In situ microwave characterization of microwire composites under
mechanical stress
Faxiang Qin, C. Brosseau, and H. X. Peng
Citation: Appl. Phys. Lett. 99, 252902 (2011); doi: 10.1063/1.3668109
View online: http://dx.doi.org/10.1063/1.3668109
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Published by the American Institute of Physics.
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APPLIED PHYSICS LETTERS 99, 252902 (2011)
In situ microwave characterization of microwire composites under
mechanical stress
Faxiang Qin,1,2 C. Brosseau,1,a) and H. X. Peng2
1
Université Européenne de Bretagne, Université de Brest, Lab-STICC, CS 93837, 6 Avenue Le Gorgeu,
29238 Brest Cedex 3, France
2
Advanced Composite Centre for Innovation and Science, Department of Aerospace Engineering,
University of Bristol, University Walk, Bristol BS8 1TR, United Kingdom
(Received 25 October 2011; accepted 18 November 2011; published online 20 December 2011)
We present results of an experimental characterization of the dielectric properties and microwave
absorption of rubber composite samples containing Fe4Co68.7Ni1B13Si11Mo2.3 amorphous
microwires which are submitted to a low uniaxial tension. Measurements of the dielectric loss and
microwave absorption as a function of strain over the frequency range of 300 MHz-6 GHz reveal
that the uniaxial elongation randomly breaks wires at about 2.8% strain and this has for effect to
decrease the loss factor for larger strain. Two possible mechanisms are identified to account for our
observations, namely, the stress and shape effects. The ability to control this stretch breaking
phenomenon will be instrumental to developing stress tunable microwire composites for sensing
C 2011 American Institute of Physics. [doi:10.1063/1.3668109]
applications. V
Multifunctional micro- and nanostructures exploiting
microwave relaxation and/or resonance phenomena are important in many technological applications from reconfigurable microwave devices1 to microwave non-destructive
testing.2 Whether generated by the application of a magnetic
field, a mechanical deformation, or even a temperature gradient, questions surrounding the coupling between the structural, electromagnetic, and mechanical properties of such
materials continue to pose many theoretical and experimental challenges.
The correlation between the materials parameters (effective permittivity and magnetic permeability) and stress in
filled polymers, e.g., carbon black filled cross-linked rubber
and plasto-ferrites, has been experimentally established.3 For
example, microwave measurements indicated large
decreases in the real and imaginary parts of the effective permittivity of axially elongated samples.4,5 This set of experiments illustrates that the microwave permittivity data scale
as a power law in frequency, where the exponent is
extremely sensitive to stress. In addition, the effective permittivity measurements under stress can be explained in
terms of the Gaussian molecular network model in the limit
of low stress.6
From a different perspective, we recently considered a
class of multifunctional microwire polymer composites for
structural health monitoring.7,8 While the magnetic field
response of these materials has been intensively studied,9,10
definite models for the stress effect remain debatable. It is
well established2 that the application of an external stress
modifies the magnetic anisotropy and domain structure of
the wires. This has the effect to change the ferromagnetic
resonance and to modify the eddy current loss, which in turn
will eventually affect the effective permittivity. We have
also observed that the permittivity spectra of such compoa)
Author to whom correspondence should be addressed. Electronic mail:
Christian.Brosseau@univ-brest.fr.
0003-6951/2011/99(25)/252902/4/$30.00
sites can be modulated by the application of a mechanical
constraint.6,11,12
Here, we focus on the dielectric response of microwire
polymer composites and approach this problem through a
combination of well-controlled experiments of microwave
characterization under mechanical stress. First, we perform
tests on microwire filled rubber composites which we regard
as a model material. Our experiments also show that the uniaxial elongation randomly breaks wires at about 2.8% strain,
and this has the effect to decrease the loss factor for larger
strains. This stretch breaking phenomenon suggests the possibility of controlling the dielectric properties and microwave absorption of microwire polymer composites.
glass-coated
magnetic
Fe4Co68.7Ni1B13Si11Mo2.3
microwires having diameter of 12.8 lm (MFTI, Moldova)
and silicone rubber were used for the fabrication of composite materials. The wires were chosen due to their strong
magnetoimpedance properties making them suitable for
designing complex composite media for microwavefrequency operations.7,8 Twelve continuous microwires
with length of 70 mm (wire length is comparable with the
wavelength of the exciting wave) were embedded in a parallel manner with lattice constant of 1 mm into the silicone
rubber matrix. The resultant composite has a dimension of
70 mm13 mm1.8 mm. The volume fraction of inclusions
is calculated by the ratio of the wires volume to the composite sample volume.
