Dong-Zhi Sun, Andrea Ockewitz, Andreas Trondl
Fraunhofer Institute for Mechanics of Materials IWM, Germany

Abstract. Since extrusion processes are essentially influenced by friction between billet and extrusion tools, new friction tests were performed in this work to develop a reliable friction model. Compression and torsion tests were performed at different temperatures and loading velocities to calibrate the material model for extrusion simulations. Torsion tests could be used to achieve stress vs. strain curves upto a large strain for extrusion simulations. Extrusion processes for circular rods and U-profiles were conducted at TU Berlin with backward and forward extrusion method for different extrusion ratios, billet temperatures, product velocities and cooling conditions. This work focuses on numerical simulations of the extrusion tests with the FE code HyperXtrude. Based on the calculated distributions of local strain, strain rate and temperature the recrystallized volume fraction and grain sizes were calculated with empirical models and compared with the experimental results from optical micrographs and EBSD scans. The calculated total and friction forces and temperatures were compared with the experimental results and the deviations between experiment and simulation were analyzed.


The basis for a reliable extrusion simulation is the selection and calibration of a temperature and strain-rate dependent material model, a friction model and models for calculation of microstructure. One difficulty for the determination of stress vs. strain curves for an extrusion simulation is that local strains in an extrusion process of aluminum profiles can reach very high values e.g. about 30 [1] and the standard hot compression tests can only deliver experimental data to a maximal strain less than 1. The hot torsion test is capable of producing strains of the order of 100 without the instabilities, which are caused by barreling and necking in compression and tension, respectively [1]. Since the stresses and strains over the cross section of torsion specimens are inhomogeneous and the evaluation method is complex due to the large plastic deformation, the results from the torsion tests have to be verified.

Extrusion processes, especially direct extrusion, are remarkably influenced by friction between billet and extrusion tools. The friction force at the beginning of a direct extrusion amounts to a large part of the total extrusion force and strongly decreases during the extrusion process due to the reduction of contact area. The microstructure and mechanical properties of extrudates depend considerably on friction effects [2]. One severe problem with friction is that larger local strains and strain rates and higher temperatures at contact areas lead to the formation of coarse grain zones at the surfaces of an extruded aluminum profile. Inhomogeneous microstructure over a cross section especially with coarse grain zones is not desirable. A reliable determination of friction behavior is important for the construction of extrusion tools and optimization of whole extrusion processes. Common friction tests like pin-on-disk do not 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 [3, 4]. Due to the lack of reliable experimental results about friction behavior during an extrusion process, friction is usually considered as sticking in numerical simulations. In this work a new friction test setup is suggested and simulated. Since the friction test is nearly a small scale extrusion test, the real loading conditions during extrusion processes like high hydrostatic stress and large plastic deformation can be achieved.

  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 [5, 6]. 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.

Torsion tests and simulations

Torsion specimens from EN AW-6005A were tested at three temperatures (400°C, 450°C and 500°C) and four rotation velocities (1.8°/s, 18°/s, 180°/s and 720°/s). The torsion specimens have a total length of 150 mm. The diameter and length of the testing region are 12 mm and 8 mm, respectively. Before a test the axial load was set to zero and the axial position of the torsion specimen was fixed during the test. The torque, number of rotations and temperatures at three positions were measured during the test. Figure 1 shows the torsion specimen and compares the testing section before and after torsion test at 450°C. Obviously the large plastic deformation of the region with the smallest diameter results in the formation of a pronounced rough surface. Metallographic investigation shows clearly that the surface has a wave contour due to inhomogeneous yielding. Moreover, several voids and micro cracks can be found at grain boundaries. Figure 2 shows that the averaged grain size is reduced from 88 mm to 24 mm due to plastic deformation after 31 rotations under torsion at 500°C.

Figure 1. Torsion specimen with three thermal elements (left) and comparison of the section for testing before and after test (middle and right)

Figure 2. Grain size distribution measured with EBSD, left: before and right: after torsion tests (31 rotations at720°/s, 500°C)

The measured torque vs. rotation curves for three temperatures (400°C, 450°C, 500°C) at two rotation speeds (180°/s and 720°/s) are given in Figure 3 and Figure 4. Obviously the torque decreases with increasing temperature and decreasing rotation speed.

