MODELS OF HOT DEFORMATION RESISTANCE OF A NB-TI HSLA STEEL

Acta Metallurgica Slovaca, 12, 2006, 4 (379 - 387)

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MODELS OF HOT DEFORMATION RESISTANCE OF A NB-TI HSLA STEEL Schindler I.1, Janošec M.1, Pachlopník R.2, Černý L.2 1 VŠB – Technical University of Ostrava, Institute of Modelling and Control of Forming Processes, 17. listopadu 15, 708 33 Ostrava, Czech Republic, [email protected], [email protected] 2 Mittal Steel Ostrava a.s., Vratimovská 689, 707 02 Ostrava-Kunčice, Czech Republic, [email protected], [email protected] MODELY DEFORMAČNÍCH ODPORŮ ZA TEPLA OCELI MIKROLEGOVANÉ NB A TI Schindler I.1, Janošec M.1, Pachlopník R.2, Černý L.2, VŠB – Technická univerzita Ostrava, Ústav modelování a řízení tvářecích procesů, 17. listopadu 15, 708 33 Ostrava, Česká republika, [email protected], [email protected] 2 Mittal Steel Ostrava a.s., Vratimovská 689, 707 02 Ostrava-Kunčice, Česká republika, [email protected], [email protected] 1

Abstrakt Na základě výsledků válcování plochých vzorků s odstupňovanou tloušťkou na laboratorní trati Tandem, měření a počítačové registrace válcovacích sil byly vypočítány hodnoty středního přirozeného deformačního odporu svařitelné konstrukční oceli mikrolegované niobem a titanem (0.066 % C – 1.33 % Mn – 0.20 % Si – 0.030 % Al – 0.040 % Nb – 0.016 % Ti). Byly vyvinuty matematické modely středního přirozeného deformačního odporu v závislosti na teplotě (v rozsahu 770 – 1150 °C), deformaci (cca 0.1 – 0.6, rovněž s uvažováním vlivu dynamického změkčování) a deformační rychlosti (cca 10 – 150 s-1). Výhoda daného experimentu spočívá v možnosti získat proválcováním jediného vzorku 4 hodnoty středního přirozeného deformačního odporu, odpovídající různým úběrům při shodné teplotě. Další předností této metody je jednodušší matematické zpracování výsledků, a to především proto, že se pracuje s hodnotami středních přirozených deformačních odporů, které jsou méně citlivé na různé vlivy než hodnoty okamžitých přirozených deformačních odporů. Modely mají být co nejjednodušší, aby mohly být aplikovány řídicími systémy válcovacích tratí při rychlé predikci energosilových parametrů. Nebylo možné získat jednotný model deformačních odporů a proto bylo nutné vyvinut model vysokoteplotní (pro teploty cca nad 900 °C) a nízkoteplotní (pro teploty cca pod 850 °C). Rovnice popisující deformační odpory za vysokých teplot mohla být zjednodušena vyloučením deformačních členů. Tyto modely popisují zvolené vztahy s vyhovující přesností, bez ohledu na komplikovanost zvolené závislosti. Přesnost komplexního nízkoteplotního modelu a zjednodušeného vysokoteplotního modelu je plně srovnatelná. Abstract On the basis of results of laboratory rolling of flat samples with graduated thickness and measurement of roll forces, values of mean equivalent stress of a Nb-Ti-microalloyed steel were calculated and mathematical models developed in relation to temperature (770 to 1150 °C), strain (ca 0.1 to 0.6, also with including influence of dynamic softening) and strain rate (ca 10 to 150 s-1). An advantage of the given experiment is that by rolling of one sample 4 values of


