Advances on Extrusion Technology and Simulation of Light Alloys [1 ed.] 9783038131922, 9780878494675

Citation preview

Advances on Extrusion Technology and Simulation of Light Alloys

Advances on Extrusion Technology and Simulation of Light Alloys

Edited by

Luca Tomesani and Lorenzo Donati

TRANS TECH PUBLICATIONS LTD Switzerland • UK • USA

Copyright  2008 Trans Tech Publications Ltd, Switzerland

All rights reserved. No part of the contents of this book may be reproduced or transmitted in any form or by any means without the written permission of the publisher. Trans Tech Publications Ltd Laubisrutistr. 24 CH-8712 Stafa-Zurich Switzerland http://www.ttp.net Volume 367 of Key Engineering Materials ISSN 1013-9826 Full text available online at http://www.scientific.net

Distributed worldwide by

and in the Americas by

Trans Tech Publications Ltd. Laubisrutistr. 24 CH-8712 Stafa-Zurich Switzerland

Trans Tech Publications Inc. PO Box 699, May Street Enfield, NH 03748 USA

Fax: +41 (44) 922 10 33 e-mail: [email protected]

Phone: +1 (603) 632-7377 Fax: +1 (603) 632-5611 e-mail: [email protected]

Committees

Conference Chair Prof. L.Tomesani, DIEM University of Bologna, IT

Scientific Committee Prof. L.Tomesani, DIEM University of Bologna, IT Dr. L. Donati, DIEM University of Bologna, IT Prof. G. Tani, DIEM University of Bologna, IT Prof. F. Micari, DTMPIG University of Palermo, IT Prof. P. Bariani, DIMEG University of Padova, IT Prof. F. Gabrielli, Marche Polytechnic University, IT Prof. E. Evangelista, Marche Polytech. University, IT Prof. P. Hora, IVP ETH Zurich, CH Dr. M. Schikorra, IUL Dortmund University, DE Prof. K. Mueller, ERC TU Berlin, DE Dr. J. Zhou, LMP Delft University, NL Prof. T. Sheppard, DEC Bournemouth University, UK Dr. X. Velay, DEC Bournemouth University, UK Prof. H. Valberg, NTNU, Norwegian University, NO

Industrial Committee M. Conserva, Edimet, IT W. Dalla Barba, Interall, IT V. Giacomelli, Compes S.p.A., IT G. Horst, Honsel Gmbh, DE G. Olcelli, Olex Technologies, CA A. Klaus, Alcan, DE S. Gaudin, Alcan, CH P. den Dikken, Alcoa ACES, NL J. Maier, Wefa Inotech Gmbh, DE S. Ceccato, Profilati, IT E. Carretta, Gruppo Metra, IT E. Costa, Call Project, ISML IT

Preface The following papers, presented at the conference, give a very representative snapshot of the modelling activities for processes involving extrusion. They cover a wide range of topics that were grouped into the following categories: benchmark, keynotes, material flow and constitutive equations, microstructure, seam welds and process optimization, dies and tools. However, the topics covered by the conference were many more than these, including new materials (magnesium, hard alloys and composites), new products (composite profiles) and new processes (hot profile bending, thixoextrusion). The benchmark, the core of the conference, was aimed at exploiting FEM code capabilities and users' knowledge in the simulation of an industrial extrusion process as it was realized by the conference organizers. The experiments were accurately monitored in order to provide precise reference conditions. In particular, the adoption of two very different ram speeds should allow everyone to check the aptitude of a simulation tool to correctly predict how a particular die set would behave at different processing conditions. The comparison of the output of a numerical simulation with the experimental results here presented should allow users to check whether their settings are generally adequate to the problem and software houses to verify the sensitivity of their solving methods. Clearly, a single experiment cannot be expected to cover all extrusion-related issues. Here, the attention was focused on the simulation of die pockets and their effectiveness in affecting material flow. A multi-hole die with four L-shaped profiles was built and the effect of different pocket shapes on process behaviour was evaluated. As a final remark, it must be noted that, due to the complexity of this matter, it would be useless to consider the benchmark as a contest: it is, instead, an opportunity to fix some points about everyday simulation practice, each participant having his own particular interest. We hope that it will be of use also in the future, among the next benchmark experiments. Luca Tomesani, Conference Chairman

University of Bologna Dipartimento DIEM Viale Risorgimento 2 40136 Bologna, Italy

Table of Contents Committees Preface

I. Extrusion Benchmark Extrusion Benchmark 2007 – Benchmark Experiments: Study on Material Flow Extrusion of a Flat Die M. Schikorra, L. Donati, L. Tomesani and A.E. Tekkaya

1

II. Keynotes Modifications of the Extrusion Process of Magnesium Alloys for Improved Mechanical Properties S. Müller, K. Mueller and W. Reimers Experimental Techniques to Characterize Large Plastic Deformations in Unlubricated Hot Aluminum Extrusion H.S. Valberg Innovative Methodologies for the Simulation of Static Recrystallisation during the Solution Soaking Process of Shape Extrusion T. Sheppard and X. Velay

9 17 25

III. Material Flow and Constitutive Equations Flow Front Tracking in ALE/Eulerian Formulation FEM Simulations of Aluminium Extrusion A.J. Koopman, H.J.M. Geijselaers and J. Huétink Numerical Optimization of Bearing Length in Composite Extrusion Processes T. Kloppenborg, M. Schikorra, M. Schomäcker and A.E. Tekkaya Recent Developments in the Manufacture of Complex Components by Influencing the Material Flow during Extrusion N. Ben Khalifa, D. Becker, M. Schikorra and A.E. Tekkaya FE Simulation of Extrusion to Produce a Thin-Walled Wide Profile through a Spreading Pocket Die G. Fang, J. Zhou, J. Duczczyk and X.K. Wu Aluminum Rod Extrusion and Material Modeling P.T. Moe, Y.A. Khan, H.S. Valberg and S. Støren Hot Workability and Constitutive Equations of ZM21 Magnesium Alloy M. El Mehtedi, L. Balloni, S. Spigarelli, E. Evangelista and G.I. Rosen Constitutive Models for AZ31 Magnesium Alloys C. Bruni, L. Donati, M. El Mehtedi and M. Simoncini

39 47 55 63 71 79 87

IV. Microstructure Insights to Extrusion from Finite Element Modeling H.J. McQueen and E. Evangelista Study on Thixo-Extrusion of Semi-Solid Wrought Magnesium Alloy H. Yan, M.F. Fu, X.C. Tao and H.W. Hu Microstructure Prediction of Hot-Deformed Aluminium Alloys L. Donati, J.S. Dzwonczyk, J. Zhou and L. Tomesani Application of Adaptive Mesh and ALE Method in Simulation of Extrusion of Aluminum Alloys T. Kayser, F. Parvizian, C. Hortig and B. Svendsen

V. Seam Welds and Process Optimization

95 103 107 117

b

Advances on Extrusion Technology and Simulation of Light Alloys

Seam Welds Modeling and Mechanical Properties Prediction in the Extrusion of AA6082 Alloy L. Donati and L. Tomesani A Laboratory Scale Equipment to Relieve Force and Pressure in Cold Extrusion of Lead Hollow Components L. Filice, F. Gagliardi and F. Micari Analysis of Metal Flow through a Porthole Die to Produce a Rectangular Hollow Profile with Longitudinal Weld Seams G. Liu, J. Zhou, K. Huang and J. Duczczyk Simulation-Based Design of Ram Speed Profile for Isothermal Extrusion L.X. Li, H. Zhang, J. Hu, J. Zhou and J. Duczczyk Input Parameters Determination for Predicting Ram Speed and Billet Temperature for the First Billet M. Sabater, M.L. García-Romeu and J. de Ciurana

125 137 145 153 161

VI. Dies and Tools Creep and Fatigue Damage in Hot Work Tools Steels during Copper and Aluminium Extrusion C. Sommitsch, T. Wlanis, T. Hatzenbichler and C. Redl Microscopic Examination of the Fracture Surfaces of an H 13 Hot Extrusion Die due to Failure at the Initial Usage Stage D. Tseronis, I.F. Sideris, C. Medrea and I. Chicinaş Simulation of Direct Extrusion Process and Optimal Design of Technological Parameters Using FEM and Artificial Neural Network D. Karayel Numerical Simulation of Combined Forward-Backward Extrusion B. Grizelj, M. Plancak and B. Barisic Mechanical Solutions for Hot Forward Extrusion under Plane Strain Conditions by upper Bound Method R. Domingo, A.M. Camacho, E.M. Rubio Alvir and M.A. Sebastián Different Possibilities of Process Analysis in Cold Extrusion M. Plancak, B. Barisic and B. Grizelj A New Low Friction Die Design for Equal Channel Angular Extrusion T. Canta, D. Frunză, E. Szilagyi and M. Lungu Modeling Approach for Determination of Backward Extrusion Strain Energy on AlCu5PbBi B. Barisic, B. Grizelj and M. Plancak

169 177 185 193 201 209 215 221

Key Engineering Materials Vol. 367 (2008) pp 1-8 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/KEM.367.1

Extrusion Benchmark 2007 – Benchmark Experiments: Study on Material Flow Extrusion of a Flat Die M. Schikorra1, a, L. Donati2,b, L. Tomesani2,c, A. E. Tekkaya1,d 1

Institute of Forming Technology and Lightweight Construction, Universität Dortmund, Baroper Str. 301, 44227 Dortmund, Germany 2

Department of Mechanical Construction Engineering (D.I.E.M.), University of Bologna, V.le Risorgimento 2, 40136 Bologna, Italy a

c

[email protected], b [email protected], d [email protected], [email protected]

Keywords: Extrusion, Benchmark, Material flow, Pocket geometry

Abstract. The experimental conditions chosen as a reference for the 2007 edition of the extrusion benchmark and the corresponding main results are summarized in this work. The die design stage is first explained in order to address the main features of the experiment and its objectives. The die is a flat one with multiple holes; four angular profiles were produced with different pocket geometries, the experimental plan being entirely described. The initial temperatures for the billet and the die set, together with the temperature development during the process strokes are also reported. The results are shown, for each profile, in terms of final profile length, mean exit speed, global process load, profile exit temperature. Introduction The demand for specific properties and quality of extruded profiles is ever increasing. In order to analyze the manufacturing process and, at the same time, to avoid expensive trial-and-error experiments, nowadays finite element simulations can be performed to study the material flow, temperature distribution, ram loads, and many other process-related issues. By means of the numerical simulation you can even optimize the process parameters, or enhance the product properties and, more in general, increase your knowledge at a relatively low cost. The key factors for such an outstanding performance are two: a skilled engineering analysis and a reliable software. So far, however, no common basis for evaluating the numerical code capabilities is available and, to some extent, even some physical aspects of the extrusion process are not completely clear. With the organization of periodical extrusion benchmark, developers and users of finite element simulations are asked to come together as a reference community in order to analyze the experimental work and focus on the related software issues. For a verification of these simulations in the area of aluminum extrusion a first benchmark was carried out by Hora et al. [1] in 2005 in order to analyze the result quality of today’s finite element simulations. Here, a flat die for the extrusion of five circular profiles with different diameters was studied. As a main result from the simulation outcomes, large deviations of the profiles exit velocity in comparison to the experimental results were found [2]. To analyze if the quality of simulation codes and/or the skills of the users have increased in recent years, the Benchmark 2007 was set up by the DIEM, University Bologna, Italy, in cooperation with the Institute of Forming Technology and Lightweight Construction (IUL), University Dortmund, Germany. In this benchmark experiment the simulation of an extrusion process of different profiles within one die was studied again, with particular reference to pocket dies effectiveness. In order to keep the geometry close to standard industrial applications here the extrusion of 4 L-shaped profiles was analyzed.

2

Advances on Extrusion Technology and Simulation of Light Alloys

Die design Few words to explain the principal guidelines that were adopted for determining the final die geometry for the benchmark. The first 2005 benchmark edition [2], with more than 60 mm bearing length, was aimed mainly at pointing out the loss of contact of lagrangian mesh in the bearing, due to the sharp edge always present at the bearing entry. Thus, those results have been much more interesting for software developers than for extruders because the bearing length in the typical industrial design usually are as short as possible. With the aim to stay close to issues of common concern, this benchmark tries to link practical aspects of the “every day” die design with software capabilities. Among the many different topics of interest (leg shape, seam welds, etc.), the design of die pockets was chosen for its widespread utilization in balancing the material flow and for the ever increasing importance it has achieved with respect to the classical bearing length adjustment. In contrast with their importance, the effectiveness of pockets is often under debate on whether they can correct the material flow or not, or how much, or in what condition. A multiple hole die was chosen in order to have, within the same experiment, very similar experimental conditions on the different holes, and for economical reasons as well. Two different profile thickness were adopted in order to have direct information on how much the pocket is active on this crucial factor. By presuming that during the experiment a temperature gradient could have developed in the vertical direction within the die assembly, the profiles with the same thickness were located at the same level (i.e., two thin profiles in the upper part of the die, the two thick ones in the lower), in order to have the same temperature for each couple. By presuming, again, that slightly lower temperatures could have developed in the lower part of the die, the two thicker profiles were located there, in order to decrease their exit speed to some extent. In order to avoid any possible misinterpretation of the results the die temperature was measured at three different locations as near as possible to the die exit (two in the lower part, one in the upper). The pocket entry area and position for the four profiles was exactly the same. This was done in order to limit, if not to prevent, differences arising from divided flows. The bearing length was kept small and constant (equal to 5 mm) along the profiles perimeter in order to minimize its influence on the global flow. The very controversial issue on step – versus – conical pocket was analyzed in the lower (thicker) couple of profiles. On the two thin profiles, it was decided to check the drag effect of placing the die exit as close as possible to the pocket wall. It was also thought that some differences in angular distortion could have emerged. The general layout of the four profiles was determined by the maximum diameter available at the die exit on the experimental press facility. Preparation, Die Setup, and Experimental Conditions AA6082-O aluminum billets of 140 mm diameter and 302 mm length were used for the experiments. The experiments have been carried out on a 10 MN extrusion press at the laboratory of the IUL. The diameter of the container was 146 mm, so that an upsetting of the billets takes place at the beginning of the extrusion process. The die, designed and built by Compes, Italy, was flat with four orifices. The tool material was AISI H-13 steel. All profiles were L-shaped with a length of each section of 30.5 mm, but with two different thicknesses: 2 mm for profiles n.1 and n.4 (for profile number refer to figure 1), 3 mm for profiles n.2 and n.3. Each orifice had a different pocket shape: orifice n.1 had straight pocket walls with an asymmetric positioning of the pocket, orifice 2 had a symmetric 3-stepped pocket, orifice 3 had a symmetric and conical pocket, orifice 4 had a symmetric pocket with straight walls. Due to the different wall thicknesses and different pocket shapes, an influence of the material flow could be expected. The geometrical dimensions of the pockets are shown in figure 2.

Key Engineering Materials Vol. 367

3

Figure 1: Die appearance and design (billet view)

Figure 2: Pocket geometries for the four die orifices

The general preheating details for the whole experimental plan are the following: • The billets were preheated at a temperature of 480° C in a resistance heated oven with air circulation. During transportation and loading a cooling of 20° C was evaluated to take place on the billet surface. • The container was heated to 450° C by a controlled heating system. The temperature was continuously measured by two thermocouples at different depths inside the container. Due to only small changes of +/- 5° C before and after extrusion the container temperature was considered as constant 450° C over the entire process. • The die and die holder were heated by a surrounding die heating to 400° C. The die holder was thermally isolated from the extrusion press in order keep the temperature without heating up the machine. The temperature evolution in the die was monitored throughout the experiments at three different locations within the die (positions D1, D2 and D3, see figure 3) by means of thermocouples. Two more thermocouples were used to monitor the temperature evolution of the profiles (locations P1 on profile n.1 and P2 on profile n.2); the measures were taken near the inner corner of the profiles, about 350 mm after the die package (bolster included, see figure 3). Before the experimental trials, some extrusions were performed in order to stabilize temperature in the whole system. At the be-

4

Advances on Extrusion Technology and Simulation of Light Alloys

ginning of each stroke, the billet rest exchanged heat with the die for approximately 30 sec before the extrusion could start. The extrusion experiments were performed at ram speeds of 0.5 and 5 mm/sec with a maximum ram stroke of 250 mm. In particular, the speed of 0.5 mm was used as a reference for the benchmark study. Several pressings were done in order to confirm the reliability of the results. It must be observed, in fact, that other extrusion tests (not reported here) with an empty die, as well as extrusions with a cooler die, all led to unstable results as regards the exiting speed. Thus, in order to obtain consistent results, the experiments were repeated three times with almost equal initial temperatures, thus resulting in stable and comparable results. After the beginning of the extrusion process, the exiting profiles were guided manually in order to prevent the extrudates from influencing each other or to bending excessively. No pulling of the extrudates was performed.

D1

D1

P1

350

P2

D2-D3

D2

D3

Figure 3: Thermocouples positioning in the die

Results The complete list of experimental results is shown in table 1. There, six experiments are reported, three at 0.5 mm/s ram speed and three at 5 mm/s. In the first part of table 1 the preheating details are reported as well as the measured temperatures in the die system. In the second part of table 1 the outcome of the extrusions trials are reported in terms of profile exit temperatures (465 mm after the die bearings), final length of the four profiles and maximum load. The results (in particular the profile lengths) were found to be very sensitive to temperature data in the die system and for this reason table 1 reports all the measured temperatures in close detail. Initial die temperatures are specified at billet positioning; owing to the 30 [s] time needed to start the process, the die heats up due to the contact with the billet, resulting in a temperature rise of nearly 15°C, then the ram started its stroke. Detailed values of 30 [s] values are given only for exp n.4, which was chosen to be the reference case for the benchmark. In figure 4 the temperature evolution at the location points in the die and on the profiles are shown. Initial and stationary die temperatures are evidenced (with an increase from 405° C to 470° C); in particular, it can be seen how a good steady state condition was reached after 50 mm ram stroke, although with a constant difference of 12°C between D1 and D2-D3 locations.

Key Engineering Materials Vol. 367

5

Table 1. Temperature data and results for the extrusion benchmark (oven temperature: 480°C, billet surface temperature 460°C once in the container) Exp. No.

Ram Speed [mm/s]

Ram Temp. [ºC]

Container Temp. [ºC] 450

Initial Die Temp. [ºC] D1 394 D2 390 D3 392

3

0.5

Start 373 End 409

4

0.5

Start 387 End 427

450

After 0 [s] D1 406 D2 402 D3 404 After 30 [s] D1 417 D2 418 D3 416 D1 394 D2 397 D3 ---

Stationary Die Temp. [ºC] D1 468 D2 481 D3 478

Profile Exit Temp. [ºC] P1 370 P2 444

Profile Lengths [mm]

Max. Load [MN]

P1 3030 P2 9020 P3 8470 P4 4470

7.31

D1 463 D2 479 D3 476

P1 354 P2 442

P1 2870 P2 9980 P3 9220 P4 3870

D1 462 D2 477 D3 474

P1 338 P2 444

P1 2580 P2 10370 P3 9470 P4 3250 P1 5450 P2 7910 P3 7490 P4 7270 P1 5800 P2 7840 P3 7290 P4 7690 P1 5840 P2 7610 P3 7100 P4 7930

7.13

5

0.5

Start 382 End 425

450

11

5

Start 381 End 428

450

D1 419 D2 412 D3 413

D1 510 D2 507 D3 ---

P1 482 P2 510

12

5

Start 385 End 425

450

D1 417 D2 414 D3 414

D1 508 D2 505 D3 ---

P1 488 P2 512

14

5

Start 383 End 423

450

D1 421 D2 417 D3 417

D1 507 D2 505 D3 ---

P1 500 P2 506

Figure 4: Die and profile temperature evolution over the process

7.38

8.04

8.25

8.33

6

Advances on Extrusion Technology and Simulation of Light Alloys

This difference grows between 15 and 50 mm ram stroke, thus just after the billet was completely upset in the container (at maximum load) and before the steady state condition was reached. This suggests that the temperature difference is due to friction and heat generation by deformation, particularly in that early phase when the thinner profiles were slowly creeping through the bearing while the thicker ones were already running. This difficulty of the thinner profiles to exit from the die was observed during the experiments (although it was not registered as a point-to-point variation in exiting speed), being clearly visible in the profile temperatures of figure 4. There, measurements could be taken only when the profiles had come out from the die package, which happened after 20 and 50 mm ram stroke for profiles 1 and 2, respectively. The profile exit temperatures at P1 and P2 locations (420 mm after the die exit) of fig.4 evidence a faster cooling on the thinner profile; again an almost perfectly steady condition can be evidenced. Due to the different pocket geometries, wall thickness and die temperatures, the different profiles run at different speeds, thus resulting in different profiles lengths. This parameter, as also studied in [1], is very sensitive both to the geometrical features of the die and to material temperature, so that it is a very good indicator for an accurate simulation. Here, all three experiments at 0.5 mm/s ram speed showed the same tendency in material flow: Profile n.2 (wall thickness 3 mm) led to the longest extruded profile with 9980 mm length at an average velocity of 19.81 mm/s. Profile n.3 resulted in the second longest profile with 9220 mm (vavarage,3 = 18.31 mm/s). The difference between these two and geometry 1 and 4 is extreme. Due to the smaller die orifice the exiting speed is much lower. Geometry 4 with the symmetric pocket led to a profile with 3870 mm length (vavarage,4 = 7.68 mm/s) and geometry 1 with the asymmetric pockets led to a profile length of 2870 mm (vavarage,1 = 5.7 mm/s). These outcomes are consistent with the results of experiments n.3 and 5, which gave almost identical lengths (see also appendix 1). At 5 mm/s ram speed the differences between profiles 2-3 and 1-4 are considerably reduced; profiles 2,3 and 4 run nearly at the same speed, but with the thinner profile n.4 (straight pocket) perceivably faster than the thicker profile n.3 (the one with conical pocket). The dragging effect of the asymmetric pocket n.1 continues to be effective, although in a less pronounced way than before.

Figure 5: Load-stroke diagram and profile lengths of the single rods

Key Engineering Materials Vol. 367

7

This is possibly the most interesting result of the benchmark: the pockets effectiveness changes dramatically with the processing conditions. In particular, the increase in process speed flattens the die temperatures almost to the same values at all locations (in table 1 only D1 and D2 were taken, but they undoubtedly are representative also of the other two), the effect of thickness decreases and the conical pocket reduces the exit speed below that of a thinner profile with a straight pocket. Back to the benchmark experiment, the typical load-stroke curve is shown in figure 5, with a maximum at the beginning of the process and subsequent decreasing load caused by the reduction in billet length. In figure 5 a maximum of approximately 7.13 MN was observed, correspondent to experiment n.4 of table 1. All the extruded profiles fit well to the desired geometry and showed good surface conditions. Figure 6 gives an impression of the desired profiles geometry and the cross section of the extruded profile for both thickness. Only little deviation from the desired 90° angle can be evidenced. A photograph of the extruded profiles of experiment n.4 is shown in figure 7. Independently of the perspective distortion when taking the photograph (two scales of 2000 mm are shown in the pictures in order to clear the effect), the difference in length can be easily seen. The profiles were cut approximately 1000 mm after the die exit. This was considered for the calculation of the profile lengths.

Figure 6: Desired profile geometry and extruded profiles

Figure 7: Extruded profiles (photograph, perspective distortion has to be considered)

8

Advances on Extrusion Technology and Simulation of Light Alloys

Conclusion The extrusion benchmark 2007 was carried out for extrusion of aluminum profiles. Several experiments were done in order to obtain repeatable processes for the AA 6082 aluminum alloy at two different ram speeds. In order to obtain accurate results for allowing the simulations to be verified, temperature measurements were taken at many locations on the press, on the die system and on the profiles througout the preparation procedure and the process strokes. It was found out that the different pocket geometries and wall thicknesses resulted in different profile exiting velocities at the two speed conditions.

-

At low speeds, the thicker profiles flow faster then the thinner ones; the conical pocket resulted in approximately 10% speed reduction with respect to the stepped one. The symmetric pocket resulted in a 30% faster material flow than the asymmetric one.

-

At high speeds, the exiting speeds of thick and thin profiles flatten; the conical pocket increases its slowering effect up to the point that the 2 mm profiles with straight pocket runs faster than the 3 mm conical pocket.

Acknowledgements This work was carried out with the financial support of the MIUR (Italian Ministry for Research and Innovations) and the Transregional Collaborative Research Centers SFB/TR10 and SFB/TR 30 funded by the German Research Foundation (DFG). The authors would like to thank Compes, Italy, for the construction and manufacturing of the die, Honsel, Germany, for the AA6082 billets and the IVP, ETH Zurich, Switzerland, for the characterization of the aluminum alloy. References [1] P. Hora et all: Extrusion Zürich 2005, Proceedings of the Extrusion Benchmark 10.-11. March 2005, Institute of Virtual Manufacturing, ETH Zürich. [2] P. Hora, C. Karadogan, L. Tong: Neue Entwicklungen im Bereich der virtuellen Abbildung von Strangpressprozessen, in Strangpressen by H. Gers, Wiley-VCH

APPENDIX

Appendix 1: Load-stroke diagram for different trials

Key Engineering Materials Vol. 367 (2008) pp 9-16 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/KEM.367.9

Modifications of the Extrusion process of Magnesium Alloys for improved Mechanical Properties Soeren Mueller1,a, Klaus Mueller1,b Walter Reimers2,c 1

Technical University Berlin, Institute for Materials Science and Technology, Extrusion Research and Development Center, Gustav-Meyer-Allee 25, 13355 Berlin, Germany

2

Technical University Berlin, Institute for Materials Science and Technology, Ernst-Reuter-Platz 1, 10587 Berlin, Germany a

[email protected], [email protected], [email protected]

Keywords: Magnesium, extrusion, ECAE, counter pressure, microstructure, texture, mechanical properties

Abstract. In the course of the increasing discussions about a reduction of the CO2 emissions magnesium has gained importance since it is the lightest metal for structural applications. Currently magnesium alloys are almost exclusively used as cast parts in the automotive industry because due to their microstructure extruded magnesium profiles exhibit a strong asymmetry in the mechanical properties under tensile and compressive loading (strength differential effect). In order to improve the mechanical properties a detailed knowledge about the influence of the different extrusion parameters on the microstructure of the extrudates is necessary. Therefore, the parameters extrusion method, billet temperature, product speed, extrusion ratio and cooling condition were varied for the extrusion of the magnesium alloys AZ31, AZ61 and AZ80. Subsequently the microstructure was analyzed and the mechanical properties determined. With an additional analysis of the deformation modes of the extruded and cold deformed products it could be discovered that an improvement of the mechanical properties can be achieved by a modification of the extrusion process. Since the strength differential effect in caused by twinning which due to the texture of the extrudates is only active under a compressive loading along the extrusion direction the modification of the extrusion process aims at a suppression of this twinning. Because on the one hand compared to that for dislocation glide the Hall-Petch-Constant for twinning is bigger a grain refinement of the extruded products could be achieved by a predeformation using ECAE similar processes. On the other hand a process has been developed where the profiles are extruded into a hydrostatic counter pressure in order to alter the texture during the extrusion. Thereby the twinning is already activated during the extrusion. Both modifications of the extrusion process result in an increase of the critical resolved shear stress for twinning during the subsequent cold deformation and thus in improved mechanical properties. Introduction The limited use of magnesium extrusions as structural parts is besides of cost issues due to disadvantages of the mechanical properties. The combination of texture and twinning in extruded magnesium profiles causes a strength differential effect (SDE) where the yield stress under compression is well below that under tension [1]. The SDE is calculated by [2] SDE = 2

σ comp. − σ ten. σ comp. + σ ten.

(1)

Therefore, one way to improve the mechanical is a reduction of the grain size since the CRSS for twinning is more sensitive to the grain size than deformation through glide systems. Because the

10

Advances on Extrusion Technology and Simulation of Light Alloys

primary twinning system for Mg alloys {101 2} is a tensile twinning system due to a c/a ratio < √3 these twins are only active under compression along the extrusion direction and inactive under tension along this direction. Since the activated twinning system under compression leads to a reorientation of the planes within the twin by almost 90° [3] the activation of this twinning system already during the extrusion process leads to a favorable orientation of the hexagonal crystals in the extrudate for a compressive load. Conventional Extrusion The extrusion parameters billet temperature, extrusion ratio, product speed, profile geometrie and extrusion method as well as the alloy composition are influencing the microstructure and thereby the mechanical properties of the extrudates. Since the influence of the parameters extrusion method [4, 5] and alloy composition [6] has already been described in detail. In the following the influence of the billet temperature on the extrudates will be explained. Magnesium alloys are usually extruded at a temperature between 250°C und 370°C. A first estimation of the influence of the product speed and the billet temperature on the extrusion process of magnesium alloys is given by a compressive flow curve (Fig. 1). The flow stress decreases for all products speeds with increasing billet temperature. 120 110 100 90 80 70 260 300 340 380 Temperature [°C]

Flow stress kf [MPa]

130

60 2

0,1

1,3 0,7 Deformation speed [s-1]

Figure 1: Flow curve of cast AZ31 Microstructure. The usually finely recrystallized microstructure of the extruded products coarsens with increasing billet temperature (Fig. 2). This is due to a secondary recrystallization which occurs after the extrusion if the extrudates are not quenched. Since with increasing billet temperature the product temperature increases also more energy is stored in the product. Therefore, the secondary recrystallization is benefited by a higher billet temperature. a)

b)

Figure 2: Microstructure of extruded AZ31; cross section a) billet temperature 250 °C b) billet temperature 300 °C

Key Engineering Materials Vol. 367

11

The occurrence of the secondary recrystallization with increasing billet temperature can also be seen in the textures of the extrudates. Whereas the extrudates at lower billet temperatures exhibit only a single fiber texture with the {101 0} planes perpendicular to the extrusion direction the texture of the products at higher billet temperatures changes to a double fiber texture where the {11 2 0} planes are also oriented perpendicular to the extrusion direction (Fig. 3). It has been analyzed that the additional fiber is caused by the secondary recrystallization [7]. 11 2 0

11 2 0 Max = 5.47

Max = 7.00

0001

0001

10 1 0

10 1 0

Figure 3: Inverse pole figure of the extrudates a) billet temperature 300 °C b) billet temperature 370 °C Mechanical properties. Due to the changes in the microstructure the billet temperature also influences the mechanical properties of the extruded magnesium profiles. Mainly the increase in the grain size with increasing billet temperature influences the mechanical properties under tension. Since the Hall-Petch-Constant for twinning is bigger than that for dislocation glide an increase in grain size reduces the critical resolved shear stress (CRSS) for twinning considerably more than for dislocation glide. An increase in the billet temperature results in a more significant decrease of the compressive yield stress (CYS) than the tensile yield stress (TYS) since twinning is only active under a compressive load. Therefore, the strength differential effect (SDE) increases with increasing billet temperature (Fig. 4). -0,21 -0,19 -0,17

SDE

-0,15 -0,13 -0,11 -0,09 -0,07 -0,05 250

270

290

310

330

350

370

Billet temperature [°C]

Figure 4: Strength Differential Effect in dependence of the billet temperature; AZ31

390

12

Advances on Extrusion Technology and Simulation of Light Alloys

Equal Channel Angular Extrusion The Equal Channel Angular Extrusion (ECAE) trials with aluminum alloys show a finer grained and more homogeneous microstructure after the extrusion [8]. For the grain refinement of magnesium alloys this method has been modified to a reciprocating extrusion with two moving stems. During this process the billet is extruded through a kneading die and afterwards upset by the opposing stem. After a designated number of cycles one stem can be replaced by an extrusion die so that the predeformation and extrusion can be performed with out any discontinuity out of the same container (Fig. 5).

Stempe l Stem

Probe Billet

Kneading Presskana l die

Matrize Die

Büchse Container (Aufnehm er)

Stran g Extrudate

1

cm

Figure 5: Tool set for the reciprocating extrusion process Microstructure. The reciprocating extrusion leads after 4 cycles and indirect extrusion to a fine grained microstructure with a grain size around 3 µm. In contrast to that the only indirect extruded profiles have microstructure with a grain size of 30 µm (Fig. 6a and 6b). An increase in the number of cycles up to 10 does not result in a finer or more homogeneous microstructure. The grain size after 10 cycles is around 4 µm; additionally in the micrograph after 10 cycles shearbands are observed (Fig. 6c). a)

b)

c)

Figure 6: Microstructure of the extrudates; a) indirect extrusion; b) 4 x reciprocating extrusion and indirect extrusion; c) 10 x reciprocating extrusion and indirect extrusion The texture of the extrudates after indirect extrusion either with or without a predeformation by reciprocating extrusion is mainly the same. Both show a double fiber texture with the {101 0} and {11 2 0} planes perpendicular to the extrusion direction while the basal planes are oriented parallel to the extrusion direction (Fig. 7a and 7b). Because of the finer grain size of the predeformed billet material the more grains rotate towards a favorable orientation for the deformation [9]. Therefore, the texture intensity of the extrudate after 4 cycles of reciprocating and indirect extrusion is about 90 % higher than the intensity of the just indirect extruded product.

Key Engineering Materials Vol. 367

11 2 0 a)

1120

13

11 2 0

b)

MaxMax. = 4.48 = 4.48

1120

MaxMax. = 7.78 = 7.78

0001 0001 10110010 Figure 7: Inverse pole figures; cross-section perpendicular to the extrusion direction; a) after indirect extrusion at 250°C; b) after 4 cycles reciprocating and indirect extrusion at 250°C

0001 0001

101100 10

TYS

CYS

SDE

250

400 300 200 Indirect extrusion - comp. Indirect extrusion - ten. 4x kneading + indirect extr. - comp. 4x kneading + indirect extr. - ten.

100 0

0,25

200

0,2

150

0,15

100

0,1

50

0,05

0

0

10 20 30 Tensile and compressive strain [%]

40

Figure 8: Compression and tension curves for indirect and reciprocating plus indirect extrusion at 300°C

0,3

SDE

300

500

TYS, CYS [MPa]

Tensile and compressive stress [MPa]

Mechanical Properties. As Figure 8 shows 4 cycles of reciprocating extrusion before the actual indirect extrusion cause an assimilation of the CYS and TYS. Compared to the mechanical properties after indirect extrusion the CYS increases more than 100% while the TYS decreases around 5%. By lowering of the process temperature from 300°C to 250°C a CYS which is higher than the TYS and therefore an SDE above 0 can be achieved (Fig. 9).

0 250 300 Process temperature [°C]

Figure 9: CYS, TYS and SDE in dependence of the reciprocating extrusion process temperature

Extrusion into a counter pressure The activation of the twinning system during the extrusion has been implemented through a hydrostatic counter pressure into the extrudate is extruded. Fig. 10 shows schematically the extrusion process with a counter pressure. The additional extrusion force that is needed because of the counter pressure does not exceed the peak force in the beginning of the indirect extrusion, therefore it is possible to extrude Mg alloys with a counter pressure on all extrusion presses that are capable to indirect extrude Mg alloys (Fig. 11). The extrusion trials with a counter pressure were performed with continuous cast AZ31 billets, a product speed of 0.9 m min-1, billet temperatures of 250°C and 300°C and a counter pressure between 0 and 70 MPa. In the following the results for the trials at 250°C with a counter pressure of 70 MPa are presented.

14

Advances on Extrusion Technology and Simulation of Light Alloys

8

Sealing

Extrusion Force FG [MN]

7

Counter pressure chamber

Filling and building up the counter pressure

Extrusion into a constant counter pressure

6 5 4 3 2 without counter pressure

1

with counter pressure

0

High pressure fluid

0

10

20

30

40

50

60

70

80

Ram Displacement [mm]

Figure 10: Extrusion with a counter pressure (schematic drawing)

Figure 11: Extrusion diagram of the extrusion of AZ31with a counter pressure of 70 MPa

Microstructure. The comparison of the inverse pole figure of an indirect extruded sample and an indirect with counter pressure extruded sample exhibits an additional texture pole for the basal plane perpendicular to the extrusion direction (Fig. 12). This texture component is caused by the activation of the {101 2} twinning system because of the applied counter pressure. b) b)

11 20 1120

a) a)

Max Max= =10.80 10.86

Max == 3.51 Max 3.51

0001 0001

11 20 1120

1010 10 1 0

0001 0001

1010 101 0

Figure 12: Texture after the extrusion; inverse pole figures perpendicular to the extrusion direction a) indirect extrusion; b) indirect extrusion with counter pressure The extrusion into a counter pressure does not only influence the texture of the extrudates it also has a positive influence on the microstructure. Fig. 13b) shows the micrograph of the cross-section of an extrudate that was extruded into a counter pressure. In comparison to Fig. 13a) that shows the cross-section of an indirect extruded sample without a counter pressure a smaller grain size of 9µm can be observed although the microstructure is still inhomogeneous. As it is already known extruded AZ31 products exhibit elongated grains along the extrusion direction [10]. These elongated grains can also be found in the products of the extrusion into a counter pressure. But in contrast to the indirect extrusion without a counter pressure the elongated grains in the products of the extrusion with a counter pressure are inclined to the extrusion axis (Fig. 13c)).

