E L S E V I E R Sensors and Actuators B 30 t 1996) 159-164 B

Analysis of dielectric sensors for the cure monitoring of resin matrix composite materials

Jin Soo Kim, Dai Gil Lee Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Kusung-dong, Yusung-ku, Taejon-shi, South Korea 305-701

Received 1 September 1994; in revised form 21 August 1995; accepted 31 August 1995

Abstract

In this study, the sensitivity of dielectric sensors for the on-line cure monitoring of resin matrix composite materials has been analysed by the FEM (finite-element method) and compared to the experimental results. Using the results of the analysis, the equation for the capacitance of the sensor as well as the effective range for which the electric field affects the medium are obtained. Also, a more sensitive sensor design than the usual planar interdigital capacitor is suggested using three-dimensional ICE analysis and experiment on the sensor types. It is found that the fabricated sensor and the electric circuit for on-line cure monitoring can be used for the smart manufacturing of resin matrix composite materials.

Keywords: Cure monitoring; Dielectric sensors; Resin matrix composites

1. Introduction

On-line cure monitoring during the curing process of ther- mosetting resin matrix composite materials is important for the improvement of quality and productivity. Among several cure-monitoring methods [ 1 ], dielectrometry is known to be a promising technique for monitoring the cure during a pro- duction moulding operation [2-4] , since it can monitor con- tinuously the change of resin cure state during the whole process where the resin changes from a monomeric liquid to a cross-linked, insoluble, high-temperature solid.

The instrumentation for dielectrometry includes two elec- trodes, which are embedded in the composite material and are connected to an alternating electric field. Since the resin in the composite material is a dielectric material, the electrode array and the composite material form a capacitor. The charge accumulated in the capacitor depends on the ability of the dipoles and ions present in the resin molecules to follow an applied alternating electric field at different stages of curing [5].

During the cure process of composite materials, however, a parallel-plate type sensor is sometimes inappropriate for obtaining the overall cure state if the shape of the composite material is either complicated or thick. However, if a small planar interdigital capacitor (IDC), which has an array of two electrodes with opposite polarity on the same plane, is fabricated and inserted into the composite material, it is not

0925-4005/96/$15.00 © 1996 Elsevier Science S.A. All rights reserved SSD10925 -4005 ( 95 ) 01793 -5

affected by the shape of material and the overall cure state throughout the material can be obtained using several sensors.

Since two electrodes of the IDC are located on the same plane, the flux line of the electric field forms a curvilinear trajectory. Thus, the capacitance of the IDC has less sensitiv- ity than a parallel-plate capacitor, which forms a linear tra- jectory of the flux line. Therefore, it is necessary to improve the capacitance of the IDC by changing its geometry. An increase of the capacitance also increases the sensitivity of measuring the dielectric constant of a material located between the two electrodes of a capacitor.

Much research has been performed on the dielectric sensor. Endres and Drost [ 6] calculated the capacitance of a unit cell by conformal mapping of the upper and lower semiplanes of the unit cell into two plate capacitors. Also, they suggested that the distance between the electrodes should be very small in order to achieve the highest change in capacitance by the sensitive coating layer. Zaretsky et al. [7] developed a gen- eral continuum model to determine the output of an interdi- gital electrode dielectrometer. With the developed model, they described the method for estimating parameters such as film thickness, film permittivity with known thickness, and film surface conductivity with known thickness. Sheppard [ 8 ] showed that the electric field calculated from the model of Zaretsky is mainly confined within a distance one third of the periodicity of the electrode structure and then he identified the electrode geometries and minimum gel-coating thickness

160 J.S. Kim, D.G. Lee/Sensors and Actuators B 30 (1996) 159-164

needed to obtain an adequate sensitivity to changes of gel- coating conductivity. Sheppard et al. [9] described the fre- quency dependence of the complex electrical impedance by an equivalent circuit incorporating an interfacial impedance. Also, they calculated cell constants of the interdigital elec- trode geometry from the electromagnetic field model of Zar- etsky. Lin et al. [ 10] suggested a way to choose between two-dimensional and three-dimensional IDC structures according to the coating material on the electrodes and found the electric field distributions of uncoated and coated IDCs using the finite-element method (FEM).

