2016
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Finite element analysis of elasticplastic solids under Vickers indentation: surface deformation
2
2
Finite element modeling has been used to study the development of surface deformation during indentation with a Vickers indenter. A wide range of materials with different elastic modulus and yield stresses are examined. Results show that in a pyramidal indentation process, for a perfectly plastic material, sinkingin during loading can change to pileup in unloading. This phenomenon depends on the elastic modulus to yield stress ratio. Results also show that the amount of pileup cannot be related solely to the strainhardening exponent, as often assumed. Rather, after initially sinkingin at small depths of penetration, the pileup for many materials evolves and increases gradually as the indenter is driven into the material. It is shown that the ratio of the plastic volume radius to the indentation depth is nearly constant during loading and it is a function of the yield stress and the Young modulus. Experimental verification in loading and unloading is carried out with the results of Alcala et al. (Acta Materialia, 2000, pp. 3451).
1

1
11


Ali
Nayebi
Shiraz University
Shiraz University
Iran
nayebi7@gmail.com
Indentation
Vickers hardness
Isotropic hardening
Pileup
Sinkin
[[1] O'Neil, H., Hardness measurements of metals and alloys. New Jersey: Chapman Hall, (1951). ##[2] Tabor, D., The hardness of metals. Oxford: Clarendon Press, (1951). ##[3] E. Söederlund and D.J. Rowcliffe, J Hard Mater., 5 (1994) 149. ##[4] G. Pintaúde, M. G. di, V. Cuppari, C. G. Schön, A. Sinatora, and R. M. Souza, Zeitschrift für Metallkunde, 96 (2005) 1252. ##[5] J. Alcala, A.E. Giannakopoulos and S. Suresh, J. Mater. Res 13 (1998) 1390. ##[6] A.K. Bhattacharya and W.D. Nix, Int. J. Solids Structures, 27 (1991) 1047. ##[7] T.A. Laursen and J.C. Simo, J. Mater. Res., 7 (1992) 618. ##[8] V. Marx and H. Balke, Acta mater, 45 (1997) 3791. ##[9] A. Bolshakov and G.M. Pharr, J. Mater. Res., 13 (1998) 1049. ##[10] A.E. Giannakopoulos, P.L. Larsson and Vestergaard, R., Int. J. Solids Structures, 31 (1994) 2679. ##[11] P.L. Larsson, A.E. Giannakopoulos, E. Söerlund, D.J. Rowcliffe, and R. Vestergaard, Int. J. Solids Structures, 33 (1996). ##[12] A.E. Giannakopoulos and P.L. Larsson, Mech. Mater., 25 (1997) 1. ##[13] J. Alcala, A.C. Barone, A.C. and M. Anglada, M., Acta mater., 48 (2000) 3451. ##[14] J.M. Antunes, L.F., Menezes, and J.V. Fernandes, Key Eng. Mat., 230 (2002) 525. ##[15] J.M. Antunes, L.F., Menezes and J.V. Fernandes, Int. J. of Solids & Struct., Vol. 43 (2006) 781. ##[16] A. Millard, Castem 2000, Rapport D.E.M.T./92 300, C.E.A, (1992). ##[17] S. Carlsson, S. Biwa and P.L. Larsson, Int. J. Mech. Sci., 42 (2000) 107. ##[18] A.E. Giannakopoulos, P.L. Larsson, R. Vestegaard, Int. J. Solids Struct., 31 (1994) 2670. ##[19] K.L. Johnson, J. of the Mech. and Phys. of Solids, 18 (1970) 115. ##[20] K.L. Johnson, Contact mechanics, Cambridge University Press, Cambridge, UK (1985). ##[21] R.K. Abu AlRub, Mech. of Mat., 39 (2007) 787. ##]
Numerical Investigation of Circular Plates Deformation under Air Blast Wave
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2
In the current research the maximum deflection of circular plates made of AA5010 and AA1100 alloys under blast load was investigated. Shock waves were produced by exploding a spherical charge in different distances from the center of plates. The ABAQUS software uses conwep equation for blast loading analysis. It was found the results of these simulations have about 30% to 40% inaccuracy in comparison with experimental results. To improve the accuracy of the simulations the Friedlander equation was used that considers the positive phase of blast wave as exponential and the negative phase as bilinear function. To this goal, the vdload subroutine was developed. Results were shown the difference between the experimental and simulation was decreased to 8%. Also, the effect of uniform and nonuniform shock waves on the deformation of structure and various types of failure were investigated. It was observed that uniform shock waves can be achieved when the minimum distance between the exploding charge and plate is about 3 times of the radius of plate.
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26


