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

The coefficient of thermal expansivity (CTE), α, 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 αb and αa was at least 4. Large negative CTEs could be obtained easily if in addition the ratio of moduli Eb and Ea 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.