Recently, the crystallographic control technology in the aluminum wire drawing process has been a key technology in the aluminum industries, which produces high-strength wires for the electric, automotive and aircraft parts. This newly proposed “process metallurgy” computational technology in the industrial forming process consists of the two-scale finite element (FE) analyses and the optimum design algorithm.We developed two-scale FE analyses code based on the crystallographic homogenization method by considering the hierarchical structure of polycrystal aluminium alloy metal. It can be characterized as the combination of two-scale structure, such as the microscopic polycrystal structure and the macroscopic elastic plastic continuum. Micro polycrystal structure is modelled as a three dimensional representative volume element (RVE). RVE is featured as 3x3x3 eight-nodes solid finite elements, which has totally 216 crystal orientations. This FE analyses code can predict the deformation, strain and stress evolutions in the wire drawing processes in the macro-scale, and simultaneously the crystal texture and hardening evolutions in the micro-scale. In this study, we analyzed the texture evolution in the “three passes” wire drawing processes by using our two-scale FE analyses code under conditions of various drawing angles of die. We evaluated the texture evolution in the surface and center regions of the wire cross section, and to clarify the effects of processing conditions on the texture evolution

Kuramae, H.

Morimoto, H.

Nakamachi, E.

Ohata, T.

Yamaguchi, T.

Yoshida, T.

