Stress monitoring capability of magnetostrictive Fe–Co fiber/glass fiber reinforced polymer composites under four-point bending

Many structural health monitoring (SHM) techniques have been investigated for damage detection in woven glass fiber reinforced polymer (GFRP) laminates. Recently, the GFRP composites integrated with sensors have received attention because the composite material can transmit information about the structural condition during operation. Magnetostrictive materials are considered as feasible candidates to realize the contactless SHM techniques by exploiting the Villari effect, but the theoretical modeling to correlate a magnetostrictive response with structural conditions is a critical issue. In this study, the analytical procedure considering the mechanics of materials and electromagnetism was proposed to model the magnetic induction by the Villari effect of magnetostrictive GFRP laminates under bending. The magnetostrictive Fe–Co fiber/GFRP composites were then developed, and the four-point bending tests were carried out to evaluate the fabricated composites’ stress monitoring capability. The magnetic flux density behavior corresponded to the bending stress fluctuation. The maximum magnetic flux density change was 70.7 mT subjected to the peak bending stress of 158 MPa. The analytical solutions showed reasonable agreement with the experimental results. The applied stress and measured magnetic flux density were correlated by the theoretical models. Thus, these results suggest an important step in realizing the novel contactless SHM technique utilizing magnetostrictive materials.

Woven glass fiber reinforced polymer (GFRP) laminates exhibit the features of thermal insulation, electrical insulation, and excellent mechanical properties, and are good materials for superconducting devices for use in the fusion reactor, such as the International Thermonuclear Experimental Reactor (ITER) 1 . However, the application of FRP laminates is prone to be limited due to their complex damage and failure morphologies, for example, interlaminar failure 2,3 . Hence, it has been required to assess the damage state and predict the remaining service life for safe operation 4 .
Structural health monitoring (SHM) is required to maintain safety protocols for these structural components during service 5 . Many researchers have studied various SHM techniques, for instance, the frequency method 6 , Lamb waves 7 , and acoustic emission 8 . However, a versatile technique for all conditions, situations, and applications has not been created because every developed technique has their own advantages, limitations, and scope of application 9 . Currently, the composites embedded with sensors have been broadly recognized as one of the SHM technologies since the composite material can inform the structural health by itself. Fiber optic sensors in composite structures have received attention due to their distinctive advantages 10 . Sánchez et al. 11 have monitored the full manufacturing process of carbon fiber reinforced polymer (CFRP) embedded with optical fiber sensors and evaluated the distributed residual strain profile. The GFRP feasibility with optical backscatter reflectometer based on Rayleigh scatter has been explored 12 . Okabe et al. 13 have demonstrated that the sensing capability of chirped fiber Bragg grating to identify crack locations in CFRP laminates. Electrical resistance measurement has been investigated since the damage and the electrical resistance in CFRP composites can be coupled 14   Here, it is assumed that the component of the magnetic field intensity vector is omitted because a bias magnetic field was not applied on the specimen 38 . Figure 2a shows the Fe-Co fiber of length L and diameter d. The magnetic flux density is induced due to the normal stress along the length (z-)direction (easy axis). Then, the Fe-Co fiber (Fig. 2a) is assumed to have two magnetic charges, ± q, at both ends (Fig. 2b). The magnetic charge due to the Villari effect is assumed to be equal to the amount of the magnetic flux in the z-direction φ f z through the magnetostrictive fiber's cross-section, i.e., where S = πd 2 /4 is the cross-sectional area of the Fe-Co fiber. Let us now consider the coordinate system, o-xyz, as shown in Fig. 2c, whose origin is positioned at the center of the magnetic charges. The magnetic flux densities at the arbitrary point A(0, y, 0) in space induced by magnetic charge + q and − q are, respectively, given by: where r is the distance between the magnetic charge and the arbitrary point A. Here, z-component of the magnetic flux density at the arbitrary point A(0, y, 0), shown in Fig. 2d, can be expressed as: where (1) sin θ +q = sin www.nature.com/scientificreports/ Therefore, we have From Eq. (10), the magnetic flux density B f z in the Fe-Co fiber will be estimated by the measurement of magnetic flux density B e z 0, y, 0 . Here, it is assumed that the estimated magnetic flux density uniformly distributes between the magnetic charges. The value of B e z changes with an external load. Hence, from the above analysis, we can predict the stress in Fe-Co fiber by monitoring the magnetic induction's variation through the magnetostrictive fiber.
Next, we consider a simply supported five layered composite beam of thickness h, width b with four GFRP layers, and one magnetostrictive layer under bending moment M(Z) as shown in Fig. 3a. The origin of the global coordinate system, O-XYZ, is at the center of the upper surface of the composite beam, the X-axis is in the width direction, and the Y-and Z-axes are in the thickness and length direction, respectively. The bending moment M(Z) is induced by the bending load, P. For simplicity, it was assumed that the magnetostrictive layer consists of n Fe-Co fibers and epoxy matrix; where n is the number of Fe-Co fibers. The magnetostrictive layer is the second layer of the composite beam. The position of the neutral plane Y N is not the center of the composite beam because of the asymmetric structure, which can be expressed as: where (E 33 ) i and A i = bh i are the Young's modulus and cross-sectional area of the ith layer, respectively, and h i is the thickness of the ith layer. The Young's moduli of the magnetostrictive layer and GFRP layer are (E 33 ) 2 = 1/s M 33 and (E 33 ) 1 = (E 33 ) 3 = (E 33 ) 4 = (E 33 ) 5 = 1/s G 33 , respectively. The superscripts M and G denote the magnetostrictive layer and GFRP layer, respectively. If the distance between the neutral plane and the center plane of the jth layer is Y′ = Y j − Y N , the normal stress in the jth layer can be expressed as: where the moment of inertia of cross-sectional area of ith layer is given by: Especially, the stress in the magnetostrictive layer is obtained as: where v f = nπd/4b is the volume fraction of the Fe-Co fiber. In this condition, the Young's modulus of the magnetostrictive layer is ( In the global coordinate system, O-XYZ, the origin of the coordinate system o-xyz is (0, Y 2 , 0), and the x-, y-, and z-axes are parallel to the X-, Y-, and Z-axes, respectively. When the average stress σ 0 ZZ in Eq. (17) is equal to the normal stress (σ ZZ ) 2 in Eq. (14) using Eqs. (4), (15), and considering condition (16), the stress acting on the Fe-Co fibers can be obtained as: By substitution of Eq. (18) into Eq. (5), the magnetic flux density B f Z in the Fe-Co fiber of the composite beam under bending moment can be calculated, which allows us to correlate the external load to the inverse magnetostrictive response. Table 1 lists the material properties used in this study. www.nature.com/scientificreports/ Finally, the magnetic flux density of Fe-Co fiber under maximum bending stress was discussed. Figure 4a shows the bending moment diagram of four-point bending test, in which the blue line denotes the general bending moment diagram. The bending moment is given by: The normal stress for Fe-Co fibers depends on the bending moment. Therefore, the amount of the magnetization of Fe-Co fibers in the specimen is different on the coordinate Z as shown in Fig. 4b. To simplify the calculation, the corrected length, L′, was then introduced such that the total amount of the magnetization does not change, and the bending moment is constant. In other words, in Fig. 4a, the area surrounded by the red line is equal to the area surrounded by the blue line. Hence, the corrected length was obtained as Substituting L′ for L into Eq. (10), the magnetic flux density of Fe-Co fiber, B f Z , was calculated using the experimental values, |Y|, B e Z (0, Y , 0) , and Y A = Y 2 -Y.

