Modeling the evolution of stress due to differential shrinkage in powder-processed functionally graded metal–ceramic composites during pressureless sintering

Pressureless sintering of powder-processed functionally graded materials is being pursued to economically produce metal–ceramic composites for a variety of high-temperature (e.g., thermal protection) and energy-absorbing (e.g., armor) applications. During sintering, differential shrinkage induces stresses that can compromise the integrity of the components. Because the strength evolves as the component is sintered, it is important to model how the evolution of the differential shrinkage governs the stress distribution in the component in order to determine when the strength will be exceeded and cracking initiated. In this investigation, a model is proposed that describes the processing/microstructure/property/performance relationship in pressurelessly sintered functionally graded plates and rods. This model can be used to determine appropriate shrinkage rates and gradient architectures for a given component geometry that will prevent the component from cracking during pressureless sintering by balancing the evolution of strength, which is assumed to be a power law function of the porosity, with the evolution of stress. To develop this model, the powder mixture is considered as a three-phase material consisting of voids, metal particles, and ceramic particles. A micromechanical thermal elastic–viscoplastic constitutive model is then proposed to describe the thermomechanical behavior of the composite microstructure. The subsequent evolution of the thermomechanical properties of the matrix material during sintering is assumed to obey a power law relationship with the level of porosity, which is directly related to the shrinkage strain, and was refined to account for the evolving interparticle cohesion of the matrix phase due to sintering. These thermomechanical properties are incorporated into a 2-D thermomechanical finite element analysis to predict the stress distributions and distortions that arise from the evolution of differential shrinkage during the pressureless sintering process. Differential shrinkage results were verified quantitatively through comparison with the shape profile for a pressurelessly sintered functionally graded nickel–alumina composite plate with a cylindrical geometry, and the stress distribution results verified from qualitative observations of the absence or presence of cracking as well as the location in specimens with different gradient architectures. The cracking was mitigated using a reverse gradient at one end of the specimen, and the resulting distortions associated with the shape profile were determined to be no more than 15% reduced from the predictions. The effects of geometry were also studied out-of-plane by transforming the plate into a rod through an increase in thickness, while in-plane effects were studied by comparing the results from the cylindrical specimen with a specimen that has a square cross-sectional geometry. By transforming from a plate to a rod geometry, the stress no longer exceeds critical levels and cracks do not form. The results from the in-plane geometric study indicated that critical stresses were reached in the square geometry at temperatures 100 °C less than in the cylindrical geometry. Additionally, the location of primary cracking was shifted towards the metal-rich end of the specimen, while the stress distribution associated with this shift and the lower temperature for the critical stress resulted in secondary cracking.