Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands
S. Koussios et al.
HOLLOW HELIX HEALING: A NOVEL APPROACH
TOWARDS DAMAGE HEALING IN FIBRE
REINFORCED MATERIALS
S. Koussios*, A.J.M. Schmets‡
* Delft University of Technology
Faculty of Aerospace Engineering, Kluyverweg 1, 2629 HS Delft
The Netherlands
e-mail: S.Koussios@tudelft.nl
‡
Delft University of Technology
Delft Centre for Materials, Kluyverweg 1, 2629 HS Delft
The Netherlands
e-mail: A.J.M.Schmets@tudelft.nl
The utilisation of fibre reinforced composite materials for structural applications has expanded significantly over
the past decades due to their easy processability and favourable structural properties [1]. However, their
susceptibility for damage due to fatigue or impact loads, limits an even further increase of their use. The recent
conception of a mechanism that counteracts the initial stages of structural damage, the mechanism of self healing
[2-3], will prolong the lifetime of these composites and make their behaviour under (random) loads more
predictable.
One particular approach to self healing is the encapsulation of ‘healing agents’ throughout the material [2-3].
Notwithstanding that the effectiveness of this concept has been proven, the healing agents are dispersed
homogeneously throughout the material, without considerations of the likelihood of damage to occur at specific
locations in the material or the minimisation of overall loss of structural strength.
In this paper the aforementioned shortcomings are tackled by means of helix shaped hollow fibres containing the
healing agent. These fibres are wrapped around the actual load carrying fibre bundles and allow for adaptation of
the healing capacity to the existing load situation and damage likelihood. In addition, the proposed composite
configuration is expected to loose less of its original strength upon introduction of the self healing mechanism as
compared to currently existing alternatives.
In this paper we discuss these aspects for the wrapped Hollow Helices. Despite the lack of laboratory tests so far,
the potential benefits of application of this new class of composite materials in structural applications can be
significant and, at the same time, trigger novel concepts of structural design.
Keywords: Fibre reinforced composites, Crack forming, Self healing
1
Introduction
Recent developments in the area of self-healing materials clearly demonstrate their potential
to tackle a large variety of mainly structural integrity related problems.
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© Springer 2007
Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands
S. Koussios et al.
Especially for applications where maintenance is difficult to carry out (space structures) or
items where even small defects can cause significant problems (composite pressure vessels,
hydrogen storage) [4] the introduction of self-healing mechanisms does present a desirable
solution. This paper focuses on self healing composite structures.
Despite their excellent mechanical properties and low weight, composite materials show a
relatively increased sensitivity to damage as compared to other constructive materials. The
main reason for this can be found in the nature of composites: they combine lightweight
polymers (referred to as matrix) with reinforcing fibres that show a spectacular stiffness. The
stiffness incompatibility of these materials inevitably introduces strain mismatch and stress
concentrations [5]. In addition, several layers can be combined with various fibre orientations.
This phenomenon introduces stress concentrations at the layer interfaces that might cause
delaminations. Furthermore, another mechanism for failure generation can be found in the socalled edge effects [6]. More specific, the unloaded edges of e.g. a composite plate (laminate)
are subjected to a complex system of stresses that are theoretically needed to preserve force
equilibrium. Fracture in composites will usually initiate at the locus where materials of
different stiffness meet each other. Therefore, the most likely damage mode is fibre-matrix
debonding. However, depending on the actual stress situation, other mechanisms could apply
as well [1].
To enhance structural integrity, the designer can apply two principles: safe life approach
where the structure should be strong enough to carry the loads, including effects like thermal
and mechanical fatigue and environmental impact, or provide self-healing mechanisms for
controlling the damage propagation, and occasionally recovering the mechanical properties.
Focusing on the second design principle, one of the most significant achievements in the field
of self-healing polymers is the development of embedded capsules with a healing agent,
together with a homogeneous distribution of Grubbs catalyst particles [2]. The developers of
this variant have concluded correctly that if any damage will occur, this will most likely be in
the vicinity of a particular reinforcing fibre bundle or on the interface between polymer and
fibres. An indirectly related variation on this theme is the development of hollow fibres
containing an epoxy agent, adjacently placed to similar fibres that contain a hardener [3].
