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Aves are an incredibly diverse class of animals, ranging greatly in size and thriving in a wide variety of environments. Here, we explore the scaling trends of bird wings in connection with their flight performance. The tensile strength of avian bone is hypothesized to be a limiting factor in scaling the humerus with mass, which is corroborated by its experimentally determined allometric scaling trend. We provide a mechanics analysis that explains the scaling allometry of the wing humerus length, LH, with body weight W, LH ∝ W0.44. Lastly, wing feathers are demonstrated to generally scale isometrically with bird mass, with the exception of the spacing between barbules, which falls within the same range for birds of all masses. Our findings provide insight into the “design” of birds and may be translatable to more efficient bird-inspired aircraft structures.
In order to investigate the effect of grain boundaries on the mechanical response in the micrometer and submicrometer levels, complementary experiments and molecular dynamics simulations were conducted on a model bcc metal, tantalum. Microscale pillar experiments (diameters of 1 and 2 μm) with a grain size of ∼ 100-200 nm revealed a mechanical response characterized by a yield stress of ∼1,500 MPa. The hardening of the structure is reflected in the increase in the flow stress to 1,700 MPa at a strain of ∼0.35. Molecular dynamics simulations were conducted for nanocrystalline tantalum with grain sizes in the range of 20-50 nm and pillar diameters in the same range. The yield stress was approximately 6,000 MPa for all specimens and the maximum of the stress-strain curves occurred at a strain of 0.07. Beyond that strain, the material softened because of its inability to store dislocations. The experimental results did not show a significant size dependence of yield stress on pillar diameter (equal to 1 and 2 um), which is attributed to the high ratio between pillar diameter and grain size (∼10-20). This behavior is quite different from that in monocrystalline specimens where dislocation ‘starvation’ leads to a significant size dependence of strength. The ultrafine grains exhibit clear ‘pancaking’ upon being plastically deformed, with an increase in dislocation density. The plastic deformation is much more localized for the single crystals than for the nanocrystalline specimens, an observation made in both modeling and experiments. In the molecular dynamics simulations, the ratio of pillar diameter (20-50 nm) to grain size was in the range 0.2 to 2, and a much greater dependence of yield stress to pillar diameter was observed. A critical result from this work is the demonstration that the important parameter in establishing the overall deformation is the ratio between the grain size and pillar diameter; it governs the deformation mode as well as surface sources and sinks, which are only important when the grain size is of the same order as the pillar diameter.
