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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 View Table of Contents: http://apl.aip.org/resource/1/APPLAB/v99/i25 Published by the American Institute of Physics. Related Articles Bending kinetics of a photo-actuating nematic elastomer cantilever Appl. Phys. Lett. 99, 254102 (2011) Maximum asymmetry in strain induced mechanical instability of graphene: Compression versus tension Appl. Phys. Lett. 99, 241908 (2011) Role of material properties and mesostructure on dynamic deformation and shear instability in Al-W granular composites J. Appl. Phys. 110, 114908 (2011) Torsion-induced mechanical couplings of single-walled carbon nanotubes Appl. Phys. Lett. 99, 231904 (2011) A unified approach for extracting strength information from nonsimple compression waves. Part II. Experiment and comparison with simulation J. Appl. Phys. 110, 113506 (2011) Additional information on Appl. Phys. Lett. Journal Homepage: http://apl.aip.org/ Journal Information: http://apl.aip.org/about/about_the_journal Top downloads: http://apl.aip.org/features/most_downloaded Information for Authors: http://apl.aip.org/authors 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: [email protected] 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. 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