Advertisement

Study of phase transformation temperatures of alloys based on Fe–C–Cr in high-temperature area

  • Ľubomíra Drozdová
  • Bedřich Smetana
  • Simona Zlá
  • Vlastimil Novák
  • Monika Kawuloková
  • Silvie Rosypalová
  • Lenka Řeháčková
  • Ondřej Martiník
  • Petr Dostál
Article

Abstract

Three alloys based on Fe–C–Cr were studied. These alloys contained carbon in a range of 0.308–0.380 mass% and chromium 1.058–4.990 mass%. Temperatures of solidus (onward used as TS), liquidus (onward used as TL) and peritectic transformation (onward used as TP) were studied in the high-temperature region. These temperatures were obtained using two thermal analysis methods: differential thermal analysis (onward used as DTA) and simple thermal analysis (onward used as TA). The Setaram Setsys 18TM was used for experiments with employment of the DTA method. All measurements were taken in an inert atmosphere of pure argon at heating rate of 10 °C min−1, and simple TA method was used for the experiments with the use of the Netzsch STA 449 F3 Jupiter. Measurements were taken in inert atmosphere of pure argon at a heating and cooling rate of 5 °C min−1. Phase transformation temperatures were obtained by heating and cooling process and were approximated to “equilibrium conditions” (DTA method: zero heating rate and sample mass, standard, TA method: only standard) (Žaludová et al. in J Therm Anal Calorim 112:465–471, 2013a. doi: https://doi.org/10.1007/s10973-012-2847-8; J Therm Anal Calorim 111:1203–1210, 2013b. doi: https://doi.org/10.1007/s10973-012-2346-y). The experimental data were compared and discussed with the calculation results using IDS (solidification analysis package) software (onward used as SW) Thermo-Calc and the TCFE8 (Thermo-Calc Fe-based alloys) database. The results of the two alloys were compared with those published for similar steels. The experimentally obtained transition temperatures were close to the calculated values. The solidus, liquidus and peritectic transformation temperatures were lowered with increasing carbon (range 0.308–0.380 mass%) and chromium content (range 1.058–4.990 mass%). The smallest difference between the experimental results and theoretical calculations was observed at the liquidus temperature for all alloys. Nonetheless, the difference measured for the solidus temperatures was much greater.

Keywords

Fe–C–Cr alloys DTA Simple TA Temperatures of phase transformations Thermo-Calc IDS 

Introduction

One of the most important binary systems of engineering practice is Fe–C system [3, 4]. At present days, they are most often used for obtaining thermophysical and thermodynamic properties of steels (phase transition temperatures, heat effects of phase transformations, heat capacity and others), empirical relationships [5] and thermodynamic calculations [6]. The amount of calculated data is increasing compared to experimental data in recent years. Theoretically obtained data are often based on experimentally studied binary to quaternary systems and their approximations [6]. The confrontation of theoretical and experimental data shows that there are differences between them, often significant [7].

The data for specific steels are difficult to obtain. They are not available, old or inaccurate. The aim was to verify temperatures of phase transformations of chosen alloys. For similar systems are encountered to differences between these temperatures (obtained experimentally and theoretically), which have technological importance. The differences between these temperatures (obtained experimentally and theoretically) occur in similar systems, which have technological importance. Alloy A is used to improve medium-stressed parts of machines. The nitriding alloy B is used for more bulky parts of machines. Alloy C is hot work tool steel for production of strain tools [8].

