Top

The International Journal of Advanced Manufacturing Technology

Published in:

07-02-2022 | ORIGINAL ARTICLE

Three-dimensional finite element analysis of unintended deformation of polycrystalline billet in micro-extrusion

Authors: Ikumu Watanabe, Toshiro Amaishi

Published in: The International Journal of Advanced Manufacturing Technology | Issue 1-2/2022

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

An unintended anisotropic deformation of a polycrystalline billet has been observed in micro-extrusion, which implies that the extruded billet shows a curved shape rather than an intended straight curve. Although the deformation is considered to originate from the anisotropy of crystal grains, three-dimensional computational analyses are yet to be conducted owing to computational challenges. In this study, the anisotropic deformation behavior of a polycrystalline billet during micro-extrusion was investigated by performing three-dimensional finite element analyses based on the anisotropic elastoplastic constitutive model of a single crystal and its robust algorithm. To explain the effect of grain size on the unintended deformation of billet in micro-extrusion, several simulations for two extrusion dies were performed considering polycrystalline billets containing crystal grains between 100 and 20,000 in number, and the results were statistically analyzed. Anisotropic deformation appeared in the billets with fewer grains, owing to the anisotropy of the single crystal. The grain size, normalized with respect to the billet diameter at which the anisotropic deformation began to appear, was quantitatively estimated. These results are in agreement with the corresponding experiments. Furthermore, simulation results indicated that the extruded crystallographic texture decreased the anisotropic deformation in the case of large grains.

previous article Thermal behavior simulation and stabilization for a mechanical spindle with external cooler across grease-coated interface

next article An improved method for manufacturing sheet-tube connection structure by double-sided annular sheet squeezing

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Kuwabara T, Ikeda S, Kuroda K (1998) Measurement and analysis of differential work hardening in cold-rolled steel sheet under biaxial tension. J Mater Process Technol 80–81:517–523. https://doi.org/10.1016/S0924-0136(98)00155-1CrossRef

Li Q, Zhang H, Chen F et al (2020) Study on the plastic anisotropy of advanced high strength steel sheet: Experiments and microstructure-based crystal plasticity modeling. Int J Mech Sci 176:105569. https://doi.org/10.1016/j.ijmecsci.2020.105569

Hill R (1948) A theory of the yielding and plastic flow of anisotropic metals. Proc R Soc Lond A 193:281–297. https://doi.org/10.1098/rspa.1948.0045MathSciNetCrossRefMATH

Gotoh M (1977) A theory of plastic anisotropy based on yield function of fourth order (plane stress state) - I. Int J Mech Sci 19:505–512. https://doi.org/10.1016/0020-7403(77)90043-1CrossRefMATH

Gotoh M (1977) A theory of plastic anisotropy based on yield function of fourth order (plane stress state) - II. Int J Mech Sci 19:513–520. https://doi.org/10.1016/0020-7403(77)90044-3CrossRefMATH

Barlat F, Aretz H, Yoon JW et al (2005) Linear transformation-based anisotropic yield functions. Int J Plast 21:1009–1039. https://doi.org/10.1016/j.ijplas.2004.06.004CrossRefMATH

Amaishi T, Tsutamori H, Nishiwaki T et al (2020) Description of anisotropic properties of sheet metal based on spline curves and hole expansion test simulation of high-strength steel. Int J Solids Struct 202:672–684. https://doi.org/10.1016/j.ijsolstr.2020.07.010CrossRef

Taylor GI (1938) Plastic strain in metals. J Inst Met 62:307–324

Hill R (1965) Continuum. Micro-mechanics of elasto-plastic polycrystals. J Mech Phys Solids 13:89–101. https://doi.org/10.1016/0022-5096(65)90023-2CrossRefMATH

10.

Lebensohn RA, Tomé CN (1993) A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals: Application to zirconium alloys. Acta Metall Mater 41:2611–2624. https://doi.org/10.1016/0956-7151(93)90130-KCrossRef

11.

Watanabe I, Terada K, Akiyama M (2005) Two-scale analysis for deformation-induced anisotropy of polycrystalline metals. Comp Mater Sci 32:240–250. https://doi.org/10.1016/j.commatsci.2004.08.002CrossRef

12.

Yamanaka A, Kamijyo R, Koenuma K et al (2020) Deep neural network approach to estimate biaxial stress-strain curves of sheet metals. Mater Des 195:108970. https://doi.org/10.1016/j.matdes.2020.108970

13.

Terada K, Watanabe I, Akiyama M et al (2010) A homogenization-based prediction method of macroscopic yield strength of polycrystalline metals subjected to cold-working. In: Vaz Jr. M, de Souza Neto EA, Munoz-Rojas PA, (Eds.), Advanced computational materials modeling: From classical to Multi-Scale Techniques, Wiley & Sons Inc., Ch.10:379–412. https://doi.org/10.1002/9783527632312.ch10

14.

