Simulation of Hot Extrusion of an Aluminum Alloy with Modeling of Microstructure

Transcription

1 Simulation of Hot Extrusion of an Aluminum Alloy with Modeling of Microstructure A. Ockewitz, a, D.-Z. Sun,b, F. Andrieux,c and S. Mueller 2,d Fraunhofer Institute for Mechanics of Materials IWM, Woehlerstrasse, 798 Freiburg, Germany 2 Extrusion Research and Development Center FZS TU Berlin, Gustav-Meyer-Allee 2, 33 Berlin, Germany a andrea.ockewitz@iwm.fraunhofer.de, b dong-zhi.sun@iwm.fraunhofer.de, c florence.andrieux@iwm.fraunhofer.de, d soeren.mueller@tu-berlin.de Keywords: aluminum extrusion, simulation, microstructure, recrystallization, friction test Abstract. In this work a numerical method for the simulation of extrusion processes with modeling of microstructure is presented. Extensive testing was done to provide a basis for the verification of simulation results. Circular rods of AA6A were extruded by backward and forward extrusion with different extrusion ratios, billet temperatures and product velocities. The extruded rods were cooled either by water or at air to distinguish between dynamic and static recrystallization. Temperature and strain-rate dependent yield stresses were determined from hot compression tests. Special friction tests on cylindrical specimens under high hydrostatic stresses at high temperatures have been performed and the parameters of a friction model were identified from the experiments. The recrystallized volume fraction and grain sizes in the extruded rods were analyzed by means of optical micrographs. The obtained results were used to determine the parameters of a recrystallization model which was implemented in the FE code HyperXtrude. The transferability of the numerical model was checked by simulating forward extrusion tests using the model parameters obtained from backward extrusion tests. Introduction Extruded aluminum components are widely used in vehicle constructions due to light weight and manufacturing considerations. The analysis of the crash behavior of extruded components is very complex, since local mechanical properties in the components are inhomogeneous as a consequence of the spatial distribution of microstructure which is influenced by numerous factors like material composition, temperature, tool design, friction, extrusion ratio and speed during the extrusion process. For the optimization of the extrusion process with regard to all these factors numerical simulation can be an essential tool. Based on results of finite element simulations of the extrusion process the microstructure in the extruded components can be predicted and then the resulting mechanical properties can be numerically determined instead of by costly trial and error methods. The aim of the work presented in this paper is the development of a numerical method for the simulation of extrusion processes with modeling of microstructure. During the thermo-mechanical processes in hot extrusion different recrystallization mechanisms like static or dynamic recrystallization or grain growth can take place []. Empirical and physical models for the description of these mechanisms have already been developed and verified by experimental and numerical investigations [2-]. A problem is that the contribution of each mechanism to the final microstructure cannot be easily determined. The occurrence of static recrystallization can however be suppressed by cooling the extrudate immediately after deformation. By comparison of the microstructure in extrudates with and without additional cooling at least the effects of static and dynamic recrystallization can be distinguished. The extrusion tests performed in this work for the validation of simulation results were designed to produce static as well as dynamic recrystallization and varying local distributions of strain, strain rate and temperature in the extruded parts.

2 Extrusion processes are essentially influenced by friction between billet and extrusion tools. Not only process parameters but also the microstructure and mechanical properties of extrudates depend strongly on friction effects. A reliable determination of friction behavior is important for the construction of extrusion tools and optimization of whole extrusion processes. The problems for characterization of friction effects in extrusion processes are that common friction tests like pin-ondisk don t give relevant information about friction in extrusion situations due to lower hydrostatic stresses. There are few results about influence of normal stress, temperature and velocity on friction [6,7]. In this work a two-step friction test was developed to achieve a loading condition with high hydrostatic stress like in extrusion processes. Experimental Investigations Extrusion Tests. For the analysis of the microstructure of AA6A and the verification of simulation results circular rods were extruded at FZS Berlin by backward as well as forward extrusion for two extrusion ratios (3: and 6:), billet temperatures of 42, 46 and ºC and different product velocities. The product velocities for the smaller extrusion ratio were 2, 8 and m/min and for the larger ratio 4, 8, and 3 m/min. The billet diameter was 2 mm, thus the rod diameter for extrusion ratio 3: is 23 mm and for 6: 6 mm. In one series of tests the rods were water-cooled immediately behind the die exit, in order to prevent the possible occurrence of static recrystallization. Recrystallization observed in these rods should be attributed to dynamic recrystallization processes. In a second series of tests the rods cooled down at air. During the extrusion tests force vs. punch displacement curves were recorded and the dies were equipped with two thermocouples for temperature measurements. The evaluated force resp. temperature vs. punch displacement curves are shown for one example in the section on simulations (Figure 9). water-cooled C 46 C 42 C air-cooled C 46 C 42 C 4 m/min 8 m/min m/min 3 m/min Figure : Micrographs of extruded rods (diameter: 6 mm) in longitudinal and transverse direction for backward extrusion, extrusion ratio 6: in dependence of billet temperature, product velocity and cooling conditions

