3 l thermodynamic analysis [5]. In the first method there V = º · V0 · + 1 . (2) l0 is the possibility of the transformation of austenite to ferrite or bainite, rather than martensite, during cool- The scaling factor in the intercritical region is assumed ing. This is more likely after intercritical annealing than to be proportional to the phase fractions according to after full austenitization, since the incubation time for pearlite or bainite formation is shorter due to smaller Å‚ Å‚ º = (1 - f )ºÄ… + f ºÅ‚ , (3) austenite grain size and no ferrite nucleation being re- quired. The second method, thermodynamic analysis, where ºÄ… and ºÅ‚ are calculated at the Ac1 and Ac3 only gives a reference for the design of the heat treat- temperature by combining the calculated volume ment schedule, but it is clearly incapable of taking with the measured l/l0. In the case of intercritical kinetics effects into account. annealing of TRIP steels, three phases, ferrite (Ä…), As compared to these two methods, dilatometric data cementite (¸) and austenite (Å‚ ), are involved. The describe in situ volume fraction change during intercrit- lattice parameter of ferrite (aÄ…) is often regarded ical annealing, since dilatometry permits the real-time as only depending on the temperature (T ) and the monitoring of the extent of reaction in terms of dimen- expansion coefficient (eÄ…) [15], according to sional changes resulting from the phase transforma- tions. As for the research on TRIP steels, dilatometry Ä… aÄ… = a0 [1 + eÄ…(T - T0)], (4) has been used for the determination of transforma- tion temperatures [5 7], which showed a good repro- Ä… ducibility. However, no work on the evaluation method where a0 is the lattice parameter at the reference tem- calculating austenite fraction from dilatometric data perature T0. For cementite, which has an orthorhombic during continuous heating and subsequent intercritical structure with lattice parameters a¸, b¸, c¸, the relation annealing has been published. This is perhaps due to is similar [15, 16]. The lattice parameter of austenite the difficulties dealing with an incomplete transforma- (aÅ‚ ), however, is closely related to the alloying element tion of ferrite and cementite to austenite during inter- concentrations (Ci, in wt%), in addition to the tempera- critical annealing, which contains two steps: a contin- ture and the expansion coefficient [12, 14, 17 22]. This uous transformation during heating to above the Ac1 can be expressed as follows: temperature and an isothermal transformation during
Å‚ holding. Therefore, the present work aims to develop aÅ‚ = a0 + xiCi 1 + eÅ‚ (T - T0) , (5) and validate a suitable evaluation method for dilatomet- i ric data on an incomplete transformation. The obtained where xi is the coefficient relating the effect of the fractions will be compared with fractions deduced by concentration Ci of alloying element i to the austenite two other methods, viz. quantitative scanning electron Å‚ lattice parameter. a0 is the lattice parameter in unal- microscopy on interruptedly quenched samples and loyed austenite at T0. From the published xi values [12, thermodynamic calculations. 14, 18], one can see that the interstitial element carbon plays a dominant role in the value of the lattice parame- 2. Background and theoretical consideration ter of austenite, in comparison to substitutional alloying Dilatometry is regarded as a powerful technique for the elements. For instance, xi is zero for silicon and that study of phase transformations in steels, since density for manganese is only 3% of the one for carbon [18]. change resulting from phase transformation gives rise Therefore, only the role of carbon is considered in the to an observable dilatation different from the thermal present case. expansion effect. Methods to calculate this change From the lattice parameters, one can easily obtain the based on the volumes of the unit cells of constituting atomic volume V of each phase in the steels. Namely, phases have been described in literature [8 14]. Under Ä… Å‚ ¸ V = (aa)3/2, V = (aÅ‚)3/4, V = (a¸b¸c¸)/12, where the assumption of isotropic dilatation behaviour, the the factors 2, 4 and 12 in the denominator arise from volume change ( V = V - V0) with respect to the the fact that the unit cells of ferrite, austenite initial volume (V0) is related to the relative length and cementite contain 2, 4 and 12 iron atoms, re- change ( l/l0) by: spectively. Considering that both the total atomic 3 volume V and the mean carbon concentration in V l 3 l = 1 + - 1 H" . (1) the material C0 follow the volume fraction rule V0 l0 l0 Ä… Ä… Å‚ Å‚ ¸ ¸ Ä… Å‚ (V = f V + f V + f V , C0 = f CÄ… + f CÅ‚ + ¸ Since the value of ( l/l0) is very small, the square and f C¸), the fractions of each phase can, in principle, cubic terms of l/l0 can be neglected. The right-hand be calculated from Equation 2. However, in case of side term in the equation above, 3 l/l0, can be directly the Ä… + Å‚ two-phase region CÅ‚ is not a constant, measured by dilatometry, while the left-hand side term, but depends on the fraction in a way defined by the V/V0, represents the volume change, which can be equilibrium line in the phase diagram. Hence an calculated based on the lattice parameters of the exist- analytical solution for the Equation 2 does not exist. 