Influence of forming parameters on the final subgrain size during hot rolling of aluminium alloys.pdf

Infl uence of forming parameters on the fi nal subgrain size during hot rolling of aluminium alloys X Duan T Sheppard DEC Bournemouth University 12 Christchurch Road Bournemouth BH1 3NA UK Abstract In thispaper the infl uence of rolling parameters i e the slab temperature roll speed rolltemperature and the ratio of the mean thickness to the contact length in the roll gap Hm L on the subgrain size is studied by the combination of fi nite element method FEM with the Taguchi experimental method The FEM is fi rst applied to simulate two existing single pass laboratory rolling schedules The predicted distribution of subgrainsizethroughthethicknessagreeswellwithmeasurements Then theTaguchimethodisappliedtodesignanorthogonalexperimental table L9 34 Atotalof9virtualexperimentsareanalysedbytheuseofFEM ThepredictedresultsarethenanalysedbytheuseoftheTaguchi method from which the infl uence of each rolling parameter on the deformed subgrain size is given and expressed in percentage The study shows that rolling temperature has the greatest infl uence on the fi nal subgrain size followed by the parameter Hm L The roll speed and roll temperature have little effect on the deformed subgrain size 2002 Elsevier Science B V All rights reserved Keywords Rolling Aluminium alloys Grain size FEM Taguchi method 1 Introduction Prediction of the subgrain size and distribution plays a very important role in the prediction of microstructural changes occurring during deformation The subgrain dis tribution and the mean size have a signifi cant infl uence on mechanical properties determining the strength ductility texture etc Thus knowledge of the distribution of subgrain size is critical for quality control It is generally accepted that the following equation can satisfactorily relate subgrain size with temperature T and strain rate e or with the temperature compensated strain rate Z after steady state deformation dss m A BlnZ 1 where Z is defi ned as Z eexp Qdef RT 2 It should be noted that e in Eq 2 is the mean strain rate Qdefthe activation energy for deformation R the universal gas constant and Tis usually the entry temperaturewhen this formula is constructed from experimental data A good fi t could be obtained for m values in Eq 1 varying from 0 35 to 1 25 1 It would appear to be a trivial task to predict the subgrain sizeanddistribution justsimplysubstitutingcomputednodal strain rate and nodal temperature directly into Eqs 1 and 2 The reported literature has shown that the computed distribution of subgrain size based on such a computation is incorrect 2 Hence some modifi cations must be made to Eqs 1 and 2 when incorporating in FEM programs For the control of product properties it would be very useful to know the extent of infl uence of each forming parameter on the fi nal subgrain size The Taguchi design method is suitable for this task The Taguchi method adopts a set of standard orthogonal arrays OAs to determine parameters confi guration and analyse results These kinds of arrays use a small number of experimental runs but obtains maximuminformation andhave highreproducibility and reliability In this study a L9 34 table is adopted Four parameters each having three levels are studied These parameters include the initial slab temperature Tslab the ratio of the mean thickness to the contact length in the roll gap Hm L the roll temperature Trolland the roll speed V 2 Experimental data and FEM model The experimental data are taken from Zaidi s experiments 3 Aluminium alloy AA1100 is studied The rolling tem perature varies from 300 to 500 8C The roll diameter is Journal of Materials Processing Technology 130 131 2002 245 249 Corresponding author E mail address xduan bournemouth ac uk X Duan 0924 0136 02 see front matter 2002 Elsevier Science B V All rights reserved PII S0924 0136 02 00811 7 250 mm The slab is 25 mm in thickness and 37 5 mm in width The thickness reduction is 20 The average strain rate is 2 s 1 After rolling the specimen is immediately quenched in ice water The locations of subgrain size measurement are taken from the middle plane along the width and hence a plane strain deformation model is used to simulate the rolling process The empirical relationship between the subgrain size and the deformation parameters in the steady state regime is dss 1 0 196 0 0153lnZ 3 A commercial FEM program FORGE21V2 9 04 is employed The Tresca friction law is used The friction factor is taken as 0 6 The heat transfer coeffi cient between the roll and the slab is 14 kW m 2K 1 This