- Email: [email protected]
Numerical analysis of void closure in metal forming
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Procedia Manufacturing 00 (2018) 000–000 Available online atatwww.sciencedirect.com Available www.sciencedirect.com Procedia online Manufacturing 00 (2018) 000–000
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www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
Procedia Manufacturing 15 (2018) 1841–1846 Procedia Manufacturing 00 (2017) 000–000 www.elsevier.com/locate/procedia
17th International Conference on Metal Forming, Metal Forming 2018, 16-19 September 2018, 17th International Conference on MetalToyohashi, Forming, Metal Japan Forming 2018, 16-19 September 2018, Toyohashi, Japan
Numerical analysis of void closure in metal forming
Numerical analysis of void closure in2017, metal forming Manufacturing Engineering Society International Conference MESIC 2017, 28-30 June 2017, Vigo (Pontevedra), Spain Jong-Jin Park* Jong-Jin Park*
Costing models for capacity optimization in Industry 4.0: Trade-off between used capacity and operational efficiency Abstract Hongik University, 94 Wawusanro, Mapo-Gu, Seoul 04066, South Korea Hongik University, 94 Wawusanro, Mapo-Gu, Seoul 04066, South Korea
Abstract
A. Santanaa, P. Afonsoa,*, A. Zaninb, R. Wernkeb
Since voids in a billet or an ingot are detrimental to tensile strength of the material, they are required to be closed by metal a Since voids in a billet or an ingot are detrimental toMinho, tensile strength of theand material, are required to be closed metal University 4800-058 Portugal forming processes. However, distributions of field ofvariables, such asGuimarães, stress strain, they imposed by the processes are inbygeneral b Unochapecó, 89809-000 Chapecó, SC, Brazil forming processes. However, distributions of field variables, such as stress and strain, imposed by the processes are in general inhomogeneous and thus prediction of void closure is difficult. In previous studies, where stress triaxiality was low in magnitude, inhomogeneous thustoprediction of void closure is difficult. previous studies, triaxiality waswas low obtained in magnitude, void closure wasand found be predicted by the effective strain atInthe location of thewhere void. stress The effective strain from void closure was found be predicted by the strain at the location the void. Theinvestigated effective strain was obtained from numerical analysis of atonon-void model. In effective the present study, this findingof was further for compressions of a numerical of aa cylinder, non-void where model.stress In the present was study, this finding wasmagnitude. further investigated compressions of ofa rectangularanalysis block and triaxiality relatively high in As a result,for a closure criterion Abstract rectangular block and a cylinder, where stress triaxiality was relatively high in magnitude. As a result, a closure criterion of spherical void was found as a function of the effective strain and stress triaxiality. The mode of void closure changed from sphericaltovoid was found as a triaxiality function of the effective strain and stress triaxiality. The mode of void closure changed from collapse contraction as stress increased in magnitude. Under concept of "Industry 4.0",increased production processes will be pushed to be increasingly interconnected, collapsethe to contraction as stress triaxiality in magnitude. information based on a real time basis and, necessarily, much more efficient. In this context, capacity optimization © 2018 The Authors. Published by Elsevier B.V. © 2018 2018 The Authors. Published by Elsevier B.V. © The Authors. Published by Elsevier B.V. goes beyond the traditional aim of capacity maximization, contributing also for organization’s profitability Peer-review responsibility of of the the scientific scientificcommittee committeeof ofthe the 17thInternational International Conference onMetal Metal Forming. and value. Peer-review under under responsibility 17th Conference on Forming. Peer-review under responsibilityand of the scientific committee of the 17th International Conference on Metal Forming. instead of Indeed, lean management continuous improvement approaches suggest capacity optimization
Keywords: Void; Metal analysis; Collapse; Contraction maximization. The forming; study ofNumerical capacity optimization and costing models is an important research topic that deserves Keywords: Void;from Metal both forming; Collapse; Contraction contributions theNumerical practicalanalysis; and theoretical perspectives. This paper presents and discusses a mathematical model for capacity management based on different costing models (ABC and TDABC). A generic model has been 1. Introduction developed and it was used to analyze idle capacity and to design strategies towards the maximization of organization’s 1. Introduction value. The trade-off capacity maximization vs operational efficiency is highlighted and it is shown that capacity Voids or pores a billet or an ingot evolve during casting due to decreased gas solubility and volume contraction. optimization mightinhide operational inefficiency. Voids or pores in a billet or an ingot evolve casting duematerial, to decreased and volume Since they are detrimental to tensile or fatigueduring strength of the they gas are solubility usually required to becontraction. closed by © 2017 The Authors. Published by Elsevier B.V. Since they are detrimental to tensile or fatigue strength of the material, they are usually required to be closed by subsequent forging or rolling processes. However, the progress in void closure differs for locations since Peer-review under responsibility of the scientific committee of the Manufacturing Engineering Society International Conference subsequent forging or rolling such processes. progress in process void closure differs inhomogeneous for locations since distributions of field variables, as stressHowever, and strain,the imposed by the are in general and 2017. distributions of of field as stress and strain, imposed by the process are in general inhomogeneous and thus prediction voidvariables, closure atsuch a certain location in a billet is difficult. thus prediction of void closure at Capacity a certain location inIdle a billet is difficult. Keywords: Cost Models; ABC; TDABC; Management; Capacity; Operational Efficiency