 Figure 3. Measured torque as function of rotation at three temperatures (400°C, 450°C, 500°C) with a speed 180°/s

Figure 4. Measured torque as function of rotation at three temperatures (400°C, 450°C, 500°C) with a speed 720°/s

To describe the deformation behavior of aluminum alloys under shear loading the von Mises equivalent stress s and the equivalent strain e on the specimen surface were calculated from the measured torque M and the number of revolutions N using the following equations [7, 1]:




r: radius of testing region

l: length of testing region

q: rotation angle (2pN)

N: number of revolutions

s: equivalent stress

e: equivalent strain

M: torque

The above equation for the calculation of equivalent stress was derived by taking into account large plastic deformation. In this case the shear stress has not a linear relationship with the radius and the maximum shear stress on the surface is no longer proportional to the torque. Since the contribution of the second term in Equation 1 to the total value is very small, it was not taken into account at the calculation of the equivalent stress in this work. Figure 5 compares the equivalent stress vs. equivalent strain curves from the torsion tests for different testing temperatures and strain rates. It can be recognized that the flow stress increases considerably with increasing strain rate and decreasing temperature. The torsion tests deliver stress vs. strain curves up to a strain of 85 without rupture. The flow stress reaches a maximum value at a strain about 0.6, after that it reduces to a stabilized level with increasing deformation. Figure 6 compares the stress vs. strain curves from the hot torsion tests with the results from hot compression tests [2] for test temperature 450°C and three strain rates. The results of the both specimen types agree up to a strain of 0.6, then the flow stresses from hot compression tests deviate from the values of torsion tests due to a remarkable rising with deformation, which may be attributed to the barreling process in the compression specimens.


Figure 5. Equivalent stress vs. equivalent strain curves of torsion tests at three temperatures and different strain rates

Figure 6. Comparison of the equivalent stress vs. equivalent strain curves from torsion and compression tests at 450°C and different strain rates

Material models in different FE programs for extrusion simulations, e.g. HyperXtrude and DEFORM, are based on the Zener-Hollomon parameter Z:


DH = 177500 J/mol
n= 5
A = 7.55454E+10 s-1
α = 3.96E-08 Pa-1

Torsion tests were simulated with different formulations in the FE code ABAQUS. Both the ALE (Arbitrary Langrangian Eulerian) formulation and the pure Eulerian formulation were used to treat the extremly large plastic deformation in the torsion specimens. The third simulation technique using 2D axisymmetric elements with twist in ABAQUS/Standard delivers the most efficient solution. These elements have a degree of freedom for rotation angle besides axial and radial displacements. The stress vs. strain curves used for the simulations were obtained from the calibrated Zener-Hollomon model. Experimental results show that the temperature in the torsion specimens increases due to the transformation of plastic work into heat. Therefore, the simulations were performed with thermal mechanical coupling or the assumption of adiabatic heating (without heat conduction). Figure 5 shows the calculated equivalent plastic strain on the undeformed mesh (a) and the calculated von Mises equivalent stress on the deformed mesh (b). Both plots in Figure 5 were obtained after three revolutions. Figure 6 compares the measured and calculated torque vs. number of rotations curves for three rotation velocities at 450°C. The maximum values of torque were well predicted. While the maximum value of the torque is hardly affected by the assumed condition for thermal conduction, the slope of the torsion moment vs. number of rotations curves depends strongly on it. The application of thermal mechanical coupling is not enough to obtain the measured reduction of torsion moment with increasing deformation. The good agreement between experiment and simulation shown in Figure 6 is achieved using the adiabatic condition (without heat conduction), which is not true especially at low rotation velocities. The intensified softening effect caused by using the adiabatic condition in the simulations compensates just the damage effect in the real specimens.


Figure 5. a) Calculated plastic equivalent strain on undeformed mesh, b) calculated von Mises equivalent stress on deformed mesh after three revolutions at 450°C and velocity 180°/s

Figure 6. Torque vs. number of rotations measured at 450°C and three rotation velocities in comparison with the results calculated with ABAQUS


To enable large plastic deformation of the specimen during a friction test under high hydrostatic loading a new test setup was suggested which is depicted in Figure 7. In this test a ring-shaped aluminum specimen is placed between a steel mandrel and a ring-shaped steel die with open bottom. The specimen is pressed by a hollow steel punch from top to bottom like in forward extrusion. During the test the punch displacement is recorded and forces are measured at the punch and the mandrel. The friction tests were conducted at 420°C, 460°C and 500°C with punch velocities of 0.1 and 0.2 mm/min.


