Skip to main content
SpringerLink
Log in

An Improved Finite Element Model for Numerical Simulation of Phase Changes of Iron Under Extreme Conditions

  • Chapter
  • First Online:
Numerical Modeling of Materials Under Extreme Conditions

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 35))

  • 1316 Accesses

Abstract

In this chapter an improved finite element model for numerical simulation of phase changes of iron is presented, which is capable of simulating iron construction behaviour under extreme conditions that include large strains/large deformations at high strain rates and temperatures. The model is based on an improved variational formulation of the conservation of energy with convective heat transfer. It employs the updated Lagrangian formulation and uses the extended NoIHKH material model for cyclic plasticity of metals. It also uses the Kelvin–Voigt model for internal damping, the Jaumann objective rate in the Cauchy’s stress update calculation and simplified rate forms of the Mehl-Avrami and Koisten-Marburger equations for ferrite, pearlite, bainite, martensite and the retaining austenite phase calculation. A numerical experiment using a cooled bar in cyclic bending is presented and briefly discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Skrzypek, J.J., Ganczarski, A.W., Rustichelli, F., Egner, H.: Advanced Materials and Structures for Extreme Operating Conditions. Springer, Berlin (2008)

    Google Scholar 

  2. Maugin, G.A.: The Thermomechanics of Plasticity and Fracture. Cambridge University Press, Cambridge (1992)

    Book  Google Scholar 

  3. Šilhavý, M.: The Mechanics and Thermodynamics of Continuous Media. Springer, Berlin (1997)

    Google Scholar 

  4. Müller, I.: Thermodynamics. Pitman Publishing LTD, London (1985)

    Google Scholar 

  5. Haupt, P.: Continuum Mechanics and Theory of Materials, 2nd edn. Springer, Berlin (2002)

    Book  Google Scholar 

  6. Holzapfel, G.A.: Nonlinear Solid Mechanics. A Continuum Approach for Engineering. Wiley, Chichester (2001)

    Google Scholar 

  7. Liu, W.K.: Development of mixed time partition procedures for thermal analysis of structures. Int. J. Num. Meth. Eng. 19, 125–140 (1983)

    Article  Google Scholar 

  8. Ray, S.K., Utku, S.: A numerical model for the thermo-elasto-plastic behaviour of a material. Int. J. Num. Meth. Eng. 28, 1103–1114 (1989)

    Article  Google Scholar 

  9. Kleiber, M.: Computational coupled non-associative thermo-plasticity. Comput. Meth. Appl. Mech. Eng. 90, 943–967 (1991)

    Article  Google Scholar 

  10. Simo, J.C., Miehe, C.: Associative coupled thermoplasticity at finite strains: Formulation, numerical analysis and implementation. Comput. Meth. Appl. Mech. Eng. 98, 41–104 (1992)

    Article  Google Scholar 

  11. Služalec, A.: Temperature rise in elastic-plastic metal. Comput. Meth. Appl. Mech. Eng. 96, 293–302 (1992)

    Article  Google Scholar 

  12. Huang, Z.P.: Arate independent thermoplastic theory at finite deformations. Arch. Mech. 46(6), 855–879 (1994)

    Google Scholar 

  13. Pantuso, D., Bathe, K.J., Bouzinov, P.A.: A finite element procedure for the analysis of thermo-mechanical solids in contact. Comput. Struct. 75, 551–573 (2000)

    Article  Google Scholar 

  14. Batra, R.C., Love, B.M.: Mesoscale analysis of shear bands in high strain rate deformations of tungsten/nickel-iron composites. J. Therm. Stresses 28, 747–782 (2005)

    Article  Google Scholar 

  15. Maugin, A.G., Berezovski, A.: On the propagation of singular surfaces in thermoelasticity. J. Therm. Stresses 32, 557–592 (2009)

    Article  Google Scholar 

  16. Služalec, A.: An evaluation of the internal dissipation factor in coupled thermoplasticity. Int. J. Non-Lin. Mech. 25(4), 395–403 (1990)

    Article  Google Scholar 

  17. Dillon Jr, O.W.: Coupled thermoplasticity. J. Mech. Phys. Solids 11, 21–33 (1963)

    Article  Google Scholar 

  18. Saracibar, C.A., Cervena, M., Chiumenti, M.: On the constitutive modeling of coupled thermomechanical phase-change problems. Int. J. Plast. 17, 1565–1622 (2001)