3 The recrystallized volume fraction and grain sizes in the extruded rods were analyzed by means of optical micrographs. Figure shows micrographs taken in longitudinal and transverse directions of rods from backward extrusion, extrusion ratio 6: for different billet temperatures, product velocities and cooling conditions. In all cases recrystallization with varying extent can be observed. For the water-cooled rods only the outer rim is affected, where for higher velocities there are larger (partially) recrystallized seams. Due to the deformation gradient recrystallization decreases towards the center of the rods where no recrystallization occurred. The recrystallized fraction increases with temperature and extrusion ratio. For the air-cooled rods recrystallization comprises the whole crosssection. Only for the lowest velocity a non-recrystallized area remains in the rod center. High temperatures and low product velocities lead to very large grain sizes which increase from rim to center. Hot Compression Tests. Hot compression tests were performed at the FZS Berlin and Fraunhofer IWM Freiburg to determine the temperature and strain-rate dependence of the flow curve of AA6A for the extrusion simulations and the evaluation of friction tests. The temperature for hot compression tests was varied between 4 C and 4 C and the strain rate was changed between. /s and 2/s. Figure 2 and Figure 3 show the measured temperature and strainrate dependence of the flow curve of AA6A from selected hot compression tests. d/dt=./s T=4 C True Stress [MPa] T=4 C T=4 C T= C True stress [MPa] d/dt=.43/s d/dt=.9/s d/dt=./s True Strain Figure 2: Temperature dependence of the true stress vs. true strain curve of AA6A at strain rate of./s True strain Figure 3: Strain-rate dependence of the true stress vs. true strain curve of AA6A at temperature of 4 C The material model in the FE program HyperXtrude for the temperature and strain-rate dependence of flow behavior is based on the Zener-Hollomon parameter Z. The results of the hot compression tests were used to fit the corresponding parameters of the material model. Figure 4 shows the determined model parameters and the good agreement between the measured flow stresses at a strain of % and the calculations. The Zener-Hollomon model does not take into account the strain-hardening effects. However, the material AA6A shows a small dependence of flow stress on strain (Figure 2 and Figure 3). Since the results of compression tests at large strains are influenced by friction and change of specimen shape, more experimental and numerical investigations are required to determine the real strain hardening behavior relevant for extrusion processes.

4 Figure 4: Measured temperature and strain-rate dependence of the flow stress at strain of % from hot compression tests in comparison with the results calculated with the Zener- Hollomon model: Z Sinh A Z exp( H / RT) / n, [MPa] [ s ] Symbols: experiments Curves: model H = 77 J/mol n = A = 7.44 s - α = Pa Temperature [ C] Friction Tests. To further investigate the frictional behavior of AA6A during an extrusion process special friction tests on cylindrical specimens under high hydrostatic stresses at high temperatures have been performed (Figure ). In the first step an aluminum cylindrical specimen is placed in a ring-shaped steel die between two punches and compressed to a certain stress state chosen according to different extrusion situations. In the second step the force of one punch (F ) is kept constant while the other punch (F 2 ) is moved by controlled displacement to shift the specimen (Figure 6). This experimental method enables a systematic change of normal stress, temperature and velocity. The diameter and the height of the aluminum specimen are 8 mm and mm, respectively. The two cylindrical steel disks have a conic form to reduce the friction between disks and die. F 2, u 2 2 Ring-shaped steel die Punch F 2 Cylindrical steel disk 2 Cylindrical Alspecimen Force [kn] Punch F F, u Cylindrical steel disk F Fric F2 F Time [s] Figure : Set up of the high pressure friction test at Fraunhofer IWM Figure 6: Development of force of two punches during a high pressure friction test The friction stress was calculated from the difference of both punch forces and the contact area A between the aluminum specimen and the steel die ( = (F 2 -F )/A). The stress normal to the contact surface 22 was determined by inserting the axial stress =4F /D 2 and shear stress into the von Mises flow condition: y 3 y : flow stress. ()