Figure 7. a): Facility with the setup for torsion tests, b): Schematic draw of the test setup, c) One cut of sample and stamp, die and mandrel after friction test

The outer and inner diameters of the samples are 16 mm and 5 mm, respectively. The outer diameter of the samples was reduced to 7 mm after the friction test and the inner diameter remains at 5 mm. Figure 8a shows the cross section of a sample after friction test at 420 °C, 0.2 mm/min with the cylindrical die. Flow lines in the specimen and a dead zone above the die can be clearly recognized. Figure 8b and 8c show grain distribution measured with EBSD method in the sample. The grain boundaries were defined based on orientation differences more than 2°, 5° and 15°. The grains at contact surfaces between die and sample and between mandrel and sample are smaller than in the center of the sample.


Figure 8. a) Cross section of the friction specimen and the tools, b) and c) grain distribution measured with EBSD after friction test at 420 °C, 0.2 mm/min


The measured punch force and friction force between the sample and the mandrel are shown in Figure 9 and Figure 10 as function of punch displacement for three testing temperatures and three testing velocities, respectively. The friction force was measured at the mandrel. The initial velocity of two friction tests at 420°C was increased after a punch displacement of about 3 mm. Both testing temperature and velocity have a large influence on the measured punch and friction force. A higher testing velocity or a lower temperature leads to a significant rise of the punch force and the friction force.




Figure 9. Measured punch force and friction force as function of punch displacement for three testing temperatures at 0.2 mm/min

Figure 10. Measured punch force and friction force as function of punch displacement for three testing velocities at 420°C

The friction tests were simulated with HyperXtrude and ABAQUS/Explicit. While HyperXtrude cannot model the filling process, ABAQUS/Explicit is able to model the whole deformation process of the friction test. To reduce the simulation expense one segment with 15° of the sample was modelled with ABAQUS/Explicit using the corresponding boundary conditions. The sample was modeled with Eulerian formulation and the die, punch and mandrel were modeled with Langrangian formulation to achieve an efficient and precise solution. As in the simulation of torsion tests the temperature and strain-rate dependence of the flow behavior measured with the hot compression tests was used in the simulations of friction tests. The contacts between the sample and tools were modelled using the Coulomb friction model with a friction coefficient which increases from 0.14 to 0.24 with increasing sliding velocity from 0 to 10 mm/s. In the simulation with HyperXtrude the contact of the sample with the die and the mandrel at the outlet position was modelled with the friction model ViscoPlastic with a friction coefficient of 0.7. The contacts at other positions were modelled with the stick option.

Figure 11 compares the measured and calculated cross section of a sample after the friction test. Obviously the flow lines, the dead zone and the gaps between the tools and the sample observed at experiment can be well predicted by both ABAQUS/Explicit and HyperXtrude. The strain values calculated with HyperXtrude are much higher than those obtained from ABAQUS/Explicit due to the assumption of stick for the most contact surfaces in the model for HyperXtrude.


Figure 11. Cross section of a sample after friction test (left) and simulated deformation with distribution of equivalent strain with ABAQUS/Explicit (middle) and with HyperXtrude (right)

Figure 12 compares the measured punch force and friction force vs. displacement curves with those calculated with ABAQUS/Explicit for three friction tests at two different temperatures and two different punch velocities. Both the punch forces and friction forces for different test conditions were well predicted with the applied friction model. The measured jumps of punch and friction forces caused by changing the punch velocity from 2 mm/s to 5 mm/s were also reproduced by the simulation. Figure 13 shows the corresponding results from HyperXtrude. As mentioned above, HyperXtrude cannot model the filling process. The influences of temperature and punch velocity on the forces can be well predicted with HyperXtrude.


