JOURNAL OF APPLIED PHYSICS 109, 07A310 (2011)
Stress tunable properties of ferromagnetic microwires and their
multifunctional composites
F. X. Qin,1,a) H. X. Peng,1 V. V. Popov,2 L. V. Panina,3 M. Ipatov,4 V. Zhukova,4 A. Zhukov,4
and J. Gonzalez4
1
Advanced Composite Center for Innovation and Science, Department of Aerospace Engineering,
University of Bristol, University Walk, Bristol BS8 1TR, United Kingdom
2
Taurida National University, Simferopol 95022, Ukraine
3
School of Computing, Communication and Electronics, University of Plymouth, Drake Circus, Plymouth,
Devon PL4 8AA, United Kingdom
4
Dpto. de Fisica de Materiales, Fac. Quimicas, Universidad del Pais Vasco, Bilbao 20018, Spain
(Presented 17 November 2010; received 1 October 2010; accepted 21 October 2010; published
online 23 March 2011)
We report the results of a systematic study on stress tunable absorption of glass-coated amorphous
Co68.7Fe4Ni1B13Si11Mo2.3 microwires and their composites. The magnetic microwires possess good
stress-impedance properties and yield a stress dependence of absorption at gigahertz frequencies. The
stress compensates the reverse effect of magnetic field on absorption. There exist strong stress
dependences of the effective permittivity and transmission parameters. Composite failure due to the
wire damage results in a dramatic change of the sign and magnitude of effective permittivity. The
double peak is identified in the stress dependence of field tunability, in contrast to the single peak for
the magnetic field tunability. All these results indicate that the present composites are very promising
C 2011 American
for detecting the ambient stress levels and interrogating the structural integrity. V
Institute of Physics. [doi:10.1063/1.3535553]
Much interest has been aroused in the study of engineered
multiphase composites containing microscale or nanoscale
fillers in terms of their electromagnetic properties for microwave applications such as fiber reinforced composite structures,1 tunable microwave devices,2 remote interrogated
sensors,3 etc. A key question of achieving effective design and
application of these composites is to understand how the wave
transport properties are modified as it interacts with the composite material in the presence of external stimuli such as temperature and/or stress. In the latter case, to decode the effect of
stress on the polarization and magnetization mechanism and the
way to control them are the basis of developing multifunctional
composites for domestic and industrial applications. Especially,
we focus on the dielectric response induced by the external
magnetic field or stress, which are often associated with the
relaxation and resonance characteristics in the spectra.4
Most recently, a smart microwire polymer composite has
been devised to realize multifunctionalities for a spectrum of
applications such as structural health monitoring. The magnetic
field effect on the effective permittivity has been systematically
presented in previous reports.5 As a step forward, the present
study targets the stress effect. The rationale is briefly described
as follows. For a composite containing ferromagnetic wires
exhibiting giant magnetoimpedance effects at microwave frequencies,5 the effective permittivity may depend on a dc magnetic field via the corresponding dependence of the surface
impedance. The surface impedance can also be changed by
applying an external stress which modifies the magnetic anisotropy and domain structure in these wires. Thus, the effective
a)
Author to whom correspondence should be addressed. Electronic mail:
faxiang.qin@bris.ac.uk.
0021-8979/2011/109(7)/07A310/3/$30.00
permittivity may also depend on the external stress or strain.
Corresponding to the stress tunable theory proposed by Panina
et al.,2 we focus on the technological aspects of developing multifunctional composites for structural interrogation applications.
The glass-coated amorphous microwires of Co68.7Fe4
Ni1B13Si11Mo2.3 with a metallic core diameter of 8.0 lm and a
glass coat’s thickness of 2.4 lm were fabricated by a modified
Taylor–Ulitovskiy process.6 The wire-composites were prepared by arranging 500 mm long microwires periodically (9
mm spacing between the wires) into silicone rubber sheets,
which were then adhered by silicon resin casting. The composite was cured at ambient temperature and the resultant dimensions are 520 mm 500 mm 1.5 mm. Glass-fiber composite
tabs were adhered on both sides of the specimen normal to the
length direction using Redux 810A/B. 1/4 in. diameter holes
were drilled on both ends of tabs for load bearing. The freespace measurements on the composites were conducted at 1–
18 GHz as described elsewhere.7 The microwave absorption of
microwires was carried out using a modified scalar network
analyzer assembly (SNA) at the X-band. In both measurements, loads were applied along the axis of the microwires.
Figure 1(a) depicts the field dependence of absorption of
the wire at varying stresses up to 233.3 MPa at 9 GHz. The
absorption shows strong magnetic field dependence and the
applied magnetic field increases the absorption until saturation
in analogy to the valvelike GMI profiles.8 With increasing
stress, the sensitivity of absorption to magnetic fields is
declined. In another aspect, the influence of stress on the
absorption increases with increasing magnetic field. In the derivative absorption profiles [Fig. 1(b)], the absorption peaks
are found to become wider and shift to a higher magnetic field
with increasing applied tensile stress.
109, 07A310-1
C 2011 American Institute of Physics
V
Author complimentary copy. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp
07A310-2
Qin et al.
FIG. 1. (Color online) Axial magnetic field dependence of absorption (a)
and derivative absorption profiles (b) in the presence of varying stresses at 9
GHz for the microwire.