Key Engineering Materials Vol. 367

a)

15

c)

b)

20 µm

20 µm

20 µm

Figure 13: Microstructure after the indirect extrusion; a) without a counter pressure cross-section; b) with a counter pressure cross-section; c) with a counter pressure longitudinal section; ↑ extrusion direction

Tensile and Compressive Stress [MPa]

Mechanical Properties. The effect of the counter pressure on the texture and the microstructure results in a positive influence on the mechanical properties of the extrudates. Under a tensile load the extrusion into a counter pressure positively influences foremost the ultimate tensile strength and the fracture strain compared to the mechanical properties of extrudates without a counter pressure. Under a compressive load the compressive yield stress can be improved by 50% compared to just indirect extruded samples whereas the fracture strain under compression decreases (Fig. 14). 450 400 350 300 250 200 indirect extrusion - compr. indirect extrusion - ten. with counter pressure - compr. with counter pressure - ten.

150 + 50%

100 50 0 0

5

10

15

20

25

30

Tensile and Compressive Strain [%]

Figure 14: Mechanical properties of indirect extruded AZ31 with and without a counter pressure The method of the extrusion with a counter pressure has been registered for German patent (10 20006 043 502.8). Conclusions Through the analyses of the influences of the extrusion parameters on the microstructure and mechanical properties of extruded magnesium profiles variations of the extrusion process could be developed in order to optimize the mechanical properties. Thereby an improvement of the SDE through an increase of the CYS was the main objective. Since the low CYS is caused by a combination of texture and twinning the variations of the extrusion process aimed at a reduction of the twinning. This is achieved by increasing the CRSS for twinning either by a reduction of the

16

Advances on Extrusion Technology and Simulation of Light Alloys

grain size or a change of the texture. The two proposed methods, the reciprocating extrusion for reducing the grain size as well as the extrusion into a counter pressure, are completely integrated in the regular extrusion process. Only some changes have been made to the extrusion process but no additional manufacturing step has to be introduced into the production process. References [1]

S.Mueller, W. Reimers, “Extrusion of Magnesium Profiles”, in: Proceeding of the 7th Esaform Conference on Metal Forming, 2004, 613-616

[2]

J.L. Raphanel, J.-H. Schmitt, P. van Houtte, “Texture Development and Strength Differential Effect in Textured b.c.c. Metals with Glide Asymmetry”, Materials Science And Engineering, A108 (1989) pp. 227 – 232.

[3]

C. S. Roberts, Magnesium and Its Alloys, John Wiley & Sons, Inc., New York, 1960.

[4]

S. Mueller, K. Mueller, M. Rosumek, W. Reimers, “Microstructure development of differently extruded Mg alloys, Part 1“, Aluminium International Journal, 82, 4 (2006) pp. 327 – 330.

[5]

S. Mueller, K. Mueller, M. Rosumek, W. Reimers, “Microstructure development of differently extruded Mg alloys, Part 2“, Aluminium International Journal, 82, 5 (2006) pp. 438 – 442.

[6]

S. Mueller, K. Mueller, H. Tao, W. Reimers, “Microstructure and mechanical properties of the extruded Mg-alloys AZ31, AZ61, AZ80”, International Journal of Materials Research, 97, 10, 2006, 1384-1391

[7]

M. T. Pérez-Prado, O. A. Ruano, “Texture evolution during annealing of magnesium AZ31 alloy”, Scripta Materialia, 46, 2002, 149-155

[8]

J. Richert., M. Richert, “A new method for unlimited deformation of metals and alloys”, Aluminium International Journal, 62, 8 (1986) pp. 604 – 607.

[9]

S. E. Ion, F. J. Humphreys, S. H. White, “Dynamic Recrystallisation and the Development of Microstructure during the high Temperature Deformation of Magnesium”, Acta Metallurgica et Materialia, 30, 1982, 1909 – 1919.

[10] J. Swiostek, J. Bohlen, D. Letzig, K.U. Kainer, Magnesium, “Comparison of Microstructure and Mechanical Properties of Indirect and Hydrostatic Extruded Magnesium Alloys”, in: Magnesium Proceedings of the 6th International Conference Magnesium Alloys and Their Applications (2003) pp. 278 – 284.

Key Engineering Materials Vol. 367 (2008) pp 17-24 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/KEM.367.17

Experimental techniques to characterize large plastic deformations in unlubricated hot aluminum extrusion Henry Valberg1, a, 1

Norwegian University of Science and Technology (NTNU), Department of Engineering Design and Materials, N-7491 Trondheim, Norway a

[email protected]

Keywords: Extrusion, Metal flow, Grid pattern technique, Experimental analysis, Deformation

Abstract. A review is given of experimental work done at the author’s university during the last two decades, to investigate metal flow in aluminum extrusion. Partially extruded billets with internal grid patterns are difficult to remove from the container without post-deforming the internal pattern during the removal operation. A technique was therefore developed by which such billets can be removed from the container without any damage. In addition to this, a special grid pattern technique was developed. This technique applies contrast material stripes in the symmetry plane of the billet, and is advantageous because the pattern obtained remains clearly visible after extrusion, even in shear zones subjected to very heavy deformations. Traditional scratched patterns become invisible in such regions, and do not provide metal flow information in shear zones. When the two techniques, i.e. the new removal technique and the new grid pattern technique, were used concurrently, “perfect” type of metal flow experiments were conducted. A three-dimensional grid pattern technique was also developed. It is well suited for characterization of metal flow in complex shape extrusion, when there is no symmetry plane in which to conduct traditional grid pattern analysis. Applications of the new techniques for metal flow studies in various cases of extrusion are reported. It is shown that precise metal flow information indeed is a necessary requirement to get metal flow correct in computer simulation. Introduction When metal extrusion was developed into an industrial process in the early 19th century a number of flow-related extrusion defects were observed to form. To understand the formation mechanism of each type of defect, and to find preventive measures to avoid occurrence of them, metal flow studies were required. A number of experimental techniques which provided information regarding the nature of metal flow were therefore developed at this time. In this way metals extrusion was industrialized. The most common of these techniques is often called the split-billet technique. When the technique is used an inscribed grid pattern is made on one half longitudinally sectioned plane of a billet, where after the two halves are added together and partially extruded. The partially extruded billet is then removed from the container and split along the initially sectioned plane. In this way the grid pattern which now is deformed in the extrusion process, is revealed. From this pattern information regarding plastic deformations in extrusion can be achieved. But in non-lubricated extrusion of metals, the split billet technique has some draw-backs. Most commonly a parting agent is applied on the split surface to avoid rewelding across the gridded surface in the extrusion experiment. During upsetting of the billet small amounts of parting agent may penetrate from the split surface, onto the surface of the die or the container. If present here, it will alter the sliding conditions between workpiece and tooling, i.e. it will lubricate the process, which was supposed to be unlubricated.

18

Advances on Extrusion Technology and Simulation of Light Alloys

Another draw-back of the split billet technique is that inscribed grid patterns tend to erase in regions of heavy deformations, as in the shear zones. Information regarding nature of flow in such regions then can not be achieved. A draw-back is also that scratched lines cannot easily be traced back into the position where they extend into the boundary interface between billet and tooling. Scratched patterns therefore do not yield precise information about contact conditions along boundary interfaces between tooling and workpiece, i.e. whether there is sticking friction or full or partial sliding over the interface. Another problem in experimental metal flow analysis is to get the partially extruded billet out of the container without damage upon removal. If one tries to push the remainder of the billet out of the container by the extrusion punch, the billet discard will stick to the container wall, and will deform plastically upon removal. Hence there will be post-extrusion deformation that does not stem from the extrusion process itself. This makes accurate deformation analysis difficult, or even impossible. Experimental techniques Internal stripe pattern technique: During experimental work performed by the author of this paper, the above mentioned draw-backs of the split-billet technique were recognized, and a modified grid pattern technique was therefore developed. The modified technique is based on insertion of radial and axial contrast pins into the mid-plane of the billet. Since pins are inserted into drilled holes it is not necessary to split the billet longitudinally, neither is it required to use parting agents. The appearance of the contrast pins on the boundary interface between billet and tooling can be identified easily when this kind of grid pattern is used. After extrusion, and removal of the partially extruded billet, the billet or the extrusion is partitioned longitudinally, ground and etched to reveal the deformed pattern. Technique for removal of partial extruded billet from container: In the experiments we eliminated the problem of post-deformation of the billet upon removal, by using an inner steel shell which was added into the container. Extrusion was done inside the shell, and partially extruded billets were removed from the container while residing undeformed inside the shell. Finally, the shell was given a thermal shock, by enforced cooling in liquid nitrogen-gas. After the treatment the metal rest was easily removed from the shell without post-extrusion deformation. The internal grid pattern was then revealed by sectioning of the billet, grinding and etching. Three-dimensional grid pattern technique: Three different billets were required to obtain a deformed 3D-pattern. Parallel slots were machined into the billets and slices of contrast material were added into the slots. In this way composite billets with alternating layers of matrix material and contrast materials were obtained. Use of three billets was required to make contrast layers that extended in each of the three orthogonal directions inside the billet. When three experiments are coupled together a three-dimensional pattern is obtained. Applications of the various techniques Selection of metal flow studies: A large number of extrusion experiments were performed with use of various internal grid patterns, over a time span of approximately 20 years. In this way we realized disadvantages and advantages of different kind of patterns. New improved experimental solutions were obtained over time, and new information regarding metal flow was achieved. A selection of nonlubricated metal flow experiments [1-14] performed during this period using various Al-alloys as extrusion material is presented in Fig. 1. Two of the cases in the figure are model material experiments in which wax-based model materials were extruded to reveal special effects also occurring in metals extrusion. The rest were metal experiments in which contrast material was used to create internal grid patterns inside the extruded billets.

Key Engineering Materials Vol. 367

a) Model material extrusion [2]

b) Forward extrusion, pattern with post-extrusion deformation

e) Backward extrusion, pattern with post-extrusion deformation

f) Backward extrusion, good pattern [4]

i) Extrusion through long choked die channel [7, 9]

19

c) Forward extrusion, pattern with postextrusion deformation [3]

d) Forward extrusion,“perfect” pattern [7]

g) Model material extrusion welding [1]

h) Extrusion welding, good pattern [8]

k) 3D-analysis of strip j) Two-hole extrusion, extrusion [6] “perfect” pattern [10]

Fig. 1. Model material and metal extrusion studied by experimental grid pattern techniques. Forward extrusion: Fig. 1a) depicts aluminum-like material flow achieved in a model material experiment using wax as model material. Fig. 1b) and c), show metal flow in aluminum extrusion when using different grid patterns inside the billet. But here the ram was used to push out the partially extruded billet, and the remainder of the billet was subjected to large post-extrusion deformations during removal. Fig. 1d) shows deformed grid patterns obtained in an experimental series where “perfect” metal flow recordings were made. The grid pattern technique described above in which contrast pins were used to create the grid pattern was applied. In addition the partial extruded billets were removed from the container without post-extrusion deformations. Hence, this is a series of “perfect” metal flow experiments that reveal true metal flow in case of unlubricated forward hot aluminum extrusion. The above mentioned “perfect” experiment was later reproduced in a FEM-model in which conditions were tuned to yield metal flow very similar experimental flow [11-13]. Fig. 2 depicts appearance of sticking (ST) and sliding zones (SL) at the boundary surface between billet and container wall as determined in the experiments. It is seen that full sticking is the

20

Advances on Extrusion Technology and Simulation of Light Alloys

dominant contact type, but there are two ring-shaped sliding zones, one at the periphery of the punch head/the rear end of billet, and one around the die mouth. The experiment was FEM-modeled by use of the FEM-code DEFORM®. When appropriate boundary conditions were specified in the model, and after slight “tuning” of input flow stress to the model, metal flow in the first three stages of the experiment was very well reproduced in the FEM-simulation, see Fig. 3. In the end stage of the extrusion process, see Fig. 3 g), similarity with the experiment was not quite so good. Without experimental metal flow information available it would have been impossible to get metal flow correct. The FEM-model was used, for instance, to show the appearance of the primary shear zone (SZ), see Fig. 4 b), which is clearly revealed in simulation because of its high effective strain-rate, as it extends from the primary deformation zone, and backwards into the billet.

Fig. 2. Appearance of contrast pins on surface of partially extruded billets documents presence of sticking and sliding zones at the billet-container surface.

a)

b)

c)

d)

e)

f)

g)

Fig. 3. Comparison of deformed grid patterns obtained in “perfect” metal flow experiments: a), c), e) and g), and in FEM-simulation: b), d) and f).

a)

b)

Fig. 4. Optimized FEM-simulation model showing the effective strain-rate distribution in forward extrusion experiment.

Key Engineering Materials Vol. 367

21

a) b) Fig. 5. Deformed grid pattern obtained in a) backward extrusion experiment and b) in FEMmodel.

Fig. 6. Amount of deformations in backward extrusion in terms of predicted effective strain distribution in FEM-simulation. Backward extrusion: Fig. 1 e) depicts the deformed grid pattern with considerable amount of post-extrusion deformation in the experiments, where the partially extruded billet was long when it was pushed out of the container. Fig. 1 f), on the other hand, shows short billet discard with internal grid pattern, pushed out of the container after the experiment. When the discard is short postextrusion-deformations are moderate. Then only the very peripheral layers of the discard will be sheared off during removal of the gridded discard. Hence the internal grid pattern of this metal rest approximately represents the true metal flow in the experiment. When we later tried to mimic the experiment in FEM-simulation, a rather similar flow pattern was obtained. This is shown in Fig. 5 where Fig. 5 a) depicts the deformed grid pattern in the experiment, and Fig. 5 b) corresponding simulated pattern. Since simulated grid pattern evolves same way as experimental pattern, the simulation model does mimic the experiment well as regards metal flow. Fig. 6 shows the FEM-computed effective strain in the backward extrusion FEM-model [14]. As depicted deformations decrease from the surface towards the centre of the extruded rod, except for in the very beginning. Another characteristic trend is that the deformations in the outer surface layer of the rod increase strongly along the length of the extruded rod. While the effective strain in the surface layer in the front end are almost zero, it has reached a level of ≈ 6 at the late stage of extrusion shown in Fig. 6 Extrusion welding in idealized extrusion die, see fig.1h): In this experiment almost planar metal flow was obtained as the billet material was split into two metal streams by a bridge,

22

Advances on Extrusion Technology and Simulation of Light Alloys

consisting of a steel beam with square cross-section, placed just below the initial billet. Behind the bridge the two streams joined into one single stream in a corresponding manner as in extrusion welding. As the length of the partially extruded billet was rather short in this case, i.e. less than the billet diameter, post-extrusion deformations of the metal rest during removal were not significant. Efforts are now undertaken at our department to build both 2D- and 3D-FEM-models of this case of extrusion, to mimic the experiment, and to gain detailed knowledge about metal flow in this particular case of extrusion. Extrusion through a choked bearing channel, see fig.1 i): In theses experiments a pattern of radial oriented stripes of contrast material was inserted into the billet. During extrusion the pattern flowed forward towards the die mouth. Due to rotation in the shear zone inside the container, the stripes of the pattern do appear as approximately longitudinal lines parallel to the bearing surface, when they approach into the die channel, see Fig. 7. From the appearance of the pattern inside the channel, i.e. the stripes which extend outwards towards the surface of the metal in the channel, at the location denoted X, see Fig. 7 b), it was concluded about the nature of contact conditions in the choked channel, see Fig. 8 a). The experiment showed that there was sticking friction deep inside the channel, but towards the end of it, at a certain distance from the outlet, there was a transition point. At this point the material started to slide against the channel wall, and did so at the rear end portion of the channel. This behavior is very different from that in long parallel channels where sliding occurs over the whole channel length, see Fig. 8 b).

Fig. 7. Metal flow experiment to map metal flow in long choked die channel.

Fig. 8. Contact conditions in long die channel in aluminium extrusion in case of a) choked die channel and b) parallel die channel.

Key Engineering Materials Vol. 367

23

Extrusion of profiles of square, or rectangular cross-section from axi-symmetric billet, see fig.1k): These are typical experiments where metal flow is of three-dimensional nature. To characterize metal flow in this case a three-dimensional grid pattern technique was developed. Composite billets were made consisting of alternating slices of contrast material with black color (upon etching), and material of Al-color. Three billets were required to do a full three-dimensional experimental analysis of metal flow, in each specific case of extrusion, see Fig. 9 a)-c). We did only record the deformed grid pattern as it appeared inside the extruded profile. This was done by means of plotting of the grid pattern as it appeared in different sections of the extruded rod. Two sections with plotted grid pattern are shown in Fig. 10. The technique is rather cumbersome and expensive to use, but gives a detailed characterization of the three-dimensional metal flow in the extrusion process investigated. It has great potential when it comes to use in case there is complex extrusion geometry, and can in such cases be used to verify FEM-modeled metal flow.

Fig. 9. Initial 3D-grid pattern applied in strip-extrusion: a)-c) layers of contrast material inserted in three different orthogonal directions in three billets. d) Pattern when coupled together into one billet.

Fig. 10. Final 3D-pattern as it appears inside different sections cut through the extruded strip a) 0.24m and b) 0.985m from the front end of the strip.

24

Advances on Extrusion Technology and Simulation of Light Alloys

Conclusions Metal flow in metals extrusion is indeed complex. To model and reproduce real metal flow by FEM-analysis there is still need for experimental work to be done, to gain fundamental knowledge of metal flow phenomena. To further develop FEM-analysis as a precise tool for predicting what takes place in extrusion processes, combined efforts are required, where FEM-models - and inputdata to the models, are improved. Characteristic metal flow phenomena must be investigated by experimental means to “tune” simulation models to reproduce real metal flow. References [1] H. Valberg, A.W. Hansen, and J.O. Loeland: "Metal Flow at the Die in Aluminium Extrusion", Proc. 3rd Int`l Al. Extr. Techn. Sem., Atlanta, Vol.1, April 22-27 (1984), pp.203-208. [2] H. Valberg: "Physical Simulation of Metal Extrusion by Means of Model Materials", Proc. 4th Int`l Al Extr. Techn. Sem., Chicago, Vol.2, April 11-14 (1988), pp.321-327. [3] G. Grasmo, K. Holthe, S. Stoeren, H. Valberg, R. Flatval, L. Hanssen, M. Lefstad, O. Lohne, T. Welo, R. Oersund and J. Herberg: "Modelling of Two-Dimensional Extrusion", Proc. 5th. Int`l Al. Extr. Techn. Sem., Chicago, Vol.2, May 19-22 (1992), pp.367-376. [4] H. Valberg and R. A. Groenseth: "Metal Flow in Direct, Indirect and Porthole Die Extrusion", Proc. 5th Int. Al. Extr. Techn. Sem., Chicago, Vol.1, May 19-22 (1992), pp.337-357. [5] H. Valberg: "Metal Flow in the Direct Axisymmetric Extrusion of Aluminium", J. Mat. Proc. Techn., Vol.31 (1992), pp.39 - 55. [6] H. Valberg, A. W. Hansen and R. Kovacs: "Deformation in Hot Extrusion investigated by means of a 3-D Grid Pattern Technique", Proc. 4th. Int. Conf. Techn. Plasticity, Bejing, Vol.I, Sept. 5-12 (1993), pp.637-645. [7] H. Valberg and T. Malvik: "An Experimental Investigation of the Material Flow inside the Bearing Channel in Aluminium Extrusion", Int. J. Mat. Prod. Techn., Vol.9 (1994), 4/5/6, pp.428-463. [8] T. Welo, A. Smaabrekke and H. Valberg: "Two-Dimensional Simulation of Porthole Extrusion", Aluminium, Vol.71 (1995), 1, pp.90-94. [9] H. Valberg and T. Malvik: "Metal Flow in Die Channels of Extrusion", Proc. 6th Int. Al. Extr. Techn. Sem., Chicago, Vol.2, May 14-17 (1996), pp.17-28. [10] H. Valberg, F. P. Coenen and R. Kopp: "Metal Flow in Two-Hole Extrusion", Proc. 6th Int. Al. Extr. Techn. Sem., Chicago, Vol.2, May 14-17 (1996), pp.113-124. [11] H. Valberg and C. Pohl: “Boundary conditions and metal flow in forward extrusion of Al alloys”, Conf. proceedings of Euromech 435, Valencienne, June 18-20 (2002), pp. 33-45. [12] H. Valberg and Oe. Sandbakk: “Direct non-lubricated Al-extrusion partitioned into the subprocesses shearing, scratching, radial compression and extrusion”, Proc. of the 6th Int. Conf. on Material Forming, Salerno, Italy, April 28-30 (2003), pp. 307-310. [13] H. Valberg and R. K. Uyyuru: “New accurate experimental techniques to quantify metal flow inside workpiece – and along boundary interface of workpiece – in metal forming”, Proc. of the 2nd Int. Conf. on Tribology in Manuf. Proc., Nyborg, Denmark, Vol.2, June 15-18 (2004), pp. 453-474. [14] H. Valberg and W. Z. Misiolek: “Plastic deformations in indirect hot extrusion of an aluminium alloy characterised by FEM-analysis with experiment”, Proceedings of the 9th Esaform Conf., Glasgow, April 26-38 (2006), pp. 487-490.

Key Engineering Materials Vol. 367 (2008) pp 25-38 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/KEM.367.25

Innovative Methodologies for the Simulation of Static Recrystallisation during the Solution Soaking Process of Shape Extrusion Terry Sheppard1, a, Xavier Velay2, b 1, 2

Bournemouth University, School of Design Engineering and Computing, Fern Barrow, BH12 5BB, Poole, United Kingdom a

[email protected], b [email protected]

Keywords: static recrystallisation, simulation, shape extrusion, aluminium alloy 2024

Abstract: Materials which form the surface and subcutaneous layers of an extrudate experience large deformations when they traverse the die land. This, when added to the inhomogeneity caused by the dead metal zone, leads to considerable modifications to the deformation parameters when compared to the remainder of the extrusion. The distribution of structure is therefore greatly inhomogeneous. Reference to both empirical and physical models of the recrystallisation process indicates that nucleation and growth will differ at these locations in those aluminium alloys that are usually solution treated and aged subsequent to the deformation process. Since static recrystallisation has a significant influence on many of the properties of the extrudate, it is therefore essential to provide the methodology to predict these variations. In the work presented, a physical model, for AA2024, based on dislocation density, subgrain size and misorientation is modified and integrated into the commercial finite element method (FEM) code, FORGE, to study the microstructure changes. Axi-symmetrical and shape extrusion are presented as examples. The evolution of the substructure influencing static recrystallisation is studied. The predicted results show an agreement with the experimental measurement. The distribution of equivalent strain, temperature compensated strain rate and temperatures are also presented to aid interpretation. Importantly the properties of hard alloys improve as the temperature of the extrusion is raised. This phenomenon is discussed and theoretically justified. This paper also presents some innovative work where the physically based models, and the Cellular Automata (CA) method, are combined to simulate the static recrystallisation process. The FEM is adopted to provide the initial morphology and state variables for the structure models, such as the equivalent strain, the temperature and the equivalent strain rate. The subgrain size, and dislocation densities are calculated from physically based models and are transferred to CA models to construct the data required to define the initial state for recrystallisation. Simulation results are compared with experimental measurements. It is demonstrated that CA integrated with the physically based models is effective in predicting the structural changes by selecting a suitable neighbourhood and reasonable transition rules. Introduction In order to model the deformation of materials it is important to recognize the structures and properties required in the final extrudate. Hence some background knowledge of the structure and properties is essential in order to ensure that the modelling results are sensible. A range of commercial Al-Cu-Mg alloys (the 2XXX designation) were developed to replace 'Dural' and AA2024 and AA2014 are now the most widely used alloys of this system. In this communication we shall take as our example the alloy 2024. The composition is shown in Table 1. Alloy [%] Cu Si Mn Mg Fe 2024 4.5 0.6 1.5 0.2 Table 1. Typical composition of AA2024.

26

Advances on Extrusion Technology and Simulation of Light Alloys

In order to achieve the optimum mechanical properties in AA2024, it is usually necessary to solution heat treat and age the wrought product. In this alloy, the desired structure after solution soaking is usually one exhibiting as little recrystallisation as possible. The changes to the grain structure of directly extruded material after a solution soak are shown in Fig. 1. Billets extruded at a temperature less than 350oC assume a completely recrystallised structure after the solution soak whilst the higher temperature extrudates appear to have retained much of the original grain structure. Fig. 1 also illustrates the mode of recrystallisation in the extrudates; the elongated nature of the recrystallisation grains in the extrusion direction is clearly due to the pinning of the boundaries by second phase particles (Fig. 1a and 1b). Fig. 1c indicates the absence of recrystallisation in the higher temperature extrudates. These specimens were extracted from extruded rod; similar micrographs were obtained from extruded shapes [1]. This indicates the complex problem to be analysed by FEM. These structures are of great importance because of the subsequent effect on properties. Thus during the extrusion and soak cycle of AA2024 the stored deformation energy within the extrudate ensures that some static recrystallisation usually occurs after the extrusion and during the soaking process and can extend to 100 percent of the material in some cases. Damage tolerance, fatigue crack propagation and corrosion, which are three technical indices important to the aerospace industry, are significantly affected by the recrystallisation grain size and by the volume fraction recrystallisation. It is necessary to show that, with the aid of FEM, we are able to model these features.

(a) (b) (c) Figure 1. Microstructure of extrudates after solution soaking at 500°C followed by water quenching [1]: a) extruded at 350°C / 0.5h soak / longitudinal, b) extruded at 350°C / 0.5h soak / transverse, c) extruded at 450°C / 0.5h soak / longitudinal. The structure of the extrudate is dependent on the total thermo-mechanical cycle but the most important consideration in terms of properties is the subgrain size and orientation which very much determines the metal response to the solution and ageing sequence. The reader should recall that the subgrain size is related to the processing parameters and has been established for AA 2024 by Sheppard and Subramaniyan [2] to be:

δ −1 = 0.082 ln Z − 1.89

(1)

for direct extrusion. In this form δ is the subgrain diameter and Z is the temperature compensated strain rate given by:  ∆H  Z = ε& exp   GT 

(2)

Key Engineering Materials Vol. 367

27

where ε& is the mean equivalent strain rate and in practical terms is governed by the extrusion ram speed. ∆Η is the activation energy for the material and is a function of alloy content, dispersoid and precipitate distribution. G is the universal gas constant and T is the temperature of the billet at the relevant location. Thus, once the homogenisation and preheat sequence have been completed, structure control is largely dependent upon the extrusion conditions. There is a variation of structure longitudinally in the extrudate which could and should be eliminated by the control of press speed during the cycle. The importance of automation and computer control of presses becomes evident with the ideal combination being indirect extrusion with full automation of preheating and press facilities. The objective being the attainment of optimum, homogeneous and reproducible properties in each extrusion. The T6 temper is the most commonly used heat treatment for 2XXX alloys and has therefore been investigated for direct and indirect extrusion [1]. The tensile properties for these billets subjected to homogenisation and a one step preheat are shown in Fig. 2 for direct extrusion. It is clear that there is a discontinuity in the proof stress and ultimate stress values which is not the result of any gradual variation of extrusion temperature. The high strength or low Z regions correspond to the partial or un-recrystallisation substructures shown in the previous section whilst the low strength levels are associated with completely recrystallisation structures. Recent work [3] has shown that the AA2024 alloy has identical ageing characteristics at both high and low temperature extrudates. This is exhibited by retained substructures and fully recrystallisation structures which indicates that although preferential precipitation does occur it has little effect on the attainment of peak strength. Hence we would expect the strength to vary with lnZ and this indeed can be detected in Fig. 2 although there are insufficient data points to suggest empirical relationships. At higher values of Z the strength increases presumably due to finer grain sizes but never achieves the levels possible when processing using low Z conditions. Thus we may conclude that as far as tensile properties are concerned there is some advantage in processing at as low a Z as possible consistent with the attainment of a satisfactory surface.

Figure 2. Variation of properties with the temperature compensated strain rate parameter. One of the most limiting factors of the extended application of high strength aluminium alloys is their relatively low fracture toughness. The structural information presented above indicates that since the structural morphology is radically altered by the prevailing conditions, then so should the fracture path. Fig. 3 shows the Ksr (short rod fracture test) value as a function of the temperature compensated strain rate from which it can be seen that the processing effects on fracture are somewhat dramatic. The results are for 2024 alloy in the T6 condition (soaked 500°C for 0.5 hour, aged at 160°C for 18 hours). The rapid decrease in fracture toughness with increasing Z is greater than can be attributed to the corresponding increase in the yield stress. This is contrary to the expected increase in fracture

28

Advances on Extrusion Technology and Simulation of Light Alloys

toughness due to the observed decrease in recrystallised grain size with increasing Z. Since all specimens received the identical solution soak and age sequence the fracture mode is clearly associated with the extrudate rather than the heat treatment. Fig. 4 indicates that a substructure may be retained through a heat treatment schedule and this has been shown to alter the fracture surface conditions.

Figure 3. Fracture toughness variation with LnZ showing remarkably higher toughness at lower Z (higher temperature).

Figure 4. Features of partially recrystallisation structures of heat treated extrudates: a) partially recrystallised structure (micro), b) retained pocket of subgrains in Fig. 4a In this paper we attempt to demonstrate that FEM coupled with a physical model can predict the structural features discussed. These are the formation of the grain size, the volume fraction recrystallisation and the subgrain size and misorientation. Excellent reviews on modelling of static recrystallisation (SRX) have been given by Gottstein et al [4,5] and by Shercliff and Lovatt [6]. Some of the modelling work has been achieved in the field of hot rolling [7-9], and recently in the field of hot extrusion by Duan and Sheppard [3] and Duan et al [10]. The majority of these constants have been reported as referenced in the theoretical section. Temperature dependent constants are found to match the experimental measurement. Theoretical Considerations Physical Models. The Avrami equation predicts the relationship between the volume fraction recrystallisation (Xv) and the holding time (t) and is generally represented as: k   t    X V = 1 − exp − 0.693    t50   

(3)

where t is annealing time, k is the Avrami exponent, t50 is the time to 50% recrystallisation. t50 is calculated based on the stored energy (PD) and the density of recrystallisation nuclei (NV) [11]. For

Key Engineering Materials Vol. 367

29

the calculation of t50, the physical model is commonly regarded as revealing the mechanics driving the transformation and therefore takes the following form:  1  t50 = M GB PD  NV C

  

1

3

(4)

Recently, Sheppard and Duan [12] have confirmed that the physical model will give better computed results than the empirical model in the simulation of aluminium extrusion. The Physical model proposed by Furu et al [13] and Zhu and Sellars [14] has been modified for use in this study. C/MGB has been reported as a constant for a given deformation and temperature. MGB, however, is temperature dependent which has not been defined for use under these conditions and in this form. Theoretically this term should be described in the following form:  ∆H  M GB = M 0 exp   GT 

(5)

The problems involved with the temperature dependence of C/MGB may be overcome by recognising that providing we may assume a value of MGB at temperature T1 then the value at any other temperature T2 is:

 C   C   ∆Η (T2 − T1 )    =   .EXP    (G )T2T1   M GB  2  M GB 1

(6)

The activation energy for grain boundary migration has not been broadly determined. However Gottstein and Mecking [15] have observed that any addition to high purity aluminium reduces this value considerably below that for self diffusion. Taheri et al [16] have also shown that even the most minor or trace conditions lower the activation energy. Clearly the alloy 2024 has substantial ‘impurities’ and, based on the above reported values, we have used a value for ∆Η of 30kJ/Mole. At a specific temperature (say T1) C/MGB can be inferred by utilising calculated individual values of NV and the microstructural information to calculate specific values of PD. These values have been utilised when the investigators [5,11] have assumed a completely isothermal deformation and anneal implying no transverse or longitudinal variation in temperature: a condition rarely obtainable. Further modifications to published models are necessary to correct for anomalies in grain boundary per unit volume and to the evolution definitions for subgrain size misorientation. FEM Simulation Setting

The FEM program, FORGE was used in the present study. It is a process simulation tool based on the finite element method. The hyperbolic sine function was programmed into the FEM to describe the material behaviour. The constitutive equation can be written as function of Z because it has been shown that: 2n  Z 1 n  Z σ = ln   +   + 1 α  A   A  

1

(7)

For the alloy 2024, ∆H=148880 kJ/mol, α = 0.016m2/MN, n=4.27 and lnA=19. 6 [17]. The flow stress could also be written in the physical nomenclature used above. However the data required for the form preferred by the authors has been obtained experimentally and has been proven to operate within the FEM framework. This is not the case for the physical model and it is

30

Advances on Extrusion Technology and Simulation of Light Alloys

clear that the terms dσ dε& and d 2σ dε& 2 , which are required within the FEM code, are not easily evaluated. The Tresca friction law was assumed for this study. This can be written in the form:

τ = −m

σ ∆V

(8)

3. ∆V

Where τ termed the shear strength, m is the friction coefficient; in effect a percentage of that which would represent sticking conditions, ∆V is the velocity difference at the interface. The Tresca law treats the interface friction as pressure independent and relates the friction stress to the yield strength. When m = 1 sticking friction occurs. Temperature evolution is represented by the following equation:

ρ .c

dT = div{k .grad (T )} + W dt

(9)

and it is associated with a certain number of boundary conditions. The FEM simulations are given in Table 2. Extrusion mode Direct - 2D Direct - 3D Direct - 3D

Material

AA2024 AA2024 AA2024

Billet Die fillet Ram speed temperature radius [mm] [mm/s] [oC] 410 0.5 3.0 350 0.5 3.0 450 0.5 3.0 Table 2. Simulation runs.

Friction coefficient Billet/Container. 0.85 0.8 0.9

Results and Discussion Two-Dimensional Investigations. The ability of the FEM code to perform the relatively simple tasks of predicting extrusion load and temperature loci during axisymmetric deformation have been presented [18,19] and showed reasonable agreement with the experimental work [17,20,21]. The %recrystallised, the grain size, the temperature and the subgrain misorientation were all in agreement with experimental values obtained by Subramaniyan [21]. Three-dimensional Simulation Results. For this work we have selected a T-section which is a close approximation to the geometry existing in aircraft wing spars. We have reported that, whereas we are able to integrate the subgrain size throughout the deformation zone the user program must specify an original dimension for this structural feature. We have chosen therefore to represent relevant illustrations from the program output but to calculate the structural parameters XV and Drex based on extraction of relevant data from the program output. This method allows an easy computation using the steady state value of the subgrain size using the following equation:

δ −1 = 0.082 ln Z − 1.89

(10)

The reader will recall that it is the characterisation of the various values obtained at the exit to the die land area which determines the structure. The dimension of the section is shown in Fig. 5.

Key Engineering Materials Vol. 367

31

12.20

punch (pressure pad)

6.10

container

3.05 plane of symmetry

(a)

0.5mm fillet radius die

6.10

(b)

(c)

Figure 5. (a) Schematic drawing of the T-shaped die (all dimensions in mm), (b) finite element model of the tooling (half symmetry) and c) details of the die land. We must also consider the effect of the soak temperature since it has long been recognised within the extrusion and rolling industry that this factor significantly affects the volume fraction recrystallisation and the recrystallised grain size as well as the textural features of the product. In this study the solution soak was post calculated. The authors acknowledge that the value of 30kJ/mole adopted for the activation energy for grain boundary mobility may not be exact. However this is not far from the actual value and, as shown in the two dimensional analysis, is effective in predicting very sensible values of XV. The temperature and the equivalent strain distribution of the two sections are shown in Figs. 6 and 7 respectively shortly after the material passes the die entry radius. These parameters are considered to be those which most influence recrystallisation. Figs. 6a and 6b show that for the bulk of the section extruded at 450oC the temperature rises to 470-472oC whilst for the 350oC extrude the comparable figure is 451-455oC. At the section change point the corresponding temperatures are 477-480oC and 459-465oC. Surprisingly there are also above average temperature rises at the mid-plane of the section at the long face which may be explained by the inherent asymmetry. These observations suggest that in the high temperature case there would be less energy available to drive the recrystallisation mechanics. This is further confirmed by the observation that the subgrain size is larger in the high temperature case: the average peripheral values are 4.0 for the 450oC extrude compared with 2.848 at the lower temperature. Figs. 7a and 7b compare the equivalent strains at the same point corresponding to the temperature results and are somewhat surprising. The overall useful strain of the extrusion is from a continuum consideration identical. However the figures show that the strains at high temperature are considerably less than their low temperature counterparts. The higher temperature extrude shows maximum mean equivalent strain of 13-17 at the sharp change in section compared with 1418.5 for the low temperature case. The strains over the bulk of the extrudate are about 5-9 in each case: the higher temperature billet being slightly smaller. In the absence of numerical analysis we would estimate the true strain as being roughly equal to lnR which is about 4. This is a typically fine example of the advantages offered by these readily available numerical techniques. Moreover the higher strains suggest that we shall observe greater recrystallisation in the low temperature mode. There are no regions of abnormal strains in those areas on the asymmetry plane in which we observed higher temperatures. This suggests that a more thorough investigation of strain distribution would form an interesting further study.