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deformation resistance, corresponding to various reductions at the same temperature, can be reached. Another of benefits of this method is uncomplicated mathematical processing of results, namely just thanks to working with values of mean equivalent stress which are less sensitive to various influences than actual values of equivalent stress. The models should be as simple as possible to be used for a fast prediction of power/force parameters in control systems of rolling mills. A single model for mean equivalent stress was not possible to be obtained. Therefore a high temperature model (for temperatures above ca 900 °C) and a low temperature model (for temperatures below ca 850 °C) had to be developed. It was possible to eliminate strain as independent variable for temperatures above 900 °C. These models describe the given relationships with sufficient accuracy, without regard to the type or complexity of the applied equation. Accuracy of the more complex low-temperature model and the simplified hightemperature model is fully comparable. Keywords: microalloyed steel, strain, equivalent stress, recrystallization, deformation resistance, forming force 1. Introduction Mathematical models of deformation resistance describe equivalent stress in dependence on strain or also on temperature and strain rate. The simplest of them were created for cold forming, provided that power stress-strain relationship is sufficient in this case – see e.g. Ludwik [1]. By involving the influence of temperature (exponential relationship) and strain rate (power relationship), often mentioned equations e.g. of Andrejuk or Zjuzin for the description of hot deformation resistance, limited mostly with strains 0.3 – 0.4, were acquired [2,3]. Many authors tried to involve the influence of dynamic softening that significantly extends the range of applied strains – see e.g. [4-8]. It may beneficially be used in case of repeated deformation (see e.g. low-temperature finished rolling of microalloyed steels in the region of retarded recrystallization) or in the case of high-reduction forming processes. From the sequence of models stated above some particular types may be separated. First of them are based on polynomials of higher degree [9-11]. In spite of the fact that these models resign their pure physical meaning, they may be used to description of deformation resistance in temperature regions corresponding to various phase composition (e.g. austenite or austenite + ferrite). Models of type [12, 13] on physical base, working often with dislocation density, are not largely used in practice for their complexity. In operational conditions very simple models of mean equivalent stress are used, incorporated directly in the control system of the given rolling mill etc. Their „scientific character“ and complicacy would make running calculations excessively long. Lower accuracy of these models is sacrificed to some extent to effective operation of work, what is solved by adaptive style of function of control systems which can, based on values of forming forces measured at previous pass, normally correct deviations with size of 15 up to 30 % between predicted and actual forces. Based on measurement of forces in the laboratory hot or warm flat rolling, the effective methods of description of the phase transformation temperatures as well as the mean equivalent stress (MES) values were developed and applied to many steel grades, some intermetallic alloys and Zn-Ti-Cu alloy – see [14-17] for example. The obtained mathematical models of MES should be both rather simple and sufficiently accurate, and thus suitable for implementation in the adaptive steering systems of the hot strip mills.

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2. Materials and experimental methodics HSLA steel grade L415MB microalloyed by a combination of Nb and Ti was selected to demonstrate the mentioned experimental methods. Chemical composition of the investigated heat is introduced in Table 1. Table 1 Chemical analysis of the investigated steel in wt. % C

Mn

Si

P

S

Cu

Al

Nb

Ti

0.066

1.330

0.200

0.008

0.008

0.080

0.030

0.040

0.016

This material has been continuously cast and rolled in Mittal Steel Ostrava a.s. Their new rolling mill P1500 of Steckel type has an arrangement of two reversing four-high stands, which roll continuously with 5 or 7 „double passes“. Use of this mill seems to be optimum for utilization of these microalloying elements with viewpoint of reaching the uniform and finegrained microstructure of the material, with maintaining required final structural and mechanical properties of coils [18, 19]. Samples of two types were manufactured by cutting and milling from the delivered material. Flat samples with dimensions 7.5 x 25 x 110 mm served for determination of phase transformations on the basis of measurement of roll forces. Prismatic samples were heated in one furnace to temperature 1200 °C and then cooled down freely to forming temperature, the value of which was homogenized in the entire volume of the sample by dwell in the other furnace. Samples were rolled in stand A of the laboratory mill Tandem (with work roll diameter 159 mm) [20,21], with constant roll gap adjustment (5.3 mm) and roll revolutions N = 200 min-1. Layout of this mill is presented in Fig. 1. Roll forces measured under otherwise the same rolling conditions but various temperatures are plotted in graph in Fig. 2.

