Finite element evaluation of elasto-plastic accommodation energies during solid state transformations: Coherent, spherical precipitate in finite matrix

The molar volume difference between the matrix and the precipitate phases in the case of solid state phase transformations results in the creation of strain energy in the system due to the misfit strains. A finite element model based on the initial strain approach is proposed to evaluate elasto-plastic accommodation energies during solid state transformation. The three-dimensional axisymmetric model has been used to evaluate energies as a function of transformation for alpha-beta hydrogen transformations in the Nb-H system. The transformation has been analyzed for the cases of transformation progressing both from the center to surface and from the surface to center of the system. The effect of plastic deformation has been introduced to make the model realistic, specifically to the Nb-NbH phase transformation which involves a 4% linear misfit strain. It has been observed that plastic deformation reduces the strain energies compared to the linear elastic analysis.