5 Figure 7 shows the measured friction stress as function of punch displacement for three compression forces (F ) and three sliding velocities. The compression force was changed from 3 kn over kn to 8kN at the constant sliding velocity of. mm/s. It corresponds to a variation of the ratio of normal stress to flow stress 22 / y from.34 over 2.4 to 4.36 (Figure 8). While the influence of compression force on friction behavior is very small, the increase of sliding velocity results in a pronounced rising of the friction stress. [MPa] a kn kn 3 kn mm/s, kn mm/s, kn. mm/s, kn Punch displacement [mm] Figure 7: Influence of compression force and sliding velocity on friction stress [MPa] a V rel = mm/s V rel = mm/s V rel =. mm/s Curves: friction model Symbols: experiments Figure 8: Influence of normal stress and sliding velocity on friction stress from experiments and the friction model based on [6] Figure 8 shows the friction stress at beginning of sliding as function of normalized normal stress for three different sliding velocities. The experimental data in the elastic region (yellow points) were determined with another friction experiment which enables a loading with low hydrostatic stress. In this experiment two aluminum cubes were pushed onto a steel bar lying between both cubes and the friction process starts when the steel bar was drawn away from the aluminum cubes perpendicular to the push direction. A theoretical model from [6] with slight modifications was applied to describe the influence of normal stress and sliding velocity on friction stress. The following equation was used to fit the experimental data: d V rel n exp N V Vrel a. bc, (2) V with : flow stress, : shear flow stress, V rel : sliding velocity, V : reference sliding velocity. The parameters a=., b=c=, d=.7 and n=. were determined by fitting the results of the friction tests. Figure 8 shows that the friction stress vs. normal stress curves calculated with the friction model agree well with the experimental data presented with symbols. Since this friction model has not been implemented in a FE-code for extrusion simulation, the friction tests were only simulated with a standard friction model to analyze the loading situations in this type of friction test. Numerical Simulations of Extrusion Tests The extrusion tests were simulated with the FE code HyperXtrude [8]. HyperXtrude calculates material flow and heat transfer by solving the Eulerian form of the governing equations. A 3D model with quarter symmetry was used for the simulations. The die, container and punch were modeled as rigid bodies. The temperature and strain rate dependent flow stresses for the simulations were determined from the results of hot compression tests as described above. Friction was assumed as sticking. The heat transfer coefficient between billet and tools was set as 7 Wm -2 K -. For the backward extrusion tests the influences of extrusion ratio, billet temperature and product velocity

6 on punch force and temperature were calculated in good agreement with the measurements, as shown for one example in Figure 9 left. Extrusion force [MN] Backward extrusion Temperature inside bearing Temperature at die front surface Extrusion force 2 2 Black lines: Simulation Ram displacement [mm] Experiment Temperature [ C ] Extrusion force [MN] Forward extrusion Extrusion force Temperature inside bearing Temperature at die front surface 2 2 Black lines: Simulation Ram displacement [mm] Experiment Figure 9: Comparison of simulation results with measured forces and temperatures for extrusion ratio 3:, billet temperature 46 ºC, product velocity 8 m/min, left: backward extrusion, right: forward extrusion. In the simulations of the forward extrusion tests with the same model parameters the calculated forces and temperatures are too high compared with the measurements (Figure 9 right). This is attributed to the fact that the additional friction between billet and container in forward extrusion is overestimated by the assumption of sticking friction. In simulations with other friction models available in HyperXtrude (e.g. Coulomb or viscoplastic friction models) no general improvement of the numerical results could be obtained. To achieve a better agreement between experiments and simulation results the friction model given in Eq. 2 with the corresponding parameters would have to be implemented in HyperXtrude. Modeling of Microstructure Empirical and physical models for the description of microstructure evolution during extrusion have already been reported in the literature [2-]. As a first step in the modeling of microstructure evolution the dynamic recrystallization (drx) model from [4,] was chosen. According to this model dynamic recrystallization occurs when the strain exceeds a critical strain c : Q RT. n m a d exp c c (3) An Avrami equation is used to describe the relationship between the recrystallized volume fraction and the effective strain: k a d p X (4) drx exp d. where. is the strain for % recrystallization: Q RT. n m. a d exp c () The grain size is expressed as: h (6) 8 exp 8 8 n8 m8 d a d Q RT c drx 8. In the above equations d is the initial grain size, the strain, the strain rate and T the temperature. R is the universal gas constant. All other unknown variables in Eqs. 3-6 are material parameters which have to be fitted to experimental results Temperature [ C ]

