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Improving workability in ironing
Journal of Materials Processing Technology 130–131 (2002) 64–68
Improving workability in ironing Zlatko Kampusˇa,*, Blazˇ Nardinb a
Faculty of Mechanical Engineering, University of Ljubljana, Asˇkercˇeva 6, 1000 Ljubljana, Slovenia b TECOS, Mariborska 2, 3000 Celje, Slovenia
Abstract The paper describes the possibilities of improving workability in ironing by using a superimposed force on the cup edge. Equations for stresses and forces in ironing with superimposed force were derived on the basis of the elementary theory of plasticity. The increase in workability is shown in the workability diagram. The finite element method (FEM) served as the basis for simulating the production of cups with non-uniform wall thickness. Two theoretical models were verified by experiments. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Ironing with superimposed force; Stresses; Forces; Workability; FEM
1. Introduction The first patent which contained the principles of ironing was taken out in the USA as early as 1904 [1], however, intensive research into this procedure around the world took place only after 1950. Most papers have dealt with the calculation of stresses and the forming force. Most are based on the elementary theory of plasticity [2,3], but also on the deformation work method [4], the upper boundary method [5,6], slip-line theory [7], multifactorial planning method [8,9] and the finite element method (FEM) [10,11]. Some authors have researched the possibility of increasing the workability in ironing, either by ultrasonic vibration [12] or by the action of a superimposed force on the cup edge. The published results of ironing with superimposed force are given only on [13–15].
2. Derivation of the main normal stresses using the elementary theory of plasticity Workability is the ability of materials to withstand plastic deformation without fracture or other defects. Due to the complexity of influential parameters, workability cannot be defined in a single manner. For identical materials and constant forming conditions, the forming limit also depends on the stress state. Workability in ironing can be improved by increasing the percentage of compressive stresses in the *
Corresponding author. Tel.: þ386-1-4771-442; fax: þ386-1-2518-567. E-mail address: [email protected] (Z. Kampusˇ).
forming zone, which can be achieved with an additional compressive superimposed force on the cup edge. External forces—punch force Fp and superimposed force Fs—act on an infinitesimally small part of the cup in the forming zone (Fig. 1), and stresses take place in the axial direction sz, radial direction sr, and circular direction sy. Since axial stress sz is greater than the two other types, it can be said that sz ¼ s1 :
(1)
Cup deformation—radial upsetting and axial stretching— are much greater than cup deformation along its diameter. No major error is made by assuming that j2 ¼ 0:
(2)
By using the equilibrium condition and certain simplifications and assumptions, the following equations can be derived for the main normal stresses: The longitudinal stress in the forming zone szðRx Þ is ! b1 1 Ax ðsfs ðb1Þ1:15bsfm Þþ1:15bsfm ; szðRx Þ ¼ b1 A1 (3) the longitudinal stress at the end of the forming zone sz0 is ! b1 1 A2 sz0 ¼ ðsfs ðb 1Þ 1:15bsfm Þ þ 1:15bsfm b1 A1 (4) and the radial stress in the forming zone srðRx Þ is srðRx Þ ¼ szðRx Þ 1:15sf :
0924-0136/02/$ – see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 0 1 3 6 ( 0 2 ) 0 0 7 8 3 - 5
(5)
Z. Kampusˇ, B. Nardin / Journal of Materials Processing Technology 130–131 (2002) 64–68
65
Taking into account the plasticity condition and boundary conditions, an equation can be derived to show the variation of longitudinal stress in the cylindrical part of the die sz(h): szðhÞ ¼ 1:15sf ð1:15sf sz0 Þ eð2pR2 md hÞ=A2 ;
(7)
while the radial stress in the cylindrical part of the die sr(h) is srðhÞ ¼ ð1:15sf sz0 Þ eð2pR2 md hÞ=A2 :
(8)
Stresses in the workpiece at die exit: sza ¼ 1:15sf ð1:15sf sz0 Þ eð2pR2 md HÞ=A2
(9)
and sra ¼ ð1:15sf sz0 Þ eð2pR2 md HÞ=A2 :
(10)
Fig. 2 shows the distribution of longitudinal and radial stresses in ironing. In addition, Fig. 2a shows longitudinal and radial stresses in ironing without a superimposed force and Fig. 2b with a superimposed force. It can be seen that the superimposed force increases radial stress and reduces longitudinal stress. The maximum strain can be calculated from the condition that the maximum tensile stresses in the cup wall sza may not exceed the tensile strength of the material Su: sza ¼ 1:15sf ð1:15sf sz0 Þ eð2pR2 md HÞ=A2 Su :
(11)
Fig. 3 shows the variation of maximum strain je max with the magnitude of superimposed stress sfs for a typical material (C ¼ 750 N/mm2, n ¼ 0:21).