Figure 1 presents a section of metastable diagram of Fe–Fe3C, which was calculated in SW Thermo-Calc. Fe is pure iron, and Fe3C is cementite (iron carbide). Several important phase transformations take place, in the high-temperature region. They are performed according to the AB curve (the liquidus curve) during cooling at first solidification of melt. δ ferrite is formed in the limited region during solidification. The curve AHJN is the solidus curve. The peritectic reaction can be expressed schematically by the following equation: LIQUID + δ → γ. Liquid and δ ferrite transform directly to austenite at point J (peritectic point) by an isothermal reversible reaction which applies to the area under the HJB curve [9].
Fig. 1

Fe–C (full line) and Fe–Cr–C (dashed line, content of chromium 5 mass%) metastable equilibrium phase diagram calculated by SW Thermo-Calc

The most important temperatures of the solidus, liquidus and peritectic transformation are in the high-temperature region (for alloys based on Fe–C). These temperatures are important, for example, for adjusting of casting conditions and for simulations of real technological production processes of steels [10, 11]. Several authors deal with studies of temperatures of the eutectoid transformation, temperature of the end of the ferrite to austenite transformation and temperature of the start of the pearlite formation in the low-temperature area [7]. The elements which have the most important influence on phase transformation temperatures (in consideration of chemical composition) are carbon and chromium (They shift the temperatures of phase transformations to lower values.). That follows from the equations published in [12, 13, 14, 15] for calculation of the liquidus and solidus temperatures.

Thermal analysis methods are often used to obtain thermophysical and thermodynamical properties [16]. This paper presents results obtained by two thermal analysis methods: differential thermal analysis (DTA) and simple thermal analysis (TA). The temperature effects during continuous linear heating or cooling in the controlled atmosphere are studied by differential thermal analysis (DTA). The temperature of the analyzed sample is measured relatively to the temperature of the reference sample [16]. Simple thermal analysis (TA) is based on measurement of the temperature of the sample. Temperature measurement is taken in dependence on time during the sample heating or cooling in the controlled atmosphere [17].

There were experimentally obtained temperatures of the solidus (TS), liquidus (TL) and peritectic transformation (TP). These data were discussed and compared with results calculated using SW Thermo-Calc (ver. 2015b) and database TCFE8 and with results obtained using kinetic SW IDS.

Theoretical calculation

Temperatures of phase transformations can be calculated by thermodynamic software such as Thermo-Calc [6], MT DATA [18], Pandat [19], FACT Sage [20]. These SWs differ in user interface, graphical level and optimization calculation [21]. These software uses the CALPHAD method. The accuracy of numerical simulation depends on the quality of thermodynamic databases [22].

Theoretical calculations were performed using thermodynamic SW Thermo-Calc, version 2015b and database TCFE8 intended for alloys of steels and cast irons and kinetic SW IDS (InterDendritic Solidification). All calculations were performed by equilibrium conditions. The CALPHAD method is used for calculation by SW Themo-Calc [23]. The IDS module simulates the solidification phenomena from liquid down to 1000 °C [24].

Thermo-Calc

The software uses CALPHAD method (Thermodynamic properties are described through the Gibbs free energy.) and is used for calculations of stable and metastable heterogeneous phase equilibria, amounts of phases and their compositions, thermochemical data such as enthalpies, heat capacity and activities, transformation temperatures, such as liquidus and solidus, driving force for phase transformations, phase diagrams (binary, ternary and multi-component) and more [6].

IDS

SW IDS (InterDendritic Solidification) is a thermodynamic–kinetic–empirical tool for simulation of the solidification phenomena including phase transformations from melt down to room temperature of low-alloyed steels and stainless steels containing chromium up to 26 mass%. Temperatures of phase transformations are dependent on a steel composition, a cooling rate and a dendrite arm diameter. The calculations are made in one volume element set on the side of a dendrite arm. The SW is used for calculation of important thermophysical material properties (enthalpy, thermal conductivity, density, etc.) [24].

Theoretical calculations present a fast and relatively cheap form of obtaining of results, but they can often be inaccurate or totally misleading. For this reason, it is necessary to verify, supplement and refine them with original experimental results for a particular studied alloy.