Xu Z, Zhang C, Wang K et al (2020) Crystal plasticity prediction of texture evolution during helical extrusion process of aluminium alloys under three- dimensional deformation path. J Alloys Compd 830:154598. https://doi.org/10.1016/j.jallcom.2020.154598

15.

Miyazaki S, Shibata K, Fujita H (1979) Effect of specimen thickness on mechanical properties of polycrystalline aggregates with various grain sizes. Acta Metall 27:855–862. https://doi.org/10.1016/0001-6160(79)90120-2CrossRef

16.

Kals TA, Eckstein R (2000) Miniaturization in sheet metal working. J Mater Process Technol 103:95–101. https://doi.org/10.1016/S0924-0136(00)00391CrossRef

17.

Chan WL, Fu MW, Lu J (2011) Experimental studies and numerical modeling of the specimen and grain size effects on the flow stress of sheet metal in microforming. Mater Sci Eng, A 528:7674–7683. https://doi.org/10.1016/j.msea.2011.06.076CrossRef

18.

Fu MW, Chan WL (2013) A review on the state-of-the-art microforming technologies. Int J Adv Manuf Technol 67:2411–2437. https://doi.org/10.1007/s00170-012-4661-7CrossRef

19.

Krishnan N, Cao J, Dohda K (2007) Study of the size effects and friction conditions in micro-extrusion - Part I: Micro-extrusion experiments and analysis. J Manuf Sci Eng 129:669–676. https://doi.org/10.1115/1.2386207CrossRef

20.

Mori LF, Krishnan N, Cao J et al (2007) Study of the size effects and friction conditions in micro-extrusion - Part II: Size effect in dynamic friction for brass-steel pairs. J Manuf Sci Eng 129:667–689. https://doi.org/10.1115/1.2738131CrossRef

21.

Cao J, Zhuang W, Wang S et al (2009) An integrated crystal plasticity FE system for microforming simulation. J Multiscale Modell 1:107–124. https://doi.org/10.1142/S1756973709000037CrossRef

22.

Cao J, Zhuang W, Wang S et al (2010) Development of a VGRAIN system for CPFE analysis in micro-forming applications. Int J Adv Manuf Technol 47:981–991. https://doi.org/10.1007/s00170-009-2135-3CrossRef

23.

Quey R, Dawson PR, Barbe F (2011) Large-scale 3D random polycrystals for the finite element method: Generation, meshing and remeshing. Comput Methods Appl Mech Eng 200:1729–1745. https://doi.org/10.1016/j.cma.2011.01.002CrossRefMATH

24.

Flipon B, Keller C, Quey R et al (2020) A full-field crystal-plasticity analysis of bimodal polycrystals. Int J Solids Struct 184:178–192. https://doi.org/10.1016/j.ijsolstr.2019.02.005CrossRef

25.

Groeber MA, Jackson MA (2014) DREAM.3D: A digital representation environment for the analysis of microstructure in 3D. Integr Mater Manuf Innov 3:56–72. https://doi.org/10.1186/2193-9772-3-5CrossRef

26.

Watanabe I, Yamanaka A (2019) Voxel coarsening approach on image-based finite element modeling of representative volume element. Int J Mech Sci 150:314–321. https://doi.org/10.1016/j.ijmecsci.2018.10.028CrossRef

27.

Terada K, Watanabe I (2007) Computational aspects of tangent moduli tensors in rate-independent crystal elastoplasticity. Comp Mech 40:497–511. https://doi.org/10.1007/s00466-006-0123-0CrossRefMATH

28.

Watanabe I, Setoyama D (2016) Multiscale characterization of a polycrystalline aggregate subjected to severe plastic deformation with the finite element method. Mater Trans 57:1404–1410. https://doi.org/10.2320/matertrans.MH201514CrossRef

29.

Gurtin ME (2002) A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocations. J Mech Phys Solids 50:5–32. https://doi.org/10.1016/S0022-5096(01)00104-1MathSciNetCrossRefMATH

30.

Geers MGD, Brekelmans WAM, Janssen PJM (2006) Size effects in miniaturized polycrystalline FCC samples: Strengthening versus weakening. Int J Solids Struct 43:7304–7321. https://doi.org/10.1016/j.ijsolstr.2006.05.009CrossRefMATH

31.

Ohno N, Okumura D (2007) Higher-order stress and grain size effects due to self-energy of geometrically necessary dislocations. J Mech Phys Solids 55:1879–1898. https://doi.org/10.1016/j.jmps.2007.02.007MathSciNetCrossRefMATH

32.