We measured the room temperature effective complex
(relative) permittivity e and magnetic permeability l spectra
of these samples which are submitted to a tensile strain up to
4.5%, using a home-built experimental setup over the
0.36 GHz frequency range. Our experiments consist of
measuring the transmission and reflection coefficients of an
asymmetric microstrip transmission line containing the sample during elongation.13 The electromagnetic measurement
was carried out with a wave vector of the electromagnetic
field perpendicular to the wires. The quasi-TEM transverse
99, 252902-1
C 2011 American Institute of Physics
V
252902-2
Qin, Brosseau, and Peng
electromagnetic mode, which is the only mode that propagates in the structure, makes the analysis of the complex
transmission and reflection coefficients relatively simple. A
vector network analyzer (Agilent, model H8753ES) with
SOLT calibration is used to measure the S parameters of the
cell containing the sample under test. Using the NicolsonRoss procedure for the transformation of the load impedance
by a transmission line,10 e and l are determined by the transmission S21 and reflection S11 coefficients. The strain of the
material subjected to a uniaxial tension is defined as
k ¼ ð‘ ‘0 Þ=‘0 , where ‘ and ‘0 denote the actual and initial
lengths of a sample, respectively. The accuracy, reproducibility, and analysis of our technique were tested by measurements on a number of heterogeneous soft materials.13–15 As
was discussed in Ref. 13, these measurements require an
accurate measure of the residual air-gap between the sample
and the transmission line walls. Additional tests of the tensile
properties of the microwires were carried out by employing
the Instron 1466 testing machine equipped with a load cell of
1 kN.
In Fig. 1, the real and imaginary parts of the effective
complex permittivity spectra are presented with respect to
tensile strain up to 4.5%. The stress-strain curve of a single
wire is given in the inset. It is important to note that the linear behavior is characteristic of a typical brittle material
without yielding region. Two important features are noted
here. (1) Significant variation of e0 for the stressed samples
compared to the unstressed state is visible for k ¼ 1.4% and
4.5% at frequencies larger than 4 GHz. The stress effect
becomes insignificant at low frequency. The bandwidth of
anomalous dispersion of e0 remains independent of stress,
i.e., typically between 3.5 and 4.4 GHz. (2) The maximum
absorption corresponding to the peak of the e00 spectrum
increases as strain increased from 0 to 2.8% and shifted to a
higher frequency. With a further increase of strain, the
absorption maximum decreases and shifts to a lower frequency. This is clearly seen in Fig. 2, where the stress dependence of the permittivity is plotted for frequencies of 4.1
and 4.7 GHz. The former is close to the absorption maximum
while the latter is far away from the peak. As the frequency
FIG. 1. (Color online) The real, e0 , and imaginary parts, e00 , of the effective
complex permittivity for different values of strain. Measurements were done
over the frequency range of 300 MHz-6 GHz. The inset shows a typical tensile stress-strain curve of microwire measured by the Instron 1466 testing
machine.
Appl. Phys. Lett. 99, 252902 (2011)
FIG. 2. (Color online) The real, e0 , and imaginary parts, e00 of the effective
complex permittivity, measured at 4.1 and 4.7 GHz, as a function of strain k.
The inset shows the strain dependence of the loss factor for these two
frequencies.
is increased from 4.1 to 4.7 GHz, both e0 are decreased. It is
worth noting that the evolution of the dielectric loss e00 with
strain is very similar for these two frequencies. We further
include the strain dependence of the loss factor in the inset
of Fig. 2. The impact of stress remains identical to that
shown on e00 . It should be noted that a strain larger than 7%
annihilates the strain effect.
We now turn our attention to microwave absorption
coefficient defined as A ¼ 1 jS11 j2 jS21 j2 .3 Comparison
of the dielectric loss factor (Fig. 3(a)) and the absorption
spectra (Fig. 3(b)) is meaningful for the various values of k
tested. The very similar behavior of these spectra indicates
that the dielectric loss is the main contribution of the absorption mechanisms for our samples within the frequency range
explored. It is noted that this result differs from the observations reported by Marı́n et al.,16 who found that the absorption of microwire composites for a large wire concentration
(0.5 vol. %) is dominated by magnetic loss and associated
with the ferromagnetic resonance (FMR) of the wires. These
observations do not contradict with the current results since
we are dealing with more dilute composite systems, i.e., the
wire volume fraction is close to 0.005 vol. %. The FMR
FIG. 3. (Color online) (a) The loss factor and (b) microwave absorption
spectra for different values of strain.