In this study, with the results of finite-element analysis, a simple equation that can calculate both the electric field limit up to 99.5% and the capacitance of the unit cells was obtained and used in the design of the sensor. Also, a three-d~" ensional instead of a two-dimensional analysis was performed to cal- culate accurately the sensitivity with respect to the shapes of the sensors. From the three-dimensional FE analysis, a more sensitive sensor design than that of a usual IDC was suggested and the designed sensor was used for on-line cure monitoring.

2. Simulation

Since electrostatic field problems have Poisson-type equa- tions, they are similar to heat-conduction problems [ 11,12]. The heat-conduction equation is expressed as follows:

V. (KVT) = - q (1)

The electrostatic field equation is expressed as follows:

V. (eVV) = - p (2)

where K is the thermal conductivity [W m-1 °(2-1]. T the temperature [ °C ], q the heat generation rate [ W m- 3 ], ~ the dielectric constant [ C m - ~ V- ~ ], Vthe electric potential [V] and p the charge density [C m-3].

Due to the similarity between the heat-conduction Eq. (1) and the electrostatic Eq. (2), the electrostatic problems can be solved by FE analysis using the heat-transfer elements.

In this study, the electrostatic field problems were analysed using ANSYS 5.0 [ 13], a commercial FEM package. The two-dimensional 8-node thermal solid element (PLANE 77) was used for two-dimensional problems, while the three- dimensional 20-node thermal solid element (SOLID 90) was used for three-dimensional problems. Fig. 1 shows the two- and three-dimensional element shapes.

In the FE analysis, the electrostatic energy (W~) is obtained by summing up the energies of the elements. Then the capac- itance (C) is obtained as follows:

1 wo= ~ c ( v , -Vo ) 2 (3)

where We is the electrostatic energy [J], C the capacitance [F] and V1 - Vo the applied voltage difference [V].

Y ? "Y

=X X

(a) (b)

Fig. I. I~M element s~ucmrcs: (a) ~o-dinmnsional S-node thermal solid; (b) three-dimensional 20-node thermal solid.

In a planar interdigital capacitor (IDC), the two electrodes with opposite polarity are located interdigitally on the same plane, as shown in Fig. 2.

Fig. 3 shows the results of the two-dimensional FE analysis of the unit cell of an IDC in which GAP, W and L represent the gap between the electrodes, the width of the electrode and the length of the unit cell, respectively. The values of GAP, W and L used in this analysis were 0.1, 0.1 and 0.2 nun, respectively. Because of the symmetry of the electric field, the analysis was performed only for the lower side of the electrode, that is, the substrate coated with silicon varnish. The dielectric constant of the coating was assumed to be 3.15 E 0, which was the dielectric constant of the silicon varnish used in the experiment. The directions of the arrows represent the directions of the electric field (E) at the points and the magnitudes of the arrows represent the magnitudes of the electric field (E). Fig. 3 shows that the magnitude of the electric field becomes larger as the point approaches the elec- trode. This implies that the range of the electric field is con- fined for a given electrode shape.

Fig. 4 shows the capacitances of unit cells with respect to the coating thickness of the substrate when GAP~W= 1 and the dielectric constant of the coating was 3.15 ~o. The simu- lation is focused to finding the thickness of the coating in which the capacitance of the unit cell reaches the saturated value. When saturation occurs, the existence of the outer phase does not have an effect on the saturated values. Also, in this case, since no electric field penetrated into the outer phase, the FE analysis was carried out with the boundary condition e= 0. As shown in Fig. 4, the rate to reach the saturated value is a function of the.length (L = W+ GAP) of the unit cell. That is, the smaller L is, the faster the capacitance reaches the saturated value. Also, the thickness of coating needed to reach the saturated value decreases as L becomes small.