Fig. 1. Main stresses in ironing.
The radial stress at the end of the forming zone sr0 is sr0 ¼ sz0 1:15sf :
(6)
After forming, the longitudinal stress in the cylindrical part of the workpiece increases due to friction between the workpiece and the die.
3. Presentation of ironing in a workability diagram The variation of maximum strain je max with the stress– strain state can be shown in the workability diagram. In order
Fig. 2. Distribution of longitudinal sz and radial sr stresses in ironing. (a) without a superimposed force, (b) with a superimposed force.
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Z. Kampusˇ, B. Nardin / Journal of Materials Processing Technology 130–131 (2002) 64–68 Table 1 Forming properties Material
Flow stress
A B C
sf ¼ 500j0:24 e sf ¼ 750j0:21 e sf ¼ 960j0:17 e
Fig. 4 shows the variation of the workability parameter with the magnitude of superimposed force. Stress s1 and flow stress sf are calculated at the moment when the following condition is fulfilled:
Fig. 3. The influence of superimposed stress sfs on the maximum strain je max.
to describe the stress-strain state, it is important to select such a combination of stresses that their value is independent of the orientation of the coordinate system. Siebel [16] proposed that this should be the mean stress, which amounts to one-third of the first invariant of the stress tensor. However, the following is most often used for the workability parameter [15,17,18]: J1 s1 þ s2 þ s3 bw ¼ pffiffiffiffiffiffi0ffi ¼ se 3J2
(12)
where J1 is the first invariant of the stress tensor and J20 the second invariant of the stress deviator. It can be derived that the workability parameter for ironing is 3 2s1 2 bw ¼ pffiffiffi (13) 2 sf 3
s1 ¼ sza ¼ 1:15sf ð1:15sf sz0 Þ eð2pR2 md HÞ=A2 ¼ Su : (14) The diagram applies to three materials with different plasticity curves (Table 1).
4. Forming force in ironing with a superimposed force The total forming force in ironing with a superimposed force Ftot equals force on the punch (punch force) Fp plus superimposed force Fs. The punch force Fp equals the force pressing on the cup bottom Fb plus the force of friction between the cup and the punch Ffp, which occurs as a result of material flow in the forming zone: Ftot ¼ Fp þ Fs ¼ Fb þ Ffp þ Fs :
(15)
The friction force between the cup and the punch Ffp depends on the coefficient of friction between the cup and punch mp, radial stress in the forming zone sr, and the forming zone area A.
Fig. 4. Workability parameter bw vs. superimposed stress sfs for three different materials.
Z. Kampusˇ, B. Nardin / Journal of Materials Processing Technology 130–131 (2002) 64–68
67
Fig. 5. Production of a cup with internal wall thickening.
Fig. 6. Production of a cup with external wall thickening.
lower cup diameter is increased first, but when the punch reaches the cup bottom, ironing of the upper part of the cup begins (Fig. 6). The result is a cup with lower external wall thickening and upper wall thinning.
