Experimental studies of the material properties of the forewing of cicada (Homóptera, Cicàdidae)
1 State Key Laboratory of Nonlinear Mechanics (LNM), Institute of Mechanics,
Chinese Academy of Sciences, Beijing 100080, People's Republic of
China
2 Department of Mechanical Engineering, The University of Hong Kong, Hong
Kong, People's Republic of China
* Author for correspondence (e-mail: aksoh{at}hkucc.hku.hk)
Accepted 2 June 2004
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Summary |
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Key words: cicada, Homoptera, wing, membrane, vein
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Introduction |
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The fully developed wings of all insects normally consist of two
components: membrane and vein. From the mechanical viewpoint, the form of an
individual vein reflects its role in the production of useful aerodynamic
forces by the wing as a whole. Especially on the leading edge of the wing, the
longitudinal veins form a rigid span supporting the wing as it moves through
the air (Wootton, 1992). The
structural and mechanical properties of the wing are obviously intimately
associated with the flight capacity of insects. However, to date, the
aerodynamically relevant material properties of wings themselves have hardly
been studied in detail, with the exception of Wootton's group, who have
specifically studied the structural and mechanical properties of the hindwings
of locusts (Jensen and Weis-Fogh,
1962
; Banerjee,
1988
; Wootton et al.,
2000
; Smith et al.,
2000
; Herbert et al.,
2000
), whereas the dynamic mechanisms of the flight of insects
have been widely investigated recently
(Ellington et al., 1996
;
Van Den Berg and Ellington,
1997
; Dickinson et al.,
1999
; Birch and Dickinson,
2001
; Weis-Fogh and Jensen,
1956
; Maxworthy,
1979
).
The wings of insects have very complex structures. Their mechanical
responses to applied loads are due partly to gross structure and partly to the
properties of the materials from which these components are constructed
(Smith et al., 2000). In terms
of the morphological and mechanical properties of the wing membrane of the
insects during flight, Wootton et al.
(2000
) pointed out that the
membrane is not simply a barrier to the passage of air through the wing but,
in some areas at least, has a structural role as a stressed skin, stiffening
the framework of veins. And there may be local variation in the mechanical
properties and, hence, in the structure of the membrane within the wing, with
profound implications for its functioning in flight. Therefore, both gross
structure and material properties need to be taken into account in any
rigorous engineering analysis.
More recently, for the sake of biomimetic design of the aerofoil of micro
air vehicles, the flight of cicadas has become an attractive research topic
(Ho et al., 2002;
Fearing et al., 2000
), even
though the cicada is actually famous for its song
(Fonseca et al., 2000
;
Fonseca and Revez, 2002
). Such
research interest is attributed to the fact that (1) although the weight of
the body of the cicada is almost 100 times more than that of its own wings,
these wings are still able to lift the heavy body in the air with no
difficulty and fly rapidly and agilely and (2) the wing structure of the
cicada, in particular the arrangements of the venation of the wings, is much
simpler than that of other insects with a big and heavy body, such as locusts
or dragonflies, and therefore such wings can be easily mimicked in the design
of aerofoil of small vehicles. However, to date, the material properties of
the wings of the cicada have never been systematically investigated. Note that
even the study of the structural and mechanical properties of the wings of the
cicada, from the viewpoint of biology, is of considerable merit.
Traditionally, measurements of the properties of the wings of insects
mainly use the methods of tensile testing by some mechanical-test machines
(Smith et al., 2000). However,
tensile testing is very difficult for some small-scale samples of insect's
wings, such as when measuring the mechanical properties of a cell (a
compartment of membrane between wing veins). Therefore, it is necessary to
find a testing method that can more conveniently and accurately measure the
mechanical properties of small-scale samples, such as the cells of
insects.
The nanoindentation technique is an excellent tool for the study of the mechanical behavior of thin membranes, in particular when simple tensile tests are difficult to perform. The development of the nanoindentation technique has allowed highly localized hardness and modulus measurements to be performed on very small material volumes. In principle, if a very sharp tip is used, the contact area between the sample and the tip, and thus the volume of material that is tested, can be made arbitrarily small. Usually, the indented area is difficult to measure by microscope. Thus, the load and displacement during the indentation process are recorded and these data are analyzed to obtain the contact area and mechanical properties.