32

Advances on Extrusion Technology and Simulation of Light Alloys

(a) (b) Figure 6. Temperature distribution for (a) Ti = 450°C and (b) Ti = 350°C.

(a) (b) Figure7. Equivalent strain distribution for (a) Ti = 450°C and (b) Ti = 350 °C.

Key Engineering Materials Vol. 367

33

The predicted fraction recrystallisation factors and grain sizes at the periphery of the T-shape section are shown in Fig. 8 which depicts the cross section of the extrude at a distance of 1/3 from the front of the extrude which is the same position specified by Subramaniyan when presenting his results. All values are for the surface of the material. In obtaining these results the authors have post-processed the raw data from the program rather than define a user inserted program into the FORGE version. This was to obtain the results in a time frame acceptable to the problem. When attempting the usual user programming the running time was found to be excessive. 23 [0.083]

18 [0.093]

12 [0.102]

21 [0.080]

65 [0.053]

54 [0.064]

57 [0.055]

450oC

34 [0.072]

350oC

73 [0.050]

19 [0.102]

36 [0.078]

71 [0.049]

89 [0.041]

29 [0.084]

100 [0.015]

100 [0.018]

26 [0.089]

97 [0.032]

22 [0.092]

77 [0.046]

29 [0.088]

73 [0.054]

4 [0.165]

3 [0.218]

23 [0.076]

31 [0.072]

(a) (b) Figure 8. Cross Section of extrudate one third from the beginning showing the positional values of %XV [Drex in mm] for (a) Ti = 450°C and (b) Ti = 350 °C. For the shaped section, estimation of the depth of the recrystallisation layer was more difficult than in rod experiments, since the layer was no longer uniform. With FEM simulation, the distribution of the volume fraction recrystallisation factors can be predicted and extracted more easily. It has been found that both in previous experiments and FEM simulations that the recrystallisation layer was thicker for more complex sections due to larger temperature rises. As can be seen in Fig. 8, at the positions where the deformation is more complex, that is, where the strain and the temperature are higher, the volume fraction recrystallisation is also higher. Significantly there are large differences in the values of XV and Drex for the differing extrusion temperatures which will lead to important differences in the critical properties as discussed in the introduction. This would be the case if we assumed any value for ∆ΗGB and used this form of analysis. The experimental measurement of the average volume fraction recrystallisation factor at 450°C was about 23%, whereas the average value of the XV for the 350°C billet measured 65%. The experimental results also assumed a constant thickness of the recrystallised layer and hence must be considered as approximate. Nevertheless the values shown in Fig. 8 are clearly very reasonable. The maximum XV for the 350°C billet is 100% and is located at the two points we would expect which correspond to the change in section. For the 350°C billet the average XV is 70% which is reasonable when compared to the experimental value of 65% whilst the maximum, again detected at the points of section change is 100%. The average recrystallisation grain size for the 350°C extrusion is 0.048mm with the minimum occurring at the XV = 100% points with a value between 0.015-0.018mm. The corresponding figures for the 450°C extrusion is 0.104mm and 0.078-

34

Advances on Extrusion Technology and Simulation of Light Alloys

0.084mm which all show close agreement with the experimental results. The importance of these figures are however inconsequential. The fact that the program is able to deal with these problems (including the solution soak) as well as the purely mechanical parameters is of some import. It is obvious when considering Fig. 8 that the structure and hence the properties will vary substantially between the two extrudates. The reader should be aware that since XV for the 450oC extrudate nowhere approaches 100% in the vicinity of the surface layer implies that pockets of subgrains are retained after the solution soak sequence and we have shown an optical micrograph of a partially recrystallisation area of one such pocket in Fig. 4b. Such a structure will act as a barrier to crack growth (either fracture or corrosion) and will also increase the tensile properties of the product. Figs. 6 and 7 show that very respectable values of the structural parameters may be predicted using the combination of FEM and physical modelling. Cellular Automata The simulation of recrystallisation by the CA method has been reported by Hesselbarth and Gobel [22] and Pezzee and Dunand [23]. Davies also gave detailed discussions of the effects of varying neighbourhoods and the possibility of the application of CA into aluminium rolling [24-26]. By mapping the state variables on a two- or three-dimensional spatial grid (the neighbourhood), cellular automaton simulations are capable of considering microstructural inhomogeneities such as precipitates, dispersoids, microbands, shear bands, transition bands, heterophase interfaces, grain boundaries, or twins. These local defect structures can be described in terms of corresponding values of the state variables or their gradients [3]. The transition rule in the early literature concerning CA evaluation was completely random [27], depending purely on the geometry of the matrix. However, it is now considered in a complex and probabilistic way [28], which is dependent on the mobility of the grain boundary and the stored energy of the structure. A new type of neighbourhood was adopted in this study due to the elongated nature of the recrystallised grain shape in the extrudate, and this is shown in Fig. 9. The preferred ratio is defined as the number of cells in the preferred direction to the number of cells in the other (in two dimensions the preferred ratio is 2).

Figure 9. Side-prefer-neighbour with a ratio of 2. We should note that a preferred ratio of 15 is adopted in construction of the initial structures and a ratio of 2 is employed during the nucleation and growth stage of simulation. However, due to the predominant shear deformation during extrusion, the width of the elongated grain at the subsurface area is much less than the calculated result. There is little experimental data in the literature and hence a constant value of 8µm has been adopted by consideration of the initial grain size and equivalent strain corresponding to the conditions obtaining in the two dimensional evaluation. Before new grains impinge, the shape of the grain and its growth rate-depend on the definition of the neighbourhood. The recrystallised structure is more or less independent of the neighbourhood

Key Engineering Materials Vol. 367

35

that is chosen. After the grains have grown to maturity, and the process is terminated, the grain pattern is virtually independent of the neighbourhood chosen. The authors have not considered the prediction of the recrystallisation time. Hence the impact of different neighbourhoods is mainly on the shape of the recrystallised grain before the grains consolidate. The side preferred neighbourhood was found most suitable for the present case, which is determined by the nature of the recrystallised grain size observed in experiments. As for the transition rules, the recrystallisation designed with a probabilistic-switching rule was adopted in this study. The rule is based on the form of a probabilistic analogue of the linearised symmetric rate equation of Turnbull [29]. The local switching probability can be quantified by the ratio of the local and the maximum mobility, which is a function of the grain boundary character and by the ratio of the local and the maximum driving energy giving the following switching probability:

 mlocal p local wˆ local =  max max m p

  x& local  =  max   x&

  t max  =  local  t

  

(10)

t is the local time required by a grain boundary with velocity x& to cross the automaton cell (8µm) and is user selected, m is the boundary mobility imported from the FORGE program. Hence by setting a random number r between 0 and 1 as critical for switching the following rules could be defined:  mlocal p local accept switch if r ≤  max max m p  mlocal p local reject switch if r ≥  max max m p

  

  

(11)

In Raabe’s study, nucleation in the simulation is performed in accord with two aspects, i.e. potential nucleation sites must fulfil both the kinetic and the thermodynamic instability criterion. At the beginning of the simulation, the thermodynamic criterion, i.e. the local value of the dislocation density, was first checked for all grid points. If the dislocation density was larger than some critical value of its maximum value in the checking area (for example, 30%, 60% or 90%), the cell recrystallised without any orientation change (dislocation density assigned as zero and original crystal orientation reserved). The ordinary growth algorithm was started and the kinetics for conditions for nucleation were checked by calculating the misorientations among all recrystallised cells and their neighbourhood. If any pair of cells found a misorientation above 15°, the cell flip of the unrecrystallised cell was calculated according to equation 10. The detail of the transition rule could be found in Raabe’s work [28]. Because of the lack of methods to predict the crystal orientation at the macro-scale simulation and the shortage of experiment results, a statistical method was adopted in the present study to give the misorientation between the grains. For each cell, a randomly allocated orientation number, q, was assigned to each grain. The orientation number indicates primarily the orientation of a cell and maximum number of q was 936, which represents 936 texture components, which were equally distributed in orientation space. It has been reported by Geiger [30] that q ≥ 64 crystal orientations is necessary to simulate the recrystallisation process, and the number of 936 was taken from Raabe’s study [28]. The misorientation is obtained from the q numbers of the neighbouring grain where ∆q is the difference between orientation numbers of two adjacent grains and

0≤

∆q Cost.

(1)

To the knowledge of the authors, no experimental verification of such model has been produced. It must be pointed out that the maximum pressure always occurs at the leg tip. Alternatively, the pressure criterion can be normalized, by rating the normal pressure to the effective stress in a specific point, thus becoming: Pmn=max(pi /σi) > Cost.

(2)

At the leg tip we have the maximum pressure and the minimum effective stress, so that the criterion assumes its maximum at that point. On the other hand, a precise evaluation of the effective stress at the leg tip can be problematic in a FEM environment, being much dependent on the element size, so that a considerable scattering of the result can be foreseen by this way. An alternative criterion, proposed by Plata and Piwnik [4], is based on the integral on time of contact pressure, normalized on the actual effective stress, along a generic path for a welding element; the value obtained must exceed a critical limit, to be experimentally determined. In analytical terms:

P Q = ∫ dt ≥ cos t t

σ

(3)

Here it must be noted that at the leg tip the velocity is zero and the residence time is likely to be infinite. This criterion greatly emphasizes the “dead zone” part of the welding chamber. Basing on this observation, the authors of the present work introduced [7,8] the speed as a correction factor for that criterion, thus meaning that the flow of material effectively flowing through a generic point must also be considered (referring to fig 2, the material flow through path A, within the dead zone, is much less than that passing on path B; alternatively, referring to fig.1b, the material flow through path 3 is less than that through path 2 and so on). Thus, we have:

Key Engineering Materials Vol. 367

129

p p K = ∫ dt ⋅ v = ∫ dl ≥ Cost. t

σ

L

(4)

σ

where L is the generic path from the entrance in the welding surface up to the die exit, where pressures are zero. It is interesting to note that in this way we have the integral of pressure on length and the whole path is considered as effectively contributing to the seam weld formation. It must be reminded, however, that the p/σ integral will still gives somewhat more importance to the dead zone than the simple p integral. Leg (Side View)

A B

Leg (Top View)

A,B C

Dead zone

D

Dead zone

Leg tip

Welding Surface Welding Surface (Top view)

Figure 2. Welding surface and welding paths

In order to consider the average behavior of all the welding paths forming the welding surface (namely, referring to figure 2, paths A,B in the middle plane of the die and paths C,D in welding surface but out of the middle plane), the parameter K can be written in this form: K ad =

1 p dA ≥ Cost. w ∫A σ

(5)

where A is the area of the welding surface and w is some characteristic width of the problem. To this regard, it seems particularly useful to adopt, for the characteristic width in eq. (5), the length of the weld trace that can be seen in the profile section. In this way, the Kad factor would represent the ratio between the global welding force (the quantity under the integral) and the total welding length, thus allowing the comparison of welds on profiles with different thickness. In the particular case of a weld trace that is a line normal to the profile surface, the weld trace coincides with the profile thickness. Again, it is conceivable that either p or p/σ can be used within the Kad formulation, with a different emphasis on the dead zone, as explained. Another interesting criterion has been proposed by Bourqui et al. [6], which states that good welding conditions are achieved if the ratio between the maximum pressure in the welding s w chamber (Pw) and the pressure at the top of the leg (Ps) exceeds the value of 0.5 (figure 3):

P

P

Figure 3: Bourqui Criterion

130

Advances on Extrusion Technology and Simulation of Light Alloys

Pw/Ps>0.5

(6)

The physical meaning of this rule (which has proved to be effective in some cases) is simply to guarantee maximum pressure in the welding chamber. However, it seems doubtful that this criterion could be applied to cases with low extrusion ratios. Quality indexes based on strain have been developed recently [12] on thermo-mechanical simulator, but they have not been applied to extrusion so far. Strain indexes seem to be well suited in those cases where some contaminants are present on the welding surface. In this case the strain fractures the oxides, thus allowing the atomic contact of the substrates. Besides, applied to the extrusion cases, an high strain step corresponds also to an high hydrostatic pressure step, thus determining an equivalence between criteria of strain and welding pressure. Validation. Criteria (1) to (6) were validated by applying them to experiments performed by Valberg [3] and Donati et al. [7,8], where it was possible to fully reconstruct by FEM analysis the die geometry, the processing conditions and the final state of the weld. In each simulation, the distribution of contact pressure, velocity and effective stress has been plotted on the welding surface, and the values were used to evaluate the welding criteria. Pm Parameter

Qad Parameter

80

40,00 exp.1,2

esp.1,2

exp.4,5

esp.4,5

exp.7,8

esp.7,8

exp.9,10

esp.9,10

0,00

0

5 Ram Velocity (mm/s) 10

5 Ram Velocity (mm/s) 10

Pmn Parameter

Kad Parameter 30,00

2,50

0,00

exp.1,2

exp.1,2

exp.4,5

exp.4,5

exp.7,8

exp.7,8

exp.9,10

exp.9,10

0,00 5

10

Ram Velocity (mm/s)

5

Ram Velocity (mm/s)

10

Fig.4 Behavior of welding criteria with process velocity. The Valberg experiments, in particular, show that an increase in extrusion velocity gives worse welding quality, sometimes with the transition from a sound weld to the almost complete absence of weld. This common extruder’s experience, which is confirmed by experiments in ref. [3,4], should also be revealed by the welding criteria. By increasing the velocity from 5 to 10 mm/sec (see fig. 4), it was found that Pm failed the goal in one case (experiments n. 7,8), Qad, Pmn and Kad correctly predicted a decrease in welding quality, but only Kad could correctly separate different classes of welding quality (good quality for exp.1-5, worse quality for exp. 9-10, no weld in exp. 7-8). It must be noted that although the flow stress necessarily increases with speed, the welding parameters can decrease due to the lower interface pressure, as a result of the less converging paths behind the leg. This is not a general rule, anyway; whether the welding pressure would increase or

Key Engineering Materials Vol. 367

131

decrease with the extrusion speed, it depends on the particular geometry of the die (in particular on the final strain increment and on the leg shape). This is a very interesting matter which needs further research. Referring again to ref. [3], the experiments show that an increase in leg angle gives worse welding quality (which is also a common extruder experience). By evaluating the criteria at 45° leg angle (a typical smoothed end) and 90° leg angle (corresponding to a square leg end), it was found that (fig. 5) only Pm and Kad parameters could correctly interpret the experimental findings, with Kad parameter again being able to separate in the best way different classes of welding quality.

Qad Parameter

Pm Parameter

120

40,00

exp.1,4

exp.1,4

exp.2,5

exp.2,5

exp.3,6

exp.3,6

exp.7,9

exp.7,9 exp.8,10

exp.8,10

0

0,00

Leg angle(°)

90

45

90

Leg Angle (°)

45

Kad parameter

Pmn Parameter

30,00

2,50 exp.1,4

exp.1,4

exp.2,5 exp.3,6

exp.2,5

exp.7,9 exp.8,10

exp.7,9

exp.3,6 exp.8,10

0,00

0,00

90

Leg angle (°)

45

90

Leg angle (°)

45

Fig.5 Behavior of welding criteria with back leg angle. Another important feature of the welding criteria is to allow the comparison of the welding quality in different profile geometries. By collecting all the experiments of refs. [3] and [4], thus considering different profile thickness, lengths and die assemblies (not reported here), it emerges that the criteria that can discriminate the welding quality in classes (“good”, “defects” and “unwelded”) are the Pm and the Kad parameters. The Kad is, again, the one that more clearly defines the quality classes, while the Pm has the advantage of simplicity: it has a clear physical meaning, and remains the same regardless of the welding chamber shape. The Kad represents the mean pressure (or the mean p/σ) on the welding surface, times the welding area, ratio the welding trace width; in other words, it is the total force per unit thickness of the profile, which seems quite convincing parameter to assess the phenomenon. It is worth noting that Kad fundamentally encompasses the length of the welding chamber. As a final remark, it must be pointed out that welding pressure and welding chamber length cannot be separated: in fact, the pressure always increases toward the inside of the die, so that the longer the welding chamber length, the higher the pressure at the leg tip. This could lead some author to consider Pm as the only parameter affecting the weld formation. On the other hand, it has already been demonstrated how Pm sometimes fails to be effective, probably when the dead zone behind the leg is large and the effective Pm available for the weld is lower than that at the leg tip. Thus, it can

132

Advances on Extrusion Technology and Simulation of Light Alloys

be said that both the maximum pressure in the welding chamber and the welding chamber length are fundamental parameters for assessing the welding quality. Mechanical Proprieties UTS and Area Reduction. The experiment already described in the Process Mechanics section is fully analyzed in term of experimental test in [13]. An “H” profile of 5 mm theoretical thickness was produced which, after sectioning, fulfils the requirements for tensile test and crack propagation test. In the experiments the different die assemblies are referred to with two capital letters, the first for the feeding port (B=Big, S=Small), the second for the welding chamber length (B=Big, I=Intermediate, S=Small). Profiles without weld are referred to as NN. In the experiments different preheating temperatures were used and the process speed was increased until some defects emerged. All the profiles were tensile tested, with three repetitions each. The ultimate stress and the true strain at fracture were recorded. Each processing condition was simulated by means of complete thermo-mechanical FEM analysis (for detailed modeling data refer to [14]). For each simulation, the distribution of contact pressure and effective stress was evaluated on the welding surface. The maximum pressures inside the welding chamber were found to range from 75 to 150 MPa, corresponding to about 2.4-3.7 times the material flow stress, independently of the die arrangement. In Fig.6 the correlation between maximum pressure in the welding chamber and the mechanical properties is shown; it emerges that: • At a critical value of maximum pressure in the welding chamber (at around 50 MPa), the UTS evidences a clear transition from no resistance to full resistance; it clearly emerges that if the maximum pressure in the welding chamber exceeds the critical value, then the full resistance on the profile will be obtained; furthermore, no increase in UTS can be obtained by increasing welding pressure (as a note, it must be pointed out that in figure 6 the two unwelded points and the first two correctly welded were taken from ref. [3]). • The true strain at fracture increases from 0.2 up to 0.39 by increasing the welding pressure from 75 up to 150 MPa. No strain data were available below 75 MPa, but it seems conceivable that the same correlation will remain valid until the critical pressure of 50 MPa formerly set, below which the true strain would necessarily fall to zero. 0,45

Without welds

350

Without welds

0,4 Deform ation at Fracture

Ultim ate Tensile S trength [M pa]

400

300 250 200 150 100 50

0,35 0,3 0,25 0,2 0,15 0,1 0,05 0

0 0

50

100

150

Maximum Pressure in w elding chambe r (Mpa)

200

0

50

100

150

200

Maximum Pre ssure in w elding chamber (Mpa)

Figure 6. Mechanical properties on the profile as a function of welding pressure Thus, it emerges a direct relationship between the profile deformability and the maximum pressure in the welding chamber. The correlation between the strain at fracture and the welding parameter Kad was not investigated here, so that it is impossible to say, at this point, if the welding length would contribute to the profile properties, and to what extent. The effect of speed. Process speed is known to be another important parameter affecting the weld quality. If the effect of speed on the welding pressure is uncertain, as discussed, it was found that

Key Engineering Materials Vol. 367

133

process speeds always determined a reduction in profile deformability. In figure 7 the strain at fracture of the profiles obtained with different die assemblies as a function of process speed is shown. The interpolating lines of figure 7 suggest, for each die set, a general behavior on many tests carried out on profiles produced in different processing conditions (preheating temperature of the billet and extrusion speed). The considerable scattering of the data is the result of different facts: • The profiles were tested in the “as extruded” shape, namely with their thinning defect (the reduction of thickness with respect to the nominal one); • The higher the speed, the higher the thinning defect; in order to avoid this problem the area reduction was chosen as the best parameter to evaluate deformability; • Different conditions of preheating and speed determines different recrystallization of the profile and thus different responses to tensile test Nevertheless, the general tendency toward a decrease in deformability with process speed was clear and for this reason it has been reported here. 0,5

0,4 ln(A rea0/A reaf)

BS

BB

SI

0,3

BI

0,2 SS

0,1

0,0 0

5

10

15 Production rates(m/min)

20

25

Figure 7. Strain at fracture of the profiles with increasing extrusion speed

A relevant aspect of this behavior arises on whether the final specimen fracture starts from the weld or not. It was found that almost all the BB fractured specimens had the fracture completely outside the weld, which consequently does not represent a weak point for the profile. On the contrary, all the SS fractured specimens had a weld-initiated fracture. The die sets between these two extremes evidenced a mixed behavior. Thus, the decrease in deformability of the BB profiles must not be completely attributed to the weld; in fact, also the increased damage level present in the bulk material plays a fundamental role. This fact was clearly confirmed in [15], where the application of the Cockrof-Latham damage model to the numerical simulation lead to the following results: 1) an increase in profile damage by increasing the extrusion speed; 2) the onset of chevron cracks at a critical speed, perfectly similar to those obtained at the maximum extrusion rates of the experiments. The Cockrof-Latham damage model is linked to the plastic work experienced by the material under tensile hydrostatic stresses. In the experimental die sets these tensile stresses will increase with speed owing to the differences in exit speed between the inner and outer portion of the profile section: the outer part, being thicker, runs faster than the central one and stretches it, leading to tears when a critical damage is exceeded. Thus, two different weakening mechanisms are in competition at high speed: more bulk material damage due to unbalanced material flow and lower maximum welding pressure (depending on the particular die geometry, as explained). The first mechanism would lead to transverse cracks (which

134

Advances on Extrusion Technology and Simulation of Light Alloys

was always the case for exp.[15]), while the second would lead to unwelded stripes (which occurred in the experiment of ref. [4]). It is interesting to note that a considerable difference emerges in the maximum speed that could be obtained with the different die sets. As an example, the BB die could obtain process speed three times higher than the SS one. This was the effect of higher welding lengths, together with higher final strain increment, which increased the profile resistance to both the weakening factors. Dynamic properties. Another interesting feature of the weld, which to the knowledge of the authors has never been evaluated, is its behavior under dynamic loading; in particular the propagation speed of a crack on a seam weld was investigated, trying to correlate it to the welding parameters.

Crack growth rates (log da/dN) [m/cycle]

-5

-5,5 log DK=1,3

-6 log DK=1,3 log DK=1,1

-6,5

log DK=0,9

log DK=1.1

NN -7 log DK=0,9

-7,5

-8 40

60

80

100

120

140

160

180

Maximum Pressure in welding chamber (Mpa)

Figure 7. a) Specimen shape for crack growth tests; b) crack growth speed with Pm

A Crack Propagation Test was then performed on the extruded profiles [13] In particular, Mode I crack propagation velocity was investigated. The tests were performed following the ASTM E64705 and E399-97 standard methods. Six specimens for the BS and BB conditions and eight for the NN, having the shape shown in figure 7a) (CT) were cut, so that the weld plane was coincident to the specimen axis. In this way the investigations is focused on the weld surface and not, as in the tensile test, throughout the specimen volume. The specimens were fatigue pre-cracked in displacement control with a frequency of 20 Hz until a visible crack of 1 mm was detected. The tests were performed in load control at constant maximum load (with increasing ∆K) with a load ratio R=0.05 and a frequency of 20 Hz. The crack growth range considered was 10-8-10-5 m/cycle, where the Paris law is valid. Crack growth measurement was stopped if the crack angle respect to the axis exceeded 20° or if the fracture mode deviated from the pure I to the mixed I-III mode. In figure 7b) the results of the tests interpolating curves are reported in a logarithmic scale as a function of the maximum welding pressure Pm, which is around 95 MPa in the BS case and 135 MPa in the BB one. It can be seen that with increasing the welding pressure the crack growth rate decreases toward the growth rate of NN specimens, which had the lowest (and best) value. In all the BS specimens, the crack path was straight, always running on the weld, thus revealing a preferential crack growth zone; on the other hand, in the BB specimens it was very irregular and only occasionally located on the welded surface. In the unwelded NN specimens the path also moved away from the specimen axis. As a conclusion, it can be said that with increasing the welding pressure, the transition can be observed between a crack growing at high speed on the welding plane and a crack growing rather slowly in a random direction outside the welding plane.

Key Engineering Materials Vol. 367

135

Conclusions The mechanics of the weld formation inside extrusion dies by means of numerical simulation has been described, with emphasis on defining the relevant welding paths participating to the bond. The mechanical conditions on the welding surface were analyzed and the main criteria for assessing the welding quality were reviewed. Relevant findings are: - the maximum pressure in the welding chamber is the easiest and maybe clearest criterion to assess whether the weld is good or not; sometimes it fails to be effective, probably when pressure is too low or when large dead zones extend behind the supporting legs. The critical pressure for obtaining good welds has to be carefully evaluated, as well as its calculation in the numerical analysis, in order to avoid misinterpretation of the results. - The Kad parameter (integral of pressure on the welding surface, ratio the characteristic width), although it is more complex to evaluate, allows a much more clearer separation of the welding classes (in terms of mechanical properties), never failing within the analyzed experiments. The relationship between welding conditions and mechanical properties of the extruded profiles has been analyzed. It was found that: - the profile deformability, measured by the area reduction in a tensile test, is linearly proportional to the welding pressure; if sufficient pressure in the welding chamber is achieved, then the behavior of the profile is the same of a profile without any weld (the fracture occurring outside the welding line). - The extrusion speed decreases the profile deformability by means of two different mechanisms: the increase in damage in the bulk material and the decrease in welding pressure. The maximum speed that can be achieved within a specific die arises by the lowest of the two limits. - The dynamic response of the weld, evaluated by means of crack growth tests, was found to be, again, sensitive to the welding pressure. By increasing the welding pressure, a transition can be observed from a crack growing at high speed on the welding plane to a crack growing rather slowly in a random direction outside the welding plane. Acknowledgements The authors would like to thank Compes SpA (Italy) and MIUR (Italian Ministry for University and Research) for the financial support. References [1]

Akeret R., Properties of pressure welds in extruded aluminum alloy sections, journal of the institute of metals, 10, (1972), p. 202;

[2]

Akeret R., Extrusion welds-Quality aspects are now center stage, Proceedings of ET 1992, vol. I, (1992) pp. 319-336,;

[3]

Valberg H., Extrusion welding in aluminium extrusion, Int. J. of Materials and Product Technology, Vol. 17, N.7, 2002, pp.497-556;

[4]

Valberg H., Loeken T., Hval M., The extrusion of hollow profiles with a gas pocket behind the bridge, Int. J. of Materials and Product Technology, Vol. 10, Nos 3-6, (1995), pp. 222-267;

136

Advances on Extrusion Technology and Simulation of Light Alloys

[5]

Plata M., Piwnik J., Theoretical and experimental analysis of seam weld formation in hot extrusion of aluminum alloys, Proc. 7th Int. aluminum extrusion technology seminar ET 2000,vol. I,(2000), pp.205-211;

[6]

Bourqui B, A. Huber, C Moulin, A. Bunetti, Improved weld seam quality using 3D FEM simulations in correlation with practice, Proceedings of first EAA (European Aluminum Association-extruders division-) Montichiari -BS-,(2002);

[7]

Donati L., Tomesani L., The prediction of seam welds quality in aluminum extrusion, Journal of Material Processing Technology, 153—154, (2004), pp.366-373;

[8]

Donati L., Tomesani L., Evaluation of a new FEM criterion for seam welds quality prediction in aluminum extruded profiles, Proceedings of 8th Int. Conf. Aluminum Extrusion technology Seminar (ET2004), Orlando, 18-21 May 2004, vol.2, pp.221-235

[9]

Donati L., Tomesani L., The effect of die design on the production and seam weld quality of extruded aluminium profiles, J. of Material Processing Technology, 164-165 (2005) pp. 1025-1031

[10]

Fratini L., Tomesani L., Donati L., Buffa G., Solid state bonding in extrusion and FSW: process mechanics and analogies, J. Mat. Processing Technology, 177/1-3 (2006), pp. 344347

[11]

J. Lof, J. Heutink, FEM simulations of the material flow in the bearing area of the aluminum extrusion process, Proc. 7th Int. aluminum extrusion technology seminar ET 2000,vol. II, (2000) pp.211-222;

[12]

Edwards S.-P., Bakker A.J. den, Neijenhuis J.L., Kool W.H., Katgerman L., JSME International Journal, Series A 49/1, (2006), pp. 63–68,.

[13]

Donati L., Tomesani L., Minak G., Characterization of seam weld quality in AA6082 extruded profiles Journal of Materials Processing Technology 191 (2007) pp. 127–131

[14]

Donati L., Tomesani L., Deformability prediction in aluminum extruded hollow profiles by means of process simulation, Acts 7° Conf. AITEM Lecce, September 2005, pp. 123-124

[15]

Donati L., Tomesani L., Prediction of hot damage in aluminum extrusion by means of FEM simulations, Proc. 7th WCCM (World Congress on Computational Mechanics) Los Angeles (2006);

Key Engineering Materials Vol. 367 (2008) pp 137-144 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/KEM.367.137

A Laboratory Scale Equipment to Relieve Force and Pressure in Cold Extrusion of Lead Hollow Components L. Filice1,a, F. Gagliardi1,b, F. Micari2,c 1

University of Calabria, Department of Mechanical Engineering, Arcavacata di Rende (CS), 87036 - Italy 2

University of Palermo, Department of Mechanical Technology, Production and Management Engineering, University of Palermo, Palermo, 90128 Italy a

[email protected], [email protected], [email protected]

Keywords: Extrusion, Numerical Simulation, Pressure Measurement.

Abstract. Nowadays, many researchers are involved in studies aimed to the explanation of some peculiar aspects regarding manufacturing processes. In this paper, an experimental campaign was carried out in order to reproduce tube extrusion starting from a cylindrical billet. In particular, the development of a proper equipment is presented: the aim was to measure both the total load, by using the testing machine load cell, and the local pressure value on the porthole. The latter task was carried out performing a proper system based on the use of a small load-cell. The tube was extruded with a good surface quality and the external area does not show any welding line evidence. Pure Lead was used for the experimental analysis; this material was chosen due to its high ductility which allows to carry out the process at room temperature. The material was characterized by compression tests at different strain rates and the obtained material law was used to perform a numerical analysis using SFTC Deform 3D numerical code. The Numerical analysis was carried out to show both the advantages and drawbacks of the modern FE codes when extrusion processes are investigated. Introduction Extrusion process, developed in the late 1700s to produce lead pipes [1], is nowadays widely utilized for manufacturing several typologies of raw materials and finished parts, both concerning bulk pieces and thin products. Extrusion is characterized by the generation of large free surfaces and thermal softening; furthermore, high strains are applied to the processed material. Many information are well assessed about process mechanics and the technology may be surely regarded as a mature one. In addition, many guidelines were published in the last years, concerning different aspects such as load analysis, prediction of defect insurgence, material flow and so on. In the past, this process was studied mostly by the upper bound method [2-3]; for example, Venkata Reddy et al.[2] carried out an upper bound analysis including strain hardening to compare different die shapes. The influence of several process variables was investigated such as the area reduction, the friction coefficient, the die length and so on. The proposed technique was combined with the slab method and was, also, able to predict the die pressure distribution showing good agreement with some compared to published experimental results. The prediction of the latter variable is important to avoid die breaking during the extrusion process and was already investigated in different papers [4]. Moreover, the introduction of finite element simulation heavily impacted with the process analysis and opened new perspectives [5-6]. Peng et al. [6], for instance, studied the influences of different parameters like the tapered billet and varying ram speed on the material flow pattern. Besides, the effectiveness of FEM simulation to predict material flow and the formation of the extrudate surface was proved by Velay et al. [7]. Extrusion is extensively used also to manufacture long, straight hollow components, with a constant section. Seamless tubes are, in fact, manufactured by several techniques such as rotary piercing, rolling and extrusion; it is important to highlight that the extrusion process is flexible enough to accommodate a wide range of sizes, materials and reductions compared to the other process. There

138

Advances on Extrusion Technology and Simulation of Light Alloys

are several parameters to be considered in order to obtain a good quality of extruded tubes, like the temperature of the metal in the deformation zone, the friction effects and the pressure in the joining material zone influenced by the dies shape. Venkata Reddy et al. [8] carried out a comprehensive investigation of an axisymmetric steady-state tube extrusion through a streamlined die by the finite element method to study the influence of process variables on tool design and final product quality for a strain hardening material. An analysis of the die land effect, an uncommonly investigated die extrusion parameter, on the lead extrusion pressures was experimentally and theoretically carried out by Ajiboye et al. [9]; they included, the ironing effect at the die land using the upper bound method. Onuh et al.[10], instead, made an experimental investigations about the effects of die reduction in area, die angle, loading rate on the quality of the extrusion products, extrusion pressures and flow pattern of cold extruded aluminium and lead alloys shapes of inner circular sections with four symmetrical projections. They found the radii of curvature for both the worked materials and the average hardness values of the extruded products along the projections and along the circumferential solid positions increase with increase in die reduction in area, and slightly with increase of the loading rates. Onuh discussed the extrusion defects and the flow patterns of complex-shaped section. The strong reduction in area heavily impacts on the remeshing-rezoning code capability and this becomes a possible reason of results inaccuracy [11]. The investigation here addressed concerns lead tube extrusion; pure lead was chosen for experimental analysis due to its high ductility which allows to carry out the process at room temperature. The scope of the work was to measure both the total load and the pressure on a point placed on the porthole. It is clear that the measure of the pressure on the porthole could be a suitable variable in order to verify the accuracy of any numerical simulation of the process. In fact, pressure is a local variable which depends on several simulation and material parameters; therefore its effectiveness to “measure” the accuracy of model is much larger than other global variables, such as the extrusion punch load. The investigated problem and the experimental equipment As mentioned, a 3D tube extrusion process was carried out; the process sequence starts from a initial cylindrical billet that, due to a suitable porthole, undergoes a first splitting action followed by a welding to create the tube wall. Fig.1 reports the experimental equipment; the porthole can be divided in two different parts called respectively the middle and the lower die. The first one was drawn with four separated holes, obtained by electro-discharge machine, that cause the material splitting during the extrusion process. The diameter of the central part of the middle die is equal to the tube internal width. The lower part, instead, is used to limit the axial material movement and to cause the welding and the tube creation. Fig.2 reports the sketch of the equipment. To measure the pressure on a point placed on a porthole, a special device was created developing a proper system based on the use of a small load-cell with a maximum load capacity equal to 2kN. For sake of completeness, two different equipments were manufactured with the aim to obtain a defected and a round tube. In fact, one of the aims was the investigation of material flow and resulting pressure on the welding surface in order to verify the code ability to predict also these variables.

Key Engineering Materials Vol. 367

139

Figure 1:The experimental equipment used for the lead tube extrusion process. A sensor pin was developed in order to transmit a signal to the load cell proportional to the pressure revealed on the porthole. The pin manufacturing was a very critical task since its dimension has to be a trade between friction occurrence and material protrusion through the external surface and die hole.

Figure 2: A sketch of the built equipment. The initial material billet diameter was 45 mm; the L/D ratio was equal to 2, i.e. lower than the industrially utilized one, but sufficient to ensure steady state conditions during the process. Besides, the principal dies dimensions for the experimental analysis are reported in Table 1. Table 1: The principal dies dimensions for the different equipments. Dimensions Equipment 2 Equipment 1 [mm] L0 20 17 L1 23 23 L2 6 26 L3 90 42 R0 9 9 R1 11 10.70 - 9.95

140

Advances on Extrusion Technology and Simulation of Light Alloys

As far as material is concerned, cast lead was utilized for the tests. In fact, for sake of simplicity, the experiments were carried out at room temperature and due to the heaviness of the process, other materials could determine relevant problems for the die and equipment integrity. The equipment was mounted on a hydraulic machine Instron/MTS 1276 able to provide a maximum ram load equal to 1000 kN. The total punch load was measured by using the testing machine cell. The plastic behavior of lead was investigated by means of a set of compression tests with different strain rates on cylindrical specimens, run on an Instron 8501 hydraulic testing machine. No significant strain rate influence was found and so, for sake of simplicity, a power law, was determined, according to the next Eq. 1. σ = 48.9ε0.289.

