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Transcript
2648
The Journal of Experimental Biology 216, 2648-2657
© 2013. Published by The Company of Biologists Ltd
doi:10.1242/jeb.082545
RESEARCH ARTICLE
The impact behaviour of silk cocoons
Fujia Chen, Thomas Hesselberg, David Porter* and Fritz Vollrath
Department of Zoology, University of Oxford, South Park Road, Oxford OX1 3PS, UK
*Author for correspondence ([email protected])
SUMMARY
Silk cocoons, constructed by silkmoths (Lepidoptera), are protective structural composites. Some cocoons appear to have
evolved towards structural and material optimisation in order to sustain impact strikes from predators and hinder parasite
ingress. This study investigates the protective properties of silk cocoons with different morphologies by evaluating their impact
resistance and damage tolerance. Finite element analysis was used to analyse empirical observations of the quasi-static impact
response of the silk cocoons, and to evaluate the separate benefits of the structures and materials through the deformation and
damage mechanism. We use design principles from composite engineering in order to understand the structure–property–
function relationship of silkworm cocoons. Understanding the highly evolved survival strategies of the organisms building natural
cocoons will hopefully lead to inspiration that in turn could lead to improved composite design.
Key words: silk, composite, silk moth, finite element analysis, deformation.
Received 6 November 2012; Accepted 1 March 2013
INTRODUCTION
Fundamental research on silkworms tends to focus on increasing
our understanding of the material and biochemical properties of their
silk fibres (Porter and Vollrath, 2009). More applied silkworm
research tends to focus on methods to best extract the silk from the
cocoons of the domesticated silkworm Bombyx mori or from wild
cocoons (Gheysens et al., 2011; Kundu et al., 2012), or indeed on
turning those silks into useful textiles or other products. In contrast,
the structure of the cocoon itself has largely been ignored, although
recent research shows that cocoons can be considered as hierarchical
composites composed of silk fibres and sericin bonds, which
confers a number of unique properties to the cocoon (Chen et al.,
2012a; Chen et al., 2012b; Chen et al., 2012c).
Cocoon properties may be of great interest in the biomimetic
development of flexible, damage-resistant, lightweight composites.
For example, many silkworms have silk cocoons with a laminated
structure (see examples of B. mori, Antheraea pernyi and
Opodiphthera eucalypti cocoons in Fig.1). Although the cocoons of
each species have their own individual features, they all have a multilayer structure with fewer fibres connecting layers than aligned in the
individual layers. The interlayer bonding is much weaker than the
intralayer bonding. The porosity of the cocoon layers decreases from
inner to outer layers (Chen et al., 2012b). This structure shares a
morphological similarity with conventional laminated composites, in
which the fibre prepregs are stacked and bonded by resin matrix
between the layers. Furthermore, cocoon structures (and therefore
cocoon properties) are optimised for combinations of different
biological functions across the species range against a range of
different threats and environmental challenges. Importantly, the
animal uses a very limited number of material components, usually
only silk fibre and sericin. Some cocoons also have additional features,
such as extra calcium oxalate crystals on the cocoon surface in A.
pernyi cocoons or the incorporation of hairs and spines (Chen et al.,
2012a). In addition, some cocoons might display rather large holes,
e.g. the cocoon walls of O. eucalypti (Fig.1, insets), which will be
relevant for discussions later in this paper. As the predominant
nonwoven structures in a number of silk cocoons have a similar
microstructure to other stochastic fibrous materials (such as paper,
nonwoven textiles and electrospun polymer mats), the bioengineering
design principles evolved in silkworm cocoons make them excellent
natural prototypes and models for the study of structural composites
(Chen et al., 2010b).
However, in order to fully utilise the biomimetic potential of the
cocoons, we need to better understand the natural (native)
relationships between their structure and function, which have been
‘optimised’ over millions of years of evolution. All cocoons appear
to be multifunctional and possible functions include camouflage
(Danks, 2004), thermoregulation (Lyon and Cartar, 1996) and
humidity control (Blossman-Myer and Burggren, 2010). However,
despite surprisingly little experimental data, the main function of
all cocoons is likely to be the mechanical protection of the enclosed
pupae from predators (Scarbrough et al., 1972; Waldbauer, 1967),
similar to the protection against both general and specialised
predators provided by the silken cocoons enclosing spider egg sacs
(Hieber, 1992). Clearly, the exact way in which the cocoon offers
protection depends on the nature of its main predators.
There seem to be three main strategies that predators employ to
penetrate a cocoon. (1) Penetration of the cocoon wall by drilling.
