Theoretical and Experimental Analysis of Drawing of Square Wire and Square Twisted Wire Maciej Suliga 1a, Sebastian Mróz 1, Piotr Szota 1

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1 Solid State Phenomena Vol. 165 (2010) pp Online: (2010) Trans Tech Publications, Switzerland doi: / Theoretical and Experimental Analysis of Drawing of Square Wire and Square Twisted Wire Maciej Suliga 1a, Sebastian Mróz 1, Piotr Szota 1 1 Czestochowa University of Technology, Faculty of Materials Processing Technology and Applied Physics, Institute of Modelling and Automation of Plastic Working Processing Armii Krajowej 19, Czestochowa, Poland a suliga@wip.pcz.pl Keywords: square twisted wire, wire drawing simulation Abstract. Numerical analysis of drawing square and square twisted wires is presented. The thermomechanical simulation of the drawing process of square wire was carried out using the viscoplastic body model for a three-dimensional strain state with the use of Forge2007 software, while the properties of the material being deformed were described with the Norton-Hoff law. In this paper the distribution of effective strains and longitudinal stresses during changes of the crosssection and twisting of the wires has been demonstrated. It was determined that square twisted wires are characterized by significant inhomogeneity of strain. For verification of obtained numerical results experimental investigation was performed for square and square twisted wire drawing in laboratory conditions. The analysis of drawing stresses in square twisted wires used for modeling and experimental investigation indicated high material effort, which was much higher than in the case of drawing of square and round wires. Introduction Square twisted nails, as compared to traditional round nails, provide a greater resistance of joined elements to loosening under the action of variable external loads, and are commonly used in the making of wooden pallets [1]. To accomplish the process of drawing square twisted wire, drawing dies are used, in which the simultaneous transformation of the round profile into the square one occurs during drawing, with the lateral surface of the wire taking on the shape of a helical surface [2-4]. For the correct representation of the process kinetics during simulation, it is necessary to employ so called rotary floating tools that allow the free rotation of the drawing die [5]. For these reasons, it is considered justifiable to use FEM-based software applications for the analysis of the process of drawing square wire and square twisted wire. In the present work, the Forge2007 software was used for numerical analysis of process of drawing square and square twisted wires. The elastoviscoplastic model of metal deformed in a three-dimensional state of strain was assumed in the theoretical studies. The mechanical state of deformed material was described with the Norton-Hoff law [6-7]. Selection of the kinetic parameters and boundary conditions of the square and square twisted wire drawing process The application of the Forge2007 software using the thermomechanical models incorporated in it requires the definition of boundary conditions which are crucial to the correctness of numerical computation. Therefore, computation results are particularly affected by the properties of the steel examined, friction conditions, and the kinetic and thermal parameters describing the drawing process. The material used for the tests was steel 10. For the numerical studies, the following boundary conditions were assumed: drawing die and ambient temperature, 20 C; initial wire temperature, 20 C; friction coefficient, µ 0.06; coefficient of heat exchange between the wire and the drawing die, α 1000 [W/Km 2 ]; coefficient of heat exchange between the wire and the air, α p 10 [W/Km 2 ]. For the experimental tests and numerical studies of the drawing process, drawing dies and their three-dimensional models created in a CAD-type program were used (Fig. 1). The drawing All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, (ID: , Pennsylvania State University, University Park, USA-09/10/15,05:27:27)