Experimental

Samples characterization

Three alloys based on Fe–C–Cr were studied. These alloys contained carbon in a range of 0.308–0.380 mass% and chromium 1.058–4.990 mass%. Alloys are marked in Fe–Fe3C system at Fig. 1. Chemical composition that was determined directly on samples for thermal analysis is presented in Table 1. Samples for analysis were mechanically cut from the downsprue.
Table 1

Chemical composition of studied alloys/mass%

Alloy

C

Cr

Mn

Si

P

Mo

Ni

Nb

Ti

Cu

V

Al

N

S

Ca

A

0.308

1.058

0.750

0.265

0.016

0.243

0.040

0.002

0.001

0.090

0.004

0.028

0.004

0.003

0.002

B

0.320

1.540

0.460

0.270

0.008

0.190

0.890

0.003

0.004

0.100

0.820

0.002

0.001

C

0.380

4.990

0.380

0.940

0.008

1.160

0.260

0.009

0.003

0.090

0.430

0.025

0.007

0.001

The samples for DTA analysis were processed into the form of cylinders with a diameter of 3.5 mm and a height of approx. 3 mm. The mass of the cylinders was 190 ± 5 mg. The samples for simple TA analysis were processed into the form of cone. The samples were polished (The possible oxidation layer was removed) and cleaned by ultrasonic impact in acetone before analysis.

Temperature calibration was performed using Ni (4N5) or Pd (5N) for both alloys. Corrections were performed with respect to the influence of the heating rate and the sample mass for DTA method.

In SW Thermo-Calc elements Sn, As, Sb, Pb and Bi (This element is not defined in software database.) are not included in calculation; diamond and graphite phases are also excluded. In SW IDS, the calculation did not include elements Sn, B, As, Sb, Pb and Bi.

Experimental conditions

For obtaining the phase transformation temperatures with help of differential thermal analysis (DTA) Setaram Setsys 18 TM (with DTA sensor, S-type, tri-couple, Fig. 2), the measurements were taken in alumina crucibles with a volume of 100 μL. An empty corundum crucible served as a reference sample. Dynamic atmosphere of argon was maintained in the furnace during analysis in order to protect the sample against oxidation. The purity of argon was higher than 99.9999%. The heating rate was 10 °C min−1. Each type of alloy was analyzed by three measurements at the same conditions at heating process (Three samples was made for each alloy.). DTA sensor has one thermocouple with three thermocouple “ends” in series, and simple TA sensor has one thermocouple, see arrangement at Fig. 2.
Fig. 2

Arrangement of DTA and TA sensor

For obtaining the values of temperatures of phase transformations by use of simple thermal analysis (TA) was used Netzsch STA 449 F3 Jupiter (simple TA, S—type, thermocouple, Fig. 2). The measurements were taken in alumina crucibles with volume of 14 mL. Dynamic atmosphere of argon was maintained in the furnace during analysis in order to protect the sample against oxidation. The purity of argon was higher than 99.9999%. The heating and cooling rates were 5 °C min−1. Each type of alloy was observed by two measurements at the same conditions at the controlled cycling experiments—two heating runs and two cooling runs.

Results and discussion

Temperatures of phase transformations were obtained on the basis of DTA curves (Fig. 3), and heating and cooling of simple TA curves evaluation (Figs. 46). Figure 3 shows the DTA curves obtained for the analyzed alloys at the heating rate of 10 °C min−1. Three thermal effects are observed for each alloy on the DTA curve. Fourth small thermal effect is observed for alloy B. This effect could probably agree to the dissolution of minor particles of carbides. These thermal effects correspond to melting process. The temperature of solidus (TS) corresponds to the start of the deviation from the baseline. The temperature of liquidus (TL) corresponds to the maximum of the second peak. Heat effect of temperature of peritectic transformation (Tp) was observed, and TP temperature was evaluated between temperatures of solidus and liquidus. Temperatures TS, TP, TL were also obtained from the evaluation of heating and cooling curves (Figs. 46) at the heating and cooling rate 5 °C min−1 by means of TA method. Experimental phase transition temperatures and theoretical values are presented in Table 2. The figures present primary data (experimental data without correction), and table presents data approximated to the “equilibrium conditions.”
Fig. 3

DTA curves of analyzed alloys, heating rate 10 °C min−1, melting

Fig. 4

Heating and cooling curve of alloy A, heating and cooling rate 5 °C min−1, melting and solidification