Fig.1 Layout of laboratory rolling mill Tandem of Institute of Modelling and Control of Forming Processes at VŠB – Technical University of Ostrava


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Fig.2 Temperature dependence of the roll force measured in rolling of prismatic samples, influenced by transformation austenite/ferrite and probably by precipitation of Nb(C,N) at temperatures below 1000 °C

Samples with thickness graded in size (see Fig. 3) were used for gaining data on MES at various rolling modes. Each sample was carefully measured and then heated in the furnace to austenitizing temperature 1200 °C within 24 minutes. This high-temperature heating lead to transfer of sufficient parts of microalloying elements in the solid solution, but at the same time it caused significant scaling of samples with negative influence on accuracy of evaluation of the results. Each sample was, after partial cooling, inserted for 4 minutes into the furnace heated to forming temperature. The heated sample was immediately after discharging the furnace rolled in the two-high stand A of the mill Tandem.

Fig.3 Initial shape of the sample with thickness graded in size

In rolling of each sample the temperature was changed, together with roll gap adjustment (and thus the total strain of individual grades of the sample) and nominal revolutions of rolls (and thus the strain rate values). Roll forces and the actual speed of roll rotation were computer-registered – their time-dependent example is given in Fig. 4.


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Fig.4 Sample of measured total rolling force F and actual rolls speed N (set 200 min-1) depending on time t [s] at rolling of flat samples graded in size; temperature 1050 °C

For each grade of the particular sample the total roll force FΣ and corresponding variable N is determined. After cooling of the rolling stock, width and thickness for individual grades are measured; spreading is affected mainly by the height reduction size, thickness is affected by the roll force size (elastic contraction of rolls). With particular samples the temperature was changed, as well as adjustment of the roll gap (and hence the total reduction corresponding to specific grades of each sample) and nominal revolutions of rolls N. By all here specified factors the achieved mean height strain rate é [s-1] is given. The registered total roll forces FΣ [N] and actual revolutions of rolls, as well as dimensions of the rolled products, serve for automatic calculation of height strain eh = ln(H0/H1), mean strain rate and mean equivalent stress σm [MPa] for each element of the rolled sample. For the calculation the following formulae are used [22, 23]: é=

2 3

⋅

vr

R ⋅ (H 0 − H 1 )

⋅ eh

(1)

where H0, or H1 [mm] is entry, or exit thickness of the rolling stock in a given place; vr [mm/s] is real circumferential speed of rolls with radius R [mm]. Mean equivalent stress is calculated as follows:

σm =

FΣ

Q Fr ⋅ R ⋅ (H 0 − H 1 ) ⋅ B s

(2)

where QFr is a forming factor, corresponding to a specific rolling mill stand, and Bs [mm] is mean width of the rolling stock in a given place (an average value of the width before and after rolling). The member R ⋅ (H 0 − H 1 ) represents contact length of the roll bite, i.e. ld [mm]. Credibility of calculation of MES is influenced most of all by an exact estimate of the forming factor, which – as matter of fact – transfers deformation resistance to values of equivalent stress

384


(i.e. of that which corresponds to a defined uniaxial stress state). Values of QFr for both stands of the rolling mill Tandem were obtained by previous research and they are described in relation to aspect ratio ld/Hs by equations of type [24] ⎛ l Q Fv = A − B ⋅ exp⎜⎜ − C ⋅ d Hs ⎝

⎞ ⎛ H ⎟ + exp⎜ D ⋅ s ⎟ ⎜ ld ⎠ ⎝

⎞ ⎟ ⎟ ⎠

(3)

where A ... D are constants for a given facility, verified e.g. by comparison of power/force parameters, determined during laboratory rolling, torsion test, or industrial rolling; Hs [mm] is mean thickness in a given place. 3. Mathematical processing of results It was assumed that in low temperature rolling the influence of the developed softer ferrite would be compensated to some extent by the precipitation hardening effect, and so MES of the investigated steel would be possible to describe with sufficient accuracy by one equation in the whole temperature range. This imagination was eroded by the results of rolling of prismatic samples where a considerable fall of roll forces in the temperature region of ca 880950 °C was indicated (see Fig. 2), especially in effect of transformation austenite/ferrite. We expected some problems with these relationships when we tried to describe MES by one equation. Unfortunately, these concerns showed to be well-founded already at the first attempt to describe MES by multiple non-linear regression in program UNISTAT 5.5. Therefore two models had to be developed – one for the low temperature region (below ca 850 °C) and one for the high temperature one (above ca 900 °C). Based on previous own experience [14, 15, 24] a simple model for description of MES of the investigated material was chosen, in dependence on deformation (with taking dynamic softening in consideration), temperature and strain rate. The result of complex calculations is represented by the following equations: for temperatures below 850 °C