7 The parameters were determined for selected backward extrusion tests from the water-cooled test series with extrusion ratio 6:. The distributions of temperatures, strain rates and strains through the cross-sections of the rods from the simulations were related to the microstructure of corresponding extrusion tests through Eqs For c (Eq. 3) the following parameters were obtained: a d n = 2.66E-, m = -6.2E-3, Q = 8332 Jmol - and c =. Figure shows the radial distribution of the computed strain, which is independent of temperature and velocity (black line), and of the critical strain c for four selected tests. Dynamic recrystallization is activated where > c. The strain for % recrystallization. in Eq. was set to a constant value of. as in [4]. For the recrystallized volume fraction (Eq. 4) the remaining parameters are: ß d = k d = a =. The parameters determined for the grain size (Eq. 6) are: a 8 d h8 = 4.E+6, n 8 =, m 8 = -.3, Q 8 = -624 Jmol - and c 8 =. The model was implemented as a user function in HyperXtrude. The influences of product velocity and billet temperature on dynamic recrystallization can be well predicted with the determined model parameters (Figure ) and the calculated recrystallized volume fraction and grain size agrees as well with the experimental results for extrusion ratio 3: (Figure 2) and forward extrusion (Figure 3). Further investigations will deal with the modeling of static recystallization where the cooling down at air of the extruded rods has to be simulated to account for the time dependence of the activation criteria for static recrystallization C 4m/min c Grain size [µm] 42 C 3m/min C 4m/min C 3m/min Cent er c c r [mm] c Surf ace Figure : Radial distribution of strain and critical strain c for activation of drx for selected backward extrusion tests, extrusion ratio 6: Grain size [µm] 42 C 4m/min C 3m/min Figure : Calculated distributions of grain size due to drx through the cross-section for selected backward extrusion tests, ratio 6: C 2m/min Grain size [µm] 42 C 2m/min C 8m/min C m/min Figure 2: Calculated distributions of grain size due to drx through the cross-section for selected backward extrusion tests, ratio 3: Figure 3: Calculated distributions of grain size due to drx through the cross-section for selected forward extrusion tests, ratio 3:

8 Summary and Conclusions A numerical method for the simulation of extrusion processes with modeling of microstructure was developed. For the verification of simulation results circular rods of AA6A were extruded by backward and forward extrusion with different extrusion ratios, billet temperatures, product velocities and cooling conditions to provide a wide range of microstructure evolution. The recrystallized volume fraction and grain sizes in the extruded rods were determined and correlated with the computed local distributions of strain, strain rate and temperature for selected backward extrusion tests thus identifying the parameters of a recrystallization model. The model was implemented in the FE code HyperXtrude and then used for simulations of forward extrusion tests. The computed microstructure is in good agreement with the experimental results. A two-step friction test was developed which makes it possible to examine friction effects under high hydrostatic stresses characteristic for extrusion processes. This experimental method enables a systematic change of normal stress, temperature and velocity. A theoretical model was applied to describe the influence of normal stress and sliding velocity on friction stress. An application of this friction model for simulation of forward extrusion tests would result in a better prediction of extrusion forces and distributions of local strains and temperatures in the aluminum rods. Acknowledgements This work has been funded with budget funds of the Federal Ministry of Economics and Technology (BMWi) via the German Federation of Industrial Research Associations Otto von Guericke e.v. (AiF) (IGF-Nr.: 8 N) and supported by the Association of Metals (WVM). The authors would like to thank all parties involved for the funding and the support. References [] G. Gottstein: Physikalische Grundlagen der Materialkunde, Springer, Berlin, 27 [2] T. Sheppard, X. Duan: Journal of Materials Science, vol. 38 (23) pp [3] X. Duan, T. Sheppard: Materials Science and Engineering, vol. A3 (23) pp [4] M. Schikorra, L. Donati, L. Tomesani, A.E. Tekkaya: Journal of Materials Processing Technology, vol. 2 (28) pp [] DEFORM 3D Version. User s Manual, Scientific Forming Technologies Corporation, 29 [6] B.-A. Behrens, M. Alasti, A. Bouguecha, T. Hadifi, J. Mielke, F. Schäfer, in: Proceedings of the 2th ESAFORM Conference on Material Forming, Enschede (Netherlands), April 29 (edited by A.H. van den Boogaard and R. Akkermann, University of Twente) [7] C. Karadogan, a, R. Grueebler, b and P. Hora: Key Engineering Materials Vol. 424 (2) pp 6-66 [8] HyperXtrude. User s Guide, Altair Engineering Inc.