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Influence of forming parameters on the final subgrainsize during hot rolling of aluminium alloysX. Duan*, T. SheppardDEC, Bournemouth University, 12 Christchurch Road, Bournemouth BH1 3NA, UKAbstractIn thispaper,the influence of rolling parameters (i.e. the slab temperature, roll speed, rolltemperature and the ratio of the mean thickness tothe contact length in the roll gap Hm/L) on the subgrain size is studied by the combination of finite element method (FEM) with the Taguchiexperimental method. The FEM is first applied to simulate two existing single pass laboratory rolling schedules. The predicted distribution ofsubgrainsizethroughthethicknessagreeswellwithmeasurements.Then,theTaguchimethodisappliedtodesignanorthogonalexperimentaltable,L9(34).Atotalof9virtualexperimentsareanalysedbytheuseofFEM.ThepredictedresultsarethenanalysedbytheuseoftheTaguchimethod from which the influence of each rolling parameter on the deformed subgrain size is given and expressed in percentage. The studyshows that rolling temperature has the greatest influence on the final subgrain size, followed by the parameter Hm/L. The roll speed and rolltemperature have little effect on the deformed subgrain size.# 2002 Elsevier Science B.V. All rights reserved.Keywords: Rolling; Aluminium alloys; Grain size; FEM; Taguchi method1. IntroductionPrediction of the subgrain size and distribution plays avery important role in the prediction of microstructuralchanges occurring during deformation. The subgrain dis-tribution and the mean size have a significant influence onmechanical properties: determining the strength, ductility,texture, etc. Thus knowledge of the distribution of subgrainsize is critical for quality control.It is generally accepted that the following equation cansatisfactorily relate subgrain size with temperature T, andstrain rate_? e, or with the temperature compensated strain rateZ after steady-state deformation:dss?m A BlnZ(1)where Z is defined asZ _? eexpQdefRT?(2)It should be noted that_? e in Eq. (2) is the mean strain rate,Qdefthe activation energy for deformation, R the universalgas constant and Tis usually the entry temperaturewhen thisformula is constructed from experimental data. A good fitcould be obtained for m values in Eq. (1) varying from 0.35to 1.25 1.It would appear to be a trivial task to predict the subgrainsizeanddistribution,justsimplysubstitutingcomputednodalstrain rate and nodal temperature directly into Eqs. (1) and(2). The reported literature has shown that the computeddistribution of subgrain size based on such a computation isincorrect 2. Hence, some modifications must be made toEqs. (1) and (2) when incorporating in FEM programs.For the control of product properties, it would be veryuseful to know the extent of influence of each formingparameter on the final subgrain size. The Taguchi designmethod is suitable for this task. The Taguchi method adoptsa set of standard orthogonal arrays (OAs) to determineparameters configuration and analyse results. These kindsof arrays use a small number of experimental runs butobtains maximuminformation andhave highreproducibilityand reliability. In this study, a L9(34) table is adopted. Fourparameters, each having three levels, are studied. Theseparameters include: the initial slab temperature Tslab, theratio of the mean thickness to the contact length in the rollgap Hm/L, the roll temperature Trolland the roll speed V.2. Experimental data and FEM modelThe experimental data are taken from Zaidis experiments3. Aluminium alloy AA1100 is studied. The rolling tem-perature varies from 300 to 500 8C. The roll diameter isJournal of Materials Processing Technology 130131 (2002) 245249*Corresponding author.E-mail address: xduanbournemouth.ac.uk (X. Duan).0924-0136/02/$ see front matter # 2002 Elsevier Science B.V. All rights reserved.PII: S0924-0136(02)00811-7250 mm. The slab is 25 mm in thickness and 37.5 mm inwidth. The thickness reduction is 20%. The average strainrate is 2 s?1. After rolling, the specimen is immediatelyquenched in ice water. The locations of subgrain sizemeasurement are taken from the middle plane along thewidth and hence a plane strain deformation model is used tosimulate the rolling process. The empirical relationshipbetween the subgrain size and the deformation parametersin the steady-state regime isdss?1 ?0:196 0:0153lnZ(3)A commercial FEM program, FORGE21V2.9.04, isemployed. The Tresca friction law is used. The frictionfactor is taken as 0.6. The heat transfer coefficient betweenthe roll and the slab is 14 kW m?2K?1. This value wasobtained by matching the computed temperature historywith the recorded values in the literature 4. The materialbehaviour