The use of free-space microwave non-destructive techniques: simulation of

damage detection in carbon fibre reinforced composites.

Daniela Munalli1∗, Georgios Dimitrakis2, Dimitrios Chronopoulos1,Steve Greedy3, and Andrew Long1

1The Composites Research Group, The University of Nottingham, Nottingham, UK2Department of Chemical and Environmental Engineering, The University of Nottingham, Nottingham, UK

3School of Electrical and Electronic Engineering, The University of Nottingham, Nottingham, UK

*corresponding author, E-mail: Daniela.Munalli@nottingham.ac.uk

AbstractMicrowave non-destructive testing (MNDT) methods rep-

resent an effective solution in detecting defects within com-

posite structures with relatively low electrical conductivity.

They offer the advantage to overcome the problems of tra-

ditional NDT techniques such as coupling, danger coming

from ionizing radiation, limited depth of operation, large

wavelengths, time consuming post processing. Near-field

microwave and millimetre non-invasive inspections have

been successfully used for detecting defects such as dis-

bond and delamination in complex structures. In dielectric

materials, they can be used for dielectric properties char-

acterization, degree of porosity evaluation, degree of age-

ing, anisotropy, dielectric mixture constituents determina-

tion, state of cure. When it comes to the analysis of car-

bon fibre reinforced polymers (CFRPs), the use of these

non-destructive techniques is restricted by the composite

relatively high conductivity of about 104 S/m. In this pa-

per, the investigation of a free-space microwave method for

non-destructive testing of unidirectional CFRPs has been

carried out by means of a pair of standard gain horn anten-

nas, covering a frequency range from 26.5 GHz to 40 GHz.

With the simulations, experimental results related to the

presence/severity of the analysed defects are linked to the

variations of the measured scattering parameters Sij . The

approach is based on the comparison between the electro-

magnetic signal reflected and transmitted through a healthy

sheet material under test, when a radio frequency (RF) wave

is incident on it, and the one reflected and transmitted by a

damaged sheet. The eventual presence of the defect is re-

vealed by measuring the mismatch between the two trans-

mitted waveforms. The performance of this radio wave

technique is investigated in relation to surface defects and

also in relation to those types of defects that are less de-

tectable with this method, such as delaminations, cavities

and inclusions. The simulations make use of the finite

integration technique (FIT) and the finite element method

(FEM).

1. Introduction

Carbon fibre-reinforced polymer (CFRP) composites are

extensively being used in the aerospace industry due to their

outstanding mechanical properties, such as light weight,

fatigue tolerance, corrosion resistance and high specific

strength and modulus [1, 2]. Structural components of air-

planes and helicopters such as frames, rotor blades, cowl-

ing, control surfaces, wing skin, leading edge and trailing

edge panels are made of CFRPs [3]. Because of their phys-

ical characteristics, the application of carbon fibre compos-

ites to modern aircraft has progressed even more in recent

years; about 40% of the structural weight of the Eurofighter

is carbon-fibre reinforced composite material [4], 50% of

the weight of the Boeing 787 Dreamliner consists of com-

posite materials, resulting in an airframe comprising nearly

half carbon fibre reinforced plastic and other composites

[5].

Unlike metals, composite materials present non-

homogeneity and anisotropy or eventually orthotropic be-

haviour [6]. The damage propagation is diffused and pro-

gressive instead of being confined to a single macrofrac-

ture and involves different modes of failures such as fibre

breakages, matrix transverse cracking and delamination [7].

In addition, manufacturing defects can be embedded in the

structure and may grow during the in service life. Com-

monly induced flaws, which can originate from lack in the

manufacture process control, include porosity, presence of

foreign bodies, fibre or ply misalignment, incorrect fibre

volume fraction, bonding defects [8]. In many occasions,

the damage evolves internally and is hardly visible. Hence,

because of the complexity of damage prediction in com-

posites, it is important to assess their structural integrity

through accurate routine checks.

