INTERNATIONAL CONFERENCE ON ADVANCES IN MATERIALS AND PROCESSING TECHNOLOGIES (AMPT2010), October 2010, Paris, (France)

Transcription

1 Provie by the author(s) an University College Dublin Library in accorance with publisher policies. Please cite the publishe version when available. Title Extrusion process by finite volume metho using OpenFoam software Author(s) Martins, Marcelo Matos; Bressan, Jose Divo; Button, Sergio Tonini; Ivankovic, Alojz Publication ate Conference etails 20 INTERNATIONAL CONFERENCE ON ADANCES IN MATERIALS AND PROCESSING TECHNOLOGIES (AMPT200), October 200, Paris, (France) Publisher American Institute of Physics Item recor/more information Publisher's statement Publisher's version (DOI) The following article appeare in INTERNATIONAL CONFERENCE ON ADANCES IN MATERIALS AND PROCESSING TECHNOLOGIES (AMPT200), October 200, Paris, (France), : an may be foun at The article may be ownloae for personal use only. Any other use requires prior permission of the author an the American Institute of Physics. Downloae T23:47:22Z The UCD community has mae this article openly available. Please share how this access benefits you. Your story matters! (@uc_oa) Some rights reserve. For more information, please see the item recor link above.

2 Extrusion Process by Finite olume Metho Using OpenFoam Software Marcelo Matos Martins a ; Jose Divo Bressan b ; Sergio Tonini Button c ; Alojz Ivankovic a, c Department of Materials Engineering, Faculty of Mechanical Engineering, State University of Campinas, Campinas, Sao Paulo, Brazil. b Department of Mechanical Engineering, Centre for Technological Science, University of Santa Catarina State, Joinville, Santa Catarina, Brazil. School of Electrical, Electronic an Mechanical Engineering, University College Dublin, Dublin, Republic of Irelan. Abstract. The computational coes are very important tools to solve engineering problems. In the analysis of metal forming process, such as extrusion, this is not ifferent because the computational coes allow analyzing the process with reuce cost. Traitionally, the Finite Element Metho is use to solve soli mechanic problems, however, the Finite olume Metho (FM) have been gaining force in this fiel of applications. This paper presents the velocity fiel an friction coefficient variation results, obtaine by numerical simulation using the OpenFoam Software an the FM to solve an aluminum alloy irect col extrusion process, an comparisons with the experimental results obtaine by Thomsen an Frisch. Keywors: Finite olume Metho, Extrusion, Friction, Aluminium. PACS: x, x, z, , Qp, fq, 8.20.Hy, La INTRODUCTION Nowaays, in the engineering practice, the inustrial process of fabrication of parts an proucts are increasingly being moele mathematically by employing the computational coes. The metal forming has a huge importance insie of the fabrication techniques of metallic parts, where the extrusion process has an important role because is wiely utilize to prouce bars of complex cross section profile. In an extrusion process, the knowlege of the metal behavior aspect such as: velocity fiel, eformations, stresses, friction an temperature can help to preict failure in components or proucts prouce by extrusion. One way to etermine such information is the numerical metho, that are fast an accurate an by this manner, helping to reuce the cost that coul appear in the experimental process. Traitionally, the numerical metho use to solve solis mechanic problems has been the Finite Element Metho. However, the Finite olume Metho (FM) has been gaining space in the resolution of solis mechanic problems in the last ecae. In 90 s at Imperial College of Lonon, a free coe package written in C++ an using the FM to make iscretization of the mathematical equations, was create by Professor Hrvoje Jasak s research group. This free coe package was use to

