Interaction of Martensitic Microstructures in Adjacent Grains

  • John M. BallEmail author
  • Carsten Carstensen
Conference paper
Part of the The Minerals, Metals & Materials Series book series (MMMS)


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.


Bicrystal Compatibility Grain boundary Hadamard jump condition 



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.


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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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