sensors Article
A Smart Eddy Current Sensor Dedicated to the Nondestructive Evaluation of Carbon Fibers Reinforced Polymers Mohammed Naidjate 1,2, *, Bachir Helifa 1 , Mouloud Feliachi 2 , Iben-Khaldoun Lefkaier 1 , Henning Heuer 3 and Martin Schulze 3 1 2 3
*
Laboratoire de Physique des Matériaux, Université de Laghouat, Laghouat 03000, Algeria; [email protected] (B.H.); [email protected] (I.-K.L.) IREENA-IUT, Université de Nantes, 44602 Saint-Nazaire, France; [email protected] Fraunhofer Institute for Ceramic Technologies and Systems IKTS, 01109 Dresden, Germany; [email protected] (H.H.); [email protected] (M.S.) Correspondence: [email protected]; Tel.: +213-668-132-376
Received: 6 July 2017; Accepted: 25 August 2017; Published: 31 August 2017
Abstract: This paper propose a new concept of an eddy current (EC) multi-element sensor for the characterization of carbon fiber-reinforced polymers (CFRP) to evaluate the orientations of plies in CFRP and the order of their stacking. The main advantage of the new sensors is the flexible parametrization by electronical switching that reduces the effort for mechanical manipulation. The sensor response was calculated and proved by 3D finite element (FE) modeling. This sensor is dedicated to nondestructive testing (NDT) and can be an alternative for conventional mechanical rotating and rectangular sensors. Keywords: multi-element sensor; eddy current; CFRP characterization; nondestructive testing (NDT); electromagnetic field computation; FEM modeling
1. Introduction Non-destructive testing (NDT) is one of the most common and powerful techniques employed in the inspection of materials during their manufacture or use. When dealing with an electrically conductive body, eddy current non-destructive testing (EC-NDT) is the most efficient way to test the state of health of materials (low cost, readily implemented...). The efficiency of EC-NDT depends directly on the performance of the sensor used. During the last few years, researchers have focused their work to a new generation of EC probes consisting of miniaturized sensors forming a rectangular sensor array that could detect defects with high accuracy, even in complex materials such as carbon fiber-reinforced polymers (CFRP), the material studied as an application in this article. Nevertheless, the highly anisotropic and complex structure of CFRP may require, depending on the type of control to be performed, specific EC sensor configurations. For the detection of defects or the fibers’ orientation, actual solutions are based on high frequency sensors [1], rotating sensors [2,3] or rectangular sensors [4,5] These types of sensors are used to draw a polar diagram giving the intensity of the measured signal in terms of the rotation angle of the sensor. The angles of the obtained lobes determine the different fibers orientations whereas their amplitude indicates the position of the ply in the sample. In this work, a new multi-element sensor array design is suggested with the aim of evaluating CFRP materials. This multi-element sensor is presented as an alternative to the rotating and the rectangular sensors in order to increase the sensitivity and resolution and to reduce the mechanical effort for rotation.
Sensors 2017, 17, 1996; doi:10.3390/s17091996
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Sensors 2017, 17, 1996 Sensors 2017, 17, 1996
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of 10 The proposed sensor consists of flat triangular coils combined into an array. Figure 1 2displays The proposed sensor consists of flat triangular combinedgeometry into an array. Figure 1 as displays the design of the sensor’s elements as well as thecoils simplified introduced input to the 2. Conception the design of the sensor’s elements as well as the simplified geometry introduced as input to the computational code for simulation. computational code for simulation. The proposed sensor consists of flat triangular coils combined into an array. Figure 1 displays The triangular form allows a higher flexibility on the desired shapes of the generated electromagnetic The triangular allows a higher flexibility on the desired shapes of theasgenerated the design of the form sensor’s elements as well the simplified input to the (EM) field. The elements are arranged that theyas can give a large geometry number ofintroduced possible EM configurations, electromagnetic (EM) field. The elements are arranged that they can give a large number of possible computational code for simulation. thereby, avoid the mechanical swiveling of the sensor occurring in conventional characterization. EM configurations, thereby, the mechanical swivelingon of the occurring The triangular formavoid allows a higher flexibility thesensor desired shapes inofconventional the generated In addition to this, In such a structure can cover a relatively wide inspection area which saves the number of characterization. addition to this, a structure can cover relatively wide areaof which electromagnetic (EM) field. The such elements are arranged thata they can give a inspection large number possible manual scanning operations. The size of the sensor elements can be selected to optimize precision saves number of manual scanning operations. Theswiveling size of theofsensor elements can beinselected to in the EMthe configurations, thereby, avoid the mechanical the sensor occurring conventional defect detection. optimize precision inInthe defect to detection. characterization. addition this, such a structure can cover a relatively wide inspection area which
saves the number of manual scanning operations. The size of the sensor elements can be selected to optimize precision in the defect detection.
Figure 1. (Left) Design of a single element and (Right) the simplified array configuration.
Figure 1. (Left) Design of a single element and (Right) the simplified array configuration.
The basicFigure idea 1. rests onDesign the fact theelement EM fields two parallel wires traversed by (Left) of that a single andgenerated (Right) theby simplified array configuration. currents with the same amplitude and in opposite direction cancel each other. This property is The basic idea rests on the fact that the EM fields generated by two parallel wires traversed exploited to generate different field forms, acting only on the excitation currents’ distribution. The basic idea rests on the fact that the EM fields generated by two parallel wires traversed by is by currents with the same amplitude and in opposite direction cancel each other. This property Thereby, Figure four triangular excited in a way that the resulting field is similar to is currents with2 represents the same amplitude and coils in opposite direction cancel each other. This property exploited to generate different field forms, acting only on the excitation currents’ distribution. Thereby, thatexploited obtained by square coil: the fields by currents flowing in the “diagonal” to agenerate different fieldgenerated forms, acting only on the excitation currents’conductors distribution. Figure 2 represents four triangular coils excited in a way that the resulting field is similar to that oppose and cancel other. Then, resulting field is practically the currents flowing Thereby, Figureeach 2 represents four the triangular coils excited in a waythat thatdue the to resulting field is similar to obtained by a square coil: the fields generated by currents flowing in the “diagonal” conductors in the that“external obtainedquadrature” by a square conductors. coil: the fields generated by currents flowing in the “diagonal” conductors oppose andmode cancel each other. thethe resulting field isispractically to the thecurrents currentsflowing flowing in The calculation isThen, described hereafter. oppose and of cancel each other. Then, resulting field practicallythat that due due to the “external quadrature” conductors. in the “external quadrature” conductors. The mode of calculation is described hereafter. The mode of calculation is described hereafter.
Figure 2. Top view of the current flow upon jointly exciting the four coils (left) and perspective view of the three-dimensional distribution of the magnetic potential vector for the four coils (right). Top view of the current flow upon jointly exciting the four coils (left) and perspective view FigureFigure 2. Top2. view of the current flow upon jointly exciting the four coils (left) and perspective view 3. SensorofCharacteristics the three-dimensional distribution of the magnetic potential vector for the four coils (right). of the three-dimensional distribution of the magnetic potential vector for the four coils (right).
