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10.1 Magnetic Properties of Composites

Due to the inclusion of magnetic fillers, the polymer composite becomes magnetic, i.e. responsive to the external static or dynamic magnetic field. Although most studies are devoted to the dynamic response of these kinds of heterogeneous composite media [1], i.e. complex permeability, it is worth exploring the static magnetic properties of microwire composites for two reasons: (i) the composite with wire arrays could be of some application interest in the magnetic sensing field, as quite a few studies are devoted to the microwire arrays [2–7]. (ii) ac permeability is associated with the static magnetic properties such as saturation magnetisation and the anisotropy field, according to the modified model based on Snoek’s law proposed by Acher et al. [8, 9].

$$\int\limits_{0}^{F} {\mu^{\prime \prime } \left( f \right)} f{\text{d}}f \le \frac{\pi }{6}\tau \left( {\bar{\gamma }4\pi M_{\text{s}} } \right)^{2} ,$$
(10.1)

where µ is the imaginary part of complex permeability, f is the frequency, τ denotes the volume fraction of magnetic fillers, \(\bar{\gamma }\) is the gyromagnetic factor with a value of 2.8 MHz/Oe, and M s is the saturation magnetisation. In this connection, this section addresses some of the static magnetic properties of microwire composites.

Phan et al. [10] prepared E-glass prepreg-based composites with bundles of microwires and measured their magnetic properties in comparison with those of the single wires. Figure 10.1 shows the M–H curves of the single microwire and composite. It is interesting to note that, for both longitudinal and transverse measurements, the coercivity of the as-prepared composite is much smaller than that of the single microwire. This indicates better soft magnetic properties for the microwire composite than single wires. It is also shown that the effective anisotropy field for the bundles of microwire is strongly increased as compared to the single wire [11]. Such changes of magnetostatic and magnetoelastic characteristics are due to the long-range dipolar interactions [7, 12] between neighbouring wires, as well as the interfacial stress between microwires and the matrix. The dipolar interactions have a strong impact on the magnetic properties in a similar way to classical spins interacting throughout the long-range interactions, resulting in the changes in the hysteresis loop. Equally, interfacial stress of the order of hundreds of MPa [13, 14], resulting from the different coefficients of thermal expansion between the microwire and polymer matrix, will have a significant effect on the magnetoelastic features of the wires according to \(K_{\text{me}} = 3/2\lambda (\sigma_{i} + \sigma_{\text{app}} )\), where \(K_{\text{me}}\) is the magnetoelastic energy component, \(\lambda\) is the magnetostriction constant, and \(\sigma_{\text{i}}\) and \(\sigma_{\text{app}}\) are the internal stress and applied stress on the wire, respectively [15, 16]. In the case of Fe-based wire of a length greater than the critical length, due to the dipolar interactions, the coercivity and anisotropy field should increase with the number of wires. On the other hand, the coercivity is decreased with increasing stress, and anisotropy presents an opposite trend [13, 15, 17]. The combination of these two mechanisms results in the observed contrast between the microwire composites and monolithic wire. The presented magnetic properties indicate that the microwire composites are promising for magnetic sensing applications [18].

Fig. 10.1
figure 1

Comparison of magnetic hysteresis loops of a single magnetic microwire and its as-prepared composite. Reproduced with permission from [10], copyright 2007 AIAA

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Due to the involvement of the polymer, magnetic filler, and multi-interfaces, temperature plays an important role in regulating the magnetic behaviour of composites. The glass transition temperature (tg) of the composite samples is evaluated to gain a better understanding of their magnetic properties (see Fig. 10.2). Phan et al. found that, by annealing in the vicinity of the glass transition temperature, there exists a critical temperature of 177 °C. Before the temperature reaches this, the coercivity decreases, while afterwards the opposite trend is shown. This is contrary to the conventional case that the coercivity should decrease with the stress relaxation due to the thermal annealing below the crystallisation temperature [19]. Clearly, such a complex annealing temperature dependence of coercivity involves multiple mechanisms at different interfaces, viz. the structural relaxation in the wire and the stress relief in the polymer–wire interface. The competitive and interdependent relationship between these two mechanisms varies sensitively with the temperature. At low temperatures relative to the glass transition temperature, the second mechanism prevails and can result in a rearrangement of microwires, i.e. regulation of the composite mesostructure. Thus, the coercivity could be increased due to the enhanced interaction between the wires [20]. Subsequently, a decrease of coercivity should result from the stress relief contributed by both glass transition and wire structural relaxation. The gradual decrease of remanent magnetisation can be accounted for by the reduction in the volume of the axially magnetised area as an effect of stress relief due to the positive magnetostriction constant [15, 17].

