We study the branching of twins appearing in shape memory alloys at the interface between austenite and martensite. In the framework of three-dimensional non-linear elasticity theory, we propose an explicit, low-energy construction of the branched microstructure, generally applicable to any shape memory material without restrictions on the symmetry class of martensite or on the geometric parameters of the interface. We show that the suggested construction follows the expected energy scaling law, i.e., that (for the surface energy of the twins being sufficiently small) the branching leads to energy reduction. Furthermore, the construction can be modified to capture different features of experimentally observed microstructures without violating this scaling law. By using a numerical procedure, we demonstrate that the proposed construction is able to predict realistically the twin width in a Cu-Al-Ni single crystal and to estimate an upper bound to the number of the branching generations.
Bibliographical noteFunding Information:
H.S. and B.B. acknowledge financial support from the Czech Science Foundation [grant no. 18-03834S ]. H.S. further thanks J. William Fulbright Commission (Prague) and the Ministry of Education, Youth and Sports of the Czech Republic, grant program INTER-EXCELLENCE/INTER-ACTION [grant No. LTAUSA18199]. PP thanks the MURI program ( FA9550- 16-1-0566 ) for support. RDJ benefited from the support of NSF ( DMREF-1629026 ), ONR ( N00014-18-1-2766 ), MURI ( FA9550-18-1-0095 ), the Medtronic Corp. and a Vannevar Bush Faculty Fellowship.
© 2020 Elsevier Ltd
- Martensitic microstructures
- Non-linear elasticity
- Shape memory alloys