In order to represent the results of the FE analysis of Fig. 4 in a simple equation, the least-square method was used [ 14]. Since the curve of the capacitance increased exponen- tiaUy, the equation was assumed to be an exponential func- tion. When GAP/Wffi 1, the equation for the capacitances of the unit cells was obtained by the least-square-root (LSR) approximation of the analytical results as follows:

J.S. Kim, D. G. Lee/Sensors and Actuators B 30 (1996) 159-164 161

( ) < Top View >

/ Electrode (Cu)

f W GAP tcu = 35/~m - £ - ~ _--= ~-- _....j r'///////////////////A "-I

~..,,....,.~ tsi = 0.2ram

Substrate (Si-varnish Coating)

< AA' Section >

Fig. 2. Structure of the planar interdigital capacitor ( IDC).

Coating

~¢ = 3.15~. W = O. I m m

GAP = 0.1mm

Electrode

w/2 .,. GAP w/e L

(a)

t r / I / / s ~ _ _ x \ ~

I I / / / / / ~ - -

® / / -~l 'r r ®

Electric Field (E)

(b) Fig. 3. Two-dimensional finite-element analysis of the unit cell of an IDC.

0.015

0.0128

I~ 0.0106 v

0.0084

0.0062

~ 0 2 (ram)

~ - = 0.04 (ram)

rL\ ooo,, , \ . -

"- = 0.1 (ram)

0 : by 2-D lee analysis - : by equation (4)

0.004 I I i I I [ f [ I

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Thickness of the coating ( r am)

Fig. 4. Capacitance of the unit ceils with respect to the thickness of the coating when G A P / W = 1.

C = Coo[ 1 - cl exp( - c2t/L) ] (4)

where Coo is the maximum capacitance in a given unit cell [pF ram-t] , ct, c2 are constants determined in the LSR approximation, t is the thickness of the coating [mm] and L is the length of the unit cell [ = W+ GAP, ram].

Since the capacitance (C) is linearly dependent on the dielectric constant of the medium, Co= can be expressed as k(Co)oo. Therefore, Eq. (4) becomes

C= k(Co)oo[ 1 - cl exp( - c2t/L) ] (5)

where k is the relative dielectric constant (e/Co) and (Co)oo is the maximum capacitance in the vacuum state [ pF mm- t ].

The values of cl, c2 and (Co)® of Eq. (5) were assumed to be third-degree polynomial functions of GAP in order to include all the unit cells with different GAP values. Table 1 shows the coefficients of el, c2 and (Co)®.

If tsa t represents the thickness of the coating in which C reaches the saturated value, i.e., 99.5% of Coo, then t,,t can be calculated from Eq. (4) as follows:

L 0 . 0 0 5 tsar = - - - - In - - (6)

C2 Cl

If C~t represents the capacitance of the unit cell when t is tat, it can be expressed as

C,==0.995k( Co)oo (7)

Table 1 Coefficients ofc~, cz and (Co)®

Coefficient ct c2 (Co)=

GAP 3 114.97 1293.21 - 1.962 × 10- J GAP ~ 28.85 - 164.87 4.640 X 10 -2 GAP ~ - 9.183 - 6.521 - 3.739 X 10- 3 GAP ° 1.631 6.105 4.545 X 10- 3

162 J.S. Kin, D.G. Lee~Sensors and Actuators B 30 (1996) 159-164

O. 035

e~ v

0.03

0 . 0 2 5

0 . 0 2

0 .015

0 . 0 1

0 . 0 0 5

0

with e l e c t r o d e t h i c k n e s s

ffi 0 .01 p F / m m

w i t h o u t e l e c t r o d e t h i c k n e e s

I i , I i i I i i

0 0 . 0 5 0.1 0 .15 0 .2 0 . 2 5 0 .3 0 .35 0 , 4 0 . 4 5 0 . 5

Thickness of the coating (mm)

Fig. 5. Two-dimansional finite-elerncnt analysis results with and without consideration of the electrode thickness.

Type 1

Type 3

<Top View>

All t y p e s are d e s i g n e d with the same .tensing area (3.1X 3 mm z)

Fig. 6. Three different types of sensors.

