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Thermomechanical Processing of Steels and Alloys: Multilevel Modeling

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Synonyms

Crystal plasticity

; Thermomechanical treatment of polycrystals

Definitions

Technological processes of thermomechanical treatment consist of heating, cooling, and inelastic deformation operations which are applied one by one or in some combinations. The main goal of the thermomechanical processing is putting the material structure to a state which insures that the products gain certain required operational physical and mechanical properties. The multilevel models of materials are effective in simulating and improving the processes of thermomechanical treatment. These models make it possible to explicitly describe a changing structure of materials at different scale levels.

Introduction

Physical and mechanical properties of polycrystalline materials are determined by their internal structure at different scale levels. Thermomechanical processing which includes heating, cooling, and inelastic deformation is operated successively or in a combined way; it is oriented on the...

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References

  • Anand L (2004) Single-crystal elasto-viscoplasticity: application to texture evolution in polycrystalline metals at large strains. Comput Methods Appl Mech Eng 193:5359–5383

    Article  MathSciNet  MATH  Google Scholar 

  • Anand L, Kothari MA (1996) A computational procedure for rate–independent crystal plasticity. J Mech Phys Solids 44(4):525–558

    Article  MathSciNet  MATH  Google Scholar 

  • Ardeljan M, Beyerlein IJ, Knezevic M (2014) A dislocation density based crystal plasticity finite element model: application to a two-phase polycrystalline HCP/BCC composites. J Mech Phys Solids 66:16–31

    Article  Google Scholar 

  • Asaro RJ (1983) Micromechanics of crystals and polycrystals. Adv Appl Mech 23:1–115

    Article  Google Scholar 

  • Asaro RJ, Needleman A (1985) Texture development and strain hardening in rate dependent polycrystals. Acta Metall 33(6):923–953

    Article  Google Scholar 

  • Austin R, McDowell D (2011) A dislocation-based constitutive model for viscoplastic deformation of FCC metals at very high strain rates. Int J Plast 27:1–24

    Article  Google Scholar 

  • Avrami M (1940) Kinetics of phase change. II: transformation–time relations for random distribution of nuclei. J Chem Phys 8:212

    Google Scholar 

  • Barton NR, Bernier JV, Becker R et al (2011) A multiscale strength model for extreme loading conditions. J Appl Phys 109(7):073501

    Article  Google Scholar 

  • Bate P (1999) Modelling deformation microstructure with the crystal plasticity finite–element method. Philos Trans R Soc Lond A Math Phys Eng Sci 357(1756):1589–1601

    Article  Google Scholar 

  • Beck PA (1954) Annealing of cold worked metals. Adv Phys 3(11):245–324

    Article  Google Scholar 

  • Bellon P (2012) Phase field methods. Compr Nucl Mater 1:411–432

    Article  Google Scholar 

  • Beyerlein IJ, Tome CN (2008) A dislocation-based constitutive law for pure Zr including temperature effects. Int J Plast 24:867–895

    Article  MATH  Google Scholar 

  • Beyerlein IJ, McCabe RJ, Tome CN (2011) Effect of microstructure on the nucleation of deformation twins in polycrystalline high-purity magnesium: a multi-scale modeling study. J Mech Phys Solids 59:988–1003

    Article  Google Scholar 

  • Bhadeshia H, Honeycombe R (2017) Steels: microstructure and properties, 4th edn. Elsevier, Amsterdam

    Google Scholar 

  • Bronkhorst CA, Kalidindi SR, Anand L (1992) Polycrystalline plasticity and the evolution of crystallographic texture in FCC metals. Philos Trans R Soc Lond A Math Phys Eng Sci 341(1662):443–477

    Article  Google Scholar 

  • Cahn RW (1949) Recrystallization of single crystals after plastic bending. J Inst Met 76(2):121–143

    Google Scholar 

  • Cahn RW (1950) A new theory of recrystallization nuclei. Proc Phys Soc Sect A 63(4):323

    Article  Google Scholar 

  • Cahn JW, Hilliard JE (1958) Free energy of a non-uniform systems. I. Interfacial free energy. J Chem Phys 28:258–266

