treatment at the partitioning temperature (PT), identical Communication to or higher than the QT to promote carbon diﬀusion out from martensite to stabilize austenite, and (3) a ﬁnal Numerical Investigations of the Effects quench from the partitioning temperature to room temperature. of Substitutional Elements During step (2), at PT, carbon partitioning from on the Interface Conditions During martensite to austenite is one of the key phenomena that occur during the Q&P process. Its kinetics is governed Partitioning in Quenching by carbon diﬀusion in martensite and austenite, respec- and Partitioning Steels tively, and by the carbon concentrations on each side of the martensite/austenite interface. This boundary con- dition is often assumed to be governed by constrained STEVE GAUDEZ, JULIEN TEIXEIRA, para-equilibrium (CPE). This CPE imposes ﬁrst no SEBASTIEN Y.P. ALLAIN , partition of substitutional elements (accounting for their GUILLAUME GEANDIER, MOHAMED GOUNE, supposed low diﬀusivity at PT), continuity of the carbon ´ ´ MICHEL SOLER, and FREDERIC DANOIX chemical potential across the interface, no interface mobility and, ﬁnally, absence of any carbide  precipitation. https://doi.org/10.1007/s11661-018-4630-3 In this article, we focus only on the thermodynamic The Author(s) 2018 conditions at the interface to determine all the possible tie lines for a given temperature and alloy composition, i.e., the relations between carbon concentrations at interfaces in both austenite and martensite. As shown by In quenched and partitioned steels, carbon partition-  Speers, a carbon mass balance and the assumption of ing is considered to be driven by a constraint para-equi- interface mobility permit calculating the ﬁnal state after librium at the martensite/austenite interface. Using partitioning. Thermo-Calc calculations, we investigated the eﬀect of Few previous works have proposed practical laws non-partitioned elements on the resulting interface derived from thermodynamic calculations describing condition. Among all tested elements, only aluminum these tie lines but solely in binary Fe-C steels, neglecting and chromium have signiﬁcant eﬀects. From this [1,3] the eﬀect of substitutional elements. Nevertheless, numerical study, a practical composition- and temper- most alloys used to study or produce Q&P steels contain ature-dependent relationship describing interface tie high amounts of alloying elements, such as manganese, lines was derived and calibrated for Fe-C-2.5Mn-1.5- which contributes to increasing the hardenability of the Si-X wt pct alloys (X = Cr or Al). steel or the silicon, which helps retard cementite carbide The quenching and partitioning (Q&P) process was  precipitation. Aluminum can be added instead for a invented by Speer et al., to meet the needs of the supposed similar eﬀect on carbide precipitation as automotive sector for the development of a third-gen- [1,2] investigated in References 4 and 5 although 6 and 7 eration advanced high-strength steel. Q&P steels showed aluminum neutrality on cementite carbide show mainly duplex ultraﬁne microstructures made of precipitation. martensite and residual austenite. These typical In this work, the inﬂuence of classical alloying microstructures are obtained by (1) an initial quench elements and temperature on the CPE condition was after austenitization down to a temperature QT (quench systematically investigated by thermodynamic calcula- temperature) between the martensite start (Ms) and tions using Thermo-Calc software. The calculations ﬁnish (Mf) temperature of the alloy to induce a partial were ﬁrst conducted taking the binary Fe-C system as a martensitic transformation, (2) an isothermal holding reference. We deduced from this work that only aluminum and chromium have a signiﬁcant eﬀect on the interface condition, and we established a composi- tion- and temperature-dependent relationship for a STEVE GAUDEZ, JULIEN TEIXEIRA, SEBASTIEN Y.P. typical Fe-2.5Mn-1.5Si-X wt pct alloy (X = Al or Cr). ALLAIN, and GUILLAUME GEANDIER are with the Institut In the calculations conducted below, we consider a Jean Lamour, UMR CNRS-UL 7198, Nancy, France. Contact e-mail: martensite/austenite interface at temperature PT. The email@example.com MOHAMED GOUNE is with the objective of the numerical procedure is to establish a Institut de Chimie de la matie´ re Condense´ e de Bordeaux, UPR 9048, Pessac, France. MICHEL SOLER is with the ArcelorMittal Maizie´ res relationship between carbon contents at the interface