2017
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Hot Deformation Behavior of 177 PH Stainless Steel
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To investigate the hot deformation behavior of 177 PH stainless steel, hot compression tests were carried out at the temperatures of 950, 1050 and 1150 oC and strain rates of 0.001 s1 to 0.1 s1. Accordingly, the hot working behavior was studied by the analyses of flow stress curves, work hardening rate versus stress curves, exponent type constitutive equations and deformed microstructures. Meanwhile, the average normalized critical stress for initiation of dynamic recrystallization (DRX) was determined using a 3rd order polynomial curve fitting. The results show that the flow stress depends strongly on the deformation temperature and the strain rate, and it increases with the deformation temperature decreasing and the strain rate increasing. Furthermore, it was found out that the co existence of δ ferrite lowers the softening rate at high Z (Zener Holloman parameter) conditions. The experimental results were then used to determine the constants of constitutive equations. There is a good agreement between the measured and predicted results indicating a high accuracy of exponent type constitutive equations.
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11


M.
Zeinali
Maleke Ashtar University of Technology
Maleke Ashtar University of Technology
Iran
zeinali.mohammad.mse@gmail.com


E.
Shafiei
Amirkabir University of Technology
Amirkabir University of Technology
Iran
shafiei.ehsan.mse@gmail.com


K.
Farmanesh
Maleke Ashtar University of Technology
Maleke Ashtar University of Technology
Iran
e.shafiei@aut.ac.ir


R.
Hosseini
Shiraz University
Shiraz University
Iran
e.shafiei1@aut.ac.ir


R.
Sooltanipor
Maleke Ashtar University of Tech.
Maleke Ashtar University of Tech.
Iran
e.shafiei2@aut.ac.ir
: Hot deformation
Dynamic recrystallization
Constitutive analysis
177 PH stainless steel
[[1] H. Mirzadeh, M. H. Parsa and D. Ohadi, Hot deformation behavior of austenitic stainless steel for a wide range of initial grain size, Mater. Sci. Eng., A, 569 (2013) 5460. ##[2] L. L. Wang, R. B. Li, Y. G. Liao and M. Jin, Study on characterization of hot deformation of 403 steel, Mater. Sci. Eng., A, 567 (2013) 8488. ##[3] M. A. Mostafaei and M. Kazeminezhad, Hot deformation behavior of hot extruded Al–6Mg alloy, Mater. Sci. Eng., A, 535 (2012) 216221. ##[4] H. Mirzadeh, J. M. Cabrera and A. Najafizadeh, Constitutive relationships for hot deformation of austenite, Acta Mater., 59 (2011) 64416448. ##[5] E. Shafiei and K. Dehghani, Prediction of singlepeak flow stress curves at high temperatures using a new logarithmicpower function, J. Mater. Eng. Perform., 25(2016)40244035. ##[6] M. Marchattivar, A. Sarkar, J. K. Chakravarty and B. P. Kashyap, Dynamic recrystallization during hot deformation of 304 austenitic stainless steel, J. Mater. Eng. Per., 22 (2013) 21682175. ##[7] C. M. Cepeda Jimenez, O. A. Ruano, M. Carsi and F. Cerreno, Study of hot deformation of an Al–Cu–Mg alloy using processing maps and microstructural characterization, Mater. Sci. Eng., A, 552 (2012) 530539. ##[8] A. Najafizadeh and J. J. Jonas, Predicting the critical stress for initiation of dynamic recrystallization, ISIJ Int., 46 (2006) 16791684. ##[9] E. Shafiei and R. Ebrahimi, A modified model to estimate single peak flow stress curves of TiIF Steel, ISIJ Int., 52 (2012) 569573. ##[10] Y. Han, G. Liu, D. Zou, R. Liu and G. Qiao, Deformation behavior and microstructural evolution of ascast 904L austenitic stainless steel during hot compression, Mater. Sci. Eng., A, 565 (2013) 342350. ##[11] A. Dehghan Manshadi and P. D. Hadgson, Effect of δferrite coexistence on hot deformation. and recrystallization of austenite, J. Mater. Sci., 43 (2003) 62726277. ##[12] H. J. McQueen and N. D. Ryan, Constitutive analysis in hot working, Mater. Sci. Eng., A, 322 (2002) 4347. ##[13] E. Shafiei and