# Computer simulation of the aluminum extrusion

## Introduction

Modern computer program for modeling an extrusion of aluminum capable of providing an effective improvement of the quality of extruded aluminum profiles even at the design stage extrusion dies. Computer modeling can improve the quality of manufactured aluminum profiles according to the following indicators:

• dimensional accuracy and profile shapes
• strength and appearance of welds
• The grain microstructure
• mechanical properties of the material.

For the average user this model, it often remains “black box”, whose internal structure is unknown or unclear. Below we will try to explain some of the properties of these models, and also to show their potential usefulness for practice production of aluminum extruded products.

## computer model

### Finite element technique

Almost all computer models are based on the finite element method (FEM). The Finite Element Method - is a numerical method for solving problems in various branches of physics and engineering, such as, mechanics of materials, Heat Transfer, for liquids and the electromagnetic field. The analytical solution of these problems require complex solutions of partial differential equations, which is possible only in the simplest cases. The formulation of the same tasks in the finite element method reduces to the solution of large systems of algebraic equations, which modern computers can easily cope with [1].

To solve the problem of modeling the object is divided into small elements of simple shape – finite elements. For two-dimensional problems, such simplest elements are triangles (figure 1) and quadrangles, for three-dimensional - tetrahedra and parallelepipeds. Finite elements interconnected, but only at the connection points – sites. Using mathematical relationships, which define the relationship between stresses and strains (in the simplest case – Hooke's law), simulate the behavior of each of the finite elements during loading or moving its components.

Figure 1 - triangular finite elements
with components of nodal displacements [1]

Then all of these finite elements are combined into larger systems of algebraic equations, which already model the entire object as a whole (figure 2). These systems of equations and solves computer.

Figure 2 - Three-dimensional finite element mesh
for simulation of the aluminum extrusion
in the computer program QForm [2].

### material model

The flow of material through the container and die most strongly depends on:

• aluminum temperature and
• Aluminum strain rate.

Therefore, most often the behavior of aluminum is represented by models of a rigid-viscous-plastic material [2-4]. Typically, these models do not take into account the elastic deformation of the material, that in general it is justified, as in the process flow of aluminum through the container and the elastic deformation of the matrix is ​​negligibly small fraction of the total deformation. However, in the channel operating belts elastic behavior of the material can play an important role and have a significant impact on the simulation results. Therefore, to more accurately simulate aluminum velocity at the exit of the matrix is ​​often used visco-elastic-plastic material model.

Strain hardening of the material is usually neglected, so says, in the temperature range of aluminum extrusion is compensated by dynamic recrystallization.

In the end, model links the stress in the material and its rate of deformation of certain mathematical relations, parameters which are specific for each aluminum alloy.

### friction Model

An important condition for adequate modeling is also a model of friction between the aluminum and pressing tool, which reflects the true interaction with the aluminum walls of the container and the elements of matrix, including, with its running web.

### aluminum matrix during and deflections

It is known, that the elastic deflection elements of the matrix can have a significant impact on the course material. In turn, These deformations of the matrix depend on the pressure, which renders it passing therethrough material. Therefore modern simulation methods are based on an integrated approach, which combines in one model based on the finite element method (FEM):

• calculation of the plastic flow of aluminum through the matrix and its temperature;
• calculating the elastic strain and temperature steel matrix.

calculation procedure involves several iterations, in which there is an automatic realignment calculated finite element mesh.

This approach provides the most accurate results for:

• the flow of aluminum through the matrix;
• the size and shape of the extruded aluminum profile;
• temperature of aluminum in the workpiece and profile;
• temperature matrix.

## Optimization of the properties of aluminum profile

With the help of modern computer simulation of aluminum extrusion is already at the stage of designing the matrix measures are taken – design and technological – to improve the quality of the profile according to the following indicators [2, 3]:

• dimensional accuracy and profile shape;
• location, strength and appearance of welds;
• optimization of the grain microstructure of the profile material;
• efficiency thermal hardening profile material while minimizing its buckling under cooling at the outlet from the press.

### The size and shape of the profile

Simulation shows a possible distortion of the shape of the profile and possible deviations thickness of its walls and shelves at the output of matrix. These phenomena can largely be exacerbated by the elastic deformation of the elements of the matrix. Examples of such troughs are troughs so-called "tongue" in the planar array, as a result of which there is a significant change in the angle of inclination of the planes of the working belts relative to the pressing axis (figure 3).