A price that usually has to be paid for these kinds of self healing polymers is a reduction (that
might be considerable) in the mechanical properties of the undamaged laminate. In addition,
the presence of self healing agents is only required at laminate areas where the probability for
damage is rather high. Moreover, the geometry of such hollow fibres should preferably be
adjusted to the stress situation in that area. Therefore one should create maximized self
healing ability at spots where it is needed, while ensuring a minimal reduction of the
mechanical properties of the laminate as compared to the non self healing variant.
Focusing on composite materials, we propose here a novel self-healing, hollow fibre based,
helix-shaped configuration that is relying on proven concepts. The helix containing the
healing agent /catalyst combination is to be wrapped around the load carrying fibre bundles.
The combination enables tuning of the self healing capabilities versus loss of initial strength
according to the local stress state and the associated damage likelihood. After a short
categorisation and explanation of various loading conditions and damage mechanisms, a
selection of the most critical, and thus self healing demanding, load-geometry combinations is
made.
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© Springer 2007
Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands
S. Koussios et al.
This selection is additionally demonstrated by typical composite strength values.
The self healing mechanism is then outlined and a fracture mechanics based procedure is
described for estimating crack growth rate and arrest by encapsuling the healing process in
two parameters: quality of bonding and reaction velocity / volume of the healing agents. Since
the research is at its initial stage, we can only provide some estimation for the expected results
in terms of healing capability and structural performance. In addition, some applications are
proposed. The paper ends with the outline of several conclusions and recommendations.
2
Loads & failure mechanisms
2.1
In-plane loading
2.1.1 Longitudinal tension / compression
Ideally, a flat composite panel that consists of a matrix that is reinforced with parallel placed
fibres should be loaded in the fibre direction. Although this condition does not guarantee
general optimality, in most cases it holds validity. Intuitively, the much stiffer fibres (as
compared to the matrix) are the main components for carrying the applied loads [1, 5, 6]. In
this sense, cracks in the matrix might not be considered as critical. However, in some cases,
even minor cracks are not allowed, e.g. when considering pressure vessels [4]. Generally, we
can conclude that matrix cracking is not very critical for bearing longitudinal tensile loads.
When the applied load is compressive, a major issue of concern is buckling of the fibres. In
this case the matrix is playing the role of fibre support to prevent buckling. Therefore, largescale damage in the matrix is expected to reduce the compressive strength of the considered
composite plate. Naturally, these cracks initiate at the level of micro cracking, e.g. having a
length of 50 μm [7]. Depending on the load history and intensity, the buckling-affecting stage
can be reached. In conclusion, matrix cracking can affect the compressive strength of a
laminate, but only after significant damage accumulation.
2.1.2 Transverse tension / compression
In the case of tensional load perpendicular to the fibre direction, the load sharing role of the
matrix is critical. One can view the matrix and fibre elements as a series linkage if springs. It
is not a surprise that in this case the adhesion between fibres and matrix will play an
important role. Typically, the transverse tensional strength of such a laminate is of the same
order or even less than the strength of the matrix itself. In most cases, the failure initiates in
the form of micro cracking. Many investigations have been reported on this problem [5, 6].
A comprehensive overview is given in [6]. These models can be divided in several categories.
The simplest, providing satisfactory results is the shear-lag based theory. Without proceeding
into details, it is justified to provide here some order of magnitude regarding the expected
strength and stiffness reduction as a function of normalised crack density. The latter is a
statistical quantity derived by assuming uniform crack spacing leading to an axial stress in the
90° layers that is equal to their transverse strength at 50% of the laminate length. For a typical
[0/902]s carbon/epoxy laminate loaded in tension (figure 1) the crack spacing is given by 1/λ
and the thickness of the 90° layer by 2h2.
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© Springer 2007
Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands
S. Koussios et al.
When these quantities are equal, the so-called limiting crack density is reached. At this stage,
the normalized axial modulus as dropped to 90% of the original value.
The same reduction can be observed for the shear modulus. The normalised transverse
modulus of the cracked 90° layer has been reduced to 25% of its original value (figure 2). At
the same time, the normalized transverse stress (transverse stress divided by transverse
strength) has reached the value 3. This implies a great reduction in strength of the cracked
laminate, particularly in the 90° layer.
In regard to transverse compressive loading, the quality of load transfer between fibres and
matrix is less critical. However, in the case where these elements show significant differences
in Poisson ratios, premature matrix-fibre separation might occur. Another mechanism that can
trigger failure can be found in the stacking sequence. When two neighbouring layers have
significant fibre orientation differences, the deformation incompatibility between fibres and
matrix of one layer is more sensitive to the appearance of micro cracking.