English

UPCommons. Portal del coneixement obert de la UPC

XII International Conference on Computational Plasticity. Fundamentals and Applications COMPLAS XII E. Oñate, D.R.J. Owen, D. Peric and B. Suárez (Eds)     CRYSTAL TEXTURE EVOLUTION ANALYSES  IN METAL DRAWING PROCESSES BY USING  TWO-SCALE FINITE ELEMENT METHOD   T. YOSHIDA*†, H. KURAMAE††, H. MORIMOTO†††, T. YAMAGUCHI†,                T. OHATA†††† AND E. NAKAMACHI† † Dept. of Biomedical Engineering, Doshisha Univ., Kyotanabe, Kyoto, 610-0394, Japan †† Dept. of Technol. Management, Osaka Institute of Technol., Asahiku, Osaka, 535-8585, Japan ††† Furukawa Electric Co. Ltd., Okano, Nishiku, Yokohama, Kanagawa, 220-0073, Japan †††† Dept. of Mechanical Engineering, Osaka Sangyo Univ., Daito, Osaka, 574-8530, Japan Key words: Computational Plasticity, Drawing Process, Finite Element, Texture evolution, Multi scale. Abstract. Recently, the crystallographic control technology in the aluminum wire drawing process has been a key technology in the aluminum industries, which produces high-strength wires for the electric, automotive and aircraft parts. This newly proposed “process metallurgy” computational technology in the industrial forming process consists of the two-scale finite element (FE) analyses and the optimum design algorithm.We developed two-scale FE analyses code based on the crystallographic homogenization method by considering the hierarchical structure of polycrystal aluminium alloy metal. It can be characterized as the combination of two-scale structure, such as the microscopic polycrystal structure and the macroscopic elastic plastic continuum. Micro polycrystal structure is modelled as a three dimensional representative volume element (RVE). RVE is featured as 3x3x3 eight-nodes solid finite elements, which has totally 216 crystal orientations. This FE analyses code can predict the deformation, strain and stress evolutions in the wire drawing processes in the macro-scale, and simultaneously the crystal texture and hardening evolutions in the micro-scale. In this study, we analyzed the texture evolution in the “three passes” wire drawing processes by using our two-scale FE analyses code under conditions of various drawing angles of die. We evaluated the texture evolution in the surface and center regions of the wire cross section, and to clarify the effects of processing conditions on the texture evolution.  1 INTRODUCTION Recently, the aluminum wire is used for the transmission line from the viewpoint of weight reduction. However, the pure aluminum wire has a problem of low strength, even though its high conductivity. Until now, several trials have done to generate a high strength and high formability wire in the aspects of material and process design. The main effort of these studies has been spent on the mechanical and material analyses, such as the drawing processes, the tool shapes, the lubrication and the material itself. In recent years, the study of drawing process is focused on the microstructure design of material, such as the crystallographic Crystal texture evolution analyses in metal drawing processes by using two-scale finite ele-ment method  1427T. Yoshida, H. Kuramae, H. Morimato, T. Yamaguchi, T. Ohata and E.  Nakamachi.  2 morphological design based on the crystal plasticity theory[1]. A specified texture with a preferred orientation, which is evolved in the drawing process, shows a high formability and high strength characteristics. Therefore, there occurred a very high demand to develop a fusion numerical technique of “process metallurgy simulation” by combining the multi-scale finite element (FE) analysis and the process optimization algorithm[2-5]. It can control the material property at the micro-scale - the crystal structure and the texture - through the drawing process optimization. Inakazu has reported that a particular drawn wire, which has a texture of {110} <111> orientation, shows a very high strength, by enormous experimental observations[6]. However, a numerical technique to search the optimum crystallographic structure by considering the drawing process effect has not been invented yet. In this study, we develop a fusion simulation technique combined with the two-scale finite element analysis and drawing process analysis to design a new highly functionalized aluminum alloy.  2 TWO-SCALE ELASTIC/ PLASTIC FINTE ELEMENT PROCEDURE 2.1 FORMULATION OF TWO-SCALE FINITE ELEMENT ANALYSIS             Fig.1 shows double scale structures, such as a macro-continuum   and a micro-crystal structure Y. In the micro-structure, the RVE (representative volume element) consists of an polycrystal aggregation and is very small compared with the macro region   by a scale factor 1 .We introduce both microscopic and macroscopic coordinate systems so that physical quantities are represented by two different length scales; one is  in the macroscopic region  and the other is  in the microscopic region Y.  Equations in the micro- and macroscopic levels are derived by employing defined velocities,  and . : in the macroscopic region, (1)  :in the microscopic region. (2)  We assume that the perturbed velocity  equals to zero on the boundary of the micro crystal structure Y, such as , to satisfy the periodicity condition. The equation of virtual power principle for the micro polycrystalline structure is expressed as: [010][100][001]   (a) Macro continuum       (b) Micro structure                 (c) RVE               (d) Crystal lattice Figure 1: Macro continuum and micro polycrystal structures, and coordinates xｉ and yｉ xi yi ti iixy 1428T. Yoshida, H. Kuramae, H. Morimato, T. Yamaguchi, T. Ohata and E.  Nakamachi.  3 YyxuYyxuyxuYyxuyxu jiY ijiY iY ii d),(d),(),(d),(),( ,     (3) : on the boundary of region Y, (4) where  and  are the mass density and the viscosity coefficient, respectively.  By solving the governing equation, Eq. (4), we obtain the Cauchy stresses.  