This strategy is employed by ichneumonid wasps, which lay eggs
in or on the pupae that develop into larvae that parasitise the pupae
(Marsh, 1937). (2) Creating a hole in the cocoon by removing silk
by tearing and shearing movements. This strategy is employed by
mice and other small mammals (Scarbrough et al., 1972). (3)
Creating a hole in the cocoon by breaking individual fibres and the
cocoon wall by making an indentation in the cocoon. This strategy
is employed by birds, which either use their beaks to compress the
cocoon walls or, like woodpeckers, attempt to directly hack holes
in the cocoons (Waldbauer, 1967).
THE JOURNAL OF EXPERIMENTAL BIOLOGY
The impact behaviour of silk cocoons
Inner layer
1 cm
Outer layer
200 µm
2649
Layers
200 µm
200 µm
Fig.1. The morphologies of the layer structure of the cocoons of Bombyx mori (first row), Antheraea pernyi (second row) and Opodiphthera eucalypti (third
row). The first column shows photographs of the cocoon morphology, while SEM photographs of the outer and inner layer structure are shown in columns
two and three. Porosity is found to decrease from inner to outer layers. Inset of A. pernyi cocoon: calcium oxalate crystals found on outer cocoon surface.
Inset of O. eucalypti cocoon: fabricated hole structure found on cocoon surface. The final column shows SEM photographs of cross-sections of layer
structures of the cocoons.
All three strategies involve impact strikes on the outer cocoon
wall. Defences against these strategies would include the ability
to either resist the impact with little damage, or to tolerate the
damage by maintaining the structure. As a cocoon acts as a
protective structure for the pupa, it should evolve to have
engineering benefits such as impact resistance and damage
tolerance by combining the structure and material properties. In
the present study, we focus on how cocoons might have evolved
counter-measures against the third predator strategy (creating a
hole) using an engineering approach. We describe how cocoons
deform during quasi-static localised indentation, and we analyse
these observations with the help of a simple finite element analysis
(FEA) model designed to simulate this behaviour and highlight
key features of the cocoon deformation and failure mechanisms.
This combination of experiment and simulation provides
important insights into the defensive strategy of silkworms,
whose cocoons have structural and materials properties that appear
optimised for achieving a high impact resistance and damage
tolerance.
Importantly, FEA has previously been extremely useful to better
understand the form and function relationships of spider webs
(Hesselberg and Vollrath, 2012; Ko and Jovicic, 2004; Lin et al.,
1995). Indeed, one might go as far as to say that without this
engineering approach such insights would have been impossible
(Vollrath, 2000). After all, FEA requires detailed statements of the
mechanical properties of all component parts, as well as (for truthing)
solid empirical data on the behaviour of the composite itself in
addition to a good understanding of the biological and abiotic
(environmental) frame parameter under which the structure operates
and for which it has evolved. While spider’s webs are lightweight,
airborne net structures that fish for aerial prey, silkworm cocoons
are complex, rather solid composite constructions that house a
delicate inhabitant. Yet in both cases FEA provides key insights
into structure–property–function relationships.
MATERIALS AND METHODS
Study animals
The cocoons used in this study were obtained through commercial
trade. Bombyx mori (Linnaeus 1758) (family Bombycidae) cocoons
were acquired from ICIPE (Nairobi, Kenya). Antheraea pernyi
(Guérin-Méneville 1855) and Opodiphthera eucalypti (Scott 1864)
(both family Saturniidae) cocoons from Korea and Australia were
purchased through Worldwide Butterflies (Sherbourne, UK). All the
cocoons were spun in free space without attaching cocoon walls to
the substrates. In order to keep the intact structure of the cocoons,
samples were frozen at −5°C for 24h to kill the pupae inside before
the emerging adults tunnelled through the cocoon and broke the
structure.
The cocoons were then cut into two halves to release the pupae
without contaminating the cocoon materials. This was done to isolate
the effects of the material properties of the cocoon from any
potentially confounding effects of the pupae. The geometry of the
cocoons replicated in the models was measured using a Mitutoyo
IP65 micrometer (Andover, UK).
THE JOURNAL OF EXPERIMENTAL BIOLOGY
2650 The Journal of Experimental Biology 216 (14)
Tensile experiments
Indentation experiments
Each half of the cocoon samples was affixed (with superglue) at
its cut edge onto a glass slide. The central points of the samples
were measured and marked to be the compressive points.