R. Ebrahimi, A new constitutive equation to predict single peak flow stress curves, J. Eng. Mater. Tech., 135 (2013) 011006 4. ##[14] H. Mirzadeh and A. Najafizadeh, The rate of dynamic recrystallization in 174 PH stainless steel, Mater. Des.,31 (2010) 4577 4583. ##[15] E. I. Poliak and J. J. Jonas, Critical strain for dynamic recrystallization in variable strain rate, ISIJ Int., 43 (2003) 692 700. ##[16] H. Mirzadeh and A. Najafizadeh, Prediction of the critical conditions for initiation of dynamic recrystallization, Mater. Des.,31 (2010) 1174 1179. ##[17] A. Etaadi and K. Dehghani, Mater. Chem. Phy., A study on hot deformation behavior of Ni42.5 Ti7.5 Cu alloy, 140 (2013) 208 215. ##[18] H. Y. Wu, J. C. Yang, F. J. Zhu and C. T. Wu, Hot compressive flow stress modeling of homogenized AZ61 Mg alloy using straindependent constitutive equation, Mater. Sci. Eng., A,574 (2013)1724 1726.##]
A Robust RBFANN Model to Predict the Hot Deformation Flow Curves of API X65 Pipeline Steel
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Abstract In this research, a radial basis function artificial neural network (RBFANN) model was developed to predict the hot deformation flow curves of API X65 pipeline steel. The results of the developed model was compared with the results of a new phenomenological model that has recently been developed based on a power function of ZenerHollomon parameter and a third order polynomial function of strain power m (m is a constant). Root mean square error (RMSE) criterion was used assess the prediction performance of the investigated models. According to the results obtained, it was shown that the RBFANN model has a better performance than that of the investigated phenomenological model. Very low RMSE value of 0.41 MPa was obtained for RBFANN model that shows the robustness of it to predict the hot deformation flow curves of tested steel. The results can be further used in mathematical simulation of hot metal forming processes.
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M.
Rakhshkhorshid
Department of Mechanical Engineering, Birjand University of Technology, POBOX 97175569, Birjand, Iran
Department of Mechanical Engineering, Birjand
Iran
m_rakhshkhorshid@yahoo.com
Hot deformation
Neural Computing
Radial Basis Function
Constitutive equations
Flow stress
[[1] G.R. Johnson and W.H. Cook, "A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. In: Proceedings of the 7th international symposium on ballistics, (1983) 541–543. ##[2] E. Voce, The relationship between stress and strain for homogeneous deformation. J. Inst. Met., 74 (1948) 537–562. ##[3] A.S. Khan and S. Huang, Experimental and theoretical study of mechanical behavior of 1100 aluminum in the strain rate range 10−5− 104 s−1, Int. J. Plast., 8 (1992) 397–424. ##[4] H. Mirzadeh and A. Najafizadeh, Flow stress prediction at hot working conditions, Mater. Sci. Eng. A, 527(2010) 1160–1164. ##[5] Y.C. Lin and X.M. Chen, A critical review of experimental results and constitutive descriptions for metals and alloys in hot working, Mater. Des., 32 (2011) 1733–1759. ##[6] H. Shi, A.J. McLaren, C.M. Sellars, R. Shahani and R. Bolingbroke, Constitutive equations for high temperature flow stress of aluminium alloys, J. Mater. Sci. Technol., 13 (1997) 210216. ##[7] Y.C. Lin, M.S. Chen and J. Zhang, Constitutive modeling for elevated temperature flow behavior of 42CrMo steel, Comput Mater Sci, 424 (2008) 470–477. ##[8] M.Y. Zhan, Z. Chen, H. Zhang and W. Xia, Flow stress behavior of porous FVS0812 aluminum alloy during hotcompression, Mech. Res. Commun., 33 (2006) 508–514. ##[9] P.J. Zerilli and R.W. Armstrong, Dislocationmechanicsbased constitutive relations for material dynamics calculations, J. Appl. Phys., 61 (1987) 18161825. ##[10] G.Z. Voyiadjis and A.H. Almasri, A physically based constitutive model for FCC metals with applications to dynamic hardness, Mech. Mater., 40 (2008) 549563. ##[11] Y.C. Lin, M.S. Chen and