3 manipulate an operate tensor fiel an it was in the beginning an for a long time a CFD (Computational Flui Dynamic) package [5,6,7]. This free coe package was calle OpenFoam (Open Fiel Operation an Manipulation) [8,9] an nowaays is also being use to solve solis mechanic problems. Following the tenency to apply the FM in soli mechanic problems an using the OpenFoam tool, it was written a computational program to preict the velocity fiel an the friction variation in an aluminum alloy irect col extrusion process. MATHEMATICAL MODEL FOR COLD METAL EXTRUSION Governing Equations In a col extrusion process, the governing equations for metal flow are given by the principles of conservation of mass an momentum that are escribe in the integral form an Eurelian approach [] by: t t % # $ % # v " S! 0 () S % # v $ % # vv" S! % & " S $ # b (2) S S % where, # is the specific mass, t is the time, v is the velocity vector, is the volume, S is the surface area, b are boy forces an & are the surface forces. Constitutive Equations Usually, the constitutive equations use in an extrusion process are for a material with rigi-visco-plastic behavior an the elastic properties are neglecte. In this moel, the equation that make the relation between stresses with strain rate is given by generalize Stocks Law presente by Eq. 3, the strain rate tensor is given by Eq. 4, the ynamic viscosity is calculate using the Levy-Mises flow Law, that for perfect-plastic case, i.e., material with no strain harening, is presente by Eq. 5. &! ) pi $ 2('! (3), gra v $ * gra v+ - T '!! (4) 2 & y (! 3 '! (5) Where, & is the stress tensor, '! is the strain rate tensor, p is the pressure, I is ientity tensor, ( is the ynamic viscosity, v is the velocity vector, is the yiel stress, '! is the effective strain rate. Eq. 5 is vali for '!. 0, otherwise, the material & y

4 woul behave as rigi. Because of numerical stability in the simulation process, a ) 3 ) minimum value must be efine an this value use was about '! / 0 s. Numerical Metho The OpenFoam software use a numerical structure escribe in the numerical metho presente with etails in [-2]. In the numerical metho presente, the governing equations jointly with the Eq. 3 can be represente by the general transport equation that, after iscretize, it can be written in the following manner: n n t j! S j j! S j Rate of Change Convective term Diffusive term f f f % # B $ 0% # v " S ) 0% 2gra" S! 0% q S " S $ % q n S j j! source term (6) where, the generic variable represent the velocity components v i an the meaning of the others terms can be foun in the reference [,2]. In the iscretization process of the Eq. 6, the time was ivie in a finite number of the subinterval 3 t an the spatial omain was ivie in a finite number of contiguous controls volumes of arbitrary shape an consiering the computational point situate in the control volume center. Assembling the terms of the Eq. 6 generate a set of couple non-linear algebraic equations that are solve employing segregate iterative proceure. This proceure ecouple the set of equations, generating a linear algebraic equations system. The system is solve using the conjugate graient metho with incomplete Cholesky preconitioning. Others etails of the proceure are foun in [,2]. The coupling of velocity-pressure was mae using the PISO metho that is presente in etails in the reference [3]. To complete the mathematical moel, for the col extrusion process, it shoul be specifie the initial conitions an the bounary conitions. In the initial conitions must be impose a value of velocity to all omain points. The OpenFoam allow the impose or Dirichlet bounary conition type where the velocity is specifie in the bounary either the Neumann kin, where the velocity graient can be impose in the bounary. RESULTS Case Description The investigate case with the OpenFoam FM was the irect col extrusion process of aluminum alloy which was performe experimentally by Thomsen an Frisch [4]. The simulation employe an unstructure an three-imensional mesh with hexaherical elements. The ensity of aluminum was 2850 g m an yiel stress ) 5 was 80 MPa. The extrusion velocity was v!.9 " 0 m s an minimum effetctive strain rate was ) 3 ) '!! 7 " 0 s. Figure shows the extrue geometry an the mesh, o 0

5 where it can be observe that the reuction was from a square profile to a square bar. It was simulate two kins of cases: in the first case, it was impose no friction conition in the ie wall surface contact that was given by a zero velocity graient. In the secon case, it was impose a ifferent friction conition by applying ifferent velocity graient on the ie wall contact surface, imposing a ifferent friction factor. FIGURE. Geometry of extrusion an the unstructure mesh for the simulate case. Discussions Results Figure 2 shows the comparison between OpenFoam-FM results for the half left sie with the right sie experimental results presente in [4]. The experimental test was carrie out ensuring zero friction. To simulate this conition on the OpenFoam FM, it was impose zero graient onto the tangential velocity component on the ie wall contact surface an it was fixe a value zero onto the normal velocity component. The results presente in the Figure 2 represent the profile of constant velocity contours calculate by v v0. In Figure 2, it can be observe that there is a goo agreement between the OpenFoam FM results with the experimental results presente in [4]. However, the profile of constant velocity contours in the billet center part show better agreement than the profile velocity contours near the ie wall contact surface (a) (b) Die wall contact FIGURE 2. Comparison between profile of constant velocity contours, v v0, for no friction extrusion process of aluminum alloy. (a) OpenFoam FM results, (b) experimental results by Thomsen [4].

