A Comprehensive Dynamical Study of Nucleation and Growth in a One--Dimensional Shear Martensitic Transition

We have constructed a complete hydrodynamic theory of nucleation and growth in a one--dimensional version of an elastic shear martensitic transformation with open boundary conditions where we have accounted for interfacial energies with strain--gradient contributions. We have studied the critical martensitic nuclei for this problem: Interestingly, the bulk critical nuclei are {\em twinned} structures, although we have determined that the dominant route for the formation of martensite is through {\em surface nucleation}. We have analytically solved for the surface nuclei and evaluated exact nucleation rates showing the strong preference for surface nucleation. We have also examined the growth of martensite: There are two possible martensitic growth fronts, {\em viz}., dynamical twinning and so-called two--kink solutions. These transformation fronts are separated by a {\em dynamical} phase transition. We analytically derive this phase diagram and determine expressions for the speeds of the martensitic growth fronts.