Figure 1: Normalised axial modulus of a [0,902]s Carbon / Epoxy laminate as a function of normalized transverse
crack density. Source: [6]
Figure 2: Normalised transverse modulus of cracked 90° layer in [0,902]s Carbon / Epoxy laminate as a function
of normalized transverse crack density. Source: [6]
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© Springer 2007
Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands
S. Koussios et al.
2.1.3 In-plane shear
In the case of in-plane shear loading, the bonding between matrix and fibres definitely plays a
critical role. At the same time, the shear strength and stiffness of the matrix will dominate the
structural behaviour of the laminate under examination. Hence micro cracking will have more
influence on the structural integrity, as compared to the previous cases.
To assess the influence of matrix interruption at the vicinity of a particular fibre bundle, one
can use shear lag theory based approximations [8]. Application of such an approach on a
micro scale however, is still questionable.
2.2
Special load cases
2.2.1 Fibre load introduction
For the analysis of laminated composite plates, a general assumption is that the fibre is loaded
by the matrix in a constant fashion. In reality however, this is not true. Assuming that the fibre
length is greater than the so-called critical length (minimum length for utilising the fibre
strength) the load introduction is realised by means of a shear stress gradient along the matrixfibre interface (figure 3). This mechanism implies that at the edges of a particular laminate,
the matrix will experience increased levels of shear stress. Obviously, micro cracking will
cause stress concentrations.
Figure 3: Normal stress (σf) in fibre and shear stress (τi) along its periphery according to the Shear Lag theory.
The stresses are generated by load transfer from the matrix onto the fibre. Source: [8]
2.2.2 Stress concentration
Around every rigid enclosure or hole in a laminate, one can expect stress concentrations.
Depending on the anisotropy, the maximum stresses can reach several times the average stress
magnitude. Timoshenko [9] has derived a simple equation providing the maximum stress
value for elliptical holes in isotropic materials:
⎛
⎝
a⎞
b⎠
σ = S ⎜1 + 2 ⎟
(1)
where σ is the maximum stress, S the average stress, 2a the axis of the hole perpendicular to
the applied tension direction, and 2b is the other axis. In the case of a crack, the aspect ratio of
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© Springer 2007
Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands
S. Koussios et al.
the supposed elliptical hole will reach impressive values. For line-shaped cracks, the stress
could even become infinite. In this case, a fracture mechanics approach is preferable. In first
instance however, this approach does not cope with the stress infinity problem unless a plastic
deformation zone is assumed [6, 8]. For the evaluation of stresses in various anisotropic
materials, we refer here to the work of Lekhnitskii, Savin, Tan and De Jong.
2.2.3 Interlaminar stresses & edge effects
Particularly in the case of thick laminates with significant fibre orientation difference in
neighbouring layers, edge effects can cause strength reduction. The work of Pipes and Pagano
has demonstrated that at the very edge of such a laminate, significant in and out of plane shear
stresses (figure 4) can be generated. Obviously these stress gradients will additionally load the
matrix and will tend to enhance micro cracking. The majority of damage initiation cases take
indeed place at the edges of a laminate; hence these regions should deserve special attention.
Figure 4: Typical in-plane and transverse shear stress development due to free edge effects on a laminate.
Source: [6]
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© Springer 2007
Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands
2.3
S. Koussios et al.
Failure
2.3.1 Mechanisms
In figure 5 we present an overview of possible damage modes in composite materials [1].
On a local scale, fibre matrix debonding and longitudinal matrix failure are the most common
mechanisms. Transverse matrix failure is less critical since the surrounding, perpendicularly
placed fibres in the crack area will act as crack stoppers. However, when the crack density is
large enough, failure of the material will still occur. In a larger scale, one can expect
delamination; this is the separation of individual layers (usually with distinctive fibre
orientations).
Figure 5: Fracture mechanisms observed in laminates. Source: [1]
2.3.2 Fracture mechanics
The fracture mechanics approach is based on elastic material behaviour and often used for the
characterisation of crack growth resistance. Important parameters in this characterisation
procedure are the so-called stress intensity factors K and the fracture toughness (some times
referred to as strain energy release rate). To assess the expected benefits from the proposed
self healing mechanism we present here the three basic deformation modes around a crack
(figure 6). The most common among them are mode I and mode II. For an infinite plate that
contains a sharply formed crack, one can utilise analytical solutions. Limitation of the
obtained stresses to realistic values requires the assumption of plasticity at the crack tip.