1586 Nevertheless, the numerical solution for the volume tion. The thermodynamic analysis was performed us- fraction can be readily found using an iterative method. ing the MTData software package with a temperature In the present case, the Newton-Raphson method is interval of 1ć%C in the calculations. Programs to cal- used because of its simplicity and great speed [23]. culate the austenite fraction from the measured length Carbon concentration in austenite can be accordingly change were compiled using Matlab. calculated when the fraction is known. In case of a multi-component structure, it is well known that the Ae1 line in the Fe-Fe3C equilibrium 4. Results and discussion phase diagram is modified by the addition of alloy- 4.1. Thermodynamic analysis ing elements. This modification results in a three phase and SEM observation (Ä…, ¸ and Å‚ ) co-existence region between the Ac1 and As it is not clear whether the substitutional alloying the Ac temperature, a temperature at which the cemen- elements diffuse during intercritical annealing [26] or 1 tite is completely dissolved. In this three-phase region, not [24], it is assumed here that ortho-equilibrium, one can assume the carbon concentration in austenite rather than para-equilibrium, pertains. The MTData- (CÅ‚ ) to be nearly constant and equal to the eutectoid calculated temperature dependence of the volume frac- composition. Therefore, the following relation can be tions and the carbon concentration in austenite for the analytically derived from Equation 2: 0.16C-1.5Mn-0.4Si TRIP steel is shown in Fig. 1. One Ä… ¸ ºÄ…V0(3 l/l0 + 1) - k2V - (1 - k2)V Å‚ f = (6) Å‚ Ä… ¸ V - k1V - (1 - k1)V - (ºÅ‚ - ºÄ…)V0(3 l/l0 + 1) C¸ - CÅ‚ C¸ - C0 where k1 = ; k2 = . C¸ - CÄ… C¸ - CÄ… One can see that the constants k1 and k2 coincide can see that when the temperature is below the Ae1 tem- with the equilibrium volume fractions of ferrite at the perature (684ć%C), the material consists of 97.63 wt% of eutectoid composition (pearlite) and at the nominal ferrite (Ä…) and 2.37 wt% of cementite (¸). As the tem- composition (C0), respectively. It is clear from the equa- perature increases to above the Ae1 temperature, both tion that the resulting austenite fraction depends on the cementite and ferrite start to transform to austenite (Å‚ ) values used for the lattice parameters of the phases until the Ae temperature (698ć%C) is reached, at which 1 involved. the cementite is completely decomposed. In this tem- perature range, the carbon concentration (CÅ‚ , in wt%) in austenite slightly increases as a function of temper- 3. Experimental ature, from 0.61% to 0.65%. When the temperature is A 0.16C-1.5Mn-0.4Si (wt%) low silicon TRIP multi- above the Ae temperature, the ferrite further trans- phase steel was used in this investigation. The com- 1 forms to austenite and CÅ‚ decreases as a function of position of silicon in this alloy is close to the lowest temperature, until the Ae3 temperature (818ć%C). Since possible addition for significant TRIP properties [24]. the equilibrium austenite fraction can be regarded as The hot-rolled material was machined to a cylinder of the upper-limit of austenite fraction during intercriti- Ć4mm× 10 mm and the dilatometry experiments were cal annealing, the thermodynamic data are helpful to performed on a Bähr 805 dilatometer. In the exper- understand the calculated results from the dilatometric iments, the samples were heated with a heating rate data. of 100ć%C/min to 750ć%C, 800ć%Cor 900ć%C, respectively, SEM observations of interruptedly quenched sam- isothermally held for 10 min, and quenched to room ples provide another means to determine the austenite temperature. These three annealing temperatures rep- resent three different microstructures during continu- ous heating: at 750ć%C, three phases, austenite, ferrite and cementite, co-exist, 800ć%C is in the intercritical re- gion where austenite and ferrite exist and 900ć%Cis in the fully austenitic region. Two S-type thermocouples were spot-welded on the surface of the sample to con- trol the heating power and to record the temperature homogeneity. The cross-section of quenched samples for the scan- ning electron microscopy (SEM) observations were first tempered for 2 hours at 200ć%C and then etched with 2% nital for 13 seconds to get a better contrast [25]. The image was analyzed using a software package named Visilog and the austenite fraction was averaged over the Figure 1 The temperature dependence of volume fractions and carbon results from at least 25 different surface areas to reduce concentration in austenite (CÅ‚ , in wt%) in a 0.16C-1.5Mn-0.4Si steel, the influence of inhomogeneity of the phase distribu- calculated from ortho-equilibrium thermodynamic analysis. 