Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

Elastically induced pattern formation in the initial and frustrated growth regime of bainitic subunits

1 Institut für Energie- und Klimaforschung IEK-2, Forschungszentrum Jülich, D-52425 Jülich, Germany
2 Metals and Alloys, University Bayreuth, Ludwig-Thoma-Strae 36b, 95447 Bayreuth, Germany
3 Jülich Aachen Reseach Alliance Energy, RWTH Aachen University, D-52056 Aachen, Germany

We present analytical and numerical results for the dominant mechanisms of pattern selection in two growth regimes which are crucial in elastically influenced solid-solid transformations like the bainitic one. The first growth regime comprises the very early regime, when in a nucleation scenario the size of the nucleus is so small that the bulk crystal structure is typically not yet fully developed and the phase is elastically softened. Here we see a dominant effect of curvature effects in analogy to the theory on growth of lenticular melt inclusions. The second growth regime is of specific interest to bainitic steels. During the bainitic reaction subunits form, grow up to a point where the thermodynamic driving force is kinetically overcome by a deformation-induced growth barrier, stop growth and then nucleate new subunits. Thus, the regime prior to the new subunit nucleation corresponds to the limiting case of vanishing growth velocity. For both, analytical and numerical approach, we use sharp interface descriptions of the problem, for the numerical approach we invoke a representation of the problem in terms of boundary integral equations.
  Article Metrics


1. Karbasian H, Tekkaya AE (2010) A review on hot stamping. J Mater Process Tech 210: 2103– 2118.    

2. Feuser P, Schweiker T, Merklein M (2011) Partially hot-formed parts from 22MnB5-process window, material characteristics and component test results. Proceedings of the 10th International Conference on Technology of Plasticity, Aachen, 25–30.

3. Aaronson HI, Rigsbee JM, Trivedi RK (1986) Comments on an overview of the bainite reaction. Scr Metall 20: 1299–1304.    

4. Bhadeshia HKDH, Christian JW (1990) Bainite in steels. Metall Trans A 21: 767–797.    

5. Hillert M (1994) Diffusion in growth of bainite. Metall Mater Trans A 25: 1957–1966.    

6. Speer JG, Edmonds DV, Rizzo FC, et al. (2004) Partitioning of carbon from supersaturated plates of ferrite, with application to steel processing and fundamentals of the bainite transformation. Curr Opin Solid St M 8: 219–237.    

7. Bhadeshia HKDH (2001) Bainite in steels, 2 Eds., London: The Institute of Materials.

8. Hillert M, Hglund L, Agren J (1993) Escape of carbon from ferrite plates in austenite. Acta Metall Mater 41: 1951–1957.    

9. Olson GB, Bhadeshia HKDH, Cohen M (1989) Coupled diffusional/displacive transformations. Acta Metall 37: 381–390.    

10. Olson GB, Bhadeshia HKDH, Cohen M (1990) Coupled diffusional/displacive transformations. Part II. Solute trapping. Metall Trans A 21: 805–809.

11. Mujahid SA, Bhadeshia HKDH (1993) Coupled diffusional/displacive transformations: effect of carbon concentration. Acta Metall Mater 41: 967–973.    

12. Brener EA, Iordanskii SV, Marchenko VI (1999) Elastic effects on the kinetics of a phase transition. Phys Rev Lett 82: 1506.    

13. Steinbach I (2011) Phase-field models in materials science. Model Simul Mater Sc 17: 073001.

14. Chen LQ (2002) Phase-field models for microstructure evolution. Annu Rev Mater Res 32: 113–140.    

15. Fleck M , Hüter C, Pilipenko D, et al. (2010) Pattern formation during diffusion limited transformations in solids. Philos Mag 90: 265–286.    

16. Brener EA, Marchenko VI, Spatschek R (2007) Influence of strain on the kinetics of phase transitions in solids. Phys Rev E 75: 041604.    

17. Spatschek R, Müller-Gugenberger C, Brener EA (2007) Phase field modeling of fracture and stress-induced phase transitions. Phys Rev E 75: 066111.    

18. Brener EA, Boussinot G, Hüter C, et al. (2009) Pattern formation during diffusional transformations in the presence of triple junctions and elastic effects. J Phys-Condens Mat 21: 464106.    

19. Pilipenko D, Brener EA, Hüter C (2008) Theory of dendritic growth in the presence of lattice strain. Phys Rev E 78: 060603.    

20. Fleck M, Brener EA, Spatschek R, et al. (2010) Elastic and plastic effects on solid-state transformations: A phase field study. Int J Mater Res 4: 462–466.

21. Pilipenko D, Fleck M, Emmerich H (2011) On numerical aspects of phase-field fracture modelling. Eur Phys J Plus 126: 100.    

22. Mushongera LT, Fleck M, Kundin J, et al. (2015) Phase-field study of anisotropic $\gamma'$-coarsening kinetics in Ni-base superalloys with varying Re and Ru contents. Adv Eng Mater 17: 1149–1157.    

23. Bouville M, Ahluwalia R (2006) Interplay between diffusive and displacive phase transformations: Time-Temperature-Transformation Diagrams and Microstructures. Phys Rev Lett 97: 055701.    

24. Kassner K, Misbah C (1991) Spontaneous parity-breaking transition in directional growth of lamellar eutectic structures. Phys Rev A 44: 6533.    

25. Echebarria B, Folch R, Karma A, et al. (2004) Quantitative phase-field model of alloy solidification. Phys Rev E 70: 061604.

26. Sneddon IN (1946) The distribution of stress in the neighbourhood of a crack in an elastic solid. Proc R Soc Lond A 187: 229–260.    

27. Herring C (1950) Diffusional viscosity of a polycrystalline solid. J Appl Phys 21: 437–445.    

28. Nozieres P (1993) Amplitude expansion for the Grinfeld instability due to uniaxial stress at a solid surface. J Phys I (France) 3: 681–686.    

29. Brener EA, Marchenko VI (1992) Formation of nucleation centers in a crystal. Sov JETP Lett 56: 368.

30. Mullins WW, Sekerka RF (1963) Morphological stability of a particle growing by diffusion or heat flow. J Appl Phys 35: 323–329.

© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Article outline

Show full outline
Copyright © AIMS Press All Rights Reserved