J. Zhang, Prediction of 42CrMo steel flow stress at high temperature and strain rate, Mech. Res.Commun., 35 (2008) 142–50. ##[12] Y.C. Lin, X.M. Chen, D.X. Wen and M.S. Chen, A physicallybased constitutive model for a typical nickelbased superalloy, Comput. Mater. Sci., 83(2014) 282–289. ##[13] M. Rakhshkhorshid and S.A. TeimouriSendesi, Bayesian Regularization Neural Networks for Prediction of Austenite Formation Temperatures (Ac1 and Ac3), J. Iron Steel Res. Int., 21(2) (2014) 246 – 251. ##[14] V. Senthilkumar and A. Balaji, D. Arulkirubakaran, Application of constitutive and neural network models for prediction of high temperature flow behavior of Al/Mg based nanocomposite, Trans. Nonferrous Met. Soc. China, 23 (2013) 17371750. ##[15] Y. Zhu, W. Zeng, Y. Sun, F. Feng and Y. Zhou, Artificial neural network approach to predict the flow stress in the isothermal compression of ascast TC21 titanium alloy, Comp. Mater. Sci., 50 (2011) 1785– 1790. ##[16] H. Mirzadeh, J.M. Cabrera, J.M. Prado and A. Najafizadeh, Modeling and prediction of hot deformation flow curves, Metall. Mater. Trans. A, 43 (2012) 108–123. ##[17] N. Haghdadi, A. ZareiHanzaki, A.R. Khalesian and H.R. Abedi, Artificial neural network modeling to predict the hot deformation behavior of an A356 aluminum alloy, Mater. Des., 49 (2013) 386391. ##[18] Y.C. Lin, X. Fang and Y.P. Wang, Prediction of metadynamic softening in a multipass hot deformed low alloy steel using artificial neural network, Mater. Sci., 43 (2008) 55085515. ##[19] N.S. Reddy, Y.H. Lee, C.H. Park and C.S. Lee, Prediction of flow stress in Ti–6Al–4V alloy with an equiaxed [alpha]+[beta] microstructure by artificial neural networks, Mater. Sci. Eng.A, 492 (2008) 276 282. ##[20] H.Y. Li, D.D. Wei, Y.H. Li and X.F. Wang, Application of artificial neural network and constitutive equations to describe the hot compressive behavior of 28CrMnMoV steel, Mater. Des., 35 (2012) 557562. ##[21] S. Toros, F. Ozturk, Flow curve prediction of Al–Mg alloys under warm forming conditions at various strain rates by ANN, Appl. Soft. Comput., 110 (2011) 1891–1898. ##[22] S. Mandal, P.V. Sivaprasad, S. Venugopal and K.P.N. Murthy, Artificial neural network modeling to evaluate and predict the deformation behavior of stainless steel type AISI 304L during hot torsion, Appl. Soft. Comput., 9 (2009) 237–244. ##[23] M. Rakhshkhorshid, Modeling the hot deformation flow curves of API X65 pipeline steel, Int. J. Adv. Manuf. Tech., 77 (2015) 203210. ##[24] M. Rakhshkhorshid and A.R. Maldar, A comparative study on constitutive modeling of hot deformation flow curves in AZ91 magnesium alloy, Iranian journal of materials Forming, 3(1) (2016) 2737. ##[25] M. Rakhshkhorshid and S.H. Hashemi, Experimental study of hot deformation behavior in API X65 steel, Mater. Sci. Eng. A, 573 (2013) 37–44. ##[26] API Specifications 5L, Specifications for Line Pipe, 44th Edition, American Petroleum Institute, USA (2007). ##[27] M.S. Ozerdem and S. Kolukisa, Artificial neural network approach to predict the mechanical properties of Cu–Sn–Pb–Zn–Ni cast alloys, Mater. Des., 30 (2009), 764–769. ##[28] M. Zounematkermani, O. Kisi and T. Rajaee, Performance of radial basis and LMfeed forward artificial neural networks for predicting daily watershed run off, Appl. Soft. Comput., 13 (2013) 4633– 4644. ##[29] S. Garg, S.K. Pal and D. Chakraborty, Evaluation of the performance of backpropagation and radial basis function neural networks in predicting the drill flank wear, Neural Comput. &Applic., 16 (2007) pp. 407–417. ##[30] .A. Mehrsai, H.R. Karimi, K.D. Thoben and B. ScholzReiter, Application of learning pallets for real time scheduling by the use of radial basis function network, Neurocomputing, 101 (2013) 82–93. ##[31] M. Rakhshkhorshid and S.H. Hashemi, Firefly algorithm assisted optimized NN to predict the elongation of API X65 pipeline steel, IJMMNO, 4(3) (2013), 238 – 251. ##[32] MATLAB® software (2008) (Neural Network Toolbox, User's Guide) ##[33] H. Sarnel and Y. Senol, Accurate and robust image registration based on radial basis neural networks, Neural Comput.&Applic., 20 (2011) 1255–1262. ##]