Terada K, Watanabe I, Akiyama M (2006) Effects of shape and size of crystal grains on the strengths of polycrystalline metals. Int J Multiscale Comp Eng 4:445–460. https://doi.org/10.1615/IntJMultCompEng.v4.i4.30CrossRef

33.

Watanabe I, Setoyama D, Iwata N et al (2010) Characterization of yielding behavior of polycrystalline metals with single crystal plasticity based on representative characteristic length. Int J Plast 26:570–585. https://doi.org/10.1016/j.ijplas.2009.09.005CrossRefMATH

34.

Hall EO (1951) The deformation and ageing of mild steel: III discussion of results. Proc Phys Soc Sect B 64:747–753CrossRef

35.

Armstrong RW (2014) 60 years of Hall-Petch: Past to present nano-scale connections. Mater Trans 55:2–12. https://doi.org/10.2320/matertrans.MA201302CrossRef

36.

Zhang H, Dong X (2016) Experimental and numerical studies of coupling size effects on material behaviors of polycrystalline metallic foils in microscale plastic deformation. Mater Sci Eng, A 658:450–462. https://doi.org/10.1016/j.msea.2016.01.116CrossRef

37.

Miehe C, Schröder J, Schotte J (1999) Computational homogenization analysis in finite plasticity simulation of texture development in polycrystalline materials. Comput Methods Appl Mech Eng 171:387–418. https://doi.org/10.1016/S0045-7825(98)00218-7MathSciNetCrossRefMATH

38.

Funazuka T, Takatsuji N, Dohda K et al (2018) Effect of grain size on formability in micro-extrusion – Research on forward-backward micro-extrusion of aluminum alloy 1st report –. J Jpn Soc Technol Plast 59:8–13 (in Japanese). https://doi.org/10.9773/sosei.59.8

39.

Funazuka T, Takatsuji N, Dohda K (2018) Effect of die angle and friction condition on formability in micro extrusion – Research on forward-backward micro-extrusion of aluminum alloy 2nd report –. J Jpn Soc Technol Plast 59:101–106 (in Japanese). https://doi.org/10.9773/sosei.59.101

40.

Barret CR, Nix WD, Tetelman AS (1973) The principles of engineering materials. Prentice- Hall Inc, Englewood Cliffs

41.

Cao Y, Ni S, Liao X et al (2018) Structural evolutions of metallic materials processed by severe plastic deformation. Mater Sci Eng, R 133:1–59. https://doi.org/10.1016/j.mser.2018.06.001CrossRef

42.

Simmons G, Herbert W (1971) Single crystal elastic constants and calculated aggregate properties. MIT Press, Cambridge

43.

Sevillano JG, Van Houtte P, Aernoudt E (1980) Large strain work hardening and textures. Prog Mater Sci 25:69–134. https://doi.org/10.1016/0079-6425(80)90001-8CrossRef

44.

Parasiz SA, Kinsey BL, Mahayatsanun N et al (2011) Effect of specimen size and grain size on deformation in microextrusion. J Manuf Processes 13:153–159. https://doi.org/10.1016/j.jmapro.2011.05.002CrossRef

45.

Watanabe I, Sun Z, Kitano H et al (2020) Multiscale analysis of mechanical behavior of multilayer steel structures fabricated by wire and arc additive manufacturing. Sci Technol Adv Mater 21:461–470. https://doi.org/10.1080/14686996.2020.1788908CrossRef

46.

Chen T, Watanabe I, Liu D et al (2021) Data-driven estimation of plastic properties of alloys using neighboring indentation test. Sci Technol Adv Mater Methods 1:143–151. https://doi.org/10.1080/27660400.2021.1959838CrossRef

Title: Three-dimensional finite element analysis of unintended deformation of polycrystalline billet in micro-extrusion
Authors: Ikumu Watanabe
Toshiro Amaishi
Publication date: 07-02-2022
Publisher: Springer London
Published in: The International Journal of Advanced Manufacturing Technology / Issue 1-2/2022
Print ISSN: 0268-3768
Electronic ISSN: 1433-3015
DOI: https://doi.org/10.1007/s00170-022-08726-y

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Other articles of this Issue 1-2/2022

Mapping ductile-to-fragile transition and the effect of tool nose radius in diamond turning of single-crystal silicon

Study on quarter-wave generation mechanism in DP980 steel during cold rolling

Time-optimal trajectory optimization of serial robotic manipulator with kinematic and dynamic limits based on improved particle swarm optimization

Type-1 and type-2 radial basis function neural networks Mandami system to evaluate quality features

Numerical simulation of end face heating in alternating current flash butt welding based on electrical–thermal bidirectional coupling

An improved SegNet network model for accurate detection and segmentation of car body welding slags

Premium Partners