The inspection methods used to verify the quality state

of a structure without causing any damage or significant

change in the structure itself are defined as Non Destructive

Testing (NDT) techniques. NDT methodologies range from

simple visual inspection and the so-called coin tapping to

very sophisticated techniques; the most suitable for com-

posites are ultrasonic inspections, acoustic emission, ther-

mography, radiography and optical techniques (shearogra-

phy) [9]. However, no single method exists that can detect

all types of manufacturing defects and in-service damage,

and a combination of more techniques can be required for a

detailed inspection of a structural component [10].

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An alternative method of damage inspection and char-

acterization of composite materials consists in the use of

microwave and millimeter wave techniques. Electromag-

netic waves are sent from a transmitting antenna to the sam-

ple under test (SUT) in microwave and millimeter wave

regime (300 MHz to 300 GHz); the portion of the signal

reflected and/or transmitted through the SUT to a receiver

antenna is analyzed in order to evaluate hidden or embed-

ded objects [11]. These methods are indicated to overcome

the limitations of conventional NDT; they work easily in

reflection and transmission configurations, they do not re-

quire a coupling agent, the microwave testing systems are

safe to use due to their low power needs, the probe can be

located at a distance from the analyzed structure making

possible high temperature inspections and testing on mov-

ing objects, it is possible to achieve real time applications

and repetitiveness of measurements [12].

As a matter of fact, microwave non-destructive testing

(MNDT) techniques have been so far extensively applied

to dielectric materials, due to the ability of microwaves to

pass through non-conducting media [13]. In near-field ap-

plication, Qaddoumi et al. detected aluminium inclusion

and flat bottom holes in fibreglass composites [14, 15],

rust under composite laminate coatings [16], and charac-

terized electric properties (dielectric permittivity, dielectric

loss) of cured and uncured resin binder for fibreglass rein-

forced composites (GFRP) [17] by using open-ended rect-

angular waveguides. Similarly, near-field microwave imag-

ing was employed to detect defects in sandwich compos-

ites, such as skin/core debonding, core cracking and impact

damage [18, 19]. In far-field application, Yu et al. used

a measurement system made of a horn antenna and reflec-

tors to identify debonding in artificially damaged GFRP-

concrete cylinders [20, 21, 22]. A free-space measurement

system, composed of two horn antennas in transmitting

and receiving configurations, was successfully used to de-

termine complex permittivity and complex permeability in

several microwave-absorbing materials [23, 24] and fibre-

glass composites [25].

In recent years, MNDT methods are being considered

for application towards CFRPs. A detailed survey about

this topic was proposed by Li et al [26]. However, the use

of microwave techniques is constrained by the high elec-

trical conductivity of the carbon fibres, which ranges from

3.84×104 S/m to 105 S/m in accordance with the typology

of graphitisation treatment [27]. In this case, the high con-

ductivity of the carbon fibres shields the electromagnetic

radiation, making the material scarcely penetrable by elec-

tromagnetic waves. Therefore, the use of MNDT is con-

sidered limited to surface defects (impact damage, surface

irregularity, indentation), and to defects contained in the

first layers of the laminate, due to the severe skin effect

of carbon fibre polymers [28]. As evidence, in literature

MNDT techniques have been proved valid for the detec-

tion of fibre breakage and fibre orientation in unidirectional

(UD) CFRPs [29], disbonds between CFRP patches and

concrete structures [30, 31], detection of impact damage

[32, 33], surface and sub-surface defects identification on

CFRP sheets [34, 35]. Furthermore, most commonly used

sensors for this typology of damage detection operate in

near-field applications and consist of open-ended rectangu-

lar waveguides [29, 30], horn antennas in reflection config-

uration [32, 36], microwave resonators [33, 35].

In this paper, the use of a free-space MNDT technique

for damage detection in unidirectional CFRPs is investi-

gated. Experimental simulation data of the near-field mi-

crowave technique are presented in the Ka band, where

the homogenized properties of the material were obtained

through comparisons with a meso-scale FEM modeling of

the laminate under study. In this way, a simplified electro-

magnetic model of a carbon fibre composite can be rep-

resented through electromagnetic analysis software, such

as CST (Computer Simulation Technology) MWS (mi-

crowave studio), saving computational costs. Once applied

to the SUT, the free-space MNDT method was proved use-

ful for detecting defects, such as delaminations, foreign

bodies and surface indentation.