Fig. 10.2
figure 2

Magnetic hysteresis loops of the as-prepared composite annealed at Ta = 375, 405, and 435 K. The glass transition temperature is 449.5 K. Reproduced with permission from [10], copyright 2007 AIAA

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10.2 Giant Magnetoimpedance Effect

As with wires, their composite also presents a significant GMI effect. It has been shown by Phan et al. [10] that, at a given frequency of 10 MHz, the GMI ratio and its field sensitivity reached the highest values of 450 and 45 %/Oe for those composites containing four wires, while the composite containing only one wire gave 14 and 1 %/Oe, respectively (see Fig. 10.3). The wire addition effect on the GMI is believed to be attributed to the reduction in resistivity as one of the causes. Another cause is the combination of the high circumferential permeability of the microwire, and a multiwire parallel configuration is likely to cause a magnetic flux closure and hence resulted in an extremely high effective permeability [20, 21]. It is worth noting both GMI and anisotropy field are enhanced, which is highly desirable for realising high-performance sensing entailing large sensitivity and broad working range. In addition, compared to single wire, the existence of polymer matrix could accommodate a versatile and judiciously designed multiwire system, which provides more possibility to extend its applications. However, the GMI presented in Ref. [10] is very weak, with the suitable optimisation of single wires via advanced annealing techniques such as stress–Joule annealing [22] and recently reported multiangle annealing techniques [23], and the GMI of wire composite could be further improved.

Fig. 10.3
figure 3

Frequency dependence of GMI profiles with varying wire number n = 1, 2, 3, 4 mm. Reproduced with permission from [24], copyright 2007 Elsevier

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Qin et al. [25] also demonstrated the pronounced improvement of the maximum MI ratio with the increasing number of wire inclusions, attributed to the effective response of all the wires. The microwire composite is shown to yield a larger GMI at higher frequencies but with a minor increase of energy loss, which is desirable for sensing applications. The multiwires in the parallel manner constitute an increase of the total cross-sectional area of the wires, resulting in a stronger skin effect when considering the ratio of radius and penetration depth. Consequently, the GMI effect is improved. In addition, if the wire is simply dealt with as a single-domain substance, the interactions between wires in the multiwire composites induce a magnetic closure to make the whole structure more stable, although the total internal energy is increased [12]. These results differ significantly from those reported by Garcia [26], who demonstrated a multiwire system exhibiting a reduced GMI effect with the number of wires, which is explained by the authors as an effect of shielding between wires. This difference should be ascribed to the functions of the matrix and the curing process for our composite media. The wire sample underwent annealing in the curing stage, and the domain structure was significantly modified. It is suggested that the confinement of the matrix also helps maintain the modified configuration, giving rise to the peculiarity of the GMI behaviour. Of note is that the involvement of a polymer matrix opens up new routes to modulate the GMI performance, although limited study has been hitherto reported. A particularly important aspect is interface. The homogeneities of the interface would be critical to the GMI characteristics, so it is necessary to study the detailed interfacial conditions. Surface treatment using chemical agents such as silane or nanotubes [27] could also be considered to enhance both the interfacial bonding and GMI properties. Another aspect of practical interest [28, 29] is to develop superior bonding technology to accommodate multiple wires so that a highly stable GMI signal output can be ensured.

It is well established that the GMI effect of microwires associated with the magnetic properties is strongly influenced by the length of the wires [3, 30–33]. The argument holds true for the microwire composite system. It has been revealed that the GMI ratio increased from 15.5 to 268 % as the microwire length decreased from 4 to 1 mm [10]. This is attributed to the decrease of the electric resistivity in the multiwire system compared to the single wire, in spite of the increase of the demagnetising effect [3] for single wire. Based on the outstanding magnetic properties of microwire composites, they show a promising application perspective. Indeed, the polymer matrix provides a “platform” to assemble the microwires and exhibit the properties that are significantly different from the single wire, which is the motivation for developing these composites [34].