In the present study, our investigations focus on the structural and mechanical properties of the forewings of the cicada, in particular the membranes and veins of the wings. By means of some experimental techniques, we obtained the relevant geometrical and physical characteristics of the wings. Based on these characteristics, the Young's modulus and the strength of the membranes and veins of the wings were measured using the methods of nanoindentation and tensile testing, respectively. The results obtained by these two testing methods are in good agreement. Finally, we briefly analyzed and discussed all the results.
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Materials and methods |
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Based on the fact that the wing material properties change fairly rapidly
after being removed from the insect (Smith
et al., 2000), all mechanical testing samples were directly
removed from the relevant region of the forewings of living cicadas and
rapidly installed and examined on the relevant experimental machines within
10 min. Therefore, the examined properties of the materials are deemed
approximately the same as those of the parts of a living cicada.
Structural measurements
The morphological and geometrical characteristics of the forewings of
cicadas were determined as follows. The length and width of the wings and the
bodies were measured using an electronic caliper with ±0.1 mm accuracy
(Mitutoyo, Takatsuku, Kawasaki, Japan), and the mass of the wings and bodies
was measured using an electronic balance with ±0.1 mgaccuracy
(Mitutoyo). The thickness of the membrane cells and the diameter of the veins
of the wings were measured using a micrometer gauge with ±0.1 µm
accuracy (Mitutoyo).
In order to measure the real area of the wing, we used a rectangle, which had the area of span x chord of the wing being measured and was equally divided into 100x100 grids, to cover the pictures of the wings measured on the computer. We then removed any grids that did not cover any parts of the wings. The remaining number of grids was considered to be the approximate area of the wings.
Mechanical testing
In order to measure the mechanical properties of the forewings of the
cicada, indentation experiments were first carried out using a nanoindenter
(TriboScope, Hysitron INC, Minneapolis, MN, USA) with a Berkovich diamond
indenter tip (TriboScope) to test the membrane of each and every cell on the
wings.
The membrane of each cell was cut off from the wings to be tested and separately glued on a substrate material using instant adhesive (3M, No. 171). Pure Nickel circular plates, whose hardness, diameter and thickness were 0.26 GPa,20 mm and 2 mm, respectively, were used as substrates. In order to determine the modulus of the membrane accurately using the nanoindentation technique, the adhesive between the membrane and the plate should, firstly, be paved as thin and uniform as possible and, secondly, the line profile of the membrane surface should be measured by the nanoindenter.
Based on the theory of nanoindentation, the reduced modulus,
Er, can be evaluated from the nanoindentation measurements
by employing the following equation:
![]() | (1) |
![]() | (2) |
For evaluating Er, the contact stiffness,
(dP/dh)unload, and the contact area A
should be determined accurately from load against displacement graph measured
during the indentation process. The least mean squares method was employed for
fitting to 90% of the unloading curve according to the hypothesis that the
unloading data can be expressed as a power law
(Oliver and Pharr, 1992):
![]() | (3) |
|
The expression for the contact area using the Berkovich indenter is
approximated by the following formula:
![]() | (4) |
The hardness (H) can be obtained from the following equation:
![]() | (5) |
The effects of a non-rigid indenter on the load displacement behavior can
be taken into account by defining an effective modulus,
Er, as follows:
![]() | (6) |
where E is Young's modulus and is Poisson's ratio of the
specimen; Ei and
i are the corresponding
values of the indenter. For the diamond indenter used in our experiments,
Ei=1141 GPa and
i=0.07. Also, in all
calculations,
is assumed to be 0.25. From equations 1-6, Young's modulus
and the hardness of the membrane can be obtained.
The hardness and elastic modulus of the membrane were measured by employing
the multi-cycles testing method, in which a sequence of multiple
loading-unloading cycles was applied at the same lateral position. This method
enables the determination of material properties with varying indentation
depth. Moreover, the data collected are not affected by the lateral lack of
homogeneity of the sample (Wolf and
Richter, 2003). This is important since the membrane cannot be
deposited to the substrate using physical vapor deposition (PVD) or chemical
vapor deposition (CVD), which ensures homogeneity of the adhesive between the
membrane and the substrate system. Note that for each cycle, the indenter was
loaded to a certain prescribed load over 5 s and then held at this peak load
for 10 s prior to being unloaded to 10% of the said peak load. A sequence of
10 loading-unloading cycles in one experiment was performed. Five to seven
indentations were made on each membrane cell in order to obtain the mean
values. The nanoindentation load, together with the corresponding displacement
data, was analyzed by employing the method of Oliver and Pharr
(1992
) to determine the
nanoindentation hardness and elastic modulus. However, it is difficult to
examine the modulus of the vein using the nanoindentation method, since the
center of the vein of the wing is hollow in shape.