Experimental procedure
The specimens were fabricated using GFRP prepregs (EGP-87 LA18BR, SPIC Corporation, Japan) with a plain weave and magnetostrictive Fe-Co fibers (K-MP70, Tohoku Steel Co. Ltd., Japan) with 100 μm diameters, and the composition of the Fe-Co fibers was Fe 29 Co 71 . Figure 5 shows the microstructure of the Fe-Co fiber. The Fe-Co fiber's saturation magnetization, M s , residual magnetization, M r , and coercivity, H c , were 1.44 MA/m, 0.31 MA/m, and 6.24 kA/m, respectively. Figure 6 shows the specimen preparation's scheme. The system of rectangular Cartesian coordinate O-XYZ is introduced such that the origin of the system is at the center of the upper surface and the X-, Y-, and Z-axes are along the direction of the specimen's width, thickness, and length, respectively. Four GFRP prepregs and Fe-Co fibers were laminated followed by curing for 2 h at 130 ºC. The Fe-Co fibers were located on the second layer of the laminate and the distance from the upper surface, Y 2 , was 0.1875 mm. The number of Fe-Co fibers, n, was 5, 10, 20, and 37. The Fe-Co fibers were closely spaced at the center of the laminate's width since the measured magnetic flux density will decrease if the Fe-Co fibers are equally spaced. After curing, a laminate was cut and polished so that the specimen's length, l, width, b, and thickness, h, became 40, 7.5, and 0.65 mm, respectively. The warp direction of GFRP prepreg and the longitudinal direction of Fe-Co fibers are parallel to the Z-axis, and the fill direction is parallel to the X-axis. Therefore, the prepared specimens can be assumed to be a five-layered composite of which the magnetostrictive layer is located on the second layer. Four-point bending tests were carried out using Autograph (AG-50kNXD, Shimadzu Corporation, Japan). Figure 7a shows the experimental setup of the four-point bending test. The load and support spans were L 1 = 12 and L 2 = 34 mm, respectively. Three Hall probes (HG-302C, Asahi Kasei Microdevices Corporation, Japan) were (20)  www.nature.com/scientificreports/ positioned above the specimens to measure the magnetic flux density change B e Z in the longitudinal (Z-)direction as shown in Fig. 7b. The distance between the specimen surface and the center of the Hall probe, |Y|, was 5, 9, and 13 mm, respectively (shown in Fig. 7c). Figure 7d shows a four-point bending test program. The specimens were loaded under stress control at a rate of 5 MPa/s, and the maximum load was approximately 150 MPa. Four-point bending tests were carried out to evaluate the reproducibility of inverse magnetostrictive responses corresponding on bending load without a bias magnetic field. All the analog signals, which are load, P, and load point displacement, δ, from Autograph, and voltage, V, from Hall probes were simultaneously collected by the data logger (NR-500 series, KEYENCE Corporation, Japan). The magnetic flux density, B e Z , was computed by multiplying the measured voltage from a Hall probe with the coefficient, 0.8 mT/mV, obtained from the data sheet of the Hall probe.

