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 g rowth in a one-dimensional (1-D) version of an elastic shear martensit ic transformation with open boundary conditions, where we have account ed for interfacial energies with strain-gradient contributions. We hav e studied the critical martensitic nuclei for this problem: Interestin gly, 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 surfa ce nuclei and evaluated exact nucleation rates showing the strong pref erence for surface nucleation. We have also examined the growth of mar tensite: There are two possible martensitic growth fronts, viz., dynam ical twinning and so-called two-kink solutions. These transformation f ronts are separated by a dynamical phase transition. We analytically d erive this phase diagram and determine expressions for the speeds of t he martensitic growth fronts.