Bahman
Veisi
K. N. Toosi University of Technology
K. N. Toosi University of Technology
Iran
bwaisy@mail.kntu.ac.ir


Keivan
Narooei
K.N. Toosi university of Technology
K.N. Toosi university of Technology
Iran
knarooei@kntu.ac.ir


Jamal
Zamani
K. N. Toosi University of Technology
K. N. Toosi University of Technology
Iran
zamani@kntu.ac.ir
Blast loading
Friedlander equation
Circular plate
Failure
Explosive forming
[[1] F. W. Travis and W. Johnson, Experiments in the dynamic deformation of clamped circular sheets of various metals subject to an underwater explosive charge, Sheet Met. Indust, 39(1961) 456. ##[2] W. Johnson, A. Poynton, H. Singh, and F. W. Travis, Experiments in the underwater explosive stretch forming of clamped circular blanks, Int. J. Mech. Sci., 8,4(1966) 237–270. ##[3] C. P. Vendhan, K. Ramajeyathilagam and V. Bhujanga Rao, Nonlinear transient dynamic response of rectangular plates under shock loading, Int. J. Impact Eng., 24, 10(2000) 999–1015. ##[4] V. H. Balden and G. N. Nurick, Numerical simulation of the postfailure motion of steel plates subjected to blast loading, Int. J. Impact Eng., 32, 1(2005) 14–34. ##[5] A. Neuberger, S. Peles and D. Rittel, Scaling the response of circular plates subjected to large and closerange spherical explosions. Part I: Airblast loading, Int. J. Impact Eng., 34, 5(2007) 859–873. ##[6] G. J. McShane, C. Stewart, M. T. Aronson, H. N. G. Wadley, N. A. Fleck and V. S. Deshpande, Dynamic rupture of polymermetal bilayer plates, Int. J. Solids Struct., 45, 16(2008) 4407–4426. ##[7] K. Narooei and A. Karimi Taheri, A study on sheet formability by a stretchforming process using assumed strain FEM, J Eng Math, (2009) 311–324. ##[8] M. S. Chafi, G. Karami and M. Ziejewski, Numerical analysis of blastinduced wave propagation using FSI and ALEmultimaterial formulations, Int. J. Impact Eng., 36, 10(2009) 1269–1275. ##[9] A. Neuberger, S. Peles and D. Rittel, Springback of circular clamped armor steel plates subjected to spherical airblast loading, International Journal of Impact Engineering, (2009) 53–60. ##[10] G. S. Langdon, D. Karagiozova, M. D. Theobald, G. N. Nurick, G. Lu and R. P. Merrett, Fracture of aluminium foam core sacrificial cladding subjected to airblast loading, Int. J. Impact Eng., 37, 6(2010) 638–651. ##[11] J. Zamani, H. Shariati, A. Gamsari and A. Sheykhi, Effect of strain rate on the circular plate under dynamic loading by introducing a dynamic rather than static failure, J. Energ. Mater., 10, 2(2011). ##[12] M. D. Goel, V. A. Matsagar and A. K. Gupta, Dynamic Response of Stiffened Plates under Air Blast, Int. J. Prot. Struct., 2, 1(2011) 139–156. ##[13] P. Kumar, D. S. Stargel and A. Shukla, Effect of plate curvature on blast response of carbon composite panels, Compos. Struct., 99(2013) 19–30. ##[14] K. Spranghers, I. Vasilakos, D. Lecompte, H. Sol and J. Vantomme, Numerical simulation and experimental validation of the dynamic response of aluminum plates under free air explosions, International Journal of Impact Engineering, (2013) 8395. ##[15] P. Longere, A. Greza, B. Leble and A. Dragon, Ship structure steel plate failure under nearfield air blast loading: Numerical simulations vs experiment, International Journal of Impact Engineering, 62(2013) 8898. ##[16] H. R. Tavakoli