【正文】 the in pressibility. According to the variational principle, the basic equation for the finiteelement formulation is expressed as：where is equivalent stress； s equivalent strainrate。 is surface tractions。 is velocity field。In this simulation, the material flow behavior isdetermined by the flow stress data obtained in the thermomechanical simulation experiment .where is equivalent strain。 and is temperature. Hot rolling is a thermomechanical process analyzed by solving the heat conduction equation coupled to a deformation analysis. During the rolling process, the temperature distribution in the strip can be calculated using the governing partial differential equation.where is density。 c is specific heat。 is thermal conductivity。 is time。 and is heat generation. The heat transfer mechanism during hot rolling is very plex. The heat loss between stands is mainly caused by the convection and radiation to the air, and more rapid during descaling or cooling by water. After the rolled stock enters the rolling deformation region, heat generation occurs because of the deformation energy and the friction work at the contact surface.Austenite grain evolution of hot deformation is one of the physical metallurgical phenomena in hot strip rolling, and its evolution pattern mainly consists of four types, namely, dynamic recrystallization (DRX) during hot deformation, static recrystallization ( SRX) , and metadynamic recrystallization(MRX) after deformation, as well as grain growth after plete recrystallization when the dynamic and static recoveries are not only affect the resistance of the metal deformation directly, These not only affect the resistance of the metal deformation directly,but also, to a great extent, determine the final microstructure and properties of the rolled product.In general, higher strains and shorter inter strains times in hot rolling increase the possibility of DRX,This can be initiated either by a single pass or by multipass strain accumulation. In 2050 mm 7stand hot strip tandem mill, the most important ponents of the finishing train include seven 4high finishing stands F1 to F7。 the laminar cooling section, and the cooling water spray system with low pressure and high flowrate in the nterstands, which are used to control the increasing temperature because of the plastic deformation. An FE analysis model for a single pass rolling is first built, in which the interstand tension stress is put on the stock to realize the whole rolling patibility. The stock is meshed using the quadrilateral element with four nodes and the total number of elements is 1350. The stock material is SS400 and the initial thickness is 45. 9 mm. The rolling schedule in the simulation is shown in Table 1. Other initial data such as the temperature and the grain size are obtained from the simulated results of 2050 mm roughing mill.2 Results and DiscussionThe FE analysis of the actual rolling process is done using the FE model described above. The temperature and the austenite grain size distributions predicted by the present FE model are demonstrated in Fig. 3, which contains the temperature changes on the surface and at the center of the strip as well as the measured results.From the temperature curves in Fig it can be seen that the twice temperature great drops before rolling are due to the descaling water action. On the F1 stand rolling, the strip surface temperature drops rapidly in the roll gaps and thereafter increases slowly because of the relatively cold roll. The center temperature of the stock increases to some extent in the deformation region because of the heat generation from plastic work and decreases slowly in the interstands because of the heat loss ,of convection and radiation. Moreover, the large temperature drops also occur in the interstand owing to the low pressure cooling water. After rolling, the strip passes through the laminar cooling section and the temperature rapidly decreases from about 900 39。C to 580 39。C. The temperature on the strip surface after the stand F7 was measured to be 904 39。C and the temperature before coiler was measured to be 560 C. The predicted temperatures agree well with the measured temperatures. The temperature on the strip surface after the stand F7 was measured to be 904 39。C and the temperature before coiler was measured to be 560 C. The predicted temperatures agree well with the measured temperatures.From Fig 3, it is found that the austenite grain size is refined from an initial size of at the center and at the surface to and , respectively. The maximum change of the grain size exists at the stand F1, and it subsequently decreases slowly by actions of deformation refinement. The final austenite grain size grade measured is about 8 ( ). Thus, the predicted grain size of austenite is in good agreement with the measured result.Fig. 4 shows the simulated distributions of DRX and SRX volume fractions in hot strip continuous rolling process. In the hot rolling process, the steel is deformed using higher strain rates at considerably lower temperature, but the plastic strains at the first three passes are greater than the critical strains, and the DRX fraction at the stand F1 is %. Therefore,DRX still has a great effect on the grain size and cannot be ignored. During the time intervals among the first four finishing stands, full SRX can be obtained but some fractions are smaller than 1,while, the remanent softening can be plete by MRX according to the calculation procedures described above.When the stock passes through the runout table,the austenite microstructure of the steel is gradually transformed into ferrite and pearlite with decreasing the temperature. The predicted ferrite grain size after transformation is presented in with a span of to . shows the actual metallograph of ferrite and pearlite,and the measured ferrite grain size is about . Thus, the calculated grain size of fe