Opodiphthera eucalypti cocoon samples were cut to avoid the
fabricated holes on the cocoon wall. The tests were carried out in
a Zwick/Roell Z0.5 test machine (Ulm, Germany) under
displacement control at a loading rate of 5mmmin–1. The
indentation load was applied through a steel rod with a round flat
end (1.56mm diameter). The unloading was performed at a speed
of 15mmmin–1. The samples flexed back but did not recover
completely their un-deformed shape. The cocoon samples respond
to form a concave area under the indentor. The shapes of cocoons
crushed during the indentation until the indentor reached the slide
underneath the sample were recorded.
Finite element model
For the finite element modelling, we performed simulations of the
quasi-static response of cocoons in order to understand the failure
modes caused by the local indentation described above. In previous
work we have shown that models based upon open-cell foam
structures describe the mechanical properties of silk cocoons (Chen
et al., 2010b). Here we therefore use the finite element software
ABAQUS/CAE 6.8-4 (Dassault Systèmes, Vélizy-Villacoublay,
France) to simulate the indentation behaviour of the cocoons in this
study, as previous work on simulating deformation in foam materials
was carried out using ABAQUS (Gilchrist and Mills, 2001; Li et
al., 2000; Rizov et al., 2005).
An axisymmetrical idealisation was used for the geometry of the
three cocoon types. The mesh consisted of 94,400 finite elements
with two elements through the wall thickness (Fig.2). All degrees
of freedom at the boundary of the specimen bottom were constrained,
simulating a rigid fixed support. The indenter was modelled as a
force applied to a circular area on the upper surface of the cocoon
in the program. All degrees of freedom of the indenter were
constrained, except in the vertical direction.
RESULTS
Material properties
Four types of silk cocoon were categorised according to their different
mechanical behaviours in a previous paper (Chen et al., 2012c): (1)
‘lattice’ cocoons, with a loose scaffold structure, (2) ‘weak’ cocoons,
with high porosity and weak interlayer bonding properties, (3)
‘brittle’ cocoons, with low porosity, strong interlayer bonding and
brittle mechanical properties, and (4) ‘tough’ cocoons, with medium
porosity, interlayer bonding and tough mechanical properties. Here
a typical cocoon was selected from each of the latter (2–4) three
nonwoven cocoon categories in order to investigate their failure
mechanisms. Bombyx mori cocoons have high porosity: the inter-fibre
bonding breaks gradually with the increasing strain, leading to a
reducing modulus; the stress drops when the breakage of the structure
reaches a percolation point, then the unbonded fibres unravel from
the structure. Opodiphthera eucalypti cocoons, in comparison, have
low porosity and strong bonding between the fibres; a crack starts
from the sericin binding matrix and propagates to the fibres; the
structure fails when the fibres break perpendicular to the tensile load,
which is seen in the stress–strain curves as a dramatic drop of the
stress (Fig.3). The A. pernyi cocoon has a medium porosity compared
with the other two cocoons: it exhibits yielding below 20% strain,
which absorbs the energy to produce a tough behaviour; the structure
fails when more than half of the sericin binder matrix fragments; the
fibres then pull out from the structure, which is seen as a stress tail
in stress–strain curves.
We have previously shown that B. mori cocoons have a graded
layer structure, where the innermost layer exhibits a strong but brittle
behaviour, while the outermost layer is usually the weakest layer
(Chen et al., 2012b). This is due to the gradual increase of porosity
and the decrease of the number of sericin binding points from the
innermost to the outermost layer. In this paper, a similar behaviour
of A. pernyi cocoons is shown. The fibres break at the innermost
layer and disentangle in the outer layers. The graded morphology
140
Bombyx mori
Antheraea pernyi
Opodiphthera eucalypti
120
100
Stress (MPa)
The tensile strength and modulus of the cocoon materials were
measured with a crosshead speed of 2mmmin–1 in an Instron 5542
(Instron, High Wycombe, UK). Test specimens were individually
cut from the cocoon wall with a sharp blade into dogbone-shaped
samples having a width of 5mm and a length of 15mm.
Opodiphthera eucalypti cocoon samples were cut to avoid the
fabricated holes on the cocoon wall. The gauge length of samples
in the tensile test was 5mm. The samples were aligned using a
rectangular guiding tool from the Instron instrument. Three samples
of each cocoon species were tested.
80
60
40
20
0
Fig.2. The finite element analysis geometry model of half of a Bombyx mori
cocoon.