    Article  Google Scholar 

  19. Júnior, M.V: Computational approaches to simulation of metal cutting processes. Thesis, University of Wales. Swansea (1998)

    Google Scholar 

  20. Schönauer, M.: Unified numerical analysis of cold and hot metal forming processes. Thesis, University of Wales, Swansea (1993)

    Google Scholar 

  21. Oden, T.J.: Finite Elements of Nonlinear Continua. McGraw-Hill, New York (1972)

    Google Scholar 

  22. Lemaitre, J., Chaboche, J.L.: Mechanics of Solid Materials. Cambridge University Press, Cambridge (1994)

    Google Scholar 

  23. Ibrahimbegovic, A.: Nonlinear Solid Mechanics. Theoretical Formulations and Finite Element Solution Methods. Springer, Dordrecht (2009)

    Google Scholar 

  24. Écsi, L., Élesztős, P.: Constitutive equation with internal damping for materials under cyclic and dynamic loadings using a fully coupled thermal-structural finite element analysis. Int. J. Multiphys. 3(2), 155–165 (2009)

    Article  Google Scholar 

  25. Porter, D.A., Easterling, K.E.: Phase Transformations in Metals and Alloys, 2nd edn. Chapman & Hall, London (1992)

    Book  Google Scholar 

  26. Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Springer, New York (1998)

    Google Scholar 

  27. Nemat-Nasser, S.: Plasticity. A Treatsie on Finite Deformation of Heterogenous Inelastic Materials. Cambridge University Press, Cambridge (2009)

    Google Scholar 

  28. Lemaitre, J.: Handbook of Material Behavior Models. Deformations of Materials, vol. 1. Academic Press, London (2001)

    Google Scholar 

  29. Lemaitre, J.: Handbook of Material Behavior Models. Failures of Materials, vol. 2. Academic Press, London (2001)

    Google Scholar 

  30. Lemaitre, J.: Handbook of Material Behavior Models. Multiphysics Behaviors, vol. 3. Academic Press, London (2001)

    Google Scholar 

  31. Suresh, S.: Fatigue of Materials, 2nd edn. Cambridge University Press, Cambridge (1998)

    Book  Google Scholar 

  32. Lemaitre, J.: A Course on Damage Mechanics. Springer, Berlin (1992)

    Book  Google Scholar 

  33. Needleman, A., Tvergaard, V.: Analysis of a brittle-ductile transition under dynamic shear loading. Int. J. Solids Struct. 32(17–18), 2571–2590 (1995)

    Article  Google Scholar 

  34. Zhou, M., Ravichandran, G., Rosakis, A.J.: Dynamically propagating shear bands in impact-loaded prenotched plates—II. Numerical simulations. J. Mech. Phys. Solids 44(6), 1007–1032 (1996)

    Article  Google Scholar 

  35. Li, S., Liu, W.K., Rosakis, A.J., Belytschko, T., Hao, V.: Mesh-Free Galerkin simulations of dynamic shear band propagation and failure mode transition. Int. J. Solids Struct. 39, 1213–1240 (2002)

    Article  Google Scholar 

  36. Liang, R., Khan, A.S.: A critical review of experimental results and constitutive models for BCC and FCC metals over wide range of strain rates and temperatures. Int. J. Plast. 15, 963–980 (1999)

    Article  Google Scholar 

  37. Caboche, J.L.: A review of some plasticity and viscoplasticity constitutive theories. Int. J. Plast. 24, 1642–1693 (2008)

    Article  Google Scholar 

  38. Rusinek, A., Rodríguez-Martínez, J.A., Arias, A.: A thermo-viscoplastic model for FCC metals with application to OFHC copper. Int. J. Mech. Sci. 52, 120–135 (2010)

    Article  Google Scholar 

  39. Holmquist, T.J., Templeton, D.W., Bishnoi, K.D.: Constitutive modelling of aluminium nitride for large strain high-strain rate, and high-pressure applications. Int. J. Impact Eng. 25, 211–231 (2001)

    Article  Google Scholar 

  40. Rodríguez-Martínez, J.A., Rusinek, A., Klepaczko, J.R.: Constitutive relation for steels approximating quasi-static and intermediate strain rates at large deformations. Mech. Res. Commun. 36, 419–427 (2009)