in ´ ´ Research SA, Maizie´ res-le´ s-Metz, France. FREDERIC DANOIX is martensite and austenite, respectively. with the Groupe de Physique des Mate´ riaux, UMR CNRS-INSA-UR The thermodynamic conditions derived from CPE at 6634, Saint Etienne du Rouvray, France. temperature PT are deﬁned by two equalities: Manuscript submitted November 15, 2017. Article published online April 20, 2018 2568—VOLUME 49A, JULY 2018 METALLURGICAL AND MATERIALS TRANSACTIONS A the CPE interface conditions for the binary Fe-C system u ¼ u ½1 at the same temperature, i.e., all the possible tie lines for i i this particular equilibrium. For each element, three where u = x /(1 x ), with x the atomic concentra- i i C i diﬀerent levels of alloying element addition were con- tion of substitutional element i and x that of carbon. sidered (1.5, 2.5 and 3.5 wt pct for manganese and 0.5, The u fraction of substitutional element i represents its 1.5 and 2.5 wt pct respectively for the other elements). amount in the substitutional lattice in martensite (a¢) Manganese, chromium and molybdenum increase the or austenite (c). carbon content in ferrite for a given carbon content in a austenite (the slope of the curve describing the CPE l ¼ l ½2 C C interface condition increases). The only signiﬁcant increase was however observed for chromium. where l and l are the carbon chemical potentials in C C On the contrary, aluminum, nickel and silicon martensite (a¢) and austenite (c), respectively. decrease the carbon content in ferrite for a given carbon This set of equations allows one degree of freedom. content in austenite (the slope of the curve describing This allows establishing a relationship between w and the CPE interface condition decreases). The only signif- w , i.e., the weight carbon concentration in martensite  icant decrease was however observed for aluminum. (a) and austenite (c), respectively. In this study, In addition, the eﬀects of phosphorus and cobalt calculations were performed using the S version of additions were also investigated (with content ranging Thermo-Calc software. The CPE relationship was from 0 to 0.1 wt pct for phosphorus considered as a established in two steps. First, the relationship between  substitutional element and from 0 to 1 wt pct for / / l and wðÞ / ¼ a or c was established separately in C C cobalt). Both elements show a negligible eﬀect on the each phase a and c. Second, both calculations were CPE interface condition. combined considering Eq.  to obtain the CPE These trends have been observed at diﬀerent temper- relationship. This method permits describing all the atures, suggesting that among all the tested elements possible tie lines at interfaces during partitioning. To only aluminum and chromium additions signiﬁcantly determine the operative tie lines, it is necessary to carry aﬀect the interface conditions. We can expect that the out a thermokinetic calculation involving a carbon mass addition of aluminum will increase the partitioning balance between phases. These last calculations are kinetics by increasing the carbon concentration in beyond the scope of this short communication solely austenite and thus increasing the carbon gradients at dedicated to the thermodynamic aspects. the interface. Chromium is supposed to aﬀect the Three databases were used: SSOL4, TCFE7 and partitioning mechanism in the opposite way. TCFE9. In these commercial databases, the martensite To go farther, we numerically investigated the eﬀect phase has not been described explicitly so far (even in of aluminum and chromium addition on a reference the most recent ones). This is why we decided to use the quaternary alloy. We chose the alloy Fe-C-2.5Mn-1.5Si  ferrite phase to represent the behavior of martensite studied by our group without losing generality, as even if far higher carbon concentrations can be expected manganese and silicon have independently weak eﬀects. (up to 0.5 wt pct in martensite at 400 C, for We veriﬁed that the cross eﬀects of alloying elements are [9,10] instance). limited. This reference alloy is also interesting as it is the For the same calculations, the tested databases gave [13–16] basis of a few studies on Q&P steels. signiﬁcantly diﬀerent results. The carbon contents found The interface conditions were thus studied in in ferrite were also systematically lower than the Fe-C-2.5Mn-1.5Si-X wt pct(X = Al or Cr)alloysat  relationship proposed for a Fe-C binary system by diﬀerent temperatures (between 373 K and 773 K with 50-K Santoﬁmia et