7th Asia-Pacific Workshop on Structural Health Monitoring

November 12-15, 2018 Hong Kong SAR, P.R. China

Capacitance Mapping of Composites

Gokul Raj R 1*, C. V. Krishnamurthy 1

1 Department of Physics, Measurement and Modelling Lab, Indian Institute of Technology, Chennai-

600036, India

Email: gokulrajnambiar@gmail.com; cvkm@iitm.ac.in

ABSTRACT

Non-contact capacitance mapping is proposed as a complimentary technique for structural health

monitoring of dielectric media in general and composites in particular. An XY scanner has been

fabricated with parallel electrode as probes with a provision for maintaining a constant air gap, both at

the top and bottom surface of flat samples to enable spatial mapping of capacitance. The probes

connected to an impedance analyser provides the real and imaginary parts of capacitance/ impedance

respectively over a frequency range of 100 Hz to 1 MHz . Spatial maps of the complex capacitance are

obtained for 50 mm x 200 mm Glass fibre reinforced composite and 30 mm x 100 mm Plexiglas with

and without defects. A discussion on the role of electrode dimensions, probe lift-off and scan step

would be presented. Results on the contrast between defect-free and defective regions and the effect of

sample thickness variations on the measured capacitance would be described. Finally, a scheme

involving model-assisted extraction of dielectric constant from measured capacitance will be presented.

KEYWORDS: Parallel Electrode Capacitor, Dielectric Constant, Capacitance Mapping.

1. Introduction

Non-contact capacitance mapping is proposed as a complimentary technique for structural health

monitoring of dielectric media in general. The challenge is to identify the local capacitance/ dielectric

changes which arises from the inhomogeneities in the samples.Recently, some studies have been

reported with non-contact measurement of dielectric samples[1-3].Capacitance mapping has been

reported with co-planar electrode configuration. However, non-contact capacitance mapping with

electrodes on either side of an extended planar dielectric medium has received very little attention.

Such non-contact mapping would be valuable for planar dielectric media in general and composites in

particular where access is available on both sides. We present preliminary results on capacitance

mapping over a range of frequencies of extended defect-free dielectric media and media with

engineered defects. Simulations, carried out to assist in the interpretation of the measured results, are

also described.

2. Experiments

2.1 Description of the experimental set-up

The experimental set up as shown in figure 1 consists of parallel square electrode capacitor having

dimensions 10mm×10mm and electrode thickness 2mm. The electrode/probe has been attached to the

arms of the scanner which can be moved along X, Y and Z directions with the aid of stepper motor.

The stepper motor has been controlled using a lab-view program.The sample holder holds the sample,

* Corresponding author.

Creative Commons CC-BY-NC licence https://creativecommons.org/licenses/by/4.0/

Mor

e in

fo a

bout

this

art

icle

: ht

tp://

ww

w.n

dt.n

et/?

id=

2408

1

over which the probe moves. The scan step has to be fixed depending on the nature of the defect. The

probe moves to a particular location and then waits till the impedance analyser completes a frequency

sweep at that location. Solartron SI 1260 impedance analyser has been employed to measure the

impedance/capacitance response for a wide range of frequencies, 100Hz-1MHz. A potential difference

of 1V has been maintained across the parallel square electrodes. The Solartron impedance analyser

provides an averaging option as “integration over cycles” to minimize the noise. The value of integration over cycles has been chosen to be 1000 cycles for the entire set of samples in the current

investigation.

The schematic of the experimental set-up is shown in figure 2.

Impedance Analyzer Scanner with stepper motors

Figure 2. Schematic representation of the experimental set up.

Figure 1.The experimental set up: (a) XY Scanner with stepper motors and square electrode

attached to its arm (b) The parallel square electrode capacitor with fixed air gap between top and

bottom electrodes (probe-holder) (c)Solartron SI1260 impedance analyser to measure

impedance/capacitance.