3.1.3. Geometrical Characterization Sensor Characteristics
3. Sensor Characteristics
The proposed sensor is an array assembly of 36 identical coils in the shape of isosceles triangles 3.1. Geometrical Characterization whose angles at the base worth 45°. In each coil, the developed length or the total length of the wire 3.1. Geometrical Characterization ltotal and The the proposed total effective Stotal assembly are givenofby Equations (1)the and (2) of respectively (see sensorsurface is an array 36 the identical coils in shape isosceles triangles Appendix A): The proposed is an array of the 36 identical in or thethe shape isosceles whose angles atsensor the base worth 45°.assembly In each coil, developedcoils length total of length of the triangles wire ◦ l total and the total effective surface S total are given by the Equations (1) and (2) respectively whose angles at the base worth 45 . In each coil, the developed length or the total length(see of the Appendix A):
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wire ltotal and the total effective surface Stotal are given by the Equations (1) and (2) respectively (see Appendix A): Sensors 2017, 17, 1996 3 of 10 √ 2 ltotale ≈ n 2 + 2 D − (n − 1) l p + E p 1 + (1) tan(π/8) 2 2 1+ ltotale ≈nn 2 + 2 D − ( n − 1) ( l p + E (1) p ) tan(π 1/ 8) 1 Stotale ≈ ∑ D − (k − 1) l p + E p 1 + (2) 2 k =1 tan(π/8)
(
)
2
E is the inter-lines distance 1 Figure 1), l is the 1width, where D is the external rib of the Stotalecoil (2) ≈ (see D − ( k − 1) ( l p +p E p ) 1 +line p 2 k =1 tan( / 8) π and n is the number of turns. These geometrical parameters are indispensable to calculate the electrical parameters their where as D is the influence external ribisofdirect. the coil (see Figure 1), lp is the line width, Ep is the inter-lines distance n
and n is the number of turns. These geometrical parameters are indispensable to calculate the
3.2. Electrical electricalCharacterization parameters as their influence is direct.
The theoretical model of a coil is given in Figure 3 [6]. To determine the coil inductance L, 3.2. Electrical Characterization and for the sake of accuracy, an evaluation of the stored magnetic energy (Equation (5)) was provided The theoretical model of a coil4.is However, given in Figure 3 [6]. To determine the coil inductance L, and C, via the FE model developed in Section to determine the resistance R and the capacitance for the sake of accuracy, an evaluation of the stored magnetic energy (Equation (5)) was provided via basic models have been adopted to simplify the calculation. The relations through which the electrical the FE model developed in Section 4. However, to determine the resistance R and the capacitance C, parameters have been estimated are given below: basic models have been adopted to simplify the calculation. The relations through which the electrical parameters have been estimated are given below: ρ×l totale , × lhtotale lρp × p , R=
R=
l p ×h p
(3)
(3)
# −1 n h p ×lk −1 C = ∑ n 1/ε (4) h p × lk , E (4) C= , k =2 1 / ε p E k =2 p ω y 1 → 2 L = 2ω (5) 1 B 2 dΩ , L I= 2 µ B d Ω , (5) Ω I Ω μ wherewhere hp is the height of the line, ρ is its electrical ofthe thewire, wire, ε is electric permittivity, hp is the height of the line, ρ is its electricalresistivity resistivity of ε is thethe electric permittivity, ω is the angular frequency, Ω isΩthe whole computation (sensorand andairair box), is the magnetic ω is the angular frequency, is the whole computation area area (sensor box), μ isµ the magnetic permeability and B is the magnetic flux density. permeability and B is the magnetic flux density. "
Figure Electricalmodel model of aa coil. Figure 3. 3.Electrical coil.
3.3. Physical Characterization 3.3. Physical Characterization Knowledge of its geometrical and electrical characteristics is necessary but insufficient to fully
Knowledge of its geometrical and electrical characteristics is necessary but insufficient to fully qualify the electromagnetic behaviour of a coil. As an EM sensor, the coil needs to meet other qualify the electromagnetic behaviour of a coil. As an EM sensor, the coil needs to meet other requirements depending on the intended mode of its use. As an emitter, its emissive ability must be requirements depending the intended mode oftoits use. As its ansensitivity emitter, its ability must calculated. If it’s usedon as receiver, it is necessary determine andemissive its electrical noise be calculated. If it’s used as receiver, it is necessary to determine its sensitivity and its electrical signal. In the proposed sensor, coils have the versatility to work in emission and reception noise simultaneously signal. In the or proposed sensor, have the versatility to work and reception separately, which coils implies a complete and rigorous studyin of emission the sensitive element. Ravat, C. [6]orexposes in his which work these parameters as follows: simultaneously separately, implies a complete and rigorous study of the sensitive element. Ravat, C.According [6] exposes in his work these parameters as follows: to Faraday-Lenz’s law, at a frequency f, the sensitivity of a coil is:
According to Faraday-Lenz’s law, at a frequency f, the sensitivity of a coil is: dV = 2π f Stotale , S= (6) dB dV = 2π f Stotale , S = by where dV is the voltage variation provoked a variation in the received magnetic induction dB. dB
(6)
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The noise of a coil when it is not carrying current is only a thermal agitation noise. This effective voltage b atis a the temperature T and inprovoked measuring is givenmagnetic by; wherevdV voltage variation byfrequency a variationrange in theΔfreceived induction dB. The noise of a coil when it is not carrying current is only a thermal agitation noise. This effective v = 4K ×T × R ×Δf , (7) voltage vb at a temperature T and inbmeasuring frequency range ∆f is given by; where K is Boltzmann’s constant. p (7) vb = 4K × T × R × ∆ f , The emissive ability Pe is the ratio between the emitted field “B” and the current “I” necessary for itswhere emission: K is Boltzmann’s constant.
The emissive ability Pe is the ratio between the B emitted L , field “B” and the current “I” necessary for (8) pe = = its emission: I B Stotale L , (8) pe = = I Stotale 3.4. Optimization of the Coil 3.4. Optimization of the Coil The relationship between the geometrical, electrical and physical characteristics developed previously allows us tobetween study the of each parameter thus to determine thedeveloped optimum The relationship theinfluence geometrical, electrical andand physical characteristics dimensionsallows of the us coiltoappropriate for a desired application. Table provides the characteristics of previously study the influence of each parameter and 1thus to determine the optimum the selected coil to non-destructively evaluate a CFRP. According to 1the theoretical (Figure 3), dimensions of the coil appropriate for a desired application. Table provides the model characteristics of Figure 4 shows frequency response of a triangular using data given in Tablemodel 1. It can be seen the selected coilthe to non-destructively evaluate a CFRP. coil According to the theoretical (Figure 3), that the4coil can the be used as EMresponse field sensor 800 kHz shows a strong inductive Figure shows frequency of aabove triangular coilwhere usingitdata given in Table 1. It canbehavior be seen with a phase greater than much higher than 100 MHz.inductive behavior that the coil can be used as60°. EMThe fieldcut-off sensorfrequency above 800iskHz where it shows a strong ◦ with a phase greater than 60 . The cut-off frequency is much higher than 100 MHz.
Table 1. Numerical values of the coil characteristics calculated at 1 MHz. Table 1. Numerical values of the coil characteristics calculated at 1 MHz.