0
0.2
0.4
Strain
0.6
Fig.3. The mechanical tensile behaviour and breaking mechanism of
cutouts of three typical nonwoven cocoons [for a large set of data
highlighting intraspecific variance, see Chen et al. (Chen et al., 2012c)].
The insets show SEM photographs of the microstructural failure in the
cutouts, with scale bar lengths of 0.5 mm for the top inset and 1.0 mm for
the two lower insets.
THE JOURNAL OF EXPERIMENTAL BIOLOGY
The impact behaviour of silk cocoons
2651
A
120
80
40
0
0
Load (N)
120
Fig.4. Photographs of the quasi-static impact tests of three cocoons
showing their deformation: (A) Bombyx mori; (B) Opodiphthera eucalypti;
(C) Antheraea pernyi.
observed from the scanning electron micrographs in Fig.1 confirms
the same mechanism as in the B. mori cocoons. Opodiphthera
eucalypti cocoons show a clean failure in the structure because of
their low porosity, even in the outermost layer. However, the sericin
bonds still start at the outermost layer and then propagate into the
inner layers. We conclude that all three nonwoven cocoons tested
have a graded layer structures in which the mechanical strength
increases from the outer to the inner layers.
Indentation experiments
Typical load–indentation behaviour and load–deflection curves for
the three cocoon types are shown in Figs4 and 5, respectively, with
deflection given as a fraction of the maximum strain until the
indenter reached the glass plate and with load shown on the same
scale for all the cocoons for comparison. The B. mori cocoon
load–deflection curve shows a gradual decrease in stiffness before
the stress reaches a plateau level with the emission of a noise
(cracking sounds) (Fig.5), which are attributed to the extensive
sericin breakage and delamination in the cocoon sample (Fig.6).
The damage process is also reflected in the fluctuations in the load
response. Bombyx mori cocoons have the largest delamination areas
among the three cocoons and nearly all the interconnectivity
between layers in the concave area is broken (Fig.6). The B. mori
response is relatively consistent, and the five curves shown in Fig.5
reflect the full range of responses, which are attributed here to
relatively consistent size and shape of the cultivated cocoons,
compared with the other wild cocoons.
The indentation behaviour of A. pernyi and O. eucalypti cocoons
has much more variation that that of B. mori cocoons (Fig.5). This
is attributed to their inconsistent geometrical shapes and sizes arising
from them being spun in the wild, in contrast to the cultivated B.
mori cocoons. Generally, both cocoons also have nonlinear
behaviour (Fig.5). The onset of inter-laminar delamination of the
cocoons is again associated with the gradual decrease of the
stiffness in the load–deflection curves. After that, the cocoons are
extensively damaged, which can be seen from the pronounced
fluctuations in the load–deflection curves. Antheraea pernyi cocoons
have extensive sericin breakage and some delamination after
0.2
0.4
0.6
0.8
1.0
0.2
0.4
0.6
0.8
1.0
0.4
0.6
0.8
1.0
B
80
40
0
0
C
120
80
40
0
0
0.2
Deflection (mm mm–1)
Fig.5. Load–deflection curves of impact tests of cocoon samples from (A)
Bombyx mori, (B) Antheraea pernyi and (C) Opodiphthera eucalypti. The
solid lines are specific cocoon measurements, and the dashed lines for
A. pernyi show the higher and lower limits for the wide range of cocoon
geometries.
indentation tests. In contrast, general fibre and layer breakages are
found in O. eucalypti cocoons with less damage propagation and
large-scale failure found close to the indentation area. The
indentation terminates with a clear penetration of fibre and layer
breakage in O. eucalypti cocoons (Fig.6).
One of each of the three experimental tests from both A. pernyi
and O. eucalypti cocoons were selected for finite element modelling.
Their specific geometrical data were collected for FEA calculations,
and their experimental curves were used for comparison with the
simulation results.
FEA: constitutive model for materials
An open-cell foam model was used to describe the tensile properties
of cocoon walls based upon the similarity of cocoon morphology
with that of cellular materials (Chen et al., 2010b). The compression
behaviour of cocoon shells can be described by a comparable opencell foam model using the appropriate deformation geometry of the
cell walls under compression (Chen et al., 2010b). To complicate
things further, the inter-laminar debonding contributes to the
mechanical properties of cocoon walls and thereby must be included
THE JOURNAL OF EXPERIMENTAL BIOLOGY
2652 The Journal of Experimental Biology 216 (14)
Fig.6. SEM pictures of cocoon
microstructures showing damage
mechanisms after penetration. Above:
delamination. Bottom: breakage of the
fibre and sericin. (A)Bombyx mori.