Results and discussion
The bending stress at the bottom surface σ f = σ ZZ (0, h, 0) and the magnetic flux density change B e Z (0, Y , 0) are plotted in Fig. 8 as a function of the time t for the specimen with 37 Fe-Co fibers. The magnetic flux density's behavior corresponded to the bending stress fluctuation. As expected, the variation of the magnetic flux density change decreased with an increase in the distance between the specimen's surface and the Hall probe's center. At the end of a cycle, the bending stress almost became 0 MPa; however, the magnetic flux density did not return to the initial value. This result can be understood since the residual magnetization of the Fe-Co fiber affects the behavior. The residual magnetization will be an important problem for sensor applications; however, the reproducible behavior of the magnetic flux density's change was observed under the bending stress. The similar  www.nature.com/scientificreports/ results were obtained for the specimens with 5, 10, and 20 Fe-Co fibers. These results indicate that Fe-Co fiber/ GFRP composites can monitor bending stress. Table 2 shows the maximum change of the magnetic flux density B e Z,max of all specimens. Here, the maximum change of the magnetic flux density was calculated by taking the difference between the peak value and the end of cycle value. The result of the specimen with 37 Fe-Co fibers was the largest of all specimens.      www.nature.com/scientificreports/ Table 3 lists the calculated values of the magnetic flux density of Fe-Co fiber B f Z (0, Y 2 , 0) = B f z (0, 0, 0) by Eq. (10) and magnetic charge q by Eq. (6) under maximum bending stress. Here, n Fe-Co fibers closely spaced at the center of the magnetostrictive layer's width were assumed as one Fe-Co fiber with length, L′, and crosssectional area, S = πnd 2 /4, and the single fiber was located at the center of the magnetostrictive layer (single magnetic rod model). The magnetic charges, + q and − q, are placed at (0, Y 2 , L′/2) and (0, Y 2 , − L′/2), respectively. Figure 9 shows the schematic of a modeled single Fe-Co fiber and arbitrary point A. Figure 10 gives a plot of the magnetic flux density change in the air with the distance between the specimen surface and the Hall probe's center showing the calculated values and the experimental data for all specimens. The dots are the average values obtained by the experimental data at |Y|= 5, 9, and 13 mm. The dashed lines were plotted by substituting the values in Table 3 to Eq. (10). The trend is sufficiently similar between the calculation and the experiment. This result implies that the suggested model is useful, and that the Fe-Co fiber's magnetic flux density can be predicted during the four-point bending test by monitoring the variation of the magnetic induction around the Fe-Co fiber/GFRP composites with a Hall probe. The magnetic charges q in Table 3 will be discussed later. Figure 11a illustrates the scheme of estimating the Fe-Co fibers' magnetostrictive response under the bending moment from the bending load (Calculation 1) and the measured magnetic flux density (Calculation 2). Figure 11b shows the magnetic flux versus the number of Fe-Co fibers. The dashed line denotes the calculated data φ f z based on the composite beam model consisting of one magnetostrictive layer and four GFRP layers. The magnetic flux increases with increase in the number of Fe-Co fibers. The line represents the good agreement with the dots q from Table 3 when the magnetoelastic constant d ′f 33 is assumed as 900 × 10 −12 m/A. When the applied bending stress is assessed using a coil or a Hall probe, the amount of magnetic flux is important because it affects the difficulty of monitoring magnetic flux density in space. This result implies the validity of the composite beam model and single magnetic rod model to correlate the external bending load in relation to the magnetostrictive response. In other words, the analytical procedure was proposed to monitor bending stress σ f from magnetic flux density B e in space, as shown in Fig. 1.

Conclusion
This study focused on establishing the novel models to correlate an inverse magnetostrictive response and a bending stress. The Fe-Co fiber was assumed to have two magnetic charges at both ends, and the magnetic charges virtually induced the magnetic field in the air. The five-layered composite beam with four GFRP layers and one magnetostrictive layer was considered under bending. The magnetostrictive layer consisted of n Fe-Co fibers and