The macroscopic Cauchy stress tensor, which means the homogenized stress tensor, is obtained by averaging Cauchy stresses in microstructure as follow:  (5) where,  is Cauchy stress at Gaussian integration point (IP) G of a finite element in the microscopic region,  is the Jacobian at the IP,  is the total number of IPs. We introduced the homogenized stress  and then formulate the virtual power equation of the macro continuum as follow:    d)()()d()d()d()()d()(jiHijiiiiiiii xUUTUfUUUU xxxxxxxx  (6) where  and  are the volume, force boundary surface, the body force and the external surface force. : for the micro structure (7) :for the macro structure (8) where  and  are the mass and damping matrices,  and  are the internal and external force vectors,  and  are the micro and macro displacement vectors, respectively.   The displacement vectors of the next time step for the micro and macro levels can be obtained without solving simultaneous equations. In order to obtain the internal force vector , the macroscopic stresses are required on all Gaussian integration points using FE analysis of micro FE mesh.  Therefore, the most of the computation time is consumed in the homogenized stress using micro-mesh. 2.2 ELASTIC/CRYSTAL PLASTICITY CONSTITUTIVE LAW The conventional elastic/ crystalline viscoplastic constitutive equation is employed to predict deformation of  micro-polycrystal structure [7-12].          110ττmgg     (9)      gg   (10)       hg ,         hqqhh  1  (11) 1429T. Yoshida, H. Kuramae, H. Morimato, T. Yamaguchi, T. Ohata and E.  Nakamachi.  4    100)(  nCnChh   (12) Here,    denotes the shear strain rate at the slip system(  ),  τ the resolved shear stress(RSS), )(g  the reference shear stress,   0 the reference shear strain rate and m the material rate sensitivity, h the hardening coefficients, abq  the self and latent hardening matrices, ,0  the critical resolved shear stress (CRSS) , h0 the initial hardening ratio, n the strain hardening exponent and C the hardening coefficient.  The tangent modulus method is introduced for the stable time integration. Finally, Jaumann rate of Cauchy stress can be related to the rate of deformation Dij as follow;      fRDC ijklVijklijˆ  (13) A static explicit FE is used for a plastic strain induced texture, anisotropy evolutions and yield loci prediction. A dynamic explicit FE code is applied to analyze the sheet metal forming process. 3 DRAWING PROCESS ANALYSIS  3.1 Material parameter identification We constructed FE models for the texture evolution analyses of the drawing process of the pure aluminum A1050. The crystal orientations measured by SEM-EBSD were introduced into integration points of the micro-finite elements of the representative volume element (RVE). We measured the crystal orientation distribution on the surface by using SEM-EBSD as shown in Fig. 2(a) and searched a minimum number of crystal orientations (grains) to represent the crystal plasticity constitutive law, which satisfied both the periodicity of crystallographic morphology and constitutive law. Finally we found that 216 crystal orientations were enough for RVE - 3x3x3 micro finite elements -. Figure 2(b) shows the crystal orientation distributions of RVEs -{111} pole figure -. Three crystal material parameters, 0, h0 and n, of the hardening evolution equation (12) were identified by the least square method using FE simulation results of the uni-axial tension tests through the comparison with the experimental results. Figure 3 shows stress-strain curves obtained by the experiments of tensile test in the drawing direction (DD) and the multi-scale FE results by employing 27 (= 3×3×3) micro FEs with 216 Gaussian integration points. Table 2 summarizes the crystal plastic material properties.      1430T. Yoshida, H. Kuramae, H. Morimato, T. Yamaguchi, T. Ohata and E.  Nakamachi.  5                   (a) Crystal orientation distributions obtained by SEM-EBSD                      (b) {111} pole figure Figure 2: SEM-EBSD measurement results and {111} pole figure of the pure aluminum            Figure 3: Stress-strain curves obtained by experiments and FE analyses using RVE-FE model Table 1: Material properties of crystal plasticity constitutive model     3.2 FE model of wire and tool model The wire drawing process of diameter reduction was performed by three conical die passes. We analyzed tree-passes by using the conical dies as shown in Fig. 4(a) to investigate the texture evolution at each drawing process. Fig.4(a) shows a wire FE models, which diameter is 10mm and the initial length is 80mm. Its macro-continuum FE model employed 8-node iso-parametric solid element, and a total number of finite elements was 1620. We have modeled so as to enter smoothly into the conical die by using initially squeezed edge as shown in Fig. 4(a). The micro- FE model - RVE polycrystal model -  was divided into 27 (= 3×3×3) 8-node solid elements with 216 crystal orientations. We employed the enforced displacement in the drawing direction (DD) at the tip of the round wire. We employed the conical die angle as shown in ig. 4(a) such as 6 deg, to design the reduction in area as 20%. Diameters of die edge were different as shown in Fig. 4(b). The coefficient of friction between the die and wire was set as 0.02. n  0.1 [MPa] 4 [MPa] 241431T. Yoshida, H. Kuramae, H. Morimato, T. Yamaguchi, T. Ohata and E.  Nakamachi.  6                                           Wire                                                                         Die       (a) FE models and three conical die models for three-passes drawing process                                          1st-pass                                       2nd-pass                                              3rd-pass (b) Die set up for three passes wire drawing process  Figure 4: Macro-FE models of the wire and three conical dies for the wire drawing process simulation 3.3 Results of multi-scale FE analyses of three-passes wire drawing We carried out two-scale FE analyses of the three passes wire drawing process. Figure 5 shows deformed meshes obtained by macro-FE analyses and comparisons of shear strain distributions of wire FE models at three passes. Figure 5 shows the axial-radial sectional views of shear strain distributions at three passes, because of the axisymmetric deformation.  