Modélisation et simulation du couplage changement de phases-mécanique par la méthode des champs de phases

摘要

A general constitutive framework is proposed to incorporate linear and nonlinear mechanical behaviour laws (i.g. elastoviscoplasticity) into a standard phase field model. A finite element formulation of a coupled phase field/diffusion/mechanical problem for alloys is proposed within the general framework of continuum thermodynamics. This formulation is based on the concept of generalized stresses as proposed by Gurtin, where an additional balance equation for generalized stresses, called microforces, associated with the order parameter and its first gradient, is postulated. The formulation is used to simulate the complex morphological evolutions of the heterogeneous microstructures and to describe the diffuse interface between two phases in the presence of the stresses induced by phase transformation. Using the principles of the thermodynamics of irreversible processes, the balance and constitutive equations are clearly separated in the formulation. Also, boundary and initial conditions for the displacement, concentration and order parameter and their dual quantities are clearly stated within the formulation. The theory is shown to be well-suited for a finite element formulation of the initial boundary value problems on nite size specimens with arbitrary geometries and for very general non-periodic or periodic boundary conditions. In the diffuse interface region where both phases coexist, mixture rules taken from homogenization theory are introduced into the formulation. The consequences of the choice of a specific interface behaviour is investigated, with regard to the mechanical effect on phase equilibria (equilibrium compositions and volume fractions of the coexisting phases), as well as on the transformation kinetics. The set of coupled evolution equations, which are the local static equilibrium, the balance of generalized stresses and the balance of mass, is solved using a finite element method for the space discretization and a finite difference method for the temporal discretization. To validate the numerical finite element implementation and to illustrate the ability of the proposed model to handle precipitation together with mechanical contribution effect, some elementary initial boundary value problem in coupled diusion-elasto-plasticity on finite size specimens has been solved and validated against corresponding sharp interface analytical solutions.