Near-zero thermal expansivity 2-D lattice structures: Performance in terms of mass and mechanical properties

Abstract

The coefficient of thermal expansivity (CTE), a, of a 2-D dual-material lattice and the effects of varying the constituent materials and geometry were explored in a parametric study. The lattices had geometries similar to those found in lightweight structures in many transport applications including aerospace and spacecraft. The aim was to determine how to reduce the CTE of such structures to near zero, by using two constituent materials with contrasting CTEs, without incurring penalties in terms of other elastic and failure properties, mass and manufacturability. The results are scale independent and so generic to all such lattices. Lattice CTE was primarily driven by the geometry of the lattice and the mismatch in the constituent's CTE and elastic moduli, with zero CTE attainable if (i) the relative lengths of internal members a and b were in the range of 1.4-1.6, and (ii) the contrast between a b and a a was at least 4. Large negative CTEs could be obtained easily if in addition the ratio of moduli E b and E a was more than 10. It was shown that pairings of commonly used materials, in lattices with commonly used geometries, can give near-zero and negative CTEs. It was shown that this dual-material mechanism effectively exchanges distortion for internal stress. With carefully chosen material pairings there were either small or no penalties for the reduced CTE in terms of other key mechanical performance indices, e.g. premature failure. Two lattices were manufactured, one monolithic and one dual-material (grade 2 titanium and aluminium 6082). Their thermal expansivity was measured and found to match closely the analytical model's prediction.

Effects of pyrolusite additive on the microstructure and mechanical strength of corundum–mullite ceramics

“…The absolute value ratio of the ionic radius difference is |Δ|E8.8%o15%. However, the ionic radii of Mn 2 þ , Mn 3 þ , Fe 2 þ , Fe 3 þ and Ti 4 þ have comparatively large difference with that of Al 3 þ , and they cannot easily pile into the crystal lattice or replace the lattice elements [21,22]. Accordingly, Mn 4 þ of MnO 2 and Al 3 þ of mullite that have similar crystal structure (octahedron) and similar ionic radius are much conducive to form continuous solid-solution.…”

Optimal design of periodic frame structures with negative thermal expansion via mixed integer programming

“…Ducted exhaust systems of engines of low-observable aircrafts are also subjected to very large thermal stresses (Deaton and Grandhi 2013). Other examples include aerospace structures subjected to non-uniform heating, such as satellite telescope structures (Jacquot et al 1998) and lattice structures for supporting satellite antennae and photovoltaic arrays (Palumbo et al 2011). These structures undergo large temperature differences between sunny and shady sides.…”

Metamaterials with negative Poisson’s ratio and non-positive thermal expansion

“…Through tessellations of this unit, many 2-D and 3-D structures could be designed to attain a tunable negative, zero or positive CTE. Palumbo et al (2011) designed lattice structures with two constituent materials based on lightweight structures found in aerospace and spacecraft applications. These types of structures are similar to those proposed by Grima et al (2007) that are fully triangular lattice structures made from more than two materials.…”