Numerical simulation of strain hardening and recrystallization in the hot forming processes

Recent developments for the finite-element modelling of the plastic forming of the metallic materials are described in the paper. The model consists of three parts; mechanical, thermal and microstructural components. First two are described in earlier publication and the focus here is put on the modelling of the microstructural phenomena. Two approaches are described. First uses conventional closed-form equations describing processes of recrystallization and grain growth. Second employs three differential equations giving time derivatives of the dislocation density, recrystallized volume fraction and the grain size. INTRODUCTION Fast development of the finite element method in 70-ies and 80-ies led to its wide application to the simulation of metal flow and heat transfer in various metal forming processes. Thermal-mechanical solutions for rolling [I], drawing [2] and upsetting [3] have been developed by the author. Recently, the scientific interest of several researchers focuses on the modelling of the microstructure evolution during hot forming. Several publications dealing with this problem have been published [4-71, but the majority of the authors solves the problem by a connection of the closed form equations describing recrystallization with less or more advanced thermal-mechanical models. However, the information supplied by the finite element modelling of metal flow and heat transfer would allow to use more advanced and accurate description of the microstructural events. The objectives of the present paper have been formulated with the above remarks in mind. A description of the conventional thermalmechanical-microstructural approach and its abilities is given in the first part of the paper. Then, the advantage is taken from a possibility of an accurate evaluation of temperatures, strain rates and stresses as time functions and simulation of the rec~ystallization and grain growth in the varying conditions of plastic deformation is performed. CONVENTIONAL APPROACH In this approach, more advanced thermal and mechanical components of the model are connected with the conventional description of the microstructural phenomena. Typical flow formulation [8] is coupled with a thermal model based on a finite element solution of the general convective-diffusion equation, yielding the following equations: Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jp4:19937181 1164 JOURNAL DE PHYSIQUE IV where: o yield strength, v vector of velocities, B matrix of derivatives of shape functions, h Lagrange multiplier, C = { 1 , 1 , o ) ~ for the plane strain problems and C = { 1 , 1 , 1 , 0 ) for the axisymmetrical problems, F boundary tractions, T vector of temperatures, k conductivity, p density, c, specific heat, Q rate of heat generation due to plastic work, w matrix of weighting functions, N matrix of shape functions, a heat transfer coefficient, T o ambient temperature or tool temperature, q rate of heat generation due to friction. Detailed description of this thermal-mechanical model and boundary conditions is given in [I]. This model is connected first with the conventional equations developed by Sellars [4] and Roberts et al. [9] describing processes of recrystallization and grain growth. In consequence, the thermalmechanical-microstructural model is developed; this model has been validated experimentally in the laboratory conditions and, finally, has been applied to the simulation of hot rolling [6,10] and forging [I 11 processes and proved to be very helpful in designing the technological parameters. Microstructural component of the model has been validated experimentally in a number of rolling and forging tests [10,12]. Fig.1 shows the results of one of the published earlier experiments. A reverse hot rolling process in three passes is considered here and measured and calculated distributions of the austenite rain size on the cross section of the steel sample after second and third passes are presented in the &we. The parameters of the experiment include the initial thickness of 11.6 mm, temperature in the furnace 10500C, reductions 0.18,0.17 and 0.24 in three passes respectively, time intervals: furnace 7 s first pass 9.3 s second pass 9.6 s third pass -5 s quenching. It is seen in Fig.1 that the calculated austenite grain size is within the standard deviation of the measurements. A larger number of results and the microstructures for all the experiments are given in [12]. grain size, m 60 r 1 20 1 after 2 passes after 3 passes 43calculations calculatlons * measurements measurements I I I 1 J 0 1 2 3 4 5 coordinate y, mm Fig.1. Measured and calculated grain size on the cross section of the carbon steel samples after reverse hot rolling in 2 and 3 passes. In order to present model's predictive abilities, a typical results of the simulation of the microstructure evolution in the industrial hot strip rolling are presented below. The hot strip mill in the Sendzimir still works in Krakow consisting of 5 roughing stands and 7 finishing stands has been taken as an example. Since the influence of the initial grain size after heating in the furnace on the microstructure diminishes after few cycles of deformation and recrystallization and the current austenite grains depend on the temperature and strain fields in the last few passes, the results for the finishing mill only will be presented here. The estimated austenite grain size at the entry to the finishing mill is 150 p m . Current analysis includes an investigation of the controllable parameters (heating temperature, rolling velocity, delay time on the transfer table, amount of water in the descalers and in the laminar cooling, draft schedules) on the microstructure of the product as well as on the rolling forces, roll torques and temperatures. The basic technological parameters of the investigated process, together with the results of calculations, are given in Table 1. F1g.2 shows how the heating temperature in the furnace and the work of the water descaler before the entry to the finishing train affect the finite austenite grains. An increase of the heating temperaturewithin the range of 500C has slight influence on the microstructure; an increase of the grain size being observed with the increasing temperature. The work of the descaler has stronger influence. Turning off the descaler results in about 15 percent coarser grains. Table 7 8 9 10 11 12 1 Pas schedule and process parameters for rolling of 2x830 mm strip [13]. h thickness r reduction T .. average temperature a heat transfer coefficient F rolling force M roll torque ZI rolling velocity t . time interval D , average grain size grain size, /A rn 40 I heating temperature,OC 20