Figure 2 shows the complex permittivity spectra for the
as-prepared intact composite after being damaged with wire
breakage under tensile loads. There are pronounced changes
for both the real part e0 and imaginary part e00 of the effective
permittivity. Particularly, a drastic change of e0 is seen with a
reversal of sign from negative to positive when the damage
happened to the wires.
A stress tunable behavior parallel to the field tunable
behavior is observed in the transmission spectra (Fig. 3). Interestingly, the composite shows a similar response to stress and
magnetic field, although the evolution of transmission with
magnetic field is steadier than that with stress. To gain a deeper
insight into such stress tunable characteristics, we plot in Fig. 4
the calculated stress tunability nss21 (respectively, magnetic
field tenability nfs21 ) versus stress (respectively, magnetic field)
J. Appl. Phys. 109, 07A310 (2011)
FIG. 2. (Color online) The effective permittivity spectra of (a) as-received
composite and (b) after damage by tensile stress.
at frequencies of 1, 4.8, and 8 GHz, which are lower than,
equal to, and higher than the plasma frequency (fp), respectively. Here the tunability is defined as the ratio of the induced
transmission change to the corresponding magnetic field or
stress change. Overall the evolution of tunability remains the
same at all three frequencies. In comparison to the single peak
feature displayed in the magnetic field dependence of tunability [Fig. 4(b)], both a maximum and minimum appears in the
stress dependence of tunability [Fig. 4(a)].
The absorption constant of the microwire, by definition,
can be expressed as the reciprocal of skin depth associated
with electrical resistivity (q), circumferential magnetic permeability (l), and frequency ( f ) via the following formula:9
1
a¼ ¼
d
sffiffiffiffiffiffiffiffi
pf l
;
q
(1)
FIG. 3. (Color online) Transmission spectra of
microwire composite under tensile stresses (left
panel) and magnetic fields (right panel).
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07A310-3
Qin et al.
J. Appl. Phys. 109, 07A310 (2011)
FIG. 4. (Color online) Stress (a) and magnetic field (b) dependences of tunability at
1, 4.8, and 8 GHz. (plasma frequency
fp ¼ 4.8 GHz; the ordinate profiles are normalized by 104 and 105, respectively.)
where l is dependent on the susceptibility (v) and the angel
(h) between the magnetization vector and the wire axis, formulated as8
l ¼ 1 þ 4p cos2 ðhÞ v:
(2)
For the case of Co-rich microwires, the application of the
magnetic field along the wire axis increases the circumferential magnetic permeability by rotating the magnetization vector toward the wire axis and hence the absorption constant.
On the other hand, when a stress is applied along the microwires with a negative magnetostriction, the magnetization
vector rotates away from the axis direction.10 As a result, the
circumferential magnetic permeability is decreased and hence
the absorption is reduced. It is expected, therefore, that the
application of a longitudinal stress will compensate the effect
of the magnetic field. This can be further proved by the stress
impedance (SI) ratio derived from absorption profiles in the
presence of varying magnetic fields (not shown here), where
the SI ratio was observed to be optimal when the external
magnetic field takes the value of 10 Oe, i.e., the anisotropy
field of unstressed wire.
As mentioned above, the mechanism of stress tunable
effects for microwire composites lies in the dependence of the
effective permittivity of the composite on the external stress via
the stress-impedance effect the microwires possess. Microwire
parameters, such as composition, domain structure, and geometry,11 and the mesostructure constituted by the microwires are
critical to determine the stress tunable sensitivity of the microwire composite. The wire failure dramatically changes the
properties of microwires as well as the periodic topology in the
composite mesostructure, thereby resulting in the observed significant change of collective dielectric response.
As reported in our previous work,5 the single peak presented in nfs21 ðHÞ is associated with the anisotropy field. In
contrast, a more complex relationship of nss21 ðrÞ merits more
discussion. As discussed above, the circumferential magnetic
permeability and surface impedance is reduced upon the
application of a longitudinal stress. This explains the maximum occurred at around 13 kPa [Fig. 4(a)]. Afterwards, with
increasing stress, the well defined circumferential anisotropy
may remain unchanged and hence the surface impedance
shows very little variation to the incremental stress, giving
rise to a minimum of tunability at 40 kPa. Higher stress than
40 kPa may depreciate the circumferential anisotropy and
increase the surface impedance, which accounts for the recovery of the stress tunability.
It should be noted that tens of kPa imposed on the composite yields hundreds of MPa on each wire according to a
simple calculation as follows. As the present case meets the
isostrain condition, the following equation holds:
rc
rw
¼ ew ¼
;
(3)
ec ¼
Ec
Ew
where ec and ew denote the strain for composite and microwires, respectively; rc and rw the stress exerted on the composite and microwires, respectively; and Ec and Ew the
Young’s modulus of the composite and microwires, respectively. Using the law of mixture, the stress each microwire
experiences is given by
rc
;
(4)
rw ¼
ðEm =Ew Þfm þ fw
where fm and fw are the volume fraction of the matrix and
microwires, respectively. Due to the significant difference
between the Young’s modulus of rubber matrix (2 MPa) and
of microwires (100 GPa), 10 kPa on the composite can result
in 500 MPa on the microwires. This is within the reasonable
stress range, as commonly discussed in the literature, in
terms of the stress effect on GMI properties of microwires.12
ACKNOWLEDGMENTS
F.X.Q. was supported by the Overseas Research Students Awards Scheme and the University of Bristol Postgraduate Student Scholarship. The authors would also like to
thank Dr. Makhnovskiy of the University of Plymouth for
the valuable help with the free space measurements.
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