On the optimisation of phase fractions in harmonic structure materials

Abstract Materials with heterogeneous microstructures architected across several scales are becoming increasingly popular in structural applications due to unique strength–ductility balance. One of the most popular 3D-architected structure designs is harmonic structure (HS) where soft coarse-grain (CG) islands are embedded in a hard continuous 3D skeleton of ultrafine grains (UFGs). In this work, a series of HS with varying phase fractions and rheologies are studied based on several models. Model A focuses on a good fit with experimental data in the elastic–plastic transition region, model B focuses on a good fit at large-scale yielding, while in five intermediate models, phase rheology parameters are varied on a linear scale between the values for A and B. For each of the seven selected HS material models, structures with 19 different volumetric fractions of UFG were examined. It is found that the increase of UFG fraction leads to the monotonic increase of strength characteristics in HS material, while higher strain hardening rates in the phases lead to the enhancement of this effect. By contrast, the dependence of ductility characteristics on UFG fraction is non-monotonic having a local minimum at 30% UFG and a maximum at 60% UFG, while also significantly dependent on strain hardening in the phases. Namely, HS material with phases having significant strain hardening reveals the highest uniform elongation exceeding that in 100% CG material already at 40% UFG fraction. The fractions of UFG in a range of 58–62% form HS material with the highest possible uniform elongation.