(B)Antheraea pernyi. (C)Opodiphthera
eucalypti. Bombyx mori and A. pernyi
cocoons show sericin breakage among
the fibres, while O. eucalypti cocoon
has fibre breakage and penetration in
the structure.
n
σ
σ0 ⎛ σ ⎞
+a ⎜ ⎟ ,
(1)
E
E ⎝ σ0 ⎠
where σ is the stress, ε is the strain, E is the Young’s modulus, α
is the yield offset parameter, σ0 is the yield stress, n is the hardening
exponent and α(σ0/E) is the yield offset strain.
All these parameters come from fitting experimental tensile
stress–strain data, as shown in Fig.7 and Table1. As this is a
deformation plasticity model, which is actually an elastic model
modified to include yielding behaviour, it does not include the
rapid drop in stress at the percolation damage point in each
experimental curve. This model is chosen to simply suggest the
mechanism for initiation of the cocoon collapse in areas where
the modulus reduces significantly under load without including
the damage propagation.
ε=
FEA simulation results for shape changes of cocoon samples
Fig.8 shows the evolution of the stress on the outer surface of the
cocoons at three increasing indentation loads and also the stress
through the thickness of the cocoon wall in a cross-section through
the long axis, with red being the highest stress and blue the lowest.
Three different sets of indentation loads were selected to show the
cocoon deformations evolved from elastic, initial yield and plastic
stages. The cocoon sample has a highly deformed zone, which is
localised around the indenter, while other parts of the cocoon
undergo far less deformation. The highest tensile stress is
concentrated on the outer surface of the minor axis of the cocoon.
Indentation: comparison between experiments and
simulations
Most of our experiments and simulations of cocoon indentation
were carried out on B. mori cocoons and hence we concentrate
200
B. mori test data
B. mori simulation
A. pernyi test data
A. pernyi simulation
O. eucalypti test data
O. eucalypti simulation
160
Stress (MPa)
in the deformation and failure mechanisms, particularly where shear
(hence bending) deformation is involved through the wall thickness
(Chen et al., 2010b).
The plastic compressibility of foams results from the collapse of
the cell walls due to buckling, breaking or yielding (Rizov et al.,
2005). A localised progressive crushing mechanism for foams is
described by Li et al. (Li et al., 2000), where the plastic deformation
is usually localised into the weakest cell layer and the strain increases
rapidly in this layer and then triggers the next layer to crush. This
process is very similar to the bond fission and delamination
processes of cocoon damage. Because such foam compression
simulations have previously been calculated and modelled using
ABAQUS (Li et al., 2000), we expected to find an appropriate
constitutive model in the software that would implicitly include
damage occurring in the plasticity of the irreversible process of
cocoon indentation
A number of different constitutive plasticity models in ABAQUS
were tested for their ability to reproduce the experimental tensile
stress–strain relationships. The (generally hyperelastic) constitutive
models were selected for testing by experienced ABAQUS users
and literature examples. The selection was made by a combination
of best visual fit to material test data, and also computational
efficiency of simulations, as some models gave very slow
convergence. The most appropriate deformation plasticity model
available in our version of ABAQUS is the Ramberg–Osgood
plasticity model, which describes the strain response to an applied
stress through a yield process:
120
80
40
0
0
0.2
0.4
Strain
0.6
Fig.7. Stress–strain curves for cocoon samples tested and simulated in
uniaxial tension from the deformation plasticity model.
THE JOURNAL OF EXPERIMENTAL BIOLOGY
The impact behaviour of silk cocoons
2653
Table1. Parameters of the plasticity constitutive model used in the finite element analysis simulations
Bombyx mori
Antheraea pernyi
Opodiphthera eucalypti
Thickness (mm)
Young’s modulus (MPa)
Poisson’s ratio
Yield stress (MPa)
Exponent
Yield offset
0.61
0.43
0.25
500
730
850
0.1
0.1
0.1
43.524
77.461
127.97
11.579
4.8584
10.225
0.2842
0.377
0.3985
B. mori
A. pernyi
O. eucalypti
Applied load: 16.73 N
Max. strain: 3.3%
Applied load: 4.01 N
Max. strain: 0.48%
Applied load: 2.31 N
Max. strain: 0.24%
Applied load: 29.18 N
Max. strain: 4%
Applied load: 11.99 N
Max. strain: 4%
Applied load: 20.51 N
Max. strain: 6.5%
Applied load: 57.3 N
Max. strain: 5.6%
Applied load: 20.51 N
Max. strain: 6.1%
Applied load: 29.18 N
Max. strain: 9.2%
Concave stress
Cross-section
strain
Concave stress
Cross-section
strain
Concave stress
Cross-section
strain
Fig.8. Evolution of cocoon indentations deduced from the numerical modelling. Three applied loads were selected from the load–deflection curves of each
cocoon. The stress level in the concave and the strain level in the cross-section of the cocoon minor axis are shown. The simulation calculates the
maximum strain in the cocoon structure.