Nanotwins Formation in Accumulative RollBonded Brass
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Accumulative rollbonding (ARB) is a severe plastic deformation process that is using rolling to produce ultrafine grains in coarse grained metallic materials. In this study, ARB has been applied on 70/30 brass up to 6 cycles at ambient temperature and nonlubricated conditions to apply a true strain up to 4.8 Von Mises strain. Microstructures of ARBed brass samples were characterized by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). The results indicated that during ARB cycles, the grain size decreased from micronsize to nanosize and mechanical twins were widely observed throughout the microstructure after cycle 1. However after cycle 3, the twinning activity became significantly limited and deformation occurred via shear bands formation. After cycle 6, the measured average grain size was about 50 nm and nanotwins were observed originating from grain boundaries and gain boundary junctions. With the reduction in the grain size down to nanometer, the pole mechanism was not the dominant mechanism of nanotwin formation and nanotwins were mainly produced via partial dislocation emission from grain boundaries and grain boundary junctions.
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S.
Pasebani
School of Mechanical, Industrial, and Manufacturing Engineering
Oregon State University
Corvallis, OR 973316001
USA
School of Mechanical, Industrial, and Manufacturin
Iran
somayeh.pasebani@oregonstate.edu


M. R.
Toroghinejad
Department of Materials Engineering, Isfahan University of Technology,
Isfahan
Department of Materials Engineering, Isfahan
Iran
toroghi@cc.iut.ac.ir


G.
Dini
Isfahan University
Isfahan University
Iran
g.dini@sci.ui.ac.ir
Accumulative rollbonding
nanotwins
nanostructured
70/30 brass
[[1] Y. H. Zhao, X. Z. Liao, Z. Horita, T. G. Langdon and Y. T. Zhu, Mat. Sci. Eng. A. 493 (2008) 123129. ##[2] J. A. Venables, Philos. Mags. 6 (1961) 379396. ##[3] C.X. Huang, K. Wang, S. D. Wu, Z. F. Zhang, G. Y. Li and S .X. Li, Acta. Mater. 54 (2006) 655665. ##[4] V. Yamakov, D. Wolf, S. R. Phillpot, A. K. Mukherjee and H. Gleiter, Nature. Mater. 1(2002) 4548. ##[5] J. Schiotz and K. W. Jacobsen, Science 301 (2003) 13571359. ##[6] H. V. Swygenhoven, Science 296 (2002) 6667. ##[7] N. Tsuji, Y. Saito, S. H. Lee and Y. Minamino, Adv. Eng. Mat. 5(2003) 338344. ##[8] W. Wang, Y. B. Wang, X. Z. Liao , Y. H. Zhao, E. J. Lavernia, Y. T. Zhu, Z. Horita and T. G Langdon, Scripta. Mater. 60 (2009) 5255. ##[9] B. J. Duggan, M. Hatherly, W. B. Hutchinson and P. T. Wakefield, Metal. Science. 12 (1978) 343350. ##[10] G.H. Xiao, N. R. Tao and K. Lu, Mat. Sci. Eng. A. 513514 (2009) 1321. ##[11] F.J. Humphreys and M. Hatherly, Recrystallization and related annealing phenomena, second ed, Elsevier Science Ltd, United Kingdom, 2004. ##[12] Z. Horita, D. J. Smith, M. Nemoto, R. Z. Valiev and T. G. Langdon, J. Mater. Res. 13(1998) 446449. ##[13] X. Z. Liao, Y. H. Zhao, S. G. Srinivasan, Y. T. Zhu, R. Z. Valiev and D. V. Gunderov, Appl. Phys. Lett. 84(2004) 592594. ##[14] J. Cai, S. Shekhar, J. Wang and M. Ravi Shankar, Scripta Mater. 60(2009) 599602. ##[15] X. Z. Liao, Y. H. Zhao, Y. T. Zhu, R. Z. Valiev and D. V. Gunderov, J. Appl. Phys. 96(2004) 636640. ##[16] V. Yamakov, D. Wolf, S. R. Phillpot, A. K. Mukherjee and H. Gleiter, Nature. Mater. 3(2004) 4347. ##[17] H. V. Swygenhoven, M. Spacer and A. Caro, Acta. Mater. 47 (1999) 31173126. ##[18] X. Z. Liao, F. Zhou, E. J. Lavernia, S. G. Srinivasan, M. I. Baskes, D. W. He and Y. T. Zhu, Appl. Phys. Lett. 83 (2003) 632 634. ##[19] X. Z. Liao, F. Zhou, E. J. Lavernia, D. W. He and Y.T. Zhu, Appl. Phys. Lett. 83 (2003) 50625064. ##[20] X. Wu, Y. T. Zhu and E. Ma, Appl. Phys. Lett. 88 (2006) 121905 121907. ##[21] X. L. Wu and Y. T. Zhu, Appl. Phys. Lett. 89 (2006) 0319203194. ##[22] E. Ma, Y. M. Wang, Q. H. Lu, M. L. Sui, L. Lu and K. Lu, Appl. Phys. Lett. 85 (2004) 49324934. ##[23] L. Lu, R. Schwaiger, Z. W. Shan, M. Dao, K. Lu and S. Suresh, Acta. Mater. 53 (2005) 2169 2179.##]