σ mc = 1172 ⋅ e h 0.225 ⋅ exp( − 0 .0021 ⋅ e h ) ⋅ é 0.035 ⋅ exp( − 0 .00171 ⋅ T )

(4)

for temperatures above 900 °C

σ mc = 755 ⋅ é 0.030 ⋅ exp(−0.00128 ⋅ T )

(5)

where σmc is predicted (calculated according to the developed models) MES; T [°C] is temperature. Equation (4) includes a „hardening“ – eh0.225 – and a „softening“ – exp(-0.0021 · eh) – member, which makes it possible to determine MES in a wide range of strain, i.e. to some extent also with including possible dynamic recrystallization. It is remarkable that both deformation members could be excluded from the high-temperature model (Eq. 5). Influence of strain shows only through the strain-rate member in this case – see Eq. 1. Accuracy of gained models was evaluated simply by a relative error defined according to the relation (σm – σmc) / σm · 100 [%]. A range of experimental conditions and accuracy of the derived equations are illustrated in graphs in Fig. 5.


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Fig.5 Illustration of accuracy of the derived Eqs. 4 and 5 for calculation of MES

4. Conclusions On the basis of results of laboratory rolling of the given HSLA steel, the model of mean equivalent stress of the microalloyed steel of type L415MB was developed, which is valid


386

in a wide range of forming temperatures (770 to 1150 °C), strains (ca 0.1 to 0.6, also with including influence of dynamic softening) and in a suitable range of relatively high strain rates (ca 10 to 150 s-1). A single model for MES was not possible to be developed. Therefore a high temperature model (for temperatures above ca 900 °C) and a low temperature model (for temperatures below ca 850 °C) had to be developed. Application of these models to the transition temperature region is accompanied by increasing of the error of predicted values [25]. The models describe the given relationships with sufficient accuracy; a relative error goes beyond 15 % only exceptionally, without regard to the type or complexity of the applied equation. Accuracy of the more complex low-temperature model (Eq. 4) and the simplified hightemperature model (Eq. 5) is comparable, which seems to be rather surprising. An advantage of the given experiment is that by rolling of one sample 4 values of MES, corresponding to various reductions at the same temperature, can be reached. Another of benefits of this method is more simple mathematical processing of results, namely just thanks to working with values of MES which are less sensitive to various influences than actual values of equivalent stress. More simple models, providing directly values of mean equivalent stress σm, are generally usable more easily in automatic steering systems of the recent hot flat rolling mills. Acknowledgements This paper was developed in the framework of solution of the projects MSM 6198910015 and MPO FT-TA/091; the experimental method of calculation of the mean equivalent stress values based on rolling forces has been developed under the grant project GA CR 106/04/1351. Literature [1] Ludwik P.: Elemente der technologischen Mechanik, Berlin, Springer Verlag 1909 [2] Zjuzin V. I., Brovman M. Ja., Meľnikov A. F.: Soprotivlenije deformacii stalej při goračej prokatke, Moskva, Metallurgija 1964 [3] Andrejuk L. V., Tjulenev G. G.: Analitičeskaja zavisimosť soprotivlenija deformacii metalla ot temepratury, skorosti i stepeni deformacii. Staľ, 1972, No. 9, p. 825. [4] Kliber J., Schindler I.: Description of Stress-strain Curves on High temperature Deformed Steel. Acta Universitatis Carolinae – Mathematica et Physica, 1991, No. 1, p. 95. [5] Medina S. F., Hernández C. A.: Modélisation mathématique des courbes contraintedéformation des aciers. Application au calcul des forces de laminage à chaud. Mémoires et Études Scientifiques Revue de Métallurgie, 1992, No. 4, p. 217. [6] Pol L. A., Asensio J., Pero-sanz J. A.: Ajuste de las curvas tesión-deformación a alta temperatura de un acero microaleado Nb-Ti. Revista Metalurgia, 1997, No. 1, p. 21. [7] Davenport S. B. et al.: Development of Constitutive Equations for modelling of Hot Rolling. Materials Science and Technology, 2000, No. 5, p. 539. [8] Schindler I., Bořuta J.: Deformační odpory ocelí při vysokoredukčním tváření za tepla. Hutnické listy, 1995, No. 7 – 8, p. 47. [9] Beneš, M., Maroš, B.: Vyjádření přetvárného odporu a měrné přetvárné práce materiálu 13 240 v závislosti na teplotě a logaritmickém stupni přetváření. Hutnické listy, 1985, No. 3, p. 191. [10] Pawelski O., Rasp W., Knop J.: Ein universel anwendbarer Algorithmus zur Interpolation von Fließkurven für Metalle. Arch. Eisenhüttenwes., 1982, No. 5, p. 169.


