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Growth of austenite from as-quenched martensite during intercritical annealing in an Fe–0.1C–3Mn–1.5Si alloy
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Acta Materialia 61 (2013) 697–707 www.elsevier.com/locate/actamat
Growth of austenite from as-quenched martensite during intercritical annealing in an Fe–0.1C–3Mn–1.5Si alloy R. Wei a, M. Enomoto a,⇑, R. Hadian b, H.S. Zurob b, G.R. Purdy b b
a Department of Materials Science and Engineering, Ibaraki University, Hitachi 316-8511, Japan Department of Materials Science and Engineering, McMaster University, Hamilton, Ontario, Canada L8S4L8
Received 19 April 2012; received in revised form 12 October 2012; accepted 16 October 2012 Available online 10 November 2012
Abstract The growth of austenite from as-quenched martensite during intercritical annealing was studied in a quaternary Fe–0.1C–3Mn–1.5Si alloy. Fine austenite grains either grew from interlath-retained austenite films or were newly nucleated at lath and martensite packet boundaries. Both types grew to a size comparable to the width of the martensite lath. It was found both metallographically and by dilatometry that the austenite grew to an amount in excess of the volume fraction at final equilibrium. Simulation by DICTRA, which assumed local equilibrium at the a/c boundary, confirmed that the development of austenite is composed of three stages: initial negligible-partitioning growth controlled by rapid carbon diffusion in ferrite, which is gradually replaced by carbon diffusion in austenite; intermediate slow growth, controlled by diffusion of Mn and/or Si in ferrite; and a final stage controlled by diffusion of substitutional elements in austenite for final equilibration, which may result in the shrinkage of austenite. The formation of austenite in excess of the equilibrium amount is considered to occur due to very slow substitutional diffusion in the growing austenite compared to the boundary migration. Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Intercritical annealing; Austenite; Martensite; Local equilibrium; Growth kinetics
1. Introduction Re-austenization is a process of fundamental importance because low-alloy steels are heated in the (a + c) two-phase and the c single-phase regions during normalization, controlled rolling, forging and welding. The mechanisms of the austenization reaction are complex because it can occur from a variety of initial microstructures, such as cold-rolled or recrystallized ferrite, as-quenched or tempered martensite, or a mixture of ferrite and cementite or pearlite [1–10]. Moreover, alloying elements exert their influence in many ways at different stages of transformation. Indeed, Speich et al. [5] reported that the growth of austenite from the ferrite and pearlite mixture in a series of 1.5% Mn steels containing 0.06–0.2% C was characterized by three stages: the
⇑ Corresponding author. Tel.: +81 294 38 5058; fax: +81 294 38 5226.
E-mail address: [email protected] (M. Enomoto).
growth of austenite into pearlite; slower growth, controlled by either carbon diffusion in austenite at higher temperatures or Mn diffusion in ferrite at lower temperatures; and then final equilibration at a rate controlled by Mn diffusion in austenite. The first two stages were explored experimentally using microanalytical techniques and were numerically modeled by Wycliffe et al. for ternary Fe–C–Mn [7] and ˚ gren conducted comquaternary Fe–C–Mn–Si alloys [8]. A puter simulations of austenitization [11], and affirmed that the Mn-rich layer formed in austenite close to the a/c interface should have a large influence on late-stages austenite growth. Atkinson et al. [12] derived analytical expressions of the parabolic growth rate constants of austenite from ferrite and cementite mixture in ternary alloys assuming local equilibrium, and discussed the influence of alloying elements on the growth of austenite. In this report we focus on the austenitization from asquenched martensite. According to the simulation of isothermal annealing of a dual-phase steel [11], the volume
1359-6454/$36.00 Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.actamat.2012.10.019
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fraction of austenite exceeded the equilibrium amount before the system reached final equilibrium. This is in marked contrast to the forward ferrite transformation, in which we very often observe incomplete transformation; the transformation stops before the volume fraction reaches its final equilibrium value [13]. A quaternary Fe– 0.1C–3Mn–1.5Si alloy was employed to avoid carbide formation during heating to intercritical annealing temperature. The measured volume fractions of austenite were compared with simulation, assuming local equilibrium at the migrating a/c boundary. 2. Experimental procedure A high-purity quaternary Fe–C–Mn–Si alloy was vacuum-induction melted and hot-rolled to a plate of 10 mm thickness at 1200 °C. The chemical composition of the alloy is shown in Table 1. After homogenization at 1200 °C for 12 h, the plate was cut and cold-rolled to sheets of 1 mm in thickness. Specimens 8 12 1 mm3 in size were austenitized at 1200 °C for 10 min and quenched in iced brine to form martensite. The Ms temperature of this alloy was calculated to be 405 °C [14]. The specimens were then isothermally reacted in a salt bath at temperatures from 690 to 760 °C for varying times and quenched in iced brine. They were then mechanically polished and etched in 3% nital for optical microscopy. The volume fraction of austenite was measured by point counting. The volume fraction of austenite was also measured by dilatometry. Dilatometric samples (4 10 1 mm3) of quenched martensite were heated up to intercritical annealing temperatures, i.e. 690, 720 and 760 °C, at a rapid heating rate of 100 °C s1 and held for 1800, 1200 and 900 s, respectively. At the end of treatment the samples were rapidly cooled to 250 °C at 100 °C s1, then cooled to room temperature at 15 °C s1. One specimen quenched from the austenitizing temperature and a specimen quenched and intercritically annealed at 760 °C for 600 s were prepared for transmission electron microscopy (TEM) by electropolishing using a voltage of 25 V and a solution of 10% perchloric acid and 90% methanol maintained at 50 °C. The microstructure and the orientation relationship between austenite grains and the matrix were examined on a Philips CM12 transmission electron microscope at 120 kV. 3. Results 3.1. Microstructure of the as-quenched martensite and intercritically annealed specimen Fig. 1a and b are TEM micrographs of a specimen quenched from the c single phase field, which show the
presence of retained austenite films at lath boundaries. Fig. 1c shows Bain related diffraction patterns of martensite lath and retained austenite. Fig. 2a–c are optical micrographs of a specimen which was isothermally reacted at 760 °C for various times. Copious fine austenite grains grew from the martensite lath boundaries at an early stage, as shown in Fig. 2a. In Fig. 2b fine austenite grains were observed inside the wide laths, which may indicate that nucleation occurred within the laths. The size of the austenite grains appears to be restricted by the width of the martensite lath. Eventually, the microstructure was composed of alternate fine ferrite and austenite grains elongated in parallel to the original lath boundaries, as shown in Fig. 2c. Though not shown in the micrographs, austenite grains were also nucleated at packet and block boundaries, and at prior austenite boundaries. Fig. 3 shows TEM micrographs of a specimen intercritically annealed at 760 °C for 600 s and then quenched. In this specimen all the austenite grains transformed into martensite upon quenching from the intercritical temperature, which can be seen as regions 2 and 4 in this image. Ferrite grains formed during annealing, originating from the martensite lath, are shown as regions 1 and 3. It can be seen from the diffraction patterns that the ferrite in region 1 shares almost the same orientation variants with the martensite of region 2, and the same relationship exists between the ferrite of region 3 and the martensite of region 4. While regions 1 and 2 have about 8 degrees of misorientation with regions 3 and 4, it is possible that regions 1 and 3 originated from martensite laths of different variants and the austenite grains transformed into martensite of identical orientation as those of ferrite. A similar observation was made in other areas, which seems to indicate that the minimization of interfacial energies dictates the selection of the martensite variant [15,16]. 3.2. Dilatometric results Fig. 4a–d show the dilatometric response obtained at three different temperatures of intercritical annealing as a function of time and temperature. The strain contraction at the holding temperature is attributed to the formation of austenite during holding. It can be seen in Fig. 4a that the kinetics of austenite formation varied considerably over the temperature interval of 30–40 °C. In Fig. 4b–d the dilatometric curves deviated significantly from a straight line during heating. This is presumably because thin films of retained austenite could start to grow without a nucleation barrier. Hence, the strain contraction was measured from the dashed line extrapolated from the low-temperature part, which may more closely represent the total amount of austenite. The Ms temperature of the austenite formed
Table 1 Chemical composition of alloy (mass%). C
Mn
Si
P
Al
S
N (ppm)
O (ppm)
0.099
3.00
1.51
0.002
0.003
0.001
9
10
R. Wei et al. / Acta Materialia 61 (2013) 697–707
(a)
699
(b)
1 µm
1 µm
002α
(c) 002γ
111γ
011α//111γ
Fig. 1. (a) TEM micrograph (bright-field image) of a specimen quenched from the austenitizing temperature, (b) dark-field image using a (0 0 2)c diffraction spot and (c) corresponding selected area diffraction (SAD) pattern. The beam direction is approximately parallel to the [1 0 0]a and ½1 1 0c directions.