(1)

Fig. 3 reports the shape of the extruded tube using the equipment 1; material divergence can be observed.

Figure 3: Incorrect material welding during the first experimental campaign. The results of the above test showed that the process needs to be optimized in order to obtain the complete tube welding. As introduced, this task was done using the equipment 2 and the tube in Fig.4 was obtained at the end of the process.

Figure 4:The extruded tube obtained using the optimized equipment 2.

Key Engineering Materials Vol. 367

141

Numerical Analysis In the last years different numerical approaches for the simulation of metal forming problems were proposed. Among them the most diffused are probably the updated-Lagrangian and the Eulerian formulation. The former is able to describe the generation of new surfaces but is usually characterized by a severe mesh distortion in the extrusion area, that requires very efficient remeshing algorithms; the latter is capable to handle complex geometrical problems but does not permit free surface generation. Recently some improvements were introduced into the so-called Arbitratry Lagrangian Eulerian (ALE) approach, but some limitations still exist. A revolutionary solution will be probably achieved through the introduction of the meshless analysis [12] but its effectiveness and stability have to be fully demonstrated. In the present work, a commercial FE code, namely Deform 3D, supplied by SFTC was utilized as simulation tools. The code implements the updated Lagrangian formulation, based on the virtual work principle associated with the incompressibility and the non-penetration condition. The Newton-Raphson method is used to solve the non linear equation system which results after the discretization of the above mentioned equation. As far as material model is concerned, an isotropic rigid-viscoplastic formulation was chosen; in this case, as above mentioned, the flow stress is just function of the plastic strain. In detail, the punch and the different dies were modeled as rigid surfaces while the workpiece was initially discretized by means of 30000 tetrahedral elements. In this way, a good trade-off among contact management efficiency, generated surface resolution and computational time was obtained. About 35 hours were necessary on a PC-Dual-Xeon 2,8 GHz with 4GB RAM to complete the extrusion simulation. The constant shear formulation was used to model friction phenomena and a shear factor m=0,45 was used all over the investigated cases; this value was set to obtain a good comparison between experimental and numerical punch load. Fig.5 reports a typical FE analysis of the extrusion process.

Material Separation Lines

Figure 5: FE simulation of the optimized tube extrusion process. The simulation of hollow components extrusion introduces a critical aspect since material welding (after the previous separation in correspondence of the porthole) has to be properly modelled; material separation lines are, in fact, shown in Fig.5. Besides, the mesh becomes too distorted in same particular zones and a new one must be generated; the variables associated with material history must be mapped from the old to the new mesh by rezoning procedures, introducing,

142

Advances on Extrusion Technology and Simulation of Light Alloys

obviously, additional errors. To overcome the above said problems the meshless formulation can be utilized. Discussion of results about experimental campaign The experimental punch load required to carry out the forming process, as well as the numerical one, is reported in Fig. 6. Punch Load

Load(kN)

1000 800 600 400

Experimental

200

Numerical

0 0

5

10

15

Stroke(mm)

Figure 6: Punch load (experimental and numerical comparison). There is a good fitting between numerical and experimental result, at least, until the beginning of tube formation; at this time, above all because of the great mesh distortion, the FE outcome presents a quicker punch load increment that causes a maximum discrepancy between the two curves equals to 150 kN. The final load steady state, typical for a extrusion process, instead, shows a similar value for the two different analyses type. Another interesting comparison was carried out with reference to the predicted local pressure on the middle die. As above mentioned, in order to reduce the computational time, the dies were considered rigid; for this reason, the normal stress on the workpiece in contact with the investigated area was used as comparison value. The experimental and numerical results about the pressure state was reported in Fig.7. Bottom_Die_Pressure

Pressure(MPa)

750 600 450 300 150

Experimental Numerical

0 0

5

10

15

Stroke(mm)

Figure 7: Bottom die pressure (experimental and numerical comparison) The curves show a similar behaviour. Finally, it is very interesting to numerically analyze the difference in material flow and resulting welding pressure when using equipment 1 and 2, in which the tube is broken and well formed, respectively.

Key Engineering Materials Vol. 367

143

As it can be easily observed (Fig. 8), equipment 2 presents the best characteristics to allow the material welding thanks to a higher compressive circumferential stress. EQUIPMENT 1

EQUIPMENT 2

STRESS – X/R MPa 50

−30

−110 σ = -47MPa

σ = -143MPa

−190

X Y

−270

Z −350

Figure 8: The circumferential stress in a extruded tube section. Conclusions An experimental equipment to measure extrusion load and pressure and to analyze material flow under different geometrical conditions was developed in this work. Some interesting fundamental evidences, in order to better understand the hallow tube extrusion were obtained. Finally, a heavy 3D simulation of the process was performed to verify what is the real potential of this technique to model this kind of complex processes; besides, the numerical simulations permit to achieve a better understanding of the phenomenon and to highlight the causes of the macroscopic observations, through the analysis of some local variables distributions in the material, with particular reference to the extrusion area.

Acknowledgement This research is funded by Italian Ministry for University and Research (MIUR). The authors would like to thank Mr. F. Pulice for his technical contribution to the development of this work.

References [1] S. Kalpakjian, in: Manufacturing Processes for Engineering Materials, edited by: AddisonWesley, 3rd ed. (1997). [2] N. Venkata Reddy, P.M. Dixit, and G.K. Lal: Journal of Materials Processing Technology vol.55, (1995) p. 331. [3] H. S. Metha, A.H. Shabaik, and Kobayashi: ASME J. Engng Ind. 92 (1970) p. 403. [4] R. Di Lorenzo, L.Filice, and F. Micari: Wire 5/2000 p. 36. [5] Zou Lin, Xia Juchen, Wang Xinyun and Hu Guoan: Journal of Materials Processing Technology 142 (2003) p. 659.

144

Advances on Extrusion Technology and Simulation of Light Alloys

[6] P. Zhi Peng and Terry Sheppard: Modelling Simul. Mater. Sci. Eng. 12 (2004) p. 745. [7] X. Velay, X. Duan and T. Sheppard: Mater. Sci. Forum 3807–12 (2003) p. 426. [8] N. Venkata Reddy, P.M. Dixit, and G.K. Lal: Int. J. Mach. Tools Manufact. Vol.36, No. 11, (1996) p. 1253. [9] J.S. Ajiboye and M.B. Adeyemi: Journal of Materials Processing Technology 171 (2006) p. 428. [10] J.S. Ajiboye and M.B. Adeyemi: Journal of Materials Processing Technology 132 (2003) p. 274. [11] L. Filice, I. Alfaro, F. Gagliardi, E. Cueto, F. Micari and F. Chinesta, Proc. of the 9th Esaform Conf., Glasgow (2006) p. 79. [12] I. Alfaro, E. Cueto, M.A. Martinez and M. Doblarè, Proceedings of The 7th Esaform Conference of Material Forming, Trondheim, Norway, April 28-30, 2004, p. 49.

Key Engineering Materials Vol. 367 (2008) pp 145-152 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/KEM.367.145

Analysis of Metal Flow through a Porthole Die to Produce a Rectangular Hollow Profile with Longitudinal Weld Seams G. Liu 1,a, J. Zhou 2,b, K. Huang 1,c and J. Duszczyk 2,d 1

2

School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, China

Department of Materials Science and Engineering, Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands a

[email protected], [email protected], [email protected], [email protected]

Keywords: Extrusion; 7020 aluminium alloy; FE simulation

Abstract. A detailed analysis of metal flow through a porthole die to produce a rectangular hollow aluminium profile was performed by means of three-dimensional FE simulation using DEFORM 3D. It was aimed at revealing the flow patterns of a medium-strength aluminium alloy 7020 through a porthole die and gaining an insight into the formation of longitudinal weld seams inside the welding chamber during extrusion. In the case of extruding a rectangular hollow profile through a porthole die with four ports, two neighbouring ports were different from each other. Using an FE model including these two ports, different flow patterns of two individual metal streams were revealed. The 3D FE simulation also showed how two unequal metal streams contacted each other and became bonded in the welding chamber under a certain hydrostatic pressure and at a certain temperature, before the metal flew through the die bearing. The difference in velocity between the metal streams led to uneven flow at the die bearing and thus a wavy extrusion nose. Introduction Being a cost-effective method of producing tubular and hollow profiles, hot extrusion is extensively used in the aluminium industry. For low- and medium-strength aluminium alloys, a tubular profile can be easily produced using a conventional direct extrusion press and a porthole die. Upon entering the mandrel of a porthole die, the billet metal is split into distinct metal streams, then these streams rejoin and become welded by high pressure in the welding chamber of the die, and finally the tubular profile gains its shape and dimensions in the die bearing. In the same way, a hollow profile of a certain geometrical complexity can be produced in a semi-continuous fashion, but the extrusion die design and process control become more complicated [1]. A drawback of using such an extrusion tooling setup is that the tubular or hollow profile so produced contains a number of weld seams along its length. For most of non-structural applications of tubular and hollow extrusions, the weld seams do not pose problems in terms of mechanical properties. However, for load-carrying structural applications, the quality of bonding at the weld seams is often a concern. Reliable inspection techniques and universal criteria have not been well established. Even if they are, inspection is carried out on the basis of sampling from a batch of extrusions, inevitably leaving some degree of uncertainty about the quality of each and every extrusion in the batch. Moreover, rejection of extrusions at the end of production chain means significant losses in material, manhour, machine hour and energy. It is therefore required of both extrusion die designers and extrusion process engineers to make it sure that the longitudinal weld seams are sound. It is obvious that the weld quality depends on the complex thermal and mechanical events occurring inside the welding chamber of a porthole die with a set of geometrical parameters. The thermal and mechanical parameters inside the welding chamber are experimentally immeasurable. While it is known that the welding is a solid-state bonding process, it cannot be directly monitored. This imposes major constrains on the investigations by physical means to understand the dependence of bonding on the geometrical parameters of the die and the thermal and mechanical

146

Advances on Extrusion Technology and Simulation of Light Alloys

parameters inside the die. In recent years with remarkable advances in computing power and process-modelling software based on the finite element (FE) method, the investigations of the extrusion process to produce tubular and hollow profiles have mostly been resorted to FE simulation. While direct verification of the results from FE simulation is not straightforward, it is now possible to make quantitative analysis of temperature, strain, stress, metal velocity, their distributions inside the welding chamber and their variations throughout the process cycle in relation to die geometrical parameters, billet material and extrusion process parameters. Donati and Tomesani [2], for example, successfully used the DEFORM 3D software to investigate the effect of extrusion process parameters and die geometry on the weld quality during the extrusion of the AA6082 aluminium alloy into an H-shaped profile with a longitudinal weld seam. Jo et al [3] used the same software to reveal the metal flow and weld seam formation in the transient state during the extrusion of the AA7003 aluminium alloy and investigated the effects of billet temperature, bearing length and product thickness on extrusion load, welding pressure and surface quality. In all preceding research, the metal flow through the two neighbouring ports was equal and the weld was symmetrically placed so that an artificial rigid plane in alignment with the tip of the leg could be introduced to prevent these two metal streams from coming into intimate contact with each other. However, in reality, a large proportion of hollow aluminium profiles are produced using porthole dies with unequal ports and, because of uneven flow between two neighbouring metal streams, it is impossible to introduce such a dividing plane. In the present study, an attempt was made to gain an insight into the metal flow through a porthole die with two different neighbouring ports to form a thin-walled rectangular profile. FE simulation was performed with no dividing plane artificially imposed between two neighbouring metal streams. Real contact between two neighbouring streams was realized so that the welding phenomena inside the welding chamber could be revealed. The study was intended to provide a basic understanding of metal flow through a typical porthole die. It will pave the way for further research on the effect of die geometeric parameters on metal flow and weld quality. It must be mentioned again that the metal flow through the porthole die and the distributions of velocities, stresses and strains inside the porthole die, revealed from 3D computer simulation, are not experimentally measurable and, as a result, validation of the simulation results through experimentation is rather difficult. The results presented below are those obtained from FE simulations. Simulation and Experimental Details Materials and Geometry. A medium-strength aluminium alloy AA7020 was used as the billet material and the AISI H13 hot-work tool steel as the material for all the extrusion tooling (die, container and follower pad). The physical properties of the materials were retrieved from the DEFORM materials library in the DEFORM 3D software package. Fig. 1 illustrates the cross section of the rectangular hollow profile with a wall thickness of 4.65 mm and part of the porthole die used to produce this profile. Because the billet, extrusion tooling (container, die and follower pad) and extrudate were all symmetrical, only one-forth of these objects were modelled to save computational time. The dimensions of the billet and container as well as the extrusion process parameters used in the present FE simulations are given in Table 1. The process simulated was simplified from a commercial extrusion case, but the scale remained unchanged, i.e. extrusion from an 8 inch billet to produce a 161.9 mm wide hollow profile. Table 1 Dimensions and initial temperatures of the workpiece and extrusion tooling Billet length [mm] 812 Reduction ratio Billet diameter [mm] 202 Billet temperature [°C] Container insider diameter [mm] 203 Tooling temperature [°C] Container outside diameter [mm] 360

19.6 450 400

Key Engineering Materials Vol. 367

147

(a) (b) Fig. 1 (a) Cross section of the rectangular hollow profile with the shaded area selected for FE simulation and (b) porthole die used to produce the profile. FE Model, Simulation Parameters, Flow Stress and Friction Conditions. Fig. 2 shows the FE model for the billet and extrusion tooling to produce the rectangular hollow profile. All the extrusion tooling was meshed with tetrahedral elements and its heat exchanges with the workpiece were allowed. The simulation parameters used are given in Table 2. The total number of elements in the billet is 40,000 - 80,000 depending on the deformation complexity at a given ram displacement.

(a) (b) Fig. 2. (a) FE model for the billet and extrusion tooling (1/4 model) and (b) meshed porthole die. Table 2 Simulation parameters and boundary conditions Total number of elements in the billet Minimum size of an element [mm] Mesh density type Relative interference depth Surrounding temperature [°C]

40,000 ~ 80,000 1.3 absolute size 0.3 300

A thermo-viscoplastic material model in the DEFORM 3D v.5.1 software package was employed for the workpiece and a thermo-rigid material model for the extrusion tooling. Both of these models neglected the elastic behaviour of the workpiece and the extrusion tooling. The flow stress–strain data of the AA7020 alloy determined from hot compression tests at temperatures from 250 to 575 °C and strain rates from 0.01 to 100 s-1 and then corrected for deformational heating [4] were used as the input data of the workpiece material. The friction forces in the constant shear model defined as fs = mk, where fs is the frictional stress, k the shear yield stress and m the friction factor, were incorporated into the simulation. The friction factor between follower pad and billet, between container and billet and between die mandrel and

148

Advances on Extrusion Technology and Simulation of Light Alloys

billet was chosen to be 1.0 to represent the extreme case of extrusion with sticking interfaces at temperatures above 430 °C. A friction factor of 0.7 was chosen at the die plate interfaced with the workpiece, considering decreasing friction as the workpiece flew toward the die exit. Results and Discussion Metal Flow through the Porthole Die and Evolution of Extrusion Pressure. In Fig. 3, a series of mesh images along the ram displacement s are presented to illustrate the metal flow to fill the ports and welding chamber and then the metal to be extruded into a rectangular hollow profile. The results from the present FE simulation clearly show that the following stages can be distinguished during the initial phase of the process when metal flows into the porthole die: (i) dividing (Fig. 3a) and filling of the ports (Fig. 3b), (ii) filling of the welding chamber (Fig. 3c), and (iii) forming at the die bearing (Fig. 3d). These distinctive stages correspond to the changes of the pressure curve in the extrusion pressure/ram displacement diagram, as shown in Fig. 4, which is consistent with experimental observations [5]. From Fig. 4 it is clear that, after the upsetting of the billet in the container (being 1 mm larger than the billet), the process enters the first stage with pressure increasing from H to I. It is in the first transient state. After reaching the first pressure peak at I, the process moves on to fill the ports with decreasing extrusion pressure as the friction between the container and billet decreases. After the four ports are completely filled, the billet material flows towards the bottom of the welding chamber. The second stage starts at J and finishes at K, as the metal flows sideways to fill the welding chamber, and the two neighbouring metal streams meet each other and are forced to bond together. At this stage, the process is in the second transient state. After reaching the maximum extrusion pressure at K, the process enters the final stage of extrusion.

(a) Dividing (s = 30.0 mm)

(b) Filling of the ports (s = 94.0 mm)

(c) Filling of the welding chamber (s = 119.0 mm) (e) Start of extrusion (s = 127.9 mm) Fig. 3 Metal flow through the porthole die during the initial phase of an extrusion cycle.

Key Engineering Materials Vol. 367

600

Extrusion pressure (MPa)

K

Simulation results at 6 mm/s

500

149

Extrusion

Dividing Extrusion of legs

400

I

300

J

200

Welding chamber filling Upsetting

100

H 0 0

20

40

60

80

100

120

140

Ram displacement (mm)

Fig. 4 Pressure/ram displacement diagram obtained from FE simulation at a ram speed of 6 mm/s. Fig. 5 shows the flow of two neighbouring metal streams towards each other on a cross section near the bottom of the welding chamber at a position of z = -143 mm. It is clear that at a ram displacement of 91.5 mm (Fig. 5a), the front of the metal stream towards the shorter side of the rectangular profile has reached the bottom of the welding chamber, while the neighbouring port with a larger surface area and thus greater friction is still being filled. As the process proceeds to a ram displacement of 96.5 mm, the metal eventually to form the longer side of the rectangular profile reaches the bottom of the welding chamber, as illustrated in Fig. 5b. Thereafter, over a ram displacement from 96.5 to 104 mm, the metal in the welding chamber to form the shorter side of the rectangular profile seams to cease flowing further, Figs. 5b and 5(c), while the metal to form the longer side of the profile keeps filling the welding chamber. At a ram displacement of 117 mm, the welding chamber is mostly filled, as shown in Fig. 5d. Then, the metal flows sideways, which is also termed as the sideways extrusion stage [6]. Intimate contact between two neighbouring metal streams at the welding chamber has been established at a ram displacement of 124 mm, Fig. 5e. It is remarkable that the weld seam is formed, not exactly at the corner, but near the corner of the core that is supported by the four legs of the mandrel. As the process proceeds further, the metal in the welding chamber gradually accumulates and the welding chamber is completely filled at a ram displacement of 128 mm, as illustrated in Fig. 5(f). The two neighbouring metal streams are combined to form a sound weld seam. As the hydrostatic pressure increases in the welding chamber, metal flows out of the die aperture.

(a) s = 91.5 mm

(b) s = 96.5 mm

(c) s = 104 mm

(d) s = 117 mm

(e) s = 124 mm

(f) s = 128 mm

Fig. 5 Filling of the welding chamber and then welding on the cross section of z = -143 mm inside the welding chamber.

150

Advances on Extrusion Technology and Simulation of Light Alloys

Velocity Distribution inside the Porthole Die. Fig. 6 shows the velocity fields at selected simulation steps along the ram displacement. The metal flow through the four ports towards the bottom of the welding chamber is in the main oriented toward the z direction, as shown in Fig. 6a. At this stage, the reduction ratio is quite low, only 2.25. At a ram speed of 6 mm/s, the average velocity of the metal stream near the shorter side of the rectangular profile is 12 mm/s, while that near the longer side of the profile is 9 mm/s. Once the metal streams have reached the bottom of the welding chamber, the metal flows sideways and then the neighbouring streams start to get in contact with each other behind the legs, as shown in Fig. 6b. The velocity distribution becomes broader with the lowest velocity still at the container/die face corner (illustrated by the contour line A) and the highest velocity of 20 mm/s at the front of the metal stream near the longer side of the rectangular profile. As the process proceeds further to a ram displacement of 125 mm, Fig. 6c, the metal streams are brought to intimate contact and bonded with each other, and then the extrusion nose forms at the die bearing. The velocity of the metal at the die bearing entrance becomes larger and the extrusion nose has the highest velocity. As the velocities of neighbouring metal streams are different, the velocity at the extrusion nose is not uniform, varying from 16.7 mm/s near the shorter side of the profile to 33.5 mm/s near the longer side of the profile. As a result, the metal on the longer side of the profile is first extruded out of the die bearing through the longer side of the die land and the extrusion nose appears to be wavy, as illustrated in Fig. 3e.

(a) s = 94.0 mm

(b) s = 117.0 mm

(c) s = 125.0 mm

Fig. 6. Velocity fields (mm/s) in the welding chamber at selected simulation steps of an extrusion cycle. Fig. 7 shows the velocity fields on the A-A, B-B and C-C sections as indicated in Fig. 1. The dead metal zones with very low velocities are located at the corner between the die face and container (Zone I) and in the upper corner of the welding chamber (Zone II). It is interesting to see that the metal velocity in the corner between the bottom and the sidewall of the welding chamber is not really very small and there is no dead metal zone. The reason may be that the velocity difference between the two neighbouring metal streams from two unequal ports makes sideway flow at the welding chamber bottom relatively easy, even along the corner.

A-A

B-B

C-C

Fig. 7 Velocity fields (mm/s) on the A-A, B-B and C-C sections of the workpiece (see Fig. 2).

Key Engineering Materials Vol. 367

151

Temperature Distribution inside the Deforming Workpiece. Fig. 8 shows the temperature distributions inside the workpiece during extrusion. From Fig. 8a it is clear that, during the filling of the ports, the temperature of the metal inside the die varies from 422 to 438 °C. While the ports are being filled, the temperature differences become larger with the front of the metal stream being colder than the rest, as a result of heat conduction to the die. The highest temperature appears in the middle of the metal stream towards the shorter side of the core where larger deformation and smaller heat loss occur. As shown in Fig. 8c, at a ram displacement of 122 mm, the weld seam is formed at a temperature of about 420 °C. As the process proceeds further, the temperature of the workpiece becomes evener. At a ram displacement of 128 mm, the temperature of the extrudate is around 413 °C, as shown in Fig. 8(d).

(a) s = 91.5 mm

(b) s = 119mm

(c) s = 122mm

(d) s = 128 mm

Fig. 8 Temperature evolution (°C) during the filling of the ports and welding chamber and subsequent extrusion. Mean Stress Distribution inside the Deforming Workpiece. Fig. 9 shows the mean stress distributions in the workpiece during extrusion. (Mean stress is the average value of the three principal stress components.) Before the metal streams reach the bottom of the welding chamber, the mean stress is positive (see the metal steam towards the longer side of the rectangular profile in Fig. 9a). While the welding chamber is being filled, the mean stresses become all negative, Figs. 8(b) to (c), which means that the metal is under hydrostatic pressure, a necessary condition for solid-state bonding. At a ram displacement of 128 mm (Fig. 9d), the mean stresses in the welding chamber range from -135 to -223 MPa, leading to weld seam formation.

(a) s = 91.5 mm

(b) s = 119 mm

(c) s = 122 mm

(d) s = 128 mm

Fig. 9 Mean stresses (MPa) during the filling of the ports and welding chamber and subsequent extrusion. Effective Strain Distribution inside the Workpiece. Fig. 10 shows the effective strain distributions in the workpiece. It can be seen that the maximum effective strain in the workpiece becomes greater with increasing ram displacement. At a ram displacement of 91.5 mm, the effective strains are quite close to each other, resembling the ordinary multi-hole extrusion. However, as ram advances to 119 mm, the effective strains in the metal stream towards the longer side of the

152

Advances on Extrusion Technology and Simulation of Light Alloys

rectangular hollow profile become greater than those in the other metal stream. With ram advancing further, Figs. 10c to 10d, the effective strains tend to be even again, as a result of the contact between these metal streams and the formation of weld seams. The effective strain is the largest when the metal flows through the die bearing, see Fig. 10d.

(a) s = 91.5 mm

(b) s = 119 mm

(c) s = 122 mm

(d) 128 mm

Fig. 10 Effective strains during the filling of the ports and welding chamber and subsequent extrusion. Conclusions 1. The present FE simulation of aluminium extrusion through a porthole die with unequal ports shows distinctive stages of the process: (i) dividing and filling of the ports, (ii) filling of the welding chamber and welding, and (iii) forming at the die bearing. These stages correspond to the changes of extrusion pressure during the initial phase of the process. 2. There is indeed a velocity difference between two neighbouring metal streams when they flow into the welding chamber. The weld seam is formed near the corner of the rectangular core of the die after the two streams become contacted with each other on the shorter side of the rectangular profile. The inhomogeneity of flow velocity through these two ports leads to a wavy extrusion nose. 3. The hydrostatic pressure in the workpiece increases as ram advances. As the welding chamber is completely filled, the pressure reaches a level sufficient for solid-state bonding. In the present case, the weld seam is formed at a mean stress of 223 MPa and at a temperature of 420 °C. References [1] T. Sheppard: Extrusion of Aluminium Alloys (Kluwer Academic Publishers, Dordrecht, 1999). [2] L. Donati and L. Tomesani: J. Mater. Process. Techno. Vol. 153-154 (2004), p. 366. [3] H.H. Jo, C.S. Jeong, S.K. Lee and B.M. Kim: J. Mater. Process. Techno. Vol. 139 (2003), p. 428. [4] L. Li, J. Zhou and J. Duszczyk: J. Mater. Process. Techno. Vol. 172 (2006), p. 372. [5] G. Liu, J. Zhou and J. Duszczyk: submitted to J. Mater. Process. Techno. (2007). [6] N.C. Parson, J.D. Hankin and A.J. Bryant, in: Proceedings of the Fifth International Aluminium Extrusion Technology Seminar, Vol. II (Aluminium Association and Aluminium Extruder’s Council, Wauconda, Illinois, 1992), p. 13.

Key Engineering Materials Vol. 367 (2008) pp 153-160 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/KEM.367.153

Simulation-Based Design of Ram Speed Profile for Isothermal Extrusion L. Li1,a, H. Zhang1,b, J. Hu1,c, J. Zhou2,d and J. Duszczyk2,e 1

State Key Laboratory of Advanced Design and Manufacture for Vehicle Body, College of Materials Science and Engineering, Hunan University, Changsha, Hunan 410082, China 2

Department of Materials Science and Engineering, Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands a

[email protected], [email protected], [email protected], d [email protected], e [email protected]

Keywords: extrusion; magnesium; FE simulation

Abstract. Isothermal extrusion is a very much desired technology. However, its implementation in the light-metal extrusion practice has, up till now, been technologically constrained. In an attempt to realise isothermal extrusion, a simulation model based on the PID control algorithms was developed to establish ram speed profiles that could prevent extrudate temperature from further increase after an initial rise during an extrusion cycle. With this simulation model, extrusion ram speed could be adjusted in real time according to the simulated exit temperature. A case study was conducted on the simulated extrusion of a magnesium alloy AZ31B into a hollow profile. The results showed significantly improved temperature homogeneity not only along the extrudate length but also on its cross section in the case of extrusion in the isothermal mode with a designed ram speed profile. In addition, die temperature varied over a narrower range and the force acting on the die face was more stable over the process cycle, in comparison with extrusion in the conventional iso-speed mode. Introduction Extrusion is a thermomechanical process in which a preheated billet is forced to go through a die with a predetermined orifice. Mechanical and tribological interactions between the billet and the extrusion tooling (stem, container and die) result in complex compressive and shear stresses in the billet. The process is further complicated by the heat generated from deformation and friction, leading to continuous changes of billet temperature and extrudate temperature during an extrusion cycle [1]. Any inhomogeneity in extrudate temperature at the die exit within each extrusion cycle and between extrusion cycles may lead to undesirable variations in the shape, dimensions, microstructure and mechanical properties of the extruded product. For consistent product quality, the process may best be run in the isothermal mode [2-4]. Up till now, the success in implementing isothermal extrusion in practice across the light-metal extrusion industry in the world has been highly limited. There are many technological challenges. With the recent development of computational technology, the finite element (FE) method has been proven to be a powerful tool to predict both experimentally measurable and immeasurable process parameters and to facilitate the modifications of process conditions. The simulation results of Chanda et al [1], for example, showed that stepwise ram speed reduction enabled the extrudate temperature to stay within a prescribed range and, moreover, the productivity to increase, as a result of an increased average ram speed per extrusion cycle. The FE study on extruding 6xxx aluminium alloys into simple rods, conducted by Venas et al [5], confirmed that isothermal extrusion could be

154

Advances on Extrusion Technology and Simulation of Light Alloys

achieved by using a taper-heated billet. Moreover, in comparison with the conventional extrusion from a uniformly preheated billet, to reach the same maximum extrusion pressure and exit temperature, the isothermal extrusion from a taper-heated billet could increase the productivity by 20 - 25%. The present authors [6-9] explored the possibilities of determining ram speed profiles and billet temperature distributions for the isothermal extrusion of aluminium alloys by means of FE simulation. Their results showed that an optimum ram speed profile or an optimum billet temperature distribution could indeed be determined from computer simulation, but it would need a large number of simulation runs. While the idea and methodology are of academic interest, it is yet quite time consuming and computational intensive. Undoubtedly, with future developments in computational capabilities in the future, the procedure to generate an optimum setting for isothermal extrusion will take an industrially acceptable time. The aim of the present research was to develop a simulation model that would allow a ram speed profile for isothermal extrusion to be determined efficiently and effectively. A case study was conducted to run simulated isothermal extrusion to produce a hollow magnesium profile. Simulation Details The workpiece material used in the present three-dimensional FE simulations was a wrought magnesium alloy, AZ31B. It was cast and pre-extruded into a rod with a diameter of 47.2 mm. The rod was subsequently used as a billet with a length of 200 mm for further extrusion into a simple hollow profile (a square tube) with an outside width of 18 mm and a wall thickness of 1.5 mm. By taking advantage of its symmetry, only one-eighth of the billet, extrudate and extrusion tooling were modelled, which considerably reduced the calculation time. The extrusion tooling comprised of container, die and stem was made of the H13 tool steel. The container had a diameter of 50 mm. Because of a clearance of 2.8 mm between the container bore and the billet, upsetting took place prior to extrusion to fill the container completely. The initial temperatures of the billet and extrusion tooling, ram speed and extrusion ratio are given in Table 1. Table 1 Extrusion process and simulation parameters Process Iso-speed Isothermal o Billet temperature [ C] 350 350 o Die temperature [ C] 300 300 o Stem temperature [ C] 300 300 o Container temperature [ C] 300 300 Ram speed [mm/s] 1.3 3 (initial ram speed) Extrusion ratio 19.6 19.6 Friction factor 1 1 A DEFORM 3D software package was used for FE simulation. The workpiece was considered thermal visco-plastic and the extrusion tooling thermal rigid. Both of these material models neglected the elastic behaviour of the workpiece and tooling. The flow stress data of the AZ31B alloy as a function of strain, strain rate and temperature were obtained from hot compression tests over a temperature range from 300 to 500 °C and a strain rate range from 0.03 to 90 s-1[10]. The flow stresses obtained from the compression tests were corrected for temperature rise during the tests, caused by deformation at high strain rates. The friction at the workpiece/tooling interfaces was

Key Engineering Materials Vol. 367

155

assumed to be of shear type. A constant friction factor of 1 was assumed at the workpiece/tooling interfaces. Other simulation parameters are detailed elsewhere [10]. Results and Discussion Isothermal Extrusion through Real-Time Ram Speed Adjustment According to the Principle of PID Control. Proportional-integral-derivative controller (PID controller) is a generic control loop feedback mechanism widely used in industrial control systems. A PID controller attempts to correct the error between a measured process variable and a desired setpoint by calculating and then outputting a corrective action that can adjust the process accordingly. The PID controller calculation (algorithm) involves three separate parameters; the proportional, integral and derivative values. The proportional value determines the reaction to the current error, the integral determines the reaction based on the sum of recent errors, and the derivative determines the reaction to the rate at which the error has been changing. The weighted sum of these three actions is output to a control element such as the position of a control valve or power into a heating element. Fig. 1 shows a block diagram of a PID controller.

Fig. 1 Block diagram of a PID controller In the present research, the PID control algorithms were applied to establish a simulation model for the design of a ram speed profile for isothermal extrusion. With this model, a ram speed profile for a particular alloy and for a given extrudate shape could be determined with a few or even one single simulation run. In this way, the time and computer resources could be significantly saved and the isothermal extrusion technology might be brought one step closer to implementation on the shop floor. During the simulation of the extrusion process, an initial ram speed was input into DEFORM 3D. As soon as the exit temperature reached a critical value, ram speed would be adjusted according to the following equations: ∆v(k ) = At (k ) − Bt (k − 1) + Ct (k − 2) .

(1)

A = K P + KI + KD .

(2)

B = KP + 2 KD .

(3)

156

Advances on Extrusion Technology and Simulation of Light Alloys

where ∆v(k ) is the ram speed increment, t (k ) , t (k − 1) and t (k − 2) are the control errors at k, (k − 1) and (k − 2) sampling points, respectively, i.e. the difference between the simulated exit temperature T and the critical exit temperature T0 , and K P , K I and K D are proportional coefficient, integral coefficient and derivative coefficient, respectively. As a matter of fact, K P , K I and K D are fitting parameters and can be determined by using the cut-and-try method, according to the simulation results obtained at the initial stage of an extrusion cycle. In the present research, it was found that the simulated exit temperature could be controlled within a narrow range by adjusting the proportional item and the integral item in the PID control algorithms, while the derivative item could be neglected. In the particular case of extruding the magnesium alloy into a square tube, both the K P and K I settings were determined to be 2. Fig. 2 shows a ram speed curve determined from FE simulation for isothermal extrusion to produce the magnesium tube. The initial ram speed was set at 3 mm/s. After the simulated maximum exit temperature reached a critical value of 400 °C, ram speed decreased first quickly and then gradually and steadily. During the simulated extrusion, ram speed adjusted by itself. The slope of the ram speed change was calculated, according to the variation of the exit temperature by using Equation (1). In this particular example, the average ram speed of the simulated extrusion cycle was approximately 1.3 mm/s, corresponding to an exit speed of 1.53 m/min. 3.5

Ram speed,mm/s

3.0 2.5 2.0 1.5 1.0 0.5 0.0 0

20

40

60

80 100 120 140 160 180 200 Stroke,mm

Fig. 2 Simulated ram speed profile for the isothermal extrusion of AZ31 magnesium alloy into the square tube. Fig. 3 compares the exit temperatures between the simulated isothermal extrusion mode and the conventional iso-speed extrusion mode at the same average ram speed of 1.3 mm/s and with the same cycle time. It can be seen that, in both of the cases, the exit temperature rises steeply at the beginning of the process, due to deformation heat accumulated in the deformation zone in front of the die orifice. In the case of extrusion in the conventional iso-speed mode, the exit temperature increases continuously till the end of the cycle with an overall temperature rise of over 100 0C. However, with the ram speed profile designed for extrusion in the isothermal mode, the exit temperature remains quite stable after an initial rise of 50 °C. The exit temperature can be limited within a small range of 5 °C around the critical temperature of 400 °C over almost the whole extrusion cycle.

Key Engineering Materials Vol. 367

157

500 Isothermal process Iso-speed process,v=1.3mm/s

480 Temperature,℃

460 440 420 400 380 360 340 40

60

80

100 120 140 160 180 200 Stroke,mm

Fig. 3 Comparison in exit temperature between the simulated isothermal extrusion mode and the conventional iso-speed extrusion mode. Temperature Distribution and Variation. In the case of extrusion to produce a hollow profile, the extrudate outer surfaces, corners and tip regions would be expected to have higher temperatures than the rest of the section, due to heat generation in the shear bands between the deformation zone and the dead metal zone. However, in both of the cases of extruding the magnesium alloy into the hollow profile in the isothermal and iso-speed modes, the outer surface temperature was found to be lower than that of the inner surface, as shown in Fig. 4. The main cause for this temperature distribution might be that the temperature of the die cap was significantly lower than that of the mandrel that was surround by the hotter workpiece (Fig. 5). The minimum temperature on the cross section of the hollow profile was located at the outer corners where the surface area per volume and thus heat loss were the greatest on the whole profile cross section.

(a) (b) Fig. 4 Temperature redistributions on the cross section of the hollow profile at the die entrance and at a ram displacement of 60 mm: (a) in the isothermal extrusion mode and (b) in the iso-speed extrusion mode.

158

Advances on Extrusion Technology and Simulation of Light Alloys

A major difference between the isothermal extrusion mode and the conventional iso-speed mode was found to lie in the extent of temperature inhomogeneity on the cross section. It is obvious from Figs. 4a and b that during the extrusion in the conventional iso-speed mode, the temperature inhomogeneity on the cross section of the profile is far greater than that during the extrusion in the isothermal mode. At a ram displacement of 60 mm, the temperature difference between the outer corner and the inner surface is about 10 °C during isothermal extrusion (Fig. 4a), while it reaches 20 °C during iso-speed extrusion (Fig. 4b). The lower temperature inhomogeneity on the cross section of the profile leads to more homogeneous microstructures and mechanical properties of the extruded product.