1587 Figure 2 One of the SEM images for the samples quenched from 800ć%C(Ä…: ferrite; Ä… : martensite). volume fraction at the end of intercritical anneal- ing. Fig. 2 shows one example of such SEM im- ages. By analysis of a substantial number of images, the average austenite fraction is determined to be 0.43 Ä… 0.04 and 0.66 Ä… 0.04, after intercritical anneal- ing at 750ć%C and 800ć%C, respectively. The variation of the results may arise from the inhomogeneity of the materials. 4.2. Dilatometry curves The length change ( l) as a function of time and temperature as recorded in dilatometric experiments (a) is shown in Fig. 3 for the samples annealed at 750ć%C, 800ć%C and 900ć%C, respectively. One can see that the ex- pansion before (for all curves) and after transformation (only for the 900ć%C curve) is nearly linear, from which the expansion coefficient was derived (24.4 × 10-6/ć%C for austenite and 17.5 × 10-6/ć%C for ferrite, respec- tively). One can also see that the end of the cementite decomposition is clearly indicated by an inflexion of the curve. The Ac1, Ac and Ac3 (only from the 900ć%C 1 curve) temperatures at 100ć%C/min. are determined to be 737ć%C, 754ć%C and 847ć%C, respectively, which are about 53ć%C, 55ć%C and 29ć%C higher than the corresponding equilibrium temperatures. The smaller difference for the end temperature is due to the effect of the transfor- (b) mation kinetics. Figure 3 Length change ( l) as a function of (a) time, and (b) tem- The isothermal holding at 750ć%C and 800ć%C for perature, during intercritical annealing at 750ć%C and 800ć%C and during 10 min. leads to an approximately 6 µm and 10 µm heating to the austenite region at 900ć%C, followed by isothermal holding decrease of the l value (Fig. 3b), and most of the for 10 min. length change is taking place within the first 3 min (Fig. 3a). The absolute values of the length change at 750ć%C are higher than that at 800ć%C (Fig. 3a). This 4.3. Calculations based on lattice is due to the fact that there is more austenite formed parameters at 800ć%C and that the amount of existing phases has a According to the evaluation method described in Sec- larger effect on the length change than the tempera- tion 2, the fractions of the various phases and the car- ture rise. At the end of isothermal holding at 750ć%C bon concentration in austenite can be calculated. The and 900ć%C, one can see a jump of the curve (Fig. 3a), lattice parameters used for the calculations are listed which is an experimental artefact by the sudden intro- in Table I. Lattice parameters of ferrite and cemen- duction of gas into the sample chamber to quench the tite determined by various authors appear to show a sample. relatively small variation. This is due to the fact that 1588 ć% TABLE I The effect of temperature (T , in C) and carbon content (only for austenite, in wt%) on the lattice parameters of ferrite and austenite (in Å). For cementite the volume of the unit cell (in Å3) is given by the present authors based on Fig. 3d in reference [16] Phase Relation Ref. Austenite aÅ‚ = (3.6306 + 7.8 × 10-3 × ¾)[1 + (24.9 - 0.51 × ¾) × 10-6 × (T - 723)] [17] where ¾ = 4.650 × CÅ‚ /(3.650 × CÅ‚ + 100) Ferrite aÄ… = 2.8863[1 + 17.5 × 10-6 × (T - 527)] [17] Cementite a¸ b¸ c¸ = 153.85 + 0.00818 × T [16] (a) Figure 4 Comparison of measured (line) and calculated (circles) length change for the 900ć%C curve. the lattice parameters of ferrite and cementite are not significantly influenced by carbon concentration, as in- dicated in Equation 4. However, significant discrep- ancies exist concerning the austenite lattice parameter [17 22]. In the present work, Onink et al. s data [17] is used since using these data the ºÅ‚ value is very close to 1 (ºÅ‚ = 0.9997), which agrees with the opinion of other authors [27] that Onink et al. s data are the most reliable. In the calculations, only two other experimental data (b) besides the dilatometry curve, the starting and finish- ing austenite transformation temperatures (Ac1 and Ac3 Figure 5 The calculated austenite volume fraction (a) and carbon con- centration in austenite, (b) from the dilatometric data and from the ther- temperatures), are required as input. For the calculation modynamics, as a function of temperature. of the 750ć%C and 800ć%C curves, the scaling factor for austenite (ºÅ‚ ) is taken from the 900ć%C curve. The transi- tion point from the three-phase region to the two-phase i.e. Ä… + ¸ Å‚ , and only a small amount of austen- region, i.e. the Ac temperature, is determined when ite formed due to the Ä… Å‚ transformation, judged 1 Å‚ Å‚ the product of CÅ‚ and f equals C0. Fig. 4 compares from the transition point (Ac ) where CÅ‚ · f = C0. 