2. Electromagnetic characteristics of CFRP

materials

Materials can be classified according to their permittivity

ε(ω), that is a complex number, through the ratio between

its imaginary part and real part. Having defined the relative

permittivity of a material as:

εr =ε

ε0= ε′r − j(ε′′r +

σ

ε0ω) (1)

where ε0 is the permittivity of free space (i.e.

8.8542×10−12 F/m), the real part of εr (dielectric

constant) is related to the efficiency of the material to

store the electrical energy, while the imaginary part of εris linked to the energy losses, in particular to the Joule

effect losses through the electrical conductivity σ and to

the losses related to the orientation of the dipoles in the

medium through ε′′r . The ratio between the imaginary

part and the real part of εr, or Dissipation Factor (DF), is

used to classify materials as: perfect dielectric materials or

lossless mediums (DF = 0), low loss mediums with good

dielectric properties or poor conductors (DF ≪ 1), good

conductors or high loss mediums (DF ≫ 1) and perfect

conductors (DF = ∞) [37, 38].

Composite materials for their definition are made of

different elements with corresponding different electrical

properties. The composites under analysis are made of

epoxy resin, which is a common electric insulator with

dielectric constant of about 3÷6 [39], and continuous

carbon fibres based on Polyacrylonitrile (PAN) precursor.

The PAN based carbon fibres have about 60000-70000 S/m

of electrical conductivity [40] and their magnetic perme-

ability µ is equal to that of the free space µ0 = 4π × 10−7

H/m. Therefore, the conductivity of the whole composite

is highly dependent upon its structure and the arrangement

of the fibres inside the matrix. If the fibres were to be

perfectly straight and did not contact adjacent fibres in the

2

two transverse directions, even composites filled with high

conductive reinforcements would be highly insulating. In

reality, fibres are in contact also in the transverse directions.

Hence, it is reported in literature that the mean conductivity

σ of CFRPs is of about 104 S/m [41] and the electrical

conductivity in the direction transversal to fibres is of four

orders lower than the in plane conductivity [40]. Finally,

it is seen that the conductivity of the whole composite is

dependent upon its percolation threshold [42], and that

in function of this parameter CFRPs behave like a lossy

medium [43], or a medium-high lossy medium [44].

Consequently, to achieve optimum signal penetration

at Ka band, where the high frequency reduces the value of

the skin depth of the material, unidirectional CFRPs were

considered for this study instead of textile composites. UD

composites exhibit medium transparency to radiation when

the electric field is transverse to the fibres direction (i.e. the

number of contact points among fibres decreases), while,

if the polarization of the field is parallel to the direction of

the fibres, the transmission through the material is highly

attenuated [12]. Transverse polarization can therefore be

significant for damage identification in UD composites.

3. Transmission coefficients of textile dry

fibres

In this section, CST Studio Suite was adopted to perform

calculations of the reflection coefficient S11 and transmis-

sion coefficient S21 for dry carbon fibres in the frequency

range from 30 MHz to 1.5 GHz. The simulation software

was applied to numerically analyze the interaction of the

SUT with a far-field electromagnetic radiation in the men-

tioned frequency band; from S-parameters (Sij) calcula-

tions, it was possible to assess the shielding effectiveness

(SE) value for the material, i.e. the ability of a barrier to

block the field radiation. Subsequently, experimental mea-

Figure 1: 2/2 twill woven fabric made of TR30S 3k.

surements were carried out for validation.The material un-

der analysis is a layer of dry PAN based carbon fibres fabric

(Pyrofil TR30S), intertwined according to a 2/2 twill weave

pattern as shown in Fig. 1. The relevant properties of the

carbon fabric are listed in Table 1.

Table 1: Pyrofil TR30S properties .

