Finite element analysis of effect of precipitate aspect ratio on accommodation energies during solid state transformations

Abstract

The initial strain approach of the finite element method (FEM) has been applied to evaluate elastic and elasto-plastic accommodation energies in an ellipsoidal domain as a function of progress of α– β hydrogen transformations in the niobium–hydrogen system. In the finite system considered, the progress of transformation from the center of the system outwards and from the surface of the system inwards have been studied. The effect of changing the aspect ratio of a prolate spheroidal precipitate on the accommodation energy is addressed. The elastic analysis indicates that the total accommodation energy decreases with increasing aspect ratio for all the transformations considered. Moreover, most of the energy is accommodated in the phase in the outer region which surrounds the inner phase. Elasto-plastic finite element analysis of the hydrogen transformations reveals that plastic deformation of Nb reduces the elastic energy of the system. The elasto-plastic accommodation energies at the end of transformation are higher in the case of transformations where the final phase is niobium than in the case where the final phase is niobium hydride. The accommodation energies generally increase with increasing aspect ratio for all the transformation paths considered in the elasto-plastic analysis.