Fig. 5 Temperature distribution in the porthole die during isothermal extrusion at a ram displacement of 60 mm. 460 Isothermal process Iso-speed process,v=1.3mm/s

Temperature,℃

440 420 400 380 360 340 320 20

40

60

80

100 120 140 160 180 200 Stroke,mm

Fig. 6 Variations of temperature at the bearing of the die cap during extrusion in the isothermal mode and in the iso-speed mode. Fig. 6 compares the temperature evolutions at the bearing of the die cap die during extrusion in the isothermal mode and in the conventional iso-speed mode at an average ram speed of 1.3 mm/s. It can be seen that throughout the extrusion cycle, the die cap temperature in the conventional iso-speed mode is all the time higher than that in the isothermal mode. The two temperature

Key Engineering Materials Vol. 367

159

evolution curves tend to diverge as the process proceeds, reaching a temperature difference of 40 °C at the end of the extrusion cycle. Obviously, in the isothermal extrusion mode, the extent of die temperature rise over the whole cycle is much less. In addition, after a ram displacement of 100 mm, the maximum die temperature becomes quite stable. These clearly present additional advantages as far as extrusion die performance and lifespan are concerned and should be taken into consideration in tool steel selection for extrusion dies, die heat treatment and surface treatment, all of which affects hot strength, hardness, fatigue resistance, wear resistance and in turn die costs, die performance and die life. Die Force Variation. The force acting on the die face during extrusion is an important parameter, as it influences the die deflection and thus extrudate dimensional accuracy as well as die life. Fig. 7 clearly shows that in the case of isothermal extrusion, the force on the die face is quite stable except the initial rise, mainly as a result of stable temperature in the deformation zone of the billet. In the case of extrusion in the conventional iso-speed mode, however, the die force decreases gradually and is halved at the end of the cycle, as a result of continued temperature rise in the deformation zone. The stable die force exhibited during isothermal extrusion presents another advantage over the conventional iso-speed extrusion with regard to the consistency of the dimensions and shape of the extrudate.

Fig. 7 Variations of the die force during extrusion in the isothermal mode and in the conventional iso-speed mode. Conclusions A simulation model based on the PID control algorithms has been developed for the efficient and effective design of ram speed profiles for isothermal extrusion. With this model, an optimum ram speed profile can be obtained from a few or a single simulation run. When the model is applied to the extrusion of the magnesium alloy AZ31 into a hollow profile, the exit temperature of the extrudate can be limited within a range of 5 °C over the vast majority of the extrusion cycle. In comparison with the conventional iso-speed extrusion, the extrusion in the isothermal presents additional advantages in temperature homogeneity on the extrudate cross section as well as die temperature and die load variations.

160

Advances on Extrusion Technology and Simulation of Light Alloys

References [1]

T. Chanda, J. Zhou and J. Duszczyk: J. Mater. Process. Tech. Vol. 114 (2001), p. 145.

[2]

A.K. Biswas and B. Repgen, in: Proceedings of the Sixth International Extrusion Technology Seminar, Vol 1, Aluminium Extruders Council, Eauconda, Illinois (1996), p 37.

[3]

M. Pinkham: Aluminium Today Vol. 14 (2002), P. 31.

[4]

Z. Peng and T. Sheppard, Modelling Simul. Mater. Sci. Eng. Vol. 12 (2004), p. 745.

[5]

I. Venas, J. Herberg and I. Skauvik, in: Proceedings of the Fifth International Aluminium Extrusion Technology Seminar, Vol. I, Aluminium Extruders Council, Eauconda, Illinois (1992), p.229.

[6]

L. Li, J. Zhou and J. Duszczyk: Model. and Simul. in Mater. Sci. Eng. Vol. 11 (2003), p. 401.

[7]

J. Zhou, L. Li and J. Duszczyk: J. Mater. Process. Tech. Vol. 146 (2004), p. 203.

[8]

L. Li, J. Zhou and J. Duszczyk: J. Mater. Process. Tech. Vol. 145 (2004), p. 360.

[9]

J. Zhou, L. Li and J. Duszczyk: J. Mater. Process. Tech., Vol. 134 (2003), p. 383.

[10] L. Li, J. Zhou and J. Duszczyk: J. Mater. Process. Tech. Vol. 172 (2006), p. 372.

Key Engineering Materials Vol. 367 (2008) pp 161-168 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/KEM.367.161

Input Parameters Determination for Predicting Ram Speed and Billet Temperature for the First Billet M. Sabater1,a, M.L. Garcia-Romeu1,b, J. Ciurana1,c 1

University of Girona, Dept of Mechanical Engineering and Industrial Construction, Campus Montilivi P-II, Girona 17071, Spain a

[email protected], [email protected], [email protected]

Keywords: First billet, ram speed, billet temperature, process parameters. .

Abstract. The aim of this paper is to present the results of the first step of a defined methodology for the neural network tool development. That first step is to studying the variables that have influence on extrusion process, especially in those that affect billet temperature and extrusion speed. In order to determine those parameters, a preliminary analysis was conducted with experimental data from real industry. Then, a multiple regression analysis was carried out to define which parameters will be the inputs of the neural network prediction tool. Introduction Knowledge of optimal extrusion speed, billet temperature, and billet length help increase productivity and reduce scrap. Demand for high-speed production rates, increased product safety standards, and lower energy consumption have prompted plants to use various methods to determine optimum process conditions. One such method is use of control systems that adjust extrusion speeds using the exit temperature. These systems objective is to reach the isothermal extrusion [1]. Such controls systems are capable of dynamically updating the process conditions from billet-to-billet, and recommend near optimal press speed and billet preheat. This approach, however, still required the extrusion engineer to guess process conditions for the first billet [1]. Nowadays the first extrusion conditions need tables [2]and knowledge for determining the first values of process variables (billet temperature and extrusion speed). For example, in fig. 1, it can be seen that determination procedure of process variables values for extrusion is an iterative process [3]. Which the die correction worker and press operator use to adjust and finally find the billet temperature and ram speed when they are testing a die in the press. This kind of traditional approaches to control these aspects in hot metal forming industry are based on trial-and-error procedures, as it was mentioned, relying on the experience of the product and process designers or even on the manufacturing craftsmen [4]. They ponder the correctness of the setup and judge whether changes should be made. This traditional proceeding way turns practical production into a slow, laborious and costly approach.

Figure 1: Iterative procedure for billet temperature and ram speed determination. Extract from [3].

162

Advances on Extrusion Technology and Simulation of Light Alloys

These two parameters, billet temperature and extrusion speed, are important values to predict before the die adjustment phase: for avoiding too long unproductive/preparation times and making easy the adjustment work of the dies during the tests. But at the same time, there exist non-linear relationships among aluminum optimal extrusion speed and the optimal billet temperature and the parameters they depend on. And they depend on numerous parameters: extrusion ratio, container temperature, aluminum alloy, etc. Moreover, if extrusion speed value is unknown, it is difficult to evaluate the cost of extrusion cross section. Because extrusion speed will determine job shop occupation time, therefore the more time is consumed during extrusion manufacturing the more expensive will be the cost of the cross section per meter. Consequently, this cost is ignored by designers, who cannot obtain the most economical cross sectional form and at the same time, that this form fulfils the design requirements. So, nowadays they have to count on experience to determine speed extrusion and therefore the cross section cost. Over the years, it has been an important growth of approximate methods. Extrusion of the aluminum can be modeled with different commercial numerical methods systems and controlled by control systems. The real advantage of numerical simulation is low cost since no experiments are needed. But the simulations are again a laborious trial-and-error procedure, which is a nontrivial task. This situation points out one drawback for the use of FEM in real industry because it appears the needing of the FEM specialist [4]. On the other hand, when experiment data are already available, one can use them improve next attempt to perform similar task [5]. The aim of the project underlying this paper is to provide a prediction of billet temperature and ram speed for the first billet. That prediction value may be used by the press operator and/or die correction worker without the need of make a simulation or several trial and error tests. It might be meaningful to use an approximation and start from it either to use the traditional approach or FEM simulation [4]. Neural networks allow and provide the tool that fit the practical needs of the enduser: it does not demand neither a high user-preparation, a wide experience about the extrusion process nor an important time investment. Hence, the aim of this paper is to present the results of the first step of a defined methodology for the neural network tool development. That first step is to studying the variables that have influence on extrusion process, especially in those that affect billet temperature and extrusion speed. In order to determine those parameters, a preliminary analysis was conducted with experimental data from real industry. Then, a multiple regression analysis was carried out to define which parameters will be the inputs of the neural network prediction tool. Principal Variables on extrusion Extrusion can become impossible or can yield an unsatisfactory product when the load required exceeds the capacity of the press available or when the temperature of the extrusion exceeds the solidus temperature of the alloy. Knowledge of the initial billet temperature, the strain-rate, flow stress of the working material, and the extrusion ratio are required if correct and economical use is to be made of expensive extrusion facilities [3]. The principal variables that influence the force required to cause extrusion and the quality of material exiting from the die are as follows: extrusion ratio, working temperature, speed of deformation and alloy flow stress. Extrusion Ratio (ER). The extrusion ratio is considered a geometric variable of the extrusion process (Kalpakjian). Extrusion ratio of a multihole die is defined by Eq. 1: ER=AC/n(AE).

(1)

Key Engineering Materials Vol. 367

163

Where n is the number of symmetrical holes, AC is the area of container and AE is the area of extrusion. The extrusion ratio of a shape is a clear indication of the amount of mechanical working that will occur as the shape is extruded. Extrusion temperature (TE). Temperature is one of the most important parameters in extrusion, which is carried out at elevated temperatures for metals and alloys that do not have sufficient plasticity range at room temperature and also reduce the forces required for extrusion. The flow stress is reduced if the temperature is increased and deformation is, therefore, easier, but at the time, the maximum extrusion speed is reduced because localized temperature can lead to the incipient melting temperature. Extrusion speed (SE). The response of a metal to extrusion processes can be influenced by the speed of deformation. Increasing the ram speed produces an increase in the extrusion pressure. The temperature developed in extrusion increases with increasing ram speed. This increase is due to the fact that the strain rate is directly proportional to the ram speed, and the magnitude of the generated heat is proportional to the strain rate. Material flow stress ( σ ). The flow stress is important because in plastic deformation process, the forming load or stress is a function of part geometry of dye, friction and the flow stress of the deforming material or metallurgical structure of material. The bearing length (or part geometry of dye). The function of the bearing is to control size, shape finish and speed of extrusion. Friction at the die land is the controlling factor for retarding the metal flow. The length of bearing at any location of the die opening depends upon the extent to which the metal flow must be retarded at the point. Basically, three parameters determine the dimensions of the die bearing to control the metal flow [3]: the distance of the opening from the center of the billet, the section thickness at that location and the pocket shape size. These factors are difficult to control, so the following parameters are commonly used for characterized the extruded shapes according to geometry complexity (ASM handbook, Forming). The parameters that define the shapes and sizes of extrusions are [3]: cross-sectional area of the shape (ACS), perimeter of the shape section (P), diameter of the circle circumscribing the cross section of the shape (CCD), the shape factor (SF) and the form factor (FF). Diameter of the circle circumscribing the cross section of the shape (CCD). The larger the CCD is, the thicker the butt required will be, to minimize waviness at the end of extrusion. Shape factor. It is used as a measure of the degree of difficulty of an extruded shape [1, 3, 6, 7]. In Eq. 2, W is the weight per unit length. SF=P/W.

(2)

Form factor. It is another term, Eq. 3, linked to the degree of difficulty of a section [3], that relater the CDD to minimum wall thickness (tW). FF=CCD/min tw.

(3)

There exists another way of measure the shape complexity (ASM). It is about the classification of the extruded shapes into different groups, based on the difficulty of extrusion, Fig. 2 [8].

164

Advances on Extrusion Technology and Simulation of Light Alloys

Figure 2: a) Classification of aluminium extruded section, based on [8]. b) Example of flat section corresponding to E category. c) Example of hollow section corresponding to J category.

Methodology The developed methodology consists of obtaining all the defined parameters above-mentioned for different types of extrusion products. The methodology has two stages. In the first one, the data has been collected from the extrusion job shop of an extrusion company established in our surrounding area. In such a way, a realistic sample has been obtained. In the second stage, the sample has been statistically treated in order to establish which parameters can be considered for, in a first attempt, developing models by using a multiple regression analysis to predict first billet temperature and ram speed. As well as determining which best parameters can be considered for developing a neural network prediction tool for the same two above variables. The sample. As it has been described, a set of data has been collected. A total of 33 products were obtained and divided into two groups. In the main group 29 data were kept in order to carry out the statistical analysis, whereas 4 data were kept back with the aim of carrying out the validation of the different developed models. For each instance, several parameters were saved and can be grouped around 7 subsets: - General data: profile reference, sketch, weight (W), bar length (L). - Die data: type of section (between tube or hollow (T) section and flat (F) section), number of output holes (n), minimum wall thickness (tW), and perimeter (P). - Billet data: billet length (L), first billet temperature (TFB), alloy, total weight, - Extrusion process data: final or extrusion temperature (TE), length, ram speed or extrusion speed (SE), puller force, culot length. - Cooling conditions. - Stretching conditions. - Ageing conditions.

Key Engineering Materials Vol. 367

165

From those, the calculations needed to determine some of variables defined in the above section are made. For example, a variable that has not been defined yet, the total perimeter (PT) of a section when the extrusion has more that one hole. It has also been added the consideration of two of the most usual material properties in extrusion in accordance with the type of alloy: elongation (A) and material strength (Rm). Results : prediction models Once the information was collected and the sample was completed the next step consisted in developing the prediction models for each variable: first billet temperature and ram speed. Preliminary analysis. A linear correlation between the independent variables of each extrusion product and its first billet temperature and ram speed was established. Secondly, the models were constructed based in the results obtained in the first step. The most correlated variables with each predicted variable were used to develop the models. The study of the correlation between a dependent variable and the predictor variables was carried out with simple linear regressions. The main difference between simple and multiple regressions is that in simple regressions there is only one independent and known variable and multiple regressions involve two or more independent variables. The general form of a prediction equation for simple linear regression is presented in Eq. 4: Predicted Score = b0 + b1 X1. (4) Where, the Predicted Score represents the dependent variable. X1 is the known score of the independent variable. The constant is represented as b0 and is where the regression line intercepts the Y axis. The coefficient of regression is b1 and represents the variation of the predicted score when the independent variable X1 varies 1 unit [9]. In Table 1 are presented the results of the simple linear regressions carried out. Table 1. Results of the simple linear regressions for F, flat sections and for T, tube sections W

ER

n

min tW

CCD

F

0,84

0,39

0,25

0,05

0,00

0,83

0,08

0,04

0,03

0,07

0,00

0,00

0,19

-

0,28

T F

0,63 0,18

0,30 0,01

0,03 0,54

0,22 0,12

0,45 0,18

0,31 0,01

0,03 0,17

0,02 0,35

0,08 0,17

0,21 0,03

0,21 0,03

0,01 0,00

0,28

0,27 -

T

0,12

0,09

0,05

0,04 0,11 0,49

0,05

0,05

0,00

0,08

0,10

0,02

0,30

0,21

0,08

0,27

-

X1 R2 (SE) R2 (TFB)

P

PT

SF

FF

L

Rm

A

TE

SE

TFB

Observing the coefficients of determination R2 in Table 1 it is possible to determine the independent variables that are more correlated with the first billet temperature and ram speed. Because the values of the coefficient R2 give information about those characteristics that would better describe or predict the two variables and for that reason, it would have to be considered candidates to be included in the models. These variables are the weight (W), the perimeter (P) for extrusion speed for flat and tube sections; whereas for first billet temperature, within flat sections the variable is number of holes, and within tube sections, it is the minimum wall thickness (min tW). Only for the flat section and extrusion speed the coefficient R2 is higher than 0.70. The correlation among the variables that could better approximate the objective variables was analyzed. This information was necessary to include in the final models variables that permitted to obtain a closer approximation to the predicted score avoiding multicolinearity problems. Table 2 shows all the correlations among those independent variables that, as indicate the simple linear regressions, would better predict them. The correlation coefficient (r) indicates how strong the association between two variables is. The value of r is such that -1 < r < +1. The + and – signs are used for positive linear correlations and negative linear correlations, respectively [9]. Examining the correlation matrix it is possible to fix which variables are highly correlated. Including two high correlated variables in the models is not a good idea because doesn’t increase very much the capacity of prediction. It is advisable to avoid

166

Advances on Extrusion Technology and Simulation of Light Alloys

using predictor variables that are highly correlated (r>0.90). When the independent variables of the model are highly correlated among them it is possible to have multicolinearity problems that complicate the interpretation of the results but not the predictions. Table 2. Correlation matrix among variables for tube shapes r

W

ER

n

min tW

CCD

P

PT

SF

FF

L

Rm

A

TE

W ER n min tW CCD P PT SF FF L Rm A TE

1,00 -0,63 -0,43

1,00 -0,16

1,00

-

-

-

-

-

-

-

-

-

-

0,27

-0,49

-0,25

1,00

-

-

-

-

-

-

-

-

-

0,42 0,88 0,55 -0,55 0,06 -0,02 0,11 -0,09 0,18

-0,66 -0,34 -0,60 0,16 -0,05 -0,46 -0,02 -0,01 -0,17

0,26 -0,63 0,37 0,90 0,42 0,34 0,10 -0,13 0,01

0,02 0,09 -0,18 -0,41 -0,64 0,19 0,23 -0,08 0,35

1,00 0,36 0,70 0,06 0,59 0,28 0,29 -0,35 0,33

1,00 0,48 -0,60 0,08 -0,23 0,14 -0,16 0,19

1,00 0,27 0,53 0,10 0,20 -0,26 0,21

1,00 0,41 0,24 0,26 -0,30 0,00

1,00 0,08 0,05 -0,14 0,16

1,00 0,14 -0,13 -0,25

1,00 -0,98 0,25

1,00 -0,18

1,00

For example if the shape factor (SF) was included in the model, would not be a good idea to include also the number of holes (n), (r=0,9) as independent variables because the determination coefficient and subsequently the prediction capacity of the model wouldn’t increase very much. To sum up, from Table 1 in this preliminary analysis, it can be established that there does not exist for any of both variables (TFB and SE) a set of principal variables that would be able to better describe or predict them. And from multicolinearity analysis among them, Table 2, it can be also observed that there is not any strong relationship that could force us to rule out any of the variables considered. In accordance with these results, an alternative method has been taken into account to select which variables were going to be the predictors for the multiple regression analysis. The tool that wants to be developed pretends to be easy and useful in an extrusion job shop, in order to help the decision-maker in the preliminary stages of the determination of first billet temperature and extrusion speed values. Having this premise in mind, and the above statistical study, it has been decided which variables will be the independent variables for the models. These variables are: the extrusion ratio (ER), diameter of the circle circumscribing the cross section of the shape (CCD), the form factor (FF), the billet length (L), the elongation (A) and the (final) extrusion temperature (TE). The most of them are known values as the three last ones. Whereas the three first ones, on the one hand they could be easily calculated taking into account that the decision maker will possess the part drawing and will be take the necessary data from it to make the calculations, and on the other, they are the main parameters recognized by the most of researchers and experts in aluminum extrusion. Multiple regression analysis. After these preliminary analysis that were helpful to obtain information about the attributes and their association to the dependent variable, multiple regression studies were carried out in order to build the prediction models. Next, the two models are presented. The first one is for the first billet temperature and the second one, for the extrusion speed. First billet temperature model. The model proposed in Eq. 5 consists of the following 6 abovementioned independent variables. Depending on the value of the variables that are given next, will be valid for a flat section extrusion part o for a tube section one. The decision maker will fix these attributes looking at the requirements of the extrusion product that have to be produced. TFB = b0 + b1 ER + b2 CCD.+ b3 FF + b4 L + b5 A +b6 TE.

(5)

Key Engineering Materials Vol. 367

167

In Table 3, the regression coefficients from b0 to b6 and the parameters: multiple correlation coefficient (r), determination coefficient (R2) and standard error are shown. Table 3. First billet temp. regression coefficients and parameters for flat F and tube T sections TFB F T

b0

b1

b2

b3

b4

b5

b6

r

R2

Standard error

1002.936 247,484

0.009 -0.045

-0.099 0.057

0.637 -0.202

-0.043 0.011

-7.038 -1.554

-0.812 0.460

0.692 0,717

0,478 0,513

16.190 9.694

Extrusion speed model. The same structure it has been obtained for extrusion speed model proposed in Eq. 6. It consists of the same 6 above-mentioned independent variables. Depending on the value of the variables that are given next, will be valid for a flat section extrusion part o for a tube section one. The decision maker will fix these attributes looking at the requirements of the extrusion product that have to be produced. SE = b0 + b1 ER + b2 CCD.+ b3 FF + b4 L + b5 A +b6 TE.

(6)

Following the same structure presented in Table 3, Table 4 shows the results obtaines for the extrusion speed. Table 4. Extrusion speed regression coefficients and parameters for flat F and tube T sections SE F T

b0

b1

b2

b3

b4

b5

b6

r

R2

Standard error

211.864 -67.600

0.125 0.167

-0.001 0.060

0.149 -0.050

-0.008 0.008

-1.008 1.065

-0.341 0.088

0.868 0,763

0.755 0,582

3.753 3.79

Next an explanation of the meaning of these concepts is given: Multiple correlation coefficient (r) indicates the level of association between the independent variables and the dependent variable [9]. Determination coefficient (R2) is the square of the multiple correlation coefficients. Its value gives the proportion of the variance of the dependent variable that is predictable from the independent variables [9]. The standard error is a measure of the precision of the prediction. Represents an estimation of the standard deviation of the dependent values around the regression line; this is a variation measure around the regression line. It indicates the confidence interval of a prediction [9]. Discussion and validation The validation results with the 4 unseen data are presented in Table 5. Table 5. Results of the validation: T, tube section, F, flat section SE TFB

T1

T2

T3

F1

Real

22

18

14

20

Predict. Real

33 450

10 450

19 450

26 470

Predict.

456

456

470

479

The developed models permit a preliminary approach to the first billet temperature and extrusion speed depending on the type of extrusion part, tube or flat section, which has to be manufactured. However, there are differences between the TFB predicted and the real values of the sample as it is showed in Figure 3. The same behavior occurs for the extrusion speed, being the interval of error for extrusion speed of ±5. This wide interval leads to prove another technique as the logarithmical multiple regression without improve the r and R2 coefficients. Before the development of the neural network tool, polynomial MRA models should be considered and compared with the results presented in this paper in order to assure the complete range of this type of prediction tool.

168

Advances on Extrusion Technology and Simulation of Light Alloys

(a)

(b)

Figure 3: a) Prediction error TFB vs. chosen variables for flat sections. b) For tube sections. Conclusions Although the attributes or characteristics with better correlation with the two variables were few and they have not been used to obtain the final models, the final chosen variables are recognized by the experts in the area and at the same time are easy to use and to find and calculate in a jobshop. The low accuracy of the multiple regression models presented in this paper and the other tested during the development of this work has allowed to choose which will be the input parameters for a neural network prediction tool that will be developed in the next step, since it has been demonstrated that the multiple regression models do not provide the desired accuracy for calculating the first approach values for the first billet temperature and extrusion speed. Acknowledgments This research would not have been possible without the collaboration of Tecalum (Mr. Fernando Durante). We greatly appreciate the time and information provided by him and its company. References [1] M. Reddy, H. Bertolini and H. Biel. "HyperXtrude/Process. Extrusion Process Optimization Software" Proceedings of the Eighth International Aluminum Extrusion Technology Seminar Vol. 1(2004) p.23 [2] Anonymous Fichas técnicas A-GS (Aluminium Pechiney, 1987) [3] P. Saha and ASM International. Aluminum extrusion technology (ASM International, 2000) [4] M.L. Garcia-Romeu and J. Ciurana. Springback and geometry prediction – neural network applied to air bending process.Lecture Notes in Computer Science, Vol. 4113(2006), p.470-475 [5] Z. Lozina, I. Duplancic and B. Lela. "Optimization of aluminium extrusion and die design using neural networks and genentic algorithms, Aluminium Two Thousand 5th world congress"(2003) [6] S. Kalpakjian. Manufacturing processes for engineering materials (Prentice Hall, 2003) [7] Committee under ASM direction. Metals handbook-ASM Handbook: Forming and Forging.(American Society for Metals, 1988) [8] K. Laue. Moglichkeiten werkstoffgerechter. (Gestaltung von Leichtmetmetallprofilen, Z.f.Metallkunde 54., 1963) [9] J. Hair, R. Anderson, R. Tatham, et al. Multivariate data analysis (Prentice Hall, 1998)

Key Engineering Materials Vol. 367 (2008) pp 169-176 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/KEM.367.169

Creep and Fatigue Damage in Hot Work Tools Steels during Copper and Aluminium Extrusion Christof Sommitsch1,2,a, Thomas Wlanis1,b , Thomas Hatzenbichler3,c and Christian Redl4,d 1

Christian Doppler Laboratory for Materials Modelling and Simulation, University of Leoben, FranzJosef-Strasse 18, 8700, Leoben, Austria 2

Chair of Metal Forming, University of Leoben, Franz-Josef-Strasse 18, 8700, Leoben, Austria

3

Materials Centre Leoben, University of Leoben, Franz-Josef-Strasse 13, 8700 Leoben, Austria 4

Böhler Edelstahl GmbH, Mariazellerstrasse 25, 8605, Kapfenberg, Austria

a

[email protected], [email protected], [email protected], [email protected],

Keywords: Extrusion; Hot work tool steels; Creep-fatigue; Thermo-mechanical viscoplastic constitutive model, Damage-rate equation, Lifetime

Abstract. During hot extrusion, tools experience cyclic thermo-mechanical loads that can lead to materials degradation and failure. For a process optimization and study of the occurring damage mechanisms, the finite element method (FEM) is an appropriate means. Local inelastic strains result from the interaction of the applied temperature and stress loading and can be computed by suitable inelastic constitutive equations. Stress amplitudes and dwell times during extrusion result in creepfatigue damage. A lifetime consumption model sums increments of a damage variable over time and defines materials failure as the accumulation of the resulting damage variable to a critical value. The predominant failure mechanism, i.e. creep or fatigue, can be found by the investigation of the damage rate over several cycles. A comparison of both a creep dominated (copper extrusion) and a fatigue controlled (aluminium extrusion) lifetime consumption in an extrusion die is shown with the hot work tool steel Böhler W300 ISOBLOC in comparison with W400 VMR (both ~ EN 1.2343). Introduction During hot extrusion, tools in service (i.e. the container and the die) experience thermo-mechanical loading, its magnitude depending upon the working temperatures and the billet material [1]. In this work the focus of investigations lies on hot work steels for tools during forward extrusion of aluminium as well as copper. Both stress and temperature distributions in the tool resulting from the external loading should reach a steady state after several press cycles and can be computed by means of the finite element method. Extrusion tools in service are exchanged and dismounted, respectively, for different reasons. On the one hand a profile change causes a tool replacement on the other hand used tools are subsequently grinded and nitrated after specific intervals until the demanded dimensional tolerance is no longer ensured. A third possibility exists in the failure of the tool, which can lead to violent operational disruptions and costs. The failure usually originates from a combination of different factors, like an arising local overload, material defects, wear at the contact surface tool-billet, as well as creep-fatigue damage. The latter is temperature dependent and results from the accumulated inelastic strain and the influence of the local stress state, which depends on the applied loading during the extrusion process. The stress state additionally is superimposed by the residual stresses from the heat treatment and the surface nitration of the tool, respectively, and e.g. in the case of multipart containers by the stresses caused by the shrinking process. The portion of creep and fatigue to the entire lifetime consumption depends on the billet and the tool temperature, on the

170

Advances on Extrusion Technology and Simulation of Light Alloys

press cycle duration as well as on the stress amplitudes originating from loading and releasing within each extrusion cycle [2]. For a qualitatively and quantitatively exact estimation of the number of cycles to failure, all influencing factors specified above would have to be considered, which does not seem to be possible at the moment. A simplified model for the calculation of the creep-fatigue damage however should provide at least realistic and comparative values. In this work the preceding quenching and tempering of the material and the resulting residual stresses are not considered explicitly in the model, however the sample material for the calibration of the material and lifetime model was heat treated in a similar way as extrusion tools. The influence of wear and surface nitration is neglected in the following. Viscoplastic constitutive models have been developed in the past in order to take into account the inelastic behaviour of the material during creep-fatigue loads, see, e.g., [3-5]. For the present study a viscoplastic model according to Chaboche [5] is used (compare [2]) and is calibrated here with respect to the material behaviour of the hot work steel Böhler W300 ISOBLOC as well as the vacuum melted and remelted W400 VMR. In addition, an ageing evolution equation is taken into account in order to describe the strong time-dependent response of W300 ISOBLOC at high temperature. With the presented model for the calculation of the life time of extrusions tools a process optimization and an investigation of materials damage should be possible. In this work exemplarily both a creep and a fatigue dominated damage process during copper as well as aluminium extrusion is compared. For the copper extrusion simulation, a simple axi-symmetric die was modelled due to calculation cost reasons. However, for the aluminium extrusion process, a more complex die with rather small radii in the contact area extrude-die was chosen in order to get sufficiently high damage rates. Modelling and Simulation To predict damage, the accurate knowledge of the unsteady local thermal and mechanical loading on the die within each cycle is of particular importance. Model for the hardening and softening behaviour. The total strain ε of the constitutive model is decomposed into the thermal strain εth, the elastic strain εe, which is connected with the stress σ by Hooke’s law, and into the inelastic strain εin:

ε = ε e(σ ) + εin + ε th (T) , ε th (T) = ε th (T) 1 .

(1)

In a viscoplastic, i.e. unified inelastic, model, creep and plasticity are covered within a single inelastic strain variable. According to the viscoplastic model of Chaboche [5] the flow rule for the single inelastic strain εin reads:

J (S − X) − (k + R) ε& in = 32 2 K

n

S−X J 2 (S − X)

,

{

y , if y > 0 y := 0 , otherwise

.

(2)

The Chaboche model is based on the concept of threshold stress: if the applied stress deviator S exceeds the threshold stress (with k as the initial threshold stress), inelastic flow occurs to the extent of this overstepping. Due to inelastic straining two kinds of hardening, denoted by the scalar R and by the tensor X, arise.

Key Engineering Materials Vol. 367

171

Ageing of strength, i.e. a time-dependent decrease of an already initially present flow resistance is considered in the model by a time-dependent decrease of the viscosity. The degree of ageing can be caused in hot work tool steels by the coarsening of carbides due to a long time exposure to a high temperature. A precise description of the model can be found at [2, 6]. All thermo-physical and material parameters are temperature-dependent and have been determined for temperatures in the range of 470°C-590°C with 30°C temperature steps [2, 6]. Model for the lifetime behaviour. Fatigue lifetime in a macroscopic model means the initiation of a macro-crack (typically a fraction of millimetre). The evolution equation for the lifetime consumption D, 0 ≤ D ≤ 1, is:  σ eq  dD =   dt  A 

ml

n

 p&  l  &  p& 0 ,  p0 

(3)

where σeq is an equivalent stress (compare, e.g., the proposals of Lemaitre and Chaboche [4]) and &p the Mises equivalent inelastic strain-rate, p& 0 is a normalisation constant. For a fatigue problem the lifetime model (Eq. 3) refers not to a failure time under pure monotonous loading, i.e. the timeto-creep-fracture (as in usual time-fraction rules), instead the material parameters A and ml of the stress dependence of the lifetime behaviour are determined directly from low-cycle fatigue (LCF) tests without hold-times (strain rates 10-3 s-1). The parameter nl describes the influence of hold-times in LCF tests on the lifetime behaviour, which is very significant at high temperatures, even though the magnitude of the inelastic strain-rate ( p& ) decreases strongly during relaxation. The numbers of cycles-to-failure Nf have been calculated for the seek of simplicity by Nf ≈ 1/(∆D)3, where (∆D)3 is the lifetime consumption within the third cycle. At the investigated high temperatures subsequent cyclic softening appeared without any saturation of the hysteresis loops, but integration of the time-incremental lifetime-rule over all cycles up to the fatigue failure (D = 1) would be to costly for a real component. Nevertheless, the damage-rate Eq. (3) takes into account the whole loading complexity within a cycle [2, 6]. Finite Element Simulations The material and damage models described above were implemented in DEFORM 2DTM (subroutine USRUPD) as well as in ABAQUSTM (subroutine UVAR). In the following, examples for both the uncoupled and coupled extrusion/tool simulations will be given. Aluminium extrusion. For the chosen example of a tubular extrusion section made of aluminium alloy 6060, the thermo-mechanical loading of the die during extrusion was analysed by means of the finite element method (realised by HyperXtrudeTM), where the die was assigned a rigid behaviour. The output of these simulations was the time-dependent temperature as well as pressure boundary conditions (maximum radial stresses of ca. 300 MPa) at the contact surfaces billet-die during one cycle in the steady state regime. These boundary conditions were used for the following elastic-viscoplastic simulation of the die by Abaqus Standard v.6.5-1 (50,660 elements). The reason for this procedure is the much shorter calculation time for the elastic-viscoplastic die model with specified boundary conditions in comparison to coupled extrusion/tool simulations, especially for multiple extrusion cycles [2, 6]. The following initial, boundary as well as loading conditions have been applied on the model: Temperature calculation: Element type: DC3D8, 8-node linear brick Stress calculation: Element type: C3D8R, 8-node linear brick, reduced integration with hourglass control Loading conditions for the simulation: 300 seconds with load (pressure and temperature); 300 seconds without load, only heat transfer

172

Advances on Extrusion Technology and Simulation of Light Alloys

The extrusion die was modelled with a symmetry of 30° (Fig. 1). Within each extrusion cycle, both the heat of the billet and the pressure were applied by the above defined boundary conditions at the contact surface billet-die. Fig. 2 displays both the stresses and the temperature distribution at the end of the third extrusion cycle. The maximum temperature (approx. 538 °C) appears near the contact area billet-die, and the maximum Mises equivalent stress also has its maximum at 714MPa in this area of relatively high temperature.

Figure 1: Extrusion die from Alcan Aluminium Valais AG for aluminium tube extrusion: die (left) and meshed twelfth part of the die (right).

Figure 2: Mises equivalent stress distribution [Pa] (left) and temperature distribution [°C] (right) in W300 ISOBLOC during the third aluminium extrusion cycle. Copper extrusion. The simulations were performed with the FEM software DEFORM 2DTM v.8.1. Fig. 3 depicts the axisymmetrical model setup with billet, container, pressing pad and die with the following properties: Billet: object type: plastic; material: DIN-CuNi2S1; initial temperature: 900 °C Pressing pad: object type: rigid; material: W300 ISOBLOC / W400 VMR; initial temperature: 650 °C; velocity: 7mm/s

Key Engineering Materials Vol. 367

173

Container: object type: rigid; material: W300 ISOBLOC / W400 VMR; initial temperature: 650 °C Die: object type: elastic; material: W300 ISOBLOC / W400 VMR; initial temperature: 650 °C Element: axisymmetric, 4 nodes During the simulation the extrusion shape can be cut off by an additional object in order to shorten the profile and hence the calculation time. This procedure has to be done manually at the start of each extrusion cycle. The maximum temperature in the billet/extrude at the contact area extrude/die was ca. 970 °C and the maximum equivalent stress ca. 91 MPa. Fig. 4 shows both the temperature (a) and Mises equivalent stress distribution (b) at the end of the third extrusion cycle (loaded).

Figure 3: Objects of the copper extrusion model for circular solid shape. Points 1 and 2 experience maximum equivalent stresses, Point 2 maximum damage due to a higher temperature than Point 1 (left); Axisymmetric FEM model with mesh (right). The contact conditions tool-billet (i.e. contact pressure and temperature), used in the FEM simulations, were validated by an instrumented experimental extrusion plant by thermocouples and load cells. Detailed information can be found elsewhere [7]. Conclusions For the chosen extrusion examples, the simulations led to maximum lifetime consumption in the region of relatively high both temperature and equivalent stresses (Figs. 2, 4 and 5). During extrusion, the equivalent stress and temperature maxima are not located at exactly the same place in the tools. However, the largest accumulated damage occurs in regions that exhibit maximum overlapping temperature and equivalent stress loading.

174

Advances on Extrusion Technology and Simulation of Light Alloys

Figure 4: von Mises equivalent stress [MPa] (left) as well as temperature [°C] (right) distribution in the die at the end of the third copper extrusion cycle.