It can be derived that the force of friction is 2 b1 Z 2pr2 mp R1 1 x r22 Ffp ¼ ðsfs ðb 1Þ b1 tg a R2 R21 r22 ! ! 1:15bsfm Þ þ 1:15bsfm
1:15sf
dx:
(16) 6. Experiments
5. Production of cups with non-uniform wall thickness The FEM (program ABAQUS) was used to explore the possibilities for the manufacture of products with walls of non-uniform thickness, which can be used for example in the production of grooving or toothing. Since we were not interested in product accuracy here, rigid elements were used for the punch and die and axi-symmetric quadratic elements for the cups. In order to obtain a suitable preform, deep drawing without a blank holder was first simulated. The influence of heating was not taken into account in the model. Fig. 5 shows a simulation of the production of a cup with internal wall thickening. In the first phase of drawing, only the superimposed force acts on the cup edge. The lower part of the cup is pressed through the die. The outer diameter decreases, while the cup wall remains unchanged. Then the punch force begins to act on the cup in addition to the superimposed force. The process of ironing begins. In this manner, a cup is produced with internal wall thickening on the lower end and a thinned wall at the upper end. Even if external wall thickening is desired, only a superimposed force on the cup is used in the first phase. Then the cup edge is unloaded and only the punch begins to move, i.e. ironing begins. Since the force required to increase the inner cup diameter is smaller than the required ironing force, the
A double-action hydraulic press was used for experiments. An experimental tool was made. The upper part of the tool, the die, was clamped into the ram. The superimposed force could be changed as desired during drawing via four spacers, which were connected with the hydraulic cushion of the press. Preforms for ironing were cups made by deep drawing. The punch diameter was 40 mm and that of the inlet die opening with a tractrix shape was 55 mm.
Fig. 7. Comparison of theoretical and actual maximum strain je max vs. the magnitude of superimposed stress sfs (material C10).
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Z. Kampusˇ, B. Nardin / Journal of Materials Processing Technology 130–131 (2002) 64–68
Fig. 8. Photograph of cups with internal und external wall thickening.
Fig. 7 shows how the maximum strain varies with the size of the superimposed force sfs. The diagram also contains the theoretical values of the model. It can be seen that theoretical predictions agree well with the results of experiments. The maximum strain increases by 40% with the action of a superimposed force. When cups with a non-uniform wall thickening were produced. Fig. 8 shows a photograph of a cup with an internal and external wall thickening. This was made from AlMg3.
7. Conclusion The derived equations of stresses and forces in ironing with a superimposed force are similar to those for normal ironing. If the superimposed force equals zero, these equations become the equations of classical ironing [3]. The theoretical model and experiments showed that the maximum strain can be increased by up to 40% with the use of a superimposed force. Even a small superimposed force yields a straight cup edge, which is unusual in the ironing of cups previously made by deep drawing. A superimposed force increases the total forming force and energy, therefore it should be only as large as is required for the reliability of the process. Numerical simulation showed (and experiments confirmed) that it is possible to produce cups with partially thickened walls. References [1] D. Campion, Deep drawing and ironing—theory and practise, Sheet Met. Ind. 57 (1980) 111–119.