Figure 3 - Deflection of the tongue in a flat matrix [4]

Joint modeling as the metal flows through a die, and deformation of the matrix itself under the influence of this trend, to compensate for the elastic deformation of the matrix and to achieve compression profile size and shape, which is securely located within the tolerance. This is achieved, for example, due to the correct choice of the type of matrix and optimization of its design [3].

### Welds

There are two types of welds on extruded aluminum profiles (picture 4):

• longitudinal and
• cross.

#### Longitudinal welds

Longitudinal seams occur only in the profiles, are compressed on a matrix of type "porthol", and transverse seams - on all profiles (figure 4).

Figure 4 - Scheme of the longitudinal and transverse welds
with continuous pressing of aluminum [5]

The longitudinal welds formed, when a hot aluminum alloy is separated in matrix ports into separate streams porthol, which are then metallurgically welded just before leaving the die (Figure 5).

Figure 5 - Formation of longitudinal welds in the matrix-porthole [6]

#### Transverse welds

Transverse welds occur, when the leading end of a new workpiece comes into contact with the remaining in the metal matrix from the previous workpiece and metallurgically welded to them under high pressure and high temperature. Depending on the size and shape of the cross-sectional profile and the design matrix transverse the seam can have a considerable length, which may be about one meter or more.

#### Design of welds

These welds, as longitudinal, and transverse, can significantly spoil the appearance of facial surfaces anodized profiles, since they often differ significantly from the rest of the surface in terms of gloss or haze (picture 6). This is due to the different sensitivity of the grains of the material to alkaline pickling, which is made before anodizing operation.

Figure 6 - Stripes on matte anodized surface
along longitudinal welds [6]

Computer simulation provides the following possibilities for optimal design of welds:

• Changing the location of the welds, for example, transferring them with faces of the profile at the corner portions.
• Achievement of the specified strength of the weld by creating the required pressure and temperature in the welding chamber (selection of its dimensions and determination of the specified pressing speed).
• Optimization of the parameters of plastic deformation in the welding chambers to reduce the degree of nonuniformity of microstructure.

### The grain microstructure

#### Recovery and recrystallization

During the plastic deformation the original microstructure of the workpiece material is subjected to considerable rearrangement under the influence of such mechanisms, how the return and different types of recrystallization (figure 7). The dynamic crystallization occurs during continuous energy supply as a result of plastic deformation. Static recrystallization occurs after plastic deformation and the energy controlled, which is already stocked in the material.

Figure 7 - Processes of recovery and recrystallization in the extrusion of aluminum alloys:
a) in a stationary pressing mode; b) when the press stops to change the workpiece [7]

#### alloys 6060 and 6082

In the 6xxx series alloys nizkoprochnyh – alloys 6060 (6063) – recrystallization occurs relatively easily and profiles from these alloys usually have a completely recrystallized structure (figure 8). In the alloys with a higher level of strength, such as, 6005, 6061 and 6082, a partially recrystallized structure is often observed (figure 9). This is due to the presence in these alloys dispersoidnyh particles, which inhibit recrystallization [8].

Figure 8 - fully recrystallized alloy microstructure 6060 [6]

Figure 8 - Partially recrystallized alloy microstructure 6082 [6]

Coarse recrystallized grains are almost always located on the surface of aluminum profiles or near its. Sometimes they appear on only a portion of the surface profile. This layer of coarse grains on the surface of the aluminum profile may cause problems, such as marriage increased when machining or bending profiles, defects in appearance “Orange peel”, stripes and inhomogeneity of the gloss of the anodized surface [8].

#### factors recrystallization

The following factors influence the rate and completeness of recrystallization [8]:

• temperature at the exit from the matrix;
• workpiece temperature;
• pressing speed;
• pressing ratio (drawing);
• cooling rate during quenching;
• the presence of the chemical composition of items, inhibiting recrystallization (for example, manganese and chromium).

The computer model makes it possible to perform optimization as a design matrix, and pressing technological parameters to minimize the possibility of brute recrystallized microstructure profiles.

