Modelling of technological processes of heat treatment or welding, involving multiple heat source transitions, requires considering the phenomenon of tempering. In work have been presented results of dilatometric research of hardened C45 steel subjected to tempering. The analysis of the influence of heating rate at the kinetic determined from dilatometric curves has been made. There have also been estimated quantities of transformation expansions and thermal expansion coefficients of hardening and tempering structures (austenite, ferrite, pearlite, martensite and sorbite). The analysis of tempering time influence on the hardness of tempered steel has been made. Functions associating hardness with tempering time (rate of heating-up) in technological processes based on short-timed action of a heat source (eg. laser treatment) have been suggested.Modeliranje tehnološkog procesa toplinske obrade ili zagrijavanja, uključivo višedjelne izvore prijelaza topline, zahtijeva razmatranje fenomena toplinske obrade popuštanje. U radu su prezentirani rezultati popuštanja tvrdoće zakaljenog čelika C45. Analiza utjecaja brzine zagrijavanja na kinetiku procesa je determinirana dilatometrijskim krivuljama. Procijenjeni su kvantitativni transformacijski izrazi i koefi cijent toplinskog širenja kaljenih i propuštenih struktura (austenit, perlit, mertenzit, sorbit). Napravljena je analiza utjecaja trajanja popuštanja na tvrdoću popuštenog čelika. Preporučena je funkcija koja udružuje tvrdoću i trajanje propuštanja (brzina zagrijavanja) u tehnološkom procesu temeljena na kratkotrajnom djelovanju izvora topline (npr. tretman laserom)

A. Kulawik

J. Winczek

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9METALURGIJA 51 (2012) 1, 9-12J. WINCZEK, A. KULAWIKDILATOMETRIC AND HARDNESS ANALYSIS OF C45 STEEL TEMPERING WITH DIFFERENT HEATING-UP RATESReceived – Prispjelo: 2010-09-20Accepted – Prihvaćeno: 2011-02-10 Original scientifi c paper – Izvorni znanstveni radISSN 0543-5846METABK 51(1) 9-12 (2012)UDC – UDK 669.14-418:539.37:620.17=111Modelling of technological processes of heat treatment or welding, involving multiple heat source transitions, re-quires considering the phenomenon of tempering. In work have been presented results of dilatometric research of hardened C45 steel subjected to tempering. The analysis of the infl uence of heating rate at the kinetic determined from dilatometric curves has been made. There have also been estimated quantities of transformation expansions and thermal expansion coeffi  cients of hardening and tempering structures (austenite, ferrite, pearlite, martensite and sorbite). The analysis of tempering time infl uence on the hardness of tempered steel has been made. Functions associating hardness with tempering time (rate of heating-up) in technological processes based on short-timed ac-tion of a heat source (eg. laser treatment) have been suggested.Key words: dilatometric analysis, hardness, tempering, heat treatment, mechanical propertiesDilatrometrijska i analiza tvrdoće čelika C45 popuštanog uz različite brzine zagrijavanja. Modeliranje tehno-loškog procesa toplinske obrade ili zagrijavanja, uključivo višedjelne izvore prijelaza topline, zahtijeva razmatranje fenomena toplinske obrade popuštanje. U radu su prezentirani rezultati popuštanja tvrdoće zakaljenog čelika C45. Analiza utjecaja brzine zagrijavanja na kinetiku procesa je determinirana dilatometrijskim krivuljama. Procijenjeni su kvantitativni transformacijski izrazi i koefi cijent toplinskog širenja kaljenih i propuštenih struktura (austenit, per-lit, mertenzit, sorbit). Napravljena je analiza utjecaja trajanja popuštanja na tvrdoću popuštenog čelika. Preporuče-na je funkcija koja udružuje tvrdoću i trajanje propuštanja (brzina zagrijavanja) u tehnološkom procesu temeljena na kratkotrajnom djelovanju izvora topline (npr. tretman laserom).Ključne riječi: dilatometrijska analiza, tvrdoća, popuštanje, toplinska obrada, mehanička svojstvaINTRODUCTION In technological processes of heat treatment and welding, depending on steel genre and process param-eters, can occur quenching structures, including marten-site. In case of process connected with multiple laser beam transitions or welding electrode making next welds cause tempering of already hardened areas. Most frequently, initial heating-up of heat-treated material above MS temperature of the beginning of martensitic transformation during cooling, is used in order to pre-vent creation of austenite during to prevent creation of austenite during technolo-gical process. In other case it is essential to take into consideration tempering. In the case of welding processes in order to obtain appropriate fi nal structure, temper bead application is used [1]. In order to project fi nal structure of the material after the process or to calculate strain and stress