6 FIGURE 3. Friction factor m variation in function of the graient velocity impose on the ie wall contact surface. Figure 3 shows the friction factor m [0] variation in function of the velocity graient grau yz variation impose on the ie wall contact surface. The friction factor was calculate by the following equation:! ij 2 4 m! (7) 3 '! where, m is the friction factor an 4! ij is the plastic shear strain rate. In the graphic showe in the Figure 3, it can be observe that a variation of one hunre times in the velocity graient prouce only a variation of ten times in the friction factor. Figure 4 presents the comparison between the profiles of constant velocity contours for OpenFoam FM results with the no friction experimental results. The simulation ) results was calculate imposing a graient velocity of ) 5 s on the ie walls contact surfaces an this value prouce a friction factor equal to m! From this, it can be observe that both profiles are much ifferent, this happene because the level of friction is very ifferent. CONCLUSIONS From the analysis of the numerical simulation results for col extrusion of aluminum alloy by OpenFoam, the following conclusions can be obtaine: 6 For the extrusion process case with no friction, the profile of constant velocity contours, the comparison between OpenFoam FM an the experimental results has goo agreement; 6 If we change the velocity graient impose on the ie walls contact surfaces we can see the friction factor moification an influence; 6 OpenFoam is a powerful computational tool to operate tensors fiel that appear in solis mechanic problems; 6 FM is a numerical tool which is able to generate goo results in solis mechanic problems.

7 (a) (b) FIGURE 4. Comparison between profiles of constant velocity contours. (a) OpenFoam FM results for m! 0., (b) experimental results by Thomsen an Frisch for m 7 0 [4]. ACKNOWLEDGMENTS The authors woul like to thank the support of The National Council for Scientific an Technological Development (CNPq) Brazil, State University of Campinas (UNICAMP) Brazil, State University of Santa Catarina (UDESC) Brazil an University College Dublin (UCD) Irelan. REFERENCES. H. Basic an I. Demirzic an M. Muzaferija, Finite olume Metho for Simulation of Extrusion Processes, Int. J. Numer. Meth. Engng. 62, (2005). 2. I. Demirzic an M. Muzaferija, Numerical Metho for Couple Flui Flow, Heat transfer an Stress Analysis Using Unstructure Moving Meshes With Cells of Arbitrary Shape, Comput. Methos Appl. Mech. Engrg. 25, (995). 3. H. Jasak, "Error Analysis an Estimation for the Finite olume Metho with Applications to Flui Flows", Ph.D. Thesis, Imperial College Lonon, E. G. Thomsen an J. Frisch, Stresses an Strains in Col-Extruing 2S-O Aluminum, Trans.ASME. 77, (955). 5. A. Robert an R. Schwarze, Experimental an Numerical Investigation of a iscoplastic Carbopol Gel Injecte into a Prototype Mol Cavity, J. Non-Newtonian Flui Mech. 6, (2009). 6.. Kanyanta an A. Ivankovic an A. Karac, aliation pf a Flui-Structure Interation Numerical Moel for Preicting Flow Transients in Arteries, J. of Biomechanics. 42, (2009). 7. D. P. Schmit an S. Gopalakrishnan an H. Jasak, Multi-Dimensional Simulation of Thermal Non- Equilibrium Channel Flow, Int. J. of Multiphase Flow. 36, (200). 8. OPENFOAM The Open Source CFD Toolbox, Programmer s Guie; ersão.6, accesse September 29, OPENFOAM The Open Source CFD Toolbox, User Guie, accesse October 5, J. Rorigues an P. Martins, Atrito, Desgaste e Lubrificacao, in Tecnologia Mecânica: tecnologia a eformação plástica volume funamentos teóricos, eite by Escolar, Lisboa, 2005, pp