and F. Kiakojouri, Numerical dynamic analysis of stiffened plates under blast loading, Lat. Am. J. Solids Struct., 11, 2(2014) 185–199. ##[17] E. Sitnikova, Z.W. Guan, G.K Schleyer and W.J. Cantwell, Modelling of perforation in fiber metal laminates subjected to high impulsive blast loading, International Journal of Solids and Structures, 51(2014) 31353145. ##[18] N. Jha and B.S. Kumar, Air blast validation using ANSYS/AUTODYN, International Journal of Engineering Research & Technology (IJERT), 3, 1(2014). ##[19] E.A. FloresJohnson, L. Shen, L. Guiamatsia and G.D. Nguyen, A numerical study of bioinspired nacrelike composite plates under blast loading, Composite structures, 126(2015) 329336. ##[20] K. Micallef, A.S. Fallah, P.T. Curtis and L.A. Louca, On the dynamic plastic response of steel membranes subjected to localised blast loading, International Journal of Impact Engineering, 89(2016) 2537. ##[21] M. Larcher, Simulation of the Effects of an Air Blast Wave, I21020 Ispra, Italy, JRC Tech Notes, (2007) 417. ##[22] G. F. Kinney and K. J. Graham, Explosive shocks in air, (1985) Second Edition 282, Berlin and New York, SpringerVerlag. ##[23] T. Belytschko, W. Liu and B. Moran, Nonlinear finite elements s for continua and structures, (2000) Fourth Edition, 609615,england: wiley. ##[24] A. E. El Mokadem, A. S. Wifi and I. Salama, A study on the UNDEX cup forming, 37, 2(2009) pp. 556–562. ##[25] G. Tiwari, M. A. Iqbal and P. K. Gupta, Influence of Target Convexity and Concavity on the Ballistic Limit of Thin Aluminum Plate against by, 6, 3(2013) 365–372. ##[26] S. Menkes and H. Opat, Broken beams, Eperimental Mechanics, 13, 11(1973) pp. 480486. ##[27] N. Jones, Structural impact (2011) Cambridge University Press. ##[28] R. Rajendran and J. M. Lee, Blast loaded plates, Marine Stractures, 22(2009) 99–127. ##[29] E. Borenstein and H. Benaroya, Loading and structural response model of circular plate subjected to near field explosions, Journal of sound and Vibration, 332(2013) 1725–1753. ##]
A comparative study on constitutive modeling of hot deformation flow curves in AZ91 magnesium alloy
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2
Modeling the flow curves of materials at elevated temperatures is the first step in mathematical simulation of the hot deformation processes of them. In this work a comparative study was provided to examine the capability of three different constitutive equations in modeling the hot deformation flow curves of AZ91 magnesium alloy. For this, the Arrhenius equation with strain dependent constants, the exponential equation with strain dependent constants and a recently developed simple model (developed based on a power function of ZenerHollomon parameter and a third order polynomial function of ε power a constant number) were examined. Root mean square error (RMSE) criterion was used to assess the modeling performance of the examined constitutive equations. Accordingly, it was found that the Arrhenius equation with strain dependent constants has the best performance for modeling the hot deformation flow curves of AZ91 magnesium alloy. The results can be further used in mathematical simulation of hot deformation manufacturing processes of tested alloy.
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37


