The ease and ability to predict sintering shrinkage and densification with the Skorohod-Olevsky viscous sintering (SOVS) model within a finite-element (FE) code have been improved with the use of an Arrhenius-type viscosity function. The need for a better viscosity function was identified by evaluating SOVS model predictions made using a previously published polynomial viscosity function. Predictions made using the original, polynomial viscosity function do not accurately reflect experimentally observed sintering behavior. To more easily and better predict sintering behavior using FE simulations, a thermally activated viscosity function based on creep theory was used with the SOVS model. In comparison with the polynomial viscosity function, SOVS model predictions made using the Arrhenius-type viscosity function are more representative of experimentally observed viscosity and sintering behavior. Additionally, the effects of changes in heating rate on densification can easily be predicted with the Arrhenius-type viscosity function. Another attribute of the Arrhenius-type viscosity function is that it provides the potential to link different sintering models. For example, the apparent activation energy, Q, for densification used in the construction of the master sintering curve for a low-temperature cofire ceramic dielectric has been used as the apparent activation energy for material flow in the Arrhenius-type viscosity function to predict heating rate-dependent sintering behavior using the SOVS model.
Low temperature co-fire ceramic (LTCC) materials technology offers a cost-effective and versatile approach to design and manufacture high performance and reliable advanced microelectronic packages (e.g., for wireless communications). A critical issue in manufacturing LTCC microelectronics is the need to precisely and reproducibly control shrinkage on sintering. Master Sintering Curve (MSC) theory has been evaluated and successfully applied as a tool to predict and control LTCC sintering. Dilatometer sintering experiments were designed and completed to characterize the anisotropic sintering behavior of green LTCC materials formed by tape casting. The resultant master sintering curve generated from these data provides a means to predict density as a function of sintering time and temperature. The application of MSC theory to DuPont 951 Green Tape™ will be demonstrated.
Software has been developed and extended to allow finite element (FE) modeling of ceramic powder compaction using a cap-plasticity constitutive model. The underlying, general-purpose FE software can be used to model even the most complex three-dimensional (3D) geometries envisioned. Additionally, specialized software has been developed within this framework to address a general subclass of axisymmetric compacts that are common in industry. The expertise required to build the input deck, run the FE code, and post-process the results for this subclass of compacts is embedded within the specialized software. The user simply responds to a series of prompts, evaluates the quality of the FE mesh that is generated, and analyzes the graphical results that are produced. The specialized software allows users with little or no FE expertise to benefit from the tremendous power and insight that FE analysis can bring to the design cycle. The more general underlying software provides complete flexibility to model more complicated geometries and processes of interest to ceramic component manufacturers but requires significantly more user interaction and expertise.
In the manufacture of ceramic components, near-net-shape parts are commonly formed by uniaxially pressing granulated powders in rigid dies. Density gradients that are introduced into a powder compact during press-forming often increase the cost of manufacturing, and can degrade the performance and reliability of the finished part. Finite element method (FEM) modeling can be used to predict powder compaction response, and can provide insight into the causes of density gradients in green powder compacts; however, accurate numerical simulations require accurate material properties and realistic constitutive laws. To support an effort to implement an advanced cap plasticity model within the finite element framework to realistically simulate powder compaction, the authors have undertaken a project to directly measure as many of the requisite powder properties for modeling as possible. A soil mechanics approach has been refined and used to measure the pressure dependent properties of ceramic powders up to 68.9 MPa (10,000 psi). Due to the large strains associated with compacting low bulk density ceramic powders, a two-stage process was developed to accurately determine the pressure-density relationship of a ceramic powder in hydrostatic compression, and the properties of that same powder compact under deviatoric loading at the same specific pressures. Using this approach, the seven parameters that are required for application of a modified Drucker-Prager cap plasticity model were determined directly. The details of the experimental techniques used to obtain the modeling parameters and the results for two different granulated alumina powders are presented.