. T he bars were t hen cold drawn with intermediate anneals into wires of 1.25 m m diameter. Each intermediate anneal was followed by electropolishing to remove t he surface layer. The final anneal was either at 1273 K for 10 min or at 1173 K for 10 min, which established a grain size o f 0.048 or 0.019 mm. Nickel lead © Elsevier Sequoia/Printed in The Netherlands
66 wires were spot welded to the wire specimens of 60 mm length and a " d o p i n g " anneal was given at 1073 K for 10 min. This treatment does not alter the grain size b u t slightly increases the carbon concentration near the surface and prevents the preferential nucleation of surface martensite [9]. The effect of temperature was followed by transforming the virgin austenite at nine temperatures between 203 and 77 K. Isopentane was used in the low temperature bath cooled by liquid nitrogen. The bath temperature was maintained to within + 0.3 K. The progress of the transformation was followed b y means of an Autobalance resistance bridge, which can easily detect 0.1% of martensite. The change in resistance was calibrated in terms of the volume fraction f of martensite b y means of point counting. The microstructure revealed that the morphology was fully plate like at 193 K and below. Figure 1 shows the microstructure of the sample isothermally transformed at 77 K. The number N v o f martensire plates per unit volume of the specimen, the mean volume V (= f/Nv) of the plates and the nucleation rate N (= (dNv/dt)(1/(1 -- f)}) were obtained by quantitative metallography
[10, 11]. To study the effect of prior plastic strain, the d o p e d wires were deformed at r o o m temperature to various strains from 0.005 to 0.05 in a tensometer and then isothermally transformed at subzero temperatures. The grain size of the samples used for these experiments was 0.048 mm. The tests were carried out at 188, 173, 133 and 77 K. The elastic stress ex-
Fig. 1. Microstructure of the sample isothermally transformed to martensite at 77 K.
periments were performed on samples with a grain size of 0.019 mm. The container with the low temperature bath and the specimen were positioned between the grips of the tensometer during the test. A constant load was maintained throughout the isothermal test, Tests were carried o u t at three temperatures: 188, 130 and 77 K. In all cases the maximum tensile stress applied was less than 60% of the yield strength of the austenite at that temperature. At this stress level, there was no plastic deformation aided b y the transformation. This was confirmed by thin foil examination as well as by comparing the stress -strain curves of samples transformed to the same fraction of martensite with and without the applied stress.
3. THE OVERALL TRANSFORMATION KINETICS The overall transformation kinetics exhibits a C curve behaviour [12]. It has been analysed using the R a g h a v a n - E n t w i s l e - P a t i , C o h e n model [6, 7] which incorporates the autocatalyric effect in terms of the parameter p. The nucleation rate/V [ 10] and the overall transformation rate dr~dr [7] are c o m p u t e d from the following equations:
IV={ni+f(P--1)}pexp\ d-t-= ni + f
--
(_~Wq
RT]
(1--f)pexp\
dNv × {St + d ( l n N v ) }
(1)
RT/× (2)
where ni is the initial number of nucleation sites (taken here to be 1013 m-3), u ( ~ 10 za s-1) is the lattice vibration frequency, AWa is the activation energy for nucleation and T is the test temperature in kelvin. The value o f the vibration frequency term will depend on the details of the nucleation process. For example, if the nucleation involves the motion o f an array of dislocations as in the OlsonCohen model [ 13], the vibration frequency term may be orders of magnitude smaller and the derived activation energies will also be significantly smaller. It turns o u t that such a shift in the absolute values of the activation energies does n o t materially alter the correlations reported later in this paper between cal-
67 TABLE 1 The kinetic parameters for t h e isothermal martensitic t r a n s f o r m a t i o n derived f r o m eqns. (1) and (2)
Test temperature (K)
N°b$o.o02 (X 1010 m-3 E l )
~rcal0.oo2 a (X 1010 m-3 s-1)
P (x 1016 rn-3)
AWa (X 10- 2o J event-1)
203 193 183 173 163 153 143 133 77
0.7 1.5 6.2 8.5 12.2 5.5 4.7 3.9 1.0
0.6 0.8 4.5 11.1 12.5 6.7 5.2 3.6 1.2
1.05 1.10 1.10 1.20 1.35 1.30 1.35 1.40 1.45
10.81 10.21 9.85 8.58 8.08 7.71 7.25 6.82 4.07
aCalculated f r o m eqn. (1).