(a)
(b)
(c)
20 µm Fig. 2. Optical micrograph of a specimen annealed at 760 °C (a) for 30 s, (b) for 180 s and (c) for 600 s.
700
R. Wei et al. / Acta Materialia 61 (2013) 697–707
Fig. 3. TEM micrographs of a specimen annealed at 760 °C for 600 s and SAD patterns taken from regions 1–3.
during intercritical annealing was determined only for a specimen annealed at 760 °C, in which a steep increase of the curve was observed at 320 °C. For a specimen annealed at 720 °C, austenite grains may have transformed partially to martensite below 250 °C, and at 690 °C the Ms temperature decreased further, presumably to a subzero value; in this case, all the austenite grains probably remained untransformed at room temperature. This is primarily due to the greater extent of Mn enrichment in austenite at lower holding temperatures. Table 2 summarizes the Ms temperature, strain contraction determined from dilatometry and Mn and Si concentrations at final equilibrium, although the equilibrium was not achieved during holding at each temperature. Recrystallization did not occur in this alloy during heating. The strain contraction caused by annihilation of dislocations during recovery is likely to be an order of magnitude smaller than those shown in the table [17].
4. Discussion 4.1. Graphical construction of the interfacial tie-line of the growth of austenite under local equilibrium In the a!c transformation, either carbon or alloying element diffusion is the rate-controlling process of the growth of austenite. In order to get an overall picture of the growth mode, an Fe–0.1C–3Mn ternary alloy is first discussed with reference to Fig. 5a–c. Taking an analogy of ferrite growth in the c!a transformation [18–20], the boundary between partitioned (PLE) and negligible-partitioned (NPLE) growth of austenite can be drawn from the intersection of the c/(a + c) phase boundary with the axis of Mn concentration (point A) to the intersection of the a/(a + c) phase boundary with the axis of carbon concentration (point B) [12]. Within the (a + c) two-phase field, the growth of austenite occurs under PLE and NPLE
R. Wei et al. / Acta Materialia 61 (2013) 697–707
701
0.012 o
690 C, 1800s
0.010
Strain
0.008 0.006 0.004 0.002 0.000 -0.002 0
100
200
300
400
500
600
700
800
600
700
800
Temperature,ºC
(a)
(b) 0.012
0.012 o
760 C,900s
0.010
0.008
0.008
0.006
0.006
Strain
Strain
o
720 C,1200s
0.010
0.004
0.004
0.002
0.002
0.000
0.000
-0.002
-0.002
o
0
100
200
300
400
500
600
700
800
320 C
0
100
200
300
400
500
Temperature,ºC
Temperature,ºC
(c)
(d)
Fig. 4. Dilatometric strains accompanying heating, intercritical annealing and cooling. (a) High-temperature strain as a function of time for intercritical annealing treatments of 690 °C for 1800 s; 720 °C for 1200 s; and 760 °C for 900 s. A strain of 0.007 on heating corresponds approximately to a temperature of 550 °C. (b–d) The full dilatometric strain paths for the three intercritical treatments.
Table 2 Ms temperature and strain contraction determined from dilatometry. Isothermal holding
Ms, °C
Concentration in austenite Strain at equilibrium (mol.%) contraction Mn
760 °C for 900 s 320 4.16 720 °C for 1200 s <250 5.14 690 °C for 1800 s Subzero 6.12 temperature
Si 2.73 2.65 2.61
0.00260 0.00189 8.80 104
modes in the narrow region lying to the left of this boundary and in the wider region to the right of the boundary, respectively. In this alloy the growth starts under the NPLE mode, as shown in Fig. 5a (open circle). Only carbon in the ferrite matrix is depleted at this stage, and the composition in the untransformed ferrite matrix (solid circle) shifts to the left, keeping the interfacial tie-line motionless. The solid circle reaches the PLE/NPLE boundary in a short time and the growth mode switches to the PLE mode. In
this mode the Mn concentration at the boundary in the austenite increases with time, thus the interfacial tie-line moves upward, as illustrated in Fig. 5b. Because Mn is depleted in the ferrite matrix, the upward movement of the interfacial tie-line eventually stops and will turn back until the solid circle reaches the a/(a + c) terminus of the bulk equilibrium tie-line (see Fig. 5c). It is not clear, however, how far the interfacial tie-line moves from the initial tie-line of NPLE growth from this construction. In other words, the interfacial tie-line either goes above the bulk equilibrium tie-line or asymptotically approaches it without exceeding it. Whereas in the c!a transformation the diffusivities of carbon and alloying elements are faster by a few orders of magnitude in the growing phase, the opposite is true in the a!c transformation. Hence, simulations were carried out by DICTRA [21] to see how the growth mode, rate-controlling diffusivity and interfacial tie-line (or solute concentrations at the boundary) vary with the progress of transformation.
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R. Wei et al. / Acta Materialia 61 (2013) 697–707
Fig. 5. Isothermal sections of a ternary Fe–C–Mn phase diagram illustrating the growth mode and change in interfacial tie-line with time during annealing. (a) Growth under NPLE with a stationary tie-line, (b) growth under PLE with the tie-line approximately corresponding to the maximum Mn concentration at boundary in austenite and (c) the tie-line at final equilibrium. Open circles indicate the bulk alloy composition; solid circles represent the mean composition of the ferrite matrix changing with time.