Secondly, the mechanical properties of the wings, including the membranes and the veins, were measured using the material-testing instrument (LLOYD, LR 5K, Fareham, UK). In the testing process, we controlled the extensive displacement of each of the testing samples by the instrument at a loading rate of 0.5 mm min-1 until the testing sample was ruptured. Simultaneously, the applied tensile loads can be automatically recorded by the material-testing instrument.
Some samples were prepared by cutting the veins from the leading edges of the wings. The width and length of each of the vein samples tested were approximately 1.75 and 30 mm, respectively, and the thickness of the samples was the same as the diameter of a vein at the leading edges. Note that the testing span of each of the samples was 20 mm. Similarly, each of the membrane samples used for tensile testing was cut off from the cells of the wings. The width and length of each of the membrane samples, which were without any vein, were approximately 2 and 15-20 mm, respectively; the thickness of the samples was the same as that of the cell. Note that the testing span of each of the membrane samples was 10 mm.
According to the principle of the tensile testing of materials, the
material strain can be taken as:
![]() | (7) |
![]() | (8) |
where F is the tensile force applied on the specimen, and
A0 is the original cross-sectional area of the specimen.
In equations 7 and 8, l0 and A0 were
determined using the structural data of the wings given above;
l and F can be obtained by tensile testing of the
materials. By employing Hooke's law, the Young's modulus of the material is
given by:
![]() | (9) |
From equations 7-9, Young's modulus of the materials can be obtained. However, in order to accurately determine the Young's modulus, the force and deformation should correspond to the linear elastic part of the experimental curve of the samples measured. Due to the non-linear characteristics of biomaterials, the elastic force and deformation do not exhibit a clearly defined elastic limit. Thus, in the present study, we employ a common practice of using the offset method. The amount of 0.02% is set off on the strain or extension axis, and a line is drawn parallel to the straight line portion of the loading curve; the intersection point gives the stress of the elastic limit. Therefore, the slope calculated is deemed the Young's modulus of the biomaterials.
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Results |
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From Table 1, the aspect
ratio of the forewings, b/c, is calculated as
2.98±0.05 (mean ± S.D.), while that
of the bodies, L/W, is
2.13±0.02 (mean ±
S.D.). In terms of the samples we studied here, it was
interesting to note that the aspect ratios of both the forewings and bodies of
cicadas were more or less constant. In addition, it can be seen from the same
table that the area densities (
) of the wings tested were all about the
same, and the mean value is 2.8x10-3 g cm-2.
The cross-sectional diameters of the veins along the venation on the cicada
wings were very asymmetric, for example the maximum and the minimum diameters
of the veins of the forewings were separately found on the veins Sc and
M4, respectively, as shown in
Fig. 2B, and were measured as
approximately 256.3 µm and 50.8 µm, respectively. We measured the vein
diameters of the forewings from the five cicada samples and obtained the mean
± S.D. of the veins of the wings
(133.6±68.9 µm). In particular, the mean diameter of the leading
edges of the forewings was 255.7 µm.
In addition, the veins of the leading edge, i.e. Sc+R, as shown in
Fig. 2B, were cut from the
forewings. Since these veins were hollow in the center and were similar to two
pipes parallel to each other along the direction of the leading edge of the
wings, both pipes were carved and the mean wall thickness of the pipes was
measured as 37.8 µm. Thus, the mean diameter of each hole on the cross
sections of the leading edges was approximately 180 µm.
The thickness for each of the cells of the forewing was measured and is
presented in Table 2. In
addition, the mean thickness of the membrane that was near the edge of the
wing and outside the cells (Fig.
2B) was measured as 8.5 µm. This clearly shows that the
thickness of the cell membrane on the wings was not uniform. The mean ±
S.D. of the thickness of the cells was approximately
computed to be 12.2±1.3 µm. Note that the mean ±
S.D. of the thickness of the cells in
Table 2 does not contain that
of the membrane near the edge and outside the cells. Based on the mean
thickness of membrane, the mean density of the forewing, including the
membrane and the vein, was estimated to be approximately 2.3 g
cm-3.
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Mechanical tests
The measurements of the line profile of the membrane surface of the wing
cells indicate that the mean asperity height (the height from the mean surface
to the real surface) was 18 nm, which is sufficiently flat for performing
nanoindentation.
Fig. 3A shows a typical plot
of nanoindentation load versus displacement data for a cell membrane.
