Kinetics of diffusional phase transformation in multicomponent elastic-plastic materials

The goal of this paper is to derive a micromechanics framework to study the kinetics of transformation due to interface migration in elastic-plastic materials. Both coherent and incoherent interfaces as well as interstitial and substitutional atomic diffusion are considered, and diffusional transformations are contrasted with martensitic ones. Assuming the same dissipation for the rearrangement of all substitutional components and no dissipation due to diffusion in an interface in the case of a multicomponent diffusional transformation, we show that the chemical driving force of the interface motion is represented by the jump in the chemical potential of the lattice forming constituent. Next, the mechanical driving force is shown to have the same,form for both coherent and friction-less (sliding) interfaces in an elastic-plastic material. Using micromechanics arguments we show that the dissipation and consequently the average mechanical driving force at the interface due to transformation in a microregion can be estimated in terms of the bulk fields. By combining the chemical and mechanical parts, we obtain the kinetic equation,for the volume fraction of the transformed phase due to a multicomponent diffusional transformation. Finally, the communication between individual microregions and the macroscale is expressed by proper parameters and initial as well as boundary conditions. This concept can be implemented into standard frameworks of computational mechanics.