(a) (b)

(c)

(a)

2.2 Capacitance Scan over different dielectric media

2.2.1 Scan under ambient conditions

Scans are carried out with the square shaped electrodes of dimensions 20mm×20mm and

separated by 5.4mm. The scan step has been chosen to be 10mm. The 2D scan was carried out

under ambient conditions with temperature at 25 deg C and relative humidity of 50%. The

mean value of the capacitance is found to be 0.94 pF and the fluctuations are found to be

within 0.01pF. The results for the capacitance at 1 MHz are shown in figure 3.

2.2.2Perspex sheet with engineered defects

A Perspex sheet of 2.76mm thickness, with and without defects has been used to demonstrate the

capacitance mapping / imaging. The samples under investigation have been shown in figure 4 and the

scan has been performed over a particular column. The defects have been created as circular pits with

diameters and depths as follows:

Table 1. Circular defect parameters in Perspex sheet

Top to

bottom as

in Fig. 4

(S.No)

Diameter of the

defect(mm)

Depth of

defect(mm)

1. 10 mm 2 mm

2. 8 mm 2 mm

3. 5 mm 1.5 mm

4. 6 mm 1 mm

5. 6 mm 1 mm

Figure 3. Capacitance scan (1MHz) over a total area 40mm×100mm with parallel square electrode

capacitor with air dielectric kept at an electrode separation 5. 4mm.The dimension of square electrode has

been chosen to be 20mm×20mm, with a scan step 10mm.The histogram indicates that the distribution is

not symmetric but is skewed towards slightly lower values.

The parallel square electrodes of dimension 10mm×10mm have been placed over the sample with a

fixed air gap of 0.2mm. The electrodes were initially placed outside the sample (air dielectric) and

then allowed to move over the sample with scan steps of 2mm and finally it moves out to a region

where there is no sample. The 1-D scan (line scan) has been performed over both the defective as well

as non-defective Perspex samples, keeping all other parameters as fixed. Table 1 describes the defect

parameters over which the scan has been performed.

Figure 5 describes the capacitance response of Perspex sample with and without defects at two

different frequencies,1 kHz and 100 Hz. The impedance/capacitance response of the sample seems to

be different at different frequencies. The response at 1kHz stands better when compared to the

response at 100Hz, which looks noisier. The fluctuations at 1kHz response has been found to be

0.05pF at 1kHz and the fluctuations remains almost same at higher frequencies,making the response at

1kHz, a representative for capacitance mapping.Figure 6 presents the 2D scan of

impedance/capacitance over the defects at 1 kHz.

Figure 4.Perspex sample with (a) and without (b) engineered defects.

(a) (b)

Figure 5.Line Scan (1-D scan) over defective and non-defective sample at 1kHz and 100Hz.

The initial and final drop in capacitance as shown in figure 5 and figure 6 is caused by the edges of the

sample. As the parallel square electrodes approach the Perspex sample, the capacitance increases and

as the electrodes recede from the sample the capacitance drops. The local variations in dielectric

constant appear as dips in the capacitance map corresponding to the defects in Perspex.

2.2.3Glass epoxy composites

The Glass epoxy composites have been fabricated with Teflon defects inserted in between the layers.

The thickness of the sample was 5.1mm. A constant air gap of 0.2mm has been maintained as probe

lift-off (space between the upper electrode and upper face of the sample and lower electrode and lower

face of the sample). To begin with, the samples were scanned with 10mm×10mm and 20mm×20mm

parallel square electrodes over a range of frequencies.The scan step has been chosen to be half the

electrode dimension. Figure7 describes the spatial variation of capacitance for both 20mm×20mm and

10mm×10mm probes.

Figure 6. 2D scan of impedance/capacitance over the defects at 1kHz.

(a) (b)

Figure 7.Spatial variation of capacitance at 1MHz for (a) 20mm×20mm parallel square electrode with

10 mm scan step (b)10mm×10mm parallel square electrode with 5mm scan step.

The variation over the sample is from 0.69pF to 0.89pF, the difference amounts to be 0.2pF which can

be explained by the thickness variation in the sample.The above scan results do not indicate explicitly

detect the presence of defect. Scans in 1D were carried out at other frequencies with a finer scan step

of 0.2 mm. Figure 8 shows the 1D profile scanned at 10 kHz with 20mm×20mm electrode with

0.2mm scan step.Asmall defect-induced contrast can be seen.