Note that no significant sink-in or pile-up was observed along the sides of
the triangular indentation in the image obtained using a topographic scanning
electron microscope, as shown in Fig.
3B. This illustrates that the difference between the hardness of
the membrane and that of the substrate was very small. In fact, the substrate
was found to be a little harder than the membrane from the indentation data
below. Saha and Nix (2002)
pointed out that the effect of substrate hardness on the film hardness was
negligible in the case of soft film on hard substrate.
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In order to characterize the effects of the substrate on the membrane
hardness and Young's modulus, the parameter P/S2 was
analyzed as a function of the indentation depth relative to the membrane's
thickness (Joslin and Oliver,
1990). For homogeneous materials, P/S2 should
be constant with respect to the indentation depth.
Fig. 4 displays the variation
of P/S2 with indentation depth of some trials. It can be
seen that the parameter P/S2 remained constant when the
depth was less than 600 nm, beyond which it increased until 1600 nm. This
proved that the effects of the substrate were insignificant unless the
indentation depth was greater than 5% of the membrane thickness, which was
12.2 µm. It is important to note that only the data collected from
indentation depths below 600 nm were used to calculate the material
properties.
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From the above equations and experimental data, the Young's modulus and
hardness of the membrane were calculated as 3.7 GPa and 0.2 GPa,
respectively. Table 2 presents
such values for each cell membrane.
The mechanical properties of the veins were firstly tested. A typical
load-displacement curve for the vein from the leading edge of a forewing is
shown in Fig. 5. The elastic
force and elastic deformation were measured to be Fe=13.8
N and le=0.36 mm, respectively. The force and
deformation corresponding to the strength of the material were
Fth=20.5 N and
lth=0.68 mm,
respectively. Since there were two holes in the vein at a leading edge, Sc+R
(Fig. 2B), the original
cross-sectional area of the vein, A0, should exclude that
of the holes; therefore, A0=390.8x10-3
mm2. As a result, the Young's modulus, E, and the
strength,
th, of the vein were approximately 1.9 GPa and 52
MPa, respectively.
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Secondly, as a verification of the above nanoindentation test data, tensile
testing of the membranes was carried out to determine the Young's modulus and
strength for comparison. Fig. 6
shows a typical tensile curve of the membrane cut-off from the cell
M3 of the wing (Fig.
2B). From this figure, the elastic force and deformation were
determined to be Fe=0.58 N and
le=0.06 mm, respectively. Hence, the Young's
modulus of the membrane was calculated to be
3.87 GPa. Moreover, the
yield stress of the membrane was determined to be
29 MPa.
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Discussion |
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For the material properties of the wings, two methods were employed to
measure the Young's modulus of the membrane. The Young's moduli obtained by
the two methods were in good agreement with each other. It was found that the
Young's modulus of the cicada (3.7 GPa) was lower than that of locust membrane
(5 GPa), -keratin (4 GPa), ß-keratin (8-10 GPa) and lepidopteran
silk (10 GPa) (Smith et al.,
2000
) but was much higher than some amorphous protein polymers,
e.g. resilin (1.2 MPa; Gosline,
1980
) and abductin (4 MPa;
Alexander, 1966
). In fact, it
was not only the Young's modulus of the cicada that was very close to that of
most synthetic amorphous protein polymers (
4 GPa), as the typical
load-displacement curve (Fig.
6) for the membrane of the former was also similar to that of the
latter. Thus, the said material is probably a convenient choice for biomimetic
design of the aerofoil of small vehicles. However, more understanding of the
wing's structures and the flight mechanism is needed in order to synthesize
the biomechanical and performance studies.
From the results given above, it can be seen that the strength of the vein was greater than the yield stress of the membrane, whereas the stiffness of the membrane was greater than that of the vein. From the viewpoint of mechanics, the results should be deemed reasonable. The venation of the wing can be regarded as the framework of the wing. If the strength of the framework is too low or the stiffness of the framework is too high, the wing can be broken easily and the flight capability would be affected. The membrane of the wing is similar to a sail. If the stiffness and yield stress of the sail are too low, the flight performance would be deflected easily. It is an indication that in future design of the aerofoil of micro air vehicles, biomimetic design that involves both the aerofoil structures and the mechanical properties of the aerofoil materials selected will be employed. The results of this study should be viewed as preliminary results, which are subject to further testing incorporating flight performance. However, it is worthwhile noting that this study introduces an approach for direct measurement of the biomechanical properties of the wings of insects.
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Acknowledgments |
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