Experimental and finite element modeling study of co-sintering of multilayer, multifunctional ceramics

The co-sintering behavior of low temperature co-fired ceramics (LTCC) is investigated by combining experiment and simulation methods. The numerical method offers a way to provide quantitative information regarding the final sintered shape of multilayer ceramics, which can be used to optimize the design of multilayer, multifunctional components and help reduce tedious and expensive empirical design iterations.; To predict the sintering behavior of LTCC, parameters in the viscoplastic constitutive equations for single materials (such as shear viscosity G, bulk viscosity K, and sintering stress sigma s, etc.) need to be known. An apparatus was constructed for in situ measurements of the longitudinal and radial shrinkage during free sintering and sinter forging experiments. Cylindrical samples of individual LTCC materials (DuPont 951AX, Heraeus CT-800, Ferro A6-S) were made. Free sintering and sinter-forging experiments have been performed at various heating rates and under different intermittently applied axial loads. Various methods for analyzing the data were used to extract those parameters and their dependence on temperature and relative density.; The constitutive parameters obtained from experiments were then implemented in the user subroutine UMAT of the general-purpose finite element program ABAQUS to simulate the free sintering behavior of bi-layer structures (DU951/CT800) with different thickness ratios. The simulation results were then compared with the actual experimental results, which were obtained by free co-sintering bi-layer planar samples with different thickness ratios.; Simulation results showed the finite element analysis was successful in predicting the shape changes and the stresses at different positions during sintering of bi-layer structures. This finite element model was also used to examine the sensitivity to various parameters of the sintering results, such as elastic Poisson's ratio v, Young's modulus E, sintering stress sigmas, shear and bulk viscosities G, K. It is found that the size and shape changes during sintering are very sensitive to the activation energy for the temperature dependence of the viscosities of the materials. The sintering stress is also an important parameter that can affect the sintering results. The test results showed that the elastic parameters v and E will have a negligible effect on the free sintering behavior of the LTCC materials.