It is known that hot rolling of ferritic steel leads to formation of texture inhomogeneous through sheet thickness [1-3]. For analysis of processes, which induce formation of texture inhomogeneity, finite element method simulation of hot rolling was carried out at macro- and mesoscopic levels. Crystallographic texture is a sensitive indicator of plastic deformation process so it is possible to use it to assess the quality of the simulation. Simulated orientation distribution functions are in a good agreement with experimental result in central part of sheet (middle in thickness), but does not substantially correspond with it in outer layer. Reasons of these inconsistencies were analyzed and following were singled out: disconnection of texture with mechanical properties, possible operation of some other mechanism of deformation apart from crystallographic slip

Dobrokhotov, P

Isaenkova, M

Perlovich, Y

Rubanov, A

Zhuk, D

English

KnE Publishing Platform

 KnE Materials ScienceMIE-201715th International School-Conference “New materials – Materials of innovative energy:development, characterization methods and application’’Volume 2018Conference PaperModeling of Crystallographic TextureFormation in Hot-rolled Sheets of Ferritic SteelYu. Perlovich, M. Isaenkova, P. Dobrokhotov, D. Zhuk, and A. RubanovNational Research Nuclear UniversityMEPhI (Moscow Engineering Physics Institute), Kashirskoeshosse 31, Moscow, 115409, RussiaANNOTATIONIt is known that hot rolling of ferritic steel leads to formation of texture inhomogeneousthrough sheet thickness [1-3]. For analysis of processes, which induce formation oftexture inhomogeneity, finite element method simulation of hot rolling was carriedout at macro- and mesoscopic levels. Crystallographic texture is a sensitive indicatorof plastic deformation process so it is possible to use it to assess the quality of thesimulation. Simulated orientation distribution functions are in a good agreementwith experimental result in central part of sheet (middle in thickness), but does notsubstantially correspond with it in outer layer. Reasons of these inconsistencies wereanalyzed and following were singled out: disconnection of texture with mechanicalproperties, possible operation of some other mechanism of deformation apart fromcrystallographic slip.1. INTRODUCTIONInhomogeneous texture is observed in hot-rolled sheets of Fe-0,55%C-1%Cr-2%Ni-1%Mo steel: outer layer and central part characterized by components {112} <111>,{110} <112> and {100} <110>, {112} <110>, {554} <225> respectively [1]. It isassumed that this inhomogeneity is due to singularities of temperature and defor-mation fields induced by more intensive cooling of outer layer and friction in sheet-roll contact. There are two hypotheses about surface texture formation. In [2] it issupposed that texture formation in outer layer occurs under the action of sheardeformation near the surface of the sheet. However, in [3] developed the conceptof anomaly texture formation with a high role of dislocation climb under conditionsof surface hardening by interstitial impurities, which diffused from the surface ofthe sheet at high temperature and contact with air. Therefore, the aim of the workis to simulate the process of steel hot rolling to identify factors that introduce theinhomogeneity of the crystallographic texture in hot-rolled sheets.How to cite this article: Yu. Perlovich, M. Isaenkova, P. Dobrokhotov, D. Zhuk, and A. Rubanov, (2017), “Modeling of Crystallographic TextureFormation in Hot-Rolled Sheets of Ferritic Steel” in 15th International School-Conference “Newmaterials – Materials of innovative energy: development,characterization methods and application’’, KnE Materials Science, pages 199–208. DOI 10.18502/kms.v4i1.2144Page 199Corresponding Author:A. Rubanovtoly.rubanov@yandex.ruReceived: 21 December 2017Accepted: 15 April 2018Published: 6 May 2018Publishing services provided byKnowledge EYu. Perlovich et al. This articleis distributed under the terms ofthe Creative CommonsAttribution License, whichpermits unrestricted use andredistribution provided that theoriginal author and source arecredited.Selection and Peer-reviewunder the responsibility of theMIE-2017 ConferenceCommittee. KnE Materials Science MIE-20172. MATERIALS AND METHODSFinite element method was used for simulation of hot rolling process on macro- andmesoscopic levels. Rolling modeling was carried out separately for each rolling step,which characterized by thickness of sheet after passing through rolls (table 1). Thescheme of the relationship between different levels of the hot rolling processmodelingis shown in Figure 1.Table 1: Change in sheet thickness during rolling.Rolling step 0 1 2 3 4 5 6 7 8 9 10 11Sheet thickness 45 38 30 23 17.8 13.6 10.4 8.0 6.3 4.9 4.0 3.2Figure 1: Scheme of the hot rolling process modelling.At the macroscopic level, the simulation was carried out by direct couple termo-structure analysis in a two-dimensional formulation considering the middle plane ofthe sheet symmetry. An example of the model geometry for the first rolling pass withthe mesh is shown on Figure 2.The material was considered homogeneous and isotropic. The dependences of theyield strength, heat capacity, and thermal conductivity on temperature were set. Themodel takes into account