Most important, this theory states that there is a material related parameter K#c (where # = I,
II, III) referred to as fracture toughness. With this parameter, one can predict the maximally
allowable crack length before collapsing. In the case of multiple micro-cracks, this approach
requires the introduction of a crack distribution in the material. Several statistical models that
assume more or less uniform crack distribution can be found in [5, 6].
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© Springer 2007
Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands
S. Koussios et al.
Figure 6: Basic delamination modes in composite materials. Source: [6]
2.4
Critical cases
On a local scale, (figure 5) it is justified to assume that the critical failure modes include
matrix / fibre debonding due to shear or tension. In a larger scale, one can conclude that
delamination (layer separation) will become critical. These mechanisms are triggered by
micro crack formation that will develop as a function of load history, environmental
conditions and geometry.
In regard to geometry, critical spots are areas around holes and rigid enclosures, and edges of
rather thick laminates. At the same time, even if there are no irregularities, the theoretically
assumed in plane loading for every participating layer might induce transverse tension and
shear. The corresponding strength values for these loads are several orders lower than the in
plane longitudinal tensional strength.
For a typical composite layer, the strength ratios are presented in table 1, where we indicate
how many times lower a particular value is than the longitudinal tensile strength. It is evident
that loading a composite layer on transverse tension and in-plane shear will greatly reduce its
structural performance. As the damage initiates with micro cracking, it is evident that the
introduction of a self healing mechanism at the vicinity of the matrix / fibre interface will
provide significant advantages.
Table 1: Ratio between various strength values as compared to the longitudinal tensile strength for typical
composites. The numbers indicate the ratio “longitudinal tensile strength / strength value”
S-Glass / Epoxy
Kevlar / Epoxy
Carbon / Epoxy
Fibre volume ratio
0.50
0.60
0.63
Long. Tens. Strength
1
1
1
Transv. Tens. Strength
35
46.7
40
Long. Compr. Strength
2.5
4.2
1.3
Transv. Compr. Strength
10.9
8.9
10
In-plane Shear Strength
24.6
28.6
30
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© Springer 2007
Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands
S. Koussios et al.
In a more general fashion, to enhance structural integrity, the designer can apply two
principles: safe life approach where the structure should be strong enough to carry the loads,
including effects like thermal and mechanical fatigue and environmental impact, or provide
self healing mechanisms for controlling the damage propagation, and occasionally recovering
the mechanical properties. In the first case, the structural performance is limited by the
discrepancy of allowable stresses that correspond to different loading conditions. Therefore,
the applied safety factors have usually a rather conservative character. Based on the
knowledge that the applied materials do contain self healing capabilities, the margins of safety
can be decreased. This inevitably leads to lighter structures.
3
Proposed healing mechanism
3.1
Geometry
To comply with the previously indicated requirements and wishes for a self healing laminate,
we propose here the construction of hollow helix fibres that contain healing agents. These
fibres are placed around the periphery of the reinforcing bundles, figure 7. Similar to the
hollow fibres concept [3], the most likely strategy is the adjacent placement of fibres
containing the epoxy agent and the hardener.
An alternative to this configuration is the application of monomers containing fibres, coated
with a catalyst (figure 7). The fragile hollow fibres are designed to rupture when the
reinforcing tow will debond from the matrix or when the matrix (in the vicinity of the
reinforcing tow) will crack. In essence, collapse of the hollow fibre is triggered by either
displacements or a modification in the local stress situation.
dh
Hollow hardener fiber
de
Hollow epoxy fiber
α
Reinforcing
fiber bundle
Monomer carrier
with catalyst
ΔL
coating
Twin system:
D
epoxy + harder
Figure 7: Basic parameters defining the self healing fibres arrangement
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© Springer 2007
Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands
3.2
S. Koussios et al.
Working principle
3.2.1 Crack propagation
As known from fracture mechanics, the effect of increased stress levels around a crack can be
summarised in the stress intensity factor. According to Jones [5] this approach holds true for
composites as long as the cracks are oriented parallel to the fibre direction. Westergaard has
derived an equation expressing the magnitude of the stress intensity factor as a function of the
crack length [7]:
K # = S πa
(2)
where # stands for mode I, II, III (figure 6) and a for the half crack length. Apparently, for a
particular material there is a critical stress concentration factor K#cr. Beyond this value, the
crack will grow exponentially. The main question is; what is a safe crack length? A classical
approach is to capture the length that causes a 50% strength reduction of the material under
consideration. With su representing the strength of the composite materials in a particular
direction for a particular kind of stress, one can derive the critical crack length:
a cr =
4 K #2cr
πsu2
(3)
Assuming a composite structure under predefined fatigue conditions, one can construct an SN
curve that predicts the allowable stress level for a particular number of cycles. This practice
however, is not very common for composites.