Modeling and Experimental Study of Static Recovery and Mechanical Behavior of AA5052 Alloy During ColdWorking and Subsequent Annealing
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In the present study, the mechanical behavior of AA5052 aluminum alloy during cold deformation and subsequent isothermal annealing in a temperature range of 225300oC was investigated using the uniaxial tensile test data. It is found that by increasing the annealing time and temperature the material yield strength is decreased. The microstructural investigations of the annealed samples show that the grains are elongated and there is no evidence of recrystallization. Hence, recovery is the main restoration phenomenon during the annealing treatment. The work hardening behavior of the alloy during cold work is modeled using a dislocation density based modeling approach and the softening behavior of deformed samples during subsequent annealing is modeled by applying a kinetics equation relating the yield strength to the annealing parameters. The kinetics equation is a nonlinear differential equation and it’s solved numerically by employing RungeKuttaFehlberg (RKF) integration scheme which is coupled with GaussNewton nonlinear optimization technique to obtain the material constants of the model. The numerical results are validated using the experimental flow data.
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M.
Seyed Salehi
Department of materials science and engineering, K. N. Toosi University of Technology, Tehran, Iran
Department of materials science and engineering,
Iran
majid.seyedsalehi@gmail.com


N.
Anjabin
shiraz university
shiraz university
Iran
anjabin@shirazu.ac.ir
Kinetics of static recovery
AA5052 aluminum alloy
Cold working
Isothermal annealing
Nonlinear regression
[[1] H. J. McQueen, S. Spigarelli, M. E. Kassner, and E. Evangelista, Hot deformation and processing of aluminum alloys: CRC Press (2011). ##[2] A. Rollett, F. Humphreys, G. S. Rohrer, and M. Hatherly, Recrystallization and related annealing phenomena: Elsevier (2004). ##[3] H. Mecking and U. Kocks, Kinetics of flow and strainhardening, Acta Metallurgica, 29 (1981) 18651875. ##[4] Y. Estrin and H. Mecking, A unified phenomenological description of work hardening and creep based on oneparameter models, Acta Metallurgica, 32 (1984) 5770. ##[5] G. Borelius, S. Berglund, and S. Sjoberg, Measurements on the Evolution of Heat During the Recovery of ColdWorked Metals, Arkiv for Fysik, 6 (1953) 143149. ##[6] J. Friedel and R. Smoluchowski, Les dislocations, Physics Today, 10 (1957) 36. ##[7] D. Kuhlmann, G. Masing, and J. Raffelsieper, On the theory of recovery, Zeitsch Metall, 40 (1949) 2416. ##[8] E. Nes, Recovery revisited, Acta metallurgica et materialia, 43 (1995) 21892207. ##[9] M. Verdier, Y. Brechet, and P. Guyot, Recovery of AlMg alloys: flow stress and strainhardening properties, Acta materialia, 47 (1998) 127134. ##[10] A. Standard, E8m09: Standard Test Methods for Tension Testing of Metallic Materials, Annual Book of ASTM Standards, ASTM, West Conshohocken, PA, (2009) 127. ##[11] J. Liu and J. G. Morris, Recrystallization microstructures and textures in AA 5052 continuous cast and direct chill cast aluminum alloy, Materials Science and Engineering: A, 385 (2004) 342351. ##[12] U. Kocks, Laws for workhardening and lowtemperature creep, Journal of engineering materials and technology, 98 (1976) 7685. ##[13] R. L. Burden and J. D. Faires, Numerical Analysis.(2001) Brooks/Cole, USA. ##[14] W. Poole, M. Militzer, and M. Wells, Modelling recovery and recrystallisation during annealing of AA 5754 aluminium alloy, Materials science and technology, 19 (2003) 13611368. ##[15] A. Seeger, D. Wolf, and H. Mehrer, Analysis of tracer and nuclear magnetic resonance measurements of self‐diffusion in aluminium, physica status solidi (b), 48 (1971) 481496. ##[16] M. Mantina, Y. Wang, L. Chen, Z. Liu, and C. Wolverton, First principles impurity diffusion coefficients, Acta Materialia, 57 (2009) 41024108. ##[17] W. A. Soer, Interactions between dislocations and grain boundaries, (2006). ##[18] L. F. Mondolfo, Structure and properties of aluminum alloys, Metallurgiya, Moscow, (1979).##]
