Simulation methodologies for multiphase three-dimensional microstructures
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There is a need for simulation methodologies for multiphase three-dimensional microstructures that can be used in numerical simulations of material behavior or in exact computation of effective properties using microstructural correlation functions. Specifically, the methodology must be able to generate verifiably realistic microstructures, with complex morphology accurately represented. Striving to address that need, the research presented here develops a general microstructure simulation toolbox for multiphase two- and three-dimensional microstructures consisting of one connected phase and one or more particulate phases. Previous work by other researchers has found successful solutions to a variety of special cases of the general problem, but most of them are intended for binary microstructures, and nearly all simulate only two-dimensional microstructures. The toolbox presented here attempts to exceed those limitations. Its framework is a Metropolis stochastic-optimization routine running a simulated-anneal schedule, with particle position coordinates defining the configuration space and a range of forms available for the ﾓenergyﾔ? function. The toolbox allows several parameterizations of the microstructure, supplying all elementary properties (phase volume fractions, mean sizes, etc.) and some non-elementary properties (distributions of elementary properties, properties relating to inter-phase distances and morphology) of microstructures as possible parameters. The toolbox is able, as one special case, to simulate realistic microstructures of uniaxially compacted mixtures of elemental Al-Ti-B powders and achieve basic microstructure-processing correlation. Statistical tests involving microstructural correlation functions bear out the realism. The toolbox is also able to generate virtual microstructures for the same system, for use in the design of experiments (which are in fact high-strain-rate impact simulations), and for evaluating hypotheses involving achievable material properties. The Al-Ti-B powder compacts are potential advanced energetic materials that, when subjected to high-strain-rate impact (which may or may not constitute shock compression), explosively release heat by anaerobic reaction according as certain incompletely understood conditions are met or not. The study of those conditions and the mechanism of reaction initiation (carried out by a collaborator) is the specific application that the simulations in this work cater to. To ensure realistic morphology in simulated Al-Ti-B microstructures, this work included reconstruction (carried out by montage serial sectioning) of large three-dimensional volumes of Al-Ti and Al-B binary compacts for two sets of powders that yielded actual 3 D Ti and B particle images. Accordingly, advancement of the experimental technique of montage serial sectioning and a quantitative characterization of the real powder microstructures also formed part of this research. While only examples from Al-Ti-B powders are used throughout this work, it is clear that the methods will apply to other similar systems.