Finite element analysis (FEA) was performed on a bi-layer cylindrical structure consisting of a low-density layer on top of a high-density layer. For this model, the layers used the shrinkage behavior, viscosity, and elastic properties of barium titanate determined for the 45% and 55% green densities. The stresses predicted by FEA showed good agreement with stresses predicted using analytical equations for a linear viscous bi-layer cylinder. The model was then extended to use more complex density gradients measured by X-ray computed tomography on a bilayer compact. In this case, the shrinkage behavior and viscosity properties were extrapolated from the experimental data. In the subsequent simulation, the stresses and strains were predicted during sintering. For the bi-layer structure studied, a highly stressed region was identified on the free surface of the sintering compact and this was shown to lead to edge cracking during densification.
3027J ournal
The thermomechanical properties of a commercial barium titanate were experimentally or theoretically determined for samples with green densities ranging from 45% to 55%. For stresses less than 300 kPa, sample deformation was determined to be linear viscous for all three stages of sintering. The shrinkage rates at a given temperature can differ by up to ∼25% as the green density changes from 45% to 55%, and the maximum shrinkage rate increased with decreasing green density. The increase in shrinkage rate with lower green density samples persisted through the final sintering stage. The viscosity was determined by cyclic loading dilatometry to range from 5 to 6 GPa·s in the initial stage of sintering, to 2 GPa·s in the intermediate stage, and to increase to 10–20 GPa·s for all specimens in the final stage of sintering. Differences in the final‐stage viscosity were attributed to grain size differences. Relaxation times for the sintering body were estimated to be less than 1 s, indicating that viscous behavior is dominant throughout the sintering process.
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