Solid phase seeds in a deformable material

Abstract

An equilibrium solid phase see in a linearly elastic medium is considered. The problem of a medium with new phase equilibrium domains is reduced to equations of elasticity theory for an inhomogeneous medium with a special kind of definite “phase” deformation under an additional phase equilibrium condition /1/ that imposes a constraint on the shape of the phase boundary. An ellipsoidal inclusion of an anisotropic phase is considered in an unbounded isotropic medium in a homogeneous external field of stress. It is proved that the tensor being defined by the phase deformation, by a change in the elastic moduli and stresses within the inclusion and having the meaning of a density tensor for dislocation moments indiced by a new phase domain, is global in the case of an equilibrium inclusion. The stress fields in an equilibrium two-phase configuration (TC) are determined by this characteristic property; the surface of the equilibrium ellipsoid turns out to be a surface of equal and constant principal values of the jump of the stress tensor and the constant principal value of the jump of the strain tensor. The stress perturbation tensor deviators within the seed and the tensor governing the ellipsoid shape are proportional, which is a generalization of a result obtained for seeds of a melt /2/. An equation governing the shape and orientation of the ellipsoidal seed as a function of the external stresses and the phase transition parameters follows from the structure of the density tensor of the dislocation moments. The possibility of the existence of an equilibrium ellipsoidal solid phase seed was shown in /3/ where analogous equations were obtained for the case of isotropic phases as a result of solving a TC problem by the method described in /4/; a system of equations is presented in /5/ for the analysis of TC with an anisotropic ellipsoidal seed. The conditions for the existence of equilibrium seeds and limit configurations analogous to the melt seed configurations are determined /2/. Energetic changes are considered for TC formation. It is shown that the Gibbs energies of the initial single-phase configuration and the equilibrium TC with an ellipsodial seed are equal; the equilibrium seed turns out to be critical. Seeds can originate only in the metastable phase: for stresses allowing the existence of an equilibrium ellipsoidal seed, the Gibbs specific energy of the initial single-phase configuration is not less than the specific Gibbs energy of a homogeneous configuration in the new phase state, where the equality of these energies is possible only for a TC containing layers. For stresses equal to the stresses within the equilibrium seed the new phase material has a larger specific Gibbs energy than the initial material.