Interaction of Martensitic Microstructures in Adjacent Grains

Conference paper
Part of the The Minerals, Metals & Materials Series book series (MMMS)

Abstract

It is often observed that martensitic microstructures in adjacent polycrystal grains are related. For example, micrographs of Arlt (J Mat Sci 22:2655–2666, 1990) [1] (one reproduced in (Bhattacharya, Microstructure of martensite, 2003) [10, p 225]) exhibit propagation of layered structures across grain boundaries in the cubic-to-tetragonal phase transformation in \( {\text{BaTiO}}_{3} \). Such observations are related to requirements of compatibility of the deformation at the grain boundary. Using a generalization of the Hadamard jump condition, this is explored in the nonlinear elasticity model of martensitic transformations for the case of a bicrystal with suitably oriented columnar geometry, in which the microstructure in both grains is assumed to involve just two martensitic variants, with a planar or non-planar interface between the grains.

Keywords

Bicrystal Compatibility Grain boundary Hadamard jump condition 

Notes

Acknowledgements

The research of JMB was supported by the EU (TMR contract FMRX - CT EU98-0229 and ERBSCI**CT000670), by EPSRC (GRlJ03466, EP/E035027/1, and EP/J014494/1), the ERC under the EU’s Seventh Framework Programme (FP7/2007–2013) / ERC grant agreement no 291053 and by a Royal Society Wolfson Research Merit Award.

References

  1. 1.
    Arlt G (1990) Twinning in ferroelectric and ferroelastic ceramics: stress relief. J Mat Sci 22:2655–2666CrossRefGoogle Scholar
  2. 2.
    Ball JM (2004) Mathematical models of martensitic microstructure. Mater Sci Eng A 78(1–2):61–69CrossRefGoogle Scholar
  3. 3.
    Ball JM, Carstensen C Hadamard’s compatibility condition for microstructures (In preparation)Google Scholar
  4. 4.
    Ball JM, Carstensen C (1999) Compatibility conditions for microstructures and the austenite-martensite transition. Mater Sci Eng A 273–275:231–236CrossRefGoogle Scholar
  5. 5.
    Ball JM, Carstensen C (2015) Geometry of polycrystals and microstructure. MATEC Web Conf 33:02007CrossRefGoogle Scholar
  6. 6.
    Ball JM, James RD (1987) Fine phase mixtures as minimizers of energy. Arch Ration Mech Anal 100:13–52CrossRefGoogle Scholar
  7. 7.
    Ball JM, James RD (1991) A characterization of plane strain. Proc Roy Soc London A 432:93–99CrossRefGoogle Scholar
  8. 8.
    Ball JM, James RD (1992) Proposed experimental tests of a theory of fine microstructure, and the two-well problem. Phil Trans Roy Soc London A 338:389–450CrossRefGoogle Scholar
  9. 9.
    Bhattacharya K (1992) Self-accommodation in martensite. Arch Ration Mech Anal 120:201–244CrossRefGoogle Scholar
  10. 10.
    Bhattacharya K (2003) Microstructure of martensite, Oxford University PressGoogle Scholar
  11. 11.
    Bhattacharya K, Kohn RV (1997) Elastic energy minimization and the recoverable strain of polycrystalline shape-memory materials. Arch Ration Mech Anal 139:99–180CrossRefGoogle Scholar
  12. 12.
    Khachaturyan AG (1983) Theory of structural transformations in solids, WileyGoogle Scholar
  13. 13.
    Mardare S Personal communicationGoogle Scholar

Copyright information

© The Minerals, Metals & Materials Society 2018

Authors and Affiliations

  1. 1.Mathematical Institute, University of OxfordOxfordUK
  2. 2.Department of MathematicsHumboldt-Universität Zu BerlinBerlinGermany

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