Numerical simulation and experimental study of capacitive imaging technique as a non-destructive testing method

It was recently demonstrated that a co-planar capacitive sensor could be applied to 1 the evaluation of materials without the disadvantages associated with the other techniques. This 2 technique effectively detects changes in the dielectric properties of the materials due to, for 3 instance, imperfections or variations in the internal structure, by moving a set of simple electrodes 4 on the surface of the specimen. An AC voltage is applied to one or more electrodes and signals are 5 detected by others. This is a promising inspection method for imaging the interior structure of the 6 numerous materials, without the necessity to be in contact with the surface of the sample. In this 7 paper, Finite Element (FE) modelling was employed to simulate the electric field distribution from 8 a co-planar capacitive sensor and the way it interacts with a non-conducting sample. Physical 9 experiments with a prototype capacitive sensor were also performed on a Plexiglas sample with 10 sub-surface defects, to assess the imaging performance of the sensor. A good qualitative agreement 11 was observed between the numerical simulation and experimental result. 12


Introduction
There are several methods for evaluating the integrity of materials, and an impor- 15 tant category of them is Non-Destructive Evaluation (NDE) or Non-Destructive Testing 16 (NDT) methods. This field includes identifying and characterization the flaw on the 17 surface and under the surface of materials without cutting apart or altering the material 18 [1]. It means NDT refers to the process of evaluating and inspecting materials to iden- 19 tify or detect defects in comparison with some standards without changing the main 20 features or damage to the tested object. NDT techniques supply affordable ways of 21 assessing a specimen individually or may be applied to the whole material for testing in 22 a manufacturing system for quality control purposes [2]. 23 There are some advantages and disadvantages inherent to all NDT methods that 24 made them more or less suitable for a particular application in relation to the coverage 25 area, the penetration depth and the problems associated with the interpretation of 26 the results [3]. For instance, ultrasound testing is a mature technique allowing the 27 identification and characterization of deep defects, but requires contact with the object 28 being inspected and the use of water-based couplants (liquid or gel); radiography testing 29 provides high-resolution images and deep penetration, but requires access to both 30 sides of the object and employs ionizing radiation, which constitutes a risk of radiation 31 exposure; infrared thermography testing allows the inspection of large areas in a fast and 32 contactless manner, but is limited to relatively shallow defects and requires advanced 33 signal/image processing for defect characterization; Eddy current testing (ECT) is very 34 effective for certain types of defects (cracks, corrosion, etc.) under several layers of 35 materials, but is limited to conductive materials and is not well suited for the detection 36 of delaminations in composites; etc. It has recently been shown that an alternative 37 electromagnetic method based on a capacitive sensor can be used as an NDT method [2]. 38 For non-conducting materials, NDT methods are not as well developed as compared 39 to those for metallic materials. One approach to evaluate non-conducting materials is 40 to characterize their dielectric properties. The dielectric strength and the dielectric 41 constant are the dielectric properties of non-conducting or low conductivity materials. 42 The voltage a material can withstand before an electrical breakdown happens is called 43 "dielectric strength" and a measure of the material's capability of storing electric energy 44 is called "dielectric constant" or "permittivity".There exist alternative approaches that 45 are based on the characterization of materials permittivity such as microwave techniques 46 and resonant testing. However, these techniques require expensive equipment and/or 47 complex operating procedures. Capacitive sensing on the contrary is a straightforward 48 and inexpensive approach [2].

49
The co-planar capacitive technique was first introduced in 2006 [4]. This novel 50 approach, usually referred to as Capacitive Imaging (CI), is an electromagnetic NDT 51 method that uses arrays of electrodes to generate an electric field distribution within the 52 specimen. The electric field distribution can penetrate within dielectric materials and 53 changes in response to the structure of the material under test leading to a variation in 54 the output voltage [5,6]. The capacitive technique has shown great potential to inspect a 55 wide range of materials and structures from insulators to conductors [5].

56
CI technique offers a possible way to overcome some of the restrictions imposed 57 by existing NDT methods. For instance, the technique works in a volume averaging 58 manner and therefore the scattering issue with the ultrasonic method is absent [7]. The 59 low cost, fast response, non-intrusive, non-invasive, no ionizing radiation involved and 60 flexibility in the design of the electrodes provide CI with a great potential to be applied 61 in a wide range of applications. Furthermore, the co-planar structure allows one-sided 62 inspection [8], which is especially useful when access to both sides of the specimen is 63 limited [9]. Moreover, this is a non-contact technique [5] and the lift-off (the air gap 64 between the surface of the electrodes and specimen) can be optimized, leading to an 65 applicable method in the detection of corrosion under insulation (CUI), including the 66 detection of large surface features in metals and therefore the presence of even small 67 amounts of rust [10]. This technique is especially useful in defence where composites are 68 extensively used for both equipment and strengthening structures [11]. These features 69 of co-planar capacitive sensor make it an attractive option for applications in NDT [6], 70 material characterization [8], and imaging [12].