    Google Scholar 

  • Cailletaud G, Diard O, Feyel F, Forest S (2003) Computational crystal plasticity: from single crystal to homogenized polycrystal. Tech Mech 23(2–4):130–145

    Google Scholar 

  • Chen L-Q, Khachaturyan A (1991) Computer simulation of structural transformations during precipitation of an ordered intermetallic phase. Acta Mater 39:2533–2551

    Article  Google Scholar 

  • Cherkaoui M, Berveiller M, Sabar H (1998) Micromechanical modeling of martensitic transformation induced plasticity (trip) in austenitic single crystals. Int J Plast 14(7):597–626

    Article  MATH  Google Scholar 

  • Choudhury A (2017) Phase-field modeling as a method relevant for modeling phase transformation during interdiffusion. In: Aloke P, Divinski S (eds) Handbook of solid state diffusion. Volume 1, Diffusion fundamentals and techniques. Elsevier, Amsterdam, pp 363–389

    Chapter  Google Scholar 

  • Christian JW (2002) The theory of transformations in metals and alloys, 3rd edn. Elsevier, Amsterdam

    Google Scholar 

  • Cottrell AH, Bilby BA (1951) LX. A mechanism for the growth of deformation twins in crystals. Lond Edinb Dubl Phil Mag J Sci 42(329):573–581

    Article  MATH  Google Scholar 

  • Dancette S, Delannay L, Jodlowski T, Giovanola J (2010) Multisite model prediction of texture induced anisotropy in brass. Int J Mater Form 3(1):251–254

    Article  Google Scholar 

  • Dankov PD (1943) The mechanism of phase transformation from the point of view of the principle of orientational and dimensional correspondence. Izv Sector Phys Chem Anal USSR Acad Sci 16(1):82–95 (in Russian)

    Google Scholar 

  • de Groot SR (1951) Thermodynamics of irreversible processes. North-Holland Publishing Company, Amsterdam

    MATH  Google Scholar 

  • Entin RI (1960) The transformation of austenite into steel. Metallurgy, Moscow (in Russian)

    Google Scholar 

  • Fischlschweiger M, Cailletaud G, Antretter T (2012) A mean-field model for transformation induced plasticity including backstress effects for non-proportional loadings. Int J Plast 37:53–71

    Article  Google Scholar 

  • Frank FC (1949) Discussion on paper by NF Mott: mechanical properties of metals. Physica 15:131–133

    Google Scholar 

  • Friedel J, Smoluchowski R, Kurti N (1964) Dislocations. Pergamon Press Ltd., Elsevier

    Google Scholar 

  • Gérard C, Cailletaud G, Bacroix B (2013) Modeling of latent hardening produced by complex loading paths in FCC alloys. Int J Plast 42:194–212

    Article  Google Scholar 

  • Ghoniem NM, Busso EP, Kioussis N, Huang H (2003) Multiscale modelling of nanomechanics and micromechanics: an overview. Philos Mag 83(31–34):3475–3528

    Article  Google Scholar 

  • Gorelik SS, Dobatkin SV, Kaputkina LM (2005) Recrystallization of metals and alloys. MISIS, Moscow (in Russian)

    Google Scholar 

  • Grinfeld MA (1990) Metody mekhaniki sploshnykh sred v teorii fazovykh prevrashcheniy [Methods of continuum mechanics in the theory of phase transitions]. Nauka, Moscow (in Russian)

    Google Scholar 

  • Guo YB, Wen Q, Horstemeyer MF (2005) An internal state variable plasticity-based approach to determine dynamic loading history effects on material property in manufacturing processes. Int J Mech Sci 47:1423–1441

    Article  MATH  Google Scholar 

  • Habraken AM (2004) Modelling the plastic anisotropy of metals. Arch Comput Meth Eng 11(1):3–96

    Article  MATH  Google Scholar 

  • Hirth JP (1961) On dislocation interactions in the FCC lattice. J Appl Phys 32(4):700–706

