The Design of Bonded Bimaterial Lattices that Combine Low Thermal Expansion with High Stiffness

In engineered systems where thermal strains and stresses are limiting, the ability to tailor the thermal expansion of the constituent materials independently from other properties is desirable. It is possible to combine two materials and space in such a way that the net coefficient of thermal expansion (CTE) of the structure is significantly different from the constituents, including the possibility of zero and negative thermal expansion. Bimaterial lattices that combine low, negative, or an otherwise tailored CTE with high stiffness, when carefully designed, have theoretical properties that are unmatched by other known material systems. Of known lattice configurations with tailorable CTE, only one geometry, a pin-jointed lattice, has been shown to be stretch dominated and thus capable of having stiffness that approaches its theoretical upper bound. A related lattice with bonded joints, more amenable to fabrication, is developed that has a stiffness and CTE similar to the pinned structure. Analytical models for this rigid-jointed lattice's CTE and stiffness are developed and compared successfully with numerical results. A near space-filling, negative thermal expansion version of this lattice is devised and fabricated from titanium and aluminum. CTE measurements on this lattice are made and are well predicted by the analytical and numerical models. These insights guide the design of a family of bonded lattices with low areal density, low or negative CTE, and high stiffness to density ratio. Such lattices are shown to have a thermomechanical response that converges on pin-jointed behavior when the lattice elements are long and slender.