71
The principle of this technique involves placing two (or more) electrodes over the 72 surface of the sample and then applying an AC voltage between them. This system 73 acts as a capacitor whose altering in capacitance indicates variations in the internal 74 structure (such as the presence of a defect) [13]. Normally, in a regular capacitor, the 75 plates are parallel. When a voltage is applied between these plates, they produce a 76 uniform electric field distribution. This electric field does not restrict itself to the area 77 between the electrodes when the electrodes are gradually open, but extends to a wider 78 space and forms a fringing field [9]. This fringing field expands into the sample for plane. This kind of sensor is named a co-planar sensor in literature [9]. Figure 1 shows a 84 schematic diagram showing how the electric field distribution changes when the two 85 capacitor electrodes change from a parallel-plate to a co-planar so that the final part 86 produces a fringing field [7]. The sensor electrodes can be scanned over the surface of a into the sample which leads to a decrease in the depth of penetration [9]. The lift-off 94 should therefore be as small as possible to achieve greater signal strength and sensing 95 depth (especially for investigating dielectric material) [14] with no need to use couplant 96 materials.

97
The sensor manufacturing steps include material selection for electrodes, the in-  [15], printed circuit boards (PCB) and manual production can be selected depending on 107 sensor dimensions and costs [9].

108
To evaluate the sensor performance, it is required to explain the general design 109 parameters. Therefore, in this paper, firstly the design factors such as the geometry of the  There are several parameters in sensor design for assessing the performance of a 117 sensor. One design parameter may influence several aspects of sensor performance. On 118 the other hand, more than one design factor should be considered in order to achieve 119 the desired sensor performance. Therefore, knowing how design parameters affect 120 sensor performance leads to sensor optimization for a specific application. Additionally, 121 instrumentation-related issues should be considered in order to achieve the right mea-122 surements of a sensor [9]. The important design parameters for a co-planar capacitive

Electrodes geometry 126
The performance of a co-planar capacitive sensor is primarily determined by its 127 geometry, which includes the size, shape, and separation distance between the electrodes 128 [16]. They are the most important parameters which affect the electric field strength 129 and the penetration depth of the probe [17]. A bigger electrode size provides a deeper 130 penetration depth; however, it reduces the image resolution in imaging applications since 131 it samples a bigger area of the specimen. The shape of electrodes can be a simple form 132 such as square, rectangular, triangular shape, or complex shape, like a comb or spiral 133 shape. Free space width between adjacent electrodes refers to the separation distance 134 between the electrodes and has a significant impact on the measured output. Therefore,  the available space in the system to place the electrodes must be considered [9,16]. Generally, a shielding plate and a guard electrode are employed to shape the electric 149 field, and more importantly to eliminate stray capacitance and noise [17]. Indeed, a 150 shielding plate, which is placed on top of the main electrodes, is needed to attenuate 151 the undesirable electric field, to eliminate parasitic capacitance and noise in the sensing 152 electrodes; and a guard electrode, which surrounds the main electrodes and between 153 them, will be used to prevent the electric field lines to go directly to the sensing electrode.

154
In this way, they have to travel further into the specimen to reach the sensing electrode, 155 thus, the penetration depth will increase as shown in Figure 2. Usually, the shielding 156 plate and guard electrode are held at ground potential and different types of them can 157 be used depending on the capacitor measurement circuit [18]. in the sensor output. It is an important parameter to assess the sensor performance be-162 cause it indicates how far the sensor can sense [19]. The penetration depth is determined 163 by the material properties (such as permittivity), the noise level of the equipment, and 164 the electrode geometry (shape, size, and arrangement) [9,18]. The material permittivity 165 has certainly an important impact on the penetration depth, the higher the permittivity  can be applied to balance these trade-offs [20]. This electrode geometry is an interesting 186 choice for many situations as it would likely allow deep penetration into the material 187 being tested, with a symmetrical electric field distribution. As stated in the previous 188 section, the electric field distribution is a function of the electrode geometry and so this 189 aspect has to be designed with care [5]. The co-planar electrodes with the same overall  pair of a co-planar triangular electrode is placed above the surface of a specimen, and the 239 setup is enclosed in a 120 mm × 120 mm × 120 mm block centred at the point (x = 0, y = 0, 240 z = 0). This block was defined to be the computational domain, as shown in Figure 4 (a).

241
A physics-controlled mesh was used and the mesh generation density is set to "Finer".

242
Providing the environment and necessary system parameters the mesh is generated in 243 the model as shown in Figure 4     the generator output is up to 20 V, peak to peak. A differential amplifier is placed inside 296 Ectane to process the received signal successively. The output signal from the Ectane is a 297 simple DC voltage level that is proportional to the instantaneous value of the dielectric 298 property of the material averaged over the field distribution within the material.

299
The hidden depth of the defect is also a factor affecting the co-planar capacitive  It can be inferred that when a specimen is placed under the co-planar capacitive 319 electrodes, most of the electric field from the sensor penetrates into the specimen and 320 then ends on the sensing electrode. The dielectric properties of the specimen and defects 321 influence the electric field distribution and, hence, on the electric potential of the sensing 322 electrode. Therefore, an existing defect in the specimen will change the electric field 323 pattern, which leads to the changing in the detectable signal of the sensing electrode. It 324 is worth mentioning the penetration depth is determined mainly by the probe geometry, 325 the electric properties of the specimen and the lift-off. requires single-sided access to the specimen. The couplant such as gel or water is not 340 required, and there is no need for specific surface preparation. In addition, there are no 341 radiation exposure problems. Therefore, this technique has the potential to be used in 342 many NDT application areas where traditional methods may have difficulty.

343
In practice, the condition is typically more complicated compared to the sample 344 inspected during this work. Defect specifications will be unknown, and voids could 345 also be poorly defined. Further development of the capacitive probe is needed to 346 meet different practical requirements and provide enhanced diagnostic information, e.g.