Parameter Numerical Value external length D 1 Value Parameter Numerical Coil line width lp 6 external length D 1 dimensions inter-line space E p 3 line width lp 6 Coil dimensions number of turns n 333 inter-line space Ep number of R turns n 33 resistance 4.24 inductance LR 1.44 resistance 4.24 inductance 1.44 Electrical capacity C L 3.5 capacity C 3.5 parameters sensitivity S 35 Electrical parameters sensitivity S 35 noise voltage vb v 0.83 noise voltage 0.83 b emissive ability Pe Pe 254 emissive ability 254
Unit [mm] Unit [µm] [mm] [µm] [µm] [µm]
[ohm] [µH] [ohm] [µH] [fF] [fF] [V/T] [V/T] [µV] [µV] [mT/A] [mT/A]
Figure 4. 4. Frequency Frequency response response of of the the sensor. sensor. Figure
4. Modeling After the construction of the geometry and the mesh generation using the open-source software GMSH, the problem data are sent to our 3D finite element solver in which was implemented the magneto-dynamics formulation AV-A (Equation (9)); mathematical model chosen to describe the EM
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behaviour of our problem. The calculations are carried out in the harmonic regime. A penalty term is introduced to ensure the uniqueness the solution magneto-dynamics formulation AV-Aof (Equation (9));[7]: mathematical model chosen to describe the EM behaviour of our problem. The are carried out inthe harmonic regime. A penalty term is calculations 1 1 ∇× ∇× − ∇ ∇ ⋅ + + ∇ = A A σ j ω A V J introduced to ensure the uniqueness of the solution s [7]: , μ μ (9) → → → → → → → → → ∇ ⋅ jωσ A + ∇V = 0 ∇ × µ1 ∇ × A − ∇ µ1 ∇ · A + σ jω A + ∇V = J s , (9) → → → respectively magnetic vector where A and V are A+ ∇V = 0 potential and electric scalar potential, μ is the ∇ · jω σ the magnetic permeability and is the electrical conductivity tensor given according to the ply → orientation by [2]: where A and V are respectively the magnetic vector potential and electric scalar potential, µ is the σ / / −tensor σ⊥ electrical 2 2 magnetic permeability and σ is the conductivity according to the ply orientation sin(2θgiven ) 0 σ // cos (θ ) + σ ⊥ sin (θ ) 2 , by [2]: σ // −σ ⊥ σ / / cos 2σ(// θ )−+σσ⊥⊥ sin 2 (θ ) 0 sin(2θ ) = 2 (10) σ// σcos sin(2θ ) 0 (θ ) +2σ⊥ sin2 (θ ) 2 −σ⊥ σ// σ= (10) sin(02θ ) σ// cos2 (0θ ) + σ⊥ sinσ2zz(θ ) 0 , 2 0 0 σzz
(
(
(
)
))
where σσ// // is direction, σσ⊥ in the the transverse transverse ⊥ is where isthe theelectrical electrical conductivity conductivity in in the the fibers fibers direction, is the the conductivity conductivity in direction of the fibers and σ zz is the conductivity in the direction of the plies stacking. direction of the fibers and σzz is the conductivity in the direction of the plies stacking. 5. Results 5. The EC-NDT EC-NDT concept concept is is based based on on the the distribution distribution and and circulation circulation of of the the induced induced currents currents in in the the The component being being inspected. inspected. This distribution is strongly linked to the profile of of the the excitation excitation EM EM component field. With Withthis thisin inmind, mind,numerical numericalexperiments experimentswere werecarried carried out discern ability sensor field. out toto discern thethe ability of of ourour sensor to to emulate field configurations obtained by conventional sensors such a rectangular emulate thethe EMEM field configurations obtained by conventional sensors such as aasrectangular coil.coil. 5.1. 5.1. Sensor Sensor and and EM EM Field Field Figure Figure 55 shows shows that that the the electromagnetic electromagnetic field field generated generated by by aa set set of of triangular triangular elements elements excited excited simultaneously simultaneously is is similar similar to to the the EM EM field field created created by by aa conventional conventional rectangular rectangular coil. coil. The The electric electric field field calculated at the front surface of the load illustrated in Figure 6 confirms this equivalence of the global calculated at the front surface of the load illustrated in Figure confirms this equivalence of the global EM EM behaviour behaviour for for the the two two systems. systems. Nevertheless, Nevertheless, we we note some some electric electric field field irregularities irregularities in in the the case case of inin thethe geometry of of thethe inductor andand to of the the multi-element multi-elementsensor, sensor,which whichisisdue duetotothe thediscontinuities discontinuities geometry inductor the current singularities in the bends of triangles. to the current singularities in the bends of triangles.
Figure 5. Magnetic vector potential calculated for a system of: (a) rectangular coil; (b) proposed multiFigure 5. Magnetic vector potential calculated for a system of: (a) rectangular coil; (b) proposed element sensor. multi-element sensor.
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Figure 6. Electric field magnitude at the front surface of the load (z = 0): (a) rectangular coil; (b) multiFigure 6. Electric field magnitude at the front surface of the load (z = 0): (a) rectangular coil; element Figure 6.sensor. Electric field magnitude at the front surface of the load (z = 0): (a) rectangular coil; (b) multi(b) multi-element sensor. element sensor.
The interaction between the excited elements and those “at rest” was studied too with the aim The between the elements and those was studied tootoo with thethe aim of of evaluating the coupling effect. The obtained results inrest” Figure 7 show that thewith non-excited The interaction interaction between theexcited excited elements anddisplayed those“at “atrest” was studied aim evaluating the coupling effect. The obtained results displayed in Figure 7 show that the non-excited adjacent elements are without a The slightest action on the configuration of the fieldthat or on amplitude of evaluating the coupling effect. obtained results displayed in Figure 7 show theitsnon-excited adjacent elements are without a slightest action on the configuration of the field or on its amplitude at at the operating of 1aMHz. adjacent elementsfrequency are without slightest action on the configuration of the field or on its amplitude the operating frequency of 1 MHz. at the operating frequency of 1 MHz.
Figure 7. Electric field magnitude at the front surface of the load (z = 0): (I) without regard to non-excited elements (σ magnitude = 0); (II) non-excited elements areload physically (σ = 30, ×regard 106 S/m). Figure 7. Electric Electric field at front the front surface of the (zwithout = 0): (I)regard without to Figure 7. field magnitude at the surface of the (z =load 0): represented (I) to 6non-excited 6 S/m). 6 non-excited elements (σ = 0); (II) non-excited elements are physically represented (σ = 30, 6 × 10 elements (σ = 0); (II) non-excited elements are physically represented (σ = 30, 6 × 10 S/m).
In addition to the foregoing, the proposed sensor allows a high flexibility in terms of modes of excitation and measurement. The the figure below sensor illustrates different configurations In addition to the foregoing, proposed allows a highfield flexibility in terms obtained of modes for of In addition to the foregoing, the proposed sensor allows a high flexibility in terms of modes of different excitations. It can beThe seenfigure in Figure 8 that the sensor can substitute rectangular obtained coil oriented excitation and measurement. below illustrates different field configurations for excitation and measurement. The figure below illustrates different field configurations obtained for at 0°, 45°,excitations. 90° and −45° without recurring to mechanical rotation. property will be exploited and different It can be seen in Figure 8 that the sensor can This substitute rectangular coil oriented different excitations. It can be seen in Figure 8 that the sensor can substitute rectangular coil oriented applied a laminate CFRP. recurring to mechanical rotation. This property will be exploited and at 0°, 45°,to90° and −45°of without at 0◦ , 45◦ , 90◦ and −45◦ without recurring to mechanical rotation. This property will be exploited and applied to a laminate of CFRP. applied to a laminate of CFRP.
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Figure 8. Field configurations generated by by thethe multi-element sensor equivalent to atorectangular coilcoil Figure 8. Field configurations generated multi-element sensor equivalent a rectangular ◦ , 4590° ◦ , 90 ◦ and oriented at 0°, and −45°. oriented at 045°, −45◦ .
