Sintering is one of the oldest processes used by man to manufacture materials dating as far back as 12,000 BC. While it is an ancient process, it is also necessary for many modern technologies such a multilayered ceramic packages, wireless communication devices, and many others. The process consists of thermally treating a powder or compact at a temperature below the melting point of the main constituent, for the purpose of increasing its strength by bonding together of the particles. During sintering, the individual particles bond, the pore space between particles is eliminated, the resulting component can shrinks by as much as 30 to 50% by volume, and it can distort its shape tremendously. Being able to control and predict the shrinkage and shape distortions during sintering has been the goal of much research in material science. And it has been achieved to varying degrees by many. The object of this project was to develop models that could simulate sintering at the mesoscale and at the macroscale to more accurately predict the overall shrinkage and shape distortions in engineering components. The mesoscale model simulates microstructural evolution during sintering by modeling grain growth, pore migration and coarsening, and vacancy formation, diffusion and annihilation. In addition to studying microstructure, these simulation can be used to generate the constitutive equations describing shrinkage and deformation during sintering. These constitutive equations are used by continuum finite element simulations to predict the overall shrinkage and shape distortions of a sintering crystalline powder compact. Both models will be presented. Application of these models to study sintering will be demonstrated and discussed. Finally, the limitations of these models will be reviewed.
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.
Geologic, and historical well failure, production, and injection data were analyzed to guide development of three-dimensional geomechanical models of the Belridge diatomite field, California. The central premise of the numerical simulations is that spatial gradients in pore pressure induced by production and injection in a low permeability reservoir may perturb the local stresses and cause subsurface deformation sufficient to result in well failure. Time-dependent reservoir pressure fields that were calculated from three-dimensional black oil reservoir simulations were coupled uni-directionally to three-dimensional non-linear finite element geomechanical simulations. The reservoir models included nearly 100,000 gridblocks (100--200 wells), and covered nearly 20 years of production and injection. The geomechanical models were meshed from structure maps and contained more than 300,000 nodal points. Shear strain localization along weak bedding planes that causes casing dog-legs in the field was accommodated in the model by contact surfaces located immediately above the reservoir and at two locations in the overburden. The geomechanical simulations are validated by comparison of the predicted surface subsidence with field measurements, and by comparison of predicted deformation with observed casing damage. Additionally, simulations performed for two independently developed areas at South Belridge, Sections 33 and 29, corroborate their different well failure histories. The simulations suggest the three types of casing damage observed, and show that although water injection has mitigated surface subsidence, it can, under some circumstances, increase the lateral gradients in effective stress, that in turn can accelerate subsurface horizontal motions. Geomechanical simulation is an important reservoir management tool that can be used to identify optimal operating policies to mitigate casing damage for existing field developments, and applied to incorporate the effect of well failure potential in economic analyses of alternative infilling and development options.
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.