Table 2 Specification of the IDC

GAP (/zm) I00 W (/~m) 100 Sensing area (ram 2) 3.1 × 3 Electrode material, copper

thickness (p.m), 35 Substrate material, silicon varnish

thickness (p,m), 200 dielectric constant, 3.15 ~ at 1 kHz

When GAP=0.1 mm and k= 3.15, the value of cl, c2 and (Co)** from Table 1 are 1.116, 5.097 and 4 .439×10 -3 pF ram- 1, respectively. Substituting these values into Eqs. (6) and (7) , t~ t -0 .21 mm and C ~ t = l . 4 × 1 0 -2 pF m m - k Since the capacitance of the unit cell by FE analysis was also 1.4 × 10- 2 pF ram- ~ as shown in Fig. 4 when W= GAP ffi O. I ram, it was found that Eqs. ( 5 ) - ( 7 ) can be used instead of FE analysis. Thus, from Eq. (6) for t~,t, the substrate thick- ness of the sensor and the distance between the sensors when several sensors are used in an experiment for on-line cure monitoring can be determined.

Fig. 5 shows the capacitance of the unit cell with respect to the thickness of the coating with and without consideration of the electrode thickness when e=3 .15 eo and W= GAP-- 0.1 ram. From Fig. 5, it was found that the difference

e ~

o • r~

e~

o

2

1.9

1.8

, . 7

1.6

, . 5

1.4

, . 3

1.2

F/P~ 3 - D FE a n a l y s i s

E x p e r i m e n t

/ / / / / /

/ / / / / / / / / / / / / / : / / / / / / / / / / / / / / / /

/ / / / / / / / / / / / / / , 1

Type 1

7"77

/ / / / / / • / / /

/ / / ,

/ / ' ~

Type 2

/ / /

V /

/ / / / / / / / / / / / / / z

Type 3

Fig. 7. Comparison of the capacitances of the sensors of Fig. 6 obtained by three-dimensional finite-element analysis and experiment.

of the capacitances of the two cases had the same value (AC=0 .01 pF ram-') regardless of the thickness of the coating. The same difference implies that the thickness of the electrode can be assumed to be a parallel-plate capacitor across the gap. In the parallel-plate capacitor, the distance (d) corresponds to the gap (0.1 ram) between the electrodes and the area (A) corresponds to the electrode thickness (35 /xm). The capacitance (C) per unit length across the gap was calculated as C=~A/d--O.O1 pF m m - k Therefore, in the case where the thickness of the electrode should be taken into account, Cs,, can be calculated from

A C~'=0"995k( C°)® + k% d (8)

Now, in order to design a more efficient sensor with the same sensing area, other types of sensors besides the usual IDC were designed and analysed by the three-dimensional FEM. Fig. 6 shows three different types of sensors designed with the specification given in Table 2. Type 1 is the usual IDC, type 2 is a rectangular spiral-shaped sensor, and type 3 is a circular sensor. In the three-dimensional FE analysis, the entire sides including the electrode thickness of the sensor were analysed to compare the analytical results with the experimental results. The material for the half-space above and below the electrode was silicon varnish (e = 3.15 ¢o) and the thickness of the material was determined to be 0.2 mm from Eq. (6) .

Fig. 7 shows the capacitances of the sensors calculated by the three-dimensional FE analysis. Since the type 2 sensor had two parallel electrodes with opposite polarity in the sen- sor plane, it had more capacitance than the type 1 sensor, which had an ineffective zone at the branching comers. The type 3 sensor had the smallest capacitance of the three dif- ferent sensors because its centre area had no electrodes. From the three-dimensional FE analysis, it was found that the type 2 sensor was most efficient and sensitive.

J.S. Kira, D.G. Lee~Sensors and Actuators B 30 (1996) 159-164 163

3. Experiments

In this study, the sensors were fabricated by photolitho- graphically etching 35 tim thick copper plate except the elec- trodes after coating silicon varnish on one surface of the copper plate and photoresist on the other surface. Both the gap and width of the electrode were determined to be 100 /xm. Three different types of sensors were designed with the specification in Table 2. Since the thickness of the substrate is 0.2 mm, the electric field for the substrate works only inside the substrate from the result of Eq. (6).