### Quenching

Thermal hardening aluminum profiles 6xxx series alloys, includes two stages:

• hardening on press
• artificial aging in an oven.

Hardening in the press is sufficiently rapid cooling of the profile immediately after the release from the matrix to a temperature of about 250 ºС (figure .

The object of tempering is to keep the aluminum profile in an aluminum solid solution the maximum amount of alloying elements. For 6xxx series alloys such elements are magnesium and silicon. From this stage on Aging, artificial or natural, the level of the achieved strength properties depends (figure 10).

Figure 10 - Diagram of press hardening of aluminum profiles [9]

Each aluminum alloy has the critical cooling rate until a temperature of about 250 oC. The model is able to determine the cooling rate profile at each point and make recommendations for the cooling intensity of the surface profile, as well as the intensity of the cooling medium - air-cooling fan to the cooling water flow.

Figure 11 - Diagram of press hardening and artificial aging of aluminum profiles [10]

At the same time, the choice of cooling parameters during quenching Profile necessarily take into account the profile of resistance to warping and distortion of the shape. Compare drawings 11 and 12 shows, that in practice the cooling parameters in the hardening are a compromise between achieving high strength profile and minimizing its buckling under the shear and longitudinal profile shape tolerances.

Figure 12 - Limitations when hardening an aluminum profile on a press [10]

## Conclusion

Modern computer model aluminum extrusion are effective tools for improving the quality of extruded sections. They give a deeper understanding of the processes, which occur within the die during pressing of a profile. This saves time and money in both the design and implementation of new matrices, and in solving problems in the operation of existing matrices.

Sources:

1. Application of Finite Element Method / L. Syegyerlind – Per. with English. - World, 1979.
2. Application of QForm Program for Improvement of the Die Design and Profile Extrusion Technology /N. Biba, S. Stebunov, and A. hair – QuantorForm Ltd., Moscow, Russia – Proc. of ET2008 – 2008.
3. Quality Prediction and Improvement of Extruded Profiles by means of Simulations /N. Biba, R. Rezvykh, I. Kniazkin – Aluminium Extrusion, 2/2019.
4. CAD Implementation of Design Rules for Aluminium Extrusion Dies / G. van Ouwerkerk – University of Twente, 2009.
5. Microstructural Caracterization of Extrusion Welds in 6xxx Aluminium Alloys /X. Ren et al - IC3ME 2015.
6. Influence of Al Microstructure on Hard Anodising Quality– Profile Material/ Tom Hauge, Hydro Aluminium, Norway IHAA Symposium, 25th of September 2014, New York.
7. Characterization of Microstructure in Aluminum Alloys Based on Electron Backscatter Diffraction /T. Kayser – PhD Thesis – Technical University of Dortmund - 2011.
8. Effects of Extrusion Parameters on Coarse Grain Surface Layer in 6xxx Series Extrusions /E.D. Sweet te al – Proc. of ET2004 – 2004.
9. Distorsion Mechanisms due to the Cooling Process in Aluminum Extrusion /S. Bikass et al- Proc. of ET 2012 – 2012
10. Thermal Treatments During Processing of Aluminum— AEC Webinar Presentation /R.E. Sanders (Alcoa) – 2010

## ATTACHMENT

All, what was stated above, applies, mainly, for production of aluminum profiles of a thermally hardenable alloys 6xxx series, and, partially, thermally neuprochnyaemym alloy series 1xxx, 3xxx and 5xxx. Conditions of production of aluminum profiles of the most thermally hardenable alloys, 2xxx and 7xxx series differ significantly from those, which are characteristic of the 6xxx series alloys. This should be considered when modeling.

alloy 7075, for example, these features are as follows:

• simple cross-sections only;
• hollow profiles – from a hollow blank only;
• lower billet temperature (300-370 ºС);
• very low pressing speed (1.0-1.5 m / min);
• the specific pressing pressure is almost 3 times higher, than an alloy 6063;
• It does not have the ability to hardening on press – hardening is done from a separate heating:
• the heating furnace for quenching is located above the quenching tank: the heated profiles quickly "fall" into the bath with the quenching liquid;
• especially sensitive to recrystallization: a coarse-crystalline rim is almost always formed.

Read more about the features of the production of aluminum profiles from alloys 2xxx and 7xxx series, see. here.