Another approach for predicting lifetime is to analyse crack growth. Obviously after a
sufficiently large number of cycles, the critical crack length will be reached.
There exists a considerable variety of simple analytical models that can capture this so-called
crack growth rate. For demonstrative reasons, we present here the well-known Paris law:
da
= CK n
dt
(4)
where a is the crack length as a function of time t, K the stress intensity factor and C, n
material parameters.
3.2.2 Crack closure by self healing
Let as assume that at some fibre / matrix interface a crack of length 2a has initiated. The panel
containing this crack is loaded by a tension stress S. At the same time, rupture of the polymer
containing hollow fibres has triggered a curing reaction that tends to fill the crack. The effect
of cohesion can be captured in a crack-growth counteracting stress Sh that tends to close the
gap. The gap length still remaining open is given by 2s. The stress intensity factor is,
according to a 3D approximation [7], given by:
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© Springer 2007
Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands
K = 2S
a
π
− 2S h
S. Koussios et al.
2
a⎡ ⎛s⎞ ⎤
−
1
⎢ ⎜ ⎟ ⎥
π ⎢⎣ ⎝ a ⎠ ⎥⎦
(5)
Combination of (4) and (5) and substitution of the relation Sh = ξS leads to:
n
2
⎛
da
a ⎞ ⎛⎜
s
⎟ 1 − ξ 1 − ⎛⎜ ⎞⎟
= C ⎜⎜ 2S
π ⎟⎠ ⎜
dt
⎝a⎠
⎝
⎝
⎞
⎟
⎟
⎠
n
(6)
In this equation, the effect of self healing is captured in two parameters: ξ that expresses in
which extend the crack stresses have been relieved, and s representing the crack length that is
still open. Roughly speaking, ξ stands for the quality of bonding and s for the volume and
reaction speed of the healing agents. Obviously, when ξ = 1 and s = 0, the healing is 100%.
The challenge in the approximation presented here is to express these parameters as a function
of time.
3.2.3 Adaptation to loading conditions
In a typical load situation, to transfer the loads from the matrix to the fibres, the complete
periphery of these fibres should be in contact with the matrix material while the bonding
should be perfect. In regard to this theoretically optimal situation, placement of healing fibres
will negatively influence this load transfer mechanism. This effect is inevitable. At the same
time, placement of hollow fibres into the reinforcing bundle or parallel to it will effectively
reduce the tow stiffness. This reduction is theoretically minimal when the healing fibres run in
the periphery of the tow. In this case however, the bonding surface between the fibre bundle
and the matrix is practically vanished. Between these two extreme cases, one can optimize the
helix angle for dealing with these contradicting requirements.
Naturally, the helix angle will also be influenced by the load situation. In pure tension, the
stiffness contribution of the fibre bundles is maximal, and the quality of fibre /matrix bonding
is not relevant. In an in-plane shear load situation, the bonding quality between fibres and
matrix becomes more important. The presence of the healing fibres will reduce the bonding
surface but enhance crack closure mechanisms and therefore prolong structural lifetime.
In the case of irregularities such as holes and rigid enclosures, the density of healing
capability should locally be increased. The same applies on edges of thick laminates where
3D effects and increased interlaminar stress levels are phenomena that can not be overlooked.
In addition, due to their unpredictability, inclusion of self healing capabilities is almost a
must. In such cases of uncertainties, statistical analysis of damage likelihood together with
optimization of the helix angle and fibre dimensions (hence the pitch, figure 7) is expected to
provide interesting results.
In conclusion, the helix angle should accordingly be adjusted to the load and geometry. An
impression of such a variable helix angle is given in figure 8. As indicated in figure 7, the
pitch ΔL and the diameters of the participating fibres are closely related to the helix angle.