A Comparative Study on the Formability Prediction of TwoLayer Metallic Sheets
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Twolayer metallic sheets have wide applications in aerospace, marine, automotive and domestic industries due to their superlative characteristics. In this paper, the formability of twolayer sheet is investigated through analytical, experimental and numerical approaches. An analytical model is developed based on MarciniakKuczynski method associated Hill’s nonquadratic yield criterion. Forming limit diagrams are also obtained numerically based on finite element method using Bifurcation theory and ductile fracture criteria. Furthermore, experiments are carried out on Al3105St14 twolayer sheet. Theoretical results from various methods are compared with results obtained from experiments to evaluate the competency of discussed analytical and numerical methods to predict the formability of twolayer sheets. The results show that analytical and numerical approaches discussed in this paper have good capabilities to predict the formability of twolayer sheets. However, the analytical method based on MK model and numerical approach based on bifurcation theory are more suitable to determine the forming limit diagram of Al3105St14 twolayer sheets.
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H.
Deilami Azodi
Arak University of Technology
Arak University of Technology
Iran
hdazodi@arakut.ac.ir


R.
Darabi
Arak University of Technology
Arak University of Technology
Iran
royadrb8989@yahoo.com
Forming Limit Diagram
Twolayer Sheet
MarciniakKuczynski (MK) Method
Bifurcation Theory
Ductile Fracture
[[1] S. P. Keeler, Circular grid system – a valuable aid for evaluating sheet metal formability, SAE Technical Paper, 77 (1968) 371–379. ##[2] G. M. Goodwin, Application of strain analysis to sheet metal forming problems in press shop, SAE Transactions, 77 (1968) 380–387. ##[3] S. L. Semiatin, H. R. Piehler, Formability of sandwich sheet materials in plane strain compression and rolling, Metallurgical Transactions A, 10 (1979), 97–107. ##[4] S. L. Semiatin, H. R. Piehler, Deformation of sandwich sheet materials in uniaxial tension, Metallurgical Transactions A, 10 (1979) 85–96. ##[5] T. Mori, S. Kurimoto, Pressformability of stainless steel and aluminum clad sheet, Journal of Materials Processing Technology, 56 (1996) 242–253. ##[6] F. Yoshida, R. Hino, Forming limit of stainless steelclad aluminum sheets under plane stress condition, Journal of Materials Processing Technology, 63 (1997) 66–71. ##[7] A. Jalali Aghchai, M. Shakeri, B. Mollaei Dariani, Theoretical and experimental formability study of twolayer metallic sheet Al1100/St12, Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering manufacture, 222 (9) (2008) 1131–1138. ##[8] A.Jalali Aghchai, M. Shakeri, B. Mollaei Dariani, Influences of material properties of components on formability of twolayer metallic sheets, International Journal of Advanced Manufacturing Technoloogy, 66 (2012) 809–823. ##[9] Z. Marciniak, K. Kuczynski, Limit strains in the processes of stretchforming sheet metal, International Journal of Mechanical Sciences, 9 (1967) 609–620. ##[10] J.Z. Gronostajski, Z. Zimniak, Theoretical simulation of sheet behavior in forming processes, Journal of Materials Processing Technology, 34 (1992) 457–464. ##[11] M. Shakeri, A. Sadough, B.M. Dariani, Theoretical and Experimental Analysis of Sheet Metal Formability