4.2. DICTRA simulation of the growth of austenite The a!c transformation in the Fe–C–Mn–Si alloy was simulated by DICTRA using the TCFE6 and MOB2 databases. The growth morphology was assumed to be planar and the thickness of the ferrite matrix was set to 1 lm. Fig. 6a–d shows the variation with time of the fraction transformed and the concentrations of C, Mn and Si at the boundary between ferrite and austenite at 760 °C. The initial very rapid increase in the fraction transformed is due to the growth of austenite under NPLE. Speich et al. [5] analyzed the growth of austenite into ferrite assuming it to be controlled by the carbon diffusion in austenite in the second stage of re-austenitization during intercritical annealing of dual-phase steels. Taking into account carbon diffusion in both ferrite and austenite, the parabolic growth rate constant of the planar ferrite/austenite boundary can be calculated from the transcendental equation,
"
rffiffiffiffiffiffi Dc expða2 =4Dc Þ pffiffiffiffiffiffi p 1 þ erf ða=2 Dc Þ # rffiffiffiffiffiffi xaC x0C Da expða2 =4Da Þ pffiffiffiffiffiffi c xC xaC p 1 erf ða=2 Da Þ
x0 xcC a ¼ 2 Cc xC xaC
ð1Þ
where x0C is the initial concentration of carbon, xaC and xcC are the concentrations of carbon at the boundary in ferrite and austenite, and Da and Dc are the carbon diffusivity, respectively [22]. With the initial boundary concentrations in Fig. 6b, a was calculated to be 3.8 106 m s1/2. As expected from the carbon diffusivities, i.e. Da = 2.1 1010 m2 s1 and Dc = 9.1 1013 m2 s1 at 760 °C [23,24], the second term on the right-hand side of the above equation dominates the first term, which indicates that the growth is controlled by carbon diffusion in ferrite. However, as illustrated in Fig. 7a, the carbon diffusion profile becomes progressively flatter with time in the ferrite matrix. Hence,
R. Wei et al. / Acta Materialia 61 (2013) 697–707 2.0
0.7
C in austenite C in ferrite
1.8
0.6
1.6
0.5
1.4
Mole-Percent, C
Volume fraction
703
0.4
NPLE
0.3
PLE
0.2
1.2 1.0 0.8 0.6
bulk
0.4 0.1
a
b
c
c
b
0.0
0.0 -5
10
-4
-3
10
10
-2
10
-1
10
0
10
1
10
2
3
10
4
10
10
5
10
6
10
7
10
10
-3
10
-2
10
-1
10
0
10
1
10
2
Time,s
Time, s
(A)
(B)
5.0
10
3
10
4
10
5
10
6
10
7
5.0 Mn in austenite Mn in ferrite
4.5 4.0
Si in austenite Si in ferrite
4.5 4.0
3.5
Mole-Percent, Si
Mole-Percent, Mn
a
0.2
bulk
3.0 2.5 2.0 1.5 1.0
b
c
-3
bulk
2.5 2.0 1.5
-2
10
-1
10
0
10
1
10
2
10
3
10
4
10
5
10
a
0.5
0.0 10
3.0
1.0
a
0.5
3.5
6
10
7
10
Time,s
(C)
b
c
0.0 -3
10
-2
10
-1
10
0
10
1
10
2
10
3
10
4
10
5
10
6
10
7
10
Time,s
(D)
Fig. 6. Variations of (a) volume fraction of austenite, (b) carbon concentrations at the boundary in austenite (solid curve) and ferrite (dashed curve), (c) Mn concentration and (d) Si concentration during holding calculated at 760 °C. Arrows a, b and c correspond approximately to the growth stages in Fig. 5a, b and c, respectively.
the growth of austenite may be controlled increasingly by carbon diffusion in austenite until the diffusion of substitutional atoms begins to occur (arrow a in Fig. 6a). Indeed, the boundary advancement vs. the square root of time plot (Fig. 7b) indicates that the slope begins to decrease at 1.2 103 s (dashed arrow) from the initial value of a = 4.0 106 m s1/2. As the composition in the untransformed matrix reaches the PLE/NPLE boundary, the diffusion of alloying elements begins to occur. Fig. 8a–c shows the concentration profiles at t = 500 s, at which time the volume fraction of austenite is approaching its maximum value. It is seen that both Mn and Si are diffusing into the austenite, although the Si flux into the austenite is limited to the region near the boundary. It is emphasized that the concentrations of both Mn and Si are highly non-uniform in the austenite. Indeed, Dmitrieva et al. [25] observed Mn enrichment in the rear of the ferrite/austenite boundary in a high-Mn
maraging TRIP steel aged at 450 °C for 48 h. A very high Mn concentration immediately behind the boundary (27 at.%) was close to the local equilibrium concentration at the boundary in austenite. The concentration gradients of Mn and Si still exist at t = 105 s, at which time the transformed fraction began to decrease and gradually disappeared during prolonged holding (see Fig. 9a–c). By the time that the Mn and Si concentrations had become flat in the austenite, the boundary had moved back over a distance of 5 108 m, and this accompanied a small decrease in both Mn and Si concentrations in ferrite. 4.3. Dilatometric analysis of the austenite volume fraction The strain contraction associated with austenite formation is calculated following the method reported previously [26–28]. Assuming an isotropic behavior, the strain is calculated from the equation
704
R. Wei et al. / Acta Materialia 61 (2013) 697–707 M a M a a aM ¼ ðaM ;Fe þ k M C xC þ k Mn xMn þ k Si xSi Þ½1 þ aM ðT 298Þ; nm
aM ¼ aM;Fe þ
Fig. 7. (a) Carbon diffusion profile in the region near the ferrite/austenite boundary at an initial stage of austenite growth under NPLE, simulated by DICTRA at 760 °C. (b) Boundary advancement plotted against the square root of time. The slope begins to deviate from linearity around the time indicated by the dashed arrow.
Dl l l0 1 V ¼ ¼ 1 l0 3 V0 l0
ð2Þ
where l0 and V 0 are the length and volume of a specimen at initial temperature, and l and V are the length and volume at a given temperature, respectively. The atomic volume of a mixture of martensite and austenite can be written as V ¼ fV A þ ð1 f ÞV M
ð3Þ a2M cM =2Þ
where f is the volume fraction of austenite, V M ð¼ and V A ð¼ a3A =4Þ are the atomic volumes of martensite and austenite, aM and cM are the lattice parameters of the aand c-axes of martensite, and aA is the lattice parameter of austenite. The lattice parameter depends on the composition and temperature as
a jM C xC
þ
a jM Mn xMn ;
K
1
ð4Þ
ð5Þ
where aM,Fe is the lattice parameter of carbon-free ferrite at 25 °C, which is assumed to be equal to that of martensite [28], and aM,Fe is the thermal expansion coefficient of ferM rite in pure iron. The coefficients k M C and k Mn etc. represent the influence of carbon and alloying elements on the lattice M parameter of martensite; jM C and jMn , on the thermal a a expansion coefficient; and xC and xMn etc. are the concentration of carbon and alloying elements (here in at.%), respectively. Similar equations can be written for cM and aA, and the numerical values of these coefficients are shown in Table 3. Whereas the Mn and Si concentrations are not uniform in the austenite, the lattice parameters calculated at the boundary and in the bulk do not differ significantly. Hence, the strain contraction was calculated at the mean concentration of carbon or alloying elements in the bulk and at the boundary. Table 4 shows the volume fraction of austenite calculated from the strain contraction by means of Eq. (2). Since a composition analysis of austenite was not made, the volume fraction of austenite was also evaluated assuming two extreme cases – one with full partitioning (final equilibrium) and the other with no partitioning of the alloying elements. The results are somewhat insensitive to the assumed concentrations of carbon and alloying elements in austenite and martensite. In Fig. 10 the measured fractions transformed are compared with those simulated at diffusion cell sizes of 1 (solid curves) and 0.5 lm (dashed curves). The white symbols, measured metallographically, are in good agreement with those determined from dilatometry. They also agreed well with simulation at 760 °C in terms of both the amount of excess from final equilibrium and the time evolution. At 720 °C, the amount of excess agreed with simulation, but the excess occurred at a smaller holding time than those calculated. On the other hand, the measured volume fraction of austenite did not exceed the equilibrium volume fraction calculated at 690 °C. As discussed above, the growth of austenite is first controlled by diffusion of carbon or alloying elements in ferrite and subsequently by carbon or alloying element diffusion in austenite in both NPLE and PLE growth modes. It is noted that, in the c!a transformation, the excess of the fraction transformed over the final equilibrium value has not been reported. Moreover, a simulation assuming identical diffusivities of Mn and Si in ferrite and austenite did not exhibit an overshoot of austenite volume fraction. Hence, the ratio of diffusivity in the growing phase to that in the matrix phase may be a crucial factor for the formation of an excess amount of the product phase [7,8]. It is possible that the volume fraction of austenite increases at longer annealing times at 690 °C. However, it would be more difficult to observe the formation of an excess volume of austenite because the amount of the excess is smaller and the maximum volume, if it occurs, may be achieved at a much longer annealing time.