1. Introduction
* Corresponding author. Tel.:+82-2-320-1637; fax:+82-2-322-7003. * E-mail Corresponding Tel.:+82-2-320-1637; fax:+82-2-322-7003. address:author. [email protected] The cost of idle capacity is a fundamental information for companies and their management of extreme importance E-mail address: [email protected]
in modern©production systems. In general, it isB.V. defined as unused capacity or production potential and can be measured 2351-9789 2018 The Authors. Published by Elsevier 2351-9789 2018 Authors. Published Elsevier B.V.hours of the Peer-review underThe responsibility of theby scientific committee 17th International on Metal Forming. in several©ways: tons of production, available manufacturing, etc.Conference The management of the idle capacity Peer-review under responsibility thefax: scientific committee * Paulo Afonso. Tel.: +351 253 510of 761; +351 253 604 741 of the 17th International Conference on Metal Forming. E-mail address: [email protected]
2351-9789 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the Manufacturing Engineering Society International Conference 2017. 2351-9789 © 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the 17th International Conference on Metal Forming. 10.1016/j.promfg.2018.07.206
Jong-Jin Park / Procedia Manufacturing 15 (2018) 1841–1846 Author name / Procedia Manufacturing 00 (2018) 000–000
1842 2
Many studies have been performed to understand void closure during forging and rolling processes. They have focused on identifying important parameters for void closure as well as analyzing directly the progress in void closure. As a result, void closure was found to progress through a combination of contraction and collapse. In this context, contraction means a decrease of a void in size developed by stress triaxiality while collapse means a change of a void in shape developed by deviatoric stress around a void. Some of the studies have considered both collapse and contraction in void closure. Large reductions in height with wide dies and rolls were suggested [1-4]. In addition, a sufficient time under high magnitude of stress triaxiality was recommended for welding of closed voids [5]. A combination of asymmetric anvils in the initial stage and flat anvils in the final stage was suggested in forging of an ingot [6]. Void closure at the middle layer of a heavy slab was found to be difficult in rolling where the effective strain and stress triaxiality were smallest in magnitude [7]. The rate of void closure was related to the effective strain and the time integration of stress triaxiality [8]. Void closure was predicted by a parameter in forging of an ingot [9]. On the other hand, some of them have emphasized collapse in void closure. Aspect ratios in a range of 1~1.5 on the cross section of a bloom and process conditions to develop large spread were recommended in rolling [10-12]. The rate of void closure was related to the effective strain in forging of an ingot [13]. Differential-speed rolling was suggested for void closure in the middle layer of a thin strip [14]. Others have emphasized contraction in void closure. V-shaped dies were recommended for void closure at the center of an ingot [15]. Void closure at the center of an ingot was predicted by stress triaxiality or volumetric strain [16, 17]. For reference, void closure was found to be extremely difficult by stress triaxiality only in compaction of porous metals [18-21]. Besides the studies above, a series of studies have been performed to predict void closure by the effective strain [22-24]. In the present investigation, closure of a spherical void, which was assumed empty, was further examined numerically for plane-strain as well as simple compressions of a rectangular block and simple compression of a cylinder. A commercial FEM code DEFORM based on the rigid-plastic finite-element method was utilized for the purpose. 2. Finite element analyses In one of previous studies, closure of a circular void during compression was analyzed in two dimensions, as shown in Fig. 1 [14, 23]. As the effective strain and stress triaxiality increased in magnitude at both ends of the major axis, the void changed in shape to be elliptical and closed gradually from the ends toward the center. As shown in this example, void closure is in general progressed through a combination of contraction and collapse since both stress triaxiality and deviatoric stress develop in metal forming processes. If the void is negligibly small in size compared to the workpiece, its existence would not affect the global stress and strain distributions. Assuming this circumstance in the present investigation, it was attempted to predict void closure at a certain location by corresponding stress and strain obtained from numerical analysis of non-void model. Here, the material was assumed to be AISI-1015 and deformed at 1100 oC isothermally. The flow stress at this temperature was expressed as 𝜎𝜎𝜎𝜎� = 132𝜀𝜀𝜀𝜀̅0.144 𝜀𝜀𝜀𝜀̅̇0.165 (MPa).