is described by the following constitutive equa-tion:? s 1alnZA? ?1=nffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiZA? ?2=n1s8:9=;(4)where A, a, n are constants.3. FEM results and discussionAll subgrain sizes were measured by using a PhillipsEM301 microscope at 100 kV. The averaged subgrain sizewasevaluatedbymeasuringthelongandleastdimensionsofa subgrain and averaging. At least 50 subgrains were mea-sured from each specimen. Two typical micrographs undertwo temperatures are shown in Fig. 1. The comparisonsbetween the predicted and measured distribution of subgrainsize throughout the thickness are shown in Fig. 2. Consider-ing the measurement error (0.5 mm), it can be said thatexcellent predictions were given.From Fig. 2, it can be seen that subgrain size decreasesfrom the centre to the surface. When the rolling temperatureis low, the distribution of subgrain size is more uniform thanthat obtained at higher temperature. This phenomenon canbe attributed to the temperature difference between thematerial surface and the centre. Fig.3shows the temperaturedistribution throughout the thickness at exit. Rolling at300 8C gives a temperature difference between the surfaceand the centre to be 40 8C, whilst rolling at 500 8C, thetemperature difference is 50 8C. For the same amount ofdeformation, the plastic work generated is greater at lowtemperature than at high temperature due to the high flowFig. 1. Micrographs of subgrain size: (a) 500 and (b) 300 8C.Fig. 2. The distribution of subgrain size along the thickness.Fig. 3. The distribution of temperature along the thickness.246X. Duan, T. Sheppard/Journal of Materials Processing Technology 130131 (2002) 245249stress at low temperature. Hence, the temperature risecaused by the dissipation from plastic work to heat is alsogreater. The temperature difference between the surface andthe centre should be large at low temperature. However, acompletely reverse result is given by the FEM. The reason isattributed to the differing contribution of heat transfercoefficient under different rolling temperatures. In theFEM computation, conduction with the tool and surfacedissipation due to friction are dealt with 5:?kTn htcT ? Ttool b?b? b?toolafKjDVjp1(5)where htc is the heat transfer coefficient with the tool withtemperature Ttool, b?and b?toolthe effusivity of the part anddie, respectively, afthe friction coefficient, DV the velocitydifference between the tool and the part, and k is theconductivity. Assuming the htc and Ttoolhave the samevalues under various rolling temperatures, from the firstright term in Eq. (5), it can be seen that the surfacetemperature decrease is obviously larger at high temperaturethan at low temperature.As discussed in Section 1, some modifications must bemade inorder to use Eqs. (1) and (2) to predict subgrain size.In the present study, the averaged strain rate and nodaltemperature are adopted to derive the value of Z. Theaveraged strain rate is obtained by averaging the strain rateover the whole deformation zone in each increment duringthe finite element computation. Adopting such an averagestrategy is logical since the strain rate in Eq. (2), which isregressed from experimental data, is also a mean value overthe whole deformation zone. Thus, in each increment duringthe finite element computation, all nodes have the samestrain rate. The gradient of Z depends upon the gradient oftemperature. According to Wells et al.s study 6, tempera-ture plays an overwhelming effect on determining themicrostructure when compared with roll speed (strain rate),work roll temperature, and the friction coefficient. Hence,averaging the strain rate over the whole deformation zone isacceptable.4. Determination of the influence of rollingparameters on the subgrain sizeFromthecurvepresentedinFig.2,itisclearthatFEMgivesanexcellentprediction.This indicatesthatwecanreplacetheexperiment by FEM. The advantages of such a replacementareobvious.Thereisnoequipmentlimitation,theaccuracyofmeasurement is high, little capital investment is required andit is fast. There are several types of parameters that haveinfluence on subgrain size. They are initial geometry para-meters (width/thickness,length/thickness),deformationzoneparameters (draft, the contact length), process parameters(temperature, roll speed) and material parameters (compo-nent). Four variables, the ratio of the mean thickness to thecontact length (Hm=L H1 H2=ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiRrH1? H2pwhereH1is the entry thickness, H2the exit thickness, R is the rollradius),the roll temperature(Troll),roll speed(V) andtheslabtemperature (Tslab) that are easily controlled, are selected forthe study. Each parameter has three values, also