M.
Rakhshkhorshid
Department of Mechanical Engineering, Birjand University of Technology, POBOX 97175569, Birjand, Iran
Department of Mechanical Engineering, Birjand
Iran
m_rakhshkhorshid@yahoo.com


A.R.
Maldar
Materials Engineering Department, Hakim Sabzevari University, POBOX 397, Sabzevar, Iran.
Materials Engineering Department, Hakim Sabzevari
Iran
a.r.maldar@gmx.com
Constitutive equations
Hot deformation processes
Arrhenius equation
Exponential equation
AZ91 magnesium alloy
[[1] X. Xia, Q. Chen, J. Li, D. Shu, C. Hu, S. Huang and Z. Zhao, Characterization of hot deformation behavior of asextruded Mg–Gd–Y–Zn–Zr alloy, J. Alloys Compd., 610 (2014) 203–211. ##[2] K.U. Kainer, Magnesium—Alloys and Technology, WileyVCH, Germany (2003). ##[3] I.J. Polmear, Light Alloys—From Traditional Alloys to Nanocrystals, ButterworthHeinemann, United Kingdom (2006). ##[4] S.E. Ion, F.J. Humphreys and S.H. White, Dynamic recrystallisation and the development of microstructure during the high temperature deformation of magnesium, Acta Metall., 30 (1982) 1909–1919. ##[5] 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. ##[6] A.S. Khan and S. Huang, Experimental and theoretical study of mechanical behavior of 1100 aluminum in the strain rate range 10−5−104s−1, Int. J. Plast., 8 (1992) 397–424. ##[7] A. AbbasiBani, A. ZareiHanzaki, M.H. Pishbin and N. Haghdadi, A comparative study on the capability of Johnson–Cook and Arrheniustype constitutive equations to describe the flow behavior of Mg–6Al–1Zn alloy, Mech. Mater., 71 (2014) 5261. ##[8] A. Molinari and G. Ravichandran, Constitutive modeling of highstrainrate deformation in metals based on the evolution of an effective microstructural length, Mech. Mater., 37 (2005) 737–52. ##[9] E. Voce, The relationship between stress and strain for homogeneous deformation, J. Inst. Metals., 74 (1948) 537–562. ##[10] 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. ##[11] 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. ##[12] F.C. Ren, J. Chen and F. Chen, Constitutive modeling of hot deformation behavior of X20Cr13 martensitic stainless steel with strain effect, Transactions of Nonferrous Metals Society of China, 24 (5) (2014) 1407–1413. ##[13] W.X. Wu, L. Jin, J. Donga and W.J. Ding, Prediction of flow stress of Mg–Nd–Zn–Zr alloy during hot compression, Transactions of Nonferrous Metals Society of China, 22(5) (2012) 1169–1175. ##[14] 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. ##[15] 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. ##[16] H. Mirzadeh and A. Najafizadeh, Flow stress prediction at hot working conditions, Mater. Sci. Eng., A 527 (2010) 1160–1164. ##[17] M. Rakhshkhorshid, Modeling the hot deformation flow curves of API X65 pipeline steel, Int. J. Adv. Manuf. Technol., 77 (2015) 203–210. ##[18] A.K. Shukla, S.V.S. Narayana Murty, S.C. Sharma and K. Mondal, Constitutive modeling of hot deformation behavior of vacuum hot pressed Cu–8Cr–4Nb alloy, Materials and Design, 75 (2015) 57–64. ##[19] Z. Akbari, H. Mirzadeh and J.M. Cabrera, A simple constitutive model for predicting flow stress of medium carbon microalloyed steel during hot deformation, Materials and Design 77 (2015) 126–131. ##[20] G.R. Ebrahimi, A.R. Maldar, R. Ebrahimi and A. Davoodi, Effect of thermomechanical parameters on dynamically recrystallized grain size of AZ91 magnesium alloy, J. Alloys Compd., 509 (2011) 2703–2708. ##[21] G.R. Ebrahimi, A.R. Maldar, R. Ebrahimi and A. Davoodi, Kovove Mater., 48 (2010) 277. ##[22] L. Liu and H. Ding, J. Alloys Compd. 