Fig. 1. Distributions of effective strain and stress triaxiality around void during compression [14].
Jong-Jin Park / Procedia Manufacturing 15 (2018) 1841–1846 Author name / Procedia Manufacturing 00 (2018) 000–000
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2.1. Plane-strain compression of rectangular block A rectangular block in Fig. 2, which is 50 x 25 x 20 mm, was compressed in z direction between two flat dies under plane-strain condition, in which expansion in y direction is restricted. A spherical void of 0.5 mm in diameter was located at the center of the block. This diameter of a void was chosen for convenience of analysis although it usually ranges from tens of micrometers to several millimeters. The top die moved downward at a speed of 20 mm/s while the bottom die was stationary. The shear friction factor m was assumed at the interface.
Fig. 2. Rectangular block containing void.
The progress in void closure was predicted, as shown in Fig. 3. The void closed at a die stroke of 6.3 mm when m was 0.4, while it closed at a die stroke of 5.2 mm when m was 0.7. When a high friction factor was applied, a high magnitude of stress triaxiality developed and thus void closure was achieved with a shorter stroke. Comparing Figs. 3(a) with 3(b) as well as Figs. 3(c) with 3(d), the mode of collapse was apparent on the x-z cross section while the mode of contraction was apparent on the y-z cross section. In other words, the major axis of the void in Figs. 3(a) or 3(c) increased in length and then decreased while that in Figs. 3(b) or 3(d) decreased consistently until the void closed. Compression of the block containing no void was also analyzed under the same condition to obtain the effective strain and stress triaxiality at the location of the void at void closure. They were 0.57 and -2.45, respectively, when m was 0.4, while they were 0.54 and -2.9, respectively, when m was 0.7.
Fig. 3. Progresses in void closure on cross sections: (a) x-z (m=0.4), (b) y-z (m=0.4), (c) x-z (m=0.7) and (d) y-z (m=0.7).
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Jong-Jin Park / Procedia Manufacturing 15 (2018) 1841–1846 Author name / Procedia Manufacturing 00 (2018) 000–000
2.2. Simple compression of rectangular block The rectangular block in Fig. 2 was simply compressed in z direction between two flat dies where expansions in x and y directions were not restricted at all. The top die moved downward at a speed of 20 mm/s while the bottom die was stationary. Since the block was longer in x direction than y direction, the normal strain in x direction was smaller than that in y direction during compression. The void closed at a die stroke of 6.8 mm when m was 0.4, while it closed at a die stroke of 5.9 mm when m was 0.7. Comparing Figs. 4(a) with 4(b) as well as Figs. 4(c) with 4(d), collapse was more apparent on the y-z cross section than the x-z cross section. In other words, the major axis of the void in Figs. 4(a) or 4(c) decreased consistently while that in Figs. 4(b) or 4(d) increased and then decreased. Under the same condition, compression of the block containing no void was also analyzed. When m was 0.4, the effective strain and stress triaxiality were 0.58 and -1.3, respectively, at void closure at the location of the void. However, when m was 0.7, they were 0.59 and -1.7, respectively.
Fig. 4. Progresses in void closure on cross sections: (a) x-z (m=0.4), (b) y-z (m=0.4), (c) x-z (m=0.7) and (d) y-z (m=0.7).
2.3. Simple compression of a cylinder A cylindrical workpiece in Fig. 5, which was 50 mm in diameter and 20 mm in height, was compressed in axial direction between two flat dies. A spherical void of 0.5 mm in diameter was located at the center of the cylinder. The top die moved downward at a speed of 40 mm/s while the bottom die was stationary. The void closed at a die stroke of 7.0 mm when m was 0.4, while it closed at a die stroke of 6.0 mm when m was 0.7. The progresses in void closure are shown in Figs. 6(a) and 6(b), which are almost identical to each other but the cross sections in the latter are smaller. Compression of the cylinder containing no void was also analyzed under the same condition. The
Fig. 5. Cylindrical workpiece containing void.
