On constrained sintering-III. Rigid inclusions

In Part II of this series we examined constitutive equations that have been used primarily to analyze constrained sintering problems, including sintering of a matrix phase with rigid inclusions. For the latter problem, two important effects have been identified: generation of internal stresses (which could lead to formation of crack-like defects) and deviation of the densification behavior from the rule of mixtures. Currently available analyses give very different results for the stresses, which we show to be due to the choice of the constitutive laws. The analyses that give large values of internal stresses and significant slowing down of densification use constitutive laws that underestimate the shear relaxation of the densifying body, which leads to a negative value for the Poisson's ratio. Since this has never been observed in sinter-forging experiments, it is concluded that either the internal stresses are small (as predicted by the constitutive laws given in Part I) or the basic assumptions of linearity and isotropy used in all of the analyses are incorrect. We discuss some phenomena that could be important in explaining the densification of composites.