Fig. 5

Heating and cooling curve of alloy B, heating and cooling rate 5 °C min−1, melting and solidification

Fig. 6

Heating and cooling curve of alloy C, heating and cooling rate 5 °C min−1, melting and solidification

Table 2

Experimental and theoretical temperatures of phase transformations of alloys/°C

Temperature

Experimental

Theoretical

DTA

TA (heating)

TA (cooling)

Thermo-Calca

IDSb

Alloy A

T S

1447

1449

1451

1442

1446

T P

1486

1484

1458

1486

1482

T L

1498

1503

1499

1503

1502

Alloy B

T S

1445

1447

1437

1452

1438

T P

1471

1473

1449

1487

1461

T L

1498

1501

1495

1504

1500

Alloy C

T S

1397

1405

1410

1396

1386

T P

1438

1441

1416

1449

1432

T L

1474

1480

1476

1480

1475

aElements not included for calculation: Sn, As, Sb, Pb and Bi

bElements not included for calculation: Sn, B, As, Sb, Pb and Bi

During TA cooling, the undercooling effect is evident. The equivocal trend of undercooling in the case of nucleation of secondary phase (austenite) was observed from simple TA curves at the cooling process and under the identical experimental conditions. For that reason, TP temperatures obtained at cooling were not included for discussion because they are not representative.

Alloy A

The temperature of solidus obtained by DTA for alloy A is 1447 °C, by simple TA heating is 1449 °C and by simple TA cooling regime is 1451 °C. Solidus temperature calculated using SW Thermo-Calc is 1442 °C and by SW IDS is 1446 °C. The temperature interval of detected solidus temperature is 1447–1451 °C. The theoretical interval for solidus temperature is 1442–1446 °C. These intervals are not overlapped. Good agreement between the temperatures determined by both experimental methods was achieved in the case of TS temperature. The maximal temperature difference is 4 °C.

The start of peritectic transformation temperature for alloy A is at 1486 °C (DTA), 1484 °C (simple TA heating), 1486 °C (calculated using SW Thermo-Calc) and 1482 °C (according to SW IDS). The measured temperature interval of peritectic transformation is 1484–1486 °C, and the theoretical interval is 1482–1486 °C. These intervals overlap each other. Very good agreement between the temperatures determined by both experimental methods was achieved in case of TP temperature. The temperature difference is 2 °C.

The temperature of liquidus for alloy A obtained by DTA is 1498 °C, by simple TA heating is 1503 °C and by simple TA cooling is 1499 °C. The theoretical value obtained by SW Thermo-Calc is 1503 °C and by SW IDS is 1502 °C. The experimental interval of the detected liquidus temperature is 1498–1503 °C. The theoretical interval for the temperature of liquidus is 1502–1503 °C. These intervals are overlapped. Good agreement between the temperatures determined by both experimental methods was achieved in case of the TL temperature. The maximal temperature difference is 5 °C.

Some values of phase transition temperatures for the similar alloy were found in the accessible literature. The solidus and liquidus temperatures in a similar sample containing carbon (0.29 mass%) and chromium (1.02 mass%) were reported in work [17]. The analysis was performed by simple TA method for a sample with the mass of approximately 35 g at the cooling rate of 2 °C s−1. The temperature of solidus was 1415 °C, and temperature of liquidus was 1486 °C.

The smallest difference between experimentally obtained data by DTA method and the published values is 12 °C for TL. The largest difference between the experimental (simple TA cooling) and published values is 36 °C for TS. The temperatures stated by the authors in [16] are lower than the experimentally determined temperatures.

Alloy B

The temperature of solidus obtained by DTA for alloy B is 1445 °C, by simple TA heating 1447 °C and by simple TA cooling regime 1437 °C. Solidus temperature calculated using SW Thermo-Calc is 1452 °C and by SW IDS is 1438 °C. The experimental interval of detected solidus temperature is 1437–1447 °C. The theoretical interval for solidus temperature is 1438–1452 °C. These intervals are partially overlapped. Lower compliance between the temperatures determined by both experimental methods was achieved in case of temperature TS. The maximal temperature difference is 10 °C.