10.3 Giant Stress Impedance Effect

As mentioned above, stresses can play an important role in investigating the GMI materials, and these can be treated in two respects. One concerns the stress influence on the GMI behaviour, and a number of works have been published on this topic for various materials including ribbons [35–37] and microwires [38–40]. Second is the so-called giant stress impedance (GSI) effect, which refers to a stress-induced variation of impedance in magnetic materials. This effect in the intermediate frequencies has been evaluated on amorphous wires and ribbons. Shen [41] reported that the GSI effect of a CoSiB microwire reached about −35 % for stress σ = 140 MPa, which is 5–6 times more sensitive than a conventional semiconductor stress sensor. One kind of Fe-based ribbon was also found to possess an SI ratio of 20 % for σ = 84.8 MPa with the stress perpendicular to the geomagnetic field [42]. In this regard, the wire-based composite is expected to be a good candidate for studying the GSI effect over a wider stress range, since it can be treated as a multilayer medium consisting of a metallic core, a glass coat, and a composite matrix. Such a hierarchical structure would enable a sensitive response to the applied stress for the composite media, where the coupling of internal and external stresses is likely to be able to manipulate the GMI and GSI behaviour. Both aspects of the GSI effect of microwire composites were investigated by Qin et al. [13].

Figure 10.4 illustrates the magnetic field dependence of the GMI ratio taken at f = 1 MHz under various applied tensile stresses for the single-wire composite of four layers obtained by the method described in Sect. 9.2.2. Here, the tensile stress was applied along the microwire axis. It can be seen from the figure that the maximum GMI ratio decreased as the applied stress was increased. While the GMI ratio decreased gradually with the applied magnetic field (H dc) for the unstressed composite, the case is different for the stressed composites. With increasing H dc, the GMI ratio first increased, then reached a maximum, and finally decreased for the stressed composites. The magnetic field at which the GMI ratio reached its maximum can be considered as the circular anisotropy field (H k ) induced by the applied tensile stress.

Fig. 10.4
figure 4

GMI profiles of composites containing single wire as a function of applied stress. Reproduced with permission from [13], copyright 2011 Elsevier

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Figure 10.5a illustrates the tensile stress dependence of the maximum GMI ratio and the anisotropy field. Clearly, the GMI ratio decreased slightly from 255 % for σ = 0 to 253 % for σ = 150 MPa and drastically reduced to 151 % for σ = 600 MPa by more than 100 %. An opposite trend was observed for the σ dependence of H k . A subtle increase of H k by 8A/m for σ = 150 MPa was followed by a further increase of 112 A/m for σ = 600 MPa. The σ dependence of longitudinal coercivity (H c) was also measured, and the result is shown in Fig. 10.5b. The drop of H c was observed at σ = 600 MPa. For the case of the unstressed composite, the gradual decrease of the GMI ratio with H dc is likely to be caused by decreasing circular permeability due to the rotation of magnetic moments. However, an opposite effect observed for the stressed composites arises from the fact that the application of tensile stress to the microwire with a negative magnetostriction strengthened the circular magnetoelastic anisotropy field, giving rise to the occurrence of a maximum in GMI that shifted towards higher H dc as σ was increased. The occurrence of such a maximum in GMI for the stressed composites can be attributed to the competition in the rotational magnetisation processes between H dc and H k . The decrease of the GMI ratio with σ at H dc = 0 is attributed to a reduction in the circular permeability due to the domain wall displacement.

Fig. 10.5
figure 5

a Tensile stress dependences of anisotropy field (H k ) determined from GMI profiles and maximum GMI ratio. b Longitudinal coercivity versus applied tensile stress. Reproduced with permission from [13], copyright 2011 Elsevier

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Furthermore, it should be noted that, since the microwires were embedded in a polymer matrix, any heat treatment or variation coming from the polymer matrix is expected to have a significant influence on the GMI properties of the microwire and hence the composite. To gain insight into this, the influences of annealing treatment and the number of layers on the GMI properties are studied. The results are shown in Fig. 10.6. For the case of the as-prepared samples, the four-layer composite exhibited a higher maximum GMI ratio (255 %) when compared with the eight-layer composite (216 %). Meanwhile, the annealed composite samples (treated at 100 °C for 3 h) exhibited higher maximum GMI ratios (282 and 248 % for the four-layer and eight-layer composites, respectively) than the as-prepared ones. These findings are explained as follows. In this kind of composite, a higher stress will be induced as the number of composite layers increases. In the present study, the eight-layer composite may impose more stress in the through-thickness direction than the four-layer composite. As a result, the GMI ratio decreased and H k increased for the as-prepared composite of eight layers when compared with the as-prepared composite of four layers. On the other hand, the annealing treatment is believed to have relieved the stress between the microwire and matrix produced during the curing process. This explains consistently the larger GMI ratio and smaller H k obtained for the annealed composite samples relative to the as-prepared ones.