Type Number of Filament Diameter Yeld

Filaments [µm] [mg/m]

TR30S 3k 3000 7 200

3.1. Simulation analysis

The first step of the simulation work was to model the ge-

ometry of a single unit cell (UC) of the carbon textile at

a mesoscale level, using a specialist pre-processor such as

Texgen [45]. The in-plane dimensions of the unit cell were

obtained from direct measurements of the twill weave. The

length of a unit cell is approximately 7.8 mm, while the yarn

width is ≃ 1.6 mm as illustrated in Fig. 2. The thickness of

Figure 2: Unit cell of 2/2 twill weave pattern.

the woven fabric was measured with an electronic microm-

eter with 0.001 mm resolution and is ≃ 0.23 ± 0.023 mm.

The TexGen geometry base model (dimensions are defined

in Fig. 3) was imported in CST Studio Suite, whose fre-

quency solver is based on FEM (Finite Element Method).

The unit cell boundary condition was adopted, in order to

obtain a periodic structure in the x-y plane, as shown in Fig.

3. The excitation used was an incident plane wave polarized

Figure 3: Simulation methodology for the mesoscale fabric

layer.

according to y direction. For a carbon fibre material with

60000 S/m of conductivity, a refined mesh of 962379 tetra-

hedron elements (minimum edge length ≃ 2.9e-005 mm)

and 24 GB of RAM were required; the simulation time was

3

of 1h 37m 12s, with a Intel Xeon W-2123 CPU. A reflection

coefficient of S11 = -0.019 dB and a transmission coefficient

of S21 = -55.9 dB were obtained. These values indicate a

very high level of shielding effectiveness for just a single

layer of dry fibres, corresponding to a degree of signal at-

tenuation > 99%. It is worth to notice that this particular

structure has also the same geometric configuration along

x-axis , thus, an eventual polarization of the electromag-

netic field along this direction would give the same results

in terms of scattering parameters. The results indicate that a

non-isotropic geometry would rather allow greater penetra-

tion to electromagnetic waves, this is the case for UD fabric.

In Fig. 4, it can be noticed how conveniently changing the

value of the reference parameters can increase or decrease

the SE of the fabric. In particular, increased thickness of

the fabric layer, increased yarn width and decreased space

between yarns favor a greater electromagnetic attenuation.

Figure 4: Effect of fabric thickness, yarn width and UC

length on simulated microwave transmission coefficient.

3.2. Experimental validation

The results obtained in section 3.1 were validated through

Figure 5: Sample of TR30S fabric shaped according to

ASTM D4935 standard: (a) Reference specimen; (b) Load

specimen.

the experimental measurements presented in [46, 47]. One

of the most common methods used to measure the transmis-

sion coefficient of a planar material under normal incidence

of a plane wave, involves the transition of a guided TEM

wave in a coaxial transmission fixture containing the SUT,

in accordance with ASTM D4935 standard. The specimens

need to be shaped to fit the inner conductor and the outer

conductor, as shown in Fig. 5 and Fig. 6. Knowing the in-

Figure 6: ASTM D4935 test method for measurement of

shielding effectiveness (SE). On the left brass coaxial unit

holder. On the right SUT positioning.

put power Pi, the transmission coefficient (SEff21

) was cal-

culated measuring the power transmitted through the Refer-

ence SUT (PReft ) first, and then measuring the power trans-

mitted through the Load SUT (PLoadt ), according to equa-

tion 2:

∣

∣

∣SEff21

∣

∣

∣

dB=

∣

∣SLoad21

∣

∣

dB−∣

∣

∣SRef21

∣

∣

∣

dB= 10 log

10

PLoadt

PReft

(2)

where:∣

∣SLoad21

∣

∣

dB= 10 log

10

PLoadt

Pi

(3)

∣

∣

∣SRef21

∣

∣

∣

dB= 10 log

10

PReft

Pi

(4)

Fig. 7 displays the transmission coefficient measured

for 1 layer of carbon fabric and the results of the simulation

(Base model), allowing for comparison.

Figure 7: Measured and simulated transmission coefficient

S21 of TR30S fabric over 0.03-1.5 GHz.