The start of peritectic transformation temperature for alloy B is at 1471 °C (DTA) and 1473 °C (simple TA heating). The calculated temperature using SW Thermo-Calc is 1487 and 1461 °C by SW IDS. The experimental interval of the detected temperature of peritectic transformation is 1471–1473 °C. The theoretical interval for the temperature of peritectic transformation is 1461–1487 °C. These intervals partly overlap. The detected temperatures are lower than theoretical (calculated by SW Thermo-Calc). Very good compliance determined by both experimental methods was achieved in the case of TP temperature. The temperature difference is 2 °C.

The temperature of liquidus for alloy B obtained by DTA is 1498 °C, by simple TA heating is 1501 °C and by simple TA cooling 1495 °C. The theoretical value obtained by SW Thermo-Calc is 1504 °C and by SW IDS is 1500 °C. The temperature interval of the detected temperature of liquidus is 1495–1501 °C. The theoretical interval for the temperature of liquidus is 1500–1504 °C. These intervals are partially overlapped. Good compliance between the temperatures determined by both experimental methods was achieved in the case of temperature TL. The maximal temperature difference is 6 °C.

Similar steel with TS, TP and TL values was not found in the literature for alloy B.

Alloy C

The temperature of solidus obtained by DTA for alloy C is 1397 °C, by simple TA heating is 1405 °C and by simple TA cooling regime is 1410 °C. Solidus temperature calculated using SW Thermo-Calc is 1396 °C and by SW IDS is 1386 °C. The experimental interval of detected solidus temperature is 1397–1410 °C. The theoretical interval for solidus temperature is 1386–1396 °C. These intervals are not overlapped. The experimental temperatures of solidus are higher than theoretical. Lower compliance with the temperatures determined by both experimental methods was achieved in the case of temperature TS. The maximal temperature difference is 13 °C.

The start of peritectic transformation temperature for alloy C is at 1438 °C (DTA) and 1441 °C (simple TA heating). Temperature calculated using SW Thermo-Calc is 1449 °C and by SW IDS is 1432 °C. Experimental interval of detected temperature of peritectic transformation is 1438–1441 °C. The theoretical interval for temperature of peritectic transformation is 1432–1449 °C. These intervals are partially overlapped. Very good compliance with the temperatures determined by both methods was achieved in the case of temperature TP. The temperature difference is 3 °C.

Temperature of liquidus for alloy C obtained by DTA is 1474 °C, by simple TA heating is 1480 °C and by simple TA cooling is 1476 °C. The theoretical value obtained by SW Thermo-Calc is 1480 °C and by SW IDS is 1475 °C. The experimental interval of detected temperature of liquidus is 1474–1480 °C. The theoretical interval for temperature of liquidus is 1475–1480 °C. These intervals are overlapped. Good compliance with the temperatures determined by both experimental methods was achieved in the case of temperature TL. The maximal temperature difference is 6 °C.

In the work [17], the temperatures of the solidus, liquidus and peritectic transformation for similar steel containing 0.35 mass% of carbon and 5.20 mass% of chromium were published. The analysis was performed by simple thermal analysis for a sample with the mass of approximately 35 g at the cooling rate of 2 °C s−1. The temperature of solidus was 1335 °C, the temperature of peritectic transformation was 1370 °C and temperature of liquidus was 1471 °C. The smallest difference between experimentally obtained data in this work and the published values of TL was observed for DTA method. The difference is 12 °C. The largest difference between the experimental and published values is for temperatures TS and TP. The difference for TS between published values and simple TA cooling is 75 °C. The difference for TP between the published values and simple TA heating is 71 °C. Experimental values of TL were in an excellent compliance with the earlier published values of TL in the article [17]. The difference between the published values and DTA is 3 °C. The temperatures published by the authors in [17] are lower than the experimentally determined temperatures in our work. Significant differences between the temperatures specified in [17] and determined by simple TA and DTA method were possibly caused by different regimes of the experimental setup, different rates of heating/cooling, differences in composition and the difference in the whole experimental arrangement. These large differences illustrate how difficult it is to find the proper thermodynamic data for the specific chemical composition and the same experimental conditions.