al. who used another source of thermo- steps) and with X additions up to 4 wt pct with 0.5 wt pct dynamic data, MTDATA. One also has to mention that steps. To capture the observed variations in CPE conditions the thermodynamic data regarding the metastable a¢/c due to both alloying elements, we calibrated a composition- equilibrium came in large part from extrapolations far and temperature-dependent relationship on raw Thermo-  below the eutectoid temperature. Nevertheless, the calc results. Inspired by the prior work of Santoﬁmia et al., trend for each database was identical, which is a reason the following empirical equations were considered: why we decided in a ﬁrst step to study only the relative a cðÞ ðÞ a þ c w þðÞ b þ d T X T X eﬀects of alloying elements using a single database c w ¼ w e ½3 c c keeping in mind that the absolute carbon concentrations where a and b are temperature-dependent functions found in the phases can always be discussed. We chose T T (T the temperature in K) and c and d are tempera- to use the TCFE7 database to oﬀer a continuous and X X ture- and composition-dependent functions for both stable description of the CPE condition as the latest elements (Al or Cr). w is the weight concentration of database (TCFE9) shows a discontinuity when varying the temperature. carbon in austenite and martensite. This formalism Figure 1 shows the evolution of the weight carbon permits isolating the composition and temperature content in ferrite as a function of the weight carbon eﬀects. Possible cross eﬀects between alloying elements content in austenite under the CPE condition for are once again neglected. In the absence of alloying elements (w = 0), Eq.  can be drastically simpliﬁed diﬀerent Fe-C-X systems where X is (a) manganese, into Eq. , which can then be used to describe the (b) silicon, (c) aluminum, (d) chromium, (e) nickel and CPE condition of the reference alloy. (f) molybdenum at 673 K. The black curve represents METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 49A, JULY 2018—2569 0.01 0.01 0.01 1.5w%Mn 0.5w%Si 0.5w%Al 2.5w%Mn 1.5w%Si 1.5w%Al 3.5w%Mn 2.5w%Si 2.5w%Al 0.0075 0.0075 0.0075 0.005 0.005 0.005 0.0025 0.0025 0.0025 0 0 0 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 C content in austenite (wt%) C content in austenite (wt%) C content in austenite (wt%) (a) (b) (c) 0.01 0.01 0.01 0.5w%Cr 0.5w%Ni 0.5w%Mo 1.5w%Cr 1.5w%Ni 1.5w%Mo 2.5w%Cr 2.5w%Ni 2.5w%Mo 0.0075 0.0075 0.0075 0.005 0.005 0.005 0.0025 0.0025 0.0025 0 0 0 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 C content in austenite (wt%) C content in austenite (wt%) C content in austenite (wt%) (d) (e) (f) Fig. 1—Eﬀect of substitutional alloying elements at 673 K on the CPE condition: (a) manganese, (b) silicon, (c) aluminum, (d) chromium, (e) nickel and (f) molybdenum. The black curve is the reference of the CPE condition for a binary Fe-C steel. The carbon content ranges in austenite and martensite correspond to the levels generally found in local ﬁeld thermokinetic models in the literature. Table I. Numerical Values of Parameters a and b as Deﬁned in Eqs.  and  After Calibration i i a a a a 0 1 2 3 1 3 7 338.559 9.456 10 1.193 10 5.664 10 b b b b 0 1 2 3 1 4 8 56.107 1.663 10 2.016 10 9.033 10 These parameters permit capturing the temperature sensitivity of the CPE condition for the reference alloy Fe-C-2.5Mn-1.5Si wt pct in the temperature range 373 K to 773 K generally chosen for PT. a cðÞ a ðÞ T w þb ðÞ T 2 T c T cðÞ w ; T¼ c w þ c w þ c w T ½7 w ¼ w e ½4 X X 0 X 1 2 X c c X a and b are described by third-order polynomials: T T dðÞ w ; T¼ d w þ d w þ d w T ½8 X X 0 X 1 2 X 2 3 a ðÞ T ¼ a þ a T þ a T þ a T ½5 T 0 1 2 3 Parameters a and b must ﬁrst be adjusted on the i i reference alloy. Parameters c and d are then adjusted 2 3 i i b ðÞ T ¼ b þ b T þ b T þ b T ½6 T 0 1 2 3 for varying aluminum and chromium additions, respec- tively. In all the cases, the parameters were calibrated c and d are functions of the temperature and using a mean square method to minimize the deviation X X alloying additions: from the thermodynamic calculations and result of 2570—VOLUME 49A, JULY 2018 METALLURGICAL AND MATERIALS TRANSACTIONS A C content in martensite (wt%) C content in martensite (wt%) C content in martensite (wt%) C content in martensite (wt%) C content in martensite (wt%) C content in martensite (wt%) Table II. Numerical Values of Parameters c and d as Deﬁned in Eqs.  and  After Calibration to Capture the Eﬀect of i i Aluminum and Chromium Additions