1 the measured length change with the calculated length The calculated results of the 800ć%C curve show that the change for the 900ć%C curve, as an example, and one final austenite fraction after isothermal holding is 0.89, can see that the difference between these two length higher than the equilibrium value (0.78) and the fraction changes is negligible, indicating that the solution is from the SEM observation (0.66). The calculated Ac 1 found successfully in the iterative analysis. temperature from the 800ć%C and 900ć%C data is about The calculated temperature dependence of the 780ć%C, which is 25ć%C higher than the one from the ex- austenite fraction and the carbon concentration for the perimental curve (see Fig. 3b). These inconsistencies 750ć%C, 800ć%C and 900ć%C curves are shown in Fig. 5. are discussed in the following section. Å‚ From the final CÅ‚ or f value, one can see that isother- mal holding at 750ć%C, which is below the Ac tempera- 1 ture, results in a complete decomposition of cementite. 4.4. Discussion Å‚ This is understandable since 750ć%C is already above the In order to obtain the austenite fraction ( f ), three equilibrium Ae temperature (698ć%C). The final carbon methods were applied: ortho-equilibrium thermody- 1 concentration in austenite and the austenite fraction af- namic analysis, SEM observations and the proposed ter isothermal holding at 750ć%C is 0.57 wt% and 0.28, evaluation method based on lattice parameters and Å‚ respectively. The austenite fraction is smaller than the dilatometry data. Table II summarizes f and CÅ‚ at the equilibrium value (0.41) at 750ć%C and the concentra- end of intercritical annealing at 750ć%C and 800ć%C, and tion is higher than the equilibrium value (0.38 wt%), one can see that the difference between the values from indicating that the equilibrium is not reached yet. The different methods is significant. As described in the calculated results also indicate that most of the austenite previous sections, the austenite fraction after anneal- fraction is formed due to the cementite decomposition, ing at 750ć%C calculated using the proposed method is 1589 Å‚ TABLE II Summary of austenite fraction, f , and carbon concen- ficial in the design of processing routes in TRIP steels, tration, CÅ‚ , at the end of intercritical annealing determined by various particularly in the case that the intercritical annealing methods temperature is close to the Ac1 temperature or/and the Å‚ annealing time is short. f CÅ‚ 750ć%C 800ć%C 750ć%C 800ć%C 5. Conclusions Proposed method 0.28 0.87 0.57 wt% 0.18 wt% In this paper, the subject of quantitative determination Thermodynamics 0.41 0.78 0.38 wt% 0.20 wt% of the austenite fraction and the carbon concentration SEM 0.43 0.66 in austenite during intercritical annealing from dilato- metric data has been investigated. Based on the lat- lower than the fraction given by the other two methods. tice parameters of existing phases and introduction of Moreover the SEM-determined austenite fraction is the scaling factor, an evaluation formulation has been slightly higher than the equilibrium value. However, proposed, in which two different cases during inter- the austenite fraction after 800ć%C annealing from the critical annealing were taken into account. One case proposed method is higher than the equilibrium value, concerns the three phase region (ferrite, cementite and which is less likely. In addition to the drawbacks of austenite) just above the Ac1 temperature, in which studying down-quenched samples, the inconsistencies the carbon concentration in austenite is assumed to be may arise from the following reasons. constant. Another case is the two-phase region (fer- From the viewpoint of thermodynamics calcula- rite and austenite) with a variable carbon concentra- tion, the controversy about ortho-equilibrium or para- tion in austenite. The proposed method was applied equilibrium is not clarified. However, the discrepancy to the dilatometric data in a 0.16C-1.5Mn-0.4Si TRIP between results from these two assumptions would multiphase steel annealed at 750ć%C (a three phase mi- decrease as the temperature increases. For instance, crostructure) and 800ć%C (a two-phase microstructure) the manganese content in austenite is 2.39 wt% at with help of the data of heating up to 900ć%C. The calcu- 750ć%C and 1.72 wt% at 800ć%C under ortho-equilibrium lated results show a reasonable temperature dependence assumption, as compared to 1.5 wt% under para- of the austenite fraction and the carbon concentration equilibrium assumption. From this, one can see that during intercritical annealing. Comparison of the new the controversy would not be the major cause of the results with the results from the microscopic observa- inconsistencies. As to the proposed method, more ac- tion as well as with those from the ortho-equilibrium curate results would be obtained if the following mea- thermodynamic calculation showed a considerable sures were taken. Firstly, one can see that the method intertest variation. hinges on the point whether the lattice parameters of existing phases are exactly known. The present paper References approached the problem by means of using literature 1. Y. SAKUMA, O. MATSUMURA and O. 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Trans. 29A (1998) 2383. and accepted 29 November 2001 1591