The temperature of solidus decreases with increasing amount of carbon (0.308–0.380 mass%) and chromium (1.058–4.990 mass%) according to [12, 13, 14]. The highest TS is for alloy A, lower for alloy B and the lowest TS for alloy C. Experimental and theoretical temperature intervals do not overlap. It applies to all methods. The temperature intervals between the detected and theoretical values have the best agreement for alloy A, lower for alloy B and the lowest for alloy C. Differences between solidus temperatures obtained by the thermal analysis methods can be caused by problems with proper (clean) determination of the start of the melting process, especially by simple thermal analysis (TA). The equivocal trend of temperature shift (TS) in dependence on the chemical composition was not observed at the temperature of solidus obtained by simple TA cooling. It could be caused by different undercooling of the analyzed samples. Similar problems connected with cooling can be encountered in case of TP.

The temperature of peritectic transformation decreases with increasing carbon (range 0.308–0.380 mass%) and chromium content (range 1.058–4.990 mass%). The highest TP is at alloy A, lower at alloy B and the lowest at alloy C. It applies to all methods. The temperature intervals between the detected and theoretical values have the best compliance for alloy A and lower for alloy C. These intervals were not overlapped in case of alloy B.

With increasing amount of C (range 0.308–0.380 mass%) and Cr (range 1.058–4.990 mass%), the temperature of liquidus decreases except for TL for alloy A and B which does not change (thanks to a similar chemical composition). According to the equations for calculation of liquidus temperature, chromium reduces this temperature [12, 13, 15]. TL for alloy C is lower than for alloy A and B by 14 °C (higher content of carbon and chromium) which is in line with [12, 13, 15]. The temperature intervals between detected and theoretical values that have the best compliance for alloys A and C and for alloy B are partially overlapped. The values of coefficient of variation were the smallest for DTA method (interval 0.00–0.14%), middle for simple TA heating (interval 0.01–0.42%) and the highest for simple TA cooling (interval 0.01–1.07%). The differences between experimental results obtained by each method can be caused by different heating rates (DTA—10 °C min−1, simple TA—5 °C min−1), sample mass (Alloy samples for simple TA analysis were 100 times larger than samples for DTA analysis.). The larger sample requires more heat for the phase transformation, to effect phase transformation in a full volume, by cooling effect (undercooling) and by the different arrangement of sensors (Fig. 2).

Differences between the experimental and theoretical values may be caused by software (calculation method, simplifying assumptions, elements not included into the calculation, the database allows only the selected elements to be included in the calculation) and databases that are used by the software. Difference between the theoretical and experimental temperatures also can be caused by chemical, phase and structural heterogeneity.

Conclusions

Liquidus (TL) and solidus (TS) temperatures and start temperature of peritectic transformation (TP) were obtained experimentally by DTA and simple TA method. They were discussed and compared with theoretical calculations performed by SWs Thermo-Calc and IDS. The experimentally obtained transition temperatures were close to the calculated ones.

The temperature of solidus, liquidus and peritectic transformation decreased with increasing amount of C (range 0.308–0.380 mass%) and Cr (range 1.058–4.990 mass%). The largest difference between DTA and simple TA cooling experimental values was observed at alloy C in the temperature range 1397–1410 °C. The smallest difference between the experimental values was in the case of the temperature of peritectic transformation for alloy A (temperature range 1484–1486 °C) and alloy B (temperature range 1471–1473 °C). Differences between experimental and theoretical values of liquidus temperatures were relatively low (less than 9 °C). The difference between the theoretical and experimental values of solidus temperature and peritectic transformation grew with increasing carbon and chromium content.

Results for alloy A and alloy C were compared with results obtained for similar steels published in [17]. The published phase transition temperatures were lower than experimentally investigated data.

