Veins improve fracture toughness of insect wings

Abstract

During the lifetime of a flying insect, its wings are subjected to mechanical forces and deformations for millions of cycles. Defects in the micrometre thin membranes or veins may reduce the insect's flight performance. How do insects prevent crack related material failure in their wings and what role does the characteristic vein pattern play? Fracture toughness is a parameter, which characterises a material's resistance to crack propagation. Our results show that, compared to other body parts, the hind wing membrane of the migratory locust S. gregaria itself is not exceptionally tough (1.04±0.25 MPa√m). However, the cross veins increase the wing's toughness by 50% by acting as barriers to crack propagation. Using fracture mechanics, we show that the morphological spacing of most wing veins matches the critical crack length of the material (1132 µm). This finding directly demonstrates how the biomechanical properties and the morphology of locust wings are functionally correlated in locusts, providing a mechanically 'optimal' solution with high toughness and low weight. The vein pattern found in insect wings thus might inspire the design of more durable and lightweight artificial 'venous' wings for micro-air-vehicles. Using the vein spacing as indicator, our approach might also provide a basis to estimate the wing properties of endangered or extinct insect species.

Figure 1. Morphology of S. gregaria hind wings.

(a) Schematic illustration of the three wing zones R, B and C used for the experiments (adapted from [8]). (b) Longitudinal veins (LV) with branching cross veins (CV). Towards the edge of the hind wing the two types of veins show a different morphological structure. Whilst the longitudinal veins mostly show a circular to elliptical cross section, the cross veins show an annulated pattern. (c) Cross section through the wing membrane and a cross-vein. Note that the cutting edge of the wing membrane slightly “crumpled” during the desiccation. (d) Close-up of a cross-vein, showing the compartment-like annulated structure.

Figure 2. Crack propagation and fracture toughness of hind wings.

(a) Stress-strain curve and corresponding crack length from one wing sample with an induced notch. The numbers indicate the K_C indices (see text). With increasing strain the stress on the wing membrane increases until the crack starts growing (0). When reaching cross veins (1–4), the crack propagation temporarily stops and the stress further increases. When the cross veins break, the stress decreases and the crack continues to propagate. (b) Crack length and corresponding fracture toughness K_C. The markers 0–4 correspond to the markers in (a). (c) Fracture toughness of hind wing membrane. Although slightly decreasing towards the anal part of the wing, there was no significant difference in-between the fracture toughness K_C0 of the membrane from the tested three wing zones (F_2,16 = 2.087, p>0.1, ANOVA). (d) The membrane alone had a mean fracture toughness of 1.04±0.25 MPa√m (N = 17). The presence of the first cross-vein (index 1) significantly increased the fracture toughness of the wing structure to 1.57±0.38 MPa√m (t₉ = −3.513, p<0.01, paired t-test, both figures show mean±SD, numbers show sample size).

Figure 3. Size and distribution of wing cells in S. gregaria hind wings.

(a) Typical structure of a hind wing, showing the distribution of the wing cells’ major axis length. Cells with smaller major axis lengths are mostly arranged around the perimeter of the wing (CCL: critical crack length). (b) Mean frequency of wing cell sizes from six hind wings. The distribution of cells corresponds very well to a normal distribution around a mean major axis length of 1.103 mm (σ = 544.16, a = 7.33, R = 0.98). The cumulative membrane area formed by cells smaller than the critical crack length is 19.44% of the overall membrane area (mean ± SD, N = 5553 cells from 6 wings). The colour map of the bars corresponds to subfigure A. (c) 2D-Histogram showing the relative frequency of cell size and their distance to the wing edge. There is a significant positive correlation of the major axis length with the distance to the wing edge (ρ = 0.393, R² = 0.154, p<0.001, linear correlation, N = 5553 cells).