    Article  Google Scholar 

  41. Yu, H., Guo, Y., Zhang, K., Lai, X.: Constitutive model on the description of plastic behavior of DP600 steel at strain rate from 10−4 to 103 s−1. Comput. Mater. Sci. 46, 36–41 (2009)

    Article  Google Scholar 

  42. Rusinek, A., Zaera, R., Klepaczko, J.R.: Constitutive relation in 3-D for wide range of strain rates and temperatures-application to mild steels. Int. J. Solid. Struct. 44, 5611–5634 (2007)

    Article  Google Scholar 

  43. Yu, H., Guo, Y., Lai, X.: Rate-dependent behavior and constitutive model of DP600 steel at strain rate from 10−4 to 103 s−1. Mater. Des. 30, 2501–2505 (2009)

    Article  Google Scholar 

  44. Yin, Z.N., Wang, T.J.: Deformation of PC/ABS alloys at elevated temperatures and high strain rates. Mat. Sci. Eng. A 494, 304–313 (2008)

    Article  Google Scholar 

  45. Deseri, L., Mares, R.: A class of viscoelastoplastic constitutive models based on the maximum dissipation principle. Mech. Mater. 32, 389–403 (2000)

    Article  Google Scholar 

  46. Ramrakhyani, D.S., Lesieutre, G.A., Smith, E.C.: Modeling of elastomeric materials using nonlinear fractional derivative and continuously yielding friction elements. Int. J. Solids Struct. 41, 3929–3948 (2004)

    Article  Google Scholar 

  47. Naumenko, K., Altenbach, H.: Modeling of Creep for Structural Analysis. Springer, Berlin (2007)

    Book  Google Scholar 

  48. Hyde, T.H., Sun, W., Wiliams, J.A.: Prediction of creep failure life of initially pressurized thick walled CrMoV pipes. Int. J. Press Vessels Pip. 76, 925–933 (1999)

    Article  Google Scholar 

  49. Staroselsky, A., Cassenti, B.N.: Combined rate-independent plasticity and creep model for single crystal. Mech Mater. 42, 945–959 (2010)

    Article  Google Scholar 

  50. Aktaa, J., Petersen, C.: Challenges in the constitutive modelling of the thermo-mechanical deformation and damage behaviour of EUROFER 97. Eng. Fract. Mech. 76, 1474–1484 (2009)

    Article  Google Scholar 

  51. Saleeb, A.F., Padula II, S.A., Kumar, A.: A multi-axial, multimechanism based constitutive model for the comprehensive representation of evolutionary response of SMAs under general thermomechanical loading conditions. Int. J. Plast. 27, 655–687 (2011)

    Article  Google Scholar 

  52. Auricchio, F., Taylor, R.L., Lubliner, J.: Shape-memory alloys: macromodelling and numerical simulations of the superelastic behaviour. Comput. Methods Appl. Mech. Eng. 146, 281–312 (1997)

    Article  Google Scholar 

  53. Dan, W.J., Zhang, W.G., Li, S.H., Lin, Z.Q.: A model for strain-induced martensitic transformation of TRIP steel with strain rate. Comput. Mater. Sci. 40, 101–107 (2007)

    Article  Google Scholar 

  54. Lee, M.G., Kim, S.J., Han, H.N., Jeong, WCh.: Implicit finite element formulations for multi-phase transformation in high carbon steel. Int. J. Plast. 25, 1720–1758 (2009)

    Google Scholar 

  55. Lee, M.G., Kim, S.J., Han, H.N., Jeong, WCh.: Implicit finite element formulations for multi-phase transformation in high carbon steel. Int. J. Plast. 25, 1720–1758 (2009)

    Google Scholar 

  56. Field, J.E., Walley, S.M., Proud, W.G., Goldrein, H.T., Siviour, C.R.: Review of experimental techniques for high rate deformation and shock studies. Int. J. Impact. Eng. 30, 725–775 (2004)

    Article  Google Scholar 

  57. Das, A., Tarafder, S.: Experimental investigation on martensitic transformation and fracture morphologies of austenitic stainless steel. Int. J. Plast. 25, 2222–2247 (2009)

    Article  Google Scholar 

  58. Sedighi, M., Khandaei, M., Shokrollahi, H.: An approach in parametric identification of high strain rate constitutive model using Hopkinson pressure bar test results. Mater. Sci. Eng. A 527, 3521–3528 (2010)

    Article  Google Scholar 

  59. Crisfield, M.A.: Non-linear Finite Element Analysis of Solids and Structures. Advanced Topics, vol. 2. Wiley, Chichester (2001)