The average value of the transmission coefficient |S21| reg-

istered by the Vector Network Analyzer (VNA) is 54.5 dB,

4

Figure 8: Unit cell base model for a UD laminate with 8 layers: (a) particular of the single yarn with dimensions; (b) detailed

unit cell model, where the green color indicates the epoxy matrix; (c) periodic expansion of the unit cell, the UD fibres are

oriented along x-axis.

against 55.9 dB of the simulation. In average, the simula-

tion results are higher in SE compared to the experimental

ones, however, the numerical model corresponds to a great

extent to the measured data. Therefore, CST simulations

can be used to describe the shielding behaviour of carbon fi-

bre yarns at a mesoscale level. In the following section, this

aspect will be applied to the case of unidirectional yarns, in

order to model a unit cell of a unidirectional CFRP lami-

nate.

4. Ka-band electromagnetic simulation of

unidirectional carbon fibre composites

A unidirectional CFRP laminate composed of 8 layers

is modelled with CST FEM solver, using the procedure

Figure 9: (a) Unidirectional dry carbon fibres with warp

made of Pyrofil TR50S 15k; (b) CFRP laminate made of

8 layers of TR50S non-woven carbon fibre and XPREG

XA120 epoxy adhesive film, oriented along 0direction.

described in section 3.1. The geometry of a single layer

was implemented with Texgen, where both fibre yarn and

epoxy matrix were defined. Then, the lamina sheet (fibre

yarn and epoxy resin) was imported in CST and replicated

8 times, in order to obtain the specific unit cell as basic

structure of the periodic expansion (Fig. 8). The geometric

dimensions were chosen according to the sample shown

in Fig. 9. The thickness of the yarn corresponds to the

thickness of a UD layer of TR50S [Fig 9 (a)], and is equal

to ≃ 0.121 ± 0.007 mm. The thickness of the whole

composite reproduces the thickness of the cured laminate,

composed of 8 layers of non-woven carbon fibre cloth in

epoxy resin staked along 0direction [Fig 9 (b)], and is

equal to ≃ 1.744 ± 0.03 mm. From an electromagnetic

point of view, it was assumed not to take into account the

yarn fibre volume fraction and that very limited amount

of resin is present between adjacent yarns along y-axis to

compensate for the lack of contact points. Two adjacent

yarns can be viewed as the two parallel conductive plates of

capacitor, decreasing the distance between the two results

in an increase of displacement current in the y direction.

Hence, the yarns are modeled with a conductivity of

60000 S/m, while a dielectric constant equal to 4 and a

conductivity of 1e-011 S/m are assigned to the epoxy resin,

knowing that a typical unfilled epoxy resin has a volume

resistivity of > 108 Ωm [48]. The aim of this study was to

perform a microwave analysis of the composite laminate

taking into consideration the separate electromagnetic

modelling of fibres and matrix at a mesoscale level, and

subsequently produce an effective homogeneous equivalent

model to use for damage investigation, as illustrated in

Fig. 10. A homogeneous material is needed for damage

simulation, because commonly used electromagnetic

solvers for structures at high frequencies, such as CST and

Ansys HFSS, are computationally demanding and would

require a very large number of mesh elements to reproduce

a layered composite structure with high conductive parts.

Consequently, the goal was to obtain the anisotropic

5

electrical conductivity of the equivalent model along the

three axes, typical of a unidirectional laminate. Two

different polarization modes were chosen, Mode 1 with

polarization aligned with y-axis, in direction perpendicular

to the fibres, and Mode 2 with polarization aligned with

x-axis, in direction parallel to the fibres, in order to assess

the transmission coefficients in both directions.

Figure 10: (a) detailed unit cell model; (b) equivalent ho-

mogenized unit cell model with σ=[1000,22,0.15] S/m.

The simulated values of |S21| for the detailed unit cell

model [Fig. 10 (a)] are in average 23.9 dB along y-axis and

165 dB along x-axis, over the selected frequency range [27-

32 GHz] in the Ka band. These results were obtained with

a mesh of 35313 tetrahedrons, and a calculation time of 2m

46s occupying 2.6 GB of RAM.

