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.
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Notes
- 1.
The general form of the transformation stretch for an orthorhombic to monoclinic transformation is given in [8, Theorem 2.10(4)]. In general one can make a linear transformation of variables in the reference configuration which turns the corresponding energy wells into the form (1). However, in [4, Sect. 4.1] and the announcement of the results of the present paper in [5] it was incorrectly implied that the analysis based on K as in (1) applies to a general orthorhombic to monoclinic transformation. This is not the case because the linear transformation in the reference configuration changes the deformation gradient corresponding to austenite in [4] and to the rotated grain in the present paper. A more general, but feasible, analysis would be needed to cover the case of general orthorhombic to monoclinic transformations.
- 2.
For an explanation of gradient Young measures and how they can be used to represent possibly infinitely fine microstructures see, for example, [2].
- 3.
This extra condition, typically satisfied in practice, was accidentally omitted in the announcement in [5].
References
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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.
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Ball, J.M., Carstensen, C. (2018). Interaction of Martensitic Microstructures in Adjacent Grains. In: Stebner, A., Olson, G. (eds) Proceedings of the International Conference on Martensitic Transformations: Chicago. The Minerals, Metals & Materials Series. Springer, Cham. https://doi.org/10.1007/978-3-319-76968-4_5
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