    Article  Google Scholar 

  • Hirth JP, Lothe J (1968) Theory of dislocations. McGraw-Hill, New York

    MATH  Google Scholar 

  • Holmedal B, Van Houtte P, An Y (2008) A crystal plasticity model for strain-path changes in metals. Int J Plast 24:1360–1379

    Article  MATH  Google Scholar 

  • Honeycombe RWK (1984) Plastic deformation of metals. Edward Arnold, London

    Google Scholar 

  • Horstemeyer MF, Potirniche GP, Marin EB (2005) Crystal plasticity. In: Yip S (ed) Handbook of materials modeling. Springer, Dordrecht, pp 1133–1149

    Chapter  Google Scholar 

  • Iwamoto T (2004) Multiscale computational simulation of deformation behavior of TRIP steel with growth of martensitic particles in unit cell by asymptotic homogenization method. Int J Plast 20:841–869

    Article  MATH  Google Scholar 

  • Kalidindi SR, Bronkhorst CA, Anand L (1992) Crystallographic texture evolution in bulk deformation processing of FCC metals. J Mech Phys Solids 40(3):537–569

    Article  Google Scholar 

  • Karma A, Olabi A-G (2001) Phase field methods. In: Buschow KHJ et al (eds) Encyclopedia of materials: science and technology, 2nd edn. Elsevier, Amsterdam, pp 6873–6886

    Chapter  Google Scholar 

  • Kashchenko MP, Letuchev VV, Yablonskaya TN, Teplyakova LA (1996) A model of the formation of macroshear bands and strain-induced martensite with (HHL) boundaries. Phys Met Metallogr 82(4):329–336

    Google Scholar 

  • Khadyko M, Dumoulin S, Cailletaud G, Hopperstad OS (2016) Latent hardening and plastic anisotropy evolution in AA6060 aluminium alloy. Int J Plast 76:51–74

    Article  Google Scholar 

  • Koistinen DP, Marburger RE (1959) A general equation prescribing the extent of the austenite-martensite transformation in pure ironcarbon alloys and plain carbon steels. Acta Metall 7:59–60

    Article  Google Scholar 

  • Kondepudi D, Prigogine I (2015) Modern thermodynamics: from heat engines to dissipative structures. Wiley, Chichester

    MATH  Google Scholar 

  • Konobeevsky ST (1943) To the theory of phase transformations. J Exper Theor Phys 13(6):185–214 (in Russian)

    Google Scholar 

  • Kouznetsova VG, Geers MGD (2008) A multi-scale model of martensitic transformation plasticity. Mech Mater 40:641–657

    Article  Google Scholar 

  • Kröner E (1960) Allgemeine kontinuumstheorie der versetzungen und eigenspannungen. Arch Ration Mech Anal 4:273–334

    Article  MathSciNet  MATH  Google Scholar 

  • Kurdumov GV, Utievskiy LM, Entin RI (1977) The transformations in iron and steel. Nauka, Moscow (in Russian)

    Google Scholar 

  • Lakhtin Yu M, Leontieva VP (1980) Materials science. Mechanical Engineering, Moscow (in Russian)

    Google Scholar 

  • Lee EH (1969) Elastic plastic deformation at finite strain. ASME J Appl Mech 36:1–6

    Article  MATH  Google Scholar 

  • Lee M-G, Kim S-J, Han HN (2010) Crystal plasticity finite element modeling of mechanically induced martensitic transformation (MIMT) in metastable austenite. Int J Plast 26:688–710

    Article  MATH  Google Scholar 

  • Lin TH (1957) Analysis of elastic and plastic strains of a face – centered cubic crystal. J Mech Phys Solids 5(1):143–149

    Article  MathSciNet  MATH  Google Scholar 

  • Loginova I, Amberg G, Agren J (2001) Phase-field simulations of nonisothermaly binary alloy solidification. Acta Mater 49:573–581

    Article  Google Scholar 

  • Mandel J (1973) Equations constitutives et directeurs dans les milieux plastiques et viscoplastiquest. Int J Solids Struct 9:725–740

    Article  MATH  Google Scholar 

  • Maugin GA (2015) The saga of internal variables of state in continuum thermo-mechanics (1893–2013). Mech Res Commun 69:79–86. http://dx.doi.org/10.1016/j.mechrescom.2015.06.009