As expected, the electromagnetic wave attenuation in

the direction of the conductive fibres is very high, since any

attenuation higher than 100 dB implies that the material

is essentially impenetrable. Instead, |S21| is considerably

lower in the y direction (fewer contact points between fi-

bres), allowing penetration of electromagnetic waves. This

observation is of interest for damage inspection and the ho-

mogenized equivalent model must comply with this condi-

tion.

It was found that an anisotropic material with electrical

conductivity σ=[1000,22,0.15] S/m, Fig. 10 (b), exhibits an

attenuation of 23.9 dB along the y direction and 164.2 dB

along the x direction (average values over a frequency range

of 27-32 GHz). The model is composed of 53768 mesh el-

ements and has a calculation time of 2m 59s occupying 0.7

GB of RAM.

Fig. 11 shows the two models compared for polariza-

tion 1 and 2. The average difference in |S21| between the

two models is ∆S21(1) ≃ 0.62 dB for Mode 1 simulation,

while for Mode 2 is ∆S21(2) ≃ 2.77 dB. The equivalent

model can therefore be used in this frequency range as sub-

stitute for the detailed model for preliminary damage in-

spection analysis.

5. Damage simulation analysis using Finite

Integration Technique (FIT)

5.1. Modelling

Using the electrical conductivities of the above equiva-

lent model, a computer simulation was performed to ex-

Figure 11: S21 parameter calculated for detailed model and

equivalent model for Mode 1 and Mode 2, over 27-32 GHz.

amine whether the free-space method is appropriate for

defects’ detection. The transient solver based on the Fi-

nite Integration Technique (FIT) was used, where the FIT

method is a spatial discretization scheme to numerically

solve Maxwell’s equations in their integral form in time and

frequency domain [49].

The chosen free-space method consists of two horn

Figure 12: Free-space model used to characterize the trans-

mission scattering parameter S21, over 28-32 GHz.

antennas in transmitting and receiving configuration in the

near-field. The system shown in Fig 12 was used as base-

model for the simulations, considering normal incidence,

y-axis polarization of the field and a Gaussian-modulated

sinusoidal RF pulse [V(t)] assigned to port 1. The reflec-

tion/transmission responses are obtained from power waves

[50], in a frequency band ranging from 28 GHz to 32 GHz.

The specimen (square shaped) was placed between the two

horn antennas, whose specifications are listed in Table 2.

6

To avoid numerical dispersion, the shortest wavelength of

Table 2: LB-28-20-C horn technical specification

Frequency range [GHz] 26.5-40.0

Waveguide WR28

Gain [dB] 20 Typ

Polarization Linear

Material Cu

Size [mm] 32.1 × 40.4 × 94.0

interest was spatially sampled at a rate of 10 mesh cells

per wavelength, taking into account that the phase velocity

of the electromagnetic radiation varies in the medium and

consequently the wavelength becomes drastically shorter in

a conductive medium (λm) than in the air (λ0). In a con-

ductive medium, with σ ≫ ωε′ and DF ≫ 1, λm can be

written as:

λm ≃ 2√π√

fµσ(5)

where µ is the permeability.

5.2. Damage detection

Several damage configurations were considered for the

aforementioned specimen with σ=[1000,22,0.15] S/m. The

aim is to know whether variations of the scattered signal

can be detected due to the presence of a near-surface de-

fect. Fig. 13 shows the case of a square element of 15 mm

Figure 13: Free-space MNDT model used to characterize

S21 for inter-laminar damage and inclusions.

× 15 mm × 0.23 mm inserted in the middle section (x-y

plane) of the specimen. This element was used to simulate:

(a) delamination with PTFE patch, (b) air delamination, (c)

square inclusion with σ=104 S/m, as described in Table 3.

The transmission coefficient for the three cases is compared

with the one of the undamaged base model in Fig. 14.