called threelevels. Thesevalues are shown in Table 1. For the ratio Hm/L,thevaluesare 0.74, 1.45 and3.1(equivalentto 44,16 and4%thickness reduction, respectively, since the roll radius R andthe initial thickness H1are fixed; the values are the same asthose described in Section 2). For Troll, the values are 20, 60and100 8C.ThedesignedorthogonaltableL9(34)isshowninTable 2. L9(34) indicates that there are four parameters, eachparameter has three levels and a total of 9 test runs need to beconducted. The material is AA1100.The objective of this section is to show the relativecontribution of each parameter on dss(subgrain size). Thistask is obtained through the analysis of variance (ANOVA).ANOVA uses the sum of squares to quantitatively examinethe deviation of the control factor effect responses from theoverall experimental mean response 7.For each level, the mean of quality characteristic responseis calculated by? y 1nXni1yi(6)whereyiis the quality characteristic response. In this study, itrefers to the dss. n is the number of experiments that includethe level. InthearrayL9(34),nisa constant3.Thecalculatedmean values at different levels for each factor are shown inTable 2 under the column ? y. It can be seen from Table 3 thatlevel 1 of Hm/L is included in test runs 13. Level 3 of therolling temperature is involved in test runs 3, 4 and 8. Whenperforming level average analysis for one level of oneTable 1Test parameters and their levelsHm/LTroll(8C)V (mm/s)Tslab(8C)0.74201004001.45602004503.1100300500Table 2Experimental design and resultsTestingno.Hm/LTroll(8C)V(mm/s)Tslab(8C)Predictedsubgrainsize (mm)10.74201004004.2820.74602004504.8730.741003005005.3941.45202005005.7951.45603004004.4361.451001004505.4573.1203004505.5583.1601005007.1593.11002004005.02X. Duan, T. Sheppard/Journal of Materials Processing Technology 130131 (2002) 245249247parameter, all the influences from different levels of otherparameters will be counterbalanced because every otherparameter will appear at each different level once. Thusthe effect of one parameter at one level on the experimentalresults can be separated from other parameters. In this way,the effect of each level of every parameter can be viewedindependently.In the Taguchi method, the signal-to-noise (S/N) ratio isadopted to analyse the test results. The S/N ratio can reflectboth the average (mean) and thevariation (scatter) of qualitycharacteristics under one trial condition. The S/N function isdefined byS=N ?10logMSD(7)where MSD stands for the mean square deviation. Thepurpose of using the constant 10 is to magnify the S/Nvalue for easier analysis. In this investigation, the MSD isexpressed asMSD y2i(8)The overall mean S/N ratio of the OA is expressed asS=N 19X9i1S=Ni(9)The calculated results for the above parameters are shown inTable 3.The sum of the squares due to variation about the overallmean isSS X9i1S=Ni? S=N2(10)For the ith factor, the sum of the squares due to variationabout the mean isSSiX3j1Mj? S=Nij? S=N2(11)where Mjis the number of experiments at each level. It is aconstant of 3 in this study. The percentage of contribution ofith factor to the dsscan be calculated bySSi% SSiSS? 100%(12)The calculated contributions of each parameter are shown inTable 4. It can be seen that the rolling temperature con-tributes 64% to the dss, about twice the contributionof Hm/L.The influences of roll temperature and roll speed on the dssare negligible.5. ConclusionAn excellent agreement has been achieved for the pre-diction of subgrain size throughout the whole thickness byusing the averaged ZenerHollomon parameter and theaccurate computation of temperature. The analysis of var-iance by the use of Taguchi method shows that the mostsignificant parameter is the rolling temperature, whichaccounts for 64% of the dss, followed by the Hm/L, rolltemperature and roll speed.References1 M.A. Zaidi, T. Sheppard, Development of microstructure throughoutroll gap during rolling of aluminium alloys, Metal Sci. 16 (1982) 229238.Table 3Level average response analysis using S/N ratio for the centre pointVariablesLevelRunsy? yS/NS=NijHm/LLevel 10.7414.284.84666712.6288813.6704124.8713.7505835.3914.63178Level 21.4545.795.22333315.2535714.3031954.4312.9280765.4514.72793Level 33.175.555.90666714.8858615.3286887.1517.0861295.0214.01407TrollLevel 120 8C14.285.20666712.6288814.256145.7915.2535775.5514.88586Level 260 8C24.875.48333313.7505814.5882654.4312.9280787.1517.08612Level 3100 8C35.395.28666714.6317814.4579365.4514.7279395.0214.01407VLevel 1100 mm/s14.285.62666712.6288814.8143165.4514.7279387.1517.08612Level 2200 mm/s24.875.22666713.7505814.3394145.7915.2535795.0214.01407Level 3300 mm/s35.395.12333
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