THE JOURNAL OF EXPERIMENTAL BIOLOGY
2654 The Journal of Experimental Biology 216 (14)
Fig.9. Comparison of cocoon shapes between
experiments (above) and numerical simulations using
the Ramberg–Osgood plasticity model (bottom). Panels
A–F show the development of the indentation concave
with increasing penetration.
simulations of A. pernyi and O. eucalypti cocoon also reproduce
the experimental results before the materials yield (Fig.11).
Fig.12 shows the distribution of the stress and strain that
corresponds to the divergent point between the experimental results
and the numerical simulation at approximately 20% B. mori cocoon
deflection. The inner surface of the cocoon centre, which is localized
under the indenter, has a highly deformed zone. The outer surface
of the edge of the bending concave crater (circled) also develops
the highest general strain, which is locally above 4% strain due to
the tensile force distribution on the outer surface. This happens to
be the breaking strain of sericin (Fig.13) (Chen et al., 2010a).
The experimental observations suggest that this divergence between
simulation and experiments indicates that the model cannot predict
the initiation of damage. In the cocoon, the initiation of the damage
A
60
A. pernyi test
A. pernyi model
40
20
Load (N)
on these results in order to deduce general trends. The measured
and simulated static indentation responses of B. mori cocoon
samples are shown in Fig.9. Simulation can generally reproduce
the concave shapes of the cocoons seen in experiments at small
deflections. However, with high deflection, the shape deformation
in the simulations tends to concentrate too much around the
indenter. In the experiments, the indenter gives a broader crater
area of deformation of the cocoon, thereby giving a lower crater
height.
Different constitutive models for the cocoon wall material were
tried, including hyper-elastic models and even simple rubber models,
on the B. mori cocoon FEA (data not shown). The general concave
shape of the cocoon indentation crater can be reproduced almost
universally, but clearly with poor predictions of the load, which
suggests that the general cocoon response behaviour is generic and
independent of the material properties. The geometric shape of the
cocoon appears to have more effect on its indentation behaviour.
The measured and the simulated static indentation load responses
with the same cocoon geometries of B. mori are given in Fig.10,
but using different sets of material parameters in the constitutive
model. For the B. mori material data shown in Fig.10, the initial
elastic slope of the simulated load–indentation curve is in good
agreement with the experimental results. However, at large
deflections the numerical simulations do not reproduce the overall
‘yielding’ profile; the finite element modelling and the experimental
study diverge at approximately 20% deflection. Using the
constitutive model parameters for A. pernyi simply shifts the
simulation to higher loads due to the higher modulus. The
0
0
120
0.2
0.4
0.6
0.8
1.0
0.8
1.0
B
O. eucalypti test
O. eucalypti model
60
90
B. mori material FEM
A. pernyi material FEM
Load (N)
B. mori sericin material FEM
40
60
B. mori test
30
20
0
0
0.2
0
0.4
0.6
–1
0
0.2
0.4
0.6
0.8
Deflection (mm mm )
1.0
Deflection (mm mm–1)
Fig.10. Comparison between load–deflection curves predicted by the finite
element modelling (FEM) of different materials data input and from the
impact test on Bombyx mori cocoons. The circle highlights the diversion of
the simulation and experimental results.
Fig.11. Comparison between stress–strain curves deduced from the finite
element modelling and from the impact test for (A) Antheraea pernyi and
(B) Opodiphthera eucalypti. The solid lines are experimental results that
have the same cocoon geometry as the model simulation, and the dashed
lines are from other experiments of other cocoon geometries of the same
species.
THE JOURNAL OF EXPERIMENTAL BIOLOGY
The impact behaviour of silk cocoons
2655
Fig.12. Distribution of the stress and strain
corresponding to the maximum indentation load
obtained from Bombyx mori cocoon in the finite
element analysis. Above: stress in the cocoon concave.