252902-3
Qin, Brosseau, and Peng
FIG. 4. Images of the wire composite sample under uniaxial elongation corresponding to (a) k ¼ 1.4%, i.e., elongated but not fractured wires, (b)
k ¼ 2.8%, i.e., showing broken wires.
frequency
fr of the planar wire composites is determined by
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
fr ¼ c 4pMs ðHk þ Hn Þ,17 where k is the gyromagnetic factor, Ms is the saturation magnetization, Hk is the anisotropy
field, and Hn / iMs ða=lÞ2 is the dipole-dipole interaction
field for all neighboring wires of diameter 2a, length l, and
number i. It is instructive to examine the wire content dependence of fFMR. Unless sufficient wires are embedded into
the matrix, ensuring a large contribution of the anisotropy
and dipole-dipole interaction fields, one cannot expect a resonance induced by the magnetic loss in the range of GHz frequencies. Although the absorption performance is smaller
for dilute composites, low losses are desirable for the design
of microwave tunable composites and metamaterials based
on ferromagnetic microwires.
From now on, we focus our discussion on several
possibilities that may shed light on our understanding of
the origin of the observed difference in the stress dependence of the permittivity spectra. The wires are brittle materials with very low ductility (as seen from the inset of Fig.
1). At relatively small strain before fracture arises, the
stress effect on the dielectric response of the composite
can be described by e ¼ em þ 4pphai, where em denotes the
permittivity of the matrix, p is the wire concentration,
and hai the effective (averaged) polarisability.18 When
the strain exceeds 2.8%, breakdown of some wires occurs.
Due to nonuniform interfacial conditions, each single wire
experiences a different stress state resulting in partial but
not total fracture of all wires, as shown in Fig. 4(b). Following Makhnovskiy et al.,18 hai can be written as hai
1=2
2
icfzz
1
,
¼ 2plnðl=aÞðKaÞ
2 Kl tanðKl=2Þ 1 , with K ¼ k 1 þ xalnðl=aÞ
pffiffiffiffiffi
and k ¼ x em =c, where x is the angular frequency, c is the
velocity of the electromagnetic wave in vacuum, and fzz is
the wire surface impedance. Consequently, the wire length
plays an important role in determining the effective permittivity. A recent study by Ipatov et al.19 showed that the
reduction of the wire length can significantly decrease the
permittivity and leads to a blueshift of the resonance frequency. This explains why the present results differ from
those reported previously.7 Figure 4(a) shows an image of
the elongated but not fractured wires for low strain, i.e.,
Appl. Phys. Lett. 99, 252902 (2011)
k ¼ 1.4%. Thus, the observation here of broken wires as
strain is over 2.8% (see Fig. 4(b)) is consistent with the
decrease of the dielectric loss with stress of composites
containing a smaller number of strained continuous wires.
Some of the possible mechanisms which are involved to
explain this observation are the stress effect, i.e., the stress
changes the current distribution in the wires2,18,20 and induces a higher dielectric loss and the shape effect, i.e., wires
can be broken in shorter pieces and the anisotropy field of
the wire becomes non-uniform, resulting in the reduction
and the broadening of the resonance bandwidth. In addition, it is noted that the relevant relaxation mechanisms
attributed to dipolar relaxation and Maxwell-Wagner-Sillars
interfacial polarization3,15 due to the boundaries separating
microwires are expected to change due to wire fracture.
Thus, the local properties of wires and the composite mesostructure are significantly altered. From an engineering
perspective, we note that our work and recent results by
other groups21,22 indicate that stretch-broken fibres systems
achieve the formability of discontinuous reinforced systems
without large performance knockdowns of continuous fibre
prepreg which have restricted its use in automated manufacturing processes.
In summary, we have performed a detailed study of the
stress effect on the microwave properties of magnetic
microwire polymer composites over a broad frequency
range. The study of the permittivity spectrum demonstrates
a nonlinear tunable stress effect over a broad range of
strain. The analyses of permittivity and the strain sensitivity
afford to identify two plausible mechanisms arising when a
fraction of wires are broken, namely, the stress and shape
effects. The effect of wire concentration has also been highlighted. This study has significant implications for research
in the emerging field of stress tunable microwire composites for sensing applications.
FXQ acknowledges the financial support provided by
Conseil Général du Finistère, France.
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