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© Springer 2007
Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands
S. Koussios et al.
Other parameters to be adjusted mainly reflect on strategic placement of these hollow fibres
on spots where the possibility for crack initiation or other damage is the highest. In addition,
combination with axially running hollow fibres should be considered as well.
Figure 8: (a) Variable helix angle to optimise repair performance at damage susceptible spot. Segmentation of
the hollow fibre through twist (b) or through a double helix (c)
3.2.4 Materials
The concept described in this paper puts serious demands on the materials to be selected for
the hollow fibre. In the approach of Pang [3] hollow glass fibers were used. The wrapping of
the fibres around the tow at variable helix angles requires the material to be formable while
processed, while the helix material needs to crack and release the healing agent when the
composite is loaded. Ideally one would select a material that hardens, and becomes brittle,
while the matrix is curing. The initial flexibility of the material can be explotied to
compartmentalize the hollow fibre through winding with a similar pitch but opposite direction
a second identical fibre. At the contact points the fibre will close, and form compartments. In
this way a single fibre could be involved in various healing events, located at different places
along its axis.
Another option is to choose a material, e.g. a natural fibre, which after curing of the matrix
material can be loaded with healing agent through capillary action. For this system the
eventual release of the liquid phase into a nearby open volume will be a major challenge.
Another option in relation to the helix material’s selection is to apply a flexible (natural) fibre
bundle that is treated at a later stage with a coating. The role of the coating would be to form
an interface between the matrix material and the liquid that has been stored in the fibre. The
coating should be chosen such that it has a susceptibility to damage comparable to that of the
bulk material.
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© Springer 2007
Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands
S. Koussios et al.
It should be noted that the actual materials selection, processing and testing for the hollow
helix healing concept forms the main challenge for the eventual realization of this concept.
3.2.5 Trigger mechanisms and reaction control
The healing process is triggered by, as previously indicated, internal stresses or relative
displacements. Another option to be considered is external triggering. The idea is here to
additionally incorporate a metallic helix with high electric resistance for enabling the release
of the agents through heating and melting of either the coating layer or the wall of the hollow
fibres.
To control the diffusion of the agents through the matrix and to steer their polymerization, the
hollow fibres can be segmented by means of separating walls, twisting or a double helix
(restriction of two oppositely oriented helixes at the spots where they intersect), figure 8.
The principles of twisting and the double helix will require hollow fibre walls that are flexible
during processing but brittle during service conditions.
3.3
Expected results
3.3.1 Damage recovery
Considering composite fracture, figure 5, the expectations have to be classified according to
the depicted damage modes and the locus where this damage occurs (figure 9). Since the
hollow fibres are wrapped around the reinforcing tows, an obvious expectation is that the
effect of polymerization will have a local character. An overview of the expectation regarding
recovery of the mechanical properties is given in table 2.
Figure 9: Fibre bundle diameter and definition of the damage locus
D
Fibre bundle
Damage
location
S
Figure 9: Fibre bundle diameter and definition of the damage locus
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© Springer 2007
Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands
S. Koussios et al.
Table 2: Effectiveness of the proposed self healing solution on the recovery of the mechanical properties
D = diameter of fibre
Type of damage →
bundle
Longitudinal
Transverse
Dela
Damage location
Fibre-matrix
Fibre fracture
fracture of
fracture of
minati
debonding
distance S ↓
matrix
matrix
on
Not
Excellent
Excellent
Excellent
Little effect
applic
S≤D
able
D ≤ S ≤ 2D
Not applicable
Fair
Excellent
No effect
Fair
2D ≤ S ≤ 5D
Not applicable
Little effect
Fair
No effect
Little
effect
The degree of recovery is not given in numbers, since these they can only be determined by
further research. To provide a coarse estimation, one can interpret “excellent’ as 80 %
recovery, ‘fair” as 50 %, and “little effect” as 20 %. The reduction of the original mechanical
properties as compared to the non-healing laminate is expected to remain below 10 % (see
also [3]).
In regard to time intervals for healing and the associated modification of the mechanical
properties, the polymerization will greatly depend on the involved chemicals and the
condition where the reaction takes place in. Depending on the intended application, the
healing agents should be properly selected.