    Google Scholar 

  60. Bathe, K.J., Kojić, M.: Inelastic Analysis of Solids and Structures. Springer, Berlin (2005)

    Google Scholar 

  61. Wriggers, P.: Nonlinear Finite Element Methods. Springer, Berlin (2008)

    Google Scholar 

  62. Evans, L.C.: Partial Differential Equations, American Mathematical Society. Providence. Rhode Island (1998)

    Google Scholar 

  63. Rektorys, K.: Variační metody v inženýrských problémech a v problémech matematické fyziky. Academia, Praha (1999)

    Google Scholar 

  64. Bathe, K.J.: Finite Element Procedures in Engineering Analysis. Prentice-Hall Inc., Englewood Cliffs (1982)

    Google Scholar 

  65. Howell, J.R.: A catalog of radiation configuration factors. McGraw-Hill, New York (1976)

    Google Scholar 

  66. Écsi, L.: Numerical behaviour of a solid body under various mechanical loads using finite element method with new energy balance equation for fully coupled thermal-structural analysis. In: Proceedings of the Sixth International Congress on Thermal Stresses 2005, vol. 2, pp. 543–546. Technische Universität Wien, Wien (2005). ISBN 3-901167-12

    Google Scholar 

  67. Écsi, L, Élesztős, P.: Hysteretic heating of a solid bar using a universal constitutive equation with internal damping for fully coupled thermal-structural finite element analysis. In: Proceedings of the 8th International Congress Thermal Stresses 2009, vol. 1, pp. 233–236. University of Illinois Press, Illinois (2009). ISBN 978-0-615-28233-6

    Google Scholar 

  68. Écsi, L, Élesztős, P.: Trying to model the thermo-mechanical behaviour of a solid body under cyclic loading using a material model with internal damping. Acta Mechanica Slovaca Roč 12(3-B), 143–150 (2008)

    Google Scholar 

  69. Écsi, L, Élesztős, P.: One of the possible variational formulations of fully coupled thermal-structural analysis. J. Mech. Eng. Roč 60(3), 135–144 (2009)

    Google Scholar 

  70. Oden, T.J., Carey, F.G.: Finite Elements. A Second Course, vol. 2. Prentice-Hall Inc., Englewood Cliffs (1983)

    Google Scholar 

  71. Oden, T.J., Carey, F.G.: Finite Elements, Mathematical Aspects, vol. 4. Prentice-Hall Inc., Englewood Cliffs (1983)

    Google Scholar 

  72. Grutin, M.E.: The linear theory of elasticity. In: Flügge, S., Thruesdell, C. (eds.) Handbuch der Physic. VIa/2, pp. 1–295. Springer, New York (1972)

    Google Scholar 

  73. Oden, T.J.: Applied Functional Analysis. Prentice Hall, Englewood Cliffs (1979)

    Google Scholar 

  74. Reddy, B.D.: Introductory Functional Analysis. Springer, Berlin (1998)

    Book  Google Scholar 

  75. Sun, C.T., Lu, J.P.: Vibration Damping of Structural Elements. Prentice Hall PTR, Englewood Clifs (1995)

    Google Scholar 

  76. Asszonyi, Csl, et al.: Izotrop kontinuumok anyagtulajdonságai. Műegyetemi kiadó, Budapest (2008)

    Google Scholar 

  77. Mesquita, A.D., Coda, H.B.: Alternative Kelvin viscoelastic procedure for finite elements. Appl. Math. Model. 26, 501–516 (2002)

    Article  Google Scholar 

  78. Argiris, J., Mlejnek, H.P.: Dynamics of Structures. Elsevier Science Publishers, Amsterdam (1991)

    Google Scholar 

  79. Bathe, K.J.: Finite Element Procedures. Prentice-Hall Inc., Englewood Cliffs (1995)

    Google Scholar 

  80. Lee, U.: Spectral Element Method in Structural Dynamics. John Wiley & Sons Pte Ltd., Singapore (2009)

    Book  Google Scholar 

  81. Liu, M., Gorman, D.G.: Formulation of Rayleigh damping and its extensions. Comput. Struct. 57(2), 277–285 (1995)

    Article  Google Scholar 

  82. Belytschko, T., Liu, W.K., Moran, B.: Nonlinear finite elements for continua and structures. Wiley, Chichester (2000)