3. Simulations

Capacitance mapping involves scanning an extended dielectric medium with finite-sized electrodes. At

any location, the dielectric medium would extend beyond the lateral extent of the electrodes. The

capacitance of this configuration cannot be related to the well-known expressionԑ𝟎ԑ𝒓𝑨𝒅 . Furthermore,

since capacitance mapping involves a small but finite air-gap between the sample and the electrodes,

the measured capacitance is related to the dielectric constant of the medium in an unknown way. There

are no expressions available in the literature that can be applied to the present configuration. To

address this issue, FEM simulations have been carried out with COMSOL Multiphysics 5.2a 4for

extended dielectric media of thickness 2.76mm with a fixed air gap of 0.2mm at the top and bottom of

the medium for a range of dielectric constants. The results are shown in figure 9.

ԑ𝑟

Figure 9. Numerical values of capacitance for various dielectric constants for a fixed air gap(0.2mm)

at the top and bottom interface.

Figure 8.1D scan of capacitance over the Teflon defect of diameter 20mm using

20mm×20mm parallel square electrode with probe lift-off 0.2mm at 10kHz.

For a given dielectric constant, the capacitance value increases with increase in the dielectric extension

and the value saturates beyond a certain extension. The capacitance values plotted in figure 9 are the

saturated capacitance values. The saturation extension of dielectric has been found to be 35mm from

the electrode edge through simulations. The measured capacitance averaged over the defect-free

region of the Perspex material is taken to be 1.08pF from figure 5. This capacitance value is used with

figure 9 to read off the true dielectric constant (ԑ𝑟 = 2.8) associated with the extended medium.

Perspex sample of thickness 2.76 mm and side dimension 100 mm has been chosen to study

(experimental/simulation) the capacitance variation over the defective and non-defective portions on

the same Perspex sample. Figure 10 represents the schematic of the defects under study. The arrows

represent the centre of the defect and the markings 10mm, 30mm, 50mm, 70mm and 88mm represents

the location of the defect from the origin(O) of the Perspex sample. The diameters of the engineered

defects have been 10mm, 8mm, 5mm, 6mm, and 6mm respectively, as shown in figure 10.

Experimental 1D capacitance scans have been carried out with 10 mm x 10 mm electrodes on

defective and non-defective regions of the Perspex sample described in figure 10. Capacitance

responses have been obtained for a range of frequencies (100 Hz to 1 MHz). Figure 11 shows the

response at 1.124 kHz. The data at other frequencies shows a similar trend. The capacitance scan

response for non-defective Perspex sample shows a variation of 0.07pF across the length of the

scanned sample. This variation can be attributed to the thickness variation in the Perspex sample

which amounts to be roughly 0.1mm. Also, the signatures of the defects have been captured

successfully in the capacitance scan, with dips representing the defects.

100 mm

10mm 8 mm 5 mm 6 mm 6 mm

10mm 30mm 50mm 70mm 88mm

Figure 10. Schematic of the sample where the pit dimensions and locations are specified.

O

Figure11. 1D experimental scan of capacitance over Perspex with and without defects at 1.124

kHz.

0.07 pF

Figure. 12.1-D experimental capacitance scan over the Perspex sample

with engineered defects and its comparison with the FEM simulations

The geometry of the sample with the defects has been explicitly modelled in FEM. The regions where

Perspex is absent are assumed to be occupied by free space and a value of 1 is used to represent the

relative permittivity of free space. A dielectric constant value 2.8 was used in FEM calculations to

represent the Perspex slab such that it agrees with the experimental capacitance determined in the

defect free region of the sample away from all edges. FEM simulations have been performed over the

defective portion on the Perspex sample and the results have been compared with experiments, as

shown in figure 12.

Figure 12 shows that FEM simulations capture quite well the overall trends observed experimentally -

namely, the rapid increase in the capacitance as the electrodes moves over the sample domain, the

oscillations in the capacitance as the electrodes pass over the various defects and the rapid fall of the

capacitance as the electrodes move out of the sample domain. The spatial scan profiles obtained

through FEM closely follow the observed scan profile.