R. Wei et al. / Acta Materialia 61 (2013) 697–707
705
Fig. 8. Concentration profiles of (a) carbon, (b) Mn and (c) Si at 760 °C and t = 500 s during intercritical annealing.
5. Conclusions The growth of austenite from as-quenched martensite during intercritical annealing at 690, 720 and 760 °C was studied in a quaternary Fe–0.1C–3Mn–1.5Si alloy. Small austenite grains, several hundred nanometers in thickness, grew from thin retained austenite films between laths upon quenching. The austenite grains were also nucleated at lath boundaries, martensite packet boundaries and within laths. The martensite laths transformed from austenite during quenching and initial neighboring as-quenched martensite laths almost the same orientation. It was found both metallographically and by dilatometry that the volume fraction of austenite exceeded that at final equilibrium at both 720 and 760 °C.
The growth of austenite consisted of three stages, which included: initial no-partitioned growth of austenite, controlled by rapid carbon diffusion in ferrite, which is gradually replaced by carbon diffusion in austenite; intermediate slow growth, controlled by diffusion of Mn and/or Si in ferrite; and very slow growth, controlled by diffusion of these elements in austenite for final equilibration, which accompanies the shrinkage of austenite. The excess of austenite volume fraction over the equilibrium amount can be ascribed to the very slow substitutional diffusion in the growing austenite compared to the boundary migration. The amount of excess may depend on the ratio of diffusivities of alloying elements in the parent and growing phases, and presumably the steel composition intercritical annealing temperature as well.
706
R. Wei et al. / Acta Materialia 61 (2013) 697–707
Fig. 9. Concentration profiles of (a) carbon, (b) Mn and (c) Si at 760 °C and t = 105 and 107 s during intercritical annealing.
Table 3 Coefficients for the influence of alloying elements on the lattice parameter and the thermal expansion coefficients of martensite and austenite. aM,Fe, nm
or A kM (or k cC ), nm per at.% C
or A kM nm per at.% Mn
or A kM , nm per at.% Si
2.89 104 (a-axis) 2.58 103 (c-axis) 7.83 104
5.43 105
3.0 105
1.14 104
0.0
aM or cM
Martensite
0.2866a
aA
Austenite
0.3572a aM,Fe, K
Martensite Austenite
aM aA a
Ref. [29].
1
14.9 106 23.87 106
or A jM , C
1
K
1.9 106 0.5 106
per at.%
or A jM , Mn
1
K
per at.%
0.147 106 0.178 106
or A jM , K1 per at.% Si
0.0 0.0
R. Wei et al. / Acta Materialia 61 (2013) 697–707
707
Table 4 Volume fraction of austenite calculated from the measured strain contraction (Eq. (2)). Alloying element
Annealing temperature and time 690 °C for 1800 s
720 °C for 1200 s
760 °C for 900 s
Mean concentration Full partitioning No partitioninga
0.194 ± 0.001 0.192 0.194
0.424 ± 0.001 0.424 0.423
0.625 ± 0.0005 0.626 0.624
a
Fraction transformed of austenite
0.8
As for the carbon concentration, paraequilibrium was assumed.
[4] [5] [6] [7] [8]
1 micron 0.5 micron
0.6 o
760 C
0.4
[9] o
720 C o
690 C
0.2
[10] [11] [12] [13]
0.0 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 10 10 10 10 10 10 10 10 10 10 10 10 10
Time, s Fig. 10. Comparison of measured and calculated volume fractions of austenite. Open symbols are measured by point counting. The error bars were drawn beneath the symbols in view of the preferential etching of the boundary region. The error range of solid symbols from dilatometry was less than the size of the symbols.
Acknowledgements The authors express their sincere thanks to the research forum of ALEMI (Alloying Element Effects on Migrating Interfaces) for encouragement and invaluable discussion. Dr. Xiang Wang (McMaster University) is acknowledged for his help with the microscopy. References [1] Mo¨linder G. Acta Metall 1956;4:565. [2] Judd RW, Paxton HW. Trans TMS-AIME 1968;242:206. [3] Speich GR, Szirmae A. Trans TMS-AIME 1969;245:1063.
[14] [15] [16] [17] [18]
[19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29]
Hillert M, Nilsson K, To¨hndahl L-E. JISI 1971;209:49. Speich GR, Demarest VA, Miller RL. Metall Trans A 1981;12A:1419. Garcia CI, DeArdo AJ. Metall Trans A 1981;12A:521. Wycliffe PA, Purdy GR, Embury JD. Can Metall Quart 1981;20:339. Wycliffe PA, Purdy GR, Embury JD. In: Kot RA, Bramfitt BL, editors. Fundamentals of dual-phase steels. Warrendale, PA: TMSAIME; 1981. p. 60. Miyamoto G, Usuki H, Li ZD, Furuhara T. Acta Mater 2010;58: 4492. Li ZD, Miyamoto G, Yang ZG, Furuhara T. Metall Mater Trans A 2011;42A:1586. ˚ gren J. Acta Metall 1982;30:841. A Atkinson C, Akbay T, Reed RC. Acta Metall Mater 1995;43:2013. Aaronson HI, Reynolds Jr WT, Purdy GR. Metall Mater Trans A 2006;37A:1731. Andrews KW. JISI 1965;203:721. Morito S, Huang X, Furuhara T, Maki T, Hansen N. Acta Mater 2006;54:5323. Pham AH, Ohba T, Morito S, Hayashi T. J. Alloys Comp 2012. http://dx.doi.org/10.1016/j.jallcom.2012.02.008. Clarebrough LM, Hargreaves ME, West GW. Philos Mag 1956;1:528. ˚ gren J, Brechet Y, Hutchinson C, Philibert J, Purdy Hillert M. in: A G, editors. Thermodynamics and phase transformations. Les Ulis: EDP Sciences; 2006. p. 9. Oi K, Lux C, Purdy GR. Acta Mater 2000;48:2147. Coates DE. Metall Trans A 1973;4:1077. Andersson JO, Helander T, Ho¨glund L, Shi PF, Sundman B. Calphad 2002;26:273. Purdy GR, Kirkaldy JS. Trans AIME 1963;227:1255. ˚ gren J. Acta Metall 1982;30:841. A ˚ gren J. Scripta Met 1986;20:1507. A Dmitrieva O, Ponge D, Inden G, Millan J, Choi P, Sietsma J, et al. Acta Mater 2011;59:364. Lee SJ, Lee YK. Scripta Mater 2005;52:973. Lee SJ, Lusk MT, Lee YK. Acta Mater 2007;55:875. Lee SJ, Lee S, De Cooman BC. Scripta Mater 2011;64:649. Li CM, Sommer F, Mittemeijer EJ. Mater Sci Eng 2002;A325:307.