state in heat-treated object it is essential to have the knowledge in kinetics of phase changes tempering. A lot of works have been dedicated to examine the phenomenon of tempering. In most of them carried out experiments J. Winczek, A. Kulawik, Faculty of Mechanical Engineering and Com-puter Science, Czestochowa University of Technology, Czestochowa, Polandconcern comparative metallographic analysis and me-chanical properties before and after the tempering [2-7]. While in modelling of stress states during tempering, the infl uence of phase changes is frequently omitted [8]. In the case of heat treatment the time of heating-up amounts to several dozen minutes, while annealing can last even hours. The result is homogenous tempering structure. For such technological conditions, detailed analysis of changes in microstructure in steel C45 and Ni3.5CrMoV has been presented in work [9]. In weld-ing processes and laser treatment occurs dynamic tem-perature change, while time of peak tempearture during tempering lasts from several to hundreds of seconds. Short austenisation time, as well as of tempering lead to heterogeneous structure. Work [10] examines the micro-structure and hardness after multiple welding cycles, while in work [11] have been presented results of metal-lographic research, microhardness and impact strength of welds tempered by conventional method. The authors [12] carried out analysis of tempering kinetics of weld-ed elements basing on results of microhardness meas-urements. There is lack of works describing quantita-tively the connection between strains and temperature during welding and laser processes. The speed of heat-ing-up can signifi cantly affect kinetics of heating-up 10  METALURGIJA 51 (2012) 1, 9-12J. WINCZEK et al.:  DILATOMETRIC AND HARDNESS ANALYSIS OF C45 STEEL TEMPERING WITH DIFFERENT...transformations in steel both during austenitisation [13-16], as well as during heating-up from hardened stage (of tempering) [17,18].TEMPERING IN STEELSIn conventional heat treatment process in steels with the carbon content up to 0,2 wt.% tempering begins al-ready in the environment temperature moving coal atoms [19]. After that segregation from temperature 80 0C oc-curs liberating of carbides – it proceeds most intensively in the temperature range between 150 – 200 0C, ends mainly at 250 0C, but sometimes at 400 0C. As a result of reducing the amount of coal, tetragonality of martensite is decreasing. Created in the fi rst phase of tempering structure, consisting of supersaturated solid solution α and carbide ε is called low-tempered martensite.Between 100 and 350 0C any retained austenite be-gins to decompose. It has been suggested that this hap-pens by transformation into bainitic ferrite and cement-ite [19]. Above 350 0C martensite decomposes liberat-ing cement grains creating the phase called sorbite or troostite. Then the growth of grains occurs and coagula-tion of cementite particles, spheroidizing, i.e. forming tiny spherical particles of cementite in ferrite matrix. Tempering process ends in the temperature range 600 - 700 0C. Above 600 0C still proceeds coagulation of ce-mentite and spheroidizing of ferrite – formation of di-vorced pearlite, i.e. globular cementite in ferrite matrix of low hardness. This stage is called recrystallization.EXPERIMENTAL WORKThe chemical composition of researched steel is shown in Table 1. Table 1 Chemical composition of C45 steel substrates wt. % (max.)C Mn Si P S Al Cr Ni Mo Cu0,44 0,660 0,250 0,015 0,024 0,017 0,011 0,10 0,025 0,24Dilatometric experiments were carried out in ther-mal cycle simulator Smitweld TCS1405 (Figure 1). The infl uence of the speed of heating-up on the temperature of the beginning and the end of tempering has been re-searched for the speed of heating from 0,1 to 100 0C/s. Samples for tempering research have been heated-up to 1100 0C, then cooled with the velocity 200 0C/s. Mar-tensitic structure of hardened sample is presented in Figure 2. The average value of hardness of hardened area was HV30 = 714.For each speed of heating have been made at least 3 dilatometric researches which allowed to determine temperature average values Ts of the beginning and Tf of the end of tempering process. Average values have been presented in Table 2.Dilatometric graph for hardening-tempering cycle with the heating-up with the velocity VH = 10 0C/s during tem-pering has been presented in Figure 3. From the analysis of dilatometric graphs, we can draw a conclusion that the fi rst stage of tempering – the segregation of coal atoms and liberating carbides (to 290 0C) do not affect signifi cantly Figure 1 Thermal Cycle Simulator Smitweld 1405Figure 2 Martensitic structure of a hardened sampleTable 2 Average temperature values Ts and TfVH / 0C/s 0,1 0,5 1 2 5 10Ts / 0C 290 300 310 315 320 325Tf / 0C 420 430 435 440 450 