Estimation of solid-state sintering and material parameters using phase-field modeling and ensemble four-dimensional variational method

Abstract

Sintering is a fundamental technology for powder metallurgy, the ceramics industry, and additive manufacturing processes such as three-dimensional printing. Improvement of the properties of sintered materials requires prediction of their microstructure using numerical simulations. However, the physical values and material parameters used for such predictions are generally unknown. Data assimilation (DA) enables the estimation of unobserved states and unknown material parameters by integrating simulation results and observational data. In this paper, we develop a new model that couples an ensemble-based four-dimensional variational (En4DVar) DA with a phase-field model of solid-state sintering (En4DVar-PF model) to estimate the state of the sintered material and multiple unknown material parameters. The developed En4DVar-PF model is validated by numerical experiments called twin experiments, in which a priori assumed-true initial state and multiple material parameters are estimated. The results of the twin experiments demonstrate that, using only three-dimensional morphological data of the sintered microstructure, our developed En4DVar-PF model can simultaneously and accurately estimate the particle shape, distribution of grain boundaries, and material parameters, including diffusion coefficients and mobilities related to grain boundary migration. Furthermore, our work identifies criteria for determining appropriate DA conditions such as the observational time interval required to accurately estimate the material parameters using our developed model. The developed En4DVar-PF model provides a promising framework to obtain unobservable states and difficult-to-measure material parameters in sintering, which is crucial for the accurate prediction of sintering processes and for the development of superior materials.