484 (2009) 949 –956. ##[23] M. Rakhshkhorshid and S.H. Hashemi, Experimental study of hot deformation behavior in API X65 steel, Mater. Sci. Eng., A 573, (2013) 37–44. ##[24] M. Shaban and B. Eghbali, Determination of critical conditions for dynamic recrystallization of a microalloyed steel, Mater. Sci. Eng., A 527 (2010) 4320–4325. ##[25] E.I. Poliak and J.J. Jonas, A oneparameter approach to determining the critical conditions for the initiation of dynamic recrystallization, Acta Mater., 44 (1996) 127–136. ##[26] Y.C. Lin, M.S. Chen and J. Zhang, Constitutive modeling for elevated temperature flow behavior of 42CrMo steel, Comp. Mater. Sci., 424 (2008) 470–477. ##[27] S. Mandal, V. Rakesh, P.V. Sivaprasad, S. Venugopal and K.V. Kasiviswanathan, Constitutive equations to predict high temperature flow stress in a Timodified austenitic stainless steel, Mater. Sci. Eng., A 500 (2009) 114–121. ##]
Simulation of Foaming and Deformation for Composite Aluminum Foams
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2
In this study, at the first stage, the rupture criterion of bubbles wall in Aluminum metal foam liquid was investigated by using Lattice Boltzmann. The two phases modeling were accomplished by using a modified ShanChen model. This model was run for several bubbles in A356+3wt.%SiC melt system. Then, bubbles morphologies (virtual metallographic) for A356+3wt.%SiC foams were simulated. Results showed that simulation data and the virtual metallographic have a good agreement with the metallographic empirical results after solidification. In the second stage, several cubic A356+3wt.%SiC foams were compressed under uniaxial compression load base on ASTM E9 standard. Stressstrain curves of the foams were determined by a data acquisition system with gain 10 samples per second. Then foams plastic deformation behavior simulated based of a new asymptotic function by ABAQUS software. Discretized digital solidmodel of the solid bubbles was prepared by using virtual metallographic images which obtained from present code. Then loaddisplacement curves were plotted for simulation and experimental results. Results show both curves obtained from experimental and simulation have a good agreement with approximately 1.8% error. Therefore present software could be useful tool for predicting of metal foams plastic deformation behavior without experimental try and error.
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Hossein
Bayani
Department of Mining and Metallurgical engineering, Amirkabir University of Technology, Tehran, Iran
Department of Mining and Metallurgical engineering
Iran
hossein.bayani@gmail.com