5.2.5.2. Application to CFRP Application to CFRP The modeled system is is a stack ofoffour physical and The modeled system a stack fourplies pliesoriented orientedatat[0°, [0◦45°, , 45◦90°, , 90◦−45°]. , −45◦The ]. The physical and geometrical characteristics are given by Table 2. Figure 9 illustrates the distribution of eddy currents geometrical characteristics are given by Table 2. Figure 9 illustrates the distribution of eddy currents produced byby a rectangular inductor oriented at at 0° 0and its its equivalent generated byby thethe multi-element ◦ and produced a rectangular inductor oriented equivalent generated multi-element sensor. It is noted that the distributions of eddy currents generated by the two systems, ply of sensor. It is noted that the distributions of eddy currents generated by the two systems, in in each each ply of the the laminate, laminate,isistypically typicallyidentical. identical.This This leads to expect, consequently, an analogue dissipated leads to expect, consequently, an analogue dissipated power, power, hence an identical response in terms of impedance. hence an identical response in terms of impedance. Table 2. Numerical values of of the the system system characteristics characteristics Table 2. Numerical values
Laminate Laminate
Sensor Sensor
Parameter Parameter Number of plies Fibers orientation Number of plies Fibers orientation Conductivity (σ//, σ⊥, σzz) Conductivity (σ// , σ⊥ , σzz ) Ply thickness Ply thickness Number of coils
Numerical Values Numerical 4 Values 0°, 45°, 90° 4and −45° ◦ and 4,◦2, 90 2, 10)−45◦ 0◦(10 , 45 × 10 4 (10 , 125 2 × 102 , 10) 125 36
Unit [°] [S/m] [◦ ] [µm] [S/m] [µm]
Gap inter-coils Number of coils GapLift-off inter-coils Lift-off Current intensity Current intensity Frequency Frequency
0.08 36 0.08 0.125 0.125 20 120 1
[mm] [mm] [mm] [mA] [mm] [MHz][mA] [MHz]
Unit
Furthermore, the results presented in Figure 10 prove that the proposed sensor can detect the orientation of the pliesthe and their order of stacking. The between the amplitudes peaksthe Furthermore, results presented in Figure 10comparison prove that the proposed sensor canof detect shows that they are plies decreasing according the stacking of the between plies. However, our values do orientation of the and their order oftostacking. The order comparison the amplitudes of peaks notshows coincide calculatedaccording by [3] duetotothe thestacking mismatch of the two systems (number turnsdo thatwith theythose are decreasing order of the plies. However, ourof values and dimensions of coils). note also there is no large difference between the peaks at and not coincide with those We calculated by that [3] due to the mismatch of the two systems (number of45° turns and 90°; this can beof explained the also change sizesis(length to difference width ratio) of the equivalent rectangular dimensions coils). Webynote thatofthere no large between the peaks at 45◦ and 90◦ ; coilthis generated at 45° andby 90° (see Figure can be explained the change of8). sizes (length to width ratio) of the equivalent rectangular coil ◦ ◦ generated at 45 and 90 (see Figure 8).
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Figure 9. Eddy current distribution in different plies of laminate (0°,◦45°,◦90°,◦−45°); ◦at the right caused Figure 9. Eddy current distribution different plies laminate(0°, (0 45°, , 45 90°, , 90 −45°); , −45 at); the at the right caused Figure 9. Eddy current distribution in in different plies ofof laminate right caused by the multi-element sensor and at left by a rectangular coil (3.2 mm × 1 mm). by the multi-element sensor and at left by a rectangular coil (3.2 mm × 1 mm). by the multi-element sensor and at left by a rectangular coil (3.2 mm × 1 mm).
Figure 10. The normalized resistance of the coil as function of its rotation angle above a laminate of Figure 10. The normalized resistance of the coil as function of its rotation angle above a laminate of Figure four plies10. [0°,The 45°,normalized 90°, −45°]. resistance of the coil as function of its rotation angle above a laminate of four plies [0°, 45°, 90°, −45°]. four plies [0◦ , 45◦ , 90◦ , −45◦ ].
6. Conclusions 6. Conclusions A new design of an eddy current multi-element sensor is proposed. The EM field computation A new design of an eddy current multi-element sensor is proposed. The EM field computation results reveal that this sensor is able to control the EM field shape and generate the plurality of results reveal that this sensor is able to control the EM field shape and generate the plurality of
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6. Conclusions A new design of an eddy current multi-element sensor is proposed. The EM field computation results reveal that this sensor is able to control the EM field shape and generate the plurality of configurations often needed in EC–NDT of carbon fiber-reinforced polymers. The application of the proposed sensor on a sample of CFRP shows its capability to detect the plies’ orientations and their stacking order by acting only on the excitation currents. This sensor can thus be an alternative to the mechanical rotating sensors and the rectangular sensors. Acknowledgments: This research was partwise funded by the European Union Regional Development Fund (EFRE) and the Free State of Saxony (grant “3D-Fast”, No. 100224749). The authors would like to thank the mentioned institutions for providing the funding. Author Contributions: M.N. and B.H. modeled the sensor, wrote the manuscript, contributed to discussion, and reviewed; M.F. and I.-K.L. presented the research subject, provided guidance in modeling, contributed to discussion, and reviewed; H.H. and M.S. conceived and designed the experiments. Conflicts of Interest: The authors declare no conflict of interest.
Appendix A Appendix A.1. Calculation of the Developed Length of the Coil The coil is composed of n triangular turns (see Figure 1) numbered from the outside to the inside. These triangular turns are isosceles whose angles at the base worth 45◦ . The lengths of the three edges of the k-th turn are: 1 d1 ( k ) ≈ d2 ( k ) = D − ( k − 1) l p + E p 1 + π , (A1) tg 8 √ lp + Ep d3 ( k ) ≈ D 2 − 2( k − 1) , (A2) tg π8 where d1 and d2 are the identical edges, d3 is the hypotenuse. Therefore, the developed length of a turn number k is: l k ≈ d1 ( k ) + d2 ( k ) + d3 ( k ),
(A3)
Thus, the total developed length of the entire coil is simply the sum of lk : n
ltotale ≈
∑ lk ,
(A4)
k =1
√ l p + Ep 1 + D 2 − 2( k − 1) , ≈ ∑ 2 D − ( k − 1) l p + E p 1 + π tg 8 tg π8 k =1 n
ltotale
(A5)
Or more simply: ltotale ≈ n
2+
√ 2 D − ( n − 1) l p + E p 1 +
2 tan(π/8)
,
(A6)
Appendix A.2. Calculation of the Total Area The surface enclosed by the turn number k is: Sk ≈
2 1 1 D − ( k − 1) l p + E p 1 + , 2 tan(π/8)
(A7)
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Then, the total effective surface of the coil is: Stotale
2 1 n 1 , ≈ ∑ D − ( k − 1) l p + E p 1 + 2 k =1 tan(π/8)
(A8)
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2. 3.
4.
5.
6.
7.
