Elastic and plastic aspects of martensitic transformations

Abstract

Elastic and plastic aspects of martensitic transformations are discussed using the topological model. Here the interface comprises an array of transformation dislocations (disconnections) and dislocations (slip/twinning) superposed on coherently strained terraces. Plastic transformation strain arises by virtue of the conservative motion of the defect array, and is quantified directly in terms of the Burgers vectors of the defects. Superposition of the elastic fields of the defects and the coherency strain produces a short-range interfacial distortion field, but only rigid rotation, φ, of the phases at long-range. Furthermore, the treatment shows that, for elastically isotropic phases with similar moduli, elastic relaxations cause the habit plane to differ by φ/2 from the classical predictions where such relaxations are suppressed. A nonlinear analysis is presented suitable for instances of large values of φ. However, the plastic transformation strain, in combination with the relative orientation, φ, corresponds to the classically predicted shape deformation.

Keywords:

• martensitic transformations
• plastic strain
• elastic strain
• shape deformation
• habit plane

Acknowledgements

It was a privilege to contribute to the symposium celebrating David Bacon's outstanding career. One of us (RCP) worked with David for over thirty years at the University of Liverpool. During that period David was not only a foremost academic but also a supportive colleague and excellent administrator.

We are pleased to acknowledge that the nonlinear treatment presented here was stimulated by a long interchange with P.M. Kelly.