Jong-Jin Park / Procedia Manufacturing 15 (2018) 1841–1846 Author name / Procedia Manufacturing 00 (2018) 000–000
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Fig. 6. Progress in void closure on cross section: (a) m=0.4 and (b) m=0.7.
effective strain and stress triaxiality were 0.57 and -2.0, respectively, when m was 0.4, while they were 0.54 and -2.7, respectively, when m was 0.7. This procedure of the investigation was repeated for two other cylinders with different heights. When the height was 50 mm, the effective strain and stress triaxiality were 0.59 and -0.8, respectively, for m = 0.4, while they were 0.59 and -0.9, respectively, for m = 0.7. When the height was 100 mm, they were 0.62 and -0.5 MPa, respectively, for m = 0.4, while they were 0.63 and -0.5 MPa, respectively, for m = 0.7. 3. Closure criterion of a spherical void Values of the effective strain and stress triaxiality at void closure obtained from the present and the previous studies were collected to build a closure criterion of a spherical void in Fig. 7 [24]. The stress triaxiality in the figure is the maximum in magnitude during a course of plastic deformation that occurs in general at void closure. As stress triaxiality approached -0.5, the effective strain increased to about 0.72 in plane-strain compression but 0.62 in simple compression. As stress triaxiality decreased to -3, the effective strain decreased to 0.56 in both compressions. When only stress triaxiality was available for void closure, it should be less than -5. This fact was found in the studies on compaction of porous metals [18-21]. 4. Conclusions Closure of a spherical void was numerically investigated in compressions of a rectangular block and a cylinder under different conditions. Combining the results of the present and the previous studies, a closure criterion of a spherical void was found as a function of the effective strain and stress triaxiality.
Fig. 7. Proposed criterion for closure of spherical void.
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Jong-Jin Park / Procedia Manufacturing 15 (2018) 1841–1846 Author name / Procedia Manufacturing 00 (2018) 000–000
As stress triaxiality was about -0.5, the effective strain for void closure increased to 0.72 in plane-strain compression but 0.62 in simple compression. However, as stress triaxiality decreased to -3, it decreased to 0.56 in both compressions. As the friction factor increased, stress triaxiality increased in magnitude and thus the die stroke required for void closure decreased. Acknowledgements This work was supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (NRF-2015R1D1A1A09058893). This work was also supported by 2017 Hongik University Research Fund. The author appreciates D. Suh, J. Suh and W. Jung for their assistance in preparing the manuscript. References [1] U. Ståhlberg, H. Keife, M. Lundberg, A. Melander, A study of void closure during plastic deformation, Journal of Mechanical Working Technology, 4 (1980) 51–63. [2] Y. Fukui, J. Yonezawa, A. Mizuta, O. Tsuda, Analysis of forging effect and closing of internal cavities in free forging by rigid-plastic finite element method – study on free forging process for large products I, Journal of Japanese Society for Technology of Plasticity, 21 (1980) 975–982. [3] A. Wallero, Closing of a central longitudinal pore in hot rolling, Journal of Mechanical Working Technology, 12 (1985) 233–242. [4] S. Hamzah, U. Ståhlberg, A new pore closure concept for the manufacturing of heavy rings, Journal of Materials Processing Technology, 110 (2001) 324–333. [5] A. Wang, P.F. Thomson, P.D. Hodgson, A study of pore closure and welding in hot rolling process, Journal of Materials Processing Technology, 60 (1990) 95–102. [6] G. Banaszek, A. Stefanik, Theoretical and laboratory modeling of the closure of metallurgical defects during forming of a forging, Journal of Materials Processing Technology, 177 (2006) 238–242. [7] Y.H. Ji, J.J. Park, Development of severe plastic deformation by various asymmetric rolling processes, Materials Science and Engineering: A, 499 (2009) 14–17. [8] M. Tanaka, S. Ono, M. Tsuneno, A numerical analysis on void crushing during side compression of round bar by flat dies, Journal of Japanese Society for Technology of Plasticity, 28 (1987) 238–244. [9] H. Kakimoto, T. Arikawa, Y. Takahashi, T. Tanaka, Y. Imaida, Development of forging process design to close internal voids, Journal of Materials Processing Technology, 210 (2010) 415–422. [10] O. Tsuda, Y. Yamaguchi, H. Ohsuna, K. Tsuji, M. Tomonaga, S. Saito, Effects of rolling conditions on the closure of voids in blooms, Journal of Japanese Society for Technology of Plasticity, 24 (1983) 1056–1062. [11] U. Ståhlberg, Influence of spread and stress on the closure of a central longitudinal hole in the hot rolling of steel, Journal of Mechanical Working Technology, 13 (1986) 65–81. [12] Y. Kim, J. Cho, W. Bae, Efficient forging process to improve the closing effect of the inner void on an ultra-large ingot, Journal of Materials