    Article  Google Scholar 

  • McDowell DL (2005) Internal state variable theory. In: Yip S (ed) Handbook of materials modeling. Springer, Dordrecht, pp 1151–1169

    Chapter  Google Scholar 

  • McDowell DL (2008) Viscoplasticity of heterogeneous metallic materials. Mater Sci Eng R 62:67–123

    Article  Google Scholar 

  • McDowell DL (2010) A perspective on trends in multiscale plasticity. Int J Plast 26:1280–1309

    Article  MATH  Google Scholar 

  • McGinty RD, McDowell DL (2006) A semi–implicit integration scheme for rate independent finite crystal plasticity. Int J Plast 22:996–1025

    Article  MATH  Google Scholar 

  • M’Guil S, Ahzi S, Youssef H, Baniassadi M, Gracio JJ (2009) A comparison of viscoplastic intermediate approaches for deformation texture evolution in face-centered cubic polycrystals. Acta Mater 57:2496–2508

    Article  Google Scholar 

  • Olson GB, Cohen M (1975) Kinetics of strain-induced martensitic nucleation. Metall Trans A 6A:791–795

    Article  Google Scholar 

  • Orowan E (1934) Zur kristallplastizität. I. Zeitschrift für Physik A Hadrons and Nuclei 89(9):605–613

    Google Scholar 

  • Orowan E (1954) Dislocations in metals. American Institute of Metals, New York

    Google Scholar 

  • Polanyi M (1934) Ãœber eine Art Gitterstörung, die einen kristall plastisch machen könnte. Zeitschrift für Physik A Hadrons and Nuclei 89(9):660–664

    Google Scholar 

  • Raabe D, Becker RC (2000) Coupling of a crystal plasticity finite-element model with a probabilistic cellular automaton for simulating primary static recrystallization in aluminium. Model Simul Mater Sci Eng 8(4):445–462

    Article  Google Scholar 

  • Rollett A, Humphreys FJ, Rohrer GS, Hatherly M (2004) Recrystallization and related annealing phenomena. Elsevier, Oxford

    Google Scholar 

  • Roters F (2011) Advanced material models for the crystal plasticity finite element method: development of a general CPFEM framework. RWTH Aachen, Aachen

    Google Scholar 

  • Roters F, Eisenlohr P, Hantcherli L, Tjahjanto DD, Bieler TR, Raabe D (2010) Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: theory, experiments, applications. Acta Mater 58: 1152–1211

    Article  Google Scholar 

  • Saï K (2011) Multi-mechanism models: present state and future trends. Int J Plast 27:250–281

    Article  Google Scholar 

  • Shveykin AI, Trusov PV (2016) The comparison of geometrically nonlinear elastoviscoplastic constitutive relations formulated in terms of current configuration and formulated in terms of the stress free configuration. Phys Mesomech 19(5):48–57 (in Russian)

    Google Scholar 

  • Steinbach I, Apel M (2006) Multi-phase field model for solid state transformation with elastic strain. Phys D 217:153–160

    Article  MATH  Google Scholar 

  • Takaki T, Tomita Y (2010) Static recrystallization simulations starting from predicted deformation microstructure by coupling multi-phase-field method and finite element method based on crystal plasticity. Int J Mech Sci 52(2):320–328

    Article  Google Scholar 

  • Taylor GI (1934) The mechanism of plastic deformation of crystals. Part I. Theoretical. Proc R Soc Lond Ser A Containing Pap Math Phys Character 145(855): 362–387

    MATH  Google Scholar 

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

    Google Scholar 

  • Tjahjanto DD, Turteltaub S, Suiker ASJ (2008) Crystallographically based model for transformation-induced plasticity in multiphase carbon steels. Contin Mech Thermodyn 19:399–422

    Article  MATH  Google Scholar 

  • Tokuda M, Kratochvil J (1984) Prediction of subsequent yield surface by a simple mechanical model of polycrystal. Arch Mech 36(5–6):661–672

    Google Scholar 

  • Truesdell C (1977) A first course in rational continuum mechanics. Academic, New York