TABLE 2 T h e kinetic parameters for the isothermal martensitic t r a n s f o r m a t i o n under a superimposed elastic stress
Test temperature
Applied stress
(K)
(MPa)
188 188 188 188 188
J~°bS0.o02 (X 1 0 1 ° m -3 s-1 )
Ncalo.002 a (X 1010 m-3 s-1)
P (X 1016 m-3)
AWa (10 -20 J event-1)
0.0 9.8 29.4 49.0 68.6
1.1 2.8 3.7 21.5 75.5
0.9 2.5 4.9 17.5 66.7
1.10 1.15 1.20 1.25 1.30
9.80 9.62 9.41 9.10 8.79
130 130 130 130 130
0.0 19.6 49.0 68.6 88.2
0.9 2.5 4.8 10.5 41.5
0.6 1.6 3.8 12.9 45.0
1.40 1.40 1.45 1.50 1.60
6.90 6.76 6.62 6.41 6.21
77 77 77 77 77 77
0.0 9.8 19.6 59.0 88.2 118.0
0.5 1.0 1.2 1.3 2.5 3.2
0.6 0.8 0.9 1.4 1.8 2.7
1.45 1.50 1.55 1.65 1.75 1.90
4.093 4.083 4.072 4.044 4.030 4.003
aCalculated f r o m eqn. (1).
culated and experimentally derived activation energies. The values of the parameters p and AWa obtained from the best fit with eqn. (2) are listed in Tables 1-3. Table 1 shows that, as a function of decreasing test temperature, the autocatalytic parameter p increases slowly b u t continuously. From Table 2, it is seen that the autocatalytic parameter also increases with increasing level of the applied stress at a constant test temperature. Table 3 shows that it decreases with increasing degree of prior plastic deformation of the austenite. In all
cases the directly measured initial nucleation rate/~/°~0.0o 2 at f = 0.002 and that obtained from eqn. {1) are in good agreement. The isothermal transformation curves were calculated using eqn. (2). The agreement between the experimental and the calculated curves is very good in all cases, except for some deviation in the later stages in some cases. For example, the experimental and the calculated curves are compared in Figs. 2 - 4 as a function of test temperature (Fig. 2), applied stress at 77 K (Fig. 3) and prior plastic strain at 173 K (Fig. 4).
68
TABLE 3 The kinetic parameters for the isothermal martensitic transformation in plastically deformed austenite
Test temperature
Plastic strain
]~°bs0.002
(K)
ep
(X 1010 m-s s-1)
188 188 188 188
0.000 0.005 0.010 0.020
1.5 0.7 0.4 0.1
173 173 173 173 173 173
0.000 0.005 0.010 0.020 0.030 0.050
8.5 4.9 1.2 0.3 0.2 0.2
133 133 133 133 133
0.000 0.010 0.020 0.030 0.050
3.9 1.1 0.5 0.1 0.05
77 77 77 77 77
0.000 0.005 0.010 0.020 0.030
1.0 0.7 0.5 0.2 0.1
]~Tcal0.002a (X 1010 m-3 s-1)
p (X 1016 m-3)
AWa (x 10-20 J event-1)
2.4 0.5 0.3 0.1
1.10 1.05 1.00 0.95
9.69 10.11 10.25 10.46
11.1 3.6 0.8 0.4 0.2 0.1
1.20 1.25 1.25 1.20 1.15 1.05
8.58 8.86 9.20 9.38 9.48 9.62
3.6 0,5 0.3 0.2 0.06
1.35 1.30 1.25 1.20 1.10
6.82 7.18 7.25 7.32 7.53
1.2 0.6 0.4 0.2 0.1
1.45 1.40 1.35 1.30 1.20
4.07 4.15 4.18 4.23 4.27
aCalculated from eqn. (1). 451
I
--
I
4
J
I
I
I
r
[
2 7 - - ~
]
[
I
J
I
I
I
~ p p { MPQJ 4C
:i 2:::::
3~
yJ
o
3(
w
~
~51
//
_
15
10
5
..~-~v 20
Z~O
GO
8{3
100
120
140
160
180
TIME (rain)
0
20
-
40
60
80
100
,~-"~----T~120
140
_ 160
180
TIME (rain)
Fig. 2. Comparison of the experimental and the computed isothermal transformation curves at the indicated test temperatures: , experimental;- - - , computed.
Fig. 3. Comparison of the experimental and the computed isothermal transformation curves under a superimposed elastic stress Oapp (test temperature, 77 K): ~ , experimental;- - -, computed.
4. THE EFFECT OF APPLIED STRESS
rate rather than the mean volume of the mart e n s i t i c p l a t e s . W h e n t h e a p p l i e d stress is a b o u t 6 8 MPa, t h e i n i t i a l n u c l e a t i o n r a t e i n c r e a s e s b y a f a c t o r o f 70 a t 1 8 8 K, b y a f a c t o r o f 1 2 at 130 K and by a f a c t o r of 3 at 77 K (Table 2). T h e s t i m u l a t i n g a c t i o n o f t h e a p p l i e d stress
T h e a p p l i e d stress f i e l d s t i m u l a t e s t h e t r a n s f o r m a t i o n , as c a n b e s e e n f r o m t h e t r a n s f o r m a t i o n c u r v e s i n Fig. 3, T h e m a j o r e f f e c t o f t h e a p p l i e d stress is t o i n c r e a s e t h e n u c l e a t i o n
69 q
F
T
T--~
I
I
-2.25
4£p O0
I
I
I"
I
I
I
I
--
35"
~o~
'E -2,50
0.005 u~
~
~
%
0.010
z 20I o
0,020
w -" 4.3
< :) u __1 < c3 .U
/
I, 9,8
x
118-0,,~
× 4,00
~3.95
'
(a)
• 0.005
/
t..)
