Analytical and Computational Methods for Solidification Problems of Liquid That Expands During Freezing

Abstract

Both analytical and computational methods for solidification problems are introduced. First, the inward solidification process in a spherical vessel is studied. Expressions of the stress, displacement in the solid phase, and the liquid pressure are deduced based on the solidification interface position. A phase-change expansion orientation factor is introduced to characterize the nonisotropic expansion behavior at the freezing interface. Then, an efficient coupled thermomechanical finite-element method is proposed to evaluate the thermal stress, strain, displacement, and pressure in solidification problems with highly nonlinear constitutive relations. Two particular methods for treating the liquid phase with fixed-grid approaches are introduced. The thermal stress is computed at each integration point by integrating the elastoviscoplastic constitutive equations. Then, the boundary value problem described by the global finite-element equations is solved using the full Newton–Raphson method. This procedure is implemented into the finite-element package abaqus via a FORTRAN subroutine UMAT. Detailed implementation steps and the solution procedures are presented. The numerical model is validated first by the analytical solutions and then by a series of benchmark tests. Finally, an example of solidification in an open reservoir with a free liquid surface is introduced. Potential industrial applications of the numerical model are presented.