Fig. 10.6
figure 6

GMI profiles for the wire composites of four prepreg layers and eight prepreg layers in the as-prepared and annealed states taken at f = 1 MHz. Reproduced with permission from [13], copyright 2011 Elsevier

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It is also interesting to see that the GMI behaviour observed for the as-prepared eight-layer composite is similar to that of the four-layer composite subject to a tensile stress of 450 MPa. This clearly suggests that the applied tensile stress and residual stress imposed by the composite matrix on the microwire could affect its GMI behaviour in a similar fashion. To understand this quantitatively, the contribution of the applied stress and the matrix-induced residual stress to the anisotropy field was calculated, respectively.

In a cylindrical coordinate system (z, r, \(\phi\)), there exist three components for the residual stress in z (along the wire axis), r (radial direction), and \(\phi\) (azimuthal direction): zz, rr, and \(\phi \phi\), respectively. The magnetoelastic energy density is given by Antonov et al. [43]:

$$U_{\text{me}} = - \frac{3}{2}\lambda_{\text{s}} (\sigma_{zz} \alpha_{z}^{2} + \sigma_{rr} \alpha_{r}^{2} + \sigma_{\phi \phi } \alpha_{\phi }^{2} ),$$
(10.2)

where λ s is the saturation magnetostriction constant. α i denotes the component of the unit magnetisation vector. The residual stresses are assumed to be a function of x(r/a) only, a being the wire radius.

The anisotropy field can then be deduced by the following equation [43]:

$$H_{k} = \frac{{3\left| {\lambda_{\text{s}} } \right|}}{{M_{\text{s}} }}\left( {\sigma_{zz} - \sigma_{\phi \phi } + \frac{1}{{(1 - k)p^{2} + k}}\overline{{\sigma_{zz} }} } \right),$$
(10.3)

where all symbols have the same meaning as in Eq. (10.2).

Taking into account the residual stress imposed by the composite matrix, which is primarily along the negative radial direction (σ rr ), Eq. (10.3) can be modified to the following:

$$H_{k} = \frac{{3\left| {\lambda_{\text{s}} } \right|}}{{M_{\text{s}} }}\left( {\sigma_{zz} - \sigma_{\phi \phi } + \overline{{\sigma_{rr} }} { + }\overline{\overline{{\sigma_{zz} }}} } \right);$$
(10.4a)
$$\overline{\overline{{\sigma_{zz} }}} = \frac{1}{{(1 - k)p^{2} + k}}\overline{{\sigma_{zz} }} .$$
(10.4b)

For the four-layer composite, when \(\overline{{\sigma_{zz} }}\) = 450 MPa, given k = 0.5 and p = 0.67, one obtains the effective contribution to H k , \(\overline{\overline{{\sigma_{zz} }}}\) = 619 MPa. For the eight-layer composite, according to the difference of its anisotropy field relative to that of the unstressed four-layer composite (ΔH k  = 0.5 Oe), the concerned stress \(\overline{{\sigma_{rr} }}\) is given by the following:

$$\overline{{\sigma_{rr} }} = \frac{{\Delta H_{k} M_{\text{s}} }}{{3\left| {\lambda_{\text{s}} } \right|}}.$$
(10.5)

Given the typical numerical values: M s = 400 G, λ s = −10−7, \(\overline{{\sigma_{rr} }}\) = 667 MPa is received. The similar numerical values of \(\overline{{\sigma_{rr} }}\) and \(\overline{\overline{{\sigma_{zz} }}}\) explain the roles of applied stress and residual stress in influencing the magnetoelastic properties and GMI properties. This result affords significant technical applications in the composite industry in terms of probing the residual stress and tailoring the related manufacturing conditions.

The GSI effect in the microwire and the microwire-based composites with four and eight layers was investigated. The results are shown in Fig. 10.7. It can be readily seen that the stress impedance ratio [ΔZ/Z]max decreased monotonously with stress for all the samples. Interestingly, while the maximum stress impedance ratio ([ΔZ/Z]max) is 38.1 % for the single microwire, it is reinforced for the composite samples (41.5 and 43.0 % for the four-layer and eight-layer composites, respectively). These results indicate that the prepared composites are very appealing candidates for the stress-sensing applications. In the composite, in addition to the residual stress frozen in between the glass and metallic core, there exists residual stress at the interface between the microwire and polymer matrix. The enhancement of the GSI effect in the composites clearly points to the important coupling between the internal and external stresses that coexist in these materials.