The capacitance is based on the volume of the region sampled by the electrodes. When the volume

occupied by the defect is less than the sampled volume (electrode volume), the capacitance will be

nearly independent of the actual location of the defect volume with respect to the electrodes.

Capacitance would change appreciably however, when defect volume goes out of the sampled

volume.

The defect volumes decrease as the scan progresses from the left towards the right. The maximum

change in capacitance is for the first defect and reduces for the second defect due to reduced defect

volume as the latter has a lesser diameter than the former, even though their depths are the same.

For the third and fourth defects, the defect volumes are nearly equal and lead to nearly the same

changes in capacitance. Since the edges of each of these defects are quite close, the edges are not

clearly resolved leading to a response that is more flattened at the lower portion of the dip.

For the last defect, as the farthest edge of the defect is quite close to the sample edge, they are not well

resolved in the capacitance map.

For the larger defects (first defect), since the edges are separated, the change in capacitance as a

function of scan step resembles the step response for an edge. However, the step responses for the left

and right edges of the defect overlap, due to the electrode dimension, leading to a triangular feature in

the capacitance scan.

However, the role of the ambient air prevalent during experiments and not accounted for in FEM

simulations appears to be a possible source of the discrepancy between experiment and simulation.

Further studies are underway to address this discrepancy.

3. Conclusions

Non-contact capacitance mapping over extended dielectric media (Perspex and Glass fiber reinforced

epoxy composites) has been demonstrated with square-shaped electrodes in sandwich configuration.

The capacitance mapping is carried out over a wide range of frequencies at each scan location thus

generating a large amount of data that contains information on the degree of homogeneity in the

complex permittivity of the medium as well as on the spatial extent of local inhomgeneities in the

complex permittivity. The data in the form of 2D images can be used to quantify the medium as well

as the ‘defects’.

The detectable capacitance change sets the limits on the contrast in the dielectric constant. The

electrode dimension and the scan step determine the spatial resolution with which inhomogeneities can

be mapped. Numerical simulations have been carried out to assist in the assessment of the observed

trends in the capacitance maps. It is believed that further simulations would help establish a one-to-one

correspondence between the two making it a quantitative tool.

Capacitance mapping is proposed as an alternate non-destructive assessment technique for extended

non-metallic media such as glass and carbon composites particularly for electromagnetic applications

where inhomogeneities in the electrical permittivity play a crucial role. The proposed technique could

compliment other NDE techniques to provide a comprehensive assessment of a structure.

Acknowledgement

This work is an extension of a project (ASL/31/15/4051/CARS/054 dt. 29 July 2015) funded by

Advanced Systems Laboratory (ASL), Hyderabad, India during 2015-2017. We thank the Director,

ASL and the Director, DoNDE, ASL for the financial assistance. We also would like to thank Dr.

K.Srinivas (Sc ‘F’) at DoNDE, ASL for all the technical discussions.

References

[1] X. Xu, T. Bengtsson, J. Blennow, and S. M. Gubanski, “Enhanced accuracy in dielectric response material characterization by air reference method,” IEEE Trans. Dielectr. Electr. Insul.,

vol. 20, pp. 913–921, 2013.

[2] X. Xu, “Enhancements in Dielectric Response Characterization of Insulation Materials,” Licentiate thesis, Materials and Manufacturing Technology, High voltage engineering, Chalmers

University of Technology, Gothenburg, Sweden, 2013.

[3] Patrick P. Chavez, “Accurate Complex Permittivity Measurement with Two-Electrode Contact-

Free Apparatus,” IEEE Trans. Dielectr. Electr. Insul., vol. 25, pp. 1470-1478,2018.

[4] COMSOL Multiphysics® v. 5.2a. www.comsol.com. COMSOL AB, (Stockholm, Sweden).

[5] Gokul Raj R and C.V. Krishnamurthy, “Static dielectric constant assessment from capacitance over a wide range of electrode separations,” J. Electrostatics, vol.87, pp.19–25,2017.