[2] R.K. Busch, Abstreckringen von zylindrischen Hohlko¨ rpern mit einem oder mehreren Abstreckringen, Industrie-Anzeiger 92 (1970) 1741–1742. [3] H.G. Nagel, Die Fertigung von langen zylindrischen Werkstu¨ cken durch die Kombination der Verfahren Kaltfliespressen und Abstreckziehen, Umformtechnik 3 (1972) 33–39. [4] E.A. Popov, Osnovy Teorii Listovoi Sˇ tampovki, Masˇinostroenie, Moskva, 1977, pp. 199–212. [5] B. Musafia, Primjena Teorija Plasticˇ nosti, Svjetlost, Sarajevo, 1974. [6] S. Fukui, Analytical study of wall ironing, Considering Work Hardening C.I.R.P. 18 (1970) 593–599. [7] R. Hill, The Mathematical Theory of Plasticity, Oxford University Press, Oxford, 1950. [8] H. Djukicˇ , P. Popovicˇ , Metoda proracˇ una izvlacˇ enja sa redukcijom debljine stene zida, Obrada Deformisanjem Metala 9 (2) (1984) 45– 62. [9] H. Djukicˇ , Eksperimentalno odredjivanje zakona promjene sile pri izvlacˇ enju sa redukcijom zida omotacˇ a. 16, Savjetovanje proizvodnog masˇinstva Jugoslavije, Mostar, 1982. [10] E.I. Odell, A study of wall ironing by the finite-element technique, Trans. ASME J. Eng. Ind. 100 (1) (1978) 31–36. [11] Y.-M. Huang, L. Yuung-Hwa, C. Jia-Wine, An elasto-plastic finite element and experimental study of the ironing process, J. Mater. Process. Technol. 26 (1991) 53–80. [12] M. Jin, P. Kaewtatip, M. Murakawa, Utility of ultrasonic vibration applied to metal-forming processes, Advanced Technology of Plasticity, vol. III, Nu¨ remberg, 1999. [13] L. Bru¨ ckner, K. Po¨ hlandt, K. Lange, Gebrauchseigenschaften von durch Tiefziehen und nach-folgendes Abstreckgleitziehen gefertigten Na¨ pfen, Blech Rohre Profile 41 (1994) 9. [14] I.M. Zˇ vik, A.S. Sˇ arov, Erho¨ hung der Genaugkeit und des Umformgrades beim Abstreckziehen, Umformtechnik 10 (2) (1976). [15] Z. Kampusˇ, Ironing with superimposed force, Wire J. Int. 33 (12) (2000). [16] E. Siebel, Grundlagen und Begriffe der bildsamen Formgebung, Werkstattstech. U. Masch. 40 (1950) 11. [17] V. Vujevic, A.H. Shabaik, A new workability criterion for ductile metals, J. Eng. Mater. Technol., Trans. ASME 108 (1986) 245–249. [18] G. Ziaja, The formability of hypereutectic PM Al alloys, in: Proceedings of the 29th ICFG Plenary Meeting, Gyo¨ r, 1996.
Improving workability in ironing Zlatko Kampusˇa,*, Blazˇ Nardinb a
Faculty of Mechanical Engineering, University of Ljubljana, Asˇkercˇeva 6, 1000 Ljubljana, Slovenia b TECOS, Mariborska 2, 3000 Celje, Slovenia
Abstract The paper describes the possibilities of improving workability in ironing by using a superimposed force on the cup edge. Equations for stresses and forces in ironing with superimposed force were derived on the basis of the elementary theory of plasticity. The increase in workability is shown in the workability diagram. The finite element method (FEM) served as the basis for simulating the production of cups with non-uniform wall thickness. Two theoretical models were verified by experiments. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Ironing with superimposed force; Stresses; Forces; Workability; FEM
1. Introduction The first patent which contained the principles of ironing was taken out in the USA as early as 1904 [1], however, intensive research into this procedure around the world took place only after 1950. Most papers have dealt with the calculation of stresses and the forming force. Most are based on the elementary theory of plasticity [2,3], but also on the deformation work method [4], the upper boundary method [5,6], slip-line theory [7], multifactorial planning method [8,9] and the finite element method (FEM) [10,11]. Some authors have researched the possibility of increasing the workability in ironing, either by ultrasonic vibration [12] or by the action of a superimposed force on the cup edge. The published results of ironing with superimposed force are given only on [13–15].
