A continuum model for sintering processes incorporating elasticity effects

Abstract

A phenomenological thermodynamically consistent finite deformation sintering model incorporating viscous as well as thermo-hyperelastic effects is proposed. The thermo-mechanical constitutive behavior is completely described by a Helmholtz free energy density function, a dissipation function and a thermal conductivity function. A particular advantage of the approach utilized is that it allows for straightforward and reliable numerical evaluation of the model. Starting from a general formulation, the model is specialized to situations where it is reasonable to assume that the micro-structure of the material is not associated with preferred directions. In an example, the open constitutive functions of the model are determined for alumina ceramics from appropriate experimental data and theoretical considerations. By comparison with experiments, it is found that the model is capable of describing the sintering process of alumina ceramics as long as the underlying assumption of an isotropic micro-structure is valid. In a last step, the simulation of the sintering process of components by means of the finite element method is exemplified. An important feature of the finite element implementation utilized is that mechanical stresses can be predicted during the entire sintering process. This includes the residual stresses being present in the component after sintering.