Stresses and distortion due to green density gradients during densification

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 bi-layer 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.