Internal stress diagrams of sintering stress versus viscosity for graded multilayers

The internal stress of graded powder compacts during sintering is analyzed by using plate theory with shrinkage and warpage taken into consideration. Diagrams giving the in-plane stress on the surface of the compacts, produced by mismatch and bending, are presented as a function of sintering stress and viscosity. The diagrams show the contours of tension and compression as well as the direction of warpage for given multilayered substrate. When the viscosity of the top layer is smaller than that of the substrate, the shrinkage constrained by the substrate significantly influences the internal stress. In the opposite case, the bending stress dominates the stress condition. The tension/compression boundaries in the diagrams change according to the number and the thickness of the graded layers as well as the sintering stress and the viscosity.