    MATH  Google Scholar 

  • Trusov PV, Shveykin AI (2013a) Multilevel crystal plasticity models of single- and polycrystals. Statistical models. Phys Mesomech 16(1):23–33

    Article  Google Scholar 

  • Trusov PV, Shveykin AI (2013b) Multilevel crystal plasticity models of single- and polycrystals. Direct models. Phys Mesomech 16(2):99–124

    Article  Google Scholar 

  • Trusov PV, Ashikhmin VN, Volegov PS, Shveykin AI (2010) Constitutive relations and their application to the description of microstructure evolution. Phys Mesomech 13(1–2):38–46

    Article  Google Scholar 

  • Trusov PV, Shveykin AI, Nechaeva ES, Volegov PS (2012) Multilevel models of inelastic deformation of materials and their application for description of internal structure evolution. Phys Mesomech 15(3–4): 155–175

    Article  Google Scholar 

  • Trusov PV, Volegov PS, Shveykin AI (2013) Multilevel model of inelastic deformation of FCC polycrystalline with description of structure evolution. Comput Mater Sci 79:429–441

    Article  Google Scholar 

  • Trusov PV, Shveykin AI, Yanz A Yu (2016) About motion decomposition, frame independent derivatives and constitutive relations from the view point of a multilevel modeling. Phys Mesomech 19(2):47–65 (in Russian)

    Article  Google Scholar 

  • Turteltaub S, Suiker ASJ (2006) A multiscale thermomechanical model for cubic to tetragonal martensitic phase transformations. Int J Solids Struct 43:4509–4545

    Article  MATH  Google Scholar 

  • van Houtte P (2009) Crystal plasticity based modelling of deformation textures. In: Haldar A, Suwas S, Bhattacharjee D (eds) Microstructure and texture in steels. Springer-Verlag, London, pp 209–224

    Chapter  Google Scholar 

  • van Houtte P, Li S, Seefeldt M, Delannay L (2005) Deformation texture prediction: from the Taylor model to the advanced Lamel model. Int J Plast 21:589–624

    Article  MATH  Google Scholar 

  • Wagner F, Canova G, Van Houtte P, Molinari A (1991) Comparison of simulated and experimental deformation textures for BCC metals. Textures Microstruct 14–18: 1135–1140

    Article  Google Scholar 

  • Wang Y, Chen L-Q, Khachaturyan AG (1993) Kinetics of straininduced morphological transformation in cubic alloys with a miscibility gap. Acta Metall Mater 41(1): 279–296

    Article  Google Scholar 

  • Weng GJ (1980) Dislocation theories of work hardening and yield surfaces of single crystals. Acta Mech 37 (3–4):217–230

    Article  MathSciNet  MATH  Google Scholar 

  • Winterbone D, Turan A (2015) Advanced thermodynamics for engineers, 2nd edn. Butterworth-Heinemann Elsevier Ltd, Oxford, United Kingdom

    Google Scholar 

  • Yadegari S, Turteltaub S, Suiker ASJ (2012) Coupled thermomechanical analysis of transformation-induced plasticity in multiphase steels. Mech Mater 53:1–14

    Article  Google Scholar 

  • Yamanaka A, Takaki T, Tomita Y (2010) Elastoplastic phase-field simulation of martensitic transformation with plastic deformation in polycrystal. Int J Mech Sci 52:245–250

    Article  Google Scholar 

  • Yeremeyev VA, Freidin AB, Sharipova LL (2007) The stability of the equilibrium of two-phase elastic solids. J Appl Math Mech 71:61–84

    Article  MathSciNet  Google Scholar 

  • Zhao J, Sheng D (2006) Strain gradient plasticity by internal-variable approach with normality structure. Int J Solids Struct 43:5836–5850

    Article  MATH  Google Scholar 

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Trusov, P., Shveykin, A., Kondratev, N., Makarevich, E. (2018). Thermomechanical Processing of Steels and Alloys: Multilevel Modeling. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_145-1

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  • DOI: https://doi.org/10.1007/978-3-662-53605-6_145-1

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