Sintering of regular two-dimensional arrays of particles surface and grain boundary diffusion (original) (raw)
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Acta Materialia, 1998
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Acta Materialia, 2004
A numerical analysis of the sintering neck growth rate between rigid spherical particles of the same size is carried out. The contributions of the surface, grain-boundary and volume diffusion transport into sintering kinetics during the first and the second stages of sintering are estimated. It is shown that the three-dimensional problem of the matter redistribution during sintering can be reduced to a two-dimensional problem if the effective diffusion coefficients are introduced. The effective diffusion coefficients are the grain-boundary diffusion coefficients that include the contribution of volume diffusion. The effective diffusion coefficients are sensitive to the stage of sintering: they have different form during the first and the second stages. During the second stage of sintering, the unified effective diffusion coefficient is determined. It is demonstrated that the effective diffusion coefficients can be used also for the description of the pressure-assisted sintering.
Journal of the American Ceramic Society, 2009
Simulations based on the discrete element method (DEM) are used to investigate the relationship between the distribution of particle sizes and the macroscopic sintering behavior of ceramic powders. This is achieved by generalizing the DEM force laws for solid-state sintering in such a way that sintering of particles with different sizes can be simulated. A generation scheme for initial particle packings with realistic physical properties is presented, which allows for different distributions, ranging from monomodal to normal, log-normal, and bimodal distributions. It is shown that the type and width of the distribution has a significant effect on the strain rates and viscosity during sintering. Broader size distributions lead to reduced sintering rates, although particle rearrangement is enhanced. However, the accelerating effect of rearrangement is overcompensated by an increase of the contact area between particles when the size distribution becomes wider. The simulation results are in good agreement with experimental results on a commercial Al 2 O 3 power.
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Materials Science and Engineering: A, 2003
A single-step processing method has been established to prepare asymmetric porous alumina microstructures by a controlled sedimentation technique. Fine powder from an aqueous suspension is consolidated over a casting slab. Metastable surface chemical control of the suspension properties was able to induce a highly porous flat disc structure with a continuously increasing mean pore size from top to bottom. Formation of this gradient structure was facilitated by using a powder with a very broad particle size distribution. These structures can be used as either ultrafiltration media or as substrates for inorganic membrane making. Sintering can readily introduce defects into functionally gradient ceramics. Despite these problems, the asymmetric structures considered in this paper can be readily sintered without warpage or cracking. In this regard, a finite element method numerical simulation had been developed to model the sintering characteristics of functionally gradient ceramic structures. The key for being able to predict a non-warped structure was the incorporation into the model of the powder particle size distribution as a field variable. Across the vertical section of the structure, the distributions were broad and overlapping, all with a significant fines tail. These characteristics accelerate and homogenize local sintering rates, such that the net result is a non-warped fused structure. This paper presents recent advances with the simulation, where sample geometry, porosity and particle size distribution evolutions were traced alongside measurements made on physical specimens. In general the model corresponded well with the experimental observations. The correct accounting of observed trends lends confidence to the underlying sintering mechanisms incorporated into the model.
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JOM, 2016
Sintering is a mainstay production step in forming metal, ceramic, polymer, and composite components from particles. Since the 1940s, the sintering process is treated using a matrix of mathematical relationships that include at least seven atomic transport mechanisms, several options on powder characteristics, and three pore-grain morphology options. The interplay of these relationships is handled by numerical solutions to predict property development. An alternative approach is to track the sintering trajectory using relatively simple relationships based on bulk measures. Energy minimization dictates that initial stage sintering acts to reduce surface area. In late stage sintering, the energy minimization turns to grain boundary area reduction via grain growth. Accordingly, relationships result between density, surface area, and grain size, which largely ignore mechanistic details. These relationships are applicable to a wide variety of materials and consolidation conditions, including hot pressing, and spark sintering.
SOLID-STATE SINTERING SIMULATION: SURFACE, VOLUME AND GRAIN-BOUNDARY DIFFUSIONS
Within the general context of solid-state sintering process, this work presents a numerical modeling approach, at the grain scale, of ceramic grain packing consolidation. Typically, the sintering process triggers several mass transport paths that are thermally activated: surface, grain boundary and volume diffusions. Including this physics into a high-performance computing framework would permit to gain precious insights about the driving mechanisms which are seldom accessible at this scale.
High performance computing of sintering process at particle scale
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Within the general context of solid-state sintering process, this work presents a numerical modeling approach, at the particle scale, of ceramic particle packing consolidation. Typically, the sintering process triggers several mass transport paths that are thermally activated. Among those diffusion paths, the most important ones are: surface diffusion, grain boundary diffusion and volume diffusion. Including this physics into a high-performance computing framework would permit to gain precious insights about the driving mechanisms. The aim of the present work is to develop a model and a numerical strategy able to integrate the different diffusion mechanisms into continuum mechanics framework. In the cases of surface diffusion and volume diffusion, the mass flux is calculated as a function of the surface curvature Laplacian and the hydrostatic pressure gradient, respectively. The physical model describing these two transport mechanisms is first presented within the framework of conti...
2D aggregate evolution in sintering due to multiple diffusion approaches
Materials Chemistry and Physics, 2003
A diffuse-interface field approach is developed to model the evolution of aggregate in sintering ceramics. The aggregate microstructure is characterized by a relative density field, and multiple long-range order (LRO) parameter fields representing the crystallographic orientation of grains. The evolution of the density field is governed by Cahn-Hilliard equation, while the LRO orientation fields by the Time-Dependent Ginzburg-Landau equation (TDGL). The nonlinear dynamic equations are solved efficiently by a semi-implicit Fourier-Spectral method, providing detailed information about particle contact, neck growth and pore spheroidization. The quantitative neck growth through multiple diffusion approaches is extracted from the simulation and compared with previous thermodynamic growth analysis.
Direct 3D Simulation of Powder Sintering by Surface and Volume Diffusion
Key Engineering Materials, 2013
Within the general context of solid-state sintering process, this work presents a numerical modelling approach, at the grain scale, of ceramic grain packing consolidation. Typically, the sintering process triggers several matter diffusion routes that are thermally activated: surface, grain boundary and volume diffusions. Including this physics into a high-performance computing framework would permit to investigate and to track the changes occurring into a granular packing during sintering. In performing this kind of simulations, one will face several challenges: the strong topological changes appear during sintering simulation at the grains scale, the evolution of the structure is mainly driven by the surface tension phenomena through the Laplace's law, and the mechanical properties of the grains could, possibly, be different. The proposed numerical simulations are carried out within an Eulerian Finite Element framework and the Level-Set method is used to cope with changes in the microstructure. The results obtained with this numerical strategy are compared with success to the usual geometrical models.