Figure 5: Damage distribution in the die made from W300 ISOBLOC (left) and W400 VMR (right), respectively, at the end of the third extrusion cycle. Comparing the aluminium with the copper extrusion example, the damage evolutions (Fig. 6 top and bottom) show a very different behaviour. During copper extrusion at a relatively high temperature, the strong creep influence on damage leads to a smooth increase of the lifetime consumption during die loading (Fig. 6 bottom). The calculated numbers of cycles to failure 1/(∆D)3 on the basis of the third cycle are 548 cycles (W300 ISOBLOC) and 1,508 cycles (W400 VMR), which is an indication of a strength ageing process in W300 ISOBLOC during service. However in

Key Engineering Materials Vol. 367

175

aluminium extrusion at a lower temperature, the preponderance of fatigue causes a more cyclic rise of damage (Fig. 6 top). For the element with maximum damage (Fig. 2), the number of cycles to failure was also calculated on the basis of the inverse damage increment 1/(∆D)3 of the third cycle. The number of cycles to failure of W300 ISOBLOC (1,146 cycles) is approximately three times lower than for W400 VMR (3,323 cycles). Both the equivalent stress and temperature distributions for W300 ISOBLOC and W400 VMR are identical because of equally taken thermo-physical properties. However, the lifetime consumption evolution is very different due to dissimilar constitutive and damage model parameters [6] (Fig. 6).

Figure 6: Lifetime consumption of extrusion die (maximum damaged element) for W300 ISOBLOC and W400 VMR within three extrusion cycles. Aluminium extrusion (top) and copper extrusion (bottom). Acknowledgement The plastic FEM simulation of the extrusion process to get the temperature boundary conditions on the contact surface billet-die, done by Alcan Aluminium Valais AG in Sierre (Dr. Gaudin) is gratefully acknowledged.

176

Advances on Extrusion Technology and Simulation of Light Alloys

References [1] K. Müller: Fundamentals of Extrusion Technology (Giesel-Verlag, Isernhagen 2004). [2] C. Sommitsch, R. Sievert, T. Wlanis, B. Günther and V. Wieser: Modelling of creep-fatigue in containers during aluminium and copper extrusion, Computational Materials Science Vol. 39 (2007), p. 55. [3] A.S. Krausz and K. Krausz: Unified constitutive laws of plastic deformation (Academic Press 1996). [4] J. Lemaitre and J.-L. Chaboche: Mechanics of solid materials (Cambridge University Press 1990). [5] J.-L. Chaboche: Cyclic viscoplastic constitutive equations, Part I: a thermodynamically consistent formulation, Journal of Applied Mechanics Vol. 60 (1993), p. 813. [6] C. Sommitsch, R. Sievert, T. Wlanis and C. Redl: Lifetime evaluation of two different hot work tool steels in aluminium extrusion, Computational Materials Science (2007), in press. [7] F. Krumphals, T. Wlanis, C. Sommitsch and C. Redl: Creep-fatigue of multi-part container during hot extrusion of copper – Simulation and experimental comparison, Computer Methods in Materials Science Vol. 7 (2007), p. 47.

Key Engineering Materials Vol. 367 (2008) pp 177-184 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/KEM.367.177

Microscopic examination of the fracture surfaces of an H 13 hot extrusion die due to failure at the initial usage stage 1

2, a

D. Tseronis , I. F. Sideris

1, b

, C. Medrea

, I Chicinas

3, c

1 Technological Educational Institute of Piraeus, Department of Physics, Chemistry and Materials Technology , Athens, Greece 2 G.B. Stasinopouloi Company, 20 Athinon Str, 18540, Piraeus, Athens, Greece 2 Stasinopoyloi-Uddeholm, Steels Company S. A. , Piraeus, Athens, Greece 3 Technical University of Cluj-Napoca, Department of Materials Science and Technology, Cluj Napoca, Romania a

b

c

[email protected], [email protected], [email protected]

Keywords: aluminium extrusion die, failure analysis, fracture surfaces, microscopic examination

Abstract. This paper studies the fracture surfaces of an aluminium hot extrusion die that broke down during operation. The die was constructed, from H13 steel and was intended for the production of 60,000 Kg of aluminium profile. The male part fractured during operation after the production of 500 Kg profile. Initially, the machine and thermal treatments that were applied for construction of the die were collected and studied. The die was carefully inspected visually with a stereoscope. The fracture surfaces, some cracks, and the structure that was not affected by the failure, were investigated by optical microscopy. The thickness, quality and homogeneity of the nitrated layers were inspected. Additional information concerning the fracture was obtained by examining a primary crack using a scanning electron microscope and chemical analysis of the material was made using EDX attachment. The paper reports on some interesting observations relating to the fractured component, the type of the fractures, and the quality of the heat treatments, and presents some of the probable causes that led to the premature failure of the die. Introduction Extrusion is a plastic deformation process in which a block (billet) of metal is forced to flow by compression through the die opening of a smaller cross-sectional area. The process is widely applied to ductile metals or alloys, for the construction of difficult and complex profiles [1]. Depending on the material used, the process can be cold or hot and are used two basic types: direct and indirect. The most important and common method used in the aluminium industry is direct extrusion. The billet is placed in the container and pushed through the die by ram pressure [2].The die is the most critical extrusion component, due to its high cost based on special material and processing, very fine tolerances and high demands on repeated thermo-mechanical performance. During the operation the die is subjected to cyclic temperature changes and to increased stress and deformations and must present excellent mechanical properties [3, 4]. The tool steel producers develop cleaner and high hot strength materials in order to increase tools lifetime. Longer die life can be achieved and by making the die surface (bearing surface) more wear resistant. In order to reduce wear the dies are almost always surface treated by various forms of nitrating [5, 6]. Surface-coating by physical vapour deposition (PVD) or chemical vapour deposition (CVD) is currently being introduced as a means to further improve the wear resistance [7-9]. Although many new procedures have been designed for increase the wear resistance of die surfaces for extrusion, gas nitrating is the most common surface treatment procedure. The quality of the nitrated surfaces is essential for die life time [10]. The analysis of tool and die failure plays too an important role in the prediction and prevention of die failure [11, 12]. A few articles are available in literature presenting failure analysis based on a substantial number of samples of real die breakdowns [13, 14]. Arif studied 616 die failures

178

Advances on Extrusion Technology and Simulation of Light Alloys

involving 17 die profiles made of H13 steel [15]. He concluded that the predominant failure mode was fracture, 43%, followed by wear, 26%, deflection ,19%, mixed mode, 45%, miscellaneous, 2%, and mandrel-related, 3%. The major fracture-type failure was due to tracking/breaking of the brush path, the main wear-related one was of the dimension change variety, and the foremost deflection failure was located at the bearing. Continuous improvement of die error correction and careful elaboration of materials used for constructing them is continuously changing percentages, while permanent plastic deformation appears to be one of the most important causes of die failure. Failure analysis investigates causes of die premature destruction [16]. The method is based on the processing of information collected during the construction, processing and operation of the component, in order to discover the causes leading to its destruction. A careful examination of the fracture surfaces is usually the first step in the analysis of failures. In some cases, the causes of destruction may become apparent at this stage. In such a case, the results could lead to immediate actions and measures to be taken in design, manufacture, quality assurance and maintenance so as to reduce or avoid similar situations. This paper studies the fracture surfaces of an aluminium hot extrusion die broke down during its operation. The die was constructed from AISI H13 steel (W.Nr.1.2344) and was intended for the production of 60,000 Kg of aluminium profile. The male part fractured during operation after the production of only 500 Kg of profile. Experimental Details A die for the production of aluminium profiles (dimensions 30mm x 40mm) from ORVAR 2M steel (AISI H13) was constructed, as per Uddeholm. The H13 is the most common steel used for the construction of aluminium extrusion die. It is chromium-molybdenum-vanadium-alloyed steel and by special processing techniques and close control, it can attain high purity and a very fine structure [17]. The following machine and thermal treatments were applied for construction of the die: coarse machining and milling, using CNC machine tools. - stress relief by heating at 650 ºC, holding time 2 hours, cool slowly to 500 ºC, then freely in air - hardening: first preheating at 600 ºC for 30 min., second heating at 850 ºC for 30 min., austenitizing at 1030 ºC for 30 min., cooling in a mar-tempering bath at 500 ºC for 10 min. and then freely in air. Hardness after hardening: 48-49 HRC. - tempering: first tempering at 550 ºC for 2 hours and air cooling, second tempering at 610 ºC for 2 hours and air cooling, and third tempering at 570 ºC for 2 hours and air cooling. - cutting of final shape with wire electrical corrosion machining material - end machining, grinding and polishing - Test run (extrusion on the press) - Error correction: intervention on bridge ribs - Liquid surface nitrating at 580 ºC for 4 hours with a theoretical hardness of 1050 HV01.

Fig.1 The male part of the die

Key Engineering Materials Vol. 367

179

The die consisted of two parts, male and female, and was intended for the production of 60,000 Kg of aluminium profile. The male part fractured during operation after the production of only 500 Kg of profile (Fig.1). Die running in had been completed prior to failure. Operating conditions are considered satisfactory. The sample of the fracture area and surrounding cracks was prepared for the analysis. The sample was cut by wire electrical corrosion (Fig.2). A Mesotom cutting machine and a 01 TRE grinder were used. Fracture surfaces were cleaned with NITAL 3%, washed with methanol and air dried. The die was carefully inspected visually with a stereoscope type LEICA MZ6 [18]. The quality of the surface was tested using a portable ΤR100 Surface Roughness Tester.

Fig.2. The sample of stereoscopic analysis: (a) - front side, (b) - back side. For the metallographic examination, the sample was cut into pieces at the centre of the fracture and a piece was removed with 90º angle internal surfaces (Fig. 3.a). All the fracture section and a part of the crack adjacent to the fracture were included on the vertical internal surface of the sample (Fig. 3.b). The new sample was mounted in thermo-hardening resin made of bakelite (EPOMET MOLD COMP) and phenolic powder (Fig.3.c). After suitable processing it was etched with Nital 5% and investigated by optical microscopy. The thickness, quality and homogeneity of the nitrated layers were inspected. Additional information concerning the fracture was obtained by examining a primary crack (the cross section through the fracture) by scanning electron microscopy (SEM), using a JEOL - JSM5600 LV microscope. Local chemical analysis of the material was made by X-ray microanalysis, using an EDX Spectrometer (Oxford Inst.,Inca 200 Soft).

Fig.3. The sample of metallographic analysis

180

Advances on Extrusion Technology and Simulation of Light Alloys

Results and Discussions Visual inspection revealed that fracture areas are round and located at points where the cross section changes (Fig. 4). This is the fracture of two of the four die bulges. The die was designed asymmetrically. Die asymmetry resulted in a different aluminium flow speed. The increase in speed resulted in the creation of shearing stress. The fracture has a cup and cone form, which is a characteristic of ductile fractures (point I on Fig. 4). There are significant cracks around the bases of the two fractured bulges that reach beyond the fracture area over the die ribs (point II on Fig. 4). Small cracks are observed at the edges of the two bulges, between the body of the die and the bulge heads. Hard lines of poor machine processing and defective polishing are observed on die ribs. Symmetry is observed between the two bulges, the two fractured bases and the six cavities.

Fig. 4. The fractured part of the die Figures 5 show the fracture area following examination with a stereoscope. The fracture is typical of hardened steel. The fracture surface is not smooth: this is a characteristic of tough materials and has an orientation that is characteristic of shear stress. At the points primary and secondary cracks are observed on the fracture surfaces. Some cracks are outside the fracture surface due to stress caused by pressure that is greater than steel can withstand (point I on Fig 5a).These cracks are not complete as the die fracture with the smallest cross-section. Very small intercrystalline cracks appear in a part of the crack surface (point II on Fig.5a and b). Bright and reflective crystal surfaces are observed on the largest part of the fracture surfaces. These surfaces characterise the inter-crystalline fracture. The numerous fission plateaus are a classic case of intercrystalline fracture; these appear in the form of an image from river marks. They constitute the primary crack while tributaries form the secondary cracks.

Fig. 5.The fracture area of the sample examined with stereoscope In general, many points of inter-crystalline rupture are the result of metal compression that brought about penning and consequently an increase in hardness and finally a local change of the rupture from ductile to brittle. The edge created by shearing on the frame surrounding the fracture

Key Engineering Materials Vol. 367

181

(at certain points) is characteristic of intra-crystalline fractures. The "V" signs are apparent at the start points of the fractures, due to stress caused by shearing (point III on Fig.5a and point IV on Fig.5b). The "V" sign observed at point II is characteristic of fracture initiation due to pressure caused by shearing. Visual inspection of the die showed a satisfactory quality external surface in the areas where the die was rectified. However, it was noted that the cracks on both sides of the fracture surfaces follow a direction leading to the die’s ribs. Closer examination of the surface in this area revealed significant roughness on die ribs, as is observed in the Figure 6. That is a result of insufficient polishing. Increased roughness caused great friction forces. The crack follows the points of maximum roughness (points at which stress is concentrated), i.e. the courses presenting lowest resistance. These cracks and their ramifications are a result of resistance to shearing on each surface (point I of Fig. 6).

Fig. 6. Sample: The front (a) and the back (b) size of the fractured die rib The fracture surfaces, some cracks, and the structure that was not affected by the failure, were investigated by optical microscopy (Fig. 7). A white, thin and uneven layer appears on the external part. Gas nitrating depth is 7µm (while in other areas it was 15 µm.). The diffusion zone is 63 µm. wide and is considered fully deficient (Fig. 7 a). Black areas appear to separate the white layer from the rest of the structure. Their presence may be due to corrosion if the die had not been well cleaned before gas nitriding. Towards the inner part of the die, the structure is characteristically fine grained, with restored martensite and carbides, which are uniformly distributed (Fig 7, b). Additional information concerning the fracture was obtained by examining a primary crack using a scanning electron microscope (Fig.8 and Fig.9).

a) the section throw the surface b)core Fig.7. The microstructure of the sample on the cross section of the crack During fracture, a sub-layer is subjected to cold hardening. The deformed layer is about 60µm thick and is situated at a depth of 80µm; it lies along the fracture (Fig.8). Secondary cracks develop from the primary crack, which follow the route that shows lower resistance (point I on Fig 8b and Fig 9a).

182

Advances on Extrusion Technology and Simulation of Light Alloys

a) left side b) right side Fig.8. SEM micrographs showing the morphology of the cross section of the fracture.

a)surface b) core Fig.9. SEM micrographs showing the right side of the primary crack. Fissures have a different colour. Black fissures appear due to selective erosion of the fissure’s protrusions during etching. White fissures are probably areas in which carbides are present. Carbides are not affected by grinding, due to significant hardness and create small protrusions. Fig.10 presents the energy-dispersive x-ray spectra obtained from the cross section of the fracture, along the crack. The analyses of the most of the fracture surfaces showed only the major alloying elements of H13 steel and oxygen. The surface of the crack oxidized subsequently, all along of the crack. The atoms of the elements from the crystallites that are present on the outer surface of the crack have higher free energy and, in their effort to balance, bind oxygen and form oxides. No contaminant or corrosion products that could have contributed to the failure were found.

Fig.10.EDX spectrum obtained from a primary crack area No characteristics of fractures due to fating, erosive cracking under pressure or in the absence of pressure, fragility of liquid metal or hydrogen and creeping were observed.

Key Engineering Materials Vol. 367

183

Conclusions Several causes contributed to premature destruction of the die. Fracturing was principally caused by shearing stress. Die geometric asymmetry has led to uneven aluminium flow speed resulting in the creation of shearing stress. At certain points, shearing caused intense stress; at others, it caused intense compression resulting in die fracture at the point with the smallest cross section. The form of fractured edges is partially cup and cone, a characteristic of semi-ductile materials. At certain points, intra-crystalline fracture created an edge around the fracture as a result of ductile behaviour of the fracture from ductile to brittle, while secondary cracks are characteristic of shearing. There are also inter-crystalline cracks that are characteristic of brittle materials. Inter-crystalline fracture points are due to metal compression caused by cold working and therefore increased hardening locally. The result of this process is transformation of the fracture from ductile to brittle, while secondary cracks are characteristic of shearing. Significant roughness on die ribs was observed as a result of insufficient polishing. Increased roughness created greater that anticipated friction forces. The quality of nitrating was unsatisfactory. In certain areas it was found to be thinner and uneven. Unevenness and deficient nitrating at certain points and also insufficient smoothing does not justify die failure but, in the presence of shearing stress, favours the diffusion of the cracks which led to its immediate destruction. Other factors that could have contributed to die failure, such as the characteristics of fractures due to fatigue, erosive cracking under pressure or in the absence of pressure, fragility of liquid metal or hydrogen and creeping were not found.

References [1]

P.K. Saha: “Fundamental of Extrusion” in Aluminium Extrusion Technology, ASM International ,Ed. by American Technical Publisher,Materials Park, Ohio (2002).

[2] S. L. Semiatin: “Conventional hot extrusion” in Forming and Forging, ASM Metals Handbook, Vol.14,(1998) [3]

H. Valberg, Int. J. Mater. Product. Techn. Vol. 17, (2002), p.497

[4]

W.Z.Misiolek, in:J.Mater. Process. Techn, Vol.60 (1996), p.117

[5]

M. P. Clode, T. Sheppard: Mater. Sci. Techn., Vol. 6 (1990), p.755

[6] S.Abtahi, T. Welo, S. Storen : Proceedings of the Extrusion Technology Seminar (1996), Chicago, IL [7] K. B. Muller: J. Mater. Process. Techn., Vol.130-131(2002), p.432 [8] T. Bjork, R. Westergard, S. Hogmark: Wear, Vol. 249, (2001), p.316 [9] K. E. Cooke, S. Yang, C. Seluck, A. Kennedy, D. G .Teer, D. Beale: Surface & Techn. Vol.188-289 (2004), p.607 [10] M. Tercelj, A. Smolej, P. Fajfar, R. Turk in: Tribology Int.,Vol. 40 (2007),

Coatings

p. 374

[11] A.K. Das,”Failure: Types and Characteristics” in Metallurgy of FailureAnalysis, edited by Mc Graw-Hill Companies, New York (1997), p.67 [12] D.A. Ryder, ”General Practice in Failure Analysis”, ASM Handbook, Vol. 9, Ed. by Metals Park, Ohio, (1978), p.15

184

Advances on Extrusion Technology and Simulation of Light Alloys

[13] W. A. Kortmann, Causes and methods of avoiding failures (Proceedings of the Second Int. Congress of Al), Alumimium2000 (2000), p.219 [14] G. C. Moura, M. T. P. Aquilar, A. E. M. Pertence, P. R. Cetlin: Eng. Failure Analysis, Vol.11,(2004), p.943 [15] A. F. M. Arif, A. K. Sheikh, S. Z. Qamarin: J. Mater. Process. Techn. Vol. 134, (2003), p.318 [16] F. K. Naufmann, ”Types of Failures” in Failure Analysis, Case Histories and Methodology, ASM for Metals ,Ed. by Metals Park, Ohio,(1983),p.14 [17] Uddeholm:”Manual Orvar 2 Microliezed” in General Practice in Failure Analysis, Tool Steel Facts, (2000), p.3 [18] M. Mousoulis, D. Tseronis, I .F. Sideris, F. A. Fotopoulos, C. Medrea: Proceedings of the 9th Conference on Material Forming), ESAFORM 2006, (2006), p.503

Key Engineering Materials Vol. 367 (2008) pp 185-192 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/KEM.367.185

Simulation of Direct Extrusion Process and Optimal Design of Technological Parameters Using FEM and Artificial Neural Network Durmus Karayel1,a 1

Sakarya University, Sakarya MYO, Mechatronics, Sakarya University Sakarya MYO Kapali Spor Salonu Karsisi 54187 Sakarya, Turkey, a

[email protected]

Keywords: Extrusion, FEM Simulation, Artificial Neural Network, Optimization, Intelligence Die Design.

Abstract. This study aims the modeling and simulation of the direct extrusion process and determination of optimal process parameters using Finite Element Method (FEM) and Artificial Neural Network (ANN) cooperatively. First, the die set has been designed for direct extrusion of an aluminum rod and its numerical simulation has been prepared by mean of ABAQUS/EXPLITIC finite element code. So, both the values of the process parameters according to extrusion load and the critical stress values have been determined. After, the ANN model of the process has been developed under MATLAB and has been trained with the results of finite element simulations. Also, the optimization software which can run together the ANN model has been developed and has been used to determine the optimum process parameters. Introduction The extrusion process is an attractive production method in industry because of its ability to achieve energy and material savings, quality improvement and development of homogeneous properties throughout the component [1]. Lightweight construction, especially in the area of transportation engineering, is of increasing significance even with decreasing numbers of pieces regarding the production lot. Also, the need for high strength profiles with low density becomes more and more important due to the use of space – frame constructions in the automotive industry [2]. But, this production method is quite a lot complicated and so the process parameters must be carefully selected so that the production quality desired can be obtained. Therefore, researchers focused on the selection of optimum process parameters and the effects of these parameters on the extrusion load. A lot of experimental and numerical studies have been realized [3, 4, 5]. FEM has become a powerful technique to simulate metal forming process. Nowadays, the finite element numerical simulation not only can describe precisely the metal flow process, but also can give the fixed values of various physical fields, which is powerful tool to carry out the optimal design of technological parameters and to predict defects in the deformation process. However, a lot of trial-and-error computer tests are required in order to study the influence of the various parameters on the forming process. If the optimal design of the parameters is conducted using FEM only, many calculations are required, which results in the waste of resource [6]. However, ANN can be used to select design parameters and can considerably reduce the numerical simulation time. Therefore, ANNs have recently gained popularity as a tool for incorporating knowledge in Intelligent Manufacturing System (IMS). But, there is still a lack of use ANN and other artificial intelligence technologies in extrusion process. This study is organized as follows. In the first section, the die set has been designed for direct extrusion process and its finite element model has been prepared. The process has been simulated with various parameters using the model. In second section, ANN modeling of extrusion process bas been presented. ANNs have been trained with finite element simulation data obtained according

186

Advances on Extrusion Technology and Simulation of Light Alloys

to various process parameters. The determination of the optimum Process Parameters have been realized in third section. In fourth section, the results and discussion have been explained. The conclusions have been presented in the last section. Finite Element Simulation of Extrusion Process The die set (tool) has been designed and has been modeled and its number of finite element simulations have been performed with various process parameters such as coefficient of friction, punch velocity, die angle. The commercial finite element code, ABAQUS/Explitic, has been used to carry out the simulation. The model geometry is axi-symmetric in nature so only one half of the part has been simulated. The model, which consists of a rigid die and a deformable blank, has been shown in Figure 1.

Figure 1. Axi-symmetric model geometry of extrusion process The diameter of the cylindrical blank is 20 mm and the height is 30 mm. The blank is made of aluminum alloy AA5154 and its young’s modulus is 70.7 GPa; the Poisson’s ratio 0.33; the density is 2660 kg/m3. In this study, the radius of the blank has been reduced 60% by the extrusion process. The blank is constrained at the axis of symmetry in the r-direction. Radial expansion of the blank is prevented by contact between it and the die. In the case of ABAQUS/Explicit, penalty and kinematics contact formulations have been used in the definition of contact interactions. In the first step of the solution, the blank (the aluminum rod) has been moved to a position where contact is established and slipping of the workpiece against the die begins. In the second step, the rod has been extruded through the die to realize the extrusion process. This has been accomplished by prescribing a constant velocity for the nodes along the bottom of the rod. Undeformed configuration of the model before extrusion and deformation of the workpiece after extrusion have been shown in Figure 2. The process is carried out at room temperature. The solution has been repeated for different values of the process parameters such as punch velocity, coefficient of friction and die angle and so a number of simulations have been realized and obtained different results. The variation of extrusion load according to different process parameters has been presented in Table 1.

Key Engineering Materials Vol. 367

187

a

b Figure 2. a)Undeformed configuration of the model before extrusion, b) Deformation of the workpiece after extrusion

Table 1- The variation of extrusion load according to different process parameters Die angle(degrees) (α)

30 30 30 30 30 30 30 30 30 45 45 45 45 45 45 45 45 45 60 60 60 60 60 60 60 60

Coefficient of friction (µ)

0.1 0.1 0.1 0.15 0.15 0.15 0.2 0.2 0.2 0.1 0.1 0.1 0.15 0.15 0.15 0.2 0.2 0.2 0.1 0.1 0.1 0.15 0.15 0.2 0.2 0.2

Extrusion velocity (mm/s) (v)

1 1.5 2 1 1.5 2 1 1.5 2 1 1.5 2 1 1.5 2 1 1.5 2 1 1.5 2 1 1.5 1 1.5 2

Extrusion load (kN) (F)

69,3 144,9 147 168 172,2 247,8 210 294 315 67,2 147 153,3 94,5 168 174,3 273 315 338,1 52,5 58,8 60,9 100,8 157,5 162,75 273 294

188

Advances on Extrusion Technology and Simulation of Light Alloys

Twenty seven analyses have been realized by using different values of the parameters which consist of die angle, coefficient friction and punch velocity. So, a lot of results have been obtained after step 2 of the analysis. The deformed configuration, the contours of plastic strain and the Misses stress are principal of them. Also, time histories of plastic strain of the extruded rod have been acquired. However, only some of them can be given in this limited study. Figure 2 shows contour plots of plastic strain and the Misses stress for one of the simulation results. Whereas all load – time curves have been got, one of them has been shown in figure 3 as an example.

Figure 3. Load – time diagram obtained from the simulation The results obtained from Finite Element analyze can be summarized as following. The maximum stress occurs on the blank surface in the exit region of the die. Extrusion load has reduced with an increase in the die angle. But, it can’t be said that this correlation is absolutely correct when the angle is small. Extrusion load has increased when the friction coefficient and the punch velocity increase. The minimum extrusion load occurs if punch velocity and friction coefficient are minimum and die angle is maximum. The extrusion load has fluctuated for some cases. The reason of this matter can be comment with the mechanism that the fluctuation in the extrusion load is due to the separation of the die shoulder from the flow material. ANN model has been developed by using the process parameters in Table 1. ANN Modeling of Extrusion Process Neural Networks are popular and there are many industrial situations where they can be usefully applied. They are suitable for modeling various manufacturing function due to their ability to learn complex nonlinear and multivariable relationships between process parameters. In this study, ANN has been used as an alternative way for the modeling of extrusion process. A feed forward multilayered Neural Network has developed and trained using the results of finite element simulation. A multi – layer perception (MLP) is a feed forward network consisting of neurons in an input layer, one or more hidden layers and an output layer. The different layers are fully interconnected such that each neuron in one layer is connected to all neurons in the next layer. However, connections between the neurons in the same layer and feedback connections are not allowed. The input layer, which is also called the “buffer” layer, performs no information processing. Each of its neurons has only one input, and it simply transmits the value at its input to its output. Actual information processing is performed by the neurons in the hidden and output layers. Signals are

Key Engineering Materials Vol. 367

189

transmitted unidirectional from the input layer through the hidden layers to the output layer. Information is stored in the inter–neuron connections. Learning consists of adapting the strengths (or weights) of the connections so that the network produces desired output patterns corresponding to given input patterns. In other word, we can train a neural network to perform a particular function by adjusting the values of the connections (weights) between neurons. As each input is applied to the network, the network output is compared to the target. The error is calculated as the difference between the target output and the network output. We want to minimize the average of the sum of these errors. Each hidden or output neuron receives a number of weighted input signals from each of the units of the preceding layer and generates only one output value. The diagram for a network with a single neuron is shown in figure 4.

Figure 4. The structure of an artificial neuron Here, the scalar input (xi) is transmitted through a connection that multiplies its strength by the scalar weight (w), to form the product (wx), again a scalar. The inputs to the neuron can be from the actual environment or from the other neurons. Its output can be fed into other neurons or directly into environment. Also, this neuron has a scalar bias (bj), the output (yi) is produced by activation function and the network is trained by adjusting weights (w) and bias (b) to achieve desired end. The weights of the network is iteratively adjusted to capture the relationship between the input and output patterns. In this study, type of back – propagation is Scaled Conjugate Gradient algorithm and activation function is sigmoidal function. The weights are given quasi-random for initial values and then are iteratively updated unit they converge to the certain values using the train algorithm. The neural network architecture has been shown in figure 5. The number of neurons in input and output layers is based on the geometry of the problem. So the input layer which receives the pattern to be identified has 3 neurons. The output layer, which processes extracted features to obtain the pattern class, has one neuron. However, there is no general rule for selection of the number of neurons in a hidden layer and the number of hidden layers. Hence, the number of hidden layer and neurons in the hidden layer have determined by trial and based upon the least effective error and the optimal neural network architecture has been designed using MATLAB Neural Network Toolbox and so the model has nine neurons in the hidden layer. No smoothing factor is used.

190

Advances on Extrusion Technology and Simulation of Light Alloys

Output Vector (Extrusion load) Output Layer (1 Output Neuron)

Hidden Layer (9 Hidden neurons)

Input Layer (3 Input Neurons) α

µ

v

Input Vectors

Figure 5. The architecture of multi-layer perception (MLP) neural network The estimated values of the extrusion loads have been obtained by various neural network structures. The neurons in the input layer have unity activation (or transfer function). That is, they simply transmit the (scaled) values of the pattern points directly to the hidden layer. The processing by the neurons in the hidden and output layers is implemented with semi linear (sigmoid) activation functions. Input to the network were continuous and in the range 0–1. The network output is also continuous and in the same range. The back – propagation learning algorithm has been used in feed – forward. The type of back – propagation is scaled conjugate gradient algorithm and activation function is sigmoidal function. The extrusion load has been taken as the output neuron while the die angle, the punch velocity and the coefficient of friction are the elements of the input layer in ANN architecture. Some of the simulation data obtained for direct extrusion with the finite element model have been used to train the network. In other words, the FEM – based models provide the needed information for ANN and the network model is trained by some of the numerical simulation results. The model has been tested by using the rest numerical simulation results and the available similar literatures [7, 8, and 9]. It has been seen that the ANN results are close to the simulation and the experimental results and so the ANN model has been verified. Now, all that we need is to use the ANN model. The extrusion loads corresponding to the process parameters can be easily predicted before the operation. The neural network has been trained with different iteration number by using scaled conjugate gradient algorithm. The sum – squared error decrease with increasing iteration numbers until 2500 iterations. But, after this point, it stays constant. In other word, although the training continues and the iteration number increase, there isn’t any change in the error. On the other hand, the value of the error attained at 2500 iteration is enough for the determine error criterion. Both the iteration number and the error criterion are together considered and so a trial – and –error process is used. The training of the algorithm is stopped at 2500 iteration. The learning level of ANN for extrusion loads have been shown in figure 6. After then ANN is tested for accuracy by using the analysis results selected from the finite element simulation which haven’t been used for learning processes. The results of the test for extrusion load have been shown in figure 7. It can be seen that in most cases the neural network prediction is very close to the simulation values. The study has revealed that the predictions using ANN have more accurate results. The study shows that friction coefficient is a dominant parameter and it plays a very important role on the extrusion load.

Key Engineering Materials Vol. 367

191

Figure 6. The learning level of ANN for extrusion loads

Figure 7. The results of the test for extrusion loads

Determination of the Optimum Process Parameters An optimum selection of process parameters is extremely important issue. The extrusion load can be determined before operation using ANN model but essential aim of the study is to select the process parameters corresponding minimum extrusion load. Therefore, the optimization software which is running together ANN module has been developed. The software sent the parameters to ANN module sequentially. Each time, ANN predicts extrusion load according to received parameters and compare it with the value of the former extrusion load and record the minimum value of them to compare with the later value. Iteration continues and at last, the minimum extrusion load is acquired when all of the parameters are processed and iteration is completed. So, these parameters, which correspond to minimum extrusion load, are accepted as optimum process parameters.

192

Advances on Extrusion Technology and Simulation of Light Alloys

Conclusion In this research, the die set for the set for the direct extrusion of aluminum rod has been designed and its numerical simulations under varying friction coefficients die angles and punch velocities have been realized by using ABAQUS/Explitic finite element code. After, ANN model of the process has been prepared under MATLAB/Neural Network Toolbox and the model has been trained using simulation data. Different software to select the optimum process parameters has been developed and it has been integrated with ANN model. From the study, the following conclusions can be drawn.
The results of Finite Element Simulation can be much the same with actual extrusion process if the model is perfect and mesh can be selected as sufficient fine. So, we can observe maximum stress regions and can determine damage conditions.
The solution time of ANN is very shorter than FEM and the extrusion load can be easily obtained according to process parameters. The solution of ANN spends only five minutes while FEM continues sixty minutes for one extrusion solution.
To determine the optimum process parameters correspond to the minimum extrusion load is possible using together ANN model and optimization. It is expected that the use of artificial intelligence technologies will be open up new avenues for the control of the extrusion process. Future work will focus on to extent this study by using more process parameters and the model presented in this paper will be verified by comparing the numerical results with experimental measurements obtained under equivalent extrusion conditions. References [1] F. H. Raj, R.S. Sharma, S. Srivastava, C. Patvardhan, “Modeling of Manufacturing Process with ANNs for Intelligent Manufacturing”, International Journal of Machine Tools & Manufacturing vol. 40 (2000) pp.851-868 [2] H.-S. Lin, C.-Y. Lee, C.-H. Wu, “Hole Flanging with Cold Extrusion on Sheet Metals by FE Simulation”, International Journal of Machine Tools & Manufacturing vol. 47 (2007) pp.168174. [3] H.J. Li, L.H. Qi, H.M. Han, L.J. Guo, “Neural Network Modeling and Optimization of SemiSolid Extrusion for Aluminum Matrix Composites”, Journal of Materials Processing Technology vol.151 (2004) pp.126-132 [4] M. Kleiner, M. Schikorra, “Simulation of Welding Chamber Conditions for Composite Profile Extrusion”, Journal of Materials Processing Technology vol. 177 (2006) pp.587-590. [5] B.R. Tibbetts, J.T.-Y. Wen, “Extrusion Process Control: Modelling, Identification, and Optimization”, IEEE Transactions on Control System Technology vol. 6 (1998) pp. 134-145 [6] B.P.P.A. Gouveia, J.M.C. Rodrigues, N. Bay, P.A.F. Martins, “Finite – Element Modeling of Cold Forward Extrusion”, Journal of Materials Processing Technology vol.94 (1999) pp.85-93 [7] K.D. Hur, Y. Choi, H.T. Yeo, “A Design Method for Cold Beckward Extrusion Using FE Analysis”, Finite Elements in Analysis and Design vol. 40 (2003) 173-185 [8] X.Q. Zhang, Y.H. Peng, X.Y. Ruan, K. Yamazaki, “Feature Based Integrated Intelligent Sequence Design for Cold Extrusion”, Journal of Materials Processing Technology vol.174 (2006) pp.74-81 [9] A.V. Nagasekhar, Y. Tick-Hon, “Optimal Tool Angles for Channel Angular Extrusion of Strain Hardening Materials by Finite Element Analysis”, Computational Materials Science vol. 30 (2004) pp. 489-495

Key Engineering Materials Vol. 367 (2008) pp 193-200 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/KEM.367.193

Numerical simulation of combined forward-backward extrusion B. Grizelj 1,a, M. Plancak2,b, B. Barisic3,c. 1

University of Osijek, Mechanical Engineering Faculty, Croatia, 2

University of Novi Sad, FTN, Serbia,

3

University of Rijeka, Faculty of Engineering, Croatia,

a

[email protected], [email protected], [email protected]

Keywords: metal forming, extrusion, finite element method.

