advances in numerical modeling of manufacturing processes

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TRANS. INDIAN INST. MET., VOL. 57, NO. 4, AUGUST 2004 2.2.3 Partial recrystallization in a multi-stage deformation process Often during the rolling process, the time in the interstand is not sufficient for complete recrystallization to occur. In other words, some amount of strain is retained in the microstructure when it enters the next deformation pass. Several approaches have been proposed to handle partial recrystallization. One of the approaches is to treat the microstructure as an aggregate. The retained strain and the effective grain sizes are determined using the rule of mixtures: ε ret = ε ⋅( 1− X ) (8) d eff ( 1− X ) ⋅ d0 = X ⋅ d + (9) rex where, X is the fraction recrystallized, ε ret is the retained strain, d eff is the effective grain size, d 0 is the initial as heated grain size and d rex is the recrystallized grain size. The other approach is to treat the recrystallized and unrecrystallized fractions independently (Karhausen and Kopp 24 ). However, the number of fractions to be handled increases exponentially, which calls for tremendous amount of computer memory and time. Yanagimoto et al. 25 proposed a variation of Karhausen’s model. In this approach, the number of fractions increases linearly, which requires considerably less memory. However, as with the rule of mixtures, considerable approximation is involved and the true behavior of the system is not represented. Here, three hit compression tests were conducted to determine the validity of the rule of mixtures. In the three hit compression tests, the first inter hit time was kept deliberately short to cause partial recrystallization. The second hit was followed by a third hit with an inter-hit time between the two. The amount of recrystallization in the second inter-hit time was measured using the same procedure as was used in the double hit compression tests. It was found that the rule of mixtures shows a better correlation with the measurements for TMS80R and was hence used in the integrated model. 2.3 Microstructure dependent flow stress model Flow stress of steel at hot rolling temperatures was found to be strongly dependent on the microstructure, specifically the austenite grain size in addition to process parameters such as strain, strain rate and temperature. f ( ε , & ε , T, d ) σ = f (10) 0 A microstructure dependent flow stress model was developed and integrated into the FEM module. The flow stress model is capable of modeling the metallurgical phenomena such as strain hardening, dynamic recovery and recrystallization. Figures 3 and 4 demonstrate the capability of the flow stress to model accurately the work hardening and thermal softening processes occurring during plastic deformation of steels under constant strain rate as well as changing strain rate conditions. Details about the microstructure dependent flow stress model can be found in Pauskar et al. 16 2.4 Integrated Model and Validation The central feature of the integrated system is a three dimensional finite element program ROLPAS for simulating multi-pass shape rolling. The nonisothermal deformation analysis in ROLPAS is based on rigid-viscoplastic assumption of the material behavior as described earlier and uses eight-node isoparametric hexahedral elements. Deformation within the roll gap is assumed to be kinematically steady. Such an assumption has been successfully applied earlier to steady state processes such as extrusion and rolling. A microstructure evolution module MICON was developed and integrated into ROLPAS to enable modeling of austenite evolution. MICON uses the thermomechanical history computed by the FEM model in conjunction with microstructure evolution models to determine the evolution of austenite during hot rolling. The evolving austenite was found to significantly affect the flow stress of the material while the material flow affects recrystallization kinetics. This situation calls for an iterative approach in modeling metal flow and austenite evolution. For the first pass, an initial preheated grain size is input to the program. After deformation and heat transfer computations for each pass, the microstructure evolution module in conjunction with the heat transfer 348
RAJIV SHIVPURI : NUMERICAL MODELING OF MANUFACTURING PROCESSES Measurements of roll loads were made on the rolling mill. The process was simulated using integrated ROLPAS first with and then without microstructure modeling. It was seen that the predictions of the rolling loads with microstructure modeling were within 10% of the measurements while, the predictions without microstructure modeling were consistently much higher (Fig. 5(a)) 5,26 . Fig. 3 : Effect of temperature on flow stress. Experience with process modeling using FEM has shown that predictions of material spread are strongly dependent upon the flow stress model. A three pass rough rolling schedule being used in a steel company to convert a 6-5/8"x 6-5/8" square billet to a 5" diameter round billet was chosen to illustrate the effect of microstructure modeling on the material flow. Figure 5(b) shows the mesh at the exit of the rolls in the second pass as predicted by the finite element model with and without microstructure modeling. A sketch of the actual shape seen at the end of the second pass is also shown. It can be easily seen that the finite element model without microstructure modeling grossly under predicts the material spread. It also fails to predict the bulge profile of the workpiece. On the other hand, predictions of material spread with microstructure modeling are more accurate and the shape predicted is closer to what is seen in practice. 2.5 Benefits to Industry Fig. 4 : Flow stress predictions vs. measurements under changing strain rates analysis module computes recrystallized fraction and the austenite grain size at each node in the interstand region. In the event of complete recrystallization, grain growth after recrystallization becomes important in determining the recrystallization kinetics of the next pass. Partial recrystallization is handled using the rule of mixtures as described earlier. The non-integrated approach used in earlier studies resulted in higher predictions of rolling loads using FEM. A seven pass rough rolling sequence from a leading steel company was chosen to study the effect of microstructure modeling on the load predictions. The roll pass sequence converts a 15"x15" ingot into a 12" round bar in seven rough rolling passes. The microstructural based numerical model of multipass hot rolling and post rolling transformation provide the rolling mills the tools to carryout the following tasks: • Design and verification of roll pass sequence for given product geometry and dimensions. Finish dimensions and temperature are often the design response. • Design of thermo-mechanical processing for improved product properties and quality. Microstructure and final mechanical properties are control parameters. • Reduction of product defects such as seams, fins, segregations and cobbles. • Process control for reduced variability and scrap. 349
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