Below: strain in the cocoon cross-section. The largest
deformation is found at the innermost side of the
cocoon under the impacter. The circle highlights the
large deformation found at the edge of the cocoon
concave crater.
is the sericin breakage between the layers at the surface of the cocoon
(Chen et al., 2010b). To explore this hypothesis, a B. mori sericin
model was used in the indentation simulations. This model uses the
sericin properties (Fig.13) and has the same stress–strain behaviour
as B. mori cocoon material at low strain, but is constrained to yield
at 4% strain as for pure sericin (Fig.14). The intention was to examine
whether the local stress–strain response in the cocoon walls is
dominated by sericin failure.
The sericin model can reproduce the experimental results at low
strain shown in Fig.10, but the simulations would not converge above
a deflection of approximately 30%, which corresponds to a local strain
at the outer surface of 4.5% and suggests failure of the sericin binder
material. This suggests that the point at which the simulations diverge
from the experiments is the initiation of the sericin breakage, which
is an irreversible damage in the cocoon structure that is not included
in the constitutive model. The point at which the sericin damage
threshold is reached should correspond to delamination of the cocoon
and loss of connectivity in the planar interfibre bonding. At this point
the composite material cannot sustain load, and the stress is transferred
in a cascade to ever-deeper layers of the cocoon structure to propagate
the damage process through the full cocoon thickness, resulting in
no more increase in the indenter load.
DISCUSSION
The present study demonstrates that the silk moth cocoons show
adaptations to resist standardised impact forces in the laboratory,
which suggests that cocoons could similarly be adapted to resist
impact forces generated by predators in the wild. The moth larvae
appear to employ a number of different strategies while building
the cocoons to increase their impact resistance and damage tolerance
by combining their macro-structural shape, micro-layer structure
and properties, and component materials. These hierarchical
organisation and complicated engineering properties are inherent to
their design.
The B. mori cocoon is the most comprehensively studied type of
silkworm cocoon in terms of structure and properties (Chen et al.,
2012a). So it was used as the main example for analysing impact
resistance and damage tolerance in cocoons. Our experimental and
modelling results both suggest that the silk cocoon may indeed be
mechanically suited to withstand impact force. This is because of:
(1) the ellipsoid shape of the cocoon, (2) the component material
properties, (3) the laminated layer structure and (4) the graded layer
properties. Both the experiments and models show that loading the
cocoon centre leads to a concave shape of deformation (Fig.9). The
ellipsoid shape of the cocoon allows a certain level of elastic
deformation of the cocoon wall, and then restricts the deformation
to avoid propagation of damage. In contrast, FEA simulations
suggest the deformation process and the deformed shape of the
cocoon is relatively independent of its material properties (Fig.10).
The damage is localized at the edge of the bending concave crater
without excessive propagation of breakage. The material properties
affect only the elastic deformation rather than the damage area. This
THE JOURNAL OF EXPERIMENTAL BIOLOGY
2656 The Journal of Experimental Biology 216 (14)
60
400
Silk fibre
40
200
Sericin
O. eucalypti
Stress (MPa)
Stress (MPa)
300
A. pernyi
100
20
B. mori
0
0
20
40
B. mori test data
B. mori cocoon material simulation
B. mori sericin material simulation
60
Strain (%)
Fig.13. Stress–strain curves of silk fibre, sericin and cocoons. Data for silk
fibre and sericin were obtained from previous work (Chen et al., 2010b).
0
feature helps to keep an intact cocoon structure, and provides a good
support to avoid massive deformation onto the pupa inside the
cocoon by using limited materials.
In biological structures, the component material properties usually
closely link with the structure, as they evolve together to fit the
biological functions (Vincent, 2012; Meyers et al., 2008; Vogel,
2003). This is also found in the B. mori cocoon in its relationship
between component properties and laminated structure (Chen et al.,
2012b). The damage of the B. mori cocoon can be described by two
coupled failure modes: sericin bonds cracking and delamination.
FEA shows that sericin cracking is the first fracture event around
the edge of the cocoon concave during an impact process due to its
relatively low breaking strain compared with the fibres (Figs12,
13). After extensive breakage of sericin bonds, delamination (the
crack in the sericin bonds between layers) develops, inducing
separation of the individual layers, which has been observed from
our experimental results (Fig.6). This sacrificial breakage allows
each fibre layer to deform semi-independently rather than
transferring the stress through the layers. In contrast, silk fibres with
a high strain to failure adapt within this individual layer structure
(Fig.13). The fibre layer can have an elastic deformation without
damaging the fibre to maintain its own mechanical properties in the
fibre directions. This gives maximum energy absorption and
increases the toughness of the structure.
