Effect of Shape and Density on Electrical Conductivity of Non-Stochastic Lattice Structures

Abstract

Non-stochastic lattice structures are 3-dimensional arrays of unit cells having carefully engineered geometric properties. Until recently, these structures were not practical to manufacture. The emergence of Solid Freeform Fabrication (SFF) processes in recent years has changed that fact. It is now possible to tailor structural, thermal, or electrical properties by varying the shape and density the unit cell geometry. In this research, electrical conductivity of five different lattice cell geometries has been calculated. The geometries examined include regular hexahedrons, octahedrons, truncated octahedrons, rhombic dodecahedrons, and hexagonal lattices. The relationship between ligament length, ligament radius, relative density and electrical conductivity has been analytically derived and compared for the different cell geometries. The analysis indicates that electrical conductivity is dependent on the shape of the cell; it increases with increase in density and is linearly dependent on density at low density. Resistivity measurement of Ti-6Al-4V rhombic dodecahedrons and hexagonal lattices made via the Electron Beam Melting (EBM) process over a range of relative densities from 4% to 16% validates the effective unit cell approach for predicting electrical conductivity and the dependence of electrical conductivity on foam density. In the second part a novel concept of varying density of metal foam to obtain specific advantage in properties has been discussed. The problem of uneven distribution of resistance faced by a specific application utilizing electrical resistivity of metal foam has been analyzed, and an approach based on varying foam density is suggested.