Heuer, H.; Schulze, M.; Pooch, M.; Gäbler, S.; Nocke, A.; Bardl, G.; Cherif, C.; Klein, M.; Kupke, R.; Vetter, R.; et al. Review on quality assurance along the CFRP value chain—Non-destructive testing of fabrics, preforms and CFRP by HF radio wave techniques. Compos. Part B Eng. 2015, 77, 494–501. [CrossRef] Mook, G.; Lange, R.; Koeser, O. Non-destructive characterization of carbon-fiber reinforced plastics by means of eddy currents. Compos. Sci. Technol. 2001, 61, 865–873. [CrossRef] Menana, H.; Feliachi, M. Non destructive evaluation of the conductivity tensor of a CFRP plate using a rotating eddy current sensor. In Proceedings of the XIV International Symposium on Electromagnetic Fields, Arras, France, 10–12 September 2009. Savin, A.R.; Grimberg, R.; Chifan, S. Evaluation of delamination in Carbon Fiber Composites Using the Eddy Current Method. In Proceedings of the 15th World Conference on Non-Destructive Testing, Roma, Italy, 15–21 October 2000. Grimberg, R.; Savin, A.; Steigmann, R.; Bruma, A. Eddy current examination of carbon fibres in carbon-epoxy composites and Kevlar. In Proceedings of the 8th International Conference of the Slovenian Society for Non-Destructive Testing, Portorož, Slovenia, 1–3 September 2005; pp. 223–228. Ravat, C. Conception de Multicapteurs à Courants de Foucault et Inversion des Signaux Associés Pour le Contrôle non Destructif. Ph.D. Thesis, Sciences and Technologys of Information and telecommunications Systems, University of Paris-Sud, Paris, France, 2008. Helifa, B. Contribution à la Simulation du CND par Courants de Foucault en vue de la Caractérisation des Fissures Débouchantes. Ph.D. Thesis, Computer and Mathematical Sciences and Technologies, Nantes University, Nantes, France, 2012. © 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
A Smart Eddy Current Sensor Dedicated to the Nondestructive Evaluation of Carbon Fibers Reinforced Polymers Mohammed Naidjate 1,2, *, Bachir Helifa 1 , Mouloud Feliachi 2 , Iben-Khaldoun Lefkaier 1 , Henning Heuer 3 and Martin Schulze 3 1 2 3
*
Laboratoire de Physique des Matériaux, Université de Laghouat, Laghouat 03000, Algeria; [email protected] (B.H.); [email protected] (I.-K.L.) IREENA-IUT, Université de Nantes, 44602 Saint-Nazaire, France; [email protected] Fraunhofer Institute for Ceramic Technologies and Systems IKTS, 01109 Dresden, Germany; [email protected] (H.H.); [email protected] (M.S.) Correspondence: [email protected]; Tel.: +213-668-132-376
Received: 6 July 2017; Accepted: 25 August 2017; Published: 31 August 2017
Abstract: This paper propose a new concept of an eddy current (EC) multi-element sensor for the characterization of carbon fiber-reinforced polymers (CFRP) to evaluate the orientations of plies in CFRP and the order of their stacking. The main advantage of the new sensors is the flexible parametrization by electronical switching that reduces the effort for mechanical manipulation. The sensor response was calculated and proved by 3D finite element (FE) modeling. This sensor is dedicated to nondestructive testing (NDT) and can be an alternative for conventional mechanical rotating and rectangular sensors. Keywords: multi-element sensor; eddy current; CFRP characterization; nondestructive testing (NDT); electromagnetic field computation; FEM modeling
1. Introduction Non-destructive testing (NDT) is one of the most common and powerful techniques employed in the inspection of materials during their manufacture or use. When dealing with an electrically conductive body, eddy current non-destructive testing (EC-NDT) is the most efficient way to test the state of health of materials (low cost, readily implemented...). The efficiency of EC-NDT depends directly on the performance of the sensor used. During the last few years, researchers have focused their work to a new generation of EC probes consisting of miniaturized sensors forming a rectangular sensor array that could detect defects with high accuracy, even in complex materials such as carbon fiber-reinforced polymers (CFRP), the material studied as an application in this article. Nevertheless, the highly anisotropic and complex structure of CFRP may require, depending on the type of control to be performed, specific EC sensor configurations. For the detection of defects or the fibers’ orientation, actual solutions are based on high frequency sensors [1], rotating sensors [2,3] or rectangular sensors [4,5] These types of sensors are used to draw a polar diagram giving the intensity of the measured signal in terms of the rotation angle of the sensor. The angles of the obtained lobes determine the different fibers orientations whereas their amplitude indicates the position of the ply in the sample. In this work, a new multi-element sensor array design is suggested with the aim of evaluating CFRP materials. This multi-element sensor is presented as an alternative to the rotating and the rectangular sensors in order to increase the sensitivity and resolution and to reduce the mechanical effort for rotation.
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of 10 The proposed sensor consists of flat triangular coils combined into an array. Figure 1 2displays The proposed sensor consists of flat triangular combinedgeometry into an array. Figure 1 as displays the design of the sensor’s elements as well as thecoils simplified introduced input to the 2. Conception the design of the sensor’s elements as well as the simplified geometry introduced as input to the computational code for simulation. computational code for simulation. The proposed sensor consists of flat triangular coils combined into an array. Figure 1 displays The triangular form allows a higher flexibility on the desired shapes of the generated electromagnetic The triangular allows a higher flexibility on the desired shapes of theasgenerated the design of the form sensor’s elements as well the simplified input to the (EM) field. The elements are arranged that theyas can give a large geometry number ofintroduced possible EM configurations, electromagnetic (EM) field. The elements are arranged that they can give a large number of possible computational code for simulation. thereby, avoid the mechanical swiveling of the sensor occurring in conventional characterization. EM configurations, thereby, the mechanical swivelingon of the occurring The triangular formavoid allows a higher flexibility thesensor desired shapes inofconventional the generated In addition to this, In such a structure can cover a relatively wide inspection area which saves the number of characterization. addition to this, a structure can cover relatively wide areaof which electromagnetic (EM) field. The such elements are arranged thata they can give a inspection large number possible manual scanning operations. The size of the sensor elements can be selected to optimize precision saves number of manual scanning operations. Theswiveling size of theofsensor elements can beinselected to in the EMthe configurations, thereby, avoid the mechanical the sensor occurring conventional defect detection. optimize precision inInthe defect to detection. characterization. addition this, such a structure can cover a relatively wide inspection area which
saves the number of manual scanning operations. The size of the sensor elements can be selected to optimize precision in the defect detection.
Figure 1. (Left) Design of a single element and (Right) the simplified array configuration.
Figure 1. (Left) Design of a single element and (Right) the simplified array configuration.
The basicFigure idea 1. rests onDesign the fact theelement EM fields two parallel wires traversed by (Left) of that a single andgenerated (Right) theby simplified array configuration. currents with the same amplitude and in opposite direction cancel each other. This property is The basic idea rests on the fact that the EM fields generated by two parallel wires traversed exploited to generate different field forms, acting only on the excitation currents’ distribution. The basic idea rests on the fact that the EM fields generated by two parallel wires traversed by is by currents with the same amplitude and in opposite direction cancel each other. This property Thereby, Figure four triangular excited in a way that the resulting field is similar to is currents with2 represents the same amplitude and coils in opposite direction cancel each other. This property exploited to generate different field forms, acting only on the excitation currents’ distribution. Thereby, thatexploited obtained by square coil: the fields by currents flowing in the “diagonal” to agenerate different fieldgenerated forms, acting only on the excitation currents’conductors distribution. Figure 2 represents four triangular coils excited in a way that the resulting field is similar to that oppose and cancel other. Then, resulting field is practically the currents flowing Thereby, Figureeach 2 represents four the triangular coils excited in a waythat thatdue the to resulting field is similar to obtained by a square coil: the fields generated by currents flowing in the “diagonal” conductors in the that“external obtainedquadrature” by a square conductors. coil: the fields generated by currents flowing in the “diagonal” conductors oppose andmode cancel each other. thethe resulting field isispractically to the thecurrents currentsflowing flowing in The calculation isThen, described hereafter. oppose and of cancel each other. Then, resulting field practicallythat that due due to the “external quadrature” conductors. in the “external quadrature” conductors. The mode of calculation is described hereafter. The mode of calculation is described hereafter.