Acta Materialia 61 (2013) 697–707 www.elsevier.com/locate/actamat
Growth of austenite from as-quenched martensite during intercritical annealing in an Fe–0.1C–3Mn–1.5Si alloy R. Wei a, M. Enomoto a,⇑, R. Hadian b, H.S. Zurob b, G.R. Purdy b b
a Department of Materials Science and Engineering, Ibaraki University, Hitachi 316-8511, Japan Department of Materials Science and Engineering, McMaster University, Hamilton, Ontario, Canada L8S4L8
Received 19 April 2012; received in revised form 12 October 2012; accepted 16 October 2012 Available online 10 November 2012
Abstract The growth of austenite from as-quenched martensite during intercritical annealing was studied in a quaternary Fe–0.1C–3Mn–1.5Si alloy. Fine austenite grains either grew from interlath-retained austenite films or were newly nucleated at lath and martensite packet boundaries. Both types grew to a size comparable to the width of the martensite lath. It was found both metallographically and by dilatometry that the austenite grew to an amount in excess of the volume fraction at final equilibrium. Simulation by DICTRA, which assumed local equilibrium at the a/c boundary, confirmed that the development of austenite is composed of three stages: initial negligible-partitioning growth controlled by rapid carbon diffusion in ferrite, which is gradually replaced by carbon diffusion in austenite; intermediate slow growth, controlled by diffusion of Mn and/or Si in ferrite; and a final stage controlled by diffusion of substitutional elements in austenite for final equilibration, which may result in the shrinkage of austenite. The formation of austenite in excess of the equilibrium amount is considered to occur due to very slow substitutional diffusion in the growing austenite compared to the boundary migration. Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Intercritical annealing; Austenite; Martensite; Local equilibrium; Growth kinetics
1. Introduction Re-austenization is a process of fundamental importance because low-alloy steels are heated in the (a + c) two-phase and the c single-phase regions during normalization, controlled rolling, forging and welding. The mechanisms of the austenization reaction are complex because it can occur from a variety of initial microstructures, such as cold-rolled or recrystallized ferrite, as-quenched or tempered martensite, or a mixture of ferrite and cementite or pearlite [1–10]. Moreover, alloying elements exert their influence in many ways at different stages of transformation. Indeed, Speich et al. [5] reported that the growth of austenite from the ferrite and pearlite mixture in a series of 1.5% Mn steels containing 0.06–0.2% C was characterized by three stages: the
⇑ Corresponding author. Tel.: +81 294 38 5058; fax: +81 294 38 5226.
E-mail address: [email protected] (M. Enomoto).
growth of austenite into pearlite; slower growth, controlled by either carbon diffusion in austenite at higher temperatures or Mn diffusion in ferrite at lower temperatures; and then final equilibration at a rate controlled by Mn diffusion in austenite. The first two stages were explored experimentally using microanalytical techniques and were numerically modeled by Wycliffe et al. for ternary Fe–C–Mn [7] and ˚ gren conducted comquaternary Fe–C–Mn–Si alloys [8]. A puter simulations of austenitization [11], and affirmed that the Mn-rich layer formed in austenite close to the a/c interface should have a large influence on late-stages austenite growth. Atkinson et al. [12] derived analytical expressions of the parabolic growth rate constants of austenite from ferrite and cementite mixture in ternary alloys assuming local equilibrium, and discussed the influence of alloying elements on the growth of austenite. In this report we focus on the austenitization from asquenched martensite. According to the simulation of isothermal annealing of a dual-phase steel [11], the volume
1359-6454/$36.00 Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.actamat.2012.10.019
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fraction of austenite exceeded the equilibrium amount before the system reached final equilibrium. This is in marked contrast to the forward ferrite transformation, in which we very often observe incomplete transformation; the transformation stops before the volume fraction reaches its final equilibrium value [13]. A quaternary Fe– 0.1C–3Mn–1.5Si alloy was employed to avoid carbide formation during heating to intercritical annealing temperature. The measured volume fractions of austenite were compared with simulation, assuming local equilibrium at the migrating a/c boundary. 2. Experimental procedure A high-purity quaternary Fe–C–Mn–Si alloy was vacuum-induction melted and hot-rolled to a plate of 10 mm thickness at 1200 °C. The chemical composition of the alloy is shown in Table 1. After homogenization at 1200 °C for 12 h, the plate was cut and cold-rolled to sheets of 1 mm in thickness. Specimens 8 12 1 mm3 in size were austenitized at 1200 °C for 10 min and quenched in iced brine to form martensite. The Ms temperature of this alloy was calculated to be 405 °C [14]. The specimens were then isothermally reacted in a salt bath at temperatures from 690 to 760 °C for varying times and quenched in iced brine. They were then mechanically polished and etched in 3% nital for optical microscopy. The volume fraction of austenite was measured by point counting. The volume fraction of austenite was also measured by dilatometry. Dilatometric samples (4 10 1 mm3) of quenched martensite were heated up to intercritical annealing temperatures, i.e. 690, 720 and 760 °C, at a rapid heating rate of 100 °C s1 and held for 1800, 1200 and 900 s, respectively. At the end of treatment the samples were rapidly cooled to 250 °C at 100 °C s1, then cooled to room temperature at 15 °C s1. One specimen quenched from the austenitizing temperature and a specimen quenched and intercritically annealed at 760 °C for 600 s were prepared for transmission electron microscopy (TEM) by electropolishing using a voltage of 25 V and a solution of 10% perchloric acid and 90% methanol maintained at 50 °C. The microstructure and the orientation relationship between austenite grains and the matrix were examined on a Philips CM12 transmission electron microscope at 120 kV. 3. Results 3.1. Microstructure of the as-quenched martensite and intercritically annealed specimen Fig. 1a and b are TEM micrographs of a specimen quenched from the c single phase field, which show the
presence of retained austenite films at lath boundaries. Fig. 1c shows Bain related diffraction patterns of martensite lath and retained austenite. Fig. 2a–c are optical micrographs of a specimen which was isothermally reacted at 760 °C for various times. Copious fine austenite grains grew from the martensite lath boundaries at an early stage, as shown in Fig. 2a. In Fig. 2b fine austenite grains were observed inside the wide laths, which may indicate that nucleation occurred within the laths. The size of the austenite grains appears to be restricted by the width of the martensite lath. Eventually, the microstructure was composed of alternate fine ferrite and austenite grains elongated in parallel to the original lath boundaries, as shown in Fig. 2c. Though not shown in the micrographs, austenite grains were also nucleated at packet and block boundaries, and at prior austenite boundaries. Fig. 3 shows TEM micrographs of a specimen intercritically annealed at 760 °C for 600 s and then quenched. In this specimen all the austenite grains transformed into martensite upon quenching from the intercritical temperature, which can be seen as regions 2 and 4 in this image. Ferrite grains formed during annealing, originating from the martensite lath, are shown as regions 1 and 3. It can be seen from the diffraction patterns that the ferrite in region 1 shares almost the same orientation variants with the martensite of region 2, and the same relationship exists between the ferrite of region 3 and the martensite of region 4. While regions 1 and 2 have about 8 degrees of misorientation with regions 3 and 4, it is possible that regions 1 and 3 originated from martensite laths of different variants and the austenite grains transformed into martensite of identical orientation as those of ferrite. A similar observation was made in other areas, which seems to indicate that the minimization of interfacial energies dictates the selection of the martensite variant [15,16]. 3.2. Dilatometric results Fig. 4a–d show the dilatometric response obtained at three different temperatures of intercritical annealing as a function of time and temperature. The strain contraction at the holding temperature is attributed to the formation of austenite during holding. It can be seen in Fig. 4a that the kinetics of austenite formation varied considerably over the temperature interval of 30–40 °C. In Fig. 4b–d the dilatometric curves deviated significantly from a straight line during heating. This is presumably because thin films of retained austenite could start to grow without a nucleation barrier. Hence, the strain contraction was measured from the dashed line extrapolated from the low-temperature part, which may more closely represent the total amount of austenite. The Ms temperature of the austenite formed
Table 1 Chemical composition of alloy (mass%). C
Mn
Si
P
Al
S
N (ppm)
O (ppm)
0.099
3.00
1.51
0.002
0.003
0.001
9
10
R. Wei et al. / Acta Materialia 61 (2013) 697–707
(a)
699
(b)
1 µm
1 µm
002α
(c) 002γ
111γ
011α//111γ
Fig. 1. (a) TEM micrograph (bright-field image) of a specimen quenched from the austenitizing temperature, (b) dark-field image using a (0 0 2)c diffraction spot and (c) corresponding selected area diffraction (SAD) pattern. The beam direction is approximately parallel to the [1 0 0]a and ½1 1 0c directions.
