Co-firing of functionally graded ceramic systems: A multi-scale modelling approach

Co-firing of multi-layer powder compacts is often used to produce functionally graded ceramics (FGCs) with spatially tailored properties. However, co-firing induces internal stresses that can cause distortion or cracking, making process optimisation essential, while experimental approaches remain costly and time-consuming. This study presents a predictive multi-scale model combining discrete element method (DEM) with the continuum theory of sintering. DEM simulations on representative volume elements are used to extract constitutive parameters, including viscosities and sintering stress, as functions of microstructural state variables, which are passed to a viscoelastic model within a finite element code. The approach is validated against experimental data of a bilayer produced from alumina. It is also used to study characteristic stages of deformations during co-firing. Furthermore, the applicability of DEM-informed reduced-order model for shape distortions in bilayers is discussed. The developed method reduces reliance on experiments and provides a transferable approach for optimising the co-firing of FGCs.