The graded layer structure is another feature that may have
evolved to improve the impact resistance of the cocoon. This is based
on the FEA simulation results that the largest deformation of the
cocoon happens at the innermost layer of the area under the impacter
(Fig.12). After delamination damage, the individual layer would be
able to deform independently, and the properties of each layer would
determine its own damage mechanism. We have learnt from our
previous publication that the mechanical properties of cocoon
layers decrease from the inner to the outer direction (Chen et al.,
2012b). This is also confirmed by tensile tests of the cocoons in
this project (Fig.3). FEA simulation, in contrast, shows that the
deformation of layers decreases from inner to outer layers (Fig.12).
It has been pointed out by Zhao et al. (Zhao et al., 2005) that this
material–structure relationship may have evolved to adapt to the
cocoon bending behaviour, which is part of the impact deformation,
0
0.3
0.6
0.9
Strain
Fig.14. Stress–strain curves for the Bombyx mori cocoon experimental test
(red), the cocoon material simulation (black) and the sericin material
simulation (blue).
as the inner layer would sustain more tensile force than the outer
layers.
The A. pernyi cocoon has a breakage mechanism similar to that
of the B. mori cocoon, where the damage initiates at the brittle sericin
and leads to an extensive delamination between the layers (Fig.6).
The separated layers deform to absorb the impact energy and the
relatively strong inner layers provide stiffness and stress to the
structure. Given the species-specific geometry and identical loading
regimes, peak stress was lower in the A. pernyi cocoon because of
its bigger size, leading to less damage and higher impact resistance
(Fig.5). Further, the calcium oxalates crystals found on the cocoon
surface (Chen et al., 2012a) may also help to improve the hardness
of the materials and therefore the impact resistance.
In comparison, the O. eucalypti cocoon seems to employ another
strategy to protect the pupa. It has a high stiffness material property
from its fibre connectivity structure because of its low porosity
(Figs1, 3). This reduces the ability to deform the structure and
damage of the materials, resulting in a high impact resistance. Apart
from sericin cracking, fibre breakage is its significant energyabsorbing mechanism. It leads to a catastrophic penetration when
the sericin crack propagates to the fibres and the failure reaches a
critical extent (Fig.6). This mechanism localises the damage under
the impacter, avoids excessive damage and maintains the structure
integrity in other undamaged areas. In nature, O. eucalypti seems
to have tolerance of holes in the cocoon, as it fabricates woven holes
around its attachment in the cocoon construction (Fig.1). This may
be a compensating strategy for ventilation as it has very low porosity
in the cocoon walls compared with other species (Chen et al., 2012c).
These fabricated holes do not appear to interfere with the structure
and mechanical properties of the rest of the cocoon wall, unlike
other nonwoven cocoons. In this case, it is not surprising that the
O. eucalypti cocoon would employ a penetration-breaking mode in
its cocoon impacting behaviour.
THE JOURNAL OF EXPERIMENTAL BIOLOGY
The impact behaviour of silk cocoons
The impact behaviour of cocoon composites is very similar to
that of conventional composite laminates, where layers of aligned
unidirectional carbon fibres stack with epoxy matrix bonding
between the fibres (Chen and Hodgkinson, 2011). Materials and
structural design are the key tools for controlling energy absorption
and toughness of composites. These design principles in composites
engineering can be used to understand the design criteria of cocoon
structure by connecting the materials and structure with their
engineering functionality. On the one hand, comparative analyses
of cocoons from a broader sample of wild species are essential to
test whether the observed cocoon properties and structures are a
result of adaptations to predators employing different strategies to
penetrate the cocoon walls. On the other hand, as a complicated
engineering product arisen from millions of years of evolution to
fit their individual functions, silk cocoons may be able to provide
a wealth of examples of how to apply biomechanical engineering
principles in the design of synthetic structural composites.
AUTHOR CONTRIBUTIONS
F.C. conceived the study, executed the experiments and the data analysis, and
wrote the main body of the text. T.H. constructed the cocoon model and
performed the FEA simulations. D.P. developed the material models for
simulations from experimental data. F.V. provided the biological background for
the study and revised the text.
COMPETING INTERESTS
No competing interests declared.
FUNDING
This work was supported by The Air Force Office of Scientific Research (grant
number F49620-03-1-0111 to F.C.), the Intra-European Marie Curie Fellowship for
Career Development (project number 234818, to T.H.) and the European
Research Council (grant number SP2-GA-2008-233409 to D.P. and F.V.).
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