It was confirmed that the closer to the surface the higher the shear strain, and further the more the number of drawing pass the larger the strain.  Fig.6 shows comparisons of the strain paths of the surface region and the center region, which correspond to the described macro finite elements, marked by the red color circle as shown in Fig.6. The vertical axis shows the shear strain and the horizontal one the tensile strain in the drawing direction. It was confirmed that the shear strain increased drastically in 40 50TD DD ND WireDie1Die2Die380Half die angle6 deg Wire1432T. Yoshida, H. Kuramae, H. Morimato, T. Yamaguchi, T. Ohata and E.  Nakamachi.  7 the surface region and the tensile strain was dominated in both the surface and center regions. The strain increased rapidly at the first and second passes according to the combination effect of the cross sectional reduction and hardening evolution.  Fig.7 shows {111} pole figures and the inverse pole figures to compare the texture evolutions at 1st, 2nd and 3rd passes. We confirmed that the more the pass, the more the concentration toward {111} orientation. Further, it was demonstrated that the region closer to the surface, the more the concentration toward {111} orientation was found.  On the other hand, we observed the double texture structure, {111} and {100} orientations in the center region, which is the typical texture of FCC metal by drawing process. Fig.8 shows ODF results of orientation contours at deg. plane at 1st, 2nd and 3rd passes to compare the texture evolution at the surface and center regions. The similar results with the pole figures as shown in Fig. 7 were obtained.        (a) 1st-pass        (b) 2nd-pass     (c) 3rd-pass  Figure 5: deformed shapes of macro-FE models with shear strain               Figure 6: Strain strain paths of FEs of the surface and the  center regions Tensile strain(εyy)0.060.080.100.120.04 0.020.14 0.000.0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.0 0.1 εyz surface center Shear strain Shear strain Shear strain 1433T. Yoshida, H. Kuramae, H. Morimato, T. Yamaguchi, T. Ohata and E.  Nakamachi.  8                Figure 7: Texture evolutions at each pass of drawing by employing {111} pole figure and the inverse pole figure             Figure 8:  ODF results of orientation contours at deg. plane at 1st, 2nd and 3rd passes 4 CONCLUSIONS Numerical results of two-scale FE analyses of three passes wire drawing process show clearly the strain evolution at the macro-scale and the texture evolution at the micro-scale. It suggests that our two-scale analyses could predict the texture evolution, indicated as below; 1. The shear strain increases in the surface region and the tensile strain is dominated in both the surface and center regions. 2. The more the pass, the more the concentration toward {111} orientation in the surface region is observed. The double texture structure, {111} and {100} orientations, was found in the center region, which is the typical texture of FCC metal by drawing process. Shear TextureInitial｛111｝1434T. Yoshida, H. Kuramae, H. Morimato, T. Yamaguchi, T. Ohata and E.  Nakamachi.  9 In the future, our two-scale FE analyses of multi-passes wire drawing process will be a powerful tool to design the micro crystallographic structure of wire, by employing the conventional FE analyses to predict the strength of wire. REFERENCES [1] J. CHEN, W. YAN, C.x. LIU, R.g. DING and X.h. FAN, Dependence of texture evolution on initial orientation in drawn single crystal copper, Mater Charact,62(2011) 237-242. [2] E. Nakamachi, N.N. Tam, H, Morimoto, Multi-scale finite element analyses of sheet  materials by using SEM-EBSD measured crystallographic RVE models, Int. J. Plasticity, 23 (2007) 450-489. [3] E. Nakamachi, C.L. Xie, H. Morimoto, K. Morita, N. Yokoyama, Formability assessment  of FCC aluminum alloy sheet by using elastic/crystalline viscoplastic finite element analysis, Int. J. Plasticity, 18 (2002) 617-632. [4] E. Nakamachi, K. Hiraiwa, H. Morimoto, M. Harimoto, Elastic/crystalline viscoplastic  finite element analyses of single- and poly-crystal sheet deformations and their experimental verification, Int. J. Plasticity, 16 (2000) 1419-1441. [5] E. Nakamachi, X. Dong, Study of texture effect on sheet failure in a limit dome height test  by using elastic/crystalline viscoplastic finite element analysis, J. App. Mech., 64 (1997) 519-524. [6] N. Inakazu, Drawing and fiber texture formation for aluminum, J. JILM, 37(1987)381-393. [7] A. Needleman, Finite element for finite strain plasticity problems, Proc. The Workshop on  Plasticity of Materials at Finite Strain, 1981, 1-11.  [8] R.J. Asaro, Crystal plasticity, J. App. Mech., 50 (1983) 921-934. [9] R.J. Asaro, A. Needleman, Texture development and strain hardening in rate dependent  polycrystals, Acta Metallurgica, 33 (1985) 923-953. [10] J. Pan, J.R. Rice, Rate sensitivity of plastic flow and implications for yield-surface  vertices, Int. J. Solid and Struct., 19 (1983) 973-987. [11] Y. Zhou, K.W. Neale, L.S. Tóth, A modified model for simulating latent hardening during  the plastic deformation of rate-dependent FCC polycrystals, Int. J. Plasticity, 9 (1993) 961-978. [12] J. Harder, Crystallographic model for the study of local deformation processes in  polycrystals, Int. J. Plasticity, 15 (1999) 605-624. 1435

Crystal texture evolution analyses in metal drawing processes by using two-scale finite element method

https://upcommons.upc.edu/bitstream/2117/183444/1/COMPLAS2013-134_Crystal%20texture%20evolution.pdf

Crystal texture evolution analyses in metal drawing processes by using two-scale finite element method

Abstract

Similar works

Full text

Available Versions

UPCommons. Portal del coneixement obert de la UPC