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

TL;DR

This paper develops a hydrodynamic theory for nucleation and growth in a one-dimensional shear martensitic transition, revealing surface nucleation dominance and a dynamical phase transition in growth fronts.

Contribution

It introduces an analytical framework for understanding nucleation and growth in 1D shear martensitic transformations, highlighting surface nucleation and growth front dynamics.

Findings

Surface nucleation is the dominant formation route for martensite.

Analytical solutions for surface nuclei and nucleation rates are provided.

A dynamical phase transition separates two growth front types.

Abstract

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.