Constraint and anisotropy during sintering of a LTCC material

The present work deals with a continuum mechanical description of sintering of glass ceramic materials used in the Low Temperature Co-fired Ceramics (LTCC) technology. In a first part of this thesis, uniaxial viscosity and viscous Poisson's ratio of an LTCC system were successfully determined. Since the magnitude of the loads and density range for which they were applied was crucial for the anisotropy development, discontinuous sinter forging (DSF) for a validity range of 0.5% of relative density was performed. When anisotropy was induced, the apparent value of the uniaxial viscosity changed drastically and reached a maximum soon after applying large loads. Sintering parameters were further correlated to microstructure: the microstructure became more anisotropic since pores and alumina particles oriented to a large extent perpendicular to the applied load. As a result, the apparent uniaxial viscosity increased. The obtained uniaxial viscosities measured by DSF increased with density and by decreasing the sintering temperature. The viscous Poisson's ratio presented the same trend for both sintering temperature profiles with a small initial decrease, attributed to the anisotropic free sintering behavior and then an increase, attributed to the increase of density. The second part of this thesis was to study the sintering of laminates. Two case studies have been investigated experimentally and theoretically: (i) asymmetrical bi-layers and (ii) symmetrical sandwich structures. For each case, elastic and viscous materials were used as constraining substrates. In the first case, an asymmetric stress state arose due to the differential shrinkage and lead to the camber of the sample. With a viscous constraining substrate, two available models (models by Cai and Kanters) were discussed and compared to experiments. The isotropic simulation failed to reproduce quantitatively the experimental results. It was mainly attributed to the significant anisotropy development due to the constraint. A new model was developed to describe the camber of a viscous layer on an elastic substrate. In the second case, when the constraining substrate did not allow any in-plane shrinkage, the shrinking layer was fully constrained. Isotropic modeling failed to predict the densification behavior of such laminate since it exhibited a limit of densification. Evidences of anisotropy were highlighted: (i) pore area increased by a factor of about 20 at 86% of relative densities compared to pore area determined for freely sintered samples and (ii) pores were oriented in the perpendicular direction to the plane of the laminate. It was further experimentally observed that the densification behavior and microstructure depended to a large extent on the Young's modulus of the outer layers of a sandwich structure. A simple theoretical approach was developed to account for the elastic deformation of the constraining layers. It was determined that the stress built into the shrinking layer was reduced by this effect