This paper applies the stability theory of crystalline solids presented in the companion paper (Part I) to the study of martensitic transformations found in shape memory alloys (SMA's). The focus here is on temperature-induced martensitic transformations of bi-atomic crystals under stress-free loading conditions. A set of temperature-dependent atomic potentials and a multilattice description are employed to derive the energy density of a prototypical SMA (B2 cubic austenite crystal). The bifurcation and stability behavior are then investigated with respect to two stability criteria (Cauchy-Born (CB) and phonon). Using a 4-lattice description five different equilibrium crystal structures are predicted: B2 cubic, L10 tetragonal, B19 orthorhombic, Cmmm orthorhombic, and B19′ monoclinic. For our chosen model only the B2 and B19 equilibrium paths have stable segments which satisfy both the CB- and phonon-stability criteria. These stable segments overlap in temperature indicating the possibility of a hysteretic temperature-induced proper martensitic transformation. The B2 and B19 crystal structures are common in SMA's and therefore the simulated jump in the deformation gradient at a temperature for which both crystals are stable is compared to experimental values for NiTi, AuCd, and CuAlNi. Good agreement is found for the two SMA's which have cubic to orthorhombic transformations (AuCd and CuAlNi).
Bibliographical noteFunding Information:
This work was supported by the National Science Foundation grant CMS 0409084 (Dr. Ken Chong, Program Director), the Department of Energy Computational Science Graduate Fellowship Program of the Office of Scientific Computing and Office of Defense Programs in the Department of Energy under contract DE-FG02-97ER25308 (for R. Elliott), and a CAREER grant from the National Science Foundation (for J. Shaw).
- Asymptotic analysis
- Finite strain
- Phase transformation
- Stability and bifurcation