(a)
(b)
(c)
20 µm Fig. 2. Optical micrograph of a specimen annealed at 760 °C (a) for 30 s, (b) for 180 s and (c) for 600 s.
700
R. Wei et al. / Acta Materialia 61 (2013) 697–707
Fig. 3. TEM micrographs of a specimen annealed at 760 °C for 600 s and SAD patterns taken from regions 1–3.
during intercritical annealing was determined only for a specimen annealed at 760 °C, in which a steep increase of the curve was observed at 320 °C. For a specimen annealed at 720 °C, austenite grains may have transformed partially to martensite below 250 °C, and at 690 °C the Ms temperature decreased further, presumably to a subzero value; in this case, all the austenite grains probably remained untransformed at room temperature. This is primarily due to the greater extent of Mn enrichment in austenite at lower holding temperatures. Table 2 summarizes the Ms temperature, strain contraction determined from dilatometry and Mn and Si concentrations at final equilibrium, although the equilibrium was not achieved during holding at each temperature. Recrystallization did not occur in this alloy during heating. The strain contraction caused by annihilation of dislocations during recovery is likely to be an order of magnitude smaller than those shown in the table [17].
4. Discussion 4.1. Graphical construction of the interfacial tie-line of the growth of austenite under local equilibrium In the a!c transformation, either carbon or alloying element diffusion is the rate-controlling process of the growth of austenite. In order to get an overall picture of the growth mode, an Fe–0.1C–3Mn ternary alloy is first discussed with reference to Fig. 5a–c. Taking an analogy of ferrite growth in the c!a transformation [18–20], the boundary between partitioned (PLE) and negligible-partitioned (NPLE) growth of austenite can be drawn from the intersection of the c/(a + c) phase boundary with the axis of Mn concentration (point A) to the intersection of the a/(a + c) phase boundary with the axis of carbon concentration (point B) [12]. Within the (a + c) two-phase field, the growth of austenite occurs under PLE and NPLE
R. Wei et al. / Acta Materialia 61 (2013) 697–707
701
0.012 o
690 C, 1800s
0.010
Strain
0.008 0.006 0.004 0.002 0.000 -0.002 0
100
200
300
400
500
600
700
800
600
700
800
Temperature,ºC
(a)
(b) 0.012
0.012 o
760 C,900s
0.010
0.008
0.008
0.006
0.006
Strain
Strain
o
720 C,1200s
0.010
0.004
0.004
0.002
0.002
0.000
0.000
-0.002
-0.002
o
0
100
200
300
400
500
600
700
800
320 C
0
100
200
300
400
500
Temperature,ºC
Temperature,ºC
(c)
(d)
Fig. 4. Dilatometric strains accompanying heating, intercritical annealing and cooling. (a) High-temperature strain as a function of time for intercritical annealing treatments of 690 °C for 1800 s; 720 °C for 1200 s; and 760 °C for 900 s. A strain of 0.007 on heating corresponds approximately to a temperature of 550 °C. (b–d) The full dilatometric strain paths for the three intercritical treatments.
Table 2 Ms temperature and strain contraction determined from dilatometry. Isothermal holding
Ms, °C
Concentration in austenite Strain at equilibrium (mol.%) contraction Mn
760 °C for 900 s 320 4.16 720 °C for 1200 s <250 5.14 690 °C for 1800 s Subzero 6.12 temperature
Si 2.73 2.65 2.61
0.00260 0.00189 8.80 104
modes in the narrow region lying to the left of this boundary and in the wider region to the right of the boundary, respectively. In this alloy the growth starts under the NPLE mode, as shown in Fig. 5a (open circle). Only carbon in the ferrite matrix is depleted at this stage, and the composition in the untransformed ferrite matrix (solid circle) shifts to the left, keeping the interfacial tie-line motionless. The solid circle reaches the PLE/NPLE boundary in a short time and the growth mode switches to the PLE mode. In
this mode the Mn concentration at the boundary in the austenite increases with time, thus the interfacial tie-line moves upward, as illustrated in Fig. 5b. Because Mn is depleted in the ferrite matrix, the upward movement of the interfacial tie-line eventually stops and will turn back until the solid circle reaches the a/(a + c) terminus of the bulk equilibrium tie-line (see Fig. 5c). It is not clear, however, how far the interfacial tie-line moves from the initial tie-line of NPLE growth from this construction. In other words, the interfacial tie-line either goes above the bulk equilibrium tie-line or asymptotically approaches it without exceeding it. Whereas in the c!a transformation the diffusivities of carbon and alloying elements are faster by a few orders of magnitude in the growing phase, the opposite is true in the a!c transformation. Hence, simulations were carried out by DICTRA [21] to see how the growth mode, rate-controlling diffusivity and interfacial tie-line (or solute concentrations at the boundary) vary with the progress of transformation.
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R. Wei et al. / Acta Materialia 61 (2013) 697–707
Fig. 5. Isothermal sections of a ternary Fe–C–Mn phase diagram illustrating the growth mode and change in interfacial tie-line with time during annealing. (a) Growth under NPLE with a stationary tie-line, (b) growth under PLE with the tie-line approximately corresponding to the maximum Mn concentration at boundary in austenite and (c) the tie-line at final equilibrium. Open circles indicate the bulk alloy composition; solid circles represent the mean composition of the ferrite matrix changing with time.