seyed mohammad
Mirbagheri
Amirkabir university of technology
Amirkabir university of technology
Iran
smhmirbagheri@aut.ac.ir
Metal Foam Aluminum A356
Lattice Boltzmann Method
ShanChen model Plastic deformation
mIR asymptotic model
[[1] J. Banhart, Manufacturing routes for metallic foams, Jom, 52 (2000) 2227. ## [2] J. Banhart, Manufacture, characterization and application of cellular metals and metal foams, Prog. Mater. Sci, 46 (2001) 559632. ##[3] J. Banhart, J. Baumeister and M. Weber, Powder metallurgical technology for the production of metallic foams, in European Conference on Advanced PM Materilas, ed Brimimgham, (1995), pp. 201208. ##[4] C. Koerner, Integral Foam Molding of Light Metals, Springer, (2008). ##[5] M. Thies, Lattice Boltzmann Modeling with Free Surfaces Applied to Formation of Metal Foams, PhD, University of Erlangen, Nurenberg, (2005). ##[6] C. Korner, Foam formation mechanisms in particle suspensions applied to metal foams, Materials Science and Engineering A, 495 (2008) 227235. ##[7] C. Y. Chow, An Introduction to Computational Fluid Mechanics, Wiley (1979). ##[8] D. P. Playne, K. Hawick and M. G. B. Johnson, Simulating and benchmarking the shallowwater fluid dynamical equations on multiple graphical processing units, (2013). ##[9] B. T. Pearce and K. Hawick, Interactive simulation and visualisation of falling sand pictures on tablet computers, (2013) ##[10] K. Hawick, Visualising multiphase lattice gas fluid layering simulations, (2011). ##[11] C. Peng, The lattice boltzmann method for fluid dynamics: Theory and applications, Master, EPFL , Switzerland, (2013). ##[12] A. Gupta and R. Kumar, Lattice Boltzmann simulation to study multiple bubble dynamics, International Journal of Heat and Mass Transfer, 51 (2008) 5192  5203. ##[13] E. D. Manev and A. V. Nguyen, Critical thickness of microscopic thin liquid films, Advances in Colloid and Interface Science, 114115 (2005) 133146. ##[14] A. Scheludko, B. Radoev and T. Kolarov, Tension of liquid films and contact angles between film and bulk liquid, Transactions of the Faraday Society, 64 (1968) 22132220. ##[15] A. Vrij and J. T. G. Overbeek, Rupture of thin liquid films due to spontaneous fluctuations in thickness, Journal of the American Chemical Society, 90 (1968) 30743078. ##[16] B. P. Radoev, A. D. Scheludko and E. D. Manev, Critical thickness of thin liquid films: Theory and experiment, Journal of Colloid and Interface Science, 95 (1983) 254265. ##[17] A. Scheludko, Thin Liquid Films, Advances in Colloid and Interface Science, (1967) 391464. ##[18] E. Manev, R. Tsekov and B. Radoev, Effect of thickness nonhomogeneity on the kinetic behaviour of microscopic foam film, Journal of Dispersion Science and Technology, 18 (1997) 769788. ##[19] J. Bibette, F. L. Calderon and P. Poulin, Emulsions: basic principles, Rep. Prog. Phys., 62 (1999) 969–1033. ##[20] H. Stanzick, M. Wichmann, J. Weise, L. Helfen, T. Baumbach and J. Banhart, Process control in aluminium foam production using realtime Xray radioscopy, Advanced Engineering Materials, 4 (2002) 814823. ##[21] H. Bayani and S. M. H. Mirbagheri, Strainhardening during compression of closedcell Al/Si/SiC + (TiB2 & Mg) foam, Materials Characterization, 113 (2016) 168179. ##[22] N. R. Koosukuntla, Towards Development of a Multiphase Simulation Model Using Lattice Boltzmann Method (LBM), MSc, University of Toledo, Ohio, 2011. ##]
Experimental Investigations on Stretchability of an Austentic Stainless Steel 316L
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2
The purpose of this investigation is to examine the viability of using the sheet metal for forming applications. Forming limit diagram (FLD) composed of negative and positive minor strain with respect to major strain which occurs at directional zero strain with the critical thickness of sheet metal. The negative minor strain region of FLD is predicted by localized necking. However there is no directional zero strain in the positive minor region of FLD is predicted with help of MarcinaikKuczynski assumption. The present work aims to determine the stretchability in terms of limiting strain of Austentic stainless steel 316L using M K analysis and hemi spherical dome stretching. Strain hardening exponent was derived from uni axial tensile test of Austentic stainless steel 316L under different in homogeneity conditions. C++ programme was developed to predict the theoretical FLD and results were compared with experimental value. The limiting strain of material is found as 0.4 in experimental and Marcinaik  Kuczynski analysis. Fractography shows the large amount of cleavage fracture and evidence for cleavage initiating because of other inclusions.
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64