In case of inter-laminar defect, an artificial delamina-

tion of 0.23 mm in thickness was created filling the inset of

Fig. 13 with PTFE (Teflon) or air. The scattering curves

for the two delamination models, shown in Fig. 14, exhibit

Table 3: Inner defects considered for simulation.

Type of defect Execution EM Properties

Delamination Teflon patch ε′r=2.1

Delamination Air ε′r=1.00059

Inclusion/Clumped fibres Lossy medium σ=104 S/m

greater power transmission through the specimen with re-

spect to the undamaged model, and slightly overlap each

other. This behaviour is the result of the interruption of

the flow of electric current along the thickness, due to the

discontinuity generated by the delamination. On the other

Figure 14: Comparison of the simulated transmission coef-

ficient S21 of damaged models with undamaged case, over

28-32 GHz.

hand, when the element of Fig. 13 is used to simulate an

inclusion with higher conductivity that the host material,

the SE increases, the electromagnetic wave is further re-

flected back at the interface between the inset and surround-

ing composite (greater return loss) and at the same time also

the absorption loss increases.

The experimental data for the delamination models

were obtained with a mesh of 21895335 hexahedral ele-

ments for a simulation that lasted ≃ 50 min and 2.6 GB

of RAM needed. Instead, the analysis of the conduc-

tive inclusion required 168269500 hexahedral elements (the

wavelength inside the conductive material decreases signif-

icantly and consequently the number of cells increases, be-

ing their dimension equal to 1/10 of λm), and had a duration

of ≃ 7 h using 19.8 GB of RAM. For the models, opportune

condition of symmetry were chosen to reduce the calcula-

tion domain, it was assumed ~Ht=0 on yz plane and ~Et=0

on xz plane.

In both the examples produced, delamination and inclu-

sion, it was possible to clearly assess the presence of the

damage, through changes in the magnitude of S21 with re-

spect to the undamaged model. The same can be said in

case of detection of surface defects, such as indentations

(Fig. 15). A square indentation of 4.7 mm × 4.7 mm ×0.3 mm can be easily identified, as illustrated in the graphic

of Fig. 16. The first boundary encountered by the radia-

tion changes compared to the undamaged model, affecting

7

Figure 15: Free-space MNDT model used to characterize

S21 for surface damage.

the reflection loss and resulting in a lower SE. A surface

defect is expected to be identified with the MNDT meth-

ods and the experimental data confirm the results produced

in literature. The analysis required 21895335 hexahedral

elements, a duration of ≃ 50 min and 2.6 GB of RAM.

Figure 16: Transmission coefficient S21 for specimen with

indentation and without indentation, over frequency span of

28-32 GHz.

6. Conclusions

In this study, CST was successfully used to simulate the

electromagnetic behaviour of a carbon woven textile. Con-

sidering the promising result, it is suggested that the simu-

lation tool could be employed to study the applicability of

near-field MNDTs to damage detection in carbon compos-

ite laminates before practical application.

For this purpose, a free-space microwave method, con-

sisting of two horn antennas in transmission and reception,

was considered to numerically analyze defects in UD lami-

nates with a suitable polarization perpendicular to the fibres

direction. The simulation results indicate that inter-laminar

damage, such as delamination, can be easily detected in

transmission configuration and the same can be said for sur-

face defects and foreign bodies.

The MNDT analysis was possible due to an opportune

simplified electromagnetic model of a unidirectional carbon

fibre composite, allowing for modelling of composites with

electromagnetic high frequencies analysis tools.

In further work, the optimum selection of the angle of

the incident radiation is to be explored, which could be ben-

eficial to extend the application of the free-space method

from the case of unidirectional laminate to the case of car-

bon textile composites.

Acknowledgement

This work was funded by the INNOVATIVE doctoral

programme. The INNOVATIVE programme is partially

funded by the Marie Curie Initial Training Networks (ITN)

action (project number 665468) and partially by the Insti-

tute for Aerospace Technology (IAT) at the University of

Nottingham.

The work was supported through the provision of a coop-

eration license for the CST Studio Suite by CST (Dassault

Systemes).

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