2. Derivation of the main normal stresses using the elementary theory of plasticity Workability is the ability of materials to withstand plastic deformation without fracture or other defects. Due to the complexity of influential parameters, workability cannot be defined in a single manner. For identical materials and constant forming conditions, the forming limit also depends on the stress state. Workability in ironing can be improved by increasing the percentage of compressive stresses in the *
Corresponding author. Tel.: þ386-1-4771-442; fax: þ386-1-2518-567. E-mail address: [email protected] (Z. Kampusˇ).
forming zone, which can be achieved with an additional compressive superimposed force on the cup edge. External forces—punch force Fp and superimposed force Fs—act on an infinitesimally small part of the cup in the forming zone (Fig. 1), and stresses take place in the axial direction sz, radial direction sr, and circular direction sy. Since axial stress sz is greater than the two other types, it can be said that sz ¼ s1 :
(1)
Cup deformation—radial upsetting and axial stretching— are much greater than cup deformation along its diameter. No major error is made by assuming that j2 ¼ 0:
(2)
By using the equilibrium condition and certain simplifications and assumptions, the following equations can be derived for the main normal stresses: The longitudinal stress in the forming zone szðRx Þ is ! b1 1 Ax ðsfs ðb1Þ1:15bsfm Þþ1:15bsfm ; szðRx Þ ¼ b1 A1 (3) the longitudinal stress at the end of the forming zone sz0 is ! b1 1 A2 sz0 ¼ ðsfs ðb 1Þ 1:15bsfm Þ þ 1:15bsfm b1 A1 (4) and the radial stress in the forming zone srðRx Þ is srðRx Þ ¼ szðRx Þ 1:15sf :
0924-0136/02/$ – see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 0 1 3 6 ( 0 2 ) 0 0 7 8 3 - 5
(5)
Z. Kampusˇ, B. Nardin / Journal of Materials Processing Technology 130–131 (2002) 64–68
65
Taking into account the plasticity condition and boundary conditions, an equation can be derived to show the variation of longitudinal stress in the cylindrical part of the die sz(h): szðhÞ ¼ 1:15sf ð1:15sf sz0 Þ eð2pR2 md hÞ=A2 ;
(7)
while the radial stress in the cylindrical part of the die sr(h) is srðhÞ ¼ ð1:15sf sz0 Þ eð2pR2 md hÞ=A2 :
(8)
Stresses in the workpiece at die exit: sza ¼ 1:15sf ð1:15sf sz0 Þ eð2pR2 md HÞ=A2
(9)
and sra ¼ ð1:15sf sz0 Þ eð2pR2 md HÞ=A2 :
(10)
Fig. 2 shows the distribution of longitudinal and radial stresses in ironing. In addition, Fig. 2a shows longitudinal and radial stresses in ironing without a superimposed force and Fig. 2b with a superimposed force. It can be seen that the superimposed force increases radial stress and reduces longitudinal stress. The maximum strain can be calculated from the condition that the maximum tensile stresses in the cup wall sza may not exceed the tensile strength of the material Su: sza ¼ 1:15sf ð1:15sf sz0 Þ eð2pR2 md HÞ=A2 Su :
(11)
Fig. 3 shows the variation of maximum strain je max with the magnitude of superimposed stress sfs for a typical material (C ¼ 750 N/mm2, n ¼ 0:21).
Fig. 1. Main stresses in ironing.
The radial stress at the end of the forming zone sr0 is sr0 ¼ sz0 1:15sf :
(6)
After forming, the longitudinal stress in the cylindrical part of the workpiece increases due to friction between the workpiece and the die.
3. Presentation of ironing in a workability diagram The variation of maximum strain je max with the stress– strain state can be shown in the workability diagram. In order
Fig. 2. Distribution of longitudinal sz and radial sr stresses in ironing. (a) without a superimposed force, (b) with a superimposed force.
66
Z. Kampusˇ, B. Nardin / Journal of Materials Processing Technology 130–131 (2002) 64–68 Table 1 Forming properties Material
Flow stress
A B C
sf ¼ 500j0:24 e sf ¼ 750j0:21 e sf ¼ 960j0:17 e
Fig. 4 shows the variation of the workability parameter with the magnitude of superimposed force. Stress s1 and flow stress sf are calculated at the moment when the following condition is fulfilled:
Fig. 3. The influence of superimposed stress sfs on the maximum strain je max.