4.2. DICTRA simulation of the growth of austenite The a!c transformation in the Fe–C–Mn–Si alloy was simulated by DICTRA using the TCFE6 and MOB2 databases. The growth morphology was assumed to be planar and the thickness of the ferrite matrix was set to 1 lm. Fig. 6a–d shows the variation with time of the fraction transformed and the concentrations of C, Mn and Si at the boundary between ferrite and austenite at 760 °C. The initial very rapid increase in the fraction transformed is due to the growth of austenite under NPLE. Speich et al. [5] analyzed the growth of austenite into ferrite assuming it to be controlled by the carbon diffusion in austenite in the second stage of re-austenitization during intercritical annealing of dual-phase steels. Taking into account carbon diffusion in both ferrite and austenite, the parabolic growth rate constant of the planar ferrite/austenite boundary can be calculated from the transcendental equation,
"
rffiffiffiffiffiffi Dc expða2 =4Dc Þ pffiffiffiffiffiffi p 1 þ erf ða=2 Dc Þ # rffiffiffiffiffiffi xaC x0C Da expða2 =4Da Þ pffiffiffiffiffiffi c xC xaC p 1 erf ða=2 Da Þ
x0 xcC a ¼ 2 Cc xC xaC
ð1Þ
where x0C is the initial concentration of carbon, xaC and xcC are the concentrations of carbon at the boundary in ferrite and austenite, and Da and Dc are the carbon diffusivity, respectively [22]. With the initial boundary concentrations in Fig. 6b, a was calculated to be 3.8 106 m s1/2. As expected from the carbon diffusivities, i.e. Da = 2.1 1010 m2 s1 and Dc = 9.1 1013 m2 s1 at 760 °C [23,24], the second term on the right-hand side of the above equation dominates the first term, which indicates that the growth is controlled by carbon diffusion in ferrite. However, as illustrated in Fig. 7a, the carbon diffusion profile becomes progressively flatter with time in the ferrite matrix. Hence,
R. Wei et al. / Acta Materialia 61 (2013) 697–707 2.0
0.7
C in austenite C in ferrite
1.8
0.6
1.6
0.5
1.4
Mole-Percent, C
Volume fraction
703
0.4
NPLE
0.3
PLE
0.2
1.2 1.0 0.8 0.6
bulk
0.4 0.1
a
b
c
c
b
0.0
0.0 -5
10
-4
-3
10
10
-2
10
-1
10
0
10
1
10
2
3
10
4
10
10
5
10
6
10
7
10
10
-3
10
-2
10
-1
10
0
10
1
10
2
Time,s
Time, s
(A)
(B)
5.0
10
3
10
4
10
5
10
6
10
7
5.0 Mn in austenite Mn in ferrite
4.5 4.0
Si in austenite Si in ferrite
4.5 4.0
3.5
Mole-Percent, Si
Mole-Percent, Mn
a
0.2
bulk
3.0 2.5 2.0 1.5 1.0
b
c
-3
bulk
2.5 2.0 1.5
-2
10
-1
10
0
10
1
10
2
10
3
10
4
10
5
10
a
0.5
0.0 10
3.0
1.0
a
0.5
3.5
6
10
7
10
Time,s
(C)
b
c
0.0 -3
10
-2
10
-1
10
0
10
1
10
2
10
3
10
4
10
5
10
6
10
7
10
Time,s
(D)
Fig. 6. Variations of (a) volume fraction of austenite, (b) carbon concentrations at the boundary in austenite (solid curve) and ferrite (dashed curve), (c) Mn concentration and (d) Si concentration during holding calculated at 760 °C. Arrows a, b and c correspond approximately to the growth stages in Fig. 5a, b and c, respectively.
the growth of austenite may be controlled increasingly by carbon diffusion in austenite until the diffusion of substitutional atoms begins to occur (arrow a in Fig. 6a). Indeed, the boundary advancement vs. the square root of time plot (Fig. 7b) indicates that the slope begins to decrease at 1.2 103 s (dashed arrow) from the initial value of a = 4.0 106 m s1/2. As the composition in the untransformed matrix reaches the PLE/NPLE boundary, the diffusion of alloying elements begins to occur. Fig. 8a–c shows the concentration profiles at t = 500 s, at which time the volume fraction of austenite is approaching its maximum value. It is seen that both Mn and Si are diffusing into the austenite, although the Si flux into the austenite is limited to the region near the boundary. It is emphasized that the concentrations of both Mn and Si are highly non-uniform in the austenite. Indeed, Dmitrieva et al. [25] observed Mn enrichment in the rear of the ferrite/austenite boundary in a high-Mn
maraging TRIP steel aged at 450 °C for 48 h. A very high Mn concentration immediately behind the boundary (27 at.%) was close to the local equilibrium concentration at the boundary in austenite. The concentration gradients of Mn and Si still exist at t = 105 s, at which time the transformed fraction began to decrease and gradually disappeared during prolonged holding (see Fig. 9a–c). By the time that the Mn and Si concentrations had become flat in the austenite, the boundary had moved back over a distance of 5 108 m, and this accompanied a small decrease in both Mn and Si concentrations in ferrite. 4.3. Dilatometric analysis of the austenite volume fraction The strain contraction associated with austenite formation is calculated following the method reported previously [26–28]. Assuming an isotropic behavior, the strain is calculated from the equation
704
R. Wei et al. / Acta Materialia 61 (2013) 697–707 M a M a a aM ¼ ðaM ;Fe þ k M C xC þ k Mn xMn þ k Si xSi Þ½1 þ aM ðT 298Þ; nm
aM ¼ aM;Fe þ
Fig. 7. (a) Carbon diffusion profile in the region near the ferrite/austenite boundary at an initial stage of austenite growth under NPLE, simulated by DICTRA at 760 °C. (b) Boundary advancement plotted against the square root of time. The slope begins to deviate from linearity around the time indicated by the dashed arrow.
Dl l l0 1 V ¼ ¼ 1 l0 3 V0 l0
ð2Þ
where l0 and V 0 are the length and volume of a specimen at initial temperature, and l and V are the length and volume at a given temperature, respectively. The atomic volume of a mixture of martensite and austenite can be written as V ¼ fV A þ ð1 f ÞV M
ð3Þ a2M cM =2Þ
where f is the volume fraction of austenite, V M ð¼ and V A ð¼ a3A =4Þ are the atomic volumes of martensite and austenite, aM and cM are the lattice parameters of the aand c-axes of martensite, and aA is the lattice parameter of austenite. The lattice parameter depends on the composition and temperature as
a jM C xC
þ
a jM Mn xMn ;
K
1
ð4Þ
ð5Þ
where aM,Fe is the lattice parameter of carbon-free ferrite at 25 °C, which is assumed to be equal to that of martensite [28], and aM,Fe is the thermal expansion coefficient of ferM rite in pure iron. The coefficients k M C and k Mn etc. represent the influence of carbon and alloying elements on the lattice M parameter of martensite; jM C and jMn , on the thermal a a expansion coefficient; and xC and xMn etc. are the concentration of carbon and alloying elements (here in at.%), respectively. Similar equations can be written for cM and aA, and the numerical values of these coefficients are shown in Table 3. Whereas the Mn and Si concentrations are not uniform in the austenite, the lattice parameters calculated at the boundary and in the bulk do not differ significantly. Hence, the strain contraction was calculated at the mean concentration of carbon or alloying elements in the bulk and at the boundary. Table 4 shows the volume fraction of austenite calculated from the strain contraction by means of Eq. (2). Since a composition analysis of austenite was not made, the volume fraction of austenite was also evaluated assuming two extreme cases – one with full partitioning (final equilibrium) and the other with no partitioning of the alloying elements. The results are somewhat insensitive to the assumed concentrations of carbon and alloying elements in austenite and martensite. In Fig. 10 the measured fractions transformed are compared with those simulated at diffusion cell sizes of 1 (solid curves) and 0.5 lm (dashed curves). The white symbols, measured metallographically, are in good agreement with those determined from dilatometry. They also agreed well with simulation at 760 °C in terms of both the amount of excess from final equilibrium and the time evolution. At 720 °C, the amount of excess agreed with simulation, but the excess occurred at a smaller holding time than those calculated. On the other hand, the measured volume fraction of austenite did not exceed the equilibrium volume fraction calculated at 690 °C. As discussed above, the growth of austenite is first controlled by diffusion of carbon or alloying elements in ferrite and subsequently by carbon or alloying element diffusion in austenite in both NPLE and PLE growth modes. It is noted that, in the c!a transformation, the excess of the fraction transformed over the final equilibrium value has not been reported. Moreover, a simulation assuming identical diffusivities of Mn and Si in ferrite and austenite did not exhibit an overshoot of austenite volume fraction. Hence, the ratio of diffusivity in the growing phase to that in the matrix phase may be a crucial factor for the formation of an excess amount of the product phase [7,8]. It is possible that the volume fraction of austenite increases at longer annealing times at 690 °C. However, it would be more difficult to observe the formation of an excess volume of austenite because the amount of the excess is smaller and the maximum volume, if it occurs, may be achieved at a much longer annealing time.