the oxide layer effect on the metal surface heat exchangeby setting the appropriate properties (heat capacity, thermal conductivity) for thenodes on the outer surface of the sheet. As boundary conditions for the heat equation,heat exchange with the surrounding environment was determined by convection andradiation and thermal conductivity in contact with the rolls. An additional heating ofthe rolled sheet due to plastic deformation was taken into account. The initial tem-peratures of the rolls and sheet are set before the start of rolling as 200∘C and 1100∘Crespectively. In subsequent rolling passes, the temperature field from the previousstage of deformation was used as the initial temperature distribution.For mechanical analysis the roll was rotated about its axis. Roll interaction with therolled sheet was contact with friction. At the transition from one pass to the next, strainDOI 10.18502/kms.v4i1.2144 Page 200 KnE Materials Science MIE-2017Figure 2: Geometry model with the mesh for first rolling pass.hardening was not taken into account because of the annealing of the defects at hightemperature (i.e., there is no hardening of the material at the beginning of each rollingstep).On mesosсopic level the calculation of grain reorientation was carried out for eachrolling step by cube of 8 × 8 × 8 material points. For boundary conditions deformationfield from macroscopic level simulations was used. Plastic properties of material weregiven by phenomenological dislocation-basedmodel [4] with slip systems {110} <111>and {112} <111> for ferrite and {111} <110> for austenite. Relaxed grain clusters (RGC)[5] homogenization scheme with eight elements in cluster was applied. On the firstrolling step random initial orientation were chosen and at each subsequent rolling stepthe orientation of the elements was set from the previous one. Figure 3 shows thedistribution of the Euler angle φ1 after the eighth pass.For texture changes analysis orientation distribution function (ODF) was calculated.In our case it is convenient to represent the ODF by cross section at φ2 = 45∘, whichcontains the main texture components characteristic for materials with a cubic crys-tal structure. The schematic arrangement of typical texture components is shown onFigure 4.3. RESULTSAs a result of macroscopic simulation the distributions of the strain tensor componentsfor different sheet layers and the distribution of temperatures at each rolling step areobtained. The parameter S, which is given by the relative distance to the sheet centerDOI 10.18502/kms.v4i1.2144 Page 201 KnE Materials Science MIE-2017Figure 3: Euler angle φ1 distribution after the 8𝑡ℎ rolling step.Figure 4: The arrangement of typical texture components on ODF cross section at φ2 = 45∘.along its thickness S = (t0-t)/t0, where t is the distance from the surface of the sheetand 2t0 is the initial thickness of the sheet, is used as the coordinate specifying theposition in the sheet section. Figure 5 (a) shows the distribution of temperature fromthe number of the pass and the rolling time, while fig. 5 (b, c, d) shows the distributionof strain tensor components for different values of parameter S. It can be seen thatthe near-surface layers of the sheet cools down faster than the central layers, andthe majority of the time it is in the ferrite temperature range (below the straight lineA1). The component ε𝑥 of the strain tensor varies little over the entire thickness of thesheet, while ε𝑦 and ε𝑥𝑦 in different layers have different values. It should be noted thatDOI 10.18502/kms.v4i1.2144 Page 202 KnE Materials Science MIE-2017at the 2-4 steps of rolling the shear component of the strain tensor in the near-surfacepart of the sheet is greater than the normal components.Figure 5: Distribution of temperature (a) and strain tensor components (b, c, d) for successive stages ofrolling and various parameters S.With deformation tensor components (fig. 5) mesoscopic simulationwas carried out.Strain tensor for central (S = 0) and outer layer (S = 0.9) was chosen for calculation.In central layer, first eight rolling steps take place in austenitic temperature range,and other steps take place in ferritic. Thus, the first eight passages weremodeled usingthe {111} <110> slip systems for austenite, after which the orientations of the ele-ments were recalculated in accordancewith the Kurdjumov-Sachs orientation relations{111}γ//{011}α and <011>γ//<111>α [6]. On the remaining stages the slip systems{110} <111> and {112} <111> for ferrite were used. Based on the simulation results,the ODF cross sections at φ2 = 45 ∘ for the austenitic temperature range are shown inFig. 