Figure 2. Top view of the current flow upon jointly exciting the four coils (left) and perspective view of the three-dimensional distribution of the magnetic potential vector for the four coils (right). Top view of the current flow upon jointly exciting the four coils (left) and perspective view FigureFigure 2. Top2. view of the current flow upon jointly exciting the four coils (left) and perspective view 3. SensorofCharacteristics the three-dimensional distribution of the magnetic potential vector for the four coils (right). of the three-dimensional distribution of the magnetic potential vector for the four coils (right).
3.1.3. Geometrical Characterization Sensor Characteristics
3. Sensor Characteristics
The proposed sensor is an array assembly of 36 identical coils in the shape of isosceles triangles 3.1. Geometrical Characterization whose angles at the base worth 45°. In each coil, the developed length or the total length of the wire 3.1. Geometrical Characterization ltotal and The the proposed total effective Stotal assembly are givenofby Equations (1)the and (2) of respectively (see sensorsurface is an array 36 the identical coils in shape isosceles triangles Appendix A): The proposed is an array of the 36 identical in or thethe shape isosceles whose angles atsensor the base worth 45°.assembly In each coil, developedcoils length total of length of the triangles wire ◦ l total and the total effective surface S total are given by the Equations (1) and (2) respectively whose angles at the base worth 45 . In each coil, the developed length or the total length(see of the Appendix A):
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wire ltotal and the total effective surface Stotal are given by the Equations (1) and (2) respectively (see Appendix A): Sensors 2017, 17, 1996 3 of 10 √ 2 ltotale ≈ n 2 + 2 D − (n − 1) l p + E p 1 + (1) tan(π/8) 2 2 1+ ltotale ≈nn 2 + 2 D − ( n − 1) ( l p + E (1) p ) tan(π 1/ 8) 1 Stotale ≈ ∑ D − (k − 1) l p + E p 1 + (2) 2 k =1 tan(π/8)
(
)
2
E is the inter-lines distance 1 Figure 1), l is the 1width, where D is the external rib of the Stotalecoil (2) ≈ (see D − ( k − 1) ( l p +p E p ) 1 +line p 2 k =1 tan( / 8) π and n is the number of turns. These geometrical parameters are indispensable to calculate the electrical parameters their where as D is the influence external ribisofdirect. the coil (see Figure 1), lp is the line width, Ep is the inter-lines distance n
and n is the number of turns. These geometrical parameters are indispensable to calculate the
3.2. Electrical electricalCharacterization parameters as their influence is direct.
The theoretical model of a coil is given in Figure 3 [6]. To determine the coil inductance L, 3.2. Electrical Characterization and for the sake of accuracy, an evaluation of the stored magnetic energy (Equation (5)) was provided The theoretical model of a coil4.is However, given in Figure 3 [6]. To determine the coil inductance L, and C, via the FE model developed in Section to determine the resistance R and the capacitance for the sake of accuracy, an evaluation of the stored magnetic energy (Equation (5)) was provided via basic models have been adopted to simplify the calculation. The relations through which the electrical the FE model developed in Section 4. However, to determine the resistance R and the capacitance C, parameters have been estimated are given below: basic models have been adopted to simplify the calculation. The relations through which the electrical parameters have been estimated are given below: ρ×l totale , × lhtotale lρp × p , R=
R=
l p ×h p
(3)
(3)
# −1 n h p ×lk −1 C = ∑ n 1/ε (4) h p × lk , E (4) C= , k =2 1 / ε p E k =2 p ω y 1 → 2 L = 2ω (5) 1 B 2 dΩ , L I= 2 µ B d Ω , (5) Ω I Ω μ wherewhere hp is the height of the line, ρ is its electrical ofthe thewire, wire, ε is electric permittivity, hp is the height of the line, ρ is its electricalresistivity resistivity of ε is thethe electric permittivity, ω is the angular frequency, Ω isΩthe whole computation (sensorand andairair box), is the magnetic ω is the angular frequency, is the whole computation area area (sensor box), μ isµ the magnetic permeability and B is the magnetic flux density. permeability and B is the magnetic flux density. "
Figure Electricalmodel model of aa coil. Figure 3. 3.Electrical coil.
3.3. Physical Characterization 3.3. Physical Characterization Knowledge of its geometrical and electrical characteristics is necessary but insufficient to fully
Knowledge of its geometrical and electrical characteristics is necessary but insufficient to fully qualify the electromagnetic behaviour of a coil. As an EM sensor, the coil needs to meet other qualify the electromagnetic behaviour of a coil. As an EM sensor, the coil needs to meet other requirements depending on the intended mode of its use. As an emitter, its emissive ability must be requirements depending the intended mode oftoits use. As its ansensitivity emitter, its ability must calculated. If it’s usedon as receiver, it is necessary determine andemissive its electrical noise be calculated. If it’s used as receiver, it is necessary to determine its sensitivity and its electrical signal. In the proposed sensor, coils have the versatility to work in emission and reception noise simultaneously signal. In the or proposed sensor, have the versatility to work and reception separately, which coils implies a complete and rigorous studyin of emission the sensitive element. Ravat, C. [6]orexposes in his which work these parameters as follows: simultaneously separately, implies a complete and rigorous study of the sensitive element. Ravat, C.According [6] exposes in his work these parameters as follows: to Faraday-Lenz’s law, at a frequency f, the sensitivity of a coil is:
According to Faraday-Lenz’s law, at a frequency f, the sensitivity of a coil is: dV = 2π f Stotale , S= (6) dB dV = 2π f Stotale , S = by where dV is the voltage variation provoked a variation in the received magnetic induction dB. dB
(6)
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The noise of a coil when it is not carrying current is only a thermal agitation noise. This effective voltage b atis a the temperature T and inprovoked measuring is givenmagnetic by; wherevdV voltage variation byfrequency a variationrange in theΔfreceived induction dB. The noise of a coil when it is not carrying current is only a thermal agitation noise. This effective v = 4K ×T × R ×Δf , (7) voltage vb at a temperature T and inbmeasuring frequency range ∆f is given by; where K is Boltzmann’s constant. p (7) vb = 4K × T × R × ∆ f , The emissive ability Pe is the ratio between the emitted field “B” and the current “I” necessary for itswhere emission: K is Boltzmann’s constant.
The emissive ability Pe is the ratio between the B emitted L , field “B” and the current “I” necessary for (8) pe = = its emission: I B Stotale L , (8) pe = = I Stotale 3.4. Optimization of the Coil 3.4. Optimization of the Coil The relationship between the geometrical, electrical and physical characteristics developed previously allows us tobetween study the of each parameter thus to determine thedeveloped optimum The relationship theinfluence geometrical, electrical andand physical characteristics dimensionsallows of the us coiltoappropriate for a desired application. Table provides the characteristics of previously study the influence of each parameter and 1thus to determine the optimum the selected coil to non-destructively evaluate a CFRP. According to 1the theoretical (Figure 3), dimensions of the coil appropriate for a desired application. Table provides the model characteristics of Figure 4 shows frequency response of a triangular using data given in Tablemodel 1. It can be seen the selected coilthe to non-destructively evaluate a CFRP. coil According to the theoretical (Figure 3), that the4coil can the be used as EMresponse field sensor 800 kHz shows a strong inductive Figure shows frequency of aabove triangular coilwhere usingitdata given in Table 1. It canbehavior be seen with a phase greater than much higher than 100 MHz.inductive behavior that the coil can be used as60°. EMThe fieldcut-off sensorfrequency above 800iskHz where it shows a strong ◦ with a phase greater than 60 . The cut-off frequency is much higher than 100 MHz.