value was obtained by matching the computed temperature history with the recorded values in the literature 4 The material behaviour is described by the following constitutive equa tion s 1 a ln Z A 1 n ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffiffi Z A 2 n 1 s 8 9 4 where A a n are constants 3 FEM results and discussion All subgrain sizes were measured by using a Phillips EM301 microscope at 100 kV The averaged subgrain size wasevaluatedbymeasuringthelongandleastdimensionsof a subgrain and averaging At least 50 subgrains were mea sured from each specimen Two typical micrographs under two temperatures are shown in Fig 1 The comparisons between the predicted and measured distribution of subgrain size throughout the thickness are shown in Fig 2 Consider ing the measurement error 0 5 mm it can be said that excellent predictions were given From Fig 2 it can be seen that subgrain size decreases from the centre to the surface When the rolling temperature is low the distribution of subgrain size is more uniform than that obtained at higher temperature This phenomenon can be attributed to the temperature difference between the material surface and the centre Fig 3shows the temperature distribution throughout the thickness at exit Rolling at 300 8C gives a temperature difference between the surface and the centre to be 40 8C whilst rolling at 500 8C the temperature difference is 50 8C For the same amount of deformation the plastic work generated is greater at low temperature than at high temperature due to the high fl ow Fig 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 130 131 2002 245 249 stress at low temperature Hence the temperature rise caused by the dissipation from plastic work to heat is also greater The temperature difference between the surface and the centre should be large at low temperature However a completely reverse result is given by the FEM The reason is attributed to the differing contribution of heat transfer coeffi cient under different rolling temperatures In the FEM computation conduction with the tool and surface dissipation due to friction are dealt with 5 k T n htc T Ttool b b b tool afKjDVjp 1 5 where htc is the heat transfer coeffi cient with the tool with temperature Ttool b and b tool the effusivity of the part and die respectively af the friction coeffi cient DV the velocity difference between the tool and the part and k is the conductivity Assuming the htc and Ttoolhave the same values under various rolling temperatures from the fi rst right term in Eq 5 it can be seen that the surface temperature decrease is obviously larger at high temperature than at low temperature As discussed in Section 1 some modifi cations must be made inorder to use Eqs 1 and 2 to predict subgrain size In the present study the averaged strain rate and nodal temperature are adopted to derive the value of Z The averaged strain rate is obtained by averaging the strain rate over the whole deformation zone in each increment during the fi nite element computation Adopting such an average strategy is logical since the strain rate in Eq 2 which is regressed from experimental data is also a mean value over the whole deformation zone Thus in each increment during the fi nite element computation all nodes have the same strain rate The gradient of Z depends upon the gradient of temperature According to Wells et al s study 6 tempera ture plays an overwhelming effect on determining the microstructure when compared with roll speed strain rate work roll temperature and the friction coeffi cient Hence averaging the strain rate over the whole deformation zone is acceptable 4 Determination of the influence of rolling parameters on the subgrain size FromthecurvepresentedinFig 2 itisclearthatFEMgives anexcellentprediction This indicatesthatwecanreplacethe experiment by FEM The advantages of such a replacement areobvious Thereisnoequipmentlimitation theaccuracyof measurement is high little capital investment is required and it is fast There are several types of parameters that have infl uence on subgrain size They are initial geometry para meters width thickness length thickness deformationzone parameters draft the contact length process parameters temperature roll speed and material parameters compo nent Four variables the ratio of the mean thickness to the contact length Hm L H1 H2 ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi Rr H1 H2 p where H1is the entry thickness H2the exit thickness R is the roll radius the roll temperature Troll roll speed V andtheslab temperature Tslab that are easily controlled are selected for the study Each