Fig. 10.7
figure 7

GSI profiles for amorphous wire, four-layer wire composite, and eight-layer wire composite in the as-prepared states taken at f = 1 MHz. Reproduced with permission from [13], copyright 2011 Elsevier

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10.4 Mechanical Properties

Since the fabricated composite is intended for structural applications, its mechanical properties are one of the major concerns. Also, the influence of microwires on the mechanical integrity of the composite is a key issue for the success of such sensor-embedded technology. Therefore, it is necessary to discuss the mechanical properties of the composite matrix influenced by the embedded wires [25, 44–46].

Qin et al. [25, 46] found that, in a dilute composite with glass fibre-reinforced epoxy as a matrix, the fibre shows little effect, as shown in Fig. 10.8, which displays the stress–strain curves obtained for blank composite samples and 10-wire and 50-wire samples under a maximum force of 30 kN [25]. The tensile strengths are summarised in Table 10.1. It is observed that all the mechanical parameters are very close to each other for the different types of samples. In terms of the tensile strength, the coefficients of variation (CV) for each type of sample are 6.3, 5.6, and 3.8. Upon performing cross-comparison of their average properties, the CV is 3.7. The negligible wire effect can be understood from the basic law of mixture that postulates a considerable volume fraction of fillers needed to realise reinforcement.

Fig. 10.8
figure 8

Stress–strain curves of blank composites (free of wires), composites containing 10 wires and 50 wires measured by a 30 kN load cell. Reproduced with permission from [25], copyright 2010 Elsevier

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Table 10.1 Mean values and coefficients of variation (CV*) of tensile strength for each set of samples
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Qin et al. [47] also studied the impact resistance of this kind of microwire composite. With reference to the obtained time dependences of the impact force for all tested samples (Fig. 10.10), one can see that the additional wires yield negligible changes in the impact resistance of the composites parametrised by the impact energy, in that the major energy dissipation mechanism is delamination rather than fibre failure, as shown in a typical damage pattern at the surface (inset of Fig. 10.10; the bright region indicates the delamination). This suggests that the embedded wires do not degrade the interfacial bonding. This is of particular importance for aeronautical structures that are subject to low-velocity impact caused by, e.g. dropped tooling or runway debris, throughout their service life [48]. Another notable feature concerns the first load peak, which exhibits a significant increase for the sample containing three layers of wires as compared to other samples. This clearly indicates that the fibre failure occurred near the surface as the initial impact damage [49]. The metallic wires with the strong tensile strength of 3–4 kMPa effectively improve the fracture load. It can be expected that, for high-velocity impact, the addition of wires can also improve the toughness of the composites. In considering the wide application of glass fibre composites in wind turbines, the addition of microwires can simultaneously improve the impact resistance performance and electromagnetic interference shielding (this will be discussed in Chap. 12) of the composites, rendering such microwire composites particularly useful for improving on the current green energy technology.

Back in the 1980s, Goto et al. [44, 45] had done excellent work in connection with the mechanical performance of metallic filament-reinforced composites. Goto et al. [44] studied the reinforcing effect of metallic wires with and without glass coats on the epoxy matrix and reported that the mechanical properties of epoxy are strongly enhanced in wires without a glass coating, with the tensile strength reaching 600 MPa at 30 vol.% wire volume. Meanwhile, the glass-coated wires do not show such a good reinforcing effect due to the poor bonding between the metallic core and glass coating. These effects are readily demonstrated in the fracture morphology images (Fig. 10.9). Apparently, the quality of the interfaces plays a critical role in determining the ultimate mechanical performance of the wire composites. These fine wires, after removing the glass coating, are also found to be capable of improving the thermal properties of the composite by increasing the glass transition temperature, as the wires can hinder the molecular motion (Fig. 10.10).

Fig. 10.9
figure 9

Fracture morphology of microwire (glass coat removed)/epoxy composite (a) and glass-coated microwire/epoxy composite (b). Reproduced with permission from [44], copyright 1987 Springer

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Fig. 10.10
figure 10

Time dependence of impact force for blank sample and heavily wire-loaded composites containing one layer of microwires (embedded depth h = 1 mm), two layers (h 1 = 0.75 mm h 2 = 1.25 mm), and three layers (h 1 = 0.5 mm, h 2 = 1 mm, h 3 = 1.5 mm). Each layer contains 200 microwires. The inset shows in-plane view of the damaged spot in the 950 E-glass laminates after the impact test

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Although the microwires can reinforce the polymer materials with adequate concentration and proper orientation, a trade-off is often inevitable if one tends to integrate the structural function and other functionalities which do not necessarily favour a large concentration or unidirectional fillers. For the designers of such multifunctional composites, it is necessary to maximise the most desirable function for the targeted application, while keeping the cost of other functionalities as low as possible.