2 378 Mechatronic Systems and Materials: Materials Production Technologies die model was constructed from a triangle-based grid (Fig. 1b), while the wire (stock) model was constructed from tetrahedral elements (Fig. 1c). The finite-element grid in the location of contact with the drawing die was condensed in order to more accurately represent the shape during drawing. The wire model was built from ca. 14 thousand elements, each of average edge length of 1 mm, while in the locations of wire-to-drawing die contact the average edge length of the element was 0.25 mm. In computer simulations, the capability of drawing die rotation relative to the longitudinal drawing die axis was accomplished by using a "floating" tool, with the friction between the drawing die and the rotation-enabling bearing was omitted. a) b) c) Fig. 1. Computer models of the drawing die and the wire: a) constructional dimensions of the drawing die, where: Dz drawing die outer diameter, Dp drawing die inner diameter, Lr working part length, Lc drawing die length, ak initial drawing die dimension, α drawing angle, β working part torsional angle, λ sizing part torsional angle, b) the drawing die model constructed from a triangular planar grid, c) the wire model constructed from a tetrahedral spatial grid Table 1. Constructional dimensions of the drawing die Type of die Dz Dp Lr Lc ak α [ ] β [ ] λ [ ] I II The initial wire diameter was equal to 3.7 mm, while the side of the square wire and the square twisted wire was equal to 2.8 mm. The initial wire diameter was selected based on the results of studies in [8], which have revealed that the correct shape of square twisted wire is obtained, when the initial wire diameter equals 1.3 times the square side. Results of numerical computations and experimental tests Purpose of numerical analysis was to determine the distribution of strain intensities, longitudinal strains and drawing stresses in the process of drawing square wire and square twisted wire. The obtained results of the distribution of strain intensities on the longitudinal section and on the crosssections in the die approach angle and in the sizing part of the drawing die are provided in Fig. 2. The distribution of strain intensities in the die approach angle and in the sizing part of the drawing die is shown on wire cross-sections that were obtained after introducing 5 cutting edges in such a manner that the first of the planes was positioned in the location of wire contact with the drawing die (the plane of wire entry to the deformation region), and the fifth plane was positioned in the location of wire exit from the sizing part. Planes No. 2 and 4 were positioned in the midlength of the conical part of the drawing die and in the mid-length of the sizing part of the die, while plane No. 3 was positioned in the location of transition of the conical part of the drawing die into its sizing part (Fig. 2).

3 Solid State Phenomena Vol a) b) Fig. 2. Distribution of strain intensities on the longitudinal section and the cross-sections during the drawing of: a) square wire (drawing die Variant I), b) square twisted wire (drawing die Variant II) The obtained distributions of strain intensities on the longitudinal sections of wires drawn (Fig. 2) indicate that the metal deforms most intensively in the sub-surface layers. With this, the magnitude of deformation increases with decreasing height of the drawing die conical part. When analyzing the distributions of strain intensities on the wire cross-sections it was found that the material was deformed most by the flat parts of the drawing die (sections 2-5) during the drawing of both square wire and square twisted wire. The lowest strain intensity values were observed at the wire corners that come into contact with the drawing die surfaces. Hence, the lateral shape of the wires, as shown in sections 5, Figs. 2a & 2b, has rounded corners. As a result of the additional twist of the wire in the drawing die sizing part (Fig. 2b), the strain intensity value increases in this zone, too, as compared to the drawing of square wire (Fig. 2a). Another important parameter to be determined, aside from the strain intensity, is the distribution of longitudinal stresses, σ x, and of the drawing stress in the process of drawing square wires and square twisted wires. The drawing stress is ranked among the basic parameters of the drawing process [1]. It is its value that the coefficient of material effort is dependent on. Fig. 3 provides the distribution of longitudinal stresses, σ x, in the process of drawing square wires and square twisted wires. a) b) Fig. 3. Distribution of longitudinal stresses σ x (in the drawing direction) on the longitudinal section during the drawing: a) of square wire, b) square twisted wire

