Self-accommodation of B19′ martensite in Ti–Ni shape memory alloys. Part III. Analysis of habit plane variant clusters by the geometrically nonlinear theory

Abstract

Competition between the invariant plane (IP) condition at the habit plane, the twin orientation relation (OR) and the kinematic compatibility (KC) at the junction plane (JP) of self-accommodated B19′ martensite in Ti–Ni was investigated via the geometrically nonlinear theory to understand the habit plane variant (HPV) clusters presented in Parts I and II of this work. As the IP condition cannot be satisfied simultaneously with KC, an additional rotation Q is necessary to form compatible JPs for all HPV pairs. The rotation J necessary to form the exact twin OR between the major correspondence variants (CVs) in each HPV was also examined. The observed HPV cluster was not the cluster with the smallest Q but the one satisfying Q = J with a {1}_B19′ type I twin at JP. Both Q and J are crucial to understanding the various HPV clusters in realistic transformations. Finally, a scheme for the ideal HPV cluster composed of six HPVs is also proposed.

Keywords:

• geometrically non-linear theory
• self-accommodation
• martensitic transformations
• crystallography
• Ni–Ti alloys

Acknowledgements

This work was supported by the Global COE program of the Ministry of Education, Culture, Sports, Science and Technology, Japan. This work was also partially supported by the Advanced Low Carbon Technology Research and Development Program (JY220218) of the Japan Science and Technology Agency, the Funding Program for Next Generation World-Leading Researchers (LR015) and a Grant-in-Aid for Scientific Research (B) (No. 20360291) from the Japan Society for the Promotion of Science.