6.DOI 10.18502/kms.v4i1.2144 Page 203 KnE Materials Science MIE-2017Figure 6: Simulated ODF sections φ2 = 45∘ for rolling steps in austenitic range of temperature (centrallayer).Figure 7 shows simulated ODF sections for ferritic temperature range. Experimentaltexture components for austenite (a) and ferrite (b) after hot rolling are placed onFigure 8.Figure 7: Simulated ODF sections φ2 = 45∘ for rolling steps in ferritic range of temperature (central layer).In outer layer all rolling steps take place in ferritic temperature range. ODF sectionsfor outer layer are shown on Figure 9. Experimental ODF section for correspondinglayer placed on Figure 10.4. DISCUSSIONIt can be seen from the graphs in Fig. 5 that the sheetmaterial undergoes an inhomoge-neous deformation through the sheet thickness during hot rolling, which is manifestedDOI 10.18502/kms.v4i1.2144 Page 204 KnE Materials Science MIE-2017 a                                                                            b     Figure 8: Experimental obtained ODF section φ2 = 45∘ for austenite (a) [6] and ferrite (b) in central partof sheet.Figure 9: Simulated ODF sections φ2 = 45∘ for outer layer.in the difference between the components of the strain tensor in different layers,i.e. for different values of the parameter S. This is due to the fact that the outerlayers of the sheet cools down faster than internal layers, and layers with differenttemperatures have different mechanical properties. Therefore, the difference betweenthe components of the strain tensor is greater at those stages of rolling where there isDOI 10.18502/kms.v4i1.2144 Page 205 KnE Materials Science MIE-2017Figure 10: Experimental ODF section φ2 = 45∘ for outer layer.the greatest temperature difference between the layers of sheet (passes 2-6). In thiscase, a higher shear component of the strain tensor ε𝑥𝑦 is observed near the surfaceof the sheet relative to the central part of the sheet. The shear component is larger inmagnitude than the normal components ε𝑥, ε𝑦 (passes 2-4), which is a result of frictionin the contact between the roll and the sheet.The simulated texture components for the austenite {110} <112>, {110} <001>{112} <111> and ferrite {100} <110>, {111} <110>, {554} <225> are in satisfactoryagreement with the experimental ones [1, 6]. A certain difference in the ODF can beexplained by the discrepancies in the rolling conditions of the sheet studied experi-mentally and those used in the simulation.In the outer layers, the modeled texture components do not correspond to theexperimental ones. The resulting texture components are close to the components{100} <110>, {112} <110>, {554} <225>, characteristic to the central layer. Thus, adeformation with a shear component ε𝑥𝑦 using the systems {110} <111> and {112}<111> does not result in the formation of an anomalous texture on the sheet surface.Possible reasons for the discrepancy between the results of modeling and experi-ment can be the not considering in the model of the relationship between the textureand the mechanical properties of the material, as well as the likely effect of otherdeformation mechanisms in addition to crystallographic slip in the systems mentionedabove. As other mechanisms, one can consider slip in other systems or grain boundarysliding under conditions of dynamic recrystallization or phase transformations. Theproposed model does not consider the possibility of the material surface hardeningdue to interstitial impurities diffusing from the surface of the sheet during hot rolling,as shown in [3].DOI 10.18502/kms.v4i1.2144 Page 206 KnE Materials Science MIE-2017Thus, in order to obtain a coincidence of the modeling results of the texture for-mation process in the outer layers of hot-rolled steel sheet with experimental ones,further improvement of themodel used and additional study of the deformationmech-anisms operating under conditions of hot rolling in outer layer are necessary.5. CONCLUSIONS1. Modeling of ferritic steel hot rolling at macro- and mesoscopic levels was carriedout. It is established that the deformation of the sheet is inhomogeneous inthickness due to the temperature gradient and friction in the contact of the sheetwith the rollers.2. The crystallographic texture components obtained by modeling in the centrallayers of the hot-rolled sheet satisfactorily correspond with the components ofthe texture observed experimentally.3. In the surface layers of a hot-rolled sheet, the modeled components do not agreewith the experimental ones, which are anomalous for the deformation of bccmaterials.ACKNOWLEDGMENTThe reported study was funded by RFBR according to the research project No. 16-32-00180 mol_a and was supported by the MEPhI Academic Excellence Project (agree-ment with the Ministry of Education and Science of the Russian Federation of August27, 2013, project no. 02.a03.21.0005).References[1] Yu. Perlovich, M. Isaenkova, P. Dobrokhotov, S. Stolbov, O. Bannykh et al AIPConference Proceedings 1896, 190019 (2017)[2] O. Engler, C.N. Tomé, M.Y Huh. A study of through-thickness texture gradients inrolled sheets // Metall. and Mat. Trans. A. – 2000. – Vol. 31, No. 9 – pp.2299-2315.[3] Yu. Perlovich, M. Isaenkova Int J Mater Form (2010) Vol. 3 Suppl 1.[4] Crystal Plasticity Finite Element Methods. F. Roters, P. Eisenlohr, T.R. Bieler andD. Raabe. – KGaA, Weinheim,2010 — 207 p.[5] D.D. Tjahjanto et al. 2010 Modelling Simul. Mater. Sci. Eng. 18 015006DOI 10.18502/kms.v4i1.2144 Page 207 KnE Materials Science MIE-2017[6] Microstructure and Texture in Steels and other materials. A. Haldar, S. Suwas, D.Bhattacharjee (Eds.) – Springer-Verlag London Limited, 2009 – 488 p.DOI 10.18502/kms.v4i1.2144 Page 208

Modeling of Crystallographic Texture Formation in Hot-rolled Sheets of Ferritic Steel

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Modeling of Crystallographic Texture Formation in Hot-rolled Sheets of Ferritic Steel

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