Al c c c 0 1 2 156.193 389.189 6.054 10 d d d 0 1 2 100.250 210.517 8.469 10 Cr c c c 0 1 2 69.285 164.219 5.467 10 d d d 0 1 2 87.991 129.354 8.556 10 In addition, with parameters a and b given in Table I, these parameters permit describing the CPE condition for Fe-C-2.5Mn-1.5Si-X wt pct i i alloys in the temperature range 373 K to 773 K. 0.5 0.5 Reference Reference T=673K T=673K 0.5wt%Al 0.5wt%Cr 0.4 0.4 2.0wt%Al 2.0wt%Cr 4.0wt%Al 4.0wt%Cr 0.3 0.3 0.2 0.2 0.1 0.1 0 0 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 C content in austenite (wt%) C content in austenite (wt%) (a) (b) 0.5 0.5 Reference Reference T=773K T=773K 0.5wt%Al 0.5wt%Cr 0.4 0.4 2.0wt%Al 2.0wt%Cr 4.0wt%Al 4.0wt%Cr 0.3 0.3 0.2 0.2 0.1 0.1 0 0 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 C content in austenite (wt%) C content in austenite (wt%) (c) (d) Fig. 2—Carbon composition at martensite/austenite interfaces predicted by a CPE interface condition for Fe-C-2.5Mn-1.5Si-X wt pct alloys (X = Al or Cr) at 673 and 773 K. (a) X = Al, T = 673 K; (b) X = Cr, T = 673 K; (c) X = Al, T = 773 K; (d) X = Cr, T = 773 K. The black curves represent the CPE condition for the reference alloy Fe-C-2.5Mn-1.5Si wt pct (Eq. ). The dots are the results of the thermodynamic computation performed with Thermo-Calc software and the TCFE7 database, and the continuous lines are calculated with Eq.  after calibration. Eq. . The maximum relative error made using the (X = Al or Cr) at 673 K and 773 K. Figures 2(a) and proposed relationship is lower than 0.5 pct in the studied (c) corresponds to aluminum additions and Figures 2(b) ranges of compositions and temperatures. The numer- and (d) to chromium additions. The correlation is ical values of the parameters calibrated on raw excellent in all the cases. Thermo-Calc ’s results are given in Tables I and II. Our relationship permits good reproduction of the Figure 2 represents the result of raw thermodynamic temperature sensitivity of the CPE condition. Increas- calculation (dots) and the result of Eq.  after ing PT leads in fact to a decrease in the carbon [1,3] calibration (continuous lines) corresponding to the concentration in austenite and thus to slower CPE conditions of Fe-C-2.5Mn-1.5Si-X wt pct alloys partitioning kinetics. An addition of aluminum METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 49A, JULY 2018—2571 C content in martensite (wt%) C content in martensite (wt%) C content in martensite (wt%) C content in martensite (wt%) increases the carbon concentration in austenite, con- OPEN ACCESS trary to chromium, as already shown in Figure 1. This This article is distributed under the terms of the qualitatively conﬁrms that cross eﬀects between alloy- Creative Commons Attribution 4.0 International Li- ing elements (Mn/Si with Al/Cr) are limited for such cense (http://creativecommons.org/licenses/by/4.0/), calculations. which permits unrestricted use, distribution, and re- To summarize, the inﬂuence of substitutional alloying production in any medium, provided you give appro- elements on the CPE interface condition was thoroughly priate credit to the original author(s) and the source, investigated based on calculations with Thermo-Calc provide a link to the Creative Commons license, and software with the TCFE7 database. This interface condi- indicate if changes were made. tion is often met at the martensite/austenite interface during the partitioning step of Q&P treatments. Except aluminum and chromium, all the investigated REFERENCES elements (manganese, silicon, nickel, molybdenum, 1. J. Speer, D.K. Matlock, B.C. 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Goune´,F. Danoix, S. Aoued, and A. Poulon-Quintin: Mater. Sci. Eng. A, 2018, vol. 710, pp. 245–50. 14. J.C. Hell, M. Dehmas, S. Allain, J.M. Prado, A. Hazotte, and J.P. This work was supported by the French State Chateau: ISIJ Int., 2011, vol. 51 (10), pp. 1724–32. through the CAPNANO project (ANR-14-CE07-0029) 15. M.J. Santoﬁmia, L. Zhao, R. Petrov, C. Kwakernaak, W.G. Sloof, operated by the National Research Agency (ANR), and J. Sietsma: Acta Mater., 2011, vol. 59 (15), pp. 6059–68. the Materalia Cluster and LABEX DAMAS (ANR- 16. S.Y.P. Allain, G. Geandier, J.C. Hell, M. Soler, F. Danoix, and M. 11-LABX-0008-01) from Lorraine. Goune´ : Metals, 2017, vol. 7, 232. 2572—VOLUME 49A, JULY 2018 METALLURGICAL AND MATERIALS TRANSACTIONS A
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Published: Apr 20, 2018
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