Figure 12. Comparison of measured punch force and friction force vs. displacement curves with the results calculated with ABAQUS/Explicit

Figure 13. Comparison of measured punch force and friction force vs. displacement curves with the results calculated with HyperXtrude

Extrusion of U-Profiles To validate the applied numerical methods U-profiles with different wall thicknesses were extruded at FZS Berlin using backward and forward processes at different temperatures, velocities and cooling conditions [8]. The grain sizes and recrystallized volume fractions were determined with metallography and EBSD analysis. The extrusion processes of the U-profiles were simulated with HyperXtrude and ABAQUS/Explicit based on the model parameters determined before. The dynamic recrystallization (drx) model from [6, 9] was chosen for the simulation with HyperXtrude. According to this model dynamic recrystallization occurs when the strain exceeds a critical strain ec. The parameters for the microstructure calculation were determined by modeling the backward extrusion of circular rods with extrusion ratio 60:1 with water-cooling.

One half of the U-profile was modelled by using the corresponding symmetry boundary conditions. Figure 14 compares the results from experiment and simulation for a forward extrusion of a U-profile at temperature of 500°C and punch velocity of 1.1 mm/s with immediate water cooling after the extrusion. Although the measured temperatures at three positions in the bearing, the total force, the friction force and the forces on die were overestimated to different extents, the forms of the measured curves agree with the calculated ones very well. The deviations may be attributed to the assumed thermal conditions and possible deviations in geometries of the extrusion tools in experiment and simulation. Simulations of other forward extrusion tests at different process conditions show a similar agreement. The influences of temperature and press velocity on press forces and temperature changes could be predicted in a satisfactory manner. The measured force vs. displacement curves in the backward extrusion tests on the U-profiles were slightly more overestimated. This may be caused by an inaccuracy in the modeling of the complex boundary conditions in the two pockets between billet and bearing. Figure 14 also shows the calculated distribution of local strain in the U-profile during extrusion. The maximum value of local strain reaches about 21. 

Metallographic investigation shows that the parameters of extrusion processes, the cooling condition and the wall thickness have a significant influence on formation of microstructure. In many cases a reduction of temperature results in the suppression of recrystallization and an increase of press velocity promotes recrystallization. Figure 15 shows that narrow zones with coarse grains were formed at the surfaces of a forward extruded U-profile and the simulation could predict this effect.

 Figure 14. Measured total force, die force and friction force as function of the punch displacement for forward extrusion of a U-profile at 500°C, 1.1 mm/s, water cooling in comparison with the results calculated with HyperXtrude (left) calculated distribution of equivalent strain (right)


Figure 15. Calculated distributions of grain size due to drx through the half cross-section of U-profile (left) and the experimal part  at 500°C, 1.1 mm/s, water cooling (right)

Conclusions        To calibrate the material and friction models for extrusion simulations hot torsion and friction tests on EN AW-6005A were performed at different temperatures and deformation velocities. As an advantage torsion tests can deliver true stress vs. strain curves up to very large strains which occur in a real extrusion process. There is no problem with instability or friction effects which take place in standard compression tests. The disadvantage of the torsion tests lies in that the performance of the torsion tests e.g concerning temperature measurement is complex and the true stresses and true strains determined from torsion tests can be influenced by specimen geometry and the applied evaluation model. Numerical simulations of the torsion tests can be used to check the evaluated experimental results. The dependence of the flow stress on temperature and strain rate determined by hot compression tests up to a strain of about 0.6 was confirmed by the hot torsion tests. A friction test setup which enables large plastic deformation of the sample under the nearly same loading case as in real extrusion was suggested. The developments of total force, friction force and temperatures were experimentally determined. It was found that friction stress depends strongly on temperature and sliding velocity. Different numerical models in HyperXtrude and ABAQUS/Explicit were used to simulate the friction tests. The best agreements between experiment and simulation were obtained with ABAQUS/Explicit using a combination of the Eulerian formulation for the sample and the Langrangian formulation for punch, die and mandrel. The Coulomb friction model in ABAQUS with a friction coefficient which depends on sliding velocity is suitable for the simulations of the friction tests.

Extrusion tests on U-profiles performed at FZS Berlin were simulated with HyperXtrude and ABAQUS/Explicit. The development of microstructure like grain size and recrystallized volume fraction in extruded profiles was investigated by means of metallographic investigation and EBSD analysis. A strong influence of process conditions (extrusion ratios, billet temperatures, product velocities and cooling conditions) on formation of microstructure was determined. An empirical model for modeling of recrystallization was applied to calculate the microstructure development in different extrusion products. The model parameters determined by fitting selected extrusion tests on rods were applied to the U-profiles. The computed microstructure is in good agreement with the experimental results.


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