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 (1-D) 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 twinned structures, although we have determined that the dominant route for the formation of martensite is through 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, viz., dynamical twinning and so-called two-kink solutions. These transformation fronts are separated by a dynamical phase transition. We analytically derive this phase diagram and determine expressions for the speeds of the martensitic growth fronts.