Processing Technology, 211 (2011) 1005–1013. [13] K.J. Lee, W.B. Bae, J.R. Cho, D.K. Kim, Y.D. Kim, FEM analysis for the prediction of void closure on the free forging process of a large rotor, Transactions of Materials Processing, 16 (2007) 126–131. [14] J.J. Park, Effect of shear deformation on closure of a central void in thin-strip rolling, Metallurgical and Materials Transactions: A, 47 (2016) 479–487. [15] S.P. Dudra, Y.T. Im, Analysis of void closure in open-die forging, International Journal of Machine Tools and Manufacture, 30 (1990) 65– 75. [16] M. Nakasaki, I. Takasu, H. Utsunomiya, Application of hydrostatic integration parameter for free-forging and rolling, Journal of Materials Processing Technology, 177 (2006) 521–524. [17] X.X. Zhang, Z.S. Cui, W. Chen, Y. Li, A criterion for void closure in large ingots during hot forging, Journal of Materials Processing Technology, 209 (2009) 1950–1959. [18] R.J. Green, A plasticity theory for porous solids, International Journal of Mechanical Science, 14 (1972) 215–224. [19] S. Shima, M. Oyane, Plasticity theory for porous metals, International Journal of Mechanical Science, 18 (1976) 285–291. [20] A.L. Gurson, Continuum theory of ductile rupture by void nucleation and growth: part 1 – Yield criteria and flow rules for porous ductile media, ASME, Journal of Engineering Materials Technology, 99 (1977) 2–15. [21] J.J. Park, Constitutive relations to predict plastic deformations of porous metals in compaction, International Journal of Mechanical Science, 37 (1995) 709–719. [22] J.J. Park, Prediction of void closure in a slab during various deformation processes, Journal of Mechanical Science and Technology, 25 (2011) 2871–2876. [23] J.J. Park, Finite-element analysis of cylindrical-void closure by flat-die forging, ISIJ International, 53 (2013) 1420–1426. [24] J.J. Park, Prediction of void closure in steel slabs by finite element analysis, Metals and Materials International, 19 (2013) 259–265.
ScienceDirect ScienceDirect
Procedia Manufacturing 00 (2018) 000–000 Available online atatwww.sciencedirect.com Available www.sciencedirect.com Procedia online Manufacturing 00 (2018) 000–000
ScienceDirect ScienceDirect
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
Procedia Manufacturing 15 (2018) 1841–1846 Procedia Manufacturing 00 (2017) 000–000 www.elsevier.com/locate/procedia
17th International Conference on Metal Forming, Metal Forming 2018, 16-19 September 2018, 17th International Conference on MetalToyohashi, Forming, Metal Japan Forming 2018, 16-19 September 2018, Toyohashi, Japan
Numerical analysis of void closure in metal forming
Numerical analysis of void closure in2017, metal forming Manufacturing Engineering Society International Conference MESIC 2017, 28-30 June 2017, Vigo (Pontevedra), Spain Jong-Jin Park* Jong-Jin Park*
Costing models for capacity optimization in Industry 4.0: Trade-off between used capacity and operational efficiency Abstract Hongik University, 94 Wawusanro, Mapo-Gu, Seoul 04066, South Korea Hongik University, 94 Wawusanro, Mapo-Gu, Seoul 04066, South Korea
Abstract
A. Santanaa, P. Afonsoa,*, A. Zaninb, R. Wernkeb
Since voids in a billet or an ingot are detrimental to tensile strength of the material, they are required to be closed by metal a Since voids in a billet or an ingot are detrimental toMinho, tensile strength of theand material, are required to be closed metal University 4800-058 Portugal forming processes. However, distributions of field ofvariables, such asGuimarães, stress strain, they imposed by the processes are inbygeneral b Unochapecó, 89809-000 Chapecó, SC, Brazil forming processes. However, distributions of field variables, such as stress and strain, imposed by the processes are in general inhomogeneous and thus prediction of void closure is difficult. In previous studies, where stress triaxiality was low in magnitude, inhomogeneous thustoprediction of void closure is difficult. previous studies, triaxiality waswas low obtained in magnitude, void closure wasand found be predicted by the effective strain atInthe location of thewhere void. stress The effective strain from void closure was found be predicted by the strain at the location the void. Theinvestigated effective strain was obtained from numerical analysis of atonon-void model. In effective the present study, this findingof was further for compressions of a numerical of aa cylinder, non-void where model.stress In the present was study, this finding wasmagnitude. further investigated compressions of ofa rectangularanalysis block and triaxiality relatively high in As a result,for a closure criterion Abstract rectangular block and a cylinder, where stress triaxiality was relatively high in magnitude. As a result, a closure criterion of spherical void was found as a function of the effective strain and stress triaxiality. The mode of void closure changed from sphericaltovoid was found as a triaxiality function of the effective strain and stress triaxiality. The mode of void closure changed from collapse