The nucleation of Martensite in shape memory alloy under stress always physically sets in before the spinodal is reached, i.e. in the metastable region. Mathematically, it means that there may exist three kinds of strain solution in the region: the austenite only solution, austenite and transition solution and three-zone solution. The three-zone solution has the lowest energy, which means that the material will overcome a certain energy barrier and transform. In this thesis, a new phenomenon-based mathematical model is established to study the nucleation pattern by the nonlinear and non-local continuum theory....[ Read more ]

The nucleation of Martensite in shape memory alloy under stress always physically sets in before the spinodal is reached, i.e. in the metastable region. Mathematically, it means that there may exist three kinds of strain solution in the region: the austenite only solution, austenite and transition solution and three-zone solution. The three-zone solution has the lowest energy, which means that the material will overcome a certain energy barrier and transform. In this thesis, a new phenomenon-based mathematical model is established to study the nucleation pattern by the nonlinear and non-local continuum theory.

We first study the nucleation pattern based on 1-D strain gradient theory, and the result shows that the nucleation process is size dependent. Namely, depending on the length, the material may transform from homogeneous mode to progressive necking mode to suddenly necking mode. Furthermore, the surface energy and the interface thickness are studied in detail, which clearly reveals that they depend on the softening modulus and the strain gradient coefficient.

Further, in order to consider the 2-D coupling effect, a simple two-well energy potential is constructed for the axial symmetry 2-D problem, which is composed of two paraboloids and a saddle. Here it is clear that the soft mode corresponds to the so-called Zener one. In this model, both the rotation gradients and the stretch gradients are considered for the specific axial symmetric problem. And the simple stability analysis shows that it can explain the experimental result qualitatively. Finally, the phase transformation in a circular plate under radial stretching is studied.

Key words: metastable, nucleation, two-well energy potential, axial symmetry.