The results also demonstrate that the calculations are an effective tool for obtaining the required data, but in some cases, they can be considered as indicative only. The calculated results should always be experimentally verified.

Experimental measurements specified phase transformation temperatures more precisely at high-temperature region. This finding could improve and refill software databases (FactSage, Thermo-Calc) and improve real technological processes (e.g., casting and solidification) using simulation SW (Procast, Magmasoft). Furthermore, larger homogeneity of products and reduction of defects could be reached. The knowledge of the liquidus and solidus temperatures is a key factor affecting the proper setting of steel overheating before casting on a continuous casting machine, machine setting (cooling water flow in the primary zone, spraying intensity in the secondary zone, casting speed), casting and steel processing in a steelworks.

Notes

Acknowledgements

This paper was created on the Faculty of Metallurgy and Materials Engineering in the Project No. LO1203 “Regional Materials Science and Technology Centre—Feasibility Program” funded by Ministry of Education, Youth and Sports of the Czech Republic, GAČR Project No. 17-18668S and student project SP2017/59.

References

  1. 1.
    Žaludová M, Smetana B, Zlá S, Dobrovská J, Watson A, Vontorová J, Rosypalová S, Kukutschová J, Cagala M. Experimental study of Fe–C–O based system above 1,000 °C. J Therm Anal Calorim. 2013;112:465–71.  https://doi.org/10.1007/s10973-012-2847-8.CrossRefGoogle Scholar
  2. 2.
    Žaludová M, Smetana B, Zlá S, Dobrovská J, Vodárek V, Konečná K, Matějka V, Matějková P. Experimental study of Fe–C–O based system below 1000 °C. J Therm Anal Calorim. 2013;111:1203–10.  https://doi.org/10.1007/s10973-012-2346-y.CrossRefGoogle Scholar
  3. 3.
    Tajima M, Umeyama Y. Latent heats of phase transformations in iron and steel. High Temp High Press. 2002;34:91–7.CrossRefGoogle Scholar
  4. 4.
    Edmonds DV, Pereloma E. Phase transformations in steels. Volume 1: Fundamentals and diffusion—controlled transformations. Cambridge: Woodhead Publishing Limited; 2012.Google Scholar
  5. 5.
    Myslivec T. Physical-chemical foundations of steel industry. 2nd ed. Praha: SNTL—Technical literature publishing house; 1971.Google Scholar
  6. 6.
    Thermo-Calc Software TCFE8 Steels/Fe-alloys database version 8. Accessed June 15, 2017.Google Scholar
  7. 7.
    Kawuloková M, Smetana B, Zlá S, Kalup A, Mazancová E, Váňová P, Kawulok P, Dobrovská J, Rosypalová S. Study of equilibrium and nonequilibrium phase transformations temperatures of steel by thermal analysis methods. J Therm Anal Calorim. 2017.  https://doi.org/10.1007/s10973-016-5780-4.CrossRefGoogle Scholar
  8. 8.
    Bolzano B. Steel in motion. http://www.bolzano.cz/. Accessed Oct 15, 2017.
  9. 9.
    Ryš P, Cenek M, Mazanec K, Hrbek A. Material science I, metal science 4. 1st ed. Praha: Academia; 1975.Google Scholar
  10. 10.
    Kalup A, Smetana B, Kawuloková M, Zlá S, Francová H, Dostál P, Waloszková K, Waloszková L, Dobrovská J. Liquidus and solidus temperatures and latent heats of melting of steels. J Therm Anal Calorim. 2017.  https://doi.org/10.1007/s10973-016-5942-4.CrossRefGoogle Scholar
  11. 11.
    Smetana B, Zlá S, Kawuloková M, Gryc K, Strouhalová M, Kalup A, Tkadlečková M, Dobrovská J, Michalek K, Jonšta P, Sušovský M, Dostal P, Martiník O, Drozdová Ľ. Temperatures of solidus and liquidus of tool steel. In: Proceedings paper, METAL 2016: 25th anniversary international conference on metallurgy and materials, p. 91–6. ISBN 978-80-87294-67-3.Google Scholar