Experiments for capacitance measurement were carded out using an electric circuit. Fig. 8 shows the constructed circuit. A resistance whose magnitude is R was serially connected to a sensor and the alternating voltage V was applied to the circuit. The capacitance of the sensor can be calculated by circuit theory as follows.

C= tan dp/taR (9)

where co is the angular frequency and ~b is the phase difference between the input voltage and the voltage across the sensor. The resistance R and frequency of the sinusoidal wave used in the electric circuit were 2 MI~ and 1 kHz, respectively. The measuring error of the capacitance using the circuit was less than 2%.

The capacitances for the sensors in Fig. 6 were measured by the constructed circuit. The material used for the upper side of the sensor was silicon varnish, which was the same material as in the three-dimensional FE analysis. From Fig. 7, it was found that the experiment gave similar results to the three-dimensional FE analysis. In the experiment, it was found that the type 2 sensor had the largest capacitance. The error between the experimental results and those of the anal- ysis was less than 5%.

Also, this circuit was used for the cure monitoring of com- posite materials. Since the resin in the composite material is a real dieleclric, the composite material was represented by a parallel arrangement of a capacitance (Cm) and a resistance (R=). In the experiment for the cure monitoring, the dissi- pation factor, which represents the ratio of the energy expended in aligning dipoles and moving ions in the resin in accordance with the direction of the alternating electric field

f - . . . . -

Dielectric Sensor

C°mplarat°r

:,.,.::

B u f f e r

AC-~. DC ' , onver te :

( v )r=,

(V*)r=,

(Vm)m,

Fig. 8. Electric circuit for measuring the output of the dielectric sensor.

o

2

1.8

1.6

1.4

1.2

1

0,8

0.6

0 .4

0.2

0

dP

o o

o

Dwelling Zone o O ~ O

o g

° o

,d i i i i i

20 40 60 80 100 120 140

T i m e ( m i n )

180

140

120

I00

8o

so

40

20

0

Fig. 9. Dissipation factor nmasured with the fabricated type 2 sensor and temporatum during the cure process of the composite material.

to the energy stored in aligning dipoles in the resin, was measured and used for finding the cure state of the composite material. The dissipation factor of the composite material is defined by the following equation [ 15] :

O = 1/a~RmCm (10)

where R= is the equivalent resistance of the composite mate- rial and Cm is the equivalent capacitance of the composite material. The resistance Rm and the capacitance Cm are meas- ured by circuit theory.

Fig. 9 shows the dissipation factor measured with the fab- ricated sensor (type 2) and the constructed circuit during the cure process of the composite material. Carbon fibre epoxy prepeg USN 150 (Sun Kyung Industry of Korea), which has the same fibre properties as T300/5208 from Amoco, was used for the testing material. The autoclave vacuum bag degassing moulding process was employed to measure the dissipation factor of the specimen, the size of which was 50 mm X 50 mm with a thickness of 1.5 mm ( 10 ply thickness). The dielectric sensor and a thermocouple were embedded in the centre of the specimen.

At the beginning of the cure cycle, the resin viscosity in the uncured specimen was relatively high, so that the dipole and ion mobilities were restricted. This resulted in a low dissipation factor. As the temperature of the specimen increased, the resin viscosity reduced and the dissipation fac- tor increased owing to the greater dipole and ion mobilities. In the dwelling zone, the dissipation factor and the resin viscosity had constant values because the dipole and ion mobilities were maintained constant. As soon as the cure initiated, the resin viscosity increased rapidly and the dissi- pation factor decreased. At the end of the cure, the dissipation factor reached a constant value. From these experiments, it was found that the changes of the resin viscosity and cure state of the specimen could be on-line monitored. Therefore, it was concluded that the developed sensors and the circuit might be used for the smart manufacturing of composite materials.

164 J.S. gim, D.G. Lee/Sensors and Actuators B 30 (1996) 159-164

4, Conclusions

In this study, the sensitivity of the dielectric sensor for the cure monitoring o f resin matrix composite materials was ana- lysed by the finite-element method. Using the results of the finite-element analysis, a simple equation that can find the electric field limit up to 99.5% as well as the capacitance of the unit cells was obtained when G A P ~ W = 1 by the least- square-root approximation. From the obtained equation, the substrate thickness of the sensor was determined.