Table 1. Numerical values of the coil characteristics calculated at 1 MHz. Table 1. Numerical values of the coil characteristics calculated at 1 MHz.
Parameter Numerical Value external length D 1 Value Parameter Numerical Coil line width lp 6 external length D 1 dimensions inter-line space E p 3 line width lp 6 Coil dimensions number of turns n 333 inter-line space Ep number of R turns n 33 resistance 4.24 inductance LR 1.44 resistance 4.24 inductance 1.44 Electrical capacity C L 3.5 capacity C 3.5 parameters sensitivity S 35 Electrical parameters sensitivity S 35 noise voltage vb v 0.83 noise voltage 0.83 b emissive ability Pe Pe 254 emissive ability 254
Unit [mm] Unit [µm] [mm] [µm] [µm] [µm]
[ohm] [µH] [ohm] [µH] [fF] [fF] [V/T] [V/T] [µV] [µV] [mT/A] [mT/A]
Figure 4. 4. Frequency Frequency response response of of the the sensor. sensor. Figure
4. Modeling After the construction of the geometry and the mesh generation using the open-source software GMSH, the problem data are sent to our 3D finite element solver in which was implemented the magneto-dynamics formulation AV-A (Equation (9)); mathematical model chosen to describe the EM
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behaviour of our problem. The calculations are carried out in the harmonic regime. A penalty term is introduced to ensure the uniqueness the solution magneto-dynamics formulation AV-Aof (Equation (9));[7]: mathematical model chosen to describe the EM behaviour of our problem. The are carried out inthe harmonic regime. A penalty term is calculations 1 1 ∇× ∇× − ∇ ∇ ⋅ + + ∇ = A A σ j ω A V J introduced to ensure the uniqueness of the solution s [7]: , μ μ (9) → → → → → → → → → ∇ ⋅ jωσ A + ∇V = 0 ∇ × µ1 ∇ × A − ∇ µ1 ∇ · A + σ jω A + ∇V = J s , (9) → → → respectively magnetic vector where A and V are A+ ∇V = 0 potential and electric scalar potential, μ is the ∇ · jω σ the magnetic permeability and is the electrical conductivity tensor given according to the ply → orientation by [2]: where A and V are respectively the magnetic vector potential and electric scalar potential, µ is the σ / / −tensor σ⊥ electrical 2 2 magnetic permeability and σ is the conductivity according to the ply orientation sin(2θgiven ) 0 σ // cos (θ ) + σ ⊥ sin (θ ) 2 , by [2]: σ // −σ ⊥ σ / / cos 2σ(// θ )−+σσ⊥⊥ sin 2 (θ ) 0 sin(2θ ) = 2 (10) σ// σcos sin(2θ ) 0 (θ ) +2σ⊥ sin2 (θ ) 2 −σ⊥ σ// σ= (10) sin(02θ ) σ// cos2 (0θ ) + σ⊥ sinσ2zz(θ ) 0 , 2 0 0 σzz
(
(
(
)
))
where σσ// // is direction, σσ⊥ in the the transverse transverse ⊥ is where isthe theelectrical electrical conductivity conductivity in in the the fibers fibers direction, is the the conductivity conductivity in direction of the fibers and σ zz is the conductivity in the direction of the plies stacking. direction of the fibers and σzz is the conductivity in the direction of the plies stacking. 5. Results 5. The EC-NDT EC-NDT concept concept is is based based on on the the distribution distribution and and circulation circulation of of the the induced induced currents currents in in the the The component being being inspected. inspected. This distribution is strongly linked to the profile of of the the excitation excitation EM EM component field. With Withthis thisin inmind, mind,numerical numericalexperiments experimentswere werecarried carried out discern ability sensor field. out toto discern thethe ability of of ourour sensor to to emulate field configurations obtained by conventional sensors such a rectangular emulate thethe EMEM field configurations obtained by conventional sensors such as aasrectangular coil.coil. 5.1. 5.1. Sensor Sensor and and EM EM Field Field Figure Figure 55 shows shows that that the the electromagnetic electromagnetic field field generated generated by by aa set set of of triangular triangular elements elements excited excited simultaneously simultaneously is is similar similar to to the the EM EM field field created created by by aa conventional conventional rectangular rectangular coil. coil. The The electric electric field field calculated at the front surface of the load illustrated in Figure 6 confirms this equivalence of the global calculated at the front surface of the load illustrated in Figure confirms this equivalence of the global EM EM behaviour behaviour for for the the two two systems. systems. Nevertheless, Nevertheless, we we note some some electric electric field field irregularities irregularities in in the the case case of inin thethe geometry of of thethe inductor andand to of the the multi-element multi-elementsensor, sensor,which whichisisdue duetotothe thediscontinuities discontinuities geometry inductor the current singularities in the bends of triangles. to the current singularities in the bends of triangles.
Figure 5. Magnetic vector potential calculated for a system of: (a) rectangular coil; (b) proposed multiFigure 5. Magnetic vector potential calculated for a system of: (a) rectangular coil; (b) proposed element sensor. multi-element sensor.
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Figure 6. Electric field magnitude at the front surface of the load (z = 0): (a) rectangular coil; (b) multiFigure 6. Electric field magnitude at the front surface of the load (z = 0): (a) rectangular coil; element Figure 6.sensor. Electric field magnitude at the front surface of the load (z = 0): (a) rectangular coil; (b) multi(b) multi-element sensor. element sensor.
The interaction between the excited elements and those “at rest” was studied too with the aim The between the elements and those was studied tootoo with thethe aim of of evaluating the coupling effect. The obtained results inrest” Figure 7 show that thewith non-excited The interaction interaction between theexcited excited elements anddisplayed those“at “atrest” was studied aim evaluating the coupling effect. The obtained results displayed in Figure 7 show that the non-excited adjacent elements are without a The slightest action on the configuration of the fieldthat or on amplitude of evaluating the coupling effect. obtained results displayed in Figure 7 show theitsnon-excited adjacent elements are without a slightest action on the configuration of the field or on its amplitude at at the operating of 1aMHz. adjacent elementsfrequency are without slightest action on the configuration of the field or on its amplitude the operating frequency of 1 MHz. at the operating frequency of 1 MHz.
Figure 7. Electric field magnitude at the front surface of the load (z = 0): (I) without regard to non-excited elements (σ magnitude = 0); (II) non-excited elements areload physically (σ = 30, ×regard 106 S/m). Figure 7. Electric Electric field at front the front surface of the (zwithout = 0): (I)regard without to Figure 7. field magnitude at the surface of the (z =load 0): represented (I) to 6non-excited 6 S/m). 6 non-excited elements (σ = 0); (II) non-excited elements are physically represented (σ = 30, 6 × 10 elements (σ = 0); (II) non-excited elements are physically represented (σ = 30, 6 × 10 S/m).
In addition to the foregoing, the proposed sensor allows a high flexibility in terms of modes of excitation and measurement. The the figure below sensor illustrates different configurations In addition to the foregoing, proposed allows a highfield flexibility in terms obtained of modes for of In addition to the foregoing, the proposed sensor allows a high flexibility in terms of modes of different excitations. It can beThe seenfigure in Figure 8 that the sensor can substitute rectangular obtained coil oriented excitation and measurement. below illustrates different field configurations for excitation and measurement. The figure below illustrates different field configurations obtained for at 0°, 45°,excitations. 90° and −45° without recurring to mechanical rotation. property will be exploited and different It can be seen in Figure 8 that the sensor can This substitute rectangular coil oriented different excitations. It can be seen in Figure 8 that the sensor can substitute rectangular coil oriented applied a laminate CFRP. recurring to mechanical rotation. This property will be exploited and at 0°, 45°,to90° and −45°of without at 0◦ , 45◦ , 90◦ and −45◦ without recurring to mechanical rotation. This property will be exploited and applied to a laminate of CFRP. applied to a laminate of CFRP.