    Google Scholar 

  83. Écsi, L., Élesztős, P., Kosnáč, J.: Constitutive equation with internal damping for materials under cyclic and dynamic loadings using large strain/large deformation formulation. In: Proceedings of the International Conference on Computational Modelling and Advanced Simulations 2009, Bratislava, Slovak Republic (2009)

    Google Scholar 

  84. de Souza Neto, E.A., Perić, D., Owen, D.R.J.: Computational Methods for Plasticity. Theory and Applications. John Wiley & Sons Ltd., Singapore (2008)

    Book  Google Scholar 

  85. Bonet, J., Wood, R.D.: Nonlinear Continuum Mechanics for Finite Element Analysis. Cambridge University Press, Cambridge (1997)

    Google Scholar 

  86. Écsi, L.: Extended NOIHKH model usage for cyclic plasticity of metals. Eng. Mech. Roč 13(2), 83–92

    Google Scholar 

  87. Crisfield, M.A.: Non-linear Finite Element Analysis of Solids and Structures. Essentials, vol. 1. Wiley, Chichester (2000)

    Google Scholar 

  88. Trebuňa, F., Šimčák, F.: Príručka experimentálnej mechaniky. Edícia vedeckej a odbornej literatúry. TypoPress, Košice (2007)

    Google Scholar 

  89. Budó, Á.: Kísérleti fizika I. Nemzeti tankönyvkiadó, Budapest (1997)

    Google Scholar 

  90. Klepazko, J.R., Rusinek, A.: Experiments on heat generation during plastic deformation and stored energy for TRIP steels. Mater. Des. 30, 35–48 (2009)

    Article  Google Scholar 

  91. Johnson, W.A., Mehl, R.F.: Reaction kinetics in processes of nucleation and growth. Trans. AIME 135, 416–458 (1939)

    Google Scholar 

  92. Avrami, M.: Kinetics of phase change I. J. Chem. Phys. 7, 1103–1112 (1939)

    Article  Google Scholar 

  93. Koistinen, D.P., Marburger, R.E.: A general equation prescribing the extent of the austenite-martensite transformation in pure iron-carbon alloys and carbon steels. Acta Metall. 7, 59–60 (1959)

    Article  Google Scholar 

  94. Lee, M.G., Kim, S.J., Han, H.N., Jeong, WCh.: Implicit finite element formulations for multi-phase transformation in high carbon steel. Int. J. Plast. 25, 1726–1758 (2009)

    Article  Google Scholar 

  95. Kang, S.H., Im, Y.T.: Three-dimensional thermo-elastic-plastic finite element modelling of quenching process of plain-carbon steel in couple with phase transformation. Int. J. Mech. Sci. 49, 423–439 (2007)

    Article  Google Scholar 

  96. Ronda, J., Oliver, G.J.: Consistent thermo-mechano-metallurgical model of welded steel with unified approach to derivation of phase evolution laws and transformation induced plasticity. Comput. Methods. Appl. Mech. Eng. 189, 361–417 (2000)

    Article  Google Scholar 

  97. Hömberg, D.: A numerical simulation of the Jominy end-quench test. Acta Matter. 44(11), 4375–4385 (1996)

    Article  Google Scholar 

Download references

Acknowledgments

Funding using the VEGA grant 1/0488/09 and 1/0051/10 resources is greatly appreciated.

Author information

Authors and Affiliations

  1. Faculty of Mechanical Engineering, Slovak University of Technology in Bratislava, Námestie Slobody 17, 812 31, Bratislava, Slovakia

    Ladislav Écsi, Pavel Élesztős & Kinga Balázsová

Authors
  1. Ladislav Écsi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pavel Élesztős
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kinga Balázsová
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ladislav Écsi .

Editor information

Editors and Affiliations

  1. DICEM - Dipartimento di Ingegneria Civile e Meccanica, University of Cassino and Southern Lazio, Cassino, Italy

    Nicola Bonora

  2. Los Alamos National Laboratory, Los Alamos, USA

    Eric Brown

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Écsi, L., Élesztős, P., Balázsová, K. (2014). An Improved Finite Element Model for Numerical Simulation of Phase Changes of Iron Under Extreme Conditions. In: Bonora, N., Brown, E. (eds) Numerical Modeling of Materials Under Extreme Conditions. Advanced Structured Materials, vol 35. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54258-9_8

Download citation

Publish with us

Policies and ethics

Search

Navigation