to describe the stress-strain state, it is important to select such a combination of stresses that their value is independent of the orientation of the coordinate system. Siebel [16] proposed that this should be the mean stress, which amounts to one-third of the first invariant of the stress tensor. However, the following is most often used for the workability parameter [15,17,18]: J1 s1 þ s2 þ s3 bw ¼ pffiffiffiffiffiffi0ffi ¼ se 3J2
(12)
where J1 is the first invariant of the stress tensor and J20 the second invariant of the stress deviator. It can be derived that the workability parameter for ironing is 3 2s1 2 bw ¼ pffiffiffi (13) 2 sf 3
s1 ¼ sza ¼ 1:15sf ð1:15sf sz0 Þ eð2pR2 md HÞ=A2 ¼ Su : (14) The diagram applies to three materials with different plasticity curves (Table 1).
4. Forming force in ironing with a superimposed force The total forming force in ironing with a superimposed force Ftot equals force on the punch (punch force) Fp plus superimposed force Fs. The punch force Fp equals the force pressing on the cup bottom Fb plus the force of friction between the cup and the punch Ffp, which occurs as a result of material flow in the forming zone: Ftot ¼ Fp þ Fs ¼ Fb þ Ffp þ Fs :
(15)
The friction force between the cup and the punch Ffp depends on the coefficient of friction between the cup and punch mp, radial stress in the forming zone sr, and the forming zone area A.
Fig. 4. Workability parameter bw vs. superimposed stress sfs for three different materials.
Z. Kampusˇ, B. Nardin / Journal of Materials Processing Technology 130–131 (2002) 64–68
67
Fig. 5. Production of a cup with internal wall thickening.
Fig. 6. Production of a cup with external wall thickening.
lower cup diameter is increased first, but when the punch reaches the cup bottom, ironing of the upper part of the cup begins (Fig. 6). The result is a cup with lower external wall thickening and upper wall thinning.
It can be derived that the force of friction is 2 b1 Z 2pr2 mp R1 1 x r22 Ffp ¼ ðsfs ðb 1Þ b1 tg a R2 R21 r22 ! ! 1:15bsfm Þ þ 1:15bsfm
1:15sf
dx:
(16) 6. Experiments
5. Production of cups with non-uniform wall thickness The FEM (program ABAQUS) was used to explore the possibilities for the manufacture of products with walls of non-uniform thickness, which can be used for example in the production of grooving or toothing. Since we were not interested in product accuracy here, rigid elements were used for the punch and die and axi-symmetric quadratic elements for the cups. In order to obtain a suitable preform, deep drawing without a blank holder was first simulated. The influence of heating was not taken into account in the model. Fig. 5 shows a simulation of the production of a cup with internal wall thickening. In the first phase of drawing, only the superimposed force acts on the cup edge. The lower part of the cup is pressed through the die. The outer diameter decreases, while the cup wall remains unchanged. Then the punch force begins to act on the cup in addition to the superimposed force. The process of ironing begins. In this manner, a cup is produced with internal wall thickening on the lower end and a thinned wall at the upper end. Even if external wall thickening is desired, only a superimposed force on the cup is used in the first phase. Then the cup edge is unloaded and only the punch begins to move, i.e. ironing begins. Since the force required to increase the inner cup diameter is smaller than the required ironing force, the
A double-action hydraulic press was used for experiments. An experimental tool was made. The upper part of the tool, the die, was clamped into the ram. The superimposed force could be changed as desired during drawing via four spacers, which were connected with the hydraulic cushion of the press. Preforms for ironing were cups made by deep drawing. The punch diameter was 40 mm and that of the inlet die opening with a tractrix shape was 55 mm.
Fig. 7. Comparison of theoretical and actual maximum strain je max vs. the magnitude of superimposed stress sfs (material C10).
68
Z. Kampusˇ, B. Nardin / Journal of Materials Processing Technology 130–131 (2002) 64–68
Fig. 8. Photograph of cups with internal und external wall thickening.