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Figure 8. Field configurations generated by by thethe multi-element sensor equivalent to atorectangular coilcoil Figure 8. Field configurations generated multi-element sensor equivalent a rectangular ◦ , 4590° ◦ , 90 ◦ and oriented at 0°, and −45°. oriented at 045°, −45◦ .
5.2.5.2. Application to CFRP Application to CFRP The modeled system is is a stack ofoffour physical and The modeled system a stack fourplies pliesoriented orientedatat[0°, [0◦45°, , 45◦90°, , 90◦−45°]. , −45◦The ]. The physical and geometrical characteristics are given by Table 2. Figure 9 illustrates the distribution of eddy currents geometrical characteristics are given by Table 2. Figure 9 illustrates the distribution of eddy currents produced byby a rectangular inductor oriented at at 0° 0and its its equivalent generated byby thethe multi-element ◦ and produced a rectangular inductor oriented equivalent generated multi-element sensor. It is noted that the distributions of eddy currents generated by the two systems, ply of sensor. It is noted that the distributions of eddy currents generated by the two systems, in in each each ply of the the laminate, laminate,isistypically typicallyidentical. identical.This This leads to expect, consequently, an analogue dissipated leads to expect, consequently, an analogue dissipated power, power, hence an identical response in terms of impedance. hence an identical response in terms of impedance. Table 2. Numerical values of of the the system system characteristics characteristics Table 2. Numerical values
Laminate Laminate
Sensor Sensor
Parameter Parameter Number of plies Fibers orientation Number of plies Fibers orientation Conductivity (σ//, σ⊥, σzz) Conductivity (σ// , σ⊥ , σzz ) Ply thickness Ply thickness Number of coils
Numerical Values Numerical 4 Values 0°, 45°, 90° 4and −45° ◦ and 4,◦2, 90 2, 10)−45◦ 0◦(10 , 45 × 10 4 (10 , 125 2 × 102 , 10) 125 36
Unit [°] [S/m] [◦ ] [µm] [S/m] [µm]
Gap inter-coils Number of coils GapLift-off inter-coils Lift-off Current intensity Current intensity Frequency Frequency
0.08 36 0.08 0.125 0.125 20 120 1
[mm] [mm] [mm] [mA] [mm] [MHz][mA] [MHz]
Unit
Furthermore, the results presented in Figure 10 prove that the proposed sensor can detect the orientation of the pliesthe and their order of stacking. The between the amplitudes peaksthe Furthermore, results presented in Figure 10comparison prove that the proposed sensor canof detect shows that they are plies decreasing according the stacking of the between plies. However, our values do orientation of the and their order oftostacking. The order comparison the amplitudes of peaks notshows coincide calculatedaccording by [3] duetotothe thestacking mismatch of the two systems (number turnsdo thatwith theythose are decreasing order of the plies. However, ourof values and dimensions of coils). note also there is no large difference between the peaks at and not coincide with those We calculated by that [3] due to the mismatch of the two systems (number of45° turns and 90°; this can beof explained the also change sizesis(length to difference width ratio) of the equivalent rectangular dimensions coils). Webynote thatofthere no large between the peaks at 45◦ and 90◦ ; coilthis generated at 45° andby 90° (see Figure can be explained the change of8). sizes (length to width ratio) of the equivalent rectangular coil ◦ ◦ generated at 45 and 90 (see Figure 8).
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Figure 9. Eddy current distribution in different plies of laminate (0°,◦45°,◦90°,◦−45°); ◦at the right caused Figure 9. Eddy current distribution different plies laminate(0°, (0 45°, , 45 90°, , 90 −45°); , −45 at); the at the right caused Figure 9. Eddy current distribution in in different plies ofof laminate right caused by the multi-element sensor and at left by a rectangular coil (3.2 mm × 1 mm). by the multi-element sensor and at left by a rectangular coil (3.2 mm × 1 mm). by the multi-element sensor and at left by a rectangular coil (3.2 mm × 1 mm).
Figure 10. The normalized resistance of the coil as function of its rotation angle above a laminate of Figure 10. The normalized resistance of the coil as function of its rotation angle above a laminate of Figure four plies10. [0°,The 45°,normalized 90°, −45°]. resistance of the coil as function of its rotation angle above a laminate of four plies [0°, 45°, 90°, −45°]. four plies [0◦ , 45◦ , 90◦ , −45◦ ].
6. Conclusions 6. Conclusions A new design of an eddy current multi-element sensor is proposed. The EM field computation A new design of an eddy current multi-element sensor is proposed. The EM field computation results reveal that this sensor is able to control the EM field shape and generate the plurality of results reveal that this sensor is able to control the EM field shape and generate the plurality of
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6. Conclusions A new design of an eddy current multi-element sensor is proposed. The EM field computation results reveal that this sensor is able to control the EM field shape and generate the plurality of configurations often needed in EC–NDT of carbon fiber-reinforced polymers. The application of the proposed sensor on a sample of CFRP shows its capability to detect the plies’ orientations and their stacking order by acting only on the excitation currents. This sensor can thus be an alternative to the mechanical rotating sensors and the rectangular sensors. Acknowledgments: This research was partwise funded by the European Union Regional Development Fund (EFRE) and the Free State of Saxony (grant “3D-Fast”, No. 100224749). The authors would like to thank the mentioned institutions for providing the funding. Author Contributions: M.N. and B.H. modeled the sensor, wrote the manuscript, contributed to discussion, and reviewed; M.F. and I.-K.L. presented the research subject, provided guidance in modeling, contributed to discussion, and reviewed; H.H. and M.S. conceived and designed the experiments. Conflicts of Interest: The authors declare no conflict of interest.
Appendix A Appendix A.1. Calculation of the Developed Length of the Coil The coil is composed of n triangular turns (see Figure 1) numbered from the outside to the inside. These triangular turns are isosceles whose angles at the base worth 45◦ . The lengths of the three edges of the k-th turn are: 1 d1 ( k ) ≈ d2 ( k ) = D − ( k − 1) l p + E p 1 + π , (A1) tg 8 √ lp + Ep d3 ( k ) ≈ D 2 − 2( k − 1) , (A2) tg π8 where d1 and d2 are the identical edges, d3 is the hypotenuse. Therefore, the developed length of a turn number k is: l k ≈ d1 ( k ) + d2 ( k ) + d3 ( k ),
(A3)
Thus, the total developed length of the entire coil is simply the sum of lk : n
ltotale ≈
∑ lk ,
(A4)
k =1
√ l p + Ep 1 + D 2 − 2( k − 1) , ≈ ∑ 2 D − ( k − 1) l p + E p 1 + π tg 8 tg π8 k =1 n
ltotale
(A5)
Or more simply: ltotale ≈ n
2+
√ 2 D − ( n − 1) l p + E p 1 +
2 tan(π/8)
,
(A6)
Appendix A.2. Calculation of the Total Area The surface enclosed by the turn number k is: Sk ≈
2 1 1 D − ( k − 1) l p + E p 1 + , 2 tan(π/8)
(A7)
Sensors 2017, 17, 1996
10 of 10
Then, the total effective surface of the coil is: Stotale
2 1 n 1 , ≈ ∑ D − ( k − 1) l p + E p 1 + 2 k =1 tan(π/8)
(A8)
References 1.
2. 3.
4.
5.
6.
7.
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