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[11] Žadan V. T., et al.: Issledovanije soprotivlenija deformacii podšipnikovoj stali pri gorjačej plastičeskoj obrabotke. IVUZ Černaja metall., 1986, No. 1, p. 85. [12] Lička S.: Rovnice vazkoplastického toku kovů pro tváření za tepla. Hutnické listy, 1984, No. 3, p. 161. [13] Senuma T., et al.: Calculation Model of Resistance to Hot Deformation in Consideration of Metallurgical Phenomena in Continuous Hot Deformation Processes. Tetsu-to-Hagané, 1984, No. 10, p. 78. [14] Rusz S., et al.: Hot deformation resistance models based on the rolling forces measurement. Acta Metallurgica Slovaca, 2005, no. 2, p. 265. [15] Schindler I., et al.: Deformation behavior and microstructure development of 13Cr25 ferritic stainless steel in hot strip rolling. Acta Metallurgica Slovaca, 2005, no. 3, p. 331. [16] Kratochvíl P., Schindler I.: Conditions for Hot Rolling of Iron Aluminide. Advanced Engineering Materials, 2004, no. 5, p. 307. [17] Schindler I. et al.: Modely deformačních odporů aplikovatelné při válcování pásu ze zinkové slitiny za polotepla. In: Metal 2006. Ostrava : Tanger, 2006, CD-ROM. [18] Pachlopník R.: Válcování mikrolegovaných ocelí vyšších jakostních stupňů na trati P1500. (Výzkumná zpráva.) Ostrava 2004. Mittal Steel Ostrava a. s. [19] Černý L.: Studium vlivu parametrů válcování za tepla na deformační chování nízkouhlíkových ocelí a vlastnosti pásu. (Disertační práce.) Ostrava 2003. VŠB-TU. FMMI. [20] Schindler I., Kuře F.: Potentialities of Physical Modelling of Flat Rolling Processes at VŠB – Technical University of Ostrava. In: Ocelové pásy 2001. Společnost Ocelové pásy 2001, p. 375. [21] http://www.fmmi.vsb.cz/model/ [22] Krejndlin N. N.: Rasčot obžatij pri prokatke cvetnych metallov, Moskva, Metallurgizdat 1963 [23] Yanagimoto J. et al.: Mathematical modelling for rolling force and microstructure evolution and microstructure controllinq with heavy reduction in tandem hot strip rolling. Steel Research, 2002, no. 2, p. 56. [24] Schindler I., Pachlopník R., Černý L.: Development of models of mean equivalent stress suitable for the steering systems of hot strip rolling mills. In: Ocelové pásy 2006. Společnost Ocelové pásy 2006, p. 281. [25] Rozínek J.: Model deformačních odporů mikrolegované oceli za tepla. (Diplomová práce.) Ostrava 2005. VŠB-TU. FMMI.

MODELS OF HOT DEFORMATION RESISTANCE OF A NB-TI HSLA STEEL

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