A New Approach for Sintering Simulation of Irregularly Shaped Powder Particles—Part I: Model Development and Case Studies

Abstract

Within the FOR3010 Refrabund project, a new type of composite refractory consisting of alumina and refractory metals such as tantalum and niobium is developed. This material is characterized by its ability to conduct electricity, which offers new opportunities for functional parts in high‐temperature environments. To support the development of material properties and production technology, a new simulation approach is needed, which is able to describe irregularly shaped particles of at least two different phases. Current simulations of sintering processes work often with heavily idealized powder geometries. As sintering is mainly driven by gradients of chemical potential due to surface curvatures, a realistic description of the particle geometry is essential for achieving precise simulation results. Herein, a new approach of modeling the sintering behavior of irregularly shaped powder particles by the use of a finite differences approach is developed. A discrete description of irregular powder particles is introduced, and the diffusional flows at their surfaces and sintering necks as well as their development in time are calculated. The new model is compared with an older model using spherical particle geometries from literature. Comparison with experimental results follows in a subsequent publication.

A New Approach for Sintering Simulation of Irregularly Shaped Powder Particles—Part II: Statistical Powder Modeling

“…Over the whole time span, the morphological run shows a slightly higher shrinkage than the circular one. This corresponds to the results in Part I, [ 34 ] as tip contacts show slightly higher shrinkage and are more likely to occur with the current contact creation algorithm. The standard deviation is noticeably higher in early stages than in late stages.…”

“…As stated above, this corresponds accordingly to the results of Part I. [ 34 ] Tip contacts show lower neck radii because they act locally as they would be of lower radius. Similar to shrinkage, the standard deviation decreases with time and is higher in the morphological run.…”

“…In Part I, [ 34 ] the time axis was normalized on a characteristic time to erase the influence of the actual material parameters from the results. Here, the same approach was used, but as there were varying particle radii in the current case, the expectation of the regarded powder mixture was used instead of actual as shown in Equation ().…”

“…In the current case, a particle group will be a pair of particles consisting of a root particle, with a pinned position at the coordinate origin, and a child particle, which is able to move due to material displacement as explained in Part I. [ 34 ] Larger counts of particles were not used here because those would introduce additional complexity due to possible ring contacts and therefore reduced degrees of freedom in movement, which is not implemented in the model for now.…”

Characterization of Sintered Niobium–Alumina Refractory Composite Granules Synthesized by Castable Technology

“…The particle morphology was then statistically evaluated using the following equation describing the radius r in the polar coordinate system φ .with the base radius , the height of the first‐order peaks as fraction of , the number of peaks , and the ovality o as a fraction of . Details of the used model can be found in the study by Weiner et al [ 20 ] Figure 2b shows the obtained results of least‐square fitting, Equation (), to the extracted data of Figure 2b. As shown, the contour is only roughly reproduced by this equation.…”