Fig. 7 shows how the maximum strain varies with the size of the superimposed force sfs. The diagram also contains the theoretical values of the model. It can be seen that theoretical predictions agree well with the results of experiments. The maximum strain increases by 40% with the action of a superimposed force. When cups with a non-uniform wall thickening were produced. Fig. 8 shows a photograph of a cup with an internal and external wall thickening. This was made from AlMg3.
7. Conclusion The derived equations of stresses and forces in ironing with a superimposed force are similar to those for normal ironing. If the superimposed force equals zero, these equations become the equations of classical ironing [3]. The theoretical model and experiments showed that the maximum strain can be increased by up to 40% with the use of a superimposed force. Even a small superimposed force yields a straight cup edge, which is unusual in the ironing of cups previously made by deep drawing. A superimposed force increases the total forming force and energy, therefore it should be only as large as is required for the reliability of the process. Numerical simulation showed (and experiments confirmed) that it is possible to produce cups with partially thickened walls. References [1] D. Campion, Deep drawing and ironing—theory and practise, Sheet Met. Ind. 57 (1980) 111–119.
[2] R.K. Busch, Abstreckringen von zylindrischen Hohlko¨ rpern mit einem oder mehreren Abstreckringen, Industrie-Anzeiger 92 (1970) 1741–1742. [3] H.G. Nagel, Die Fertigung von langen zylindrischen Werkstu¨ cken durch die Kombination der Verfahren Kaltfliespressen und Abstreckziehen, Umformtechnik 3 (1972) 33–39. [4] E.A. Popov, Osnovy Teorii Listovoi Sˇ tampovki, Masˇinostroenie, Moskva, 1977, pp. 199–212. [5] B. Musafia, Primjena Teorija Plasticˇ nosti, Svjetlost, Sarajevo, 1974. [6] S. Fukui, Analytical study of wall ironing, Considering Work Hardening C.I.R.P. 18 (1970) 593–599. [7] R. Hill, The Mathematical Theory of Plasticity, Oxford University Press, Oxford, 1950. [8] H. Djukicˇ , P. Popovicˇ , Metoda proracˇ una izvlacˇ enja sa redukcijom debljine stene zida, Obrada Deformisanjem Metala 9 (2) (1984) 45– 62. [9] H. Djukicˇ , Eksperimentalno odredjivanje zakona promjene sile pri izvlacˇ enju sa redukcijom zida omotacˇ a. 16, Savjetovanje proizvodnog masˇinstva Jugoslavije, Mostar, 1982. [10] E.I. Odell, A study of wall ironing by the finite-element technique, Trans. ASME J. Eng. Ind. 100 (1) (1978) 31–36. [11] Y.-M. Huang, L. Yuung-Hwa, C. Jia-Wine, An elasto-plastic finite element and experimental study of the ironing process, J. Mater. Process. Technol. 26 (1991) 53–80. [12] M. Jin, P. Kaewtatip, M. Murakawa, Utility of ultrasonic vibration applied to metal-forming processes, Advanced Technology of Plasticity, vol. III, Nu¨ remberg, 1999. [13] L. Bru¨ ckner, K. Po¨ hlandt, K. Lange, Gebrauchseigenschaften von durch Tiefziehen und nach-folgendes Abstreckgleitziehen gefertigten Na¨ pfen, Blech Rohre Profile 41 (1994) 9. [14] I.M. Zˇ vik, A.S. Sˇ arov, Erho¨ hung der Genaugkeit und des Umformgrades beim Abstreckziehen, Umformtechnik 10 (2) (1976). [15] Z. Kampusˇ, Ironing with superimposed force, Wire J. Int. 33 (12) (2000). [16] E. Siebel, Grundlagen und Begriffe der bildsamen Formgebung, Werkstattstech. U. Masch. 40 (1950) 11. [17] V. Vujevic, A.H. Shabaik, A new workability criterion for ductile metals, J. Eng. Mater. Technol., Trans. ASME 108 (1986) 245–249. [18] G. Ziaja, The formability of hypereutectic PM Al alloys, in: Proceedings of the 29th ICFG Plenary Meeting, Gyo¨ r, 1996.