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A thermomechanical material model for aluminum alloys during extrusion



Fig. 1: Schematic illustration of direct extrusion

Extrusion is a manufacturing process where a material is pressed through a die. It is used to produce long formed objects of constant cross sections from different materials such as aluminum, copper, stainless steel and various types of plastic. Mostly rods, cables and pipes are made from copper and steel, whereas complex profiles are produced using aluminum.

This work focuses on a direct extrusion process as shown in Fig. 1 with aluminum alloys of the series 6000 (Al-Mg-Si) and 7000 (Al-Zn-Mg). Due to relaxation and re-crystallization effects the microstructure of the material changes while it flows through the die and during the following cooling process. Rapid cooling leads to better hardness properties but also to higher residual stresses. Especially in complex profiles (see Fig. 2) the microstructure evolution varies in different parts of the structure.

Understanding how temperature and microstructure evolution affect the resulting hardness properties allows a foregoing simulation. This leads to a suitable process management during the extrusion process to achieve the required hardness properties without further heat treatment.


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Fig. 2: Sample aluminum profiles (left: console of a high-performance printer; right: machining center tool holder) [1]       Fig. 3:Sample processing of aluminum profiles (left: bending of profiles; right: hydroforming)



  • model formulation based on internal variables (dislocation density, sub grain size, grain orientation mismatch, elastic distortion)
  • material parameter identification and optimization
  • model validation by comparison with real extrusion experiments
  • numerical implementation and verification of the developed model using ABAQUS with user defined elements/materials
  • extension of the model to cover following manufacturing processes such as bending or hydroforming as shown in Fig. 3



Extrusion, aluminum, internal variables, microstructure

Material model based on internal variables


Fig. 4: Microstructure evolution during extrusion process

The extrusion and the following integrated processing leads to complex thermomechanical loadings of the material. The evolution of microstructure during the manufacturing affects the material behavior and process parameters. Relaxation, diffusion, re-crystallization, and segregation processes within the material during extrusion are influenced by different process parameters such as temperature or stamp velocity (see Fig. 4). At the end the microstructure determines the mechanical properties of the final product.




Fig. 5: Schematic FE-model with regular mesh

In this early project phase the following general FE-model is used to analyze the material behavior during the extrusion process. Die and container are both modeled as 2 dimensional analytical rigid bodies. It is considered that no fraction acts between the block and die/container. This plain model is divided into two symmetric parts and only one part needs to be simulated in order to save computation time.

The high deformation rates which appear during extrusion make it necessary to implement adapting methods. Fig. 5 shows the deformation of a regular mesh without any adaptive meshing. The narrow elements at the die area cause a termination of the simulation.

The mesh in Fig. 6 is ALE optimized (Arbitrary Lagrangian Eulerian) so that the developing mesh in the rod consists of regular elements. Mesh refining which depends on the distance of the elements to the die opening is shown in Fig. 7. Splitting the elements during the mesh refinement reduces the deformation of single elements. This leads to more realistic simulation results.


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Fig. 6: ALE optimized mesh       Fig. 7: Adaptive mesh refining

First Results


The following figures display some exemplary simulation results. The used material is aluminum Al99,5 with a starting temperature of 300°C. This adiabatic simulation shows the in Fig. 8 presented distribution of temperature after nearly 3.5 sec.

In Fig. 9 one can see the material velocity in direction of the extrusion. Due to constancy of volume the velocity of the extruded rod needs to be higher than the velocity of the stamp and block (also see Fig. 1).

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Fig. 8: Temperature distribution       Fig. 9: Equivalent plastic strain

The equivalent plastic strain shown in Fig. 10 and the von Mises stress in Fig. 11 result from the model based on linear isotropic hardening.

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Fig. 10: Velocity in direction of extrusion       Fig. 11: Von Mises stress

Contact/Author information


Dr.-Ing. Tobias Kayser