Limit, Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering manufacture, 214 (2000) 821–827. ##[12] A.Assempour, M. Nurcheshmeh, The influence of material properties on the shape and level of the forming limit diagram, SAE Technical Paper, 01 (2003) 1149. ##[13] R. Hill, Theoretical plasticity of textured aggregates, Mathematical Proceedings of the Cambridge Philosophical Society, 85 (1979) 179–620. ##[14] M. Pishbin, P.P. Gillis, Forming limit diagrams calculated using Hill’s nonquadratic yield criterion Metallurgical Transactions A, 23 (1992) 19922817. ##[15] J. Gronostajski, The effect of strain path on the plastic instability, Proceedings of the 3rd International Conference on the Technology of Plasticity, Kyoto, Japan, (1990), Vol. 3, 4950. ##[16] S. S. Hecker, A cup test for assessing stretchability, Metals Engineering Quarterly, 14, (1974), 3036. ##[17] S. Storen, J.R. Rice, Localized necking in thin sheets, Journal of the Mechanics and Physics of Solids, 23 (1975) 421441. ##[18] A.Petek, T. Pepelnjak, K. Kuzman, An improved method for determining forming limit diagram in digital environment, Journal of Mechanical Engineering, 51 (2005) 330345. ##[19] T. Pepelnjak, A. Petek, K. Kuzman, Analysis of the forming limit diagram in digital environmrnt, Advanced Material Research, 68 (2005) 697704. ##[20] M.G. Cockcroft, D.J. Latham, Ductility and the Workability of Metals, Journal of the Institute of Metals, 96 (1968) 33–39. ##[21] S. I. Oh, C. C. Chen, S. Kobayashi, Ductile Fracture in Axisymmetric Extrusion and Drawing, Journal of Engineering for IndustryTransactions of the ASME, 101 (1979) 3644. ##[22] P. Brozzo, B. Deluca, R. Rendina, A New Method for the Prediction of Formability in Metal Sheets, Proceedings of the Seventh Biennial Conference of IDDRG on Sheet Metal Forming and Formability, (1972). ##]
Prediction of Extrusion Pressure in Vortex Extrusion Using a Streamline Approach
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Vortex extrusion (VE) is a severe plastic deformation technique which is based on the synergies between high strain accumulation and high hydrostatic pressure. Such a high amount of pressure, places a mandate to seek the method for investigation of the load under processing conditions. For this, kinematically admissible velocity field and upper bound terms based on Bezier formulation are developed in order to investigate relative pressure in the VE process. Effects of reduction in area, relative length, twist angle, and friction factor in power dissipation terms are systematically analyzed. It is demonstrated that increasing the twist angle and area reducing and friction factor in the VE process increases the relative pressure, which the rates of these increase varies with twist angle. Moreover, the effect of the relative length is different in various frictional conditions. Results of conventional extrusion (CE) are in good agreement with those found by Avitzur for the effect of slug length and friction factor on the relative extrusion stress.
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M.
Shahbaz
Department of Materials Science and Engineering, School of Engineering, Urmia University, Urmia, Iran
Department of Materials Science and Engineering,
Iran
mehredads1@gmail.com


J. G.
Kim
Department of Materials Science and Engineering, POSTECH, Pohang 790784, Republic of Korea
Department of Materials Science and Engineering,
Iran
junggi91@gmail.com


R.
Ebrahimi
Department of Materials Science and Engineering, School of Engineering, Shiraz University, Shiraz, Iran
Department of Materials Science and Engineering,
Iran
ebrahimy@shirazu.ac.ir


H. S.
Kim
Department of Materials Science and Engineering, POSTECH, Pohang 790784, Republic of Korea
Department of Materials Science and Engineering,
Iran
hyoungseopkim@gmail.com
Severe plastic deformation
Vortex extrusion
Bezier formulation
Upper bound theorem
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