parameter has three values also called three levels 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 and the initial thickness H1 are fi xed the values are the same as those described in Section 2 For Troll the values are 20 60 and100 8C ThedesignedorthogonaltableL9 34 isshownin Table 2 L9 34 indicates that there are four parameters each parameter has three levels and a total of 9 test runs need to be conducted The material is AA1100 The objective of this section is to show the relative contribution of each parameter on dss subgrain size This task is obtained through the analysis of variance ANOVA ANOVA uses the sum of squares to quantitatively examine the deviation of the control factor effect responses from the overall experimental mean response 7 For each level the mean of quality characteristic response is calculated by y 1 n X n i 1 yi 6 whereyiis the quality characteristic response In this study it refers to the dss n is the number of experiments that include the level InthearrayL9 34 nisa constant3 Thecalculated mean values at different levels for each factor are shown in Table 2 under the column y It can be seen from Table 3 that level 1 of Hm L is included in test runs 1 3 Level 3 of the rolling temperature is involved in test runs 3 4 and 8 When performing level average analysis for one level of one Table 1 Test parameters and their levels Hm LTroll 8C V mm s Tslab 8C 0 7420100400 1 4560200450 3 1100300500 Table 2 Experimental design and results Testing no Hm LTroll 8C V mm s Tslab 8C Predicted subgrain size mm 10 74201004004 28 20 74602004504 87 30 741003005005 39 41 45202005005 79 51 45603004004 43 61 451001004505 45 73 1203004505 55 83 1601005007 15 93 11002004005 02 X Duan T Sheppard Journal of Materials Processing Technology 130 131 2002 245 249247 parameter all the infl uences from different levels of other parameters will be counterbalanced because every other parameter will appear at each different level once Thus the effect of one parameter at one level on the experimental results can be separated from other parameters In this way the effect of each level of every parameter can be viewed independently In the Taguchi method the signal to noise S N ratio is adopted to analyse the test results The S N ratio can refl ect both the average mean and thevariation scatter of quality characteristics under one trial condition The S N function is defi ned by S N 10log MSD 7 where MSD stands for the mean square deviation The purpose of using the constant 10 is to magnify the S N value for easier analysis In this investigation the MSD is expressed as MSD y2 i 8 The overall mean S N ratio of the OA is expressed as S N 1 9 X 9 i 1 S N i 9 The calculated results for the above parameters are shown in Table 3 The sum of the squares due to variation about the overall mean is SS X 9 i 1 S N i S N 2 10 For the ith factor the sum of the squares due to variation about the mean is SSi X 3 j 1 Mj S N ij S N 2 11 where Mjis the number of experiments at each level It is a constant of 3 in this study The percentage of contribution of ith factor to the dsscan be calculated by SSi SSi SS 100 12 The calculated contributions of each parameter are shown in Table 4 It can be seen that the rolling temperature con tributes 64 to the dss about twice the contributionof Hm L The infl uences of roll temperature and roll speed on the dss are negligible 5 Conclusion An excellent agreement has been achieved for the pre diction of subgrain size throughout the whole thickness by using the averaged Zener Hollomon parameter and the accurate computation of temperature The analysis of var iance by the use of Taguchi method shows that the most signifi cant parameter is the rolling temperature which accounts for 64 of the dss followed by the Hm L roll temperature and roll speed References 1 M A Zaidi T Sheppard Development of microstructure throughout roll gap during rolling of aluminium alloys Metal Sci 16 1982 229 238 Table 3 Level average response analysis using S N ratio for the centre point VariablesLevelRunsy yS NS Nij Hm L Level 10 7414 284 84666712 6288813 67041 24 8713 75058 35 3914 63178 Level 21 4545 795 22333315 2535714 30319 54 4312 92807 65 4514 72793 Level 33 175 555 90666714 8858615 32868 87 1517 08612 95 0214 01407 Troll Level 120 8C14 285 20666712 6288814 2561 45 7915 25357 75 5514 88586 Level 260 8C24 875 48333313 7505814 58826 54 4312 92807 87 1517 08612 Level 3100 8C35 395 28666714 6317814 45793 65 4514 72793 95 0214 01407 V Level 1100 mm s14 285 62666712 6288814 81431 65 4514 72793 87 1517 08612 Level 2200 mm s24 875 22666713 7505814 33941 45 7915 25357 95 021