Naveen Sait
A
Chendhuran College of Engineering and Technology
Chendhuran College of Engineering and Technology
Iran
naveensait@yahoo.co.in


Kathiravan
S
Chendhuran College of Engineering and Technology,
Chendhuran College of Engineering and Technology,
Iran
skathiravan04@gmail.com


Ravichandran
M
Chendhuran College of Engineering and Technology
Chendhuran College of Engineering and Technology
Iran
smravichandran@hotmail.com
Forming Limit Diagram (FLD)
MarcinaikKuczynski analysis
Simulation in C++
Sheet Metal
Hill’s Theory of localized necking
[[1] E. Ishimaru, H. and Hamasaki, F. Yoshida, Deformationinduced martensitic transformation and workhardening of type 304 stainless steel sheet during drawbending, Procedia Engineering, 81 (2014) 921 – 926. ##[2] H. JongBong, F. Barlat, D. ChanAhn, H.Y. Kim and M.G. Leen, Formability of austenitic and ferritic stainless steels at warm forming temperature, International Journal of Mechanical Sciences, 75 (2013) 94–109. ##[3] G. Charca Ramos, M. Stout, R.E. Bolmaro, J.W. Signorelli, M. Serenelli, M.A. Bertinetti and P. Turner, Study of a drawingquality sheet steel. II: Forminglimit curves by experiments and micromechanical simulations, International Journal of Solids and Structures, 47 (2010) 2294–2299. ##[4] P. Dasappa, K. Inal and R. Mishra, The effects of anisotropic yield functions and their material parameters on prediction of forming limit diagrams, International Journal of Solids and Structures, 49 (2012) 3528–3550. ##[5] J. M. Allwood and D. R. Shouler, Generalised forming limit diagrams showing increased forming limits with nonplanar stress states, International Journal of Plasticity, 25 (2009) 1207–1230. ##[6] A.S. Korhonen and T. Manninen, Forming and fracture limits of austenitic stainless steel sheets, Materials Science and Engineering A, 488 (2008) 157–166. ##[7] G. Mitukiewicz, K. Anantheshwara, G. Zhou, R.K. Mishra and M.K. Jain, A new method of determining forming limit diagram for sheetmaterials by gas blow forming, Journal of Materials Processing Technology, 214 (2014) 2960–2970. ##[8] K. Hariharan, N.T. Nguyen, F. Barlat, M.G. Lee and J.H. Kim, A pragmatic approach to accommodate inplane anisotropy in forming limit diagrams, Mechanics Research Communications, 62 (2014) 5–17. ##[9] S. Panich, F. Barlat, V. Uthaisangsuk, S. Suranuntchai and S. Jirathearanat, Experimental and theoretical formability analysis using strain and stress based forming limit diagram for advanced high strength steels, Materials and Design, 51 (2013) 756–766. ##[10] G. Zhou, K. Ananthaeswara, G. Mitukiewicz, D. Li, R.K. Mishra and M.K. Jain, FE simulations of gas blow forming and prediction of forming limitdiagram of AZ31 magnesium sheet, Journal of Materials Processing Technology, 218 (2015) 12–22. ##[11] Assempour, R. Hashemi, K. Abrinia, M. Ganjiani and E. Masoumi, A methodology for prediction of forming limit stress diagrams considering the strain path effect, Computational Materials Science, 45 (2009) 195–204. ##[12] R. Makkouk, N. Bourgeois, J. Serri, B. Bolle, M. Martiny, M. Teaca and G. Ferron, Experimental and theoretical analysis of the limits to ductility of type 304 stainless steel sheet, European Journal of Mechanics A/Solids, 27 (2008) 181–194. ##[13] K.S. Chan, D.A. Koss and A.K. Ghosh, Localised necking of sheet at negative minor strain, Metallurgical Transactions A, 15 (1984) 323329. ##[14] S. Stören and J.R. Rice, Localized necking in thin sheets, Journal of the Mechanics and Physics of Solids, 23 (1975) 421441. ##[15] M. Ravichandran, A. Naveen Sait and V. Anandakrishnan, Densification and deformation studies on powder metallurgy Al–TiO2–Gr composite during cold upsetting, Journal of Materials Research, 29 (2014) 14801487. ##]
Superplasticity of a finegrained Mg–1.5 wt% Gd alloy after severe plastic deformation
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2
The strain rate sensitivity (SRS) of Mg–1.5 wt% Gd processed by conventional extrusion and 2 passes of simple shear extrusion (SSE) was investigated by shear punch testing. Shear punch tests were conducted at initial shear strain rates in the range of 0.003–0.3 s1 and at temperatures in the range of 573–773 K. A finegrained microstructure with an average grain size of about 2.5 µm, obtained after 2 passes of SSE, resulted in high SRS index (mvalue) of 0.4 at 723 K. The calculated activation energy for 2 passes deformed alloy is 116 kJ/mol which is higher than the activation energy of grain boundary diffusion in magnesium (75 kJ/mol). This higher amount of activation energy can be attributed to the presence of gadolinium in this alloy. This SRS index together with an activation energy of 116 kJ/mol are indicative of a superplastic deformation behavior dominated by grain boundary sliding accommodated by grain boundary diffusion at 723 K.
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65
74


Nazanin
Bayat Tork
School of Metallurgy and Materials Engineering, Iran University of Science and Technology
School of Metallurgy and Materials Engineering,
Iran
nazanin.bayat@yahoo.com


Seyed Hossein
Razavi
School of Metallurgy and Materials Engineering
Iran University of Science &amp; Technology
School of Metallurgy and Materials Engineering
Ir
Iran
hrazavi@iust.ac.ir


hassan
Saghafian
School of Metallurgy and Materials Engineering, Iran University of Science and Technology
School of Metallurgy and Materials Engineering,
Iran
saghafian@iust.ac.ir


Reza
Mahmudi
School of Metallurgical and Materials Engineering, College of Engineering,
University of Tehran, Tehran, Iran
School of Metallurgical and Materials Engineering,
Iran
mahmudi@ut.ac.ir
Severe plastic deformation
Simple Shear Extrusion
Superplasticity
Shear punch test
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