Non-affine fields in solid-solid transformations: the structure and stability of a product droplet
Abstract
We describe the microstructure, shape and dynamics of growth of a droplet of martensite nucleating in a parent austenite during a solid-solid transformation, using a Landau theory written in terms of conventional affine, elastic deformations and non-affine degrees of freedom. Non-affineness, φ, serves as a source of strain incompatibility and screens long-ranged elastic interactions. It is produced wherever the local stress exceeds a threshold and anneals diffusively thereafter. A description in terms of φ is inevitable when the separation between defect pairs, possibly generated during the course of the transformation, is small. Using a variational calculation, we find three types of stable solutions ( I, II and III) for the structure of the product droplet depending on the scaled mobilities of φ parallel and perpendicular to the parent-product interface and the stress threshold. In I, φ is vanishingly small, II involves large φ localized in regions of high stress within the parent-product interface and III where φ completely wets the parent-product interface. While width l and size W of the twins follows lW in solution I, this relation does not hold for II or III. We obtain a dynamical phase diagram featuring these solutions and argue that they represent specific microstructures such as twinned or dislocated martensites.