Abstract. The paper analyses the process of simulation forward-backward extrusion. In metal forming industries, many products have to be formed in large numbers and with highly accurate dimensions. To save energy and material it is necessary to understand the behavior of material and to know the intermediate shapes of the formed parts and the mutual effects between tool and formed party during the forming process. These are normally based on numerical methods which take into account all physical conditions of the deformed material during the process. For this purpose, the finite element method has been developed in the past in different ways. The paper highlights the finite element simulation as a very useful technique in studying, where there is a generally close correlation in the load results obtained with finite elements method and those obtained experimentally. Introduction Over the last years, various metals forming processes have gained significant industrial attention as a result of the rapid cost of raw materials. Compared to machining processes that involves the removal, and basically waste of portions of material, many leading manufacturers are currently turning towards more effective methods, particularly near net shape forging processes [1]. Despite this increased interest, metal forming technology at the industrial level is mostly based on experience, and trial and error methodology, rather than methods arising from a rigorous scientific approach. A great variety of modelling techniques is available today to engineers in design and development. Among various methods of solution for extrusion process, the upper bound elemental technique and slip-line method though the advantages of both are analytical approach show many difficulties. An another way is the use of numerical methods where especially the use of Finite Element Method offers the opportunity of getting important process information by simulation. Nevertheless the increasing versatility of modern hard - and software tools, the quality of the results still depends strongly on the decisions and choices made by engineers during modelling a problem. This paper focuses on the investigation of the possibility of modelling the backward extrusion process and accuracy of results and material behaviour using commercially available FEsoftware, thus predicting both the magnitude and the distribution of the stresses. In the process of backward extrusion as coupled thermal and mechanical problem, the complexity arises through the temperature and strain rate as well as stress-dependent material properties in the mechanical (stress) problem and the internal heat generation caused by plastic work which serves as input for the heat transfer problem. Modelling of the process In the presented paper investigation of the axisymmetric backward extrusion process of thebody of automatic valve of material Al-Mg3 according to ISO R-209 and DIN 1725 is analysed as an example of finite element modelling. During the process, the workpiece material in the container is treated under a high pressure. The zone of intensive plastic stresses is located around the top of the punch, while the zone of intensive plastic strain around the punch. The distribution of the stresses and strain is more

194

Advances on Extrusion Technology and Simulation of Light Alloys

complicated by the fact that in the process temperature can rises and then there are at least several sources of coupling analysis: - As the temperature changes, thermal stresses are developed due to non-zero coefficient of thermal expansion (and the presence of boundary constraints). - As the temperature changes, the mechanical properties change. In this case, it is caused by the temperature-dependent flow stress. - As the geometry changes, the heat transfer problem changes. This includes changes in the contacting interface. - As plastic work is performed, internal heat is generated. - As the bodies slide, contact friction generates heat. The problem used full Newton-Raphson iterative procedure to solve the iteration process and nonlinear equations of motions. The method has quadratic convergence properties and the stiffness matrix is reassembled at each iteration. In applied Lagrangian approach, the element stiffness is assembled in the current configuration of the element, and the stress and strain output are given with respect to the coordinate system in the updated configuration of the element. Due to the nature of the physical problem a non-positive definite solution control is forced. As the large displacements are required, an additional contribution has been made to the stiffness matrix labelled the initial stress stiffness matrix. As a default, the analysis program uses the full stress tensor at the last iteration which in general results in the fastest convergence. A residual force and moment convergence criteria with 10% tolerance has been invoked including relative mode selection. The Lanczos method algorithm that converts the original eigenvalue problem into the determinaton of the eigenvalues of tri-diagonal matrix and direct integration as a numerical method for solivng the equations of motion is flagged.

Figure 1. Distribution of equivalent plastic strain in final stage of extrusion

Key Engineering Materials Vol. 367

195

Simulation results and their interaction In this case the workpiece consisted of 1560 triangular three node isoparametric elements. They have proved as much more suitable for such great deformations that take place, instead of quadrilateral elements that are commonly recommended in MARC. The three node, isoparametric, triangular element written for axisymmetric heat transfer applications that use bilinear interpolation functions, offers better representation since the thermal gradients tend to be constant throughout the element. Updated Lagrange procedure and finite strain plasticity is vailable where crossed triangle option approach is recommended. It must be emphasised at this point, that during the material flow the elements undergo a severe mesh distortion that has found as one of the most important problems during the analysis. Since the mesh is attached to the deforming material, the distortion of the element mesh leads to a degeneration of the results. The used types of element include the updated Lagrange procedure, but in such strong distortion of the element shapes during deformation-process simulation not only cause inaccurate solutions but may result in elements turning inside out. The updated Lagrange approach has several advantages, but one serious disadvantage is putting a limit on the maximum deformation attainable. The first and the simplest way is a good choice of the initial element size i.e. to increase the number of elements. Sometimes it cannot overcome the problem, and the second way is the use of adaptive meshing where error criteria such as Zienkiewicz-Zhu, maximum stress or due to contact condition the mesh can be adaptively refined. This procedure results in greater number of elements and nodes in the region where adaptive meshing is being applied, and can lead to a substantial improvement in the accuracy of the solution. Unfortunately neither of those above mentioned procedures have been successfully applied in the considered model. In both of them, the distortion was too strong and inside out error has occurred. The third and most powerful way in large strain finite element analysis to overcome this problem is the element mesh rezoning philosophy, which has been developed in conjunction with appropriate computer coding implemented into a general purpose nonlinear finite element program.

Figure 2 The component 11, 22 and 33 of stress of the node under the top of the punch

196

Advances on Extrusion Technology and Simulation of Light Alloys

Figure 3. Distribution of equivalent von Mises stress in tool and workpiece In order to correct the distorted element shapes, the actual finite element mesh can be periodically redefined after some amount of deformation has occurred. This redefinition of the model is based on the deformed shape and on the current state of the material flow i.e. transfers of the information from old to new mesh through interpolation (figure 2 and 3). The result of this operation is the true deformed mesh which can serve as a basis for a new mesh defined through the deformed configuration. However, unlike the automatic remeshing procedure used in MARC Auto Forge program, the user has to create this mesh by hand. The new mesh should then be written to an input file requiring the creation of some new editing operations to create a proper rezoning. If the number of nodes and elements are sufficiently great, such a procedure is out of question, and it remains the last possibility to overcome the problem of severe mesh distortion. When the most critical elements were established, they have been modified through move option in such a way that the problematic or the most critical nodes have been moved in an opposite direction of deformation and material flow direction. On that way it can be expected that through the process of material flow such a predeformed element will not be so strongly destorted at the and of the forming process. The punch consisted of 382 and the die of 765 quadrilateral elements. Quadrilateral four node element is isoparametric, arbitrary written for axisymmetric application. As this element uses bilinear interpolation functions, the strains tend to be constant throughout the element. This results in poor representation of shear behaviour, but is preferred over higher order elements when used in contact analysis. The constant dilatation option eliminates potential element locking and is flagged through the geometry option. The influence of friction factor is considered, especially in the calculation of required reaction forces. Friction is a complex physical phenomenon that involves the characteristic of the surface

Key Engineering Materials Vol. 367

197

such as surface roughness, temperature, normal stress and relative velocity. In MARC the numerical modelling of the friction has been simplified to two idealistic models, and here it was used the cohesive, shear based friction model. The load punch motion curve for this problem is calculated from the total reaction forces in the plane of symmetry. As it can be seen from figure 4, the characteristic of this curve corresponds in good approximation with the experimental ones. Material flow tendency during the process can be visualised by material marker lines of equivalent plastic strain given in figure 1 and compared with flow lines in figure 5. Obviously, the simulation results differ from the experiment, caused by relative sliding in the contact area of workpiece and convex area of the die, but the area of difficult flow of material can be identified both in the computed as well as in the experimental case. Two possible reasons for this behaviour can be examined: firstly, in stationary conditions during the production process, the contact area may reach higher local temperature, which implies a reduction of flow stress; secondly, the employment of simple friction law with constant coefficient does not describe the local contact state with sufficient accuracy. Further investigation is needed to validate these assumptions.

Figure 4. Load curve obtained in experiments and simulation process Further, it was possible is to compare this results with the numerical solutions proposed for such process of deformation where it can be applied several formulas and also use the well known nomogram edited in [16]. The considerd formulas are:

F = Ad1

k fm ⋅ ϕ

ηf

d0 d 0 − d1 η f = 30 − 70%

ϕ = ln

Such an expression is proposed in [13]

198

Advances on Extrusion Technology and Simulation of Light Alloys

Another used expression that are some more detailed is: F = Ad1 ⋅ p

 µ ⋅ d1  µ  + k f 1 + k f1  0.25 +  p = k f0 1 + 3 3h0  2   where logaritmic deformaton has the same value as in the first case [16]. Yet one used expression also possible for this case is: F = Ad1 ⋅ p 2   d0         d 2    d1   p = k fm 2 + 1 +  0   ln  2   d 1    d 0      − 1   d1    For the considered case all numerical results including that obtained with nomogram here not presented, was between 220 and 250 kN, and the simulation results fit this values in well approximations as it can be perceived from figure 4. As the press on which the process was conducted has a maximum force of 1.5 MN what means that the press on disposal can satisfy all required force values.

Conclusions

The residual stress calculation indicates that the solution is somewhat in equilibrium. Compared to the reaction forces, the errors in nodal equilibrium are in order of 1%. The equivalent plastic strain is calculated from the strain components. The quality of the mesh proved to be an essential factor in performing successfully FEM analysis. The number, size and shape of the elements are of importance for the solution accuracy. The number of nodes influences especially regarding the simulation of friction forces . Also, the severe distortion of the mesh near the punch edges has caused the mesh to be modified in such a way to overcome that problem because mesh refinement and mesh/rezoning algorithms are not fully supported in current MARC K.7.1 and Mentat 3.1 version. The user has to create this mesh by hand what was impossible regarding the great number of nodes and elements in the analysis. The possibility of analysis the local stress-strain rate and stress distribution enhance an improved tool design, prevention of premature die failure and elastic displacement of the tooling might assist in the process layout phase, where a corrected tool geometry can be developed.

Key Engineering Materials Vol. 367

199

Figure 5. Material flow lines as observed in a transversal cross-section at the end of extrusion process Using the arbitrary engineering approach, it is possible to make conclusions only regarding the maximum load necessary for the deformation, where it is presumed that the forward part of extrusion is finished before the end of the process. Thus, the final load and force are computed as pure backward extrusion, but one cannot be sure if the die is regularly filled with material. Using the simulation procedure one can predict and control the flow of the material and compute the needed work for the whole process. With FEM it has become possible to predict both the magnitude and the distribution of the stresses in a workpiece due to the forming and it has thus become possible to optimise the forming process with regard to the stresses, form and number of stages as well as the needed forces and work of deformation. The number, size and shape of the elements are of importance for the accuracy of the solution, especially regarding the simulation of friction forces. The possibility of analysing the local stressstrain rate and stress distribution, meshing both the workpiece and the tool parts, enhances an improved tool design and prevention of premature die failure. The elastic displacement of tooling might assist in the process layout phase, where a corrected tool geometry can be developed (figure 3). The results showed here, demonstrate the final element approach and simulation as a useful technique in studying the process of simultaneous forward-backward extrusion, where there is generally a close correlation in the load results obtained with FEM and those obtained experimentally. The correctness of the computed results is still dependent on the selection made regarding various modelling parameters. Recent developments in the field of numerical methods, embodied in more and more reliable simulation software, together with the leap in computing power made by affordable desktop computers, makes the analysis of metal forming processes, here investigated the process of backward extrusion available to engineers on the workshop floor.

200

Advances on Extrusion Technology and Simulation of Light Alloys

Among the most important aspects which can be mentioned, the constitutive law and the boundary conditions as well as correct mesh and type of elements play a decisive role in achievement of correct results. As a general rule, computational costs are rising with the desired precision, reliability and quality of results. References [1]

Hill. R., New horizons in the mechanics of solids // J. Mech. Phys. Solids 5, 66, 1956.

[2]

Yamada Y. and Takatsuka K., Finite element analysis of nonlinear problems // J. Jap. Soc. Tech. Plasticity, 14, 758, 1973.

[3]

Larsen P. K., Large displacement analysis of shells of revolutions, including creep, plasticity and viscoplasticity // Ph. D. Thesis, University of California, Berkeley, 1971.

[4]

Needleman, A., Void growth in an elastic-plastic medium, Ph. D. Thesis, Harvard University, 1970.

[5]

McMeeking M. and Rice J. R., Finite element formulation for problems of large elastic-plastic deformation // Int. J. Solids Struc. 11, 601, 1975.

[6]

Grizelj B., Barisic B. and Math M., FEM in plate bending // J. Key Engineering Materials Vol. 344, 269-276, 2007.

[7]

Altan, T, - Application of CAD/CAM in precision forming, Steel research, VDI, Nr. 5/88, pp. 212-219, 1988.

[8]

Doege, E., - Rotarescu, M.I., Neubauer, I., Soluton accuracy of Finite- Element Modelling techniques in simulation of cold massive forming, NAFEMS World Congress'97, Volume 1, pp. 347-357, 1997.

[9]

Lange, K., -Lehrbuch der Umformtechnik, Springer-Verlag, Berlin, Heidelberg, New York, 1974.

[10] Doege, E., Meyer-Nolkemper. H., Saeed, I., - Fließkurvenatlas metalischer Werkstoffe, Hanser-Verlag, München-Wien, 1986. [11] Miles, M.P., Fourment, L., Chenot, J.L., - Calculation of tool temperature during periodic non-steady metal forming, J. Mater. Process. Technol., Nr. 45, pp. 643-648, 1994. [12] Spur, G., Stoeferle, T., -Handbuch der Fertigungstechnik, Volume 2, Hanser-Verlag, München-Wien, 1983. [13] Bathe, K.J., - Finite element procedures in engineering analysis, Prentice-Hall, Inc., Englewood Cloffs-New Jersey, 1982. [14] MARC -Users guide, MARC Analysis Corporation, Palo Alto, California, 1997. [15] Hinton, E:, -Introduction to nonlinear finite element analysis, NAFEMS, East Kilbridge, Glasgow G75 0QU, 1992. [16] Beisel, V, - Die Grenzen der Kaltumformung ind ihre Bedeutung für die Berechnung und Planung von Kaltformteilen, TZ Metalbearbeitung., Stuttgart, 1964.

Key Engineering Materials Vol. 367 (2008) pp 201-208 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/KEM.367.201

Mechanical solutions for hot forward extrusion under plane strain conditions by upper bound method R. Domingo1,a, A.M. Camacho2,b, E.M. Rubio3,c and M.A. Sebastián4,d 1,2,3,4

National Distance University of Spain (UNED), Department of Manufacturing Engineering. C/ Juan del Rosal, 12. Madrid 28040 (Spain) a

[email protected], [email protected], [email protected], d [email protected]

Keywords: Square die, Upper bound method, Plane strain, Validation, Models, Friction.

Abstract. This paper present a study focused on hot forward extrusion by upper bound method. In particular, hot forward extrusion of plates through square face dies under plane strain conditions. Slater defines the models used for large fractional reduction. Different models have been taken in account; they are dissimilar in relation to the dead metal zone (if covers or not the entire die face, partially or totally). Triangular rigid patterns of velocity discontinuities have been validated by analytical methods and a range of use for the selected configurations has been established. This methodology has been applied to other process with good results. Thus, the mechanical parameters analysed are fractional reduction, dead metal zone, length die and friction. Finally the calculation of the energy has been achieved by upper bound method. The results allow researching an optimisation of use of upper bound method in hot forward extrusion. Introduction Extrusion process is studied by different approaches such as Finite Element Method [1,2], mathematical techniques [3] and analytical methods [4,5,6]. The last one has important advantages; it allows the calculation of main parameters of process without big resources. Thus, it is especially important in small industries devoted to manufacturing, but not to design. Its use can allow selecting the adequate machine according to requirements of process. The Upper Bound Method (UBM) is an analytical technique that it has demonstrated its utility [7]. Literature shows examples in processes, such as drawing [8,9,10] or extrusion [4,5,6]. However there are not applications about hot forward extrusion under plane strain conditions by UBM in plates thought square face dies. The main objective of this paper is to carry out an energetic analysis of several models by means of triangular rigid zones. Then we could select to model that provokes a major energy and analyse the fundamental parameters. Other considerations are the following: hot extrusion does not take into account the strain hardening in energy equation; forward extrusion is interesting in the industry, in particular through a square face die [11,12]. Moreover the square face die is similar to symmetric wedge-shaped die when dead metal zone (DMZ) is formed at the die face. Finally extrusion under plane strain conditions provides a constant width that makes it easier to apply rigid models. Rigid Zone Models Rigid zone models under plane strain conditions are showed in Fig. 1, Fig. 2, Fig. 3 and Fig. 4. They describe the geometric layout of forward extrusion process. Thus, hi is the initial thickness of the plate, hf the final thickness of the plate, R is the fractional reduction, r the cross-section area reduction. We have adopted various models according to DMZ formed and the number of triangular blocks. In them and in their corresponding hodograph, Pz is the extrusion pressure, vi is the i-block velocity, and vij is the relative velocity between blocks i and j. We have taken four models, two of them have been identified to large fractional reductions [13]; they have several rigid blocks. Also we have taken two more, with a rigid block, due to similarity to the firsts. It allows comparing them.

202

Advances on Extrusion Technology and Simulation of Light Alloys

Model with a triangular zone when DMZ is not present. Model analysed and its hodograph are showed in Fig. 1. Three different zones are illustrated, zone 1 is the non-deforming region, zone 2 is the plastically deforming region and zone 3 is deformed region. vf = R = 1/1-r vi =1

A O

φ

v1 hi/2

Pz

2

v2

v2

1 φ

v23

v12

C

θ

v3 3 hf/2

θ B

Figure 1. Model with a rigid zone when DMZ is not present: Geometrical layout and hodograph Model with several triangular zones when DMZ covers partially the die face. In it the plastically deforming regions are zone 2 and zone 3 (see Fig. 2). Slater [13] illustrates this model for large fractional reductions. Also it is interesting when the friction is present in the recipient [7]. DMZ is modelled by a rectangular triangle of 45º. v4 = R v1 A

O v1 Pz

D

2 φ

hi/2 1

45º φ ψ v2 v12

45º

v3

3 C

ψ

4

θ

θ

hf/2

v34

v23

v4

B

Figure 2. Model with several triangular zones when DMZ covers partially the die face: Geometrical layout and hodograph Model with a triangular zone when DMZ covers the entire die face. It is a basic model, similar to drawing process one (see Fig. 3), although in this case the angle of DMZ (45º) is very superior to die angle in drawing process [8,9,10]. v3= R v1= 1

A O

DMZ

β

v1 Pz

hi/2

v2

2

1

v12

θ v23

C θ

β

hf/2

v3

3

B

Figure 3. Model with a triangular zone when DMZ covers the entire die face: Geometrical layout and hodograph

Key Engineering Materials Vol. 367

203

Model with several triangular zones when DMZ covers the entire die face. Slater [13] considers this one adequate for large fractional reductions, as model with several triangular zones when DMZ covers partially the die face. It is a particular representation of others identified by Rowe [11], Slater [12] or Johnson [13] for drawing process. Now the equivalent angle β of preceding case is of 90º. A O

DMZ

45º

v1 D

hi/2

Pz

C λ

hf/2

ψ

B v5 = R

v5

θ E

v3 v1 β

λ v12

v2

ψ v23

θ v34

v45

v4

Figure 4. Model with several triangular zones when DMZ covers the entire die face: Geometrical layout and hodograph Calculation of specific energy Those models are analysed taken in account fractional reduction, DMZ, length die and friction. Thus, k is shear yield stress; Pz/2k is the dimensionless extrusion pressure, m partial friction coefficient. Moreover OA represents the length of recipient considered in the computation of energy; for calculation convenience OA depends on hi. In addition, this assumption permits to establish a link between the thickness and the length of the recipient studied. Therefore we employ the total specific energy (Pz/2k)T, and its components: specific homogeneous deformation energy (Pz/2k)H, specific redundant energy (Pz/2k)R and specific friction energy (Pz/2k)F.  Pz  P  P  P    =  z  +  z  +  z   2k  T  2k  H  2k  R  2k  F

(1)

 Pz    = ln R  2k  H

(2)

P  Pz    = z  2k  R 2k

− ln R m=0

(3)

204

P  Pz    = z  2k  F 2k

Advances on Extrusion Technology and Simulation of Light Alloys

(4) m

Firstly, we will study influence of the angles of the each model and the specific redundant energy, (Pz/2k)R, calculated. The objective is to determine the model that supplies the higher energy according to UBM theory. The range of parameters considered is showed in Table 1. Table 1. Range of parameters R 2, 2.5, 3, 3.5

θ 60º, 65º, 70º

φ

ψ

Variable

85º

λ Variable

Model with a triangular zone when DMZ is not present. Eq. 5 can be deduced from geometrical layout and hodograph.  Pz  1 R−1 tan ϕ   = +m tan ϕ + + m OA 2R 2 R sin 2 θ  2k  F sin 2ϕ

(5)

Pz/2k

According to Eq. 5, Pz/2k has influence of angles φ and θ when friction lacks; furthermore the length of recipient does not affect in the calculation of specific redundant energy. Fig. 5 represents the influence of angle θ when m=0; without partial friction coefficient, the dimensionless extrusion pressure increases if θ is higher. Moreover we appreciate that the expansion between 2.5 and 3 values of fractional reductions is less than other segments.

5,5 5 4,5 4 3,5 3 2,5 2 1,5 1 0,5

θ=60º θ=65º θ=70º

2

2,5

3

3,5

R

Figure 5. Specific redundant energy Model with several triangular zones when DMZ covers partially the die face. This model possesses more complexity than previous one. Eq. 6, deduced from geometrical layout and hodograph, allows calculating the dimensionless extrusion pressure; it represents the specific friction energy.  Pz  (R − tanψ cot θ ) (1 + tanψ ) 1 R − tanψ cot θ cot θ   = + + + + 2 ( ) ( ) ( ) 2 k 2 R sin − cos tan cos + sin sin 2 R cot + 1 ϕ ϕ ψ ϕ ϕ θ ϕ R ψ (cot ϕ + 1) 2 cos  F (tanψ cot θ − 1) (1 + tanψ ) + mOA +m 2 R(cot ϕ + 1)

(6)

In absence of friction, the angles θ, φ and ψ determine the energy for each fractional reduction. Angle θ has the main influence in the energy, and the latter is superior when the fractional reduction is increased. Influence of angle φ is appreciated too (see Fig. 6), but now the specific redundant energy is higher when is φ lower.

Key Engineering Materials Vol. 367

205

5,5

Pz/2k

4,5 θ=60º φ=85º

3,5

θ=65º φ=85º 2,5

θ=70º φ=85º

1,5 0,5 2

2,5

3

3,5

R

Figure 6. Specific redundant energy Model with a triangular zone when DMZ covers the entire die face. Results are obtained from Eq. 7. They are similar to model without DMZ respect to effect of angle θ, although the values are lower in this case. Also we can detect that the specific redundant energy escalates more lineally when fraction reduction is increased (see Fig. 7).

Pz/2k

R−1 1 1  Pz  + + + m OA   = ( ) ( ) ( k R − − 2 1 cot β 2 sin β sin β cos β 2 sin θ cos θ + sin θ )  F

5,5 5 4,5 4 3,5 3 2,5 2 1,5 1 0,5

(7)

θ=60º θ=65º θ=70º

2

2,5

3

3,5

R

Figure 7. Specific redundant energy Model with several triangular zones when DMZ covers the entire die face. It is mathematically modelling in Eq. 8. A new parameter is introduced, the angle λ. Results prove an upper energy in higher angle θ (see Fig. 8). The values obtained are superior to previous model, case of a triangular zone. It is coherent with the result found in drawing process [10].

(1 + cot ψ ) (1 + cot θ ) + (cot θ + 1) (cot ψ + 1) sin λ (cot θ + 1) sin λ (cot ψ + 1) sin λ +  Pz  +   = + 2 2 2 R(sin λ − cos λ ) 2 R sin ψ (sin λ − cos λ ) 2 R sin 2 θ (sin λ − cos λ ) 2 R(sin λ − cos λ )  2k  F sin λ sin λ (1 + cot θ ) cot θ sin λ (cot ψ + 1) + − + + m OA (8) sin λ − cos λ R(sin λ − cos λ ) R(sin λ − cos λ ) In general, if the fractional reduction is increased, the specific redundant energy grows. Thus, the energy achieves the major value for θ=70º and ψ=85º.

206

Advances on Extrusion Technology and Simulation of Light Alloys

5,5 5 4,5

Pz/2k

4 3,5

θ=60º ψ=85º

3

θ=65º ψ=85º

2,5

θ=70º ψ=85º

2 1,5 1 0,5 2

2,5

3

3,5

R

Figure 8. Specific redundant energy Results and discussion Former section identifies the model with superior energy; it is the model with several triangular zones when DMZ covers partially the die face (second case). Conditions of similitude of DMZ, angles, length of recipient considered and friction provide the sensibility of the model respect to different types of energy.

R=2.5 m=0.2 OA=hi/4

R=2 m=0.2 OA=hi/4

6 Pz/2k

Pz/2k

6 4

4

2

2

0

0

75

80

85

75

90

80

SRE

SHDE

SFE

T otal

SRE

SHDE

T otal

R=3.5 m=0.2 OA=hi/4

R=3 m=0.2 OA=hi/4

6 Pz/2k

6 Pz/2k

90

φ

φ SFE

85

4 2

4 2 0

0 75

80

85

90

75

80

SRE

90

φ

φ SFE

85

SHDE

T otal

SFE

Figure 9. Specific energy for θ constant

SRE

SHDE

T otal

Key Engineering Materials Vol. 367

R=2; φ=85º; θ=70º

R=2.5; φ=85º; θ=70º

10

10

9

9 8 m=0.2

7

m=0.8

Pz/2k

8 Pz/2k

207

6

6

5

5

4

4

0,00

0,10

m=0.2

7

m=0.8

0,00

0,20

0,10

hi

R=3.5; φ=85º; θ=70º

R=3; φ=85º; θ=70º 10

10

9

9 8

8 m=0.2 7

Pz/2k

Pz/2k

0,20 hi

m=0.8

m=0.2

7

6

6

5

5

m=0.8

4

4 0,00

0,10

0,00

0,20

0,10

0,20

hi

hi

Figure 10. Specific energy for different values of m R=2.5 m=0.2 OA=hi/4

15

15

10

10

Pz/2k

Pz/2k

R=2 m=0.2 OA=hi/4

5 0

5 0

55

65

75

85

55

65

ψ SFE

SRE

85

ψ SHDE

T otal

SFE

R=3 m=0.2 OA=hi/4

SRE

SHDE

T otal

R=3.5 m=0.2 OA=hi/4

15

15

10

10

Pz/2k

Pz/2k

75

5

5 0

0 55

65

75

85

55

65

SRE

85

ψ

ψ SFE

75

SHDE

T otal

SFE

SRE

Figure 11. Specific energy of θ and DMZ variable

SHDE

T otal

208

Advances on Extrusion Technology and Simulation of Light Alloys

Thus we take angle θ as constant (see Fig. 9), so the position of point B is invariable and DMZ is reduced if angle φ decreases or vice versa. For a particular fractional reduction (R=2 and R=2.5), energy diminishes not much, and for R=3 and R=3.5 is practically constant; as a result we can affirm that once selected the point B, the values of angles φ and ψ are almost irrelevant. In this case, it is observed that the effect of angle φ is superior to effect of fractional reduction. Fig. 10 represents the influence of partial friction in several points of recipient, given angles θ and φ. Thus the DMZ is the same. It is appreciated that the length is not important respect to friction coefficient (m=0.2 and m=0.8). In consequence the element more significant is the friction. Finally in Fig. 11 can be observed the evolution of energies when length of recipient (hi/4) and friction (m=0.2) are constant, and angle φ is constant for each fractional reduction. In addition θ is variable, and therefore DMZ. The variation of θ supposes that the considerations of several positions of point B (see Fig. 2). In this case, DMZ is increased when θ and consequently ψ are inferior. Fig. 11 shows for each fractional reduction, the energy is increased when ψ is higher; it supposes DMZ lower, likewise the friction in the recipient is higher. Conclusions This analysis provides some conclusions about the extrusion process modelling by means of rigid blocks and studied by analytical methods, especially UBM. We have studied four models, and the model with several triangular zones when DMZ covers partially the die face requires more energy to carry out the process. In the last one, when the point B is set, we have observed that the model is more robust for an angle θ fixed and the specific energy is stable when the angle φ changes and the coefficient friction is permanent. Moreover we have appreciated that length recipient has less influence than the friction when DMZ is constant. Finally, we can remark that when the length of recipient and the friction are fixed, an increment of DMZ provokes a reduction of energy. References [1] K.H. Min, B.D. Ko, B.S. Ham, J.H. Ok, B.B. Hwang, H.S. Koo, J.M. Seo: Key Eng Mater Vol. 340-341 (2007) p. 577. [2] D.H. Jang, B.B. Hwang: Key Eng Mater Vol. 340-341 (2007) p. 645. [3] N.S. Das, N.R. Chitkara, I.F. Collins: Int J Num Meth Eng Vol. 11 (2005) p. 1379. [4] D.K. Kim, J.R. Cho, W.B. Bae, Y.H. Kim: J Mater Proc Tech Vol. 62 (1996) p.242. [5] N. Venkata-Reddy, R. Sethuraman, G.K. Lal: J Mater Proc Tech Vol. 57 (1996) p.14. [6] S. Alexandrov, G. Mishuris, W. Miszuris, R.E. Sliwa: Int J Mech Sci Vol. 43 (2001) p. 367. [7] M.A. Sebastian, J.M. Perez, A.M. Sánchez-Pérez: Deformación Metálica Vol. 90 (1983) p.29. [8] E.M. Rubio, R. Domingo, J.M. Arenas, C. González: J Mater Proc Tech Vol. 155-156 (2004) p. 1220. [9] E.M. Rubio, C. González, M. Marcos, MA, Sebastián: J Mater Proc Tech Vol. 177 (2006) p. 175. [10] E.M. Rubio, R. Domingo, C. González, A. Sanz: Rev Metal Madrid Vol. 40 (2004) p.46. [11] G.W. Rowe: Conformado de metales (Urmo, Bilbao 1977) [12] W. Johnson, R. Sowerley, J.B. Haddow: Plane-strain slip-line fields: Theory and bibliography (Edward Arnold, London 1970) [13] R.A.C. Slater: Engineering Plasticity. Theory and Applications to Metal Forming (McMillan Press, London 2004).

Key Engineering Materials Vol. 367 (2008) pp 209-214 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/KEM.367.209

Different possibilities of process analysis in cold extrusion M. Plancak1, a, B. Barisic2, b, B. Grizelj3, c 1

University of Novi Sad, FTN, Serbia

2

University of Rijeka, Faculty of Engineering, Croatia

3

University of Osijek, Mechanical Engineering Faculty, Croatia

a

[email protected], [email protected], [email protected]

Keywords: Cold extrusion, complex shapes, analysis, experiment.

Abstract. Cold extrusion is a technology which offers a number of advantages when compared to other manufacturing technologies. High mechanical properties of extruded component, short production time as well as significant cost effectiveness which can be achieved by implementation of this technology are the main characteristics of cold extrusion process. In order to design the complete extrusion process in optimal way it is crucial to know the main process parameters such as load, die pressure, stress and strain distribution within deformation zone etc. There is a number of methods for the analysis of cold extrusion processes. Current paper gives the insight into the possibilities of process analysis in three different cases of cold extrusion. Radial extrusion of gear like elements has been analyzed theoretically (Upper Bound method), numerically by FE simulation and experimentally. Die stressing has been measured by special device (pin load cell) in the process of forward extrusion. Third analyzed process was backward extrusion with profiled punch. In this process loading characteristics as well as some of the mechanical properties of extruded component were obtained experimentally. Introduction Cold extrusion has been a subject of numerous theoretical, numerical and experimental investigations so far. These investigations have been focused at various problems of cold extrusion, such as: -

application of new workpiece materials new concepts, designs and manufacture of the extrusion tools new tool materials application of computers in all phases of the process development CAD/CAM techniques in extrusion development of new extrusion techniques “net-shape” forming increasing the range of components complexity

Great number of theoretical and experimental works related to this technology has been reported at international conferences and in relevant journals. The main aspects and principles of precision cold extrusion are presented in [1]. The author gives a definition of “Net-shape forming” and “Near-net-shape-forming” which, meanwhile, became a standard term (expression) in metal forming terminology. Significant contribution to the cold extrusion of precision parts can be found in [2] in which the author analyses the preconditions for one high-precision cold extrusion process. Kondo [3] describes a new concept in cold extrusion, so called “divided flow”, which offers possibilities to lower the extrusion load and die pressure. Author introduced the concept of flow – relief- hole and flow-relief-axis.

210

Advances on Extrusion Technology and Simulation of Light Alloys

Extrusion of spiral bevel gears has been presented in [4]. Process has been analyzed not only from technical but also from economical standpoint. Special software has been used for that purpose. For the optimal die design and process analysis the knowledge of die loading during the extrusion process is of great importance. In [5] experimental work concerning contact pressure distribution at extrusion dies and its measurement has been presented. Detailed data of applied device and measurement procedure is described. Significant contribution to the experimental investigation of bulk metal forming can be found in the work [8]. The authors developed a new tooling concepts aiming at better process development and component characteristics. Recently a number of works on numerical simulation of die loading has been published [6], [7]. In most cases simulation-data are compared with experimentally obtained results. In those simulations different software packages have been used. The current paper aims at giving the insight into some of the methods for the analysis of cold extrusion process, using concrete, practical examples: radial extrusion, forward extrusion and backward extrusion with gear-profiled punch. Radial extrusion of gear-like component In radial extrusion of gear-like elements billet material flows sideways filling up the orifices in the die. These orifices correspond to the negative profile of the final product (Fig. 1a). In the current investigation radial extrusion of gear-like component with straight radial flank profile was analyzed by Upper Bound (UB) method. Due to axial symmetry only one twelfth of the gear-like component was considered. The analysed volume was divided into four zones with common boundaries and for each zone kinetically admissible velocity field was defined (Fig. 1b). Image of the extruded component is given in Fig. 1c.

a)

1.) 2.) 3.) 4.)

Punch Die Workpiece Die insert

b)

c)

Fig.1. Radial extrusion of gear-like component with straight radial flank profile

Key Engineering Materials Vol. 367

211

Based upon the established velocity fields total power can be predicted as: ⋅

⋅

⋅

⋅

W = W d +W s +W f =

2σ e 1 ⋅ ⋅   ε ij ε ij dV + ∫ τ s ∆v dAs + ∫ τ f ∆v dAf 3 V∫  2  As Af

(1)

σ e - yield stress ⋅

ε ij - strain rates τ s - shear stress As it can be seen from (1), the total power consists of three components: internal power of deformation ( W& d ), shear losses on the boundaries of velocity discontinuities ( W& s ) and friction losses ( W& ). f

Forming load (F) and average punch pressure (p) are: F=

W& v0

F A v0 - punch velocity A - punch cross section area p=

(2)

FEM simulation of the process was performed by MSC. Marc 2001 program package. Tetrahedral body mesh using higher order elements made possible to run the program without remeshing. More details on this can be found elsewhere [11]. In order to verify theoretical and numerical results experimental investigation with Al-billets (Al99.5) has been carried out. For that purpose special tooling was designed and made. ........... Upper Bound

--___

FEM Experiment

Fig. 2. Load-stroke diagram obtained by three different methods

212

Advances on Extrusion Technology and Simulation of Light Alloys

The main elements of gear geometry were: inner radius r0 =14mm, outer radius r1 =17mm, toot height h = 15,8 mm, number of teeth 6. Yield stress of the material was σ e = 82,3 Mpa and friction coefficient µ = 0,12. During the process load-stroke diagram has been recorded. In figure 2 load-stroke diagram obtained by three different methods is given: experiment (solid line), FE (dashed line) and Upper Bound (dotted line). Forward extrusion In forward extrusion process distribution of radial stress along the container wall was determined experimentally. Experimental tooling is shown in Fig.3. In the container body measuring element (pin load cell) was embedded. During deformation pin is subjected to the elastic compression. The compression load is measured by strain gauges which are fixed on the pin body. Measuring of radial stress at different positions along the die wall was made possible by using replaceable die inserts with different heights. Measured distribution of radial stress (σ r ) along the container wall is shown in Fig. 4.

Fig.3. Experimental tooling

Fig.4. Radial stress along the container wall

Backward gear extrusion By the method of backward extrusion with profiled punch (involute-gear with 10 teeth, module 1.5) workpiece with internal tooting was produced (Fig.5). Workpiece material was low carbon steel with the stress-strain curve σ = 660ϕ 0,230 . During backward extrusion load-stroke characteristic was recorded (Fig. 6). Stress and strain within one half of the extruded gear profile was obtained by hardness measurement at the workpiece cross section and shown in Fig. 7. Prior to this relationship between hardness (HV30), strain and stress has been established experimentally.

Key Engineering Materials Vol. 367

213

Force [kN] 500

400

34

300

200

100 28 0

Fig. 5. Backward gear extrusion

2

4

6

8

10

12

14

16

Stroke [mm]

Fig. 6. Load-stroke characteristic

Fig. 7. Distribution of hardness (HV30), effective strain (ϕe ) and effective stress (σ e ) at the gear cross section Conclusion In the current paper three different cold extrusion processes have been analyzed theoretically, numerically and experimentally. a.) In the first case load-stroke characteristic in radial extrusion of gear-like elements was investigated. Load obtained by Upper Bound (UB) method shows steady, low rise dependence upon punch stroke. Up to the punch stroke of 3mm this load is higher than those obtained by other two methods. In the final stage of deformation, unlike in two other methods, UB prediction does not show any considerable load-rise. Load - stroke prediction performed by FE shows three different phases: steep rise in the beginning of the process, steady, low rise in intermediate phase and steep load jump in the final stage. Experimental results (measurements) resemble to great extend this performed by FE method. In the first phase of the process UB solution overestimates the real load (which can be explained by the inherent nature of UB method), whereas in final phase UB load values considerably underestimate the real load. This underestimation can be attributed to the fact that established velocity field in UB analysis does not take into account so called “corner filling phenomenon”.

