The strain energy and shape evolution of hydrides precipitated at free surfaces of metals

Abstract

The volume changes, which are associated with hydride formation involve large strain energy. In the present work, Finite Element calculations of the strain energy of hydrides formed at the free surface of a metal matrix is done as function of several variables: the shape of the hydride precipitate, the elastic anisotropy of the crystals with cubic symmetry, the elastic heterogeneity, elastic–plastic transition and the effect of an oxide layer on the surface. The effect of these variables on the kinematics of the elastic strains and on the distribution of the energy between the matrix and hydrides are used to interpret the results and to deduce the preferred shapes, those having the lowest energy. The elastic energy of half-spherical hydrides at the surface is found to be minimal in most of the elastic and elastic–plastic systems considered (due to different reasons). A plate-shaped hydride with broad face parallel to the free surface may become preferred in an elastic matrix if the hydride is significantly softer than the matrix, or its broad face is parallel to a soft crystallographic plane. The existence of a thick oxide layer over the free surface increases the total energy of the system and moderates the dependence of the energy on the shape. As the hydride grows, the preference of the spherical shape is enhanced. For the case of a plastic matrix covered with an oxide layer, the preferred growth shape changes from a sphere to an elongated precipitate perpendicular to the free surface.