465VH / 0C/s 20 30 40 50 60 100Ts / 0C 335 340 345 350 355 370Tf / 0C 470 475 480 485 490 500-0,004 0 0,004 0,008 0,012 0,016 0,02Dilatation / m-30100200300400500600700800900100011001200Temperature/0CTemperingHardening10 / 0CFigure 3 Dilatometric curves for hardening-tempering cycle11METALURGIJA 51 (2012) 1, 9-12J. WINCZEK et al.:  DILATOMETRIC AND HARDNESS ANALYSIS OF C45 STEEL TEMPERING WITH DIFFERENT...the shape of dilatometric curve. Distinct changes on dilato-metric graphs have been observed in the temperature range 290 - 500 0C, during forming of sorbite.The dependence of temperature Ts on the heating rate V(H) (Figure 4) has been determined by approxi-mation of dilatometric measure-ments by Hoerl regres-sion model using program CurveExpert [20]: ( ) ( )cHVHs VabVT H=  (1)where: a = 306,16454, b = 1,0007254, c = 0,025137007, correlation coeffi cient is 0,997, while standard error 2,137.In a similar way has been determined the depend-ence of temperature Tf on the heating rate V(H) (Figure 4) using Harris regression model: ( )CHHf bVaVT+=1 (2)where: a = 0,00258774, b = -0,00028544502, c = 0,15680145, correlation coeffi cient 0,999, standard er-ror 1,259.The CHT (Continuous Heating Transfor-mations) diagram is presented in Figure 5.On the basis of dilatometric measurements and re-sults of works [21] have been determined thermal ex-pansion coeffi cients and transformation expansions val-ues which are shown in Table. 3.Results of hardness measurement of samples after tempering have been presented in Table 4. Together with the decrease of tempering time (increase of heat-ing-up rate with constant cooling velocity 10 0C/s in thermal cycles) diminishes hardness.For carried out researches, the dependence of hard-ness on rate of heating-up has been approximated with function (Figure 6): ( ) edVcVbVaVVHV HHHHH ++++= 23430  (3)where: a = -2,4578808x10-6, b = 0,00054318, c = -0,030563, d = 2,0558168, e = 342,63333, correlation coeffi cient 0,999, standard error 1,608.The infl uence of tempering time t on hardness has been determined by functions (Figure 7):- for t <= 100 s ( ) 230 tcbtatHV ++=  (4)where: a = 375,85089, b = -23065,856, c = 0,1459668, correlation coeffi cient 0,999, standard error 3,2,- for t > 100 s ( ))exp(130 ctbatHV−+=  (5)where: a = 344,95107, b = -0,0070576689, c = 357598, correlation coeffi cient 0,992, standard error 2,523.CONCLUSIONSIn work has been made analysis of infl uence of the heating-up rate on tempering kinetics. On the basis of dilatometric graphs has been proposed the function bounding the rate of heating-up with the temperature of the beginning and the end of temperature of the begin-ning and the end of transformation expansions during tempering phase changes. Quantities of transformation 0 10 20 30 40 50 60 70 80 90 100VH / 0C/s250300350400450500550Temperature/0Cmodel Tfmodel TsexperimentFigure 4  Comparison of Ts(VH) and Tf(VH) models and research resultsTable 3  Structural (γ) and thermal (α) expansion coeffi  cients for phase of C45 steel.α / 1/°CAustenite 2,178⋅10-5 γF,P,S→A 1,986⋅→10-3Ferrite 1,534⋅10-5 γB→A 1,440⋅10-3Pearlite 1,534⋅→10-5 γA→F,P 3,055⋅10-3Bainite 1,171⋅→10-5 γA→B 4,0⋅10-3Martensite 1,36⋅→10-5 γA→M 6,85⋅→10-3Sorbite 1,534⋅→10-5 γM→S 1,0⋅10-30,01 0,1 1 10 100 1000 10000Time / s50100150200250300350400450500550600650700Temperature /0 CVH = 100 0.10.520 25TsTfFigure 5 CHT diagram of C45 steelTable 4  Average hardness values for diff erent rates of heating-up (tempering times)VH / 0C/s 0,1 0,5 1 2 5 10time / s 7070 1470 770 420 210 140HV30 340 343 346 349 353 360VH / 0C/s 20 30 40 50 60 100time / s 105 93,33 87,5 84 81,66 77HV30 375 389 405 422 441 54012  METALURGIJA 51 (2012) 1, 9-12J. WINCZEK et al.:  DILATOMETRIC AND HARDNESS ANALYSIS OF C45 STEEL TEMPERING WITH DIFFERENT...expansions and thermal expansion coeffi cients of hard-ening and tempering structures have been estimated.Functions associating the hardness of steel with time (the rate of heating-up) have been determined.Suggested functions and determined quantities ena-ble to describe the termomechanical changes (strain and stress) and predict the hardness in steel elements during technological processes based on short-timed action of a heat source (eg. laser treatment, welding).REFERENCES[1] M. Łomozik, Morfologia i własności plastyczne obszarów strefy wpływu ciepła w stalowych złączach spawanych w aspekcie użycia ściegów odpuszczających, Rozprawy mo-nografi e No 172, AGH W.N.D, Kraków 2007[2] K.J. Bimal, S.M. Nirmalendu, Microstructural evolution du-ring tempering of multiphase steel containing retained au-stenite, Mat. Sci. Eng. A263 (1999) 42-55[3] M. Gojic, L. Kosec, P. 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Dilatrometrijska i analiza tvrdoće čelika C45 popuštanog uz različite brzine zagrijavanja

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