Microstructure modeling and computational micromechanics of glued metallic hollow-sphere composites

This work is devoted to generating and investigating microstructure representations of glued hollow-sphere assemblies, which combine low weight with excellent damping properties for use in machine tools. As a first step, we model the microstructure of such assemblies based on a dedicated analysis of the size distribution of the hollow spheres. To model the glue, we augment a preliminary sphere packing with dedicated closing and erosion operations, prevalent in mathematical morphology. Notably, for spheres, a level-set representation of the result of the closing and erosion operations can be computed analytically based on specific Dirichlet diagrams. In this way, we obtain a resolution-independent description of the glue phase for irregular sphere arrangements. Once the microstructure is generated, we furnish the individual phases with the elastic properties of the involved materials. We use FFT-based computational micromechanics tools to compute the effective elastic properties of the assemblies and study the influence of various factors, like the sphere-size distribution, the thickness of the shell, and the employed material parameters. Of particular importance here is the use of composite voxels, which in turn rely on the previously derived level-set representation. The developed modeling approach determines the elastic material properties of the hollow-sphere composite (HSC) and identifies the leading influences as the shell thickness, the glue phase volume fraction, and the sphere packing density. This approach aligns well with the validated structure, which has an average sphere diameter of 2.85 mm, a wall thickness of 72  $\mu$ m, a sphere packing density of 54%, and an epoxy volume fraction of 16.2%.