  12. 12.
    Martiník O, Smetana B, Dobrovská J, Kalup A, Zlá S, Kawuloková M, Gryc K, Dostál P, Drozdová Ľ, Baudišová B. Prediction and measurement of selected phase transformation temperatures of steels. J Min Metall Sect B Metall. 2017.  https://doi.org/10.2298/JMMB170711030M.CrossRefGoogle Scholar
  13. 13.
    Cabrera-Marero JM, Carreño-Galindo V, Morales RD, Chávez-Alcalá F. Macro-micro modeling of the dendritic microstructure of steel billets processed by continuous casting. ISIJ Int. 1998.  https://doi.org/10.2355/isijinternational.38.812.CrossRefGoogle Scholar
  14. 14.
    Štětina J. Dynamic model of temperature field of continuously cast slabs. Ph.D. thesis, VŠB-TU Ostrava. http://ottp.fme.vutbr.cz/users/stetina/disertace/index.htm. Accessed Oct 17, 2017.
  15. 15.
    Han Z, Cai K, Liu B. Prediction and analysis on formation of internal cracks in continuously cast slabs by mathematical models. ISIJ Int. 2001.  https://doi.org/10.2355/isijinternational.41.1473.CrossRefGoogle Scholar
  16. 16.
    Gallagher PK. Handbook of thermal analysis and calorimetry: principles and practice, vol. 2. 1st ed. Amsterdam: Elsevier; 2003.Google Scholar
  17. 17.
    Jernkontoret. A guide to the solidification of steels. Technical Report. Stockholm; 1977.Google Scholar
  18. 18.
    MTDATA—Phase Diagram Software from the National Physical Laboratory. http://www.npl.co.uk/science-technology/mathematics-modelling-and-simulation/mtdata/. Accessed June 16, 2017.
  19. 19.
    Pandat Software. http://www.computherm.com/. Accessed June 16, 2017.
  20. 20.
    FactSage. The integrated thermodynamic databank system. http://www.crct.polymtl.ca/factsage/fs_general.php. Accessed June 16, 2017.
  21. 21.
    Sopoušek J. Phase equilibria and diffusion-controlled processes in selected systems of metals and their alloys (commentary). Brno: MU in Brno, Science Faculty, Chemical Institute; 2002.Google Scholar
  22. 22.
    Lašček M. Specific heat capacity of austenitic chrome-nickel steel Cr18Ni9. In: Acta Metallurgica Slovaca. http://www.ams.tuke.sk/data/ams_online/2008/number1/mag04/mag04.pdf. Accessed June 17, 2017.
  23. 23.
    Andersson JO, Helander T, Höglund L, Shi P, Sundman B. Thermo-Calc & DICTRA, computational tools for materials science. Calphad. 2002;26:273–312.CrossRefGoogle Scholar
  24. 24.
    Miettinen J. Solidification analysis package for steels-user´s manual of DOS version 2.0.0. Helsinki: University of Technology; 1999.Google Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  • Ľubomíra Drozdová
    • 1
  • Bedřich Smetana
    • 1
    • 2
  • Simona Zlá
    • 1
    • 2
  • Vlastimil Novák
    • 3
  • Monika Kawuloková
    • 1
    • 2
  • Silvie Rosypalová
    • 1
    • 2
  • Lenka Řeháčková
    • 1
    • 2
  • Ondřej Martiník
    • 1
  • Petr Dostál
    • 1
  1. 1.Department of Physical Chemistry and Theory of Technological Processes, Faculty of Metallurgy and Materials EngineeringVŠB-TU OstravaOstrava, PorubaCzech Republic
  2. 2.Faculty of Metallurgy and Materials Engineering (FMME), Regional Materials Science and Technology Centre (RMSTC)VŠB-TU OstravaOstrava, PorubaCzech Republic
  3. 3.Department of Chemistry, Faculty of Metallurgy and Materials EngineeringVŠB-TU OstravaOstrava, PorubaCzech Republic

Personalised recommendations