3.3.2 Applications
On applications level, the expected impact is significant. For the space industry, a major
problem will be solved. This problem is the reparability of damaged space structures where
material integrity plays an important role. For manufactures of high-pressure pipelines and
composite pressure vessels, the proposed solution will tackle a major problem; weeping and
crazing of the involved (usually epoxy) matrix. For aircraft manufacturers, one should focus
on damage and crack propagation. A rigorous issue in these phenomena is predictability and
control. This is induced by the fact that an aircraft should be safe, but at the same time
economic. This implies that maintenance intervals should maximally be extended, and the
repairs planning can be more reliable due to the predictive nature of the material. Naturally,
uncertainty about damage growth rate and crack propagation is a threat for the safety and
economic operation. Assuming that the proposed self healing mechanism is able to provide
reliable data for damage propagation and even realize complete (or sufficient) recovery, the
expected benefits are significant. However, at this stage it is rather difficult to provide reliable
estimations.
4
Conclusions
In this paper we have presented a novel self healing mechanism that is based on a
combination of helix shaped hollow fibres that alternatively contain an agent and a hardener.
Another option is the combination of an agent containing hollow fibres coated with a catalyst.
The proposed mechanism focuses on the fibre / matrix interface since this is the most damage
sensitive area of a typical unidirectionally reinforced composite layer.
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© Springer 2007
Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands
S. Koussios et al.
After a short overview of loads and fracture mechanisms we have motivated which failure
modes are critical and which areas of a composite plate deserve special attention. After the
description of the healing mechanism, an equation is proposed for capturing the quality and
extent of the healing process. Finally, a short qualitative assessment has been given regarding
the expected results and possible applications.
The innovative aspect here is the ability of the proposed mechanism for tuning the healing
requirements to the existing load situation and geometry. This is achieved by a variable helix
angle, the combination of straight and helix shaped fibres and the strategic determination of
cross over points over two interwoven helices. At the same time, these configurations can be
utilised for controlling the healing reaction time and the volume of the resulting hardened
adhesive or polymer. Furthermore, the conceptual idea of compartmentation of the hollow
fibres by means of twisting has been introduced.
Depending on the damage likelihood, severity and kind of loading, the designer will have a
large variety of options for optimising the structural performance of the composite structure.
A drawback of the proposed configuration, which holds true for the incorporation of healing
agents in general, is that a particular volume of the load carrying structure is now replaced by
a passive element.
On the other hand, the incorporated self healing agents are able to guarantee a certain extent
of reliability in service time and, most importantly, provide increased reliability for
controlling and even suppressing crack growth. Depending on the importance of maximising
the structural performance of the undamaged structure or guaranteeing controlled crack
forming and service time, a decision must be taken. Nevertheless, it is believed that the
proposed concept provides sufficient tailoring capabilities for that purpose.
As a part of future research a comprehensive selection and experimental evaluation of suitable
materials and hollow fibres must take place. In addition, more attention has to be focussed on
possible mathematical models for simulating crack growth and reduction, extent of stress
relief and, ultimately, lifetime prediction of damage critical structures with self healing
capabilities. Furthermore, the incorporation of statistical models and simulations for
predicting crack density and severity is to be part of the research.
REFERENCES
1.
2.
3.
4.
5.
6.
7.
8.
9.
Bertherlot, Jean-Marie. Composite Materials: Mechanical Behavior and Structural Analysis. New York:
Springer Verlag Inc, 1998.
S. R. White, N. R. Sottos, P. H. Geubelle, J. S. Moore, M. R. Kessler, S. R. Sriram, E. N. Brown, and S.
Viswanathan, "Autonomic healing of polymer composites," Nature, vol. 409, pp. 794-797, 2001.
Jody W.C. Pang and Ian P. Bond , “A hollow fiber reinforced polymer composite encompassing self-healing
and enhanced damage visibility”, Composites Science and Technology, Volume 65, Issues 11-12,
September 2005, Pages 1791-1799.
Vasiliev VV, Krikanov AA. New generation of filament-wound composite pressure vessels for commercial
applications. Composite Structures 2003: 62: 449-459.
Jones RM. Mechanics of Composite Materials. Hemisphere Publishing Corporation, New York, 1975.
Daniel IM, Ishai O. Engineering mechanics of composite materials. Oxford University Press, New York /
Oxford, 2006.
Marissen R. Craze Grow Mechanics. Polymer 41 (200) pp. 1119-1129.
Nijhof AHJ. Vezelversterkte kunststoffen: mechanica en ontwerp 9in Dutch). Delft University Press, Delft,
2004.
Timoshenko SP, Goodier JN. Theory of Elasticity. McGraw-Hill Publishing Company, New York, 1970.
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