Computational Modeling of Liquid-Phase based on Homogenization

Licentiate thesis, 2011

Liquid-phase sintering is the process where a pre-compacted powder, "green body", is heated to the point where (a part of) the solid material melts, and the specimen shrinks while keeping (almost) net shape. In the case of hardmetal, the microstructure is defined by WC-Co-particles with large pores, whereby molten Co represents the liquid phase. In the ideal case, a fully dense material is achieved when the sintering is completed. In this thesis, the sintering process is modeled within an idealized Representative Volume Element (RVE), which is evaluated at the Gaussian integration points in the macroscale FE-mesh. The "driving force" of the sintering procedure is surface tension along the free surfaces, i.e. Co-pore interfaces. In this thesis, the intrinsic deformation of both the solid phase and the melt phase is modeled as the creeping flow of the Stokes' type, whereby elastic deformation is ignored. The macroscopic properties are found via computational homogenization of the RVE's. Although the RVE is highly idealized, it shows important properties not easily captured with traditional macroscopic constitutive models. The finite element mesh of the RVE becomes heavily deformed as the surface tension pulls the particles closer; hence, it was necessary to develop a versatile surface tracking method with remeshing. As an element in the mesh reaches a certain deformed state, defined by the condition number of the Jacobian, a new mesh is created. The FE² algorithm has been implemented in the open source FE-code OOFEM (written in C++). In particular, the code is parallelized w.r.t. the Gauss points in the macroscale mesh. The most straightforward RVE-problem is that with Dirichlet b.c. on the subscale velocity field, whereby the macroscopic rate-of-deformation is the control variable. In order to deal with eventual macroscopic incompressibility of the RVE (as the porosity vanishes) a new macroscopic format is introduced which allows for mixed control in terms of the deviatoric part of the macroscopic rate-of-deformation and the macroscopic pressure. In addition, this format allows for a seamless transition between compressible and incompressible RVE's. Numerical examples are shown for different loading scenarios, where the macroscopic behavior is studied.