The microstructure in this case is close to theas received microstructure of the plate prior to the levelling. Theabove-mentioned T/C test replicates real industrial conditionsmuch better than the test performed using Gleeble. That is whyresults of the identification procedure presented in Fig. 5were usedfurther during simulation of the industrial levelling. Again, theinverse identification procedure is applied to the T/C test dataobtained using Zwick in various deformation temperatures,including room temperature.Examples of parameters of the combined hardening modelidentified on the basis of the experimental data from Gleeble andZwick for the 650 8C temperature are summarised in Table 1.3. Design of the industrial levelling operationThe identified combined hardening model for the small cyclicstrain amplitude is used during the development of the levellingoperation for long flat products. The schematic illustration of thehot leveller used in the present research is shown in Fig. 6. Duringthe research a series of numerical simulations of the hot levelling at650 8C was performed. For the selected temperature, 9 differentleveller setups were used as presented in Table 2.
Additionally, different initial plate curvatures A were analysed.The parameter A describes the amplitude of the curvature as seenin Fig. 7. Four different initial plate curvatures were investigated:A = 20, 40, 60 and 80 mm, respectively. These simulations wereused to evaluate the influence of the hot leveller setup and initialplate curvature on their final flatness. The plate flatness wascalculated as a mean square root error between the final geometryand the ideal flat plate as seen in Fig. 7:U kk ¼Pn1 ðUFEMn   UREFn Þ2n(5)where n is the number of sampling points, UFEMn and UREFn are thedisplacement in the y-direction of the nth point taken from FEsimulation and from reference position (in the flat product),respectively.tee Selected results for the two initial curvatures only, A = 20 and80 mm, obtained for various leveller setups, are presented in Fig. 8.
The higher the defined norm the more distorted plate is obtainedafter the simulations. It is seen in Fig. 8 that a clearminimumin theflatness norm is identified. Based on this observation it can beconcluded that there is a specific hot leveller setup that provides arelatively flat plate despite the initial material flatness. It is alsocrucial fromthe industrial point of viewto investigate correspond-ing loadmeasurements to eliminate any unrealistic leveller setups.The recorded maximum load values are grouped in the regionbetween dashed lines in Fig. 8. This figure is a good practice guidefor the industrial engineer responsible for selection of anappropriate leveller setup. Obtained results were initially verifiedin manufacturing conditions, however at this stage the industrialdata are not publicly available. - When a cyclic deformation process is considered, the combinedhardening model has to be used. The simple isotropic hardeningmodel does not properly predict material behaviour under cyclicdeformation conditions.- Proper identification of the combined hardening model isextremely important. Standard approaches based on thecoefficients calibrated using half-cycle test data, or stabilisedcycle test data do not provide accurate identification results.- The best results are achieved when the combined hardeningmodel with the parameters specified directly by the means ofinverse analysis is used. Thismethod can be recommended as themost accurate when dealing with identification of the nonlinearhardening model.- The capabilities and thermo-mechanical cycle have to be as closeas possible to real industrial conditions to accurately capturematerial behaviour under low cyclic deformation.- A specific leveller setup that provides a relatively flat platedespite the initial material flatness can be identifiednumerically. The best flatness results in case of investigatedplates are achieved for the range of the in gap width14–18 mm.AcknowledgementsThe research leading to these results has received fundingfrom the European Community’s Research Fund for Coal and Steel(RFCS) under grant agreement no. RFSR-CT-2007-00014. FEMCalculations were realised at the ACK CYFRONET AGH MNiSW/IBM_BC_HS21/AGH/032/2008. LMis grateful for support of the FNPwithin the Start program.References[1] 板材矫直技术的计算机辅助英文文献和中文翻译(3):http://www.751com.cn/fanyi/lunwen_53600.html