214

Advances on Extrusion Technology and Simulation of Light Alloys

Therefore, in further work on this subject improved velocity field should be created and implemented in the UB analysis. b.) Contact radial stress at the die wall in the forward extrusion process was determined experimentally, by measuring pin. It is evident that radial stress increases towards die opening. Process of forward extrusion is steady one and values of total load and radial pressure at the container wall (σ r ) remain constant during the process. c.) In backward extrusion with profiled punch load rises permanently up to 500 KN (which corresponds to a maximum punch pressure of p = 2700MPa). Then the process was stopped and extruded component was ejected from the die. The analysis of hardness, strain and stress distribution at the cross section of the components shows that the final components demonstrate significantly higher mechanical properties than the initial billet. This can be attributed to the strain hardening phenomenon. The highest values of „ ϕe ”and „ σ e ” exist in the external zone of the tooth profile while in the inner part these values are lower. References [1]

Kudo, H.: Towards net-shape Forming, Journal of Materials processing Technology, 22 (1990), pp.307-342.

[2]

Lange, K.: Zur Entwicklung des Kaltfliesspresens zu einer High-Tech Praezisionstechnologie, Umformtechnik, 26 (1992), 6, pp.412-418.

[3]

Kondo, K: Development of new precision cold forging process, 1st ICTR, Tokyo 1984, pp 876-88

[4]

Doege, E., Naegele, H.: Simulation of the precision forging process of bevel gears, Annals of the CIRP 01, Vol. 43/1/1994, pp. 241-244.

[5]

Plancak, M., Bramley, A., Osman, F.: Some observation on contact stress measurement by pin load cell in bulk metal forming, Journal of Materials processing Technology, 60 (1996), pp. 339- 342.

[6]

Plancak, M., Kuzman, K., Vilotic, D., Cupkovic, Dj.: Loading of dies in cold extrusion – FE simulation and experimental verification, ESAFORM 2006, Conference Glasgow, pp.491-495

[7]

R. E. Sliwa: Simulation of extrusion process using the ultrasonic vibrations, ESAFORM 2006, Conference Glasgow, pp 499-503.

[8]

Tuncer, C., Dean, T.A.: Int.Mach.Tools Manufacturing, 28 (1988), 407.

[9]

Plancak, M., Vilotiv, D., Vujovic, V.: One contribution to the investigation of gear extrusion, Advanced Technology of Plasticity 1996, 5th ICTP, Ohio, Columbus, USA, pp. 197-201.

[10] Plancak, M., Vilotic, D., Skakun, P.: A study of radial gear extrusion, Int. Journal of forming processes, Vol.6, No.1/2003. pp.71-87. [11] Plancak, M., Skunca, M., Math, M.: Analysis, FEM simulation and verification of gear cold extrusion, VII Conferencia internacional de forjamento – XXIII Senafor, Porto Alegre, Brazil, 2003. pp.28-39.

Key Engineering Materials Vol. 367 (2008) pp 215-220 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/KEM.367.215

A New Low Friction Die Design for Equal Channel Angular Extrusion T. Canta1, a, D. Frunza1, b, E. Szilagyi1, c, M. Lung2, d 1

Technical University of Cluj-Napoca, Department of Materials Processing, 103 Muncii Avenue, 400641 Cluj-Napoca, Romania, 2

INCDIE ICPE-CA ,313 Splaiul Unirii ,Bucharest ,Romania

a

[email protected] , [email protected], [email protected]

Keywords : ECAE, Low friction, Die design

Abstract The paper presents the experimental results on an aluminum alloy and a silver alloy processed by equal channel angular extrusion in order to refine the grains. Two type of extrusion dies have been used for experimental works: one with fixed walls and the other one with movable walls in order to reduce the friction during extrusion process. The new concept of the die consists in simultaneously pressing of two samples in one entering channel with two opposite exit channels. The channel geometry, friction contact, strain rate, extrusion load and micro structure aspects are presented.

Introduction In order to change billet shape and dimensions and to improve the mechanical properties of metals and alloys, traditional forming processes, such as rolling, forging and extrusion, are used. All these metalworking technologies require high pressure and loads, high energy consumption, special equipment and expensive tools. It is well known that heavy deformation, such as cold rolling or drawing, can result in significant refinement of microstructure at low temperatures [1, 2, 3, 4]. In recent years, several methods of sever plastic deformation techniques were used for grain refinement. One of these is equal channel angular extrusion (ECAE), as shown in Fig.1. This is a new technique, which is more practical and requires less energy [3, 5]. Segal and coworkers have introduced intense plastic strain into materials by ECAE without changing the cross sectional area of the billet. This method consists of pressing a billet through a special die having two intersecting channels with identical cross-section. A well lubricated billet, with the same cross section as the channels, is pressed by a punch and extruded into the second channel. Due to these conditions, the billet is deformed as a rigid body with a simple shear deformation on thin layer at the crossing plane of the two channels. Except its small end regions, the billet is

Fig.1 Equal-channel angular extrusion

216

Advances on Extrusion Technology and Simulation of Light Alloys

deformed in the same uniform manner. After its withdrawing from the die, the billet can be pressed again, therefore the process can be repeated easily by a number (N) of strokes in the same die. The main strain state of the deformation by ECAE is simple shear and there is no change in the cross section geometry. The highly homogeneous deformation behavior of the sample during ECAE is dependent of the die channel shape, corner angles and friction conditions. Regarding the distribution of the shear strain through a sample thickness, Segal [5] has demonstrated that actual stress/strain states during ECAE may be complicated and different from the “ideal” deformation model. Depending of the friction value between the billet and the die channel, plastic zones vary through the cross section and the length of the sample.

Fig.2 New die design for ECAE with low friction: 1-solid die block; 2-punch; 3, 3’-bilet; 4-movable walls; 5-fixing bolts The channel geometry is one of the main parameters which has a major influence on the strain. The sharp corner channels with low friction factor provide uniform shear strain. In order to attain an intensive shear, the die angle Φ must be small enough, usually Φ = 90o. For Φ < 90o, will appear a dead metal zone at the cannel corner. Contact friction is the most important boundary condition due to its influence on the shear strain distribution and on the pressing pressure. The plastic region is a thin material layer with a uniform simple shear distribution only for frictionless conditions (τ = 0). In order to reduce the friction force, both channels must be properly lubricated and movable channel walls can be used in the die [3, 5]. Depending on the frictional conditions and the tool design (fixed/movable walls), the plastic zone changes from a single line of highly shear to enlarged center fan formations and it may also include “dead metal” zones and zones with non uniform strain. In this paper, a new die for ECAE with low friction is presented.

Key Engineering Materials Vol. 367

217

Die design The new concept of the die consists of pressing of two billets (3, 3’) in the same time by the punch 2 which acts on the movable walls 4 situated in the solid die block 1 (Fig.2). Thus, the friction between the billet and the die is reduced by 75 %.In order to compare the two types of dies (with fixed walls and with the movable walls), a 10x10 mm2 cross section billet and an active length of feeding channel of 110mm were used. The channel intersection angle was Φ=90o with an inner radius corner of 1mm. The friction at the exit channel was reduced by using a calibrating length of 10 mm after the corner, followed by an enlargement to the exit channel. One separating piece was used at the bottom of the vertical channel with a taper edge of 4 mm (Fig.3). It gives an outer corner angle ψ = 190. The punch and active die walls were made of H11 tool steel heat treated at 60 HRC. The two half dies were assembled with 6 bolts (5) of 12 mm diameter. ECAE facilities (die and punch) together with the load cell and the displacement inductive sensor were set up on a 200 kN hydraulic press. During each extrusion process, the extrusion load and punch displacement were recorded by an acquisition experimental data system. The complex die assured both facilities, for fix walls and movable walls

Fig.3 The aspect of the two samples at the end of the stroke Experimental conditions and materials Commercially available extruded bars of AA 1350 Al alloy (99.5%Al, 0.05%Cu, 0.01% Mn, 0.1% Si, 0.4% Fe) with a diameter of 12 mm and a sintered Ag-4%SnO2 as a square shape of 10x10x100 mm3 have been used for experimental work. Before ECAE test, samples of Al alloy were deformed at room temperature in a square shape of 10 mm by rolling, followed by annealing at 340 °C for one hour and air cooling. Before pressing, the specimens were coated with molycote (MoS2+grafite). In order to accumulate a higher plastic strain, several samples were extruded consecutively and repeatedly by the so-called route “A” [3]. This route means that the billet is introduced after each exit in the same position (without rotation). Samples of Ag SnO2 were extruded at 600 °C by heated

218

Advances on Extrusion Technology and Simulation of Light Alloys

die at 250 °C. After ECAP processing, the samples were longitudinally sectioned for optical microscopy analysis. Extrusion load for one sample (Load -1) and two samples (Load -2) extruded in the same die, versus punch stroke are presented in Fig.4.

Fig.4 Extrusion load versus plunger stroke for: one extruded sample (Load -1) and for two extruded samples (Load -2)

Fig.5 Extrusion load for the 3-rd pass of two samples by route A (no annealing between passes) It is clear from Fig.4 that, the extrusion pressure (p=250 MPa) for ECAE of two samples is 20% lower than of ECAE of one sample (p=320 MPa). This significant reduction in the extrusion

Key Engineering Materials Vol. 367

219

pressure is due to the avoidance of friction on the surface of one sample and to the favorable new stress conditions of this technique. In order to apply the new die for multipass extrusion, one Al sample was extruded by repeating three times. The extrusion load versus punch stroke is presented in Fig.5. Due to strain hardening, the extrusion load is higher by 37.5% after three passes than after one pass. Results and discussion The effect of ECAE on silver alloy deformed at 600 °C is presented in optical micrograph (Fig.6).

Fig.6.Microstructure of Ag alloy after ECAE deformation: a, b-initial structure; c-after first pass; d-after second pass It was noticed that the microstructure of Ag alloy was refined by ECAE depending on the number of passes. The initial grain diameter was 30 µm (transversal section). This was reduced to 10 µm after the second pass. Correlated to this refined structure, the mechanical properties of the alloy improved. For example, the UTS (ultimate tensile stress) increased from the initial 110MPA to 160 MPa after the third pass. The yield stress (0.2 YS) increased from the initial 95 MPa to 154 MPa after the third pass. The new die design was suitable for applying ECAE, even for sintered Ag alloy at hot temperature and for Al alloy at room/hot temperature. Conclusions A new die design was used for ECAE with lower friction between die and billet .The extrusion pressure of this die was lower by 20% than of classical ECAE die, probably due to the avoidance of friction on one of the billet surfaces and due to the changes in stress state during the extrusion process.

220

Advances on Extrusion Technology and Simulation of Light Alloys

The ECAE process with this die was used to study the behavior of AA 1350 alloy deformed at room temperature and Ag alloy deformed at 6000C, under route A. The following conclusions were reached from the experiments: • The experimental pressure for ECAE with new die is lower (20-25%) than the classical one. • The ECAE process is an efficient method to improve some of the mechanical properties by grain refinement during severe deformation. • Commercial AA 1350 alloy is well suitable for the ECAE process at room temperature. • Silver alloy for electrical contacts Ag-4%SnO2 can be deformed by ECAE at 6000C with grain refinement. • More experiments by using the new die concept are needed in order to optimize the process parameters according to structural and mechanical properties. References [1] R.Z.Valiev, R.K. Islamgaliev and I.V. Alexandrov: Progress in Materials Science, Vol. 45 (2000), p. 103. [2] M.Vedani, P.Basani, A.Tuissi and G. Angella: Metallurgical Science and Technology, Vol. 22 (2004), p. 21. [3] V.M. Segal: Materials Science & Engineering A Vol.386 (2004), p.269. [4] Y.Iwahashi, J. Wang, Z. Horita, M, Nemoto and T. G. Langdon: Scripta Materialia, Vol. 35 (1996), p. 143. [5] V. Segal: In: Metals Handbook,vol.14-A, edited by ASMInternational, Metals Park, Ohio (2005), p. 528.

Key Engineering Materials Vol. 367 (2008) pp 221-228 © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/KEM.367.221

Modeling Approach for determination of Backward Extrusion Strain Energy on AlCu5PbBi B. Barisic1, a, B. Grizelj2, b, M. Plancak3, c 1 2

University of Rijeka, Faculty of Engineering, 51000 Rijeka, Croatia

University of Osijek, Mech. Engineering Faculty, 35000 Sl. Brod, Croatia 3

University of Novi Sad, FTN, 21000 N. Sad, Serbia

a

[email protected], [email protected], [email protected]

Key words: Backward extrusion, modeling, strain energy, experimental design.

Abstract. In the paper, firstly on the basis of different theoretical methods and by means of different strain determining criteria the analytic modeling of backward extrusion process was done. Analyzed analytical models are derived directly from the mathematical description of the backward extrusion physical phenomena and their mathematical description has been presented. Afterwards, numerical modeling of strain energy by means of ABAQUS 6.4.1. software [1] was done. Also, stochastic modeling, founded on the statistic processing of experimental data according to the mathematical theory of experimental design, has been examined. For establishing of process strain energy, the second order stochastic model has been introduced. Analytic, numerical and stochastic research and experiments were performed according to central composite design (type CCC). As industrial case, the material AlCu5Pb Bi was chosen. The power law which describes material compression properties is obtained as k f = 334.33 ⋅ ϕ 0.192 . The extrusion strain energy is dependent on the change in section size, friction coefficient, and material properties. Because of that, these parameters were varied variables at the all points of CCC design. The diameter of workpiece used in this design was set predetermined as industrial case, but both coefficient of friction and wall thickness of workpiece has been varied according to experimental design. The best results in modeling were derived by means of stochastic modeling, and the best strain energy model in the form W = -1111.82 − 88.7 ⋅ µ − 3200 ⋅ µ 2 + 625 ⋅ µ ⋅ s + 816.43 ⋅ s − 42.25 ⋅ s 2 has been obtained.

Introduction

For backward extrusion, it can be said that due to its material savings, different distributions of stresses and increasingly reduced forming time in relation to similar processes it has become one of the most promising manufacturing processes [2]. Continuous demands for reduced consumed energy and more economic parts production have led to the strain energy approach which uses different type of modeling and simulation of production process. Different modeling methods provide wider possibilities in the solving of metal forming problems. The goal of the paper is to determine the model type (analytic, numerical or stochastic) for determining of backward extrusion strain energy on AlCu5PbBi which describes this energy in the most accurate way in comparison with real material processing. A wider use of different types of modeling and simulations enables the assessing the dependency of output parameters on the variation in input parameters in order to improve process before the expensive manufacturing. The experimental design is an efficient procedure for planning experiments so that the data obtained can be analyzed in order to improve existing process. Experimental design

A central composite design is the design of experiments using for making of quadratic mathematical model for the variable determination. A central composite design contains an imbedded factorial or fractional factorial design with center points that is augmented with a set of symmetric points that

222

Advances on Extrusion Technology and Simulation of Light Alloys

allow estimation of curvature. Symmetric points represent extreme values for each factor in the design. If the length from the center of the design space to a factorial point is ±1 unit for each factor, the distance from the center of the design space to a symmetric point is ± α with α ≥ 1. The precise value α of depends on determined properties desired for the design and on the included number of factors. There are three varieties of central composite designs: central composite circumscribed (CCC) designs, central composite inscribed (CCI) designs and central composite face centered (CCF) designs. In this investigations CCC design is chosen as an experimental design. Analytic, numerical and stochastic research and experiments were performed according to CCC design for 2 variables (Table 1). In the CCC design, design points describe a circle circumscribed around the factorial square and symmetric points are at some distance from the center based on the properties desired for the design and the number of factors in the design. The CCC are rotatable designs, it means the variance of the predicted response at any point x depends only on the length of x from the design center point [3]. The value of α for 2 variables (k = 2) allows simultaneous rotatability and orthogonality. Values of α depending on the number of variables in the factorial part of the design, i.e. scaled value for α for 2 variables (wall thickness and coefficient of friction) is 2 2 /4 = 1.414. Table 1. Experimental design for 2 variables (s-wall thickness and µ -coefficient of friction) Number Coded values Physical values of exp. X0 X1 X2 µ s[mm] 1. 1 +1 +1 0.15 4.5 2. 1 -1 +1 0.05 4.5 3. 1 +1 -1 0.15 2.5 4. 1 -1 -1 0.05 2.5 5. 1 0 0 0.1 3.5 6. 1 0 0 0.1 3.5 7. 1 0 0 0.1 3.5 8. 1 0 0 0.1 3.5 9. 1 0 0 0.1 3.5 10. 1 1.414 0 0.171 3.5 11. 1 -1.414 0 0.029 3.5 12. 1 0 1.414 0.1 4.9 13. 1 0 -1.414 0.1 2.1 Experimental investigations In this paper the friction coefficient values (Table 1) and their influence on material surface has been determined by means of tribometer Tritop. Principle of measuring is made in the way that a plate (100 x 40 mm) of researched material is pressed with a certain force on another plate of a friction pair (in this research of a tool material that is cut out with a plate), which oscillates with a selected speed. Force friction is determined directly trough deformation of elements that were measured with piezoelectric tensimeter Kistler, and that were caused with an external deforming force. In Fig. 1 the tribometer Tritop is presented. It is important to point out that all means for lubrication are selected in a way to match the defined experimental design (presented in Table 1). Basic obtained data for lubrication through tribometer are: hydrolubric VG68 µ = 0.17, cold forming lubricant µ = 0.15, Zn stearat µ = 0.1, MoS2 (liqui molly) µ = 0.05, paraffinol vaseline and epoxy phenolic (GL1231-07) µ = 0.03. The determining of flow curve and compression tests on AlCu5PbBi were carried out in order to assess its influence on the analytical, numerical and stochastic analysis of backward extrusion process. The system for the determining of compression curve are: a strain ring attached to a load cell system with a sensor, a displacement transducer, measuring converter, data processing system, and press Knuth KP 200 (all presented in Fig. 2).

Key Engineering Materials Vol. 367

223

Fig. 1. TOP 3 tribometer the device for determining of friction coefficient Experimental obtained flow stress curve could be described in the form of hardening law as: k f = C ⋅ϕ n , (1) i.e. by means of system for determining of compression flow curve in the form: k f = 334.33 ⋅ ϕ 0.192 . (2) 2 2 Also, yield strength k0 = 150 N/mm and ultimate tensile strength Rm = 280 N/mm .

4

2 1

1- Strain ring 2- Measuring converter 3- Data acquisition system 4- Presss KP 200

3

Fig. 2. System for determining of compression flow curve Experimental results of backward extrusion strain energy obtained in investigations (by means of system presented in Fig. 2) are shown in Table 2 ( d 1 - diameter of punch, hp –punch stroke, h0 initial length, hi - total length of workpiece). Num. of exp. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

Table 2. Results of strain energy in experimental investigations Basic data Strain energy µ hp [mm] hi [mm] d1[mm] h0 [mm] h1 =s [mm] [Nm] 0.15 5.59 16.057 23 10.09 4.5 2044 0.05 5.59 16.057 23 10.09 4.5 1817 0.15 1.596 8.04 27 4.096 2.5 792 0.05 1.596 8.04 27 4.096 2.5 690 0.1 3.42 12.28 25 6.92 3.5 1406 0.1 3.42 12.28 25 6.92 3.5 1408 0.1 3.42 12.28 25 6.92 3.5 1404 0.1 3.42 12.28 25 6.92 3.5 1407 0.1 3.42 12.28 25 6.92 3.5 1405 0.171 3.42 12.28 25 6.92 3.5 1500 0.029 3.42 12.28 25 6.92 3.5 1320 0.1 6.51 17.46 22.2 11.41 4.9 2150 0.1 1 6.2 27.8 3.1 2.1 533

224

Advances on Extrusion Technology and Simulation of Light Alloys

In Fig. 3 different workpieces extruded according to CCC experimental design in order to determine the strain energy are presented.

Fig. 3. Different workpieces extruded according to CCC experimental design Analytic modeling In this section, different theoretical models of backward extrusion force Fbe using different criteria for strain determining has been presented. Analyzed analytical models are derived directly from the mathematical description of the backward extrusion physical phenomena and their mathematical description has been shown. Afterwards, from presented backward extrusion forces the strain energy from known punch stroke hp has been calculated. 1.Dipper’s model:  h µ    1 π ⋅ d 12  d  Fbe = + 0.25   , (3) k f 1 ⋅ 1 + ⋅ µ ⋅ 1  + k f 2 1 + 1  4  3 h s 2   1       where: h ϕ 1 = ln 1 ⇒ k f 1 , (4) h0



h

d

h 

ϕ 2 =  ln 1 + 1 ln 1  ⇒ k f 2 . (5) h 8 s h 0 0   Notation (4) means that for ϕ1 from flow stress curve the value of k f 1 has been obtained, also notation (5) means that for ϕ 2 from flow stress curve the value of k f 2 has been obtained. The similar notation will be applied on other models in analytical modeling from now on. 2. Siebel-Fangmeier’s model: kf  π ⋅ d 12  Fbe = ϕ d , 4  η def 

(6)

where:

do − 0.16 ⇒ k f 1 , (7) d o − d1 k + kf1 kf = f0 , (8) 2 k f 0 - yield strength for ϕ = 0, (start of yielding), η def - the degree of deformation efficiency that in

ϕ d = ln

the process of backward extrusion has a value 0.25 [4, 5].

Key Engineering Materials Vol. 367

3.Anikin Lukasin’s model:   2   h µ   π ⋅ d1  k f 0 Fp = + k f 1 1 + 0  + 0.25   µ ⋅ d1 s  2 4     1 −   2h1  

225

(9)

where k f 1 is calculated according to (7), and 4. Hribar’s model : 4 µl  π ⋅ d 12  µd 1 d o − d1  Fbe = k f 1+ +e (10)   4 3 h 1   where: l = hi − h1 , and ϕ d , k f 1 is calculated according to (7), k f is calculated according to (8). 5. Storožev-Popov’s model: A0 π ⋅ d 12   A0  d   ln Fbe = k f 2 + 1 + + 1 , (11) 4 A1  A0 − A1 6 ⋅ h1    A0 ϕ A0 = ln ⇒ k f1, (12) A0 − A1 where: A0 - cross section surface of workpiece, A1 - cross section surface of punch, and k f is calculated according to (8). 6. Tirosh’s model: d d  d  π ⋅ d 12  2 (13) Fbe = k f 2 ln o + ln o  4 − 0.5 ln o  , 4 d1 3 d1  d 1   A0 − A1 ⇒ k f1 , A0 where k f is calculated according to (8). 7. Kudo’s model:  d1 d1  1 −   do 7 do  π ⋅ d 12 2  Fbe = ⋅ kf 2 + , d1 d1  4 8 3  1−   d d o  o  A1 ϕ A1 = ln ⇒ k f1, A0 − A1 where k f is calculated according to (8). 8. Tarnovski’s model:  do   1 − 0.85 ⋅  π ⋅ d 12  d1  Fbe = k f 3 + 2 ⋅ , 2  4   d  1 −  o      d1    where k f is calculated according to (8), and ϕ A , k f 1 is calculated according to (12). 9. Beisel’s model: d o2  π ⋅ d 12   d o2    Fbe = k f 2 + 1 + 2  ln 2 , 4 d 1  d o − d 12   

εA =

(14)

(15)

(16)

(17)

(18)

226

Advances on Extrusion Technology and Simulation of Light Alloys

where k f is calculated according to (8), and ϕ d , k f 1 is calculated according to (7). 10. Romanowski’s model:  h µ    1 π ⋅ d 12  d  Fbe = + 0.25   , (19) k f 0 ⋅ 1 + ⋅ µ ⋅ 1  + k f 1 1 + 0  h0  s  2 4    3   where k f 1 is calculated according to (12). Taking into account the punch stroke hp the analytic models (1-10) for force can be multiplied with hp and models for strain energy can be established. Results of analytic models strain energy are presented in Table 3, and in the same Table 3 compared with experimental ones. Stochastic modeling

Working out of stochastic model is founded on the statistic processing of experimental data, when conditions are programmed according to the mathematical theory of experimental design. That has been achieved by the change of input parameters determining the limit of varying in the conditions of real process [6]. For establishing of process strain energy, the second order model has been introduced: Y = b0 + b1 x1 + b2 x 2 + b3 x3 + b12 x1 x 2 + b11 x12 + b22 x 22 .

(20)

In this way the form of polynomial approximates a determined problem and the solving boils down to the calculating of coefficients bi. Accordingly, accurate stochastic model with minimal number of experimental data has been defined. Examining of dispersion homogeneity of backward extrusion strain energy in stochastic modeling has been performed as (Cochran′s criterion for level of reliability P=0.95): max S 2j (21) Kh = N ≤ K t ( f j , n0 ) , 2 ∑Sj j =1

where: Kt – value according to Cochran′s criterion for degrees of freedom fj and N, fj – degree of 9

freedom (fj=nj -1),nj – repetition number on design,

∑S

2 j

= S 02 -variance of central points of

j =5

2 j

rotatable design, max S -maximal variance at central design. After a checking of significance for models according to Student’s criterion the checking of adequacy according to F-criterion has been examined. As the dissipation of experimental results in the central point of design is too small, and on the basis of the F-criterion it is not possible make a decision, thus as a complementary criterion of model adequacy the coefficient of multi regression has to be introduced. This coefficient for experimental design has the form:

∑ (y N

E j

- y Rj

)

2

j =1

R= 1

∑ (y N

E j

-y

)

,

E 2

j =1

where: N–number of experimental results,

∑y N

yE =

j =1

N

E j

– is the arithmetic mean of all experimental results,

(22)

Key Engineering Materials Vol. 367

(y

E j

227

)

2

- y Rj – is the quadratic expression of the difference in experimental and calculated values of response function in all points. The model adequacy according to expression (22) is satisfied. Finally, coded mathematical model has a form: Y = 1406 + 72,94 x1 + 583,1798 x 2 + 31,25 x1 x 2 - 8 x12 - 42,25 x 22 . (23) In finale stage the model’s decoding in order to obtain the strain energy in physical form has been derived: W = -1111.82 − 88.7 ⋅ µ − 3200 ⋅ µ 2 + 625 ⋅ µ ⋅ s + 816.43 ⋅ s − 42.25 ⋅ s 2 . (24) Results of stochastic models strain energy are presented in Table 3 and compared with experimental ones. Numerical modeling Numerical modeling of strain energy by means of ABAQUS 6.4.1. software was done. Model creation using ABAQUS/CAE module was done. ABAQUS/Explicit module, the part of ABAQUS which plays the role of solver was employed for analysis. Numerical models of workpiece (deformable body) are consisted of 600-700 (depending on the point of CCC design) axisymmetric quadrilateral finite elements known as CAX4R type. The die and punch were interpreted as a rigid unmovable body by means of ABAQUS/CAE - geometrical functions were used for the description of tools. One half of the workpiece and tools was taken into consideration regarding symmetry of the process. The material is described as rigid-plastic respecting von Mises yield criterion and Poisson’s ratio and modulus of elasticity were used for elastic characteristics. A mesh was created by hand and the remeshing techniques were used in backward extrusion process simulation. One of the most important sections at the material forming modeling is choosing for the correct model for the contact conditions. In ABAQUS explicit, there are two different contact algorithms, significantly influencing the computed contact forces, under integrated elements in simulations governed by large hydrostatic pressure, like extrusion processes, hourglassing effects may corrupt the simulation results. Some interactions can be modeled with the general contact algorithm, while others are modeled with the contact pair algorithm. The general contact algorithm uses a penalty method to enforce the contact constraints. In this paper at modeling contact interactions in ABAQUS/Explicit the contact pair algorithm was used. On the basis of subroutine in ABAQUS that determines the total load placed on the workpiece, the strain energy curve has been constructed. ABAQUS equation for calculating of strain energy (W) is: 1 + ν 2 3 1 − 2 ⋅ν 2 n α W= ⋅q + ⋅ p + q n +1 (25) n −1 3⋅ E 2 E n +1 E ⋅ k f 0

where: q- the Mises equivalent stress, p - the equivalent hydrostatic stress, ν- Poisson's ratio, ϕ true strain, α - yield offset in the sense when σ = k f 0 . In Table 3 the numerical results of backward extrusion strain energy in comparison with the experimental results have been presented. Conclusion

All results of analytic, stochastic and numerical modeling of strain energy are presented in Table 3. As result regarding analytic modeling can be concluded that the best analytic model is Dipper model (8 results from 13-Table 3). Also, regarding analytic modeling can be concluded that Tarnovski model gives a good approximation, but in this model there is no the influence of friction. For 2 results in analytic modeling the best results were obtained by means of Kudo model, where also there is no the influence of friction, and bad side is that for 12th point of experimental design Kudo model can not be applied. The best results in modeling were obtained by means of stochastic

228

Advances on Extrusion Technology and Simulation of Light Alloys

modeling. At this type of modeling the disadvantages are an expensive experiment and not applicable out of experimental space. The numerical modeling is very satisfactory (the better results in 3rd, 4th and 11th points of experimental design in comparison with stochastic modeling). The faster and cheaper solving of process is obtained by means of this type of modeling. Also, the best solution as savings in process and tool improvements (on the start stage of process before its establishing) can be reached by means of numerical modeling.

Design point 1. 2. 3. 4. 5-9. 10. 11. 12. 13. Romanowski model 1684.662 1574.105 683.6595 626.7383 1190.017 1251.546 1128.488 1757.901 439.2543

Table 3. Results of strain energy in modeling investigations StorozevDipper Siebel Tirosh TarnovPopov model model model ski model model 2075.816 2575.498 2738.237 885.271 1861.951 1903.357 2575.498 2738.237 885.271 1861.951 849.6525 1643.058 1576.766 211.3677 704.8889 734.8808 1643.058 1576.766 211.3677 704.8889 1449.856 2347.696 2332.424 513.5667 1345.787 1561.867 2347.696 2332.424 513.5667 1345.787 1337.846 2347.696 2332.424 513.5667 1345.787 2151.115 2552.176 2807.792 1037.664 2009.668 523.2721 1219.938 1171.584 122.1103 449.453 AnikinHribar Kudo Stoshastic Numerical Lukasin model model model model model 1149.209 1257.799 1125.728 2043.12 2030 799.9284 1257.799 923.8369 1834.74 1799 487.7703 743.2376 940.454 814.26 770 339.9274 743.2376 395.0924 730.88 685 721.5472 1168.046 786.1533 1406 1400 940.2291 1168.046 1058.686 1493.44 1490 555.75 1168.046 657.9714 1286.29 1340 904.0873 -----------2130 1073.938 2139.64 384.3286 531.8566 409.8929 506.738 500

Beisel model 2401.23 2401.23 1208.975 1208.975 1936.544 1936.544 1936.544 2506.567 858.7928 Experiment 2044 1817 792 690 1406 1500 1320 2150 533

References [1] Theory Manual Abaqus /Explicit, Ver. 6.4., Karlsson & Sorensen Inc. Editions, USA, 2003. [2] B. Barisic, M. Math, B. Grizelj, “Analytic, Numerical, And Stochastic Comparison Of Forming Force Modeling At Deep Drawing And Backward Extrusion On The Same Al 99.5 F7 Parts”, Key Engineering Materials vol.344 (2007) pp.419-426. [3] NIST/SEMATECH e-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook , 10. 04. 2007. [4] H. D. Feldmann: Fließpressen von Stahl (Springer-Verlag, Germany 1959). [5] K. Lange: Handbook of Metal Forming (McGraw-Hill Book Company, USA, 1985). [6] B. Barisic, G. Cukor, M. Math, “ Estimate of consumed energy at backward extrusion process by means of modelling approach”, Journal of Materials Processing Technology vol.153-154 (2004) pp.907-912

Keywords Index Extrusion

A AA2024 Aluminium Alloy AA6082 Aluminium Alloy AA7020 Aluminium Alloy Adaptive Mesh Aluminium Extrusion Die Aluminum (Al) Aluminum Alloy Aluminum Composite Aluminum Extrusion Analysis Artificial Neural Network (ANN)

25 125 145 117 177 63, 107, 117 95 95 71 209 185

B Backward Extrusion Benchmark Billet Temperature

221 1 161

Cold Extrusion Complex Shape Composite Constitutive Equation Constitutive Relation Counter Pressure Creep Fatigue Curved Profile

209 209 47 79 71 9 169 55

D Damage Rate Equation Dead Zones Deformation Design of Experiment (DoE) Die Die Design Direct-Chill Cast

169 95 17 71 63 215 79

E Equal Channel Angular Extrusion (ECAE) Experiment Experimental Analysis Experimental Design

F Failure Analysis FEM Modeling Filling Finite Element (FE) Simulation Finite Element Analysis (FEA) Finite Element Model (FEM) First Billet Fracture Surface Friction

9, 215 209 17 221

177 95 39 63, 125, 145, 153, 185 87 39, 107, 193 161 177 201

G Grid Distortion Grid Pattern Technique

C

1, 9, 17, 47, 55, 63, 79, 117, 125, 137, 145, 153, 169, 185, 193

95 17

H Hot Deformation Hot Work Tool Steel Hot Working Hot Zone

107 169 79 95

I Intelligence Die Design Inverse Modeling

185 71

L Lifetime Low Friction

169 215

M Magnesium Magnesium Alloy Material Flow Mechanical Properties Metal Flow Metal Forming Microstructure

9, 153 79, 87 1, 47, 55 9 17 193 9, 107, 117

230

Advances on Extrusion Technology and Simulation of Light Alloys

Mircroscopic Examination Model Modeling

177 201 221

N Numerical Simulation

103, 137

O Optimization

47, 185

P Plane Strain Pocket Geometry Pressure Measurement Pressure Stroke Curves Process Parameter Pseudo Concentration

201 1 137 95 161 39

R Ram Speed Recrystallization Rheological Model

161 107 87

S Seam Weld Shape Extrusion Simulation Square Die Static Recrystallization Strain Distribution Strain Energy Stress Distribution

125 25 25, 39, 117 201 25 95 221 95

T Texture Thermo Mechanical Viscoplastic Constitutive Model Thixoextrusion Torsion Test Twisted Profile

9 169 103 79, 87 55

U Upper Bound Method

201

V Validation

201

W Welding Criteria Wrought Magnesium Alloy

125 103

Authors Index B Balloni, L. Barisic, B. Becker, D. Ben Khalifa, N. Bruni, C.

79 193, 209, 221 55 55 87

K Karayel, D. Kayser, T. Khan, Y.A. Kloppenborg, T. Koopman, A.J.

185 117 71 47 39

C Camacho, A.M. Canta, T. Chicinaş, I.

201 215 177

L Li, L.X. Liu, G. Lungu, M.

153 145 215

D de Ciurana, J. Domingo, R. Donati, L. Duczczyk, J. Dzwonczyk, J.S.

161 201 1, 87, 107, 125 63, 145, 153 107

M McQueen, H.J. Medrea, C. Micari, F. Moe, P.T. Mueller, K. Müller, S.

95 177 137 71 9 9

E El Mehtedi, M. Evangelista, E.

79, 87 79, 95

P

63 137 215 103

R

137 161 39 193, 209, 221

S

Parvizian, F. Plancak, M.

117 193, 209, 221

F Fang, G. Filice, L. Frunză, D. Fu, M.F.

Redl, C. Reimers, W. Rosen, G.I. Rubio Alvir, E.M.

169 9 79 201

G Gagliardi, F. García-Romeu, M.L. Geijselaers, H.J.M. Grizelj, B.

H Hatzenbichler, T. Hortig, C. Hu, H.W. Hu, J. Huang, K. Huétink, J.

169 117 103 153 145 39

Sabater, M. Schikorra, M. Schomäcker, M. Sebastián, M.A. Sheppard, T. Sideris, I.F. Simoncini, M. Sommitsch, C. Spigarelli, S. Støren, S. Svendsen, B.

161 1, 47, 55 47 201 25 177 87 169 79 71 117

232 Szilagyi, E.

Advances on Extrusion Technology and Simulation of Light Alloys 215

T Tao, X.C. Tekkaya, A.E. Tomesani, L. Tseronis, D.

103 1, 47, 55 1, 107, 125 177

V Valberg, H.S. Velay, X.

17, 71 25

W Wlanis, T. Wu, X.K.

169 63

Y Yan, H.

103

Z Zhang, H. Zhou, J.

153 63, 107, 145, 153