contraction as stress increased in magnitude. Under concept of "Industry 4.0",increased production processes will be pushed to be increasingly interconnected, collapsethe to contraction as stress triaxiality in magnitude. information based on a real time basis and, necessarily, much more efficient. In this context, capacity optimization © 2018 The Authors. Published by Elsevier B.V. © 2018 2018 The Authors. Published by Elsevier B.V. © The Authors. Published by Elsevier B.V. goes beyond the traditional aim of capacity maximization, contributing also for organization’s profitability Peer-review responsibility of of the the scientific scientificcommittee committeeof ofthe the 17thInternational International Conference onMetal Metal Forming. and value. Peer-review under under responsibility 17th Conference on Forming. Peer-review under responsibilityand of the scientific committee of the 17th International Conference on Metal Forming. instead of Indeed, lean management continuous improvement approaches suggest capacity optimization
Keywords: Void; Metal analysis; Collapse; Contraction maximization. The forming; study ofNumerical capacity optimization and costing models is an important research topic that deserves Keywords: Void;from Metal both forming; Collapse; Contraction contributions theNumerical practicalanalysis; and theoretical perspectives. This paper presents and discusses a mathematical model for capacity management based on different costing models (ABC and TDABC). A generic model has been 1. Introduction developed and it was used to analyze idle capacity and to design strategies towards the maximization of organization’s 1. Introduction value. The trade-off capacity maximization vs operational efficiency is highlighted and it is shown that capacity Voids or pores a billet or an ingot evolve during casting due to decreased gas solubility and volume contraction. optimization mightinhide operational inefficiency. Voids or pores in a billet or an ingot evolve casting duematerial, to decreased and volume Since they are detrimental to tensile or fatigueduring strength of the they gas are solubility usually required to becontraction. closed by © 2017 The Authors. Published by Elsevier B.V. Since they are detrimental to tensile or fatigue strength of the material, they are usually required to be closed by subsequent forging or rolling processes. However, the progress in void closure differs for locations since Peer-review under responsibility of the scientific committee of the Manufacturing Engineering Society International Conference subsequent forging or rolling such processes. progress in process void closure differs inhomogeneous for locations since distributions of field variables, as stressHowever, and strain,the imposed by the are in general and 2017. distributions of of field as stress and strain, imposed by the process are in general inhomogeneous and thus prediction voidvariables, closure atsuch a certain location in a billet is difficult. thus prediction of void closure at Capacity a certain location inIdle a billet is difficult. Keywords: Cost Models; ABC; TDABC; Management; Capacity; Operational Efficiency
1. Introduction
* Corresponding author. Tel.:+82-2-320-1637; fax:+82-2-322-7003. * E-mail Corresponding Tel.:+82-2-320-1637; fax:+82-2-322-7003. address:author. [email protected] The cost of idle capacity is a fundamental information for companies and their management of extreme importance E-mail address: [email protected]
in modern©production systems. In general, it isB.V. defined as unused capacity or production potential and can be measured 2351-9789 2018 The Authors. Published by Elsevier 2351-9789 2018 Authors. Published Elsevier B.V.hours of the Peer-review underThe responsibility of theby scientific committee 17th International on Metal Forming. in several©ways: tons of production, available manufacturing, etc.Conference The management of the idle capacity Peer-review under responsibility thefax: scientific committee * Paulo Afonso. Tel.: +351 253 510of 761; +351 253 604 741 of the 17th International Conference on Metal Forming. E-mail address: [email protected]
2351-9789 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the Manufacturing Engineering Society International Conference 2017. 2351-9789 © 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the 17th International Conference on Metal Forming. 10.1016/j.promfg.2018.07.206
Jong-Jin Park / Procedia Manufacturing 15 (2018) 1841–1846 Author name / Procedia Manufacturing 00 (2018) 000–000
1842 2
