Constrained densification of alumina/zirconia hybrid laminates, II: Viscoelastic stress computation

To analyze the inhibited densification during sintering and differential shrinkage during cooling of Al₂O₃/ZrO₂ symmetric and asymmetric laminates, viscoelastic formulations, in which the viscosity and elastic modulus vary with time, have been developed. The viscoelastic mismatch stresses have been numerically computed over the entire processing cycle, including the heating period, the isothermal period, and the cooling period. The viscosity and free sintering rates that are needed for stress computation have been obtained by modifying the parameters that are measured for a normal isotropic densifying compact using cyclic loading dilatometry. The modification is based on the available sintering models to account for the effect of strain history on compact viscosity and sintering rates. The stress calculation shows that, with the exception of the initial heating period, the viscoelastic stress is identical to the viscous stress that is calculated solely from the strain rate mismatch. Sintering damage in the laminates is shown to occur during densification under conditions where the differential sintering stress is smaller than the intrinsic sintering pressure. The magnitude of residual stress in hybrid laminates on cooling is dependent on the cooling rate, and slower cooling rates are capable of almost completely relaxing the expansion mismatch stress at temperatures of >1200°C.