Also, from the three-dimensional finite-element analysis and experiment on sensor types designed with the same sens- ing area, a rectangular spiral sensor (type 2 of Fig. 7) proved to be more sensitive than the usual IDC.

The experiment on on-line cure monitoring of the com- posite material showed that the fabricated sensor and the constructed circuit could be used for the smart manufacturing of composite materials.

Acknowledgement

[6] H.E. Endres and S. Drost, Optimization of the geometry of gas- sensitive interdigital capacitors, Sensors and Actuators B, 4 (1991) 95-98.

[7] M.C. Zaretsky, L. Mouayad and J.R. Melcher, Continuum properties from interdigital electrode dielectrometry, IEEE Trans. Electrical lnsul., 23 (1988) 897-917.

[8] N.F. Sheppard, Jr., Design of a condoctimetric microsensor based on reversibly swelling polymer hydrogels, Proc. 6th Int. Conf. Solid-State Sensors and Actuators (Transducers '91), San Francisco, CA, USA, 24-28 June, 1991, pp. 773-776.

[9] N.F. Sheppard, Jr., R.C. Tucker and C. Wu, Electrical conductivity measurements using microfabricated interdigitated electrodes, Anal. Chem., 65 (1993) 1199-1202.

[10] J. Lin, S. Mdiler and E. Obermeier, Two-dimensional and three- dimensional interdigital capacitors as basic elements for chemical sensors, Sensors and Actuators B, 5 (1991) 223-226.

[ 11 ] J.P. Holman, Heat Transfer, McGraw-Hill, New York, 6th odn., 1986, Ch. 2.

[12] D. Halliday and R. Resnick, Fundamentals of Physics, John Wiley, New York, 2nd edn., 1981, Ch. 27.

[13] P. Kohnke (ed.), ANSYS User's Manual for Revision 5.0, Swanson Analysis Systems, Inc., Houston, TX, 1992.

[ 14] M.J. Mar'on, NumericalAnalysis, Macmillan, New York, 1982, Ch. 5. [ 15 ] R.C. Buchanan, Ceramic Materials for Electronics, Marcel Dekker,

New York, 1986, Ch. 1.

The authors would like to thank KOSEF for financial sup- port of this research. Biographies

References

[ 1 ] W.G. McDonough, B.M. Fanconi, F.I. Mopsik and D.L. Hunston, A role of cure monitoring techniques for on-line process control, Proc. 6th Annual ASM/F~D Advanced Composite Conf., Detroit, MI, USA, 8-11 Oct., 1990, pp. 637--644.

[2] D. Hudson, The use of automatic dielectrometry for autoclave moulding of low void composites, Composites, 5 ( 1974 ) 247-252.

[3] M.L. Bromberg, D.R. Day, H.L. Lee and K.A. Russell, New applications for dielectric monitoring and control, Proc. 2nd Conf. Advanced Composites, Dearborn, MI, USA, 18-20 Nov., 1986, pp. 307-31 I.

[4] D.R. Day, Cure control: strategies for use of dielectric sensors, Proc. 31st Int. SAMPE (Society for the Advancement of Materials and Process Engineering) Symp., 7-10 April, 1986, pp. 1095-1103.

[5 ] P.K. Mallick, Fiber Reinforced Composites, Marcel Dekker, New York, 1988, Ch. 5.

Jin Soo Kim was born in 1967. He obtained a B.S. degree in precision mechanical engineering from Han Yang Univer- sity in 1990 and an M.S. degree in precision engineering and mechatronics from Korea Advanced Institute o f Science and Technology (KAIST) in 1992. He is now a Ph.D. candidate at KAIST with a research interest in composite materials.

Dai Gil Lee was born in 1952. He received a B.S. degree in mechanical engineering from Seoul National University in 1975 and an M.S. degree in mechanical engineering from KAIST in 1977. In 1985 he received a Ph.D. degree in mechanical engineering from MIT, USA. He is now an asso- ciate professor in the Department o f Mechanical Engineering, KAIST. His major field of interest is composite materials and machine tools.