R. Wei et al. / Acta Materialia 61 (2013) 697–707
705
Fig. 8. Concentration profiles of (a) carbon, (b) Mn and (c) Si at 760 °C and t = 500 s during intercritical annealing.
5. Conclusions The growth of austenite from as-quenched martensite during intercritical annealing at 690, 720 and 760 °C was studied in a quaternary Fe–0.1C–3Mn–1.5Si alloy. Small austenite grains, several hundred nanometers in thickness, grew from thin retained austenite films between laths upon quenching. The austenite grains were also nucleated at lath boundaries, martensite packet boundaries and within laths. The martensite laths transformed from austenite during quenching and initial neighboring as-quenched martensite laths almost the same orientation. It was found both metallographically and by dilatometry that the volume fraction of austenite exceeded that at final equilibrium at both 720 and 760 °C.
The growth of austenite consisted of three stages, which included: initial no-partitioned growth of austenite, controlled by rapid carbon diffusion in ferrite, which is gradually replaced by carbon diffusion in austenite; intermediate slow growth, controlled by diffusion of Mn and/or Si in ferrite; and very slow growth, controlled by diffusion of these elements in austenite for final equilibration, which accompanies the shrinkage of austenite. The excess of austenite volume fraction over the equilibrium amount can be ascribed to the very slow substitutional diffusion in the growing austenite compared to the boundary migration. The amount of excess may depend on the ratio of diffusivities of alloying elements in the parent and growing phases, and presumably the steel composition intercritical annealing temperature as well.
706
R. Wei et al. / Acta Materialia 61 (2013) 697–707
Fig. 9. Concentration profiles of (a) carbon, (b) Mn and (c) Si at 760 °C and t = 105 and 107 s during intercritical annealing.
Table 3 Coefficients for the influence of alloying elements on the lattice parameter and the thermal expansion coefficients of martensite and austenite. aM,Fe, nm
or A kM (or k cC ), nm per at.% C
or A kM nm per at.% Mn
or A kM , nm per at.% Si
2.89 104 (a-axis) 2.58 103 (c-axis) 7.83 104
5.43 105
3.0 105
1.14 104
0.0
aM or cM
Martensite
0.2866a
aA
Austenite
0.3572a aM,Fe, K
Martensite Austenite
aM aA a
Ref. [29].
1
14.9 106 23.87 106
or A jM , C
1
K
1.9 106 0.5 106
per at.%
or A jM , Mn
1
K
per at.%
0.147 106 0.178 106
or A jM , K1 per at.% Si
0.0 0.0
R. Wei et al. / Acta Materialia 61 (2013) 697–707
707
Table 4 Volume fraction of austenite calculated from the measured strain contraction (Eq. (2)). Alloying element
Annealing temperature and time 690 °C for 1800 s
720 °C for 1200 s
760 °C for 900 s
Mean concentration Full partitioning No partitioninga
0.194 ± 0.001 0.192 0.194
0.424 ± 0.001 0.424 0.423
0.625 ± 0.0005 0.626 0.624
a
Fraction transformed of austenite
0.8
As for the carbon concentration, paraequilibrium was assumed.
[4] [5] [6] [7] [8]
1 micron 0.5 micron
0.6 o
760 C
0.4
[9] o
720 C o
690 C
0.2
[10] [11] [12] [13]
0.0 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 10 10 10 10 10 10 10 10 10 10 10 10 10
Time, s Fig. 10. Comparison of measured and calculated volume fractions of austenite. Open symbols are measured by point counting. The error bars were drawn beneath the symbols in view of the preferential etching of the boundary region. The error range of solid symbols from dilatometry was less than the size of the symbols.
Acknowledgements The authors express their sincere thanks to the research forum of ALEMI (Alloying Element Effects on Migrating Interfaces) for encouragement and invaluable discussion. Dr. Xiang Wang (McMaster University) is acknowledged for his help with the microscopy. References [1] Mo¨linder G. Acta Metall 1956;4:565. [2] Judd RW, Paxton HW. Trans TMS-AIME 1968;242:206. [3] Speich GR, Szirmae A. Trans TMS-AIME 1969;245:1063.
[14] [15] [16] [17] [18]
[19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29]
Hillert M, Nilsson K, To¨hndahl L-E. JISI 1971;209:49. Speich GR, Demarest VA, Miller RL. Metall Trans A 1981;12A:1419. Garcia CI, DeArdo AJ. Metall Trans A 1981;12A:521. Wycliffe PA, Purdy GR, Embury JD. Can Metall Quart 1981;20:339. Wycliffe PA, Purdy GR, Embury JD. In: Kot RA, Bramfitt BL, editors. Fundamentals of dual-phase steels. Warrendale, PA: TMSAIME; 1981. p. 60. Miyamoto G, Usuki H, Li ZD, Furuhara T. Acta Mater 2010;58: 4492. Li ZD, Miyamoto G, Yang ZG, Furuhara T. Metall Mater Trans A 2011;42A:1586. ˚ gren J. Acta Metall 1982;30:841. A Atkinson C, Akbay T, Reed RC. Acta Metall Mater 1995;43:2013. Aaronson HI, Reynolds Jr WT, Purdy GR. Metall Mater Trans A 2006;37A:1731. Andrews KW. JISI 1965;203:721. Morito S, Huang X, Furuhara T, Maki T, Hansen N. Acta Mater 2006;54:5323. Pham AH, Ohba T, Morito S, Hayashi T. J. Alloys Comp 2012. http://dx.doi.org/10.1016/j.jallcom.2012.02.008. Clarebrough LM, Hargreaves ME, West GW. Philos Mag 1956;1:528. ˚ gren J, Brechet Y, Hutchinson C, Philibert J, Purdy Hillert M. in: A G, editors. Thermodynamics and phase transformations. Les Ulis: EDP Sciences; 2006. p. 9. Oi K, Lux C, Purdy GR. Acta Mater 2000;48:2147. Coates DE. Metall Trans A 1973;4:1077. Andersson JO, Helander T, Ho¨glund L, Shi PF, Sundman B. Calphad 2002;26:273. Purdy GR, Kirkaldy JS. Trans AIME 1963;227:1255. ˚ gren J. Acta Metall 1982;30:841. A ˚ gren J. Scripta Met 1986;20:1507. A Dmitrieva O, Ponge D, Inden G, Millan J, Choi P, Sietsma J, et al. Acta Mater 2011;59:364. Lee SJ, Lee YK. Scripta Mater 2005;52:973. Lee SJ, Lusk MT, Lee YK. Acta Mater 2007;55:875. Lee SJ, Lee S, De Cooman BC. Scripta Mater 2011;64:649. Li CM, Sommer F, Mittemeijer EJ. Mater Sci Eng 2002;A325:307.