On the isotropic and anisotropic thermal conductivity of metallic hollow sphere structures

Abstract

Metallic hollow sphere structures (MHSS) combine the well-known advantages of cellular metals with the excellent material properties of solid base metals. The basic cell is a hollow sphere. Metallic hollow sphere structures can be assembled by sintering, soldering, or adhesive bonding. The macroscopic thermal property and, more specifically, the thermal conductivity is an essential material property. The objective of this work is to address the thermal conductivity of MHSS in dependence of the geometrical parameters of a single sphere and the ordering scheme of the assembled structure with a special focus on isotropy and anisotropy. From a macroscopic point of view, which is often used within the engineering design process, the characterization of the properties of MHSS demand an approximative description coming out of a homogenization. Within this paper the unit cell approach is used. The numerical analysis is done on the basis of a parameterized 3D-CAD model enabling the variation of the sphere size and wall thickness as well as the geometry of the interconnection between spheres. Periodic boundary conditions are applied. Results for the macroscopic thermal conductivity are presented for regular-packed (CP, BCC, FCC, and HCP) as well as randomly packed unit cells representing sintered or soldered MHSS. The anisotropy is discussed by the 3 × 3 thermal conductivity tensor.