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International audience; This paper presents a numerical model that is capable of simulating microstructural evolution during simple solid-state sintering of a complex 3D powder particle compact. This model, a Potts kinetic Monte Carlo model, is a true mesoscale model that can simulate a large number of particles while resolving microstructural features such as particles, necks, pores and more in detail. Furthermore, it is shown that this model can simulate all the stages of sintering from the initial particle contact to neck growth with open, percolating porosity to closed isolated pores seamlessly. The various kinetic processes that lead to densification and other microstructural changes are shown to be simulated correctly. The model is demonstrated by comparing the microstructural evolution resulting from simulation to experimental results, namely 3D microtomographic images obtained from synchrotron radiation of a Cu-powder compact while it was sintering. For quantitative comparison, we extrapolated a grain structure into the simple microtomographic image that consists of mass distribution only.

This paper discusses in detail the development of a numerical model capable of simulating microstructural evolution and macroscopic deformation during sintering of complex powder compacts. The model based on the kinetic Monte Carlo (Potts) approach simulates grain growth, vacancy diffusion, and pore annihilation at grain boundaries, which is responsible for densification. Results of 2D simulations for perfect close-packed and random starting configurations are presented and discussed. The microstructural evolution is used to obtain the sintering stress––the macroscopic stress that is equivalent to the microstructural driving force for deformation.

Microstructural evolution during simple solid-state sintering of two-dimensional compacts of elongated particles packed in different arrangements was simulated using a kinetic, Monte Carlo model. The model used simulates curvature-driven grain growth, pore migration by surface diffusion, vacancy formation, diffusion along grain boundaries, and annihilation. Only the shape of the particles was anisotropic; all other extensive thermodynamic and kinetic properties such as surface energies and diffusivities were isotropic. We verified our model by simulating sintering in the analytically tractable cases of simple-packed and close-packed, elongated particles and comparing the shrinkage rate anisotropies with those predicted analytically. Once our model was verified, we used it to simulate sintering in a powder compact of aligned, elongated particles of arbitrary size and shape to gain an understanding of differential shrinkage. Anisotropic shrinkage occurred in all compacts with aligned, elongated particles. However, the direction of higher shrinkage was in some cases along the direction of elongation and in other cases in the perpendicular direction, depending on the details of the powder compact. In compacts of simple-packed, mono-sized, elongated particles, shrinkage was higher in the direction of elongation. In compacts of close-packed, mono-sized, elongated particles and of elongated particles with a size and shape distribution, the shrinkage was lower in the direction of elongation. The results of these simulations are analyzed, and the implication of these results is discussed.

A kinetic, Monte Carlo model, capable of simulating microstructural evolution sintering in a two-dimensional system of three particles, has been presented. The model can simulate several mechanisms simultaneously. It can simulate curvature-driven grain growth, pore migration and coarsening by surface diffusion, and densification by diffusion of vacancies to grain boundaries and annihilation of these vacancies. Morphologic changes and densification kinetics are used to verify the model.

An experimental validation of a 3D kinetic, Monte Carlo model for simulation of microstructural evolution during solid state sintering will be presented. The model – a statistical mechanical model, which can simulate curvature-driven grain growth, pore migration, and vacancy formation, diffusion and annihilation – is validated by comparing microstructural evolution obtained experimentally for a copper powder compact. The 3D microstructural evolution of copper powder particles sintering was imaged in-situ by microtomography. The images show particles with internal porosity percolating through the particles. Microstructural features – e.g., neck formation and growth – from the experimental images as well as the overall densification rates are compared to the simulations.

All ceramics and powder metals, including the ceramics components that Sandia uses in critical weapons components such as PZT voltage bars and current stacks, multi-layer ceramic MET's, ahmindmolybdenum & alumina cermets, and ZnO varistors, are manufactured by sintering. Sintering is a critical, possibly the most important, processing step during manufacturing of ceramics. The microstructural evolution, the macroscopic shrinkage, and shape distortions during sintering will control the engineering performance of the resulting ceramic component. Yet, modeling and prediction of sintering behavior is in its infancy, lagging far behind the other manufacturing models, such as powder synthesis and powder compaction models, and behind models that predict engineering properties and reliability. In this project, we developed a model that was capable of simulating microstructural evolution during sintering, providing constitutive equations for macroscale simulation of shrinkage and distortion during sintering. And we developed macroscale sintering simulation capability in JAS3D. The mesoscale model can simulate microstructural evolution in a complex powder compact of hundreds or even thousands of particles of arbitrary shape and size by 1. curvature-driven grain growth, 2. pore migration and coalescence by surface diffusion, 3. vacancy formation, grain boundary diffusion and annihilation. This model was validated by comparing predictions of the simulationmore » to analytical predictions for simple geometries. The model was then used to simulate sintering in complex powder compacts. Sintering stress and materials viscous module were obtained from the simulations. These constitutive equations were then used by macroscopic simulations for simulating shrinkage and shape changes in FEM simulations. The continuum theory of sintering embodied in the constitutive description of Skorohod and Olevsky was combined with results from microstructure evolution simulations to model shrinkage and deformation during. The continuum portion is based on a finite element formulation that allows 3D components to be modeled using SNL's nonlinear large-deformation finite element code, JAS3D. This tool provides a capability to model sintering of complex three-dimensional components. The model was verified by comparing to simulations results published in the literature. The model was validated using experimental results from various laboratory experiments performed by Garino. In addition, the mesoscale simulations were used to study anisotropic shrinkage in aligned, elongated powder compacts. Anisotropic shrinkage occurred in all compacts with aligned, elongated particles. However, the direction of higher shrinkage was in some cases along the direction of elongation and in other cases in the perpendicular direction depending on the details of the powder compact. In compacts of simple-packed, mono-sized, elongated particles, shrinkage was higher in the direction of elongation. In compacts of close-packed, mono-sized, elongated particles and of elongated particles with a size and shape distribution, the shrinkage was lower in the direction of elongation. We also explored the concept of a sintering stress tensor rather than the traditional sintering stress scalar concept for the case of anisotropic shrinkage. A thermodynamic treatment of this is presented. A method to calculate the sintering stress tensor is also presented. A user-friendly code that can simulate microstructural evolution during sintering in 2D and in 3D was developed. This code can run on most UNIX platforms and has a motif-based GUI. The microstructural evolution is shown as the code is running and many of the microstructural features, such as grain size, pore size, the average grain boundary length (in 2D) and area (in 3D), etc. are measured and recorded as a function of time. The overall density as the function of time is also recorded.« less