4 380 Mechatronic Systems and Materials: Materials Production Technologies When analyzing the data in Figs. 3a-3b it can be noticed that in the zone of wire entry to the drawing die (wire contact with the drawing die), at the sub-surface layer, compressive stresses occur, which vanish in the initial phase of plastic deformation. Whereas, in the wire axis, tensile stresses occur over the whole length of the deformation region. The maximum tensile stress values were observed in the sizing part of the drawing die. During the drawing of square wires, longitudinal stresses in the range of MPa occur in the wire axis and in the intermediate wire layers in the drawing die sizing part, while in the sub-surface layers (square corners) these stresses are higher, amounting to over 580 MPa (Fig. 3a). On the other hand, during the drawing of square twisted wire, the value of these stresses was as follows: in the wire axis and in the intermediate wire layers in the drawing die sizing part, MPa; and in the sub-surface layers (square corners), over 560 MPa (Fig. 3b). The higher stress magnitudes occurring during the drawing of square twisted wire, compared to the values obtained for square wire, are the result of an additional wire twist, especially in the drawing die sizing part. Experimental tests were carried out in order to verify the obtained results of theoretical studies. The drawing process was realized on a Zwick Z100 testing machine. C10 steel wire of an initial diameter of φ3.7 mm was drawn into 2.8 mm-side square wire and square twisted wire, respectively. Table 2 summarizes the mechanical properties of wire (yield point, R 0.2 ; tensile strength, R m ); the values of the drawing force, F, and drawing stress, σ c, obtained from the experimental tests and theoretical studies; and the coefficient of material effort, σ c / R 0.2. Table 2. Mechanical properties of square wire and square twisted wire, and values of the drawing force and drawing stress Variant R 0.2, R m, F c, N σ c, MPa MPa MPa experimental theoretical experimental theoretical σ c / R 0,2 I II The correct technological process of drawing takes place, when the coefficient of material effort, defined as the ratio of the drawing stress to the yield stress of wire after drawing, is less than unit. The lower this coefficient, the higher is the probability of accomplishing the drawing process. In the drawing of round wires, it amounts to about 0.7. The present investigation has revealed that for the drawing of square wires this coefficient is slightly higher, amounting to For square twisted wires, on the other hand, the coefficient is much higher, being equal to Such high material effort coefficient is associated with the generation of both longitudinal drawing stresses and tangential stresses resulting from the formation of the helical surface. From the performed numerical computations it was established that the magnitudes of the drawing force and the drawing stress for square wires and square twisted wires were similar to those of the drawing force and the drawing stress obtained from the experimental tests. The difference between the obtained results did not exceed 4%. Summary The following findings and conclusions may be highlighted on the basis of performed research work: The obtained distribution of strain intensities in square wires and square twisted wires indicates pronounced unevenness of deformation on the cross-section of wires drawn. The wire twist resulted in increase in deformation unevenness in the wires drawn. The process of drawing square wire and square twisted wire is characterized by pronounced unevenness of the distribution of longitudinal stresses. Compressive stresses only occur in

5 Solid State Phenomena Vol the sub-surface layers of wire in the region of wire contact with the drawing die, while in the remaining deformation region longitudinal tensile stresses occur. The highest values of longitudinal tensile stresses are observed in the sizing part of the drawing die, especially in the sub-surface layer. The analysis of the drawing stresses of square twisted wires obtained from modeling and experimental tests reveal high material effort, which is much higher than in the case of drawing round wires. The increase in the material effort coefficient during the drawing of square twisted wires is associated with the generation of tangential stresses resulting from the formation of helical surface. Reference [1] F. Knap: Ciągnienie drutu kwadratowego skręconego. Hutnik-Wiadomości Hutnicze, No 2 (1993) (in Polish). [2] F. Knap: Ciągnienie drutu kwadratowego skręconego. Materiały konferencyjne Przeróbka plastyczna 93 (Krynica 1993) (in Polish). [3] M. Suliga, P. Szota, S. Mróz: Teoretyczna i doświadczalna analiza procesu ciągnienia drutu kwadratowego skręconego. Hutnik Wiadomości Hutnicze, No 1 (2008), p (in Polish). [4] M. Suliga, P. Szota, A. Stefanik: Rozkład naprężeń wzdłużnych w procesie ciągnienia drutów kwadratowych skręconych. Hutnik Wiadomości Hutnicze, No 1 (2008), p (in Polish). [5] FORGE3 Reference Guide Release 6.2 (Sophia-Antipolis 2002). [6] S. Mróz: Proces walcowania prętów z wzdłużnym rozdzielaniem pasma. Wydawnictwo Politechniki Częstochowskiej, Seria: Monografie No 138 (Częstochowa 2008) (in Polish). [7] A. L Gavrus, E. Massoni, J.L. Chenot: An inverse analysis using a finite element model for identification of rheological parameters. Journal of Materials Processing Technology, Vol. 60, (1996), p [8] F. Knap, R. Karuzel, Ł. Cieślak: Ciągnienie drutów, prętów i rur. Metalurgia No 36. Wydawnictwo Politechnika Częstochowska, (Częstochowa 2004) (in Polish).

6 Mechatronic Systems and Materials: Materials Production Technologies / Theoretical and Experimental Analysis of Drawing of Square Wire and Square Twisted Wire / DOI References [7] A. L Gavrus, E. Massoni, J.L. Chenot: An inverse analysis using a finite element model for identification of rheological parameters. Journal of Materials Processing Technology, Vol. 60, (1996), p doi: / (96)

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