Many studies have been performed to understand void closure during forging and rolling processes. They have focused on identifying important parameters for void closure as well as analyzing directly the progress in void closure. As a result, void closure was found to progress through a combination of contraction and collapse. In this context, contraction means a decrease of a void in size developed by stress triaxiality while collapse means a change of a void in shape developed by deviatoric stress around a void. Some of the studies have considered both collapse and contraction in void closure. Large reductions in height with wide dies and rolls were suggested [1-4]. In addition, a sufficient time under high magnitude of stress triaxiality was recommended for welding of closed voids [5]. A combination of asymmetric anvils in the initial stage and flat anvils in the final stage was suggested in forging of an ingot [6]. Void closure at the middle layer of a heavy slab was found to be difficult in rolling where the effective strain and stress triaxiality were smallest in magnitude [7]. The rate of void closure was related to the effective strain and the time integration of stress triaxiality [8]. Void closure was predicted by a parameter in forging of an ingot [9]. On the other hand, some of them have emphasized collapse in void closure. Aspect ratios in a range of 1~1.5 on the cross section of a bloom and process conditions to develop large spread were recommended in rolling [10-12]. The rate of void closure was related to the effective strain in forging of an ingot [13]. Differential-speed rolling was suggested for void closure in the middle layer of a thin strip [14]. Others have emphasized contraction in void closure. V-shaped dies were recommended for void closure at the center of an ingot [15]. Void closure at the center of an ingot was predicted by stress triaxiality or volumetric strain [16, 17]. For reference, void closure was found to be extremely difficult by stress triaxiality only in compaction of porous metals [18-21]. Besides the studies above, a series of studies have been performed to predict void closure by the effective strain [22-24]. In the present investigation, closure of a spherical void, which was assumed empty, was further examined numerically for plane-strain as well as simple compressions of a rectangular block and simple compression of a cylinder. A commercial FEM code DEFORM based on the rigid-plastic finite-element method was utilized for the purpose. 2. Finite element analyses In one of previous studies, closure of a circular void during compression was analyzed in two dimensions, as shown in Fig. 1 [14, 23]. As the effective strain and stress triaxiality increased in magnitude at both ends of the major axis, the void changed in shape to be elliptical and closed gradually from the ends toward the center. As shown in this example, void closure is in general progressed through a combination of contraction and collapse since both stress triaxiality and deviatoric stress develop in metal forming processes. If the void is negligibly small in size compared to the workpiece, its existence would not affect the global stress and strain distributions. Assuming this circumstance in the present investigation, it was attempted to predict void closure at a certain location by corresponding stress and strain obtained from numerical analysis of non-void model. Here, the material was assumed to be AISI-1015 and deformed at 1100 oC isothermally. The flow stress at this temperature was expressed as 𝜎𝜎𝜎𝜎� = 132𝜀𝜀𝜀𝜀̅0.144 𝜀𝜀𝜀𝜀̅̇0.165 (MPa).
Fig. 1. Distributions of effective strain and stress triaxiality around void during compression [14].
Jong-Jin Park / Procedia Manufacturing 15 (2018) 1841–1846 Author name / Procedia Manufacturing 00 (2018) 000–000
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2.1. Plane-strain compression of rectangular block A rectangular block in Fig. 2, which is 50 x 25 x 20 mm, was compressed in z direction between two flat dies under plane-strain condition, in which expansion in y direction is restricted. A spherical void of 0.5 mm in diameter was located at the center of the block. This diameter of a void was chosen for convenience of analysis although it usually ranges from tens of micrometers to several millimeters. The top die moved downward at a speed of 20 mm/s while the bottom die was stationary. The shear friction factor m was assumed at the interface.
Fig. 2. Rectangular block containing void.
The progress in void closure was predicted, as shown in Fig. 3. The void closed at a die stroke of 6.3 mm when m was 0.4, while it closed at a die stroke of 5.2 mm when m was 0.7. When a high friction factor was applied, a high magnitude of stress triaxiality developed and thus void closure was achieved with a shorter stroke. Comparing Figs. 3(a) with 3(b) as well as Figs. 3(c) with 3(d), the mode of collapse was apparent on the x-z cross section while the mode of contraction was apparent on the y-z cross section. In other words, the major axis of the void in Figs. 3(a) or 3(c) increased in length and then decreased while that in Figs. 3(b) or 3(d) decreased consistently until the void closed. Compression of the block containing no void was also analyzed under the same condition to obtain the effective strain and stress triaxiality at the location of the void at void closure. They were 0.57 and -2.45, respectively, when m was 0.4, while they were 0.54 and -2.9, respectively, when m was 0.7.
Fig. 3. Progresses in void closure on cross sections: (a) x-z (m=0.4), (b) y-z (m=0.4), (c) x-z (m=0.7) and (d) y-z (m=0.7).
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Jong-Jin Park / Procedia Manufacturing 15 (2018) 1841–1846 Author name / Procedia Manufacturing 00 (2018) 000–000
2.2. Simple compression of rectangular block The rectangular block in Fig. 2 was simply compressed in z direction between two flat dies where expansions in x and y directions were not restricted at all. The top die moved downward at a speed of 20 mm/s while the bottom die was stationary. Since the block was longer in x direction than y direction, the normal strain in x direction was smaller than that in y direction during compression. The void closed at a die stroke of 6.8 mm when m was 0.4, while it closed at a die stroke of 5.9 mm when m was 0.7. Comparing Figs. 4(a) with 4(b) as well as Figs. 4(c) with 4(d), collapse was more apparent on the y-z cross section than the x-z cross section. In other words, the major axis of the void in Figs. 4(a) or 4(c) decreased consistently while that in Figs. 4(b) or 4(d) increased and then decreased. Under the same condition, compression of the block containing no void was also analyzed. When m was 0.4, the effective strain and stress triaxiality were 0.58 and -1.3, respectively, at void closure at the location of the void. However, when m was 0.7, they were 0.59 and -1.7, respectively.
Fig. 4. Progresses in void closure on cross sections: (a) x-z (m=0.4), (b) y-z (m=0.4), (c) x-z (m=0.7) and (d) y-z (m=0.7).
2.3. Simple compression of a cylinder A cylindrical workpiece in Fig. 5, which was 50 mm in diameter and 20 mm in height, was compressed in axial direction between two flat dies. A spherical void of 0.5 mm in diameter was located at the center of the cylinder. The top die moved downward at a speed of 40 mm/s while the bottom die was stationary. The void closed at a die stroke of 7.0 mm when m was 0.4, while it closed at a die stroke of 6.0 mm when m was 0.7. The progresses in void closure are shown in Figs. 6(a) and 6(b), which are almost identical to each other but the cross sections in the latter are smaller. Compression of the cylinder containing no void was also analyzed under the same condition. The
Fig. 5. Cylindrical workpiece containing void.
Jong-Jin Park / Procedia Manufacturing 15 (2018) 1841–1846 Author name / Procedia Manufacturing 00 (2018) 000–000
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Fig. 6. Progress in void closure on cross section: (a) m=0.4 and (b) m=0.7.
effective strain and stress triaxiality were 0.57 and -2.0, respectively, when m was 0.4, while they were 0.54 and -2.7, respectively, when m was 0.7. This procedure of the investigation was repeated for two other cylinders with different heights. When the height was 50 mm, the effective strain and stress triaxiality were 0.59 and -0.8, respectively, for m = 0.4, while they were 0.59 and -0.9, respectively, for m = 0.7. When the height was 100 mm, they were 0.62 and -0.5 MPa, respectively, for m = 0.4, while they were 0.63 and -0.5 MPa, respectively, for m = 0.7. 3. Closure criterion of a spherical void Values of the effective strain and stress triaxiality at void closure obtained from the present and the previous studies were collected to build a closure criterion of a spherical void in Fig. 7 [24]. The stress triaxiality in the figure is the maximum in magnitude during a course of plastic deformation that occurs in general at void closure. As stress triaxiality approached -0.5, the effective strain increased to about 0.72 in plane-strain compression but 0.62 in simple compression. As stress triaxiality decreased to -3, the effective strain decreased to 0.56 in both compressions. When only stress triaxiality was available for void closure, it should be less than -5. This fact was found in the studies on compaction of porous metals [18-21]. 4. Conclusions Closure of a spherical void was numerically investigated in compressions of a rectangular block and a cylinder under different conditions. Combining the